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fatigue is a common complaint of 33% patients presenting in the ambulatory primary care offices in the usa . the prevalence of fatigue in the usa workforce has been estimated as 37.9% in a 2-week period . although fatigue is defined as a state of inability to maintain or sustain a force , nevertheless it is interchangeably used by the patients to describe a state of tiredness or low energy . it has significant negative impact on social life , family life , and work performance . excluding advanced systemic illness ( e.g. , malignancy ) , major organ dysfunction ( e.g. , stroke , congestive heart failure , chronic obstructive airway disorder , end stage liver disease , severe anemia , myxedema , end stage renal disease , advanced rheumatologic disease , etc . ) , or acute illness ( e.g. , infection , psychiatric illness ) ; most patients with fatigue have no obvious cause . a detailed diagnostic work up of fatigue can find a specific cause in only 5% . studies have shown an association of low vitamin d levels and fatigue in cancer patients and in patients with myasthenia gravis ; and improvement in fatigue symptom scores after normalization of vitamin d levels . there are many reports which indicate high prevalence of low vitamin d in the general population . low vitamin d leads to bone abnormalities ( e.g. , osteomalacia , osteopenia , and osteoporosis ) and worsens muscle strength . in otherwise healthy individuals , fatigue can be a manifestation of low vitamin d levels and its impact on reduced maximum functioning of skeletal muscles via vitamin d receptors . we designed this study to observe the effect of correction of low vitamin d in patients with fatigue and stable comorbid medical condition(s ) , if any . this study was a prospective non - randomized therapeutic study that observed the effect of correction of low vitamin d in fatigue scores of the patients who presented with fatigue , stable comorbid medical condition(s ) if any , and low serum 25-hydroxyvitamin d ( 25-ohd ) levels . patient enrolment started in may 2012 and the follow - up completed in november 2013 . the study was reviewed and approved by the institutional review board of the cooper health system , camden , new jersey , usa . adult patients between the ages of 18 and 75 who presented in our internal medicine office with fatigue as their chief complaint volunteered to enroll in the study . we excluded patients over age 75 due to several factors that are known to contribute fatigue in this age group such as , decline in the functional ability , physical health , sensorycapacity , cognitive and mental health , and socio - environmental limitations . furthermore , studies have shown a strong association between age greater than 75 and functional decline , and fatigue . the inclusion criteria were fatigue present for greater than 4 weeks and stable chronic medical condition(s ) , if any . the exclusion criteria were normal level of serum 25-ohd , active or advanced cancer , advanced neurological condition ( e.g. , cerebrovascular disease , degenerative neurological disease , multiple sclerosis , etc . ) , advanced cardiac condition with poor performance state ( e.g. , nyha ii - iv congestive heart failure , left ventricular ejection fraction of less than 40% ) , advanced pulmonary disorder ( e.g. , chronic obstructive or restrictive airway disease requiring ambulatory oxygen therapy ) , chronic kidney disease ( e.g. , end stage renal disease requiting hemodialysis ) , end stage liver disease ( e.g. , cirrhosis ) , hematological disorders leading to severe anemia ( hemoglobin less than 9.0 g / dl ) , uncontrolled endocrine disorder ( e.g. , uncontrolled hypothyroidism or hyperthyroidism , diabetes mellitus with glycosylated hemoglobin greater than 9% , etc . ) , advanced or uncontrolled rheumatologic disorder ( e.g. , rheumatoid arthritis , systemic lupus erythematosus , osteoarthritis , etc . ) , chronic fatigue syndrome , fibromyalgia , advanced multisystem disorder ( e.g. , sarcoidosis ) , pregnancy , nursing mother , inability to adhere with the instructions of the intervention ( e.g. , developmental disorder , mentally challenged , severe dementia , non - compliance , etc . ) , contraindication to vitamin d therapy ( e.g. , hypercalcemia ) , and established sleep disorder . after obtaining informed consent the study physicians asked patients to complete a fatigue scale assessment questionnaire ( multidimensional fatigue symptom inventory- short form , mfsi - sf ) . patients all patients with low serum 25-ohd levels ( less than 30 ng / ml ) received oral vitamin d ( ergocalciferol 50,000 usp international unit ; manufactured by sigmapharm laboratories , llc , bensalem , pennsylvania ) three times per week for 5 weeks , if not contraindicated . after completion of ergocalciferol therapy all patients were asked to complete the mfsi - sf and their serum 25-ohd were retested to ensure normalization . we collected the following data for each patient : age , gender , race , associated stable medical condition(s ) , use of over the counter supplemental vitamin d if any , pulse rate , blood pressure , mfsi - sf score before treatment , serum 25-ohd level ( ng / ml ) before treatment , mfsi - sf score after treatment , serum 25-ohd level ( ng / ml ) after treatment , and adverse effect(s ) of ergocalciferol therapy . we entered the patient data in microsoft excel 2007 spreadsheet , and analyzed using statistical package for the social sciences ( spss ) ( version 15.01 ) . a total of 116 patients were planned for sequential sampling who presented with fatigue and low serum 25-ohd levels in order to achieve the largest sample that would provide 80% power to the study hypotheses . we used wilcoxon paired test ( nonparametric analog of the paired t test ) to calculate the median difference on pre and post treatment serum 25-ohd levels assuming the distribution of difference of scores is not normal . al - sunduqchi ( 1990 ) showed that sample size and power calculations for the wilcoxon test can be made using the standard t test results with a simple adjustment to the sample size . a sample size of 116 achieved 84% power to detect a 50% relative increase in serum 25-ohd levels over an average baseline of 10 ng / ml ( + 5 ng / ml ) with a standard deviation of 10 ng / ml using a two - sided wilcoxon test with p 0.05 defining statistical significance and assuming that the actual distribution of post - pre differences is uniformly distributed over subjects . it should be noted that once the data was collected , we found that it was normally distributed and so for analysis , the paired t test was used to compare the mean of vitamin d levels and fatigue scores pre and post - intervention except for the comparison between pre and post - intervention physical score and total score . paired t test was used to compare the mean pre- and post - intervention vitamin d levels , and fatigue scores except the physical scale . wilcoxon ranked sum test was used to compare the median pre- and post - intervention physical scale scores and total scores . independent t test was used to compare continuous variables between the normal and abnormal ( low ) vitamin d group . pearson chi square and fisher exact tests were used to compare categorical variables between the normal and abnormal ( low ) vitamin d group . correlations were used to assess the relationship between pre - intervention vitamin d levels with the pre - intervention fatigue scores , and the relationship between post - intervention vitamin d levels with the post - intervention fatigue scores . multivariable logistic regression was applied to assess the relationship between having a normal post - intervention serum 25-ohd level and change on total mfsi - sf adjusting for the association for the effects of demographics and stable medical condition(s ) that were significant at the p 0.2 level . the variables that were placed in the model were race , depression , and use of over - the - counter supplemental vitamin d. this study was a prospective non - randomized therapeutic study that observed the effect of correction of low vitamin d in fatigue scores of the patients who presented with fatigue , stable comorbid medical condition(s ) if any , and low serum 25-hydroxyvitamin d ( 25-ohd ) levels . patient enrolment started in may 2012 and the follow - up completed in november 2013 . the study was reviewed and approved by the institutional review board of the cooper health system , camden , new jersey , usa . adult patients between the ages of 18 and 75 who presented in our internal medicine office with fatigue as their chief complaint volunteered to enroll in the study . we excluded patients over age 75 due to several factors that are known to contribute fatigue in this age group such as , decline in the functional ability , physical health , sensorycapacity , cognitive and mental health , and socio - environmental limitations . furthermore , studies have shown a strong association between age greater than 75 and functional decline , and fatigue . the inclusion criteria were fatigue present for greater than 4 weeks and stable chronic medical condition(s ) , if any . the exclusion criteria were normal level of serum 25-ohd , active or advanced cancer , advanced neurological condition ( e.g. , cerebrovascular disease , degenerative neurological disease , multiple sclerosis , etc . ) , advanced cardiac condition with poor performance state ( e.g. , nyha ii - iv congestive heart failure , left ventricular ejection fraction of less than 40% ) , advanced pulmonary disorder ( e.g. , chronic obstructive or restrictive airway disease requiring ambulatory oxygen therapy ) , chronic kidney disease ( e.g. , end stage renal disease requiting hemodialysis ) , end stage liver disease ( e.g. , cirrhosis ) , hematological disorders leading to severe anemia ( hemoglobin less than 9.0 g / dl ) , uncontrolled endocrine disorder ( e.g. , uncontrolled hypothyroidism or hyperthyroidism , diabetes mellitus with glycosylated hemoglobin greater than 9% , etc . ) , advanced or uncontrolled rheumatologic disorder ( e.g. , rheumatoid arthritis , systemic lupus erythematosus , osteoarthritis , etc . ) , chronic fatigue syndrome , fibromyalgia , advanced multisystem disorder ( e.g. , sarcoidosis ) , pregnancy , nursing mother , inability to adhere with the instructions of the intervention ( e.g. , developmental disorder , mentally challenged , severe dementia , non - compliance , etc . ) , contraindication to vitamin d therapy ( e.g. , hypercalcemia ) , and established sleep disorder . after obtaining informed consent the study physicians asked patients to complete a fatigue scale assessment questionnaire ( multidimensional fatigue symptom inventory- short form , mfsi - sf ) . patients all patients with low serum 25-ohd levels ( less than 30 ng / ml ) received oral vitamin d ( ergocalciferol 50,000 usp international unit ; manufactured by sigmapharm laboratories , llc , bensalem , pennsylvania ) three times per week for 5 weeks , if not contraindicated . after completion of ergocalciferol therapy all patients were asked to complete the mfsi - sf and their serum 25-ohd were retested to ensure normalization . we collected the following data for each patient : age , gender , race , associated stable medical condition(s ) , use of over the counter supplemental vitamin d if any , pulse rate , blood pressure , mfsi - sf score before treatment , serum 25-ohd level ( ng / ml ) before treatment , mfsi - sf score after treatment , serum 25-ohd level ( ng / ml ) after treatment , and adverse effect(s ) of ergocalciferol therapy . we entered the patient data in microsoft excel 2007 spreadsheet , and analyzed using statistical package for the social sciences ( spss ) ( version 15.01 ) . a total of 116 patients were planned for sequential sampling who presented with fatigue and low serum 25-ohd levels in order to achieve the largest sample that would provide 80% power to the study hypotheses . we used wilcoxon paired test ( nonparametric analog of the paired t test ) to calculate the median difference on pre and post treatment serum 25-ohd levels assuming the distribution of difference of scores is not normal . al - sunduqchi ( 1990 ) showed that sample size and power calculations for the wilcoxon test can be made using the standard t test results with a simple adjustment to the sample size . a sample size of 116 achieved 84% power to detect a 50% relative increase in serum 25-ohd levels over an average baseline of 10 ng / ml ( + 5 ng / ml ) with a standard deviation of 10 ng / ml using a two - sided wilcoxon test with p 0.05 defining statistical significance and assuming that the actual distribution of post - pre differences is uniformly distributed over subjects . it should be noted that once the data was collected , we found that it was normally distributed and so for analysis , the paired t test was used to compare the mean of vitamin d levels and fatigue scores pre and post - intervention except for the comparison between pre and post - intervention physical score and total score . paired t test was used to compare the mean pre- and post - intervention vitamin d levels , and fatigue scores except the physical scale . wilcoxon ranked sum test was used to compare the median pre- and post - intervention physical scale scores and total scores . independent t test was used to compare continuous variables between the normal and abnormal ( low ) vitamin d group . pearson chi square and fisher exact tests were used to compare categorical variables between the normal and abnormal ( low ) vitamin d group . correlations were used to assess the relationship between pre - intervention vitamin d levels with the pre - intervention fatigue scores , and the relationship between post - intervention vitamin d levels with the post - intervention fatigue scores . multivariable logistic regression was applied to assess the relationship between having a normal post - intervention serum 25-ohd level and change on total mfsi - sf adjusting for the association for the effects of demographics and stable medical condition(s ) that were significant at the p 0.2 level . the variables that were placed in the model were race , depression , and use of over - the - counter supplemental vitamin d. a total of 174 patients with fatigue completed mfsi - sf fatigue assessment questionnaires . of them , 171 ( 98.3% ) patients underwent serum 25-ohd level tests while 3 ( 1.7% ) did not . thirty - nine ( 22.8% ) patients were excluded due to normal levels of serum 25-ohd , and the rest 132 ( 77.2% ) patients received vitamin d therapy [ figure 1 ] . the prevalence of low vitamin d was 77.2% in all 171 patients , despite the fact that 51.5% patients with low vitamin d levels were regularly taking over - the - counter vitamin d-3 between 1000 and 2000 international units [ table 1 ] . majority of the patients were in the age range of 36 and 65 [ figure 2 ] , female ( 72.4% ) , and non - hispanic caucasians ( 59.6% ) [ table 1 ] . demographics of 171 patients showed a higher prevalence of low vitamin d in the african - american patients ( 88.6% ) and in the other race category ( asian and hispanic patients ) ( 85.3% ) , compared to 70.6% in the non - hispanic caucasian patients . there was no significant difference between the number of patients taking over - the - counter vitamin d-3 in low vitamin d group ( 51.5% ) and normal vitamin d group ( 64.1% ) ( p = 0.166 ) . other factors , such as associated stable comorbid conditions , pulse and blood pressure between low vitamin d group and normal vitamin d group were comparable , except for the history of depression . patients with history of depression were twice likely to have a normal vitamin d level than a low vitamin d level [ table 1 ] . after completion of vitamin d therapy 16 ( 12.1% ) patients did not go for serum 25-ohd test ; hence , they were excluded from the study [ figure 1 ] . frequency of fatigue through age ranges , gender , and vitamin d levels ( ldf = low serum 25-ohd female , ldm = low serum 25-ohd male , ndf = normal serum 25-ohd female , ndm = normal serum 25-ohd male , nrf = did not go for serum 25-ohd test female , nrm = did not go for serum 25-ohd test male ) the mfsi - sf is a 30-item form that provides scores in the empirically derived 5 subscale categories . the assessment of fatigue is based on scores on the items that are rated on a 5-point scale indicating patients agreement to the truthfulness of each statement asking about their experience during the previous week ( 0 = not at all , to 4 = extremely ) . the mfsi - sf has excellent psychometric properties , hence it is an effective substitute for a more time consuming 83-item self - report measure ( multidimensional fatigue symptom inventory ) . the questions are randomly arranged to assess five different subscales , which include general scale , physical scale , emotional scale , mental scale , and vigor scale . each scale has six questions , hence a possible maximum score for each subscale is 24 . a high level of fatigue is indicated by high scores in general , physical , emotional , and mental scales , and low score in vigor scale . the total score is calculated by subtracting the score of vigor scale from the sum of the scores of all other scales . . there was no statistically significant difference in the mean mfsi - sf scores in the general scale , emotional scale , mental scale and vigor scale ; and the median mfsi - sf scores in the physical scale and total score between all 171 patients and 116 patients with low vitamin d levels at initial encounter [ table 2 ] . there was no significant correlation between the baseline vitamin d levels and baseline mfsi - sf scores in 171 patients ; and post vitamin d therapy normalized vitamin d levels and mfsi - sf scores in 116 patients . pearson correlation was used to calculate all except for the vitamin d levels and mfsi - sf total scores , for which spearman rho correlation was used . after 5 weeks of vitamin d therapy in 116 patients , 111 ( 95.7% ) patients achieved normal levels of serum 25-ohd and 5 ( 4.3% ) patients required a second course of vitamin d therapy to achieve normal levels of serum 25-ohd . after ergocalciferol therapy mean serum 25-ohd level of all 116 patients normalized and significantly improved from a mean pre - treatment level of 19.71 ( sd , 5.98 ) ng / ml to a mean post - treatment level of 52.29 ( sd , 21.73 ) ng / ml ( p < 0.001 ) [ table 2 ] . fatigue scores : multidimensional fatigue symptom inventory - short form mean mfsi - sf scores in the general scale , emotional scale , mental scale , and vigor scale ; and the median mfsi - sf scores in the physical scale and total score improved significantly ( p < 0.001 ) after normalization of vitamin d levels [ table 2 ] . the multivariate analysis showed that history of depression was the only significant factor that impacted the post - intervention vitamin d level . patients who had a history of depression had 12 times greater odds of having a normal vitamin d level than those who did not have a history of depression ( 95% ci , 1.7 to 88 times ) . the reasons of discontinuation and consequent exclusion from the study were non - willingness for continued participation in 3 ( 1.7% ) patients , inability to go for serum 25-ohd test due to loss of medical insurance coverage in 7 ( 6.0% ) patients , and protocol violation due to a significant delay in getting serum 25-ohd test in 5 ( 3.8% ) patients . majority of the patients were in the age range of 36 and 65 [ figure 2 ] , female ( 72.4% ) , and non - hispanic caucasians ( 59.6% ) [ table 1 ] . demographics of 171 patients showed a higher prevalence of low vitamin d in the african - american patients ( 88.6% ) and in the other race category ( asian and hispanic patients ) ( 85.3% ) , compared to 70.6% in the non - hispanic caucasian patients . there was no significant difference between the number of patients taking over - the - counter vitamin d-3 in low vitamin d group ( 51.5% ) and normal vitamin d group ( 64.1% ) ( p = 0.166 ) . other factors , such as associated stable comorbid conditions , pulse and blood pressure between low vitamin d group and normal vitamin d group were comparable , except for the history of depression . patients with history of depression were twice likely to have a normal vitamin d level than a low vitamin d level [ table 1 ] . after completion of vitamin d therapy 16 ( 12.1% ) patients did not go for serum 25-ohd test ; hence , they were excluded from the study [ figure 1 ] . frequency of fatigue through age ranges , gender , and vitamin d levels ( ldf = low serum 25-ohd female , ldm = low serum 25-ohd male , ndf = normal serum 25-ohd female , ndm = normal serum 25-ohd male , nrf = did not go for serum 25-ohd test female , nrm = did not go for serum 25-ohd test male ) the mfsi - sf is a 30-item form that provides scores in the empirically derived 5 subscale categories . the assessment of fatigue is based on scores on the items that are rated on a 5-point scale indicating patients agreement to the truthfulness of each statement asking about their experience during the previous week ( 0 = not at all , to 4 = extremely ) . the mfsi - sf has excellent psychometric properties , hence it is an effective substitute for a more time consuming 83-item self - report measure ( multidimensional fatigue symptom inventory ) . the questions are randomly arranged to assess five different subscales , which include general scale , physical scale , emotional scale , mental scale , and vigor scale . each scale has six questions , hence a possible maximum score for each subscale is 24 . a high level of fatigue is indicated by high scores in general , physical , emotional , and mental scales , and low score in vigor scale . the total score is calculated by subtracting the score of vigor scale from the sum of the scores of all other scales . a high total score indicates high level of fatigue . there was no statistically significant difference in the mean mfsi - sf scores in the general scale , emotional scale , mental scale and vigor scale ; and the median mfsi - sf scores in the physical scale and total score between all 171 patients and 116 patients with low vitamin d levels at initial encounter [ table 2 ] . there was no significant correlation between the baseline vitamin d levels and baseline mfsi - sf scores in 171 patients ; and post vitamin d therapy normalized vitamin d levels and mfsi - sf scores in 116 patients . pearson correlation was used to calculate all except for the vitamin d levels and mfsi - sf total scores , for which spearman rho correlation was used . after 5 weeks of vitamin d therapy in 116 patients , 111 ( 95.7% ) patients achieved normal levels of serum 25-ohd and 5 ( 4.3% ) patients required a second course of vitamin d therapy to achieve normal levels of serum 25-ohd . after ergocalciferol therapy mean serum 25-ohd level of all 116 patients normalized and significantly improved from a mean pre - treatment level of 19.71 ( sd , 5.98 ) ng / ml to a mean post - treatment level of 52.29 ( sd , 21.73 ) ng / ml ( p < 0.001 ) [ table 2 ] . mean mfsi - sf scores in the general scale , emotional scale , mental scale , and vigor scale ; and the median mfsi - sf scores in the physical scale and total score improved significantly ( p < 0.001 ) after normalization of vitamin d levels [ table 2 ] . the multivariate analysis showed that history of depression was the only significant factor that impacted the post - intervention vitamin d level . patients who had a history of depression had 12 times greater odds of having a normal vitamin d level than those who did not have a history of depression ( 95% ci , 1.7 to 88 times ) . the reasons of discontinuation and consequent exclusion from the study were non - willingness for continued participation in 3 ( 1.7% ) patients , inability to go for serum 25-ohd test due to loss of medical insurance coverage in 7 ( 6.0% ) patients , and protocol violation due to a significant delay in getting serum 25-ohd test in 5 ( 3.8% ) patients . this prospective study of low vitamin d and fatigue demonstrated two major observations : first , a very high prevalence of low vitamin d ( serum 25-ohd ) in patients who complained of fatigue . second , a significant reduction in the severity of fatigue ( fatigue symptom scores ) after normalization of vitamin d levels . our strict exclusion criteria supported the observation that improvement in fatigue symptoms were primarily due to normalization of low vitamin d levels and not secondary to amelioration of the chronic medical condition(s ) in patients who had one or more associated stable comorbid condition(s ) . patients who suffer from fatigue have higher mortality , morbidity , and disability especially after middle age . it facilitates the absorption of calcium from the intestine , reabsorption of calcium from the kidneys , and release of calcium from the skeleton . a low vitamin d level reduces serum total and ionized calcium which results into increase in parathormone level , decrease in bone density , increase in bone turnover , decrease in urinary calcium excretion , increase in urinary phosphate excretion , and decrease in serum phosphate level , ultimately resulting into skeletal demineralization and muscle weakness . fatigue is the end result of the underlying muscle fatigue , which is more commonly encountered than muscle weakness . low vitamin d is also associated with inappropriate activation of the renin - angiotensin system , which fails to inhibit abnormal cell proliferation . additionally , vitamin d influences our innate immune system by enhancing the production of human cathelicidin antimicrobial peptide , and modulates the adaptive immune system by controlling cytokine responses and t helper cell balance . the overall impact of these mechanisms results into further lowering of vitamin d levels , which have been associated with fatigue in patients with cancer , and myasthenia gravis . low vitamin d levels are also associated with cardiovascular diseases , hypertension , congestive heart failure , cancer , diabetes mellitus , neuromuscular disorders , pneumonia , upper respiratory tract infections , chronic obstructive pulmonary disease , and all - cause mortality . a meta - analysis of 18 randomized clinical trials concluded that vitamin d supplementation was associated with lower all - cause mortality . a survey of over 18,000 subjects in the united states general population showed 6.7% current and 24.4% lifetime prevalence of fatigue . although fatigue is twice as common in women as in men , it is not strongly associated with age or occupation . more recent analysis of 74 million adults in the united states aged 51 and above showed 31.2% prevalence of fatigue , being more in women ( 33.3% ) than men ( 28.6% ) and more in minorities ( 47.5% ) than in caucasians ( 27.5% ) . in our study we found that fatigue was more common in non - hispanic caucasians ( 59.6% ) , and it affected about three - quarter ( 72.4% ) of women than men . in the usa , 41% of men and 53% of women we observed a higher prevalence of low vitamin d ( 77.2% ) in our patients who presented with fatigue , despite the fact that more than half of the patients were taking over - the - counter vitamin d-3 regularly . low vitamin d may be caused by less exposure to sunlight , application of sunscreen , elevated melanin in skin , or fully covered skin . a higher prevalence of low vitamin d in the african american patients ( 88.6% ) in our study can be explained by the racial differences in vitamin d metabolism . the african american population has an increased activity of 25-hydroxyvitamin d-1--hydroxylase ( cyp27b1 ) , either driven by increased parathormone activity or by racial differences in cyp27b1 affinity for substrate , which results into lower serum 25-ohd levels . racial difference in variable vitamin d receptor affinity for vitamin d metabolites may explain similar variation in the prevalence of low vitamin d across other races with the observation of at least one vitamin d receptor polymorphism ( foki ) which is known to differ by race and ethnicity . a critical review of methods and instruments that have been developed to measure fatigue found good psychometric properties in only 3 comprehensive instruments : fatigue symptom inventory ( fsi ) , multidimensional assessment of fatigue ( maf ) , and mfsi - sf . mfsi - sf is a valid , reliable and least time consuming instrument in the outpatient setting . functional neuroimaging offers a more objective assessment of fatigue by measuring fatigue during brain scan and correlating it with cerebral activation . a comparison of our study results with other relevant studies showed similar observations in different settings . correction of low vitamin d in breast cancer patients with fatigue showed improvement in fatigue and other musculoskeletal symptoms . similarly , improvement in fatigue scores were observed in patients with myasthenia gravis after vitamin d replacement . our findings provide a consistent body of evidence that normalization of low vitamin d levels in patients with fatigue and stable chronic medical conditions , if any , significantly improves their fatigue symptom scores . among various therapeutic regimens of oral ergocalciferol the 50,000 international unit 3 times weekly for 5 weeks regimen has shown the highest efficacy ( 82% ) , without adverse events , or toxicity . a double - blind randomized controlled trial with ergocalciferol and placebo interventions could have provided a comparative analysis , nevertheless correction of low serum 25-ohd was mandatory in all patients based on the current guidelines . normalization of low vitamin d level with ergocalciferol therapy significantly improves the severity of fatigue symptoms in adult patients who present in the primary care office with fatigue and stable chronic medical conditions , if any . with fatigue being a major presenting complaint in the primary care offices , serum 25-ohd level should be tested and low serum 25-ohd levels should be corrected with an effective ergocalciferol therapy regimen in order to improve their symptoms .

background : fatigue is a common presenting complaint of patients in the primary care offices . low levels of vitamin d have been associated with fatigue in cancer patients . normalization of vitamin d level improves their fatigue . whether low vitamin d plays a role in fatigue in medically stable patients is not known.aims:this prospective non - randomized therapeutic study observed the prevalence of low vitamin d in fatigue and the effect of normalization of vitamin d on fatigue.material and methods : one hundred and seventy four adult patients , who presented in our primary care office with fatigue and stable chronic medical conditions , completed fatigue assessment questionnaires . patients with low vitamin d levels received ergocalciferol therapy for 5 weeks . scores of pre- and post - treatment fatigue assessment questionnaires were compared.results:prevalence of low vitamin d was 77.2% in patients who presented with fatigue . after normalization of vitamin d levels fatigue symptom scores improved significantly ( p < 0.001 ) in all five subscale categories of fatigue assessment questionnaires.conclusion:the prevalence of low vitamin d is high in patients who present with fatigue and stable chronic medical conditions , if any . normalization of vitamin d levels with ergocalciferol therapy significantly improves the severity of their fatigue symptoms .

Introduction Materials and Methods Study selection Data collection Data synthesis and analysis Results Baseline characteristics Fatigue assessment score Symptom scores after normalization of vitamin D levels Discussion Conclusion

imatinib ( also known as sti571 or gleevec ) is one of the great success stories of cancer therapy and is a milestone in small - molecule drug discovery and molecular targeted therapies . imatinib is the current first - line therapy for all stages of chronic myelogenous leukemia ( cml ) , in which the chronic phase of the disease is characterized by the increased proliferation of the myeloid lineage and which is cytogenetically diagnosed by the presence of the philadelphia chromosome . this contains a fusion gene encoding the oncoprotein bcr - abl , in which a part of the bcr protein is fused to the non - receptor abl tyrosine kinase , causing it to become constitutively active . the deregulated kinase activity of bcr - abl accounts for the oncogenicity of the protein and is inhibited by imatinib . since the approval of imatinib by the us food and drug administration in may 2001 , there has been a dramatic reduction in the number of bone marrow transplants for cml in the us ; imatinib monotherapy has also been used successfully to induce a complete cytogenetic response in about 7590% of newly diagnosed cml patients , although drug resistance is a problem with advanced stages of cml . imatinib is not entirely specific and targets tyrosine kinases other than abl , notably the receptor tyrosine kinases kit and pdgfr ( platelet - derived growth factor receptor ) . this lack of specificity has been exploited in the clinic , and imatinib has also been approved for the treatment of chronic eosinophilic leukemia ( cel ) , which is caused by a fip1l1-pdgfr fusion , and for gastrointestinal stromal tumors ( gists ) , caused by mutations of kit or pdgfr ( reviewed in ) . there has been increasing interest in understanding other potential targets of imatinib to evaluate the specificity , safety and potential off - target effects of this first - in - class drug . the traditional approach to identifying imatinib targets is through in vitro assays with a panel of recombinant kinases to measure inhibitor binding . this approach is limited by the pre - selection of test targets and tends to provide poor indicators for drug activity in vivo . two recent studies circumvent this problem by using cell extracts from the cml cell line k562 to identify binding targets of imatinib . in the first , imatinib was modified to allow attachment to solid support and incubated with cell lysates , and the bound proteins were identified by tandem mass spectrometry . these mixed kinase inhibitor beads ( kinobeads ) were incubated with cell lysates and bound proteins were again identified by tandem mass spectrometry . to identify imatinib targets , cell lysates were pre - incubated with imatinib before binding to the kinobeads . proteins that no longer bound to the kinobeads , because their binding sites were occupied by imatinib , were identified by comparative analysis . both approaches have confirmed the selective nature of imatinib : no more than five proteins from k562 cell lysates bound imatinib as compared with about 30 proteins for another bcr - abl inhibitor , dasatinib . the explanation for this difference is that dasatinib targets the active kinase conformation , which is highly conserved and thus shared by other kinases , whereas imatinib targets the inactive conformation , which is unique to the abl kinase . surprisingly , both approaches also identified the first non - tyrosine kinase target of imatinib , nqo2 . others may follow : indeed , a recent screen in yeast identified the vacuolar atpase ( v - atpase ) , an evolutionarily conserved proton pump , as a target of imatinib , and imatinib may interact with other non - kinase targets that could have eluded detection by the k562 cell - based experiments . structural studies , including one just published by kuriyan and colleagues in bmc structural biology , show that this promiscuity reflects the flexibility of the inhibitor , a consideration that is likely to apply broadly to small - molecule inhibitors . the kuriyan group has analyzed the crystal structure at 1.75 of a dimer of human nqo2 bound to imatinib . the objective of the structural study was to cast light on possible side - effects attributable to imatinib binding to nqo2 , and a spectrophotometric assay confirmed binding of imatinib to nqo2 with a concentration for 50% inhibition ( ic50 ) of 82 nm , consistent with earlier reports and well within the physiological range of the concentration of imatinib found in the serum of patients ( about 1 m ; referenced in ) . nqo2 is a cytoplasmic flavoprotein that is involved in the cellular response to oxidative stress , although its mechanism of action is not well understood . nqo2 is highly expressed in myeloid cells , and knockdown by rna interference in k562 cells results in reduced proliferation ( referenced in ) . however , nqo2 knockout mice show myeloid hyperplasia and increased sensitivity to chemical carcinogenesis ( referenced in ) . the potential clinical side - effect(s ) of inhibition of nqo2 , despite the elucidation of the exact mechanism of imatinib inhibition , are thus not yet clear . the structure does show , however , that the structural flexibility that allows imatinib to bind to nqo2 is also the basis for its binding to other , more clinically relevant targets . imatinib interacts with nqo2 primarily through hydrophobic interactions , making no direct hydrogen bonds ( figure 1a ) . steric constraints lead imatinib to adopt a compacted horseshoe shape that partially extends into the solvent , and the isoalloxazine ring of the nqo2 flavin cofactor in the active site stacks with the pyridine and pyrimidine rings of imatinib . the related kinase inhibitor dasatinib can not make this stacking interaction , and this explains why it does not bind to nqo2 . the structure also demonstrates why imatinib can not bind the closely related nqo1 , which has 49% identity and a similar structure to nqo2 : steric hindrance from phe232 , tyr128 and pro68 are likely to occlude the imatinib binding site . atomic interactions of imatinib with ( a ) nqo2 ( protein data bank ( pdb ) code 1fw3 ) and ( b ) abl kinase domain ( pdb 1iep ) . ( a ) a monomer of nqo2 ( green ) is shown bound to its cofactor fad ( blue ) and to imatinib ( red ) . imatinib uses stacking interactions with fad and makes hydrophobic contacts with both subunits in the nqo2 dimer . ( b ) the abl kinase domain ( cyan ) is depicted with the dfg motif ( yellow ) and residues involved in direct hydrogen binding ( blue ) either through side chains or the peptide backbone . comparison of the nqo2-imatinib structure with that of imatinib bound to abl ( figure 1a , b ) reveals the flexibility of imatinib binding and demonstrates the difficulty in designing a drug that has no off - targets . in the abl - imatinib complexes ( reviewed in ) , the dfg motif ( asp381-phe382-gly383 ) that characterizes the activation loop of the kinase is rotated by 180 and adopts a flipped - out conformation ( figure 1b ) . this dfg - out conformation creates a binding pocket for imatinib , which on binding causes the activation loop to fold towards the active site and at the same time induces contraction of the phosphate - binding p - loop , which also binds to imatinib . overall , imatinib uses six hydrogen bonds and several van der waals interactions to stabilize the complex . in the imatinib - abl complex , imatinib adopts an extended conformation that is seen in several other kinase - imatinib structures and that differs significantly from the compact , ring - stacking conformation seen in the nqo2 structure . the structures of imatinib bound to the syk kinase , or to the desmethyl imatinib analog bound to src kinase , however , are similar to the conformation seen in nqo2 , which shows that this is a minor but not a unique conformation for imatinib . future drug designs will need to account for the distinct conformations that a small molecule inhibitor can adopt if they are to understand the full range of targets that a drug can bind . as mentioned earlier , imatinib has been approved for the treatment of cml , cel and gist because of its inhibition of the bcr - abl , pdgfr and kit tyrosine kinases ( figure 2 ) . recent clinical and preclinical studies have expanded the use of imatinib for the treatment of other diseases , including systemic mastocytosis , which also involves the kit and pdgfr tyrosine kinases , and ( in preliminary studies ) fibrotic disorders ( reviewed in ) . it probably acts in fibrotic disorders through effects on the abl tyrosine kinase , which has been implicated in tgf-induced fibrotic responses , and through the pdgfr : both of these are known to be involved in two major pro - fibrotic pathways activated in systemic sclerosis . the structure of imatinib ( from pdb 1iep ) is shown in the middle , with carbon ( green ) , nitrogen ( blue ) and oxygen ( red ) atoms displayed . cel , chronic eosinophilic leukemia ; cml , chronic myelogenous leukemia ; gist , gastrointestinal stromal tumors ; kit , receptor for stem cell factor ; pdgfr , platelet - derived growth factor receptor ; smc , systemic mastocytosis ; ssc , systemic sclerosis ; v - atpase , vacuolar atpase . in mouse models , there is evidence that imatinib may be effective in the treatment of ischemic strokes and in several inflammatory and autoimmune diseases . the effects on inflammatory and autoimmune disease are consistent with phase i clinical studies and case reports detailing positive effects in rheumatoid arthritis , psoriasis , spondyloarthritis and crohn 's disease ( referenced in ) . a recent paper , again on a mouse model , reports that imatinib may be effective for the treatment of type 1 diabetes , largely through inhibition of pdgfr . given the involvement of nqo2 in oxidative stress , it will be of interest to determine whether the inhibition of this oxidoreductase can contribute to the anti - inflammatory activity of imatinib . known mild adverse effects of imatinib include edema , muscle cramps , diarrhea and bone - marrow toxicity , and these do cause some patients to discontinue treatment . cardiotoxicity has been reported as a potentially severe adverse effect of imatinib ( reviewed in ): in this case the adverse effect seems to be due to inhibition of the primary target of imatinib , the abl kinase , but the extent to which the cardiotoxicity results from imatinib treatment is controversial . imatinib has been shown to be a versatile drug with clinical benefit for treating cml , gist and cel and has potential for use in a variety of other diseases . understanding how imatinib and other small - molecule drugs interact with their cellular targets is important for rational drug design and prediction of potential off - target effects . the limited promiscuity of imatinib may be optimal , allowing its use in a variety of diseases with mild adverse effects . imatinib has revolutionized the treatment of cml and may be poised for more clinical successes .

the protein kinase inhibitor imatinib , also known as gleevec , has been a notable success in treating chronic myelogenous leukemia . a recent paper in bmc structural biology reports a 1.75 crystal structure of imatinib bound to the oxidoreductase nqo2 and reveals insights into the binding specificity and the off - target effects of the inhibitor .

None Protein targets of imatinib Flexibility of imatinib in binding to targets Clinical effects of imatinib Acknowledgements

ovarian hyperstimulation syndrome ( ohss ) is a well - known complication of assisted reproductive techniques ( arts ) and is characterized by enlargement of the ovaries and fluid shift from the intravascular compartment to the third space . tuberculosis is common in developing countries , and peritoneal tuberculosis ( tb ) which is the 6th most frequent extrapulmonary tb usually presents with ascites . we report a case of a 31-year - old lady who presented with tubercular ascites that simulated ovarian hyperstimulation ( ohss ) . the patient had no evidence of tuberculosis as proven by a negative mantoux , chest x - ray , acid fast staining of ascitic fluid , and a negative pcr . the final diagnosis and management were based on a rising adenosine deaminase ( ada ) level and a low haematocrit of 19.8% . the uniqueness lies in the yet unreported simulation leading to a suspicion of an unknown pathological mechanism in stimulating the ovaries , which might have caused a flare - up of tuberculosis . a 31-year - old lady came to us with evidence of spontaneous abortion at 14 weeks of her pregnancy , which was conceived following in vitro fertilization . she had fever at the time , and hence a course of antibiotics was given . her hemoglobin levels were low , for which she was given a unit of packed red blood cells . she was a booked case with us and had a past history of two episodes of ascites ( ohss ) following the embryo transfer . the first episode was within 12 days of embryo transfer , and the second episode was at 9 - 10 weeks of gestation . both episodes were diagnosed as ohss and treated symptomatically with albumin infusion . at 14 weeks of gestation , she had fever and recurrence of ascites . ascites did not subside even with albumin and cabergoline ; hence other causes of ascites were evaluated by mantoux test and chest x - ray , which were negative for tuberculosis . her bleeding per vaginum persisted , for which a scan was done again which showed some retained products of conception for which she underwent dilatation and evacuation . the tissue obtained was sent for histopathology examination and came back as only degenerated products of conception and negative for mycobacterium tuberculosis by pcr . when the ascites did not disappear after the regular treatment , the ascitic fluid was tapped thrice . it was green in color , leading to suspicion of presence of bile salts or pigments in it though her liver function tests were normal . when analyzed for the same , there were no bile salts or pigments found . upon culturing it , the ascitic fluid was further investigated with acid fast staining , which showed no acid fast bacilli . a pcr sent for mycobacterium tuberculosis came back negative . she was started on antitubercular treatment with hrze ( isoniazid + rifampicin + pyrazinamide + ethambutol ) , which finally resolved the ascites within a week . ovarian hyperstimulation is a rare complication of using gnrh antagonist protocol for ovulation induction in patients undergoing assisted reproductive techniques . but when it gets severe , like it rarely does , shortness of breath and orthopnoea due to pleural effusion are also seen . upon using ovulation induction drugs , but what really causes them to go into overdrive and start secreting excessive fluid is not well understood yet . pathologically , in ovarian hyperstimulation , the fluid lost is transudate in nature . clinically , it is seen as a sudden increase in the weight of the patient along with some pelvic pains . usually , it is a mild complication , which does not require much intervention . but in some cases , it can cause massive ascites and proceed to a pleural effusion leading to life - threatening dyspnoea . furthermore , investigating with an ultrasound will show fluid in the peritoneal cavity which might also be in the pleural cavity , which can be confirmed with a chest x - ray . the routine treatment involves a 100 ml of saline with 20% albumin infusion intravenously , which will help bring the excessive fluid back into the intravascular compartment . another effective drug is cabergoline , which acts by influencing the vasoactive endothelial growth factor ( vegf ) pathway , restricting the loss of fluid into third spaces . tuberculosis is very commonly seen in the developing countries and usually affects the lungs primarily . so , a clear chest x - ray is usually taken to mean no tuberculosis anywhere else . when it affects the peritoneum and produces ascites , it is an exudate . the difference in the two underlying pathologies of ascites is that when a transudate is seen , concentration of hematocrit can be seen . on the other hand , in exudative ascites , it was the persisting hematocrit at low levels ( 19.8% ) even with ongoing ascites that led to a suspicion of a cause other than hyperstimulation of the ovaries . most of the population in such a country is affected , but a good immunity keeps the disease in check , not letting it flare up . but whenever a body experiences a kind of stress , it loses part of its immunity , and this , in turn , leads to flaring up of tuberculosis . some of the stresses known to cause flaring up are immunosuppression therapy , nephropathy , and so forth . this case gives rise to the possibility that ovulation induction might actually be a stress factor in causing flaring up of tuberculosis . estimation of adenosine deaminase ( ada ) in ascetic fluid has value in diagnosing tuberculosis . ada is a purine - degrading enzyme , widely distributed in tissues and body fluids , necessary for proliferation and differentiation of t lymphocytes . it has enough discriminatory power to either confirm or rule out the diagnosis of peritoneal tb . it can be used as a reliable test to start treatment while waiting for the report of cultures . a meta - analysis of 4 studies showed a sensitivity of 99 to 100% and specificity of 97% in diagnosing peritoneal tb . in our case though pcr and acid fast staining were negative for tuberculosis , the persisting low haematocrit levels along with rising ada levels led to the suspicion of tubercular ascites , and when treated with att , ascites was resolved completely .

ovarian hyperstimulation syndrome ( ohss ) is a known complication of using ovulation induction drugs in assisted reproductive techniques . its incidence and severity vary . tuberculosis is a very common disease in the developing world , and ascites is one of its sequelae . the newer aids in diagnosing tuberculosis include measuring levels of adenosine deaminase ( ada ) in the third - space fluids or serum . this case report is from a tertiary care center , reflecting how tubercular ascites simulated ohss , and the right diagnosis was made and managed . this is being presented due to its rarity .

1. Introduction 2. Case Report 3. Discussion

mercury is a metal of known toxic properties which occurs naturally and anthropogenically in the environment [ 1 , 2 ] . methylmercury ( mehg ) is an organic chemical form of mercury that has been widely studied due to its neurotoxic effects in humans and animal models , especially when the exposure occurs prenatally [ 36 ] . mehg is able to cross the blood - brain barrier , which is immature in embryos and fetuses , leading to an increased vulnerability of the fetal brain to the toxic effects of this organic mercury [ 79 ] . moreover , mehg tends to accumulate in fetuses due to their inability to excrete this metal . development of the central nervous system ( cns ) is slow and gradual and involves the differentiation and migration of neuronal and glial cells to organize cellular layers that comprise the brain and spinal cord . thus , damage to the developing cns caused by mehg can result in irreversible morphological and physiological impairments , which compromise postnatal motor coordination , learning , and memory functions [ 3 , 1114 ] . the effects of mehg exposure on the cns are related , particularly in adults , to neurochemical changes that include disturbances in the calcium and glutamate homeostasis [ 15 , 16 ] , reactive oxygen species generation , and oxidative stress in the brain of mammals [ 1719 ] . additionally , the mitochondrial dysfunction accompanied by the expression of apoptotic proteins has also been identified as an effect of mehg - induced neurotoxicity [ 2022 ] . although neurotoxicity caused by mehg is well documented , developmental neurotoxicity is still not fully understood . a previous work has shown that in ovo mehg exposure results in behavioral impairments , such as anomalous movements and low exploratory activity , as well as morphological and biochemical changes , including alterations in the organization of the cerebellar cortical layers and the increase of the antioxidant enzyme activity in the cerebellum of mehg - exposed chicks . in this study , we offer a new approach to the exploration of developmental neurotoxicity induced by mehg , using a chicken embryo as a model . the aim of this study was to investigate the impact of mehg on the cellular layers of the spinal cord , mainly focusing on cell proliferation and cell cycle . the spinal cord was chosen because the cellular organization of its three layers is less complex when compared to the brain and cerebellum , which makes it easier to characterize the cns cellular dynamics and thus developmental neurotoxicity . moreover , there is a lack of knowledge about the developmental neurotoxicity induced by mehg in spinal cord because the most studied impairments caused by this metal mainly relate to the brain and cerebellum . fertilized eggs of gallus domesticus were obtained from a commercial hatchery ( tyson foods brasil ltda . , the eggs were weighed ( 66.6 4.7 g ) and transferred to an incubator at 37.538.0c and 65.0% humidity . prenatal acute mehg exposure was performed at embryonic day 3 ( e3 ) , that is , 20 hh stage series . the embryos received a single dose of 0.1 g of methylmercury ii chloride ( sigma - aldrich , usa ) diluted in 50 l of saline solution administered into the yolk sac near the vitellin vessels . the dose of mehg used in this study was determined according to heinz et al . [ 25 , 26 ] and on the basis of a previous study performed by carvalho et al . . after treatment , each egg was returned to the incubator , and embryos were monitored daily in ovo up to embryonic day 10 ( e10 ) , that is , 36 hh . at e10 , the embryos were anesthetized by cooling to 4c for 1520 min , removed from the egg shell , and washed in saline solution . all experiments were carried out according to the ethics committee for animal research of the universidade federal de santa catarina , florianpolis , brazil ( approval number 355/ceua / ufsc ) . whole embryos at e10 ( n = 7 embryos per group of three independent experiments ) were fixed in 4% formaldehyde and the trunk region was dissected , embedded in paraffin , and cut into serial transversal sections ( 6 m ) . the sections were stained with hematoxylin - eosin ( he ) to analyze the spinal cord morphology and to determine the distribution and morphology of cells in the ependymal , mantle , and marginal layers . the thicknesses of the ependymal , mantle , and marginal layers were measured using a morphometric eyepiece ( olympus , usa ) ( 200x ) in midline region of the spinal cord . we evaluated mercury deposition by the autometallography ( amg ) method , in which dewaxed sections were immersed in the amg developer solution ( 60% gum arabic , 10% potassium citrate buffer , 30% hydroquinone , and 0.5% silver nitrate ) in darkness for 60 min . next , the spinal cord sections ( n = 7 embryos per group of three independent experiments ) were washed with tap water and counterstained with hematoxylin . mercury deposition was evaluated as brown stained cells , which represent silver surrounding the deposited mercury , and classified as absent ( ) , mild ( + ) , moderate ( + + ) , and intense ( + + + ) by an investigator who was blind to the treatment assignments according to mller et al . . to evaluate the effect of prenatal acute mehg exposure , we first looked for proliferation , cell cycle , and dna damage in the spinal cord using antibodies rabbit anti - phosphohistone h3 igg ( 1 : 250 ; upstate , usa ) , rabbit anti - cyclin e igg ( 1 : 100 , santa cruz biotechnology , usa ) , mouse anti - p21 igg ( 1 : 100 , santa cruz biotechnology , usa ) , and rabbit anti--h2a.x igg ( 1 : 50 , santa cruz biotechnology , usa ) . next , we investigated neuronal differentiation using antibody mouse anti - neuronal nuclei neun igg ( 1 : 100 , chemicon international , usa ) and mouse anti-iii tubulin igg ( 1 : 100 , promega , usa ) ( n = 7 embryos per group of three independent experiments ) . the sections were washed with 0.1 m phosphate - buffered saline ( pbs ) ph 7.4 + 0.3% triton x-100 and then blocked with 5% fetal bovine serum ( fbs ) in pbs . the sections were incubated overnight at 4c with primary antibodies , washed with pbs , and then incubated for 90 min at room temperature with peroxidase - conjugated secondary antibody anti - rabbit igg ( 1 : 400 , sigma , usa ) and biotin - conjugated antibodies , including anti - rabbit igg ( 1 : 200 , sigma , usa ) and anti - mouse igg ( 1 : 200 , sigma , usa ) . next , the sections were washed in 0.1 m pbs , and binding sites of antibodies were revealed with 3,3-diaminobenzidine ( dab ) ( sigma - aldrich , usa ) . for immunofluorescence , alexa fluor 488 goat anti - mouse igg ( 1 : 200 , life technologies , usa ) and alexa fluor 568 goat anti - rabbit igg ( 1 : 100 , life technologies , usa ) were used . next , the sections were incubated with 4,6-diamidino-2-phenylindole dihydrochloride ( dapi ) ( sigma - aldrich , usa ) for 3 min at room temperature . negative controls of immunohistochemical reaction were treated in the same way , except that the primary antibodies were replaced with 0.1 m pbs . we used tdt - mediated dutp nick end labeling ( tunel ) staining to identify apoptotic cells in the dewaxed spinal cord sections ( n = 7 embryos per group of three independent experiments ) . tunel staining was conducted with a tdt - fragel dna fragmentation detection kit ( calbiochem , usa ) according to the manufacturer 's instructions . tunel - stained cells displayed dark - brown precipitates in their nuclei . to quantify immunoreactive cells ( phosphohistone h3 and neun ) and tunel - positive cells , stereological analysis was performed using the m-42 test system ( weibel number 2 , tonbridge , uk ) ( 200x ) . the numerical density per area ( na ) of the cells five random fields of the spinal cord were counted for each section ( 3 sections per embryo , 7 embryos per group of three independent experiments ) . in order to quantify the -h2a.x - positive cells , the integrated density of pixels of the fluorescence digital images a scale bar was determined , and the measurement of the integrated density of pixels was determined in a 3,599.77 m frame . dissected and unfixed spinal cords were homogenized and submitted to consecutive washes with 0.1 m pbs ph 7.8 ( n = 7 embryos per group of three independent experiments ) . then , the cells were dissociated using 0.25% trypsin for 15 min at 37c and added to 5% fbs under agitation . subsequently , the samples were centrifuged at 640 g for 10 min and the supernatant was collected , incubated with primary antibodies rabbit anti - cyclin e igg ( 1 : 1000 , santa cruz biotechnology , usa ) , mouse anti - p21 igg ( 1 : 1000 , santa cruz biotechnology , usa ) , and mouse anti-iii tubulin igg ( 1 : 1000 , promega , usa ) for 1 h , and then incubated for 45 min with the secondary antibodies alexa fluor 568 anti - rabbit igg and alexa fluor 488 anti - mouse igg ( 1 : 1000 , life technologies , usa ) . previously , a run with unstained cells was performed to determine the gates of cells of interest . thus , from the dot plot with 20,000 events and considering the parameters side scatter ( ssc - a ) and forward scatter ( fsc - a ) , the gates with 1,800 events were determined . facscanto ii flow cytometer ( bd biosciences , canada ) was used for the analysis . the differences between mehg - treated and untreated control embryos were evaluated by student 's unpaired t - test . all data were expressed as mean sem , and p < 0.05 was considered statistically significant . the amg method was used to show that a single injection of 0.1 g mehg into the yolk sac could reach the embryo and its spinal cord . as expected , the mercury deposition was evident in all mehg - treated embryos but was not observed in the control embryos . the mehg deposition was recognized in three spinal cord layers , and a greater intensity of deposition was found in the ependymal and mantle layers ( figure 1 ) . considering the fact that the mercury was incorporated in the embryonic tissues , we evaluated the general features of the spinal cord . similar features of the cell morphology and distribution in the ependymal , mantle , and marginal layers were observed between mehg - treated and control embryos ( figure 2 ) . however , mehg treatment caused a significant decrease in the thickness of the mantle layer ( 172.01 m 7.41 ) when compared to control embryos ( 248.19 m 21.48 , p < 0.01 ) . the same effect was observed in the marginal layer of mehg - treated embryos ( 92.03 m 4.12 ) in comparison to controls ( 127.74 m 14.74 , p < 0.05 ) . only the thickness of the ependymal layer did not change after mehg treatment between the control ( 18.94 m 1.14 ) and mehg - treated embryos ( 20.77 m 0.38 , p > 0.05 ) . on the basis of the reduced size of the spinal cord caused by mehg exposure , the next step was evaluating the proliferation and cell cycle , which are essential for development progress . a few proliferating cells were observed in all embryos , and , after treatment , mehg caused a decrease in the number of these cells per area . in the ependymal layer , the na of proliferating cells was significantly lower in mehg - treated embryos ( 13.75 cells / mm 7.3 ) when compared to controls ( 55.01 cells / mm 13.7 , p < 0.05 ) . in the mantle layer , the highest number of proliferating cells was observed in the control ( 60.17 cells / mm 10.4 ) in comparison to mehg - treated embryos ( 21.82 cells / mm 8.6 , p < 0.05 ) . no significant difference was observed in the marginal layer between the control ( 32.64 cells / mm 10.2 ) and mehg - treated embryos ( 20.5 cells / mm 10.5 ) ( figure 3 ) . moreover , we examined the proteins p21 and cyclin e that play a crucial role in the progression of cell cycle . mehg caused an increase in the absolute number of p21-positive cells in the spinal cord of treated embryos ( 473.33 cells 62.40 ) when compared to controls ( 100.67 cells 17.47 , p < 0.05 ) . however , no changes were observed in the number of cyclin e - positive cells between mehg - treated ( 102.7 cells 15.2 ) and control embryos ( 145.0 cells 55.28 , p > 0.05 ) . figure 4 display the immunolocalization and percentage of p21 and cyclin e - positive cells in mehg - treated and control embryos . in order to verify if mehg causes dna damage , the expression of -h2a.x protein in response to dna double - strand breaks was examined . after treatment , mehg caused an increase in the expression of -h2a.x ( 53,740.89 7,834.14 m ) when compared to the control embryos ( 34,473.89 670.97 m , p < 0.05 ) . these anti--h2a.x - positive cells were found mainly in the transition zone between the ependymal and mantle layers of the mehg - treated embryos ( figure 5 ) . regarding the increase of dna damage , we investigated the occurrence of apoptotic cells after mehg treatment . few apoptotic cells were observed in the spinal cord of the control and mehg - treated embryos . a significantly high na of tunel - positive cells was observed in the mantle layer of mehg - treated embryos ( 12.73 cells / mm 3.6 ) when compared to controls ( 3.82 cells / mm 2.1 , p < 0.05 ) . however , no significant differences were found between the control ( 3.09 cells / mm 1.5 ) and mehg - treated embryos ( 2.05 cells / mm 1.2 ) in the marginal layer . additionally , no tunel - positive cells were observed in the ependymal layer of either the control or mehg - treated embryos ( figure 6 ) . we investigated whether mehg compromises the neuronal differentiation in the developing spinal cord , considering that the major effects of mehg were observed mainly in the mantle layer , where intense cell differentiation occurs . immunofluorescence using anti-iii - tubulin antibody revealed the expression of this protein in the mantle and marginal layers at e10 . after treatment , no changes were observed in the expression of iii - tubulin between the control ( 424.0 cells 40.91 ) and mehg - treated embryos ( 517.33 cells 1.85 , p > 0.05 ) ( figure 7 ) . additionally , when we analyze the expression of neun , recognized in postmitotic neurons and/or during neuronal differentiation , a significantly decrease in the na of neun - positive cells was observed in the mantle layer of mehg - treated embryos ( 14.32 cells / mm 4.1 ) when compared to controls ( 64.55 cells / mm 5.5 , p < 0.0001 ) ( figure 8) . the neurotoxicity of mehg is a well - known phenomenon , and the present study contributes new data to improve the current understanding of the embryonic cell responses after a single in ovo injection of 0.1 g mehg . although this dose did not affect the overall morphology of the spinal cord , we demonstrated here that it is related to a reduction in thickness of the spinal cord layers , as well as to impairments in cell cycle proteins and in early neuronal differentiation . in fact , in ovo development is a good model for toxicity studies because embryos develop in the absence of maternal factors , which may compromise the assay results . the metal injection in the yolk sac is effective for neurodevelopmental toxicology , and these assays have been validated in our previous studies with lead acetate and mehg [ 23 , 28 , 31 ] . moreover , the experimental design is also important , particularly the establishment of the exposure time . preliminary tests ( data not shown ) using a shorter exposure times than the 7 days adopted here were not sufficient for the incorporation of mehg by embryos . additionally , considering the exposure time , the choice of treatment and analysis ages are equally essential . in this study , we exposed embryos in earlier stage of development of cns ( e3 ) , soon after the neural tube closure . at this stage , neural tube is composed by a nondifferentiated neuroepithelium . then , to understand the neurodevelopmental toxicity of mehg , cellular analyses were performed at e10 , when the layers of the spinal cord are distinguished and composed by neuronal and glial differentiated cells . the used time gap between exposure and analyses was calculated in order to assess the period of vulnerability of embryos and then to assess the effects of mehg on essential cell mechanisms , which are inherent to development of spinal cord . our results showed that mehg causes a reduction in the thickness of the layers , reflecting the neurotoxicity of this metal in the spinal cord tissue . demonstrated the deposition of mehg in the layers of the cerebellum of chicken embryos and also showed morphological changes in the purkinje layer in the first postnatal week . studies about mehg poisoning have shown the effects of mehg on the cytoarchitecture of cns layers in humans and animals , affecting the disposition and number of neurons , as well as on the size of the brain and cerebellum [ 6 , 7 , 3235 ] . regarding the effect on the morphology of cns layers , we tested the hypothesis that mehg causes impairments in cell proliferation , an essential mechanism of development . then , we analyzed more specifically some proteins involved in cell cycle in order to better comprehend the cellular basis of mehg toxicity . our data showed a significant reduction in the number of proliferating neural cells in the ependymal and mantle layers . neural cell proliferation was disturbed by mehg , as demonstrated by in vitro and in vivo assays [ 14 , 35 , 36 ] . it was also demonstrated that mehg affects the proliferation in all regions of the developing cns , such as the spinal cord in xenopus laevis and danio rerio [ 37 , 38 ] , as well as in the murine brain and cerebellum [ 34 , 39 , 40 ] . the idea that mehg compromises the cell proliferation was explored in classic works that focused on the mitosis inhibition related to the disruption of g1 and g2 progress [ 7 , 34 , 39 ] . data about the expression of regulatory molecules involved in cell cycle checkpoints , such as p21 and cyclin , have been demonstrated mainly in the brain and hippocampal and cerebral cortex [ 40 , 41 ] . p21 protein plays a central role in cell cycle arrest in response to dna damage by inhibiting the initiation of replication in the s phase . as expected , our results showed an increase in the expression of p21 in the ependymal and mantle layers after mehg exposure . however , here we found the association of a decrease in cell proliferation with an increase of p21 expression in the developing spinal cord . taken together , these data suggest the cellular impairment caused by mehg and the fact that this organometal causes the arrest of the cell cycle in g1 . interestingly , regarding the interactive role of cyclin e and p21 , the decrease of cyclin e was expected after the mehg treatment , as demonstrated by burke et al . , falluel - morel et al . , in fact , cyclin e has been identified as a target of mehg , reducing its expression in brain development . on the other hand , our data showed that mehg did not change the cyclin e expression in the spinal cord of chicken embryos . indeed , using - h2a.x as a marker of dna damage , we verified the occurrence of dna double - strand breaks in the spinal cord of mehg - treated embryos , demonstrating the genotoxic effect of this metal . the dna damage may cause sequences of intracellular signaling that contribute to the upregulation of p21 , and unrepaired damage may cause signaling to apoptosis . here apoptotic cells were observed mainly in the mantle layer , the same layer where -h2a.x - positive cells were found . this combination of data reinforces the argument that the toxicity of mehg seems to activate the signaling cascade of programmed cell death or apoptosis in both adult [ 4446 ] and developing cns [ 6 , 14 , 22 , 35 , 38 ] . moreover , we proposed that the association between decreased proliferation and increased apoptosis may act as one cause of the reduction in the thickness of the spinal cord layers . additionally , this impairment can progress during embryonic development , as well as in childhood and adulthood phases . considering the fact that the mantle layer appears be the more affected by mehg and also that neurons are well recognized in this layer at the embryonic age evaluated , we investigated whether mehg interferes in the expression of -tubulin iii , a marker of differentiated neurons . in spite of our expectation , the dose used did not compromise this protein . however , when we analyze the expression of neun , a neuron - specific nuclear protein , which is recognized in postmitotic neurons and/or during neuronal differentiation , we observed a significant decrease on the expression of this protein . our results showed that mehg affects differentially the neuron maturation , in the same embryonic stage . this can be explained , considering that to organize the spinal cord layers during development , the cells need to differentiate and migrate in different rhythms . thus , in the same embryonic stage , we found both early and late phases of neurogenesis . in general , our results provide new insights in attempt to contribute to better understanding the cellular basis of complex mehg neurotoxicity , in developing spinal cord . the basis of how mehg acts during the spinal cord development is incompletely described . from toxicological point of view , these results are very important because they showed for the first time that in ovo mehg exposure alters spinal cord development by causing dna double - strand breaks and also disturbing the mechanisms of proliferation and cell death , differentially interfering in early and late neurogenesis phases .

the neurotoxicity caused by methylmercury ( mehg ) is well documented ; however , the developmental neurotoxicity in spinal cord is still not fully understood . here we investigated whether mehg affects the spinal cord layers development . chicken embryos at e3 were treated in ovo with 0.1 g mehg/50 l saline solution and analyzed at e10 . thus , we performed immunostaining using anti--h2a.x to recognize dna double - strand breaks and antiphosphohistone h3 , anti - p21 , and anti - cyclin e to identify cells in proliferation and cell cycle proteins . also , to identify neuronal cells , we used anti - neun and anti-iii - tubulin antibodies . after the mehg treatment , we observed the increase on -h2a.x in response to dna damage . mehg caused a decrease in the proliferating cells and in the thickness of spinal cord layers . moreover , we verified that mehg induced an increase in the number of p21-positive cells but did not change the cyclin e - positive cells . a significantly high number of tunel - positive cells indicating dna fragmentation were observed in mehg - treated embryos . regarding the neuronal differentiation , mehg induced a decrease in neun expression and did not change the expression of iii - tubulin . these results showed that in ovo mehg exposure alters spinal cord development by disturbing the cell proliferation and death , also interfering in early neuronal differentiation .

1. Introduction 2. Materials and Methods 3. Results 4. Discussion 5. Conclusion

ectopic ureters are common in females , 80% of which are duplicated and present at birth or in childhood . the urethra and vaginal vestibule are the most common sites of drainage in females . furthermore , their drainage in a completely developed mullerian system has been reported only once before , although there are reports of bilateral single - system ureteral ectopia into the urogenital sinus . we report one such case of bilateral , single ectopic ureters draining into a grossly dilated vagina that presented late in an adolescent female . a 16-year - old female presented with a complaint of involuntary leakage of urine since birth . the previous leak of a few drops had increased in amount over the past 2 months , thus prompting medical attention . she could manage with 2 to 3 pads during the day , with 10 to 12 daytime voids in amounts ranging from approximately 90 to 240 ml . her nighttime incontinence was severe ; she consistently woke up wetting her bed every night . on examination , the external urethral meatus was normal as was the external genitalia , and the vaginal introitus was moist . the right kidney was hydronephrotic with a dilated ureter and dilated vagina wrongly interpreted as a normal urinary bladder ( fig . a diethylenetriaminepentaacetic acid renal scan showed a nonfunctioning left kidney , delayed excretion phase of the right kidney , and a glomerular filtration rate of 65.71 ml / min . on cystovaginoscopy , the external urethral meatus and urethra appeared normal , with a small urinary bladder with approximately 20-ml capacity and an absent trigone . computed tomography revealed calcification in the left kidney and left ureter , a nonexcreting left kidney , hdun changes on the right side with delayed excretion , and a small urinary bladder separate from the capacious vagina ( fig . the right ureter was moderately dilated , and the left ureter was minimally dilated and calcified . the bowel contributed 90% of the reconstructed bladder wall , because the native bladder was atrophic . clean intermittent self - catheterization fourth hourly was advised for the initial few months , which the patient was later weaned from because she maintained good voiding . in our review of the available literature for the past 50 years , we found only one such published case report of bilateral , single vaginal ectopic ureters by chatterjee and chatterjee in 2011 . sheldon and welch and more recently singh et al . reported bilateral , single ectopic ureters draining into the urogenital sinus . the ureters find their way into the definitive bladder as the distal mesonephric duct is absorbed into the developing bladder to form the trigone , bladder neck , and proximal urethra . ectopic ureters draining into the female genital tract are thought to be via embryonic remnants of the mesonephric duct ( gartner 's duct ) , which breaks open into the mullerian system . this elusive embryonic event is unexplained and rare , more so in bilateral , single ectopic ureters . occurrence of a simultaneous urogenital abnormality is expected here , such as agenesis of urinary bladder or persistent urogenital sinus . bilateral single - system vaginal ectopia in a completely differentiated urogenital tract should arguably be very rare . bilateral ectopic ureters in females usually present early with constant dribbling of urine . in this case , however , the presentation was during adolescence and with 150 to 200 ml voided apparently normally . this is explained by the fact that patient had , over the years , learned to hold the urine in her vagina by contracting the pelvic floor musculature . computed tomography was crucial for arriving at a diagnosis in this case , as was reported by other authors in similar cases , although magnetic resonance urogram can be further precise . there was a therapeutic dilemma regarding reconstruction of the urinary tract . an ileocystoplasty with right ureteric reimplantation was done anticipating future need of a continence procedure or undiversion to nonorthotopic diversion . because apparently good urethral mucosal coaptation was seen on cystoscopy , orthotopic diversion was preferred . the issue of continence is also discussed by podesta et al . in their article , in which they inferred that the bladder in bilateral , single ectopic ureters may retain a good continence mechanism with adequate augmentation . hence , on the basis of this evidence , no bladder neck continence procedures were attempted in our case . fortunately , the patient was continent with cystometric capacity of 300 ml at 3 months . she was weaned off clean intermittent self - catheterization by 6 months and at present voids satisfactorily by abdominal straining ( fig .

a 16-year - old female presented with dribbling of urine along with voluntary voiding since birth . renal imaging revealed hydroureteronephrosis on the right side ; the uterus and ovary were normal . a radionuclide scan showed a left nonfunctional kidney . on cystovaginoscopy , the urethra was shown to be normal and the urinary bladder was tubular with small capacity and an absent trigone . although the vagina was capacious , no ureteric orifices were found . computed tomography corroborated the diagnosis of bilateral , single ectopic ureters draining into a grossly dilated vagina . this case is unique because it is a bilateral single - system ureteral ectopia in a completely differentiated female genital tract that presented late in adolescence . to the best of our knowledge , this is the second such ureteral abnormality reported in the literature so far . the patient underwent ileocystoplasty with right ureteric reimplantation and nephroureterectomy for the left nonfunctional kidney , which histopathology showed to be tuberculosis . the patient is continent with cystometric capacity of more than 300 ml .

INTRODUCTION CASE REPORT DISCUSSION

sudden sensorineural hearing loss ( ssnhl ) is defined as a loss of hearing of 30 db or more over at least three contiguous frequencies . usually , symptoms present unilaterally and suddenly within 2472 h. most of the cases are referred to as idiopathic sensorineural hearing loss ( issnhl ) since etiologies remain unclear in the majority of the patients . sudden snhl occurs in five to 20 cases per 100,000 per year in the united states 1 , 2 . the rate of spontaneous recovery was rated between 25 and 89% according to recent publications 4 . different treatment regimens like antioxidants , corticosteroids , vasodilatators , hyperbaric oxygen ( hbo ) , or carbogen therapy 5 have been described . among these approaches , intratympanic injection of steroids ( its ) is regarded as effective , safe , and well tolerated 6 , and was shown to be as sufficient as orally applied steroids 7 , 8 . although many studies have reported on the usefulness of steroids , the authors of a recent cochrane review came to the conclusion that the value of steroids in the treatment of issnhl remains unclear 9 . for the treatment of issnhl , hbot has been applied over decades either alone or in addition to other medical treatments 10 . in combination with hbot , however , hbot in addition to application of a vitamin cocktail and dexamethasone , did not improve chronic issnhl in another study 12 . nevertheless , since benefits of hbo in the treatment of issnhl were demonstrated 13 , the committee of the undersea and hyperbaric medical society approved issnhl as indication for hbot 14 . these authors claim that best results are achieved when hbot starts within 2 weeks and is combined with steroid treatment . the combination of hbot with systemic steroid treatment was especially successful for patients with an initial hearing loss of more than 90 db 15 . additionally , hbot resulted in an improvement of thresholds especially in the low frequencies of patients with otherwise therapyrefractory ssnhl 16 . in another study , its was compared to hbot and to a combination of both after unsuccessful systemic corticoid treatment of issnhl 17 . all three modalities resulted in an improvement of word scores and pure tone audiometry ( pta ) . however , the highest success was achieved , especially at low frequencies , after the combined use of hbot and its . despite of the excellent results that can be achieved after treating patients with acute issnhl ( duration max . 2 weeks ) with hbo , data concerning the outcome of hbot of patients with chronic ( > 6 months ) issnhl have not been reported hitherto 18 . we therefore present a case study on patients with severe issnhl receiving hbot combined with its as salvage treatment after an unsuccessful attempt with systemic steroids application . in most of the cases , the delay between onset of hearing loss and start of the combined therapy was much more than the recommended maximum of 30 days 17 . over 4 months , we prospectively identified seven consecutive cases ( three female and four male ) with idiopathic ( case 1 , 2 , 4 , and 6 ) , noise most of the patients presented after unsuccessful corticoid treatment with the symptoms persisting for up to 10 weeks ( table 1 ) . in every patient , diagnostic tests were performed in order to rule out neurologic , vascular , or other etiologies for the hearing loss . most of the patients were pretreated according to the guidelines of the german society of otorhinolaryngology for idiopathic hearing loss elsewhere . all patients , except for cases 3 and 7 , had been subjected to unsuccessful treatment with systemic corticoids elsewhere prior to being referred to our institute ( h. l , c.f . patients received bilateral paracentesis and its ( dexamethasone with hyaluronic acid ) , and were immediately transferred to the hbo chamber ( 2.5 atm for 2 30 min for each session ) . thresholds were determined by pta before the start and after finishing the salvage treatment at frequencies between 125 hz and 8 khz . in figure 1 , the ptas of all seven patients at the time of their first presentation to our institute are depicted . case 1 presented 5 weeks after ssnhl before salvage therapy , after unsuccessful treatment with systemic corticosteroids starting 3 days after the onset of unilateral issnhl and its ( four injections ) without hbot , the patients was referred for salvage treatment to our institution . since no benefits of this therapy could be detected within 6 days , the patient was referred to our institute for its and hbot . case 3 experienced bilateral hearing loss and tinnitus after intense noise exposure over several hours . he was presented at our institute , 3 weeks after the onset of the symptoms without being subjected to any other treatment or diagnosis earlier . after other conditions than the noise exposure were excluded as causes for ssnhl , hbot and intratympanic steroid application ( its ) were initiated . however , his symptoms did not improve and he presented 4 weeks later to our institution . case 5 developed combined hearing loss after noise trauma ( explosion ) , accompanied by contusio labyrinthi . he was treated with systemic steroids immediately over a period of 10 days without success . ten weeks after the noise incidence , the patient sought for salvage treatment in our institute and received concurrent hbot with its . case 6 received unsuccessful systemic corticoid treatment immediately after development of a profound issnhl at the right side . approximately 4 weeks later , she was referred to our institute for salvage treatment . although she was advised for a tympanoscopy to rule out and treat a rupture of the round window membrane , she refused surgery and was referred to our institute 3 days after the incidence . patients ' demographics and history are summarized in table 1 . in this cases series , four male and four female patients with an age range from 25 to 62 years were included . all patients experienced unilateral ssnhl , except case 3 who presented with bilateral hearing loss and tinnitus after severe noise trauma . audiograms for all cases after salvage treatment are provided for both ears in figure 2 . in case 1 , after 10 courses of hbot with three concurrent its , an improvement of hearing in the right ear could be achieved . case 2 showed a significant recovery of hearing and vanishing of her tinnitus after 33 courses of hbot , accompanied by six its . in case 3 , combined hbot and its lead to a dramatic improvement of hearing also in the higher frequencies . case 4 received 20 courses with hbot with five its and his hearing recovered mainly in the lower frequencies . in case 5 , combined hbot ( 20 ) and its ( 3 ) resulted in dramatic improvement of the leftsided hearing threshold . after 30 hbot and five its , case 6 regained hearing especially in the lower frequencies . case 7 achieved recovery of hearing only in the lower frequencies ( 33 hbot ; 13 its ) . the pta performed before treatment revealed pantonal hearing loss in all patients . in some of the patients , in addition , all patients experienced and reported substantial relieve from their symptoms during the course of the salvage therapy . the average gain in hearing for all cases ( and for case 3 for each ear ) is presented in figure 3 . the lowest gain ( 20 db ) was achieved in case 7 ( barotrauma ) even though treatment started already on day three after the trauma without any steroids as pretreatment . the mean improvements gained in patients suffering from noiseinduced ssnhl ( 37.2 db ) and issnhl ( 36.9 db ) were comparable . some patients experienced huge benefits ( more than 50 db gain for case 5 and 6 ) , whereas some only gained about 25 db ( case 2 and case 3r ) . gain in hearing threshold for all patients averaged over all frequencies ( mean standard error ) . in general , the improvement was larger at low frequencies ( figure 4 ) , whereas at high frequencies , not all patients could benefit . the average gain ranged between 15 db for 8 khz and 46.4 db for 0.125 khz . for all patients , no side effects due to hbot or other applied therapies could be observed . randomized controlled trials concerning the benefit of antiinflammatory treatment with corticoids in patients with sshl are contradictory in outcome . a metaanalysis published and recently updated in the cochrane library concludes that the value of steroids in the treatment of issnhl still remains unclear 9 , even though oral or systemic steroid application is recommended as treatment of ssnhl by the guidelines of the american academy of otolaryngologyhead and neck surgery 19 . intratympanic injection of steroids ( its ) for the local application has recently emerged to a promising treatment modality for ssnhl 6 , 11 . this is favorable as it minimizes systemic side effects 20 especially in patients with contraindications for the systemic application of corticosteroids , e.g. , diabetic patients 21 . in recent years , combined application of steroids and hbot for the treatment of ssnhl as salvage therapy has become more popular since promising results were achieved 17 , 22 . only in one of these studies , hbot and its were applied concurrently in patients refractory to other treatment regimen , and partial or even full hearing recovery in the low frequencies was achieved in most of the patients 17 . in this study , the salvage therapy was started < 1 week after the onset of hearing loss in all patients included . by contrast , in the herein presented series of patients , most of them with chronic ssnhl , we have shown that concurrent application of both its and hbot can alleviate the symptoms even if the onset of the symptoms was several months ago . the lowest recovery rate was achieved in a patient with barotrauma , even though treatment started as early as 3 days after the onset of hearing loss ( case 7 ) . here , other effects might have contributed to the hearing loss , for example , the rupture of the round window . these were documented by pta and were also based on the subjective improvement as reported by the patients at each consultation . however , evaluation of patients ' satisfaction using standardized measures such as visual analog scala was not performed . regarding possible mechanisms for the positive results achieved , some further aspects will be discussed . permeability of the round window membrane , clearance as well as the longitudinal perilymph flow rate are interindividual factors that influence accumulation of pharmacologically active substances from the cavum tympani to the perilymph . after its , a rapid loss of the drug may occur due to the clearing functions of the eustachian tube 23 . in order to accumulate in the perilymph , the round window seems to be the dominant route to the inner ear 24 . the size , concentration , solubility , and electrical charge of the drug affect its permeation through the round window membrane 25 , 26 . in addition , the thickness and the state of the round window membrane strongly influence the permeability of the drug . after transtympanic administration of gadolinium and monitoring of the threedimensional distribution using magnetic resonance imaging , permeability of the round window membrane was impaired in approximately 20% of the patients 27 . therefore , it is not surprising that some of the patients with ssnhl remain unresponsive to both systemic and intratympanic steroid application . for these patients , concurrent application of its and hbot might present a successful treatment regimen . we speculate that higher concentrations of corticoids may accumulate in the perilymph under hbot due to a potentially increased permeability of the round window membrane and that increased partial oxygen pressure may account for the benefits experienced by the patients included in our study . however , there is hitherto no evidence available to support this hypothesis . trying to understand the mechanisms that are involved , a closer look to the round window membrane is important . for example , substances like gentamycin and dexamethasone are able to pass the membrane under normal conditions , whereas bigger molecules , such as albumin , are not 28 . the permeability of the round window membrane changes under pathological conditions , for example , middle ear infection , and larger molecules are then able to penetrate to the inner ear 29 . after application via the cavum tympani , substances ( e. g. , glucocorticoids ) penetrate through the round window membrane and generate a gradient in the cochlea 30 . for dexamethasone , basoapical differences in concentration up to a factor of 1000 have been measured in guinea pigs 30 . these results show that the delivered substances mainly accumulate in the basal turn of the cochlea 30 . since permeability of the round window membrane can be modulated by pathological conditions , it seems likely that hbot may also influence its properties . to sufficiently explain the results obtained under this regimen , many pathophysiological mechanisms have to be considered and further investigations need to be performed . a hyperbaric environment may facilitate the diffusion rate of chemicals in solution , such as of corticoids into the perilymph through the round window membrane . transport functions via gap junctions and the mechanism behind could also play a role in the transport of substances into the cochlea . gap junctions allow the passage of molecules up to a size of approximately 2 nm 31 . some of them are mechanosensitive 32 and their state can be influenced , for example , by temperature . postulate that in lower temperature ranges , only small molecules can pass . at higher temperature ranges , beginning with 23c , the passage of bigger molecules becomes possible . considering these data a synergistic effect of its and hbot has been proposed in order to explain the gain of threshold : on the one side , steroids reduce inflammation in the inner ear that may be contributing to hearing loss , on the other side , hbot increases the intracochlear aiding in the recovery of hearing 17 . however , based on our experience , the hearing recovery may be achievable even if the onset of ssnhl was several weeks to months ago , if the patients were attributed to hbot immediately after its . in addition to the synergistic effort in reducing edema in the inner ear , we assume that hbot changes the permeability of the round window membrane allowing increased influx of steroids into the perilymph , especially into the basal turn of the cochlea , where dexamethasone levels can be expected to be the highest . this may explain the recovery of hearing not only in the low frequencies but also in the high frequencies that are more refractory to recovery treatment . earlier studies have reported on the role of hbot in order to enhance results achieved by systemic or oral steroid application 15 , 22 . the partial pressure of oxygen in the scala tympani in an experimental setting increased resulting in the protection of neurosensory cells and restoration of the oxidative metabolism in the vascular strip 34 . in addition , hbot improves rheology and microcirculation by lowering the blood viscosity and improving erythrocyte elasticity 35 . the guidelines of the american academy of otolaryngology head and neck surgery 19 state that the evidence supports a possible benefit of hbot as an adjuvant treatment , in cases of acute ssnhl when used within 3 months of the onset of the hearing loss . nonetheless , a recent review points out that the costs and the limited availability of hbot as well as the lack of high quality evidence make it impractical for most patients 36 . the findings of the herein presented study encourage further research on the treatment of noiseinduced ssnhl and issnhl with the concurrent use of hbot and its respecting also patients with longterm or therapyrefractory ssnhl .

key clinical messageconcurrent hyperbaric oxygen therapy ( hbot ) and intratympanic steroid application ( its ) are beneficial as salvage therapy for therapyrefractory sudden sensorineural hearing loss ( ssnhl ) . the findings encourage further research on the treatment of noiseinduced and idiopathic ssnhl with concurrent use of hbot and its respecting also patients with longterm or therapyrefractory ssnhl .

Introduction Patients and Methods Results Discussion Conflict of Interest

cancer is a huge burden of our societies with an overall worldwide incidence of 182,3 cases per 100.000 inhabitants and an overall mortality of 102,4/100.000 according to the international agency for research on cancer of the world health organization ( estimated age - standardized incidence and mortality rates ( asr ) for both sexes ) . highest incidence rates are reported for breast , colorectal and cervical cancer in women and lung and prostate cancer in men . current treatment options comprise of surgery , chemotherapy or radiation plus more recently introduced targeted therapies . targeted therapies aim to specifically address malignantly transformed cells while sparing healthy tissues . thus , receptors , which are important during embryonic development and readopted by cancer cells , belong to the most promising targets . one of the most prominent molecules of that kind is the human epidermal growth factor receptor-2 ( her-2 ) . her-2 is a receptor tyrosine kinase , mediating signals for cell proliferation , cell mobility and survival . in the absence of a known ligand her-2 is very important during embryonic development , e.g. it plays a role in ductal morphogenesis of the mammary gland , but it is almost not expressed on adult tissue , except the heart . on the contrary , her-2 is overexpressed in breast , ovarian , gastric , colorectal , pancreatic , and endometrial cancers . another closely related receptor tyrosine - kinase is the epidermal growth factor receptor ( egfr ) . its overexpression is associated with head and neck squamous cell carcinoma ( hnscc ) , non - small - cell lung cancer ( nsclc ) , colorectal cancer ( crc ) , breast and pancreatic cancer , but also with certain types of brain cancer . in contrast to her-2 , egfr senses the epidermal growth factor ( egf ) and other important growth signals , such as transforming growth factor- ( tgf- ) or amphiregulin [ 11 - 14 ] . egfr is physiologically required for promoting cell proliferation and dna repair , but can also lead to tumor growth , progression , and evasion of apoptosis via the activation of plc--pkc , ras - raf - mek , pi-3k - akt - mtor and jak2-stat3 pathways . overall , egfr and her-2 together with her-3 and her-4 belong to the erbb - family , which derives its name from the homology to the erythroblastic leukemia viral oncogene protein ( v - erb - b , ) . currently two forms of targeted therapies against egfr and her-2 are in clinical use : i ) blocking the intracellular receptor tyrosine kinase with small molecules and ii ) attacking the extracellular domains of the receptor with monoclonal antibodies . small molecules targeting egfr comprise erlotinib ( tarceva , roche ) and gefitinib ( iressa , astrazeneca ) plus the dual kinase inhibitors lapatinib ( tykerb , glaxosmithkline ) and afatinib ( gilotrif , bhringer ingelheim ) , the latter inhibiting her-2 as well ( , see table 1 ) . especially the reversible inhibitors gefitinib , being fda - approved in may 2003 and erlotinib , with fda - approval in november 2004 , are successfully applied in non - small - cell lung cancer . although gefitinib was recalled from that indication in the us , it is still widely used in japan , where patients display a higher rate of egfr - mutations in nsclc , and also received marketing authorization in the european union in 2009 . moreover , erlotinib is approved for the treatment of advanced pancreatic cancer and several next generation irreversible egfr - tyrosine kinase inhibitors , like canertinib , are under investigation for their efficacy in breast , colorectal , lung , pancreatic , renal , head and neck , gynecologic and prostate cancer . the most prominent tyrosine kinase inhibitor ( tki ) for her-2 is lapatinib ( tykerb , glaxosmithkline ) , the above mentioned reversible dual inhibitor of her-2 and egfr , which was fda - approved in march 2007 for the treatment of advanced breast cancer . also in this case , irreversible inhibitors , like neratinib or again canertinib are widely investigated . in contrast to small molecules that intracellularly interfere signaling via blocking the kinase activity , monoclonal antibodies directed against egfr and her-2 aim to extracellularly inhibit ligand binding or dimerization of these receptors , respectively . for targeting egfr , two monoclonal antibodies are currently in clinical use , cetuximab ( erbitux , merck kgaa ) , which was fda - approved in february 2004 and panitumumab ( vectibix , amgen ) , which received fda - approval in september 2006 ( , table 1 ) . in particular cetuximab , a human - murine chimeric igg1 antibody has become an indispensable cornerstone in the treatment of advanced - stage metastatic crc and advanced hnscc . cetuximab finds its epitope within the ligand - binding site of egfr ( extracellular domain iii ) and can thus block binding of growth signals . panitumumab works mechanistically similar ; it can also prevent egf - binding via sterical hindrance , but on a different epitope on domain iii , though partially overlapping . panitumumab is successfully applied in the treatment of metastatic colorectal cancer . for all above mentioned therapeutics , wild type ( wt ) kirsten rat sarcoma viral oncogene homolog ( kras)-status of the patient is of uttermost importance , as it could be demonstrated , that acquired kras mutations lead to resistance against egfr targeting . as kras is a downstream effector - protein in the egfr - signaling pathway , mutations that lead to constitutive activation of kras counteract growth signal inhibition of all egfr targeting drugs . therefore kras - status is meanwhile routinely determined for every human patient before any egfr - specific treatment is initiated . also in case of her-2 targeting , two monoclonal antibody therapies are fda - approved : trastuzumab ( herceptin , roche ) and pertuzumab ( perjeta , genentech ) . especially trastuzumab , being fda approved in september 1998 , proved to be highly successful for the treatment of metastatic breast cancer and has later received importance also for treatment of metastatic gastric cancer and tumors of the gastroesophageal junction ( gej , ) . trastuzumab has been so successful in breast cancer therapy , that very recently , in february 2013 , also a drug - conjugated trastuzumab derivate , trastuzumabemtansine ( t - dm1 , kadcyla , roche ) was approved by the fda for treatment of advanced breast cancer , fuelling the emerging field of antibody - drug conjugates . the other her-2 targeting antibody , pertuzumab received fda - approval in june 2012 and is also applied for treatment of metastatic breast cancer , as specified in table 1 . trastuzumab and pertuzumab target different epitopes on her-2 : trastuzumab binds to subdomain iv on the extracellular domain ( ecd ) of her-2 , whereas pertuzumab targets subdomain ii . as her-2 has no endogenous ligand , the mechanisms of action of trastuzumab and pertuzumab differ from those of the mentioned egfr - targeting immunoglobulins . trastuzumab sterically prevents the formation of her-2 homodimers or highly active heterodimers with other erbb - family members , mainly her-3 and egfr ( . moreover , upon trastuzumab binding , her-2 gets endocytosed and shedding of the receptor is inhibited , which otherwise would lead to an actively - signaling p95-remnant on the cancer cell surface . pertuzumab , on the other hand , binds more distant from the cell membrane , is more efficient in preventing heterodimer formation and in contrast to trastuzumab , which inhibits ligand - independent dimerization , pertuzumab especially inhibits ligand - induced her-2 heterodimers . this different mode of action prompted researchers to investigate a combination therapy of both antibodies in preclinical models , resulting in more complete her-2 blockade , and efficacy in cases where cancer had progressed after trastuzumab monotherapy . also in clinical settings , this combination therapy proved to be highly effective and peaked in june 2012 in the first fda approval of a dual her-2 targeting regimen for metastatic breast cancer . the mechanism of action of monoclonal antibodies , however , can not be confined to their growth signal inhibitory capacity only ; as all mentioned monoclonal antibodies feature fully functional human constant regions , thus they are also able to attract immune effector cells to the site of the tumor and trigger immune cell mediated cancer cell death . among the attracted immune cells are monocytes and macrophages dominant , which are known for their tumoricidic potential in mediating antibody - dependent cell - mediated cytotoxicity ( adcc ) via insertion of granzyme b and caspase enzymes . moreover , our group could demonstrate that monocytes are also able to mediate high levels of antibody - dependent cell - mediated phagocytosis ( adcp ) upon trastuzumab treatment . other attracted cell types expressing fc - receptors for antibody binding , are nk - cells and neutrophilic granulocytes , which have been shown to bear high tumoricidic potential with regard to adcc . moreover , professional antigen - presenting cells , that also express fcreceptors such as dendritic or langerhans cells can be attracted and can induce activation of tumor - reactive t - cells upon facilitated antigen uptake and presentation . this mechanism has been demonstrated to lead to tumor regression in a xenograft model of cetuximab treatment in concert with reconstituted immune cells . upon a closer look , all mentioned egfr or her-2 targeting antibodies belong to the igg class of immunoglobulins , with cetuximab , trastuzumab and pertuzumab being igg1 antibodies and panitumumab , being an igg2 . in fact , all currently fda - approved monoclonal antibodies for therapy of cancer are gamma - immunoglobulins . this is indeed astonishing as the human immunoglobulin repertoire consists of 5 different classes : iga , igd , ige , igg and igm . based on their different constant domains , all of them bear distinct physiological properties with respect to distribution , tissue penetration and function , such as complement - activation or adcc and adcp mediation : igm , the primary antibody response against pathogens is highly active in opsonization , which leads to pathogen clearance by phagocytic cells . iga protects body surfaces , such as the respiratory , gastrointestinal or genitourinary tract and is abundantly found in secrets like tear fluid or saliva , where it exerts neutralizing functions . the function of iga in mother s milk is of special interest as it protects the infant against pathogens in the mother s environment , which are also of high risk to the child . igg is the most abundant antibody isotype in the bloodstream , as it constitutes 70% of all serum immunoglobulins . igg antibodies , which can be further subdivided in igg1 - 4 in humans , exert systemic immune - protection by binding to bacteria , viruses and fungi with high affinity . in general , igg1 and igg3 antibodies are mainly produced in response to protein antigens , whereas igg2 and igg4 antibodies react against pathogens with polysaccharide capsules , like streptococcus pneumoniae . the biological role of igd , however , remains still enigmatic ; discovered late ( in 1965 ) in the serum of a myeloma patient , it was long neglected , because it is only cleaved in minor amounts . membrane - bound igd on the surface of b - cells though , was found to regulate b - cell activation . despite thorough investigation in recent years , the physiological and pathophysiological role of igd is still unclear ; however , an interesting aspect is , that igd was found to bind to certain bacterial proteins with relatively high affinity , but not via its antigen binding - site , as rather through sugar residues on its constant region . moreover , it has recently been shown , that circulating igd can activate antimicrobial , proinflammatory and b cell - stimulating effects in basophilic granulocytes . ige , finally , is the most recently discovered immunoglobulin subclass , as it was only first described in 1966 by teruko and kimishige ishizaka as a novel immunoglobulin in the serum of an atopic individual . at the same time , bennich and johannsson could purify a paraprotein from serum of a myeloma patient , which they termed ignd . they could soon link this novel ignd to asthma and it turned out to be the same protein as the group from japan had found . on a meeting in lausanne in february 1968 , finally , under the guidance of the who immunoglobuline reference laboratory , it was decided to designate this novel immunoglobuline ige . ige plays an important role in defense against parasites and is a key molecule in the pathophysiology of allergic diseases such as atopic dermatitis , asthma , food allergy or anaphylaxis . upon crosslinking of ige - antibodies , bound to fcri - receptors on the surface of mast cells or basophils , ige is mostly known for its detrimental role in allergy , but several studies have for long pointed towards a natural tumor surveillance function of this antibody isotype . interestingly , large epidemiologic studies could reveal an inverse association between the history of atopic diseases and cancer . in 2005 , turner et al . published a study enrolling 1.1 million us - american adults with self - reported , physician - diagnosed asthma or hay fever , who had no cancer at baseline and were followed up for 18 years . in this population , a relative - risk reduction for all cancer mortality could be observed [ relative risk ( rr ) = 0.88 ; 95% confidence interval ( ci ) 0.83 - 0.93 ] . however , in a separate analysis of never - smokers , this effect still persisted , but was not significant anymore . in a following literature analysis of studies from the medline database from 1966 to august 2005 , the same group described strong inverse associations for pancreatic cancer and glioma , whereas lung cancer was positively associated with asthma . however , methodical issues to these historical studies with regard to exposure assessment , confounding and bias were addressed by the authors . the most recent study investigating a possible association between ige and cancer was published in 2010 : van hemelrijck et al . reviewed 27 studies from pubmed and embase and surveyed a swedish cohort of 24.820 people , who underwent ige measurements . here , the authors could show a weak inverse association in their cohort , and a pattern by cancer type in the meta - analysis of the historical studies . another interesting observation was made when the anti - ige antibody omalizumab ( xolair , novartis ) underwent clinical trials and pooled phase i to iii data was evaluated . omalizumab , which removes ige from the circulation , is currently approved for therapy of severe persistent asthma . in those mentioned phase i to iii trials with allergics undergoing omalizumab treatment , a slightly higher number of malignant neoplasms was observed in the anti - ige - treated group ( 20 of 4127=0.5% compared to 5 of 2236=0.2% in the control group ) . malignancies that occurred in the treatment group comprised of breast , non - melanoma skin , prostate , melanoma and parotid cancer . subsequently , busse et al . analyzed 67 phase i to iv trials of omalizumab and could not confirm any possible association between omalizumab treatment and cancer in this extended study . summarizing all epidemiologic observations one can only state , that a possible association between ige and cancer remains still unclear due to the lack of big prospective studies . they could isolate ige antibodies which were not only specific for a 50 kda pancreatic cancer antigen but were indeed able to mediate adcc of pancreatic cancer cells in vitro , pointing towards a benefitial role of ige - antibodies in defense against cancer . pioneer studies with igg and ige antibodies of the same epitope specificity tested head - to - head revealed a higher potential of the ige in terms of cytotoxicity . the very first studies were performed with mov18igg and ige , antibodies that target the folate receptor ( fr)-. fr- ( also known as folate - binding protein , lk26 trophoblastic antigen or gp38 ) is a glycosylphosphatidylinositol ( gpi)-anchored membrane protein that binds folic acid and is regarded as a tumor - associated - antigen ( taa ) in gynecologic malignancies , due to its overexpression in more than 90% of epithelial ovarian cancers and in a subpopulation of uterine carcinomas . as folate is a necessary micronutrient of replicating cells , overexpression of fr- facilitates enhanced growth of cancer cells . for targeting of this receptor , gould et al could demonstrate in an ovarian cancer model , that mov18ige was able to mediate adcc of fr- expressing tumor cells in vitro and in vivo . in a mouse model using xenografted human fr- overexpressing cells , mice that received mov18ige treatment developed in the presence of human peripheral blood mononuclear cells ( pbmcs ) significantly smaller tumors than those treated with mov18igg . in a follow - up study , it could further be demonstrated , that also cytotoxic killing by monocytes can be efficiently triggered with ige . in a subsequent nude mouse study , where again fr- overexpressing tumors were grafted and pbmcs were reconstituted , the ige - treated group had shown monocytic infiltration of the tumor xenografts , which was still persistent after 3 weeks and led to significantly longer survival . moreover , upon a closer look in an in vitro flow cytometric model , specific adcc of tumor cells , executed by monocytes upon mov18ige stimulation could be displayed . finally phagocytosis of fr- positive tumor cells by monocytes armed with fr- specific ige could be displayed by fluorescence microscopy . subsequently , we could demonstrate similar results for the her-2 system in close collaboration with prof . karagiannis : upon generation of a recombinant trastuzumab - like ige , constituted of the same variable regions as original trastuzumab ( being an igg1 ) , it was shown in a flow cytometric assay , that the ige antibody is highly effective in mediating adcc of monocytes against her-2 overexpressing cells . interestingly , in this model , the ige antibody mediated high levels of adcc but only background adcp , whereas the picture was completely opposite for the igg , which mediated killing of tumor cells almost exclusively via adcp . this could be a first hint towards distinct mechanisms of tumor cell killing mediated by different immunoglobulin classes ; however , this still has to be confirmed in more extensive experiments and has to be investigated also for other cancer types . apart from a possibly higher potential for mediating adcc , ige - based immunotherapies of cancer could have other beneficial effects : first , ige antibodies have a uniquely high affinity to their receptors on immune cells ( ka~ 1010/m for fcri and ka~ 108 - 109/m for the cd23 trimer complex ) , which significantly exceeds the affinities of igg1 - 4 to their high - affinity receptor fcri . thus , due to its rapid binding to fc-receptors on cells , ige is quickly removed from the circulation , which is advantageous in terms of side - effects because of the short duration of the compound in the bloodstream . moreover , potential ige - immunotherapies would be effectively distributed to tumor tissues , as ige antibodies bound to fc-receptors on e.g. mast cells can use those cells as shuttle systems to penetrate malignancies and as mast cells are tissue - resident immune cells , this transport would be highly efficient . consistently , we would like to quote the review problems of delivery of monoclonal antibodies by reilly et al . , who wrote that the clinical success of monoclonal antibody - based cancer diagnosis and therapy depends , however , on solving a number of pharmacokinetic delivery problems . these include : ( i ) slow elimination of monoclonal antibodies from the blood and poor vascular permeability ; ( ii ) low and heterogeneous tumour uptake , and state that those two substantial challenges of anti - tumor immunotherapy could be simply addressed by using ige . other possible advantages include the high sensitivity of ige - effector cells to activation by antigens and the speed and amplitude of the response , which can most impressively be seen during allergic and anaphylactic reactions , typically beginning within minutes upon allergen exposure . that is at the same time also the biggest concern of using ige - based immunotherapies against cancer : recombinant ige , applied intravenously , always bears the risk of anaphylactic reactions ; therefore , careful selection of the target epitope is of uttermost importance in this regard . during an anaphylactic reaction , preformed ige , that is bound to fc-receptors on the surface of mast cells or basophilic granulocytes is cross - linked by allergens , which induces release of stored granules , containing vasoactive amines ( e.g. : histamine ) or lipid mediators ( e.g. prostaglandin d2 , platelet - activating factor , or leukotrienes ) . this rapid release can lead within minutes to fatal symptoms like asphyxiation from laryngeal swelling , circulatory collapse from hypotensive shock , cardiac arrest , or respiratory failure because of bronchoconstriction . in order to prevent such effects , the target structure for designing passive immunotherapies with ige - antibodies should not be expected to be cross - linking , which means , that the epitope should be monovalent andit should not circulate in the blood , or if , it should only circulate in a monomeric form . it should not circulate in the blood , or if , it should only circulate in a monomeric form . these requirements are fulfilled for the mentioned anti - fr- antibody mov18ige , but also for the anti - her-2 antibody trastuzumab - like ige . for both antibodies it could be demonstrated , that monomeric target molecules do not trigger mediator release of mast cells , which were preloaded with their specific ige - antibodies , respectively . furthermore , rudman et al . could demonstrate , that although serum levels of fr- were increased in ovarian cancer patients ( up to 40 ng / ml ) compared to healthy controls ( mean=1,73 ; sd=3,45 ) , basophilic granulocytes loaded with mov18ige were not significantly activated upon incubation with fr- even at a concentration of 300 ng / ml . on the other hand , both antibodies were shown to mediate mast cell degranulation upon incubation with tumor cells , displaying high numbers of target molecules in a repetitive manner on their surface . here , cross - linking of fc-receptors is highly efficient , and therefore local anaphylaxis at the tumor site could be expected , which would again be beneficial , as it results in initiation of a strong immune response . as mast cells also store tumorinhibiting agents in their granules , e.g. tumor necrosis factor ( tnf)- , this degranulation could also result in direct tumor cell killing . moreover , also other cells involved in anaphylactic reactions , such as eosinophils , have been shown to execute tumoricidic functions , e.g. via secretion of granzyme a or eosinophilic peroxidase . another big challenge of current immunotherapies with igg antibodies is that not all human fc-receptors are immune - activating , but one among them , fcriib is -inhibiting . therefore , the tumoricidic effects of igg - based immunotherapies also depend on the net ratio of binding to activating and inhibiting receptors . as it has recently been shown for igg4 , a subclass that shows relatively high binding affinity to fcriib , this antibody is not able to trigger immune cell - mediated tumor cell killing in vitro , despite being taa - specific . moreover it was demonstrated , that igg4 antibodies significantly impaired the killing potential of igg1 antibodies of the same specificity in vitro and in vivo . strategies to overcome this limitation include modification of the posttranslational glycosylation of the igg - constant regions heavy chains , as these sugar residues have been identified to be of high relevance for distinct binding affinities to different fc - receptors . for ige on the other hand , there are no inhibitory receptors , so again this isotype could contribute to overcome a current challenge of immunotherapies of cancer . however the fc-receptor - biology differs considerably between humans and mice , as the high affinity ige receptor fcri is only expressed on mouse basophils and mast cells , whereas it has been described in humans on mast cells , basophils , eosinophils , monocytes , langerhans and dendritic cells . this is a huge limitation of current mouse models in displaying all mentioned in vivo benefits and risks of ige - based immunotherapy of cancer and the great benefit of using a comparative oncology approach . although human and veterinary medicine share the same goals and aims , namely to treat patients and promote health , currently both of them are distinct sciences with distinct studies taught on separate universities . research is presently going on in one or the other , but there is little crosstalk between the two specialties . the concept of comparative medicine , however , aims to study naturally occurring diseases across species to improve both human and veterinary medicine . there is in fact no explicit reason for a strict separation of studies for humans or other mammals , as many pathophysiological processes have been shown to be similar and highly comparable , or as the german pathologist rudolf virchow stated : between animal and human medicine the object is different but the experience obtained constitutes the basis of all medicine . this view , which is also in line with the wider concepts of one medicine , or one health , bringing together aspects of health of humans , animals and also their environment is not really novel . browsing through the history of medicine , this approach appears at many points , starting with hippocrates and plato in ancient greece . even further back in time , physicians in ancient india were trained to treat humans and animals , especially cattle , elephants and horses and in ancient china , medical treatment for horses was highly elaborated as well . also in europe and north america human and veterinary medicine were closely interconnected for a long period of time , peaking in the 18th , 19th and early 20th century . many important findings were made by comparative observation and experimentation during that time , for instance edward jenner ( 1749 - 1823 ) noted that milkers who had been in contact with cowpox - infected cows did not develop smallpox ( variola minor ) but only the milder cowpox . he also observed that this protection could be mediated by inoculation of a small amount of pus from cowpox blisters , a method he called vaccination because of the latin word for cow , vacca . similarly , louis pasteur ( 1822 - 1895 ) worked on cholera in humans and chicken , robert koch ( 1843 - 1910 ) researched on human and bovine tuberculosis , and the mentioned rudolf virchow ( 1821 - 1902 ) worked on trichinella infections in humans and pigs . besides virchow , the most important proponent of comparative medicine was sir william osler , a canadian physician ( 1849 - 1919 ) , who studied , worked and taught in london , berlin , vienna , toronto and montreal , and was one of the four founding professors of johns hopkins hospital in baltimore . osler lectured at mcgill university for medical students as well as for students from the veterinary medical college with emphasis on comparative topics . his research in this field concentrated on infectious diseases in dogs , pigs and cattle and his deep interest is documented in many editorials of the journal of comparative medicine and surgery . recent developments are no longer dependent on distinguished individuals , but comprise the establishment of special departments for comparative medicine within universities , such as at stanford , yale or at the university of california , davis . whereas comparative medicine focused mainly on infectious diseases in previous centuries , modern approaches tend to tackle another big burden of our societies , cancer , via the principle of comparative oncology . the comparative oncology approach aims to speed up drug development simultaneously for human and animal cancer patients via clinical trials in pet patients , primarily cats and dogs . although murine models have been proven to be highly effective with regards for understanding basic principles of malignant transformation , cancer signal transduction pathways or drug resistance formation , these models often poorly mimic human cancer for drug testing . for many compounds , the translation of a safe and efficacious agent in mice into an actual drug fails , due to the poor presentation of key features of human cancer in murine tumor models , such as genomic instability , long latency periods or the lack of intra - tumor heterogeneity . moreover , the concept of toxicity studies , which are conducted in healthy animals , followed immediately by phase i and phase ii trials in humans , often leaves many important questions unanswered , before treating a relatively high number of human patients . on the other hand , also more and more extensive studies in animals can not be the solution , as it would increase the ethical dilemma that potential benefits for humans stand against the costs sustained by animals . thus , legislators and regulatory bodies state in their directives on drug development that the 3rs should be applied on animal experiments , which are : replacement , reduction , and refinement [ 143,144 ] . in line with these concepts , clinical studies in animal patients , which suffer from spontaneously developed tumors , would allow the investigation of drug effects on malignancies that developed naturally within intact immune systems , in the context of their original tumor microenvironment in pet animals that share similar environmental factors as their owners , for instance pollution . such trials in veterinary patients could replace many preclinical experiments , refine our models and ultimately reduce animal experiments . the information obtained from these studies would be highly relevant and valuable , while the treated veterinary patients would be provided with cutting edge research simultaneously . studies in this field of comparative oncology with treated dog patients , led to the advancement of surgical techniques , like limb sparing for sarcoma patients , elucidating hyperthermia or evaluating novel delivery strategies , like inhalation of cytokines or chemotherapies . ( cotc ) , a multicenter initiative of twenty comparative oncology centers throughout the usa . founded and centrally managed by the national cancer institute of the national institutes of health ( nih ) , 11 clinical trials have been conducted so far , ranging from all fields of cancer therapy attempts like evaluation of rgd targeted delivery of phage expressing tnf - alpha to tumor bearing dogs ( cotc001 , closed trial ) via preclinical comparison of three indenoisoquinolines candidates in tumor bearing dogs ( cotc007b , open trial ) to evaluation of the mtor inhibitor rapamycin in dogs with metastatic osteosarcoma one of the most successful example of a recent clinical comparative oncology trial was published in 2009 , in which the tyrosine kinase inhibitor toceranib phosphate ( palladia , su11654 , pfizer ) , targeting kit , vascular endothelial growth factor receptor 2 ( vegfr2 ) and platelet derived growth factor receptor - beta ( pdgfr ) was tested in dog cancer patients with recurrent mast cell tumors . this large clinical phase iii trial could demonstrate significant effects of toceranib phosphate with regard to overall response rates , median duration of objective responses and time to tumor progression , which has finally led to the approval of toceranib phosphate for mast cell tumors in dogs and to the approval of sunitinib ( sutent , su11248 , pfizer ) , a similar compound , for therapy of human renal cell cancer and gastrointestinal stromal tumors ( gist , ) . also for evaluation of ige - based immunotherapies of cancer , trials in dog cancer patients would be highly valuable , due to the fact that dogs , in contrast to mice , share important principles of the ige - biology with humans , underlined by the clinical observation that dogs also suffer from ige - mediated diseases , such as atopic dermatitis or food allergies . thus , the introduction of passive immunotherapy in veterinary clinical oncology would be highly valuable to elucidate the full potential of ige - based immunotherapy of cancer . we contributed to this strategy by our recent molecular characterization of canine egfr and the generation of a recombinant canine ige of the exact cetuximab specificity [ 155 , 156 ] .

antibody - based immunotherapies are important therapy options in human oncology . although human humoral specific immunity is constituted of five different immunoglobulin classes , currently only igg - based immunotherapies have proceeded to clinical application.this review , however , discusses the benefits and difficulties of ige - based immunotherapy of cancer , with special emphasis on how to translate promising preclinical results into clinical studies . pursuing the comparative oncology approach , novel drug candidates are investigated in clinical trials with veterinary cancer patients , most often dogs . by this strategy drug development could be speeded up , animal experiments could be reduced and novel therapy options could be introduced benefitting humans as well as man s best friend .

Targeted Therapies of Cancer Immunological Effects of Antibodies IgE and Cancer IgE-based Immunotherapies of Cancer - Pioneer Studies Possible Advantages and Pitfalls of IgE-based Cancer Immunotherapies Comparative Medicine Comparative Oncology

subcutaneous icd may be proposed to patients with channelopathies presenting with significant risk for sudden cardiac death . short qt syndrome is a rare channelopathy carrying the risk for inappropriate therapies with current transvenous icd because of overdetection of the ample t wave . we report on the uneventful followup after implantation of a subcutaneous icd in a patient with a short qt syndrome . because patients with short qt syndrome ( sqt ) may have tall peak t waves with short qrst intervals , inappropriate icd therapies may occur due to the possibility of double counting of both the qrs and the t wave 1 , leading to a succession of short cycle lengths , as realized for example during exertion . inappropriate icd therapies have been described earlier in sqt patients with transvenous icd , which should be prevented by tailoring the detection window characteristics 2 . if such an hazard may happen with subcutaneous icd whose ability in avoiding t wave detection is crucial is unknown , since no sqt case seems to have been reported with such a device as yet . a 30 yearold man with sqt syndrome implanted for 9 years with a transvenous icd for primary prevention ( familial sudden death due to sqt and induction of ventricular fibrillation ) his ecg showed ample t waves with 280 ms qt interval ( corrected qt 330 ms ) . we decided to reimplant the icd , using a subcutaneous icd ( sicdtm system , boston scientific , st . paul , mn , usa ) . after assuring an acceptable r / t ratio using the screening ruler ( fig . 1 ) , the pulse generator was placed subcutaneously in the anterior axillary line with the electrode inserted subcutaneously parallel to the sternal midline . ventricular fibrillation was induced and terminated by a 65 j shock ( 15 j safety margin ) . below are shown the acceptable r / t ratio using the screening ruler both at implant ( left ) and at 1 year ( right ) . testing of the device at baseline , during treadmill or during the followup never displayed t wave over sensing in any detection configuration ( primary between the pulse generator and the proximal electrode , secondary between the generator and distal electrode , or alternate between both electrodes ) . 2 ) even if there are a few missed r waves at exertion in some configuration ( arrows ) , especially when the r wave amplitude slightly decreases ( the subcutaneous icd uses a two peak average to adjust the detection profile dynamically , but in the presence of varying amplitudes such as during exertion , a few beats may be missed while adjusting to the underlying amplitudes ) . the latency sometimes observed after the r wave on markers ( red circle ) in the alternate configuration is an artifact of programmer telemetry 's ability to process increased marker activity , for example , exertion scenario at followup ( such a behavior is not observed in the ambulatory setting ) . programmer telemetry recordings in the primary ( a ) , secondary ( b ) and alternate ( c ) detection configurations at implant , during exertion and at rest at 1 year followup . s are the markers of the qrs complexes as sensed by the device ( see text for detailed explanation ) . at 1 year followup , the r wave was 1.1 mv while t wave was 0.2 mv on ecg ( r / t ratio = 5.5 ) ( fig ) . the r / t ratio was higher at implant during treadmill and during the followup in the primary configuration ( table 1 ) . amplitude and qrs : twave ratio measurements from three time points : implant , exertion and followup the patient was discharged in the primary configuration and no appropriate or inappropriate detection ( fig . short qt syndrome is a very exceptional channelopathy carrying a significant risk of sudden cardiac death due to malignant ventricular arrhythmias 3 . sqt is caused by an excessive abbreviation of repolarization duration , mainly due to some inherited gain of function in potassium channels 3 . sqt is diagnosed if corrected qt is 330 ms or 360 ms together with clinical events 4 . risk stratification to date only refers to spontaneous clinical events such as unexplained syncope or a previous cardiac arrest 4 . icd is the only recommended therapy , although medical treatment with quinidine may be used in selected cases 4 . patients with sqt syndrome often present with tall peak t waves together with the short qt interval 1 . thus , inappropriate icd therapies have been described , using transvenous icd because of double counting of both the qrs and the t wave 1 , especially during exertion . of note , this may be prevented by tailoring the detection window characteristics 2 . if such hazard may happen with subcutaneous icd whose ability in avoiding t wave detection is crucial is unknown , since no sqt implanted with subcutaneous icd seems to have been reported as yet . this case highlights the fact that patients with sqt syndrome may also benefit from subcutaneous icd . due to morbidity and complications inherent to transvenous icds , sqt syndrome may also benefit from subcutaneous icd . however , additional cases are needed to affirm the safety of such device in this setting , especially in patients with ampler t waves .

key clinical messageshort qt syndrome carries the risk for inappropriate therapies using transvenous icd because of overdetection of the ample t wave . sqt syndrome may also benefit from subcutaneous icd , although additional cases are needed to affirm the safety of such device in this setting .

Introduction Case presentation Discussion Conclusion Conflict of Interest

dual atrioventricular ( av ) nodal physiology is a common finding during electrophysiologic studies ( eps ) . even among patients with wolff - parkinson - white ( wpw ) syndrome , atrioventricular nodal reentrant tachycardia ( avnrt ) and atrioventricular reciprocating tachycardia ( avrt ) can coexist in a single patient . however , direct transition of avnrt and avrt is quite rare . retrograde atrial activation sequences during ventricular pacing and reentrant tachycardia provide important information for the localization of accessory pathways ( aps).1 ) here , we report a case of double tachycardia with direct transition and eccentric retrograde atrial activation during typical avnrt . holter monitoring and an exercise test revealed intermittent preexcitation , suggesting a left - sided ap ( fig . 1 ) . as the patient was highly symptomatic , eps and possible radiofrequency catheter ablation ( rf ablation ) were recommended . eps was performed with a steerable duo - decapolar catheter positioned in the right atrium and inside the coronary sinus ( cs ) , and two quadripolar catheters positioned at the right ventricular apex and the his bundle region . anterograde conduction via an ap was not observed . at a driving pacing cycle length ( cl ) of 600 msec , the effective refractory periods ( erps ) of the fast and slow av nodal pathways were 430 msec and 320 msec , respectively . during incremental ventricular pacing , 1:1 ventriculoatrial ( va ) conduction over the ap in the left free wall occurred at 280 msec . the erp of retrograde va conduction over the ap was 250 msec and the erp of retrograde va conduction over the av node was less than 230 msec . tachycardia with cl varying from 393 to 420 msec was reproducibly induced by single atrial extra - stimulation with ah prolongation ( fig . changing the site of earliest retrograde atrial activation to the distal cs with single premature ventricular pacing during tachycardia at a time of his - bundle refractoriness hindered discrimination of tachycardia ( fig . , there was transition of tachycardia to the other type of tachycardia with a cl ranging from 479 to 505 msec . retrograde atrial activation was eccentric and the shortest va interval was 70 msec in the distal cs recording ( fig . 2 ) . a 4-mm deflectable tip ablation catheter ( irvine biomedical , inc . , irvine , ca , usa ) was used to deliver rf current with 40 w power and temperature limit of 60. after ablation of the ap in the left free wall ( fig . 4 ) , va conduction over the av node was recorded and avnrt with concentric retrograde atrial activation was reproducibly induced by single atrial extra - stimulation with ah jump ( fig . 5 ) . holter monitoring and an exercise test revealed intermittent preexcitation , suggesting a left - sided ap ( fig . 1 ) . as the patient was highly symptomatic , eps and possible radiofrequency catheter ablation ( rf ablation ) were recommended . eps was performed with a steerable duo - decapolar catheter positioned in the right atrium and inside the coronary sinus ( cs ) , and two quadripolar catheters positioned at the right ventricular apex and the his bundle region . anterograde conduction via an ap was not observed . at a driving pacing cycle length ( cl ) of 600 msec , the effective refractory periods ( erps ) of the fast and slow av nodal pathways were 430 msec and 320 msec , respectively . during incremental ventricular pacing , 1:1 ventriculoatrial ( va ) conduction over the ap in the left free wall occurred at 280 msec . the erp of retrograde va conduction over the ap was 250 msec and the erp of retrograde va conduction over the av node was less than 230 msec . tachycardia with cl varying from 393 to 420 msec was reproducibly induced by single atrial extra - stimulation with ah prolongation ( fig . 2 ) . the ah and hv intervals were 284 msec and 53 msec , respectively . changing the site of earliest retrograde atrial activation to the distal cs with single premature ventricular pacing during tachycardia at a time of his - bundle refractoriness hindered discrimination of tachycardia ( fig . , there was transition of tachycardia to the other type of tachycardia with a cl ranging from 479 to 505 msec . retrograde atrial activation was eccentric and the shortest va interval was 70 msec in the distal cs recording ( fig . a 4-mm deflectable tip ablation catheter ( irvine biomedical , inc . , irvine , ca , usa ) was used to deliver rf current with 40 w power and temperature limit of 60. after ablation of the ap in the left free wall ( fig . 4 ) , va conduction over the av node was recorded and avnrt with concentric retrograde atrial activation was reproducibly induced by single atrial extra - stimulation with ah jump ( fig . 5 ) . multiple supraventricular tachycardias with multiple reentry circuits are relatively common in a patient during eps . however , direct transition between double tachycardias is rarely observed . delacretaz et al.2 ) reported a case of direct transition from avnrt to avrt , and rakovec3 ) described a patient with wpw syndrome , in whom transition occurred from avrt into avnrt . kuo et al.4 ) reported 3 cases of double tachycardia with transition . in their report , kuo et al.4 ) proposed that similarity in tachycardia cls may predispose to transition and the cutoff point of 25 msec had 80% positive predictive value for transition between double tachycardias . usually , transitions were induced by premature beats or block of the av nodal pathway or aps . in the present case , tachycardia cls of the two tachycardias were quite different and the difference was greater than 25 msec . transition occurred with slight prolongation or shortening of the tachycardia cls , rather than being induced by premature activities in the atria or ventricles . however , an ap was located in the right posterior region relatively proximal to the av nodal region and the difference in the cl of the tachycardia was less than 25 msec . in contrast , avrt using the left lateral ap as a retrograde limb of the circuit was far distal to the av node in this particular patient . therefore , it is difficult to expect spontaneous transition of avnrt or atrial fusion with the retrograde fast pathway . the following factors might have contributed to or may have facilitated the spontaneous transition of tachycardia in the present patient : 1 ) anterograde or retrograde av nodal conduction may be influenced by the preceding cycle length or autonomic tone.5 ) intense variation of tachycardia cl and va intervals was observed around the time of transition . 2 ) although spatial distance of the ap was relatively far from the av node , va interval in the left free wall region ( 70 msec ) was similar to that in the proximal cs recording ( 56 msec ) . however , the exact circuit of avnrt remains unelucidated . also , it is difficult to postulate the mechanisms underlying tachycardia transition in complicated avnrt . the possibilities for unusual cs activation during narrow qrs tachycardia include multiple aps , atypical avnrt,6 ) left superior ap,7 ) and intra - atrial block.8 ) eccentric atrial activation sequences during avnrt , which was an unexpected type of tachycardia in a patient with wpw syndrome , were caused by the left lateral ap in this patient . these findings were prone to misinterpretation regarding the retrograde sequence of atrial activation and led us away from the correct diagnosis . this instructive case emphasizes the need for careful interpretation of retrograde atrial activation sequences in the cs region in order to correctly identify the presence and location of aps . in summary , we described a rare case of direct transition between avnrt and avrt in a patient with wpw syndrome . fusion of retrograde activation of the atrium occurred via the fast pathway and the ap caused eccentric avnrt . this case highlights the importance of the retrograde atrial activation sequence in the localization of aps and suggests that differential pacing maneuvers are not feasible in transitional tachycardia with atrial fusion .

among patients with wolff - parkinson - white syndrome , atrioventricular reciprocating tachycardia ( avrt ) and atrioventricular nodal reentrant tachycardia ( avnrt ) can coexist in a single patient . direct transition of both tachycardias is rare ; however , it can occur after premature atrial or ventricular activity if the cycle lengths of the two tachycardias are similar . furthermore , persistent atrial activation by an accessory pathway ( ap ) located outside of the av node during ongoing avnrt is also rare . this article describes a case of uncommon atrial activation by an ap during avnrt and gradual transition of the two supraventricular tachycardias without any preceding atrial or ventricular activity in a patient with preexcitation syndrome .

Introduction Case Clinical history Electrophysiologic study Tachycardia characteristics Mapping and radiofrequency catheter ablation Discussion

the complex rumen microbiome plays essential roles in digesting feeds and supplying nutrients to host animals . to positively affect rumen functions , dietary interventions have been attempted to modulate this microbiome . the rumen microbiome as a whole and its individual populations are often analyzed to unveil the underpinning of dietary interventions . community fingerprinting by dgge , t - rflp , and arisa have been used in accessing overall dietary effects . however , detailed assessments come from analysis of 16s rrna gene ( rrs ) clone libraries or quantitative comparisons of populations of known species or groups , such as f. succinogenes , r. albus , r. flavefaciens , butyrivibrio fibrisolvens [ 5 , 6 ] , prevotella spp . however , most of these known species or populations account for only a small portion of the rumen microbiome , as exemplified by f. succinogenes , r. albus , and r. flavefaciens , which together represent only 4.59% of the total bacteria in the rumen of sheep . analysis of rrs clone libraries can identify both known ( i.e. , cultured ) and novel bacteria ( i.e. , uncultured ) . of the bacteria identified by rrs sequences of rumen origin , cultured bacteria only accounted for 6.5% . large numbers of uncultured bacteria represented by novel rrs sequences were especially found within families ruminococcaceae , lachnospiraceae , and order clostridiales . function and ecology of uncultured bacteria are often inferred from closely related species , while their relative abundance , and thus weight or importance to the entire microbiome , is typically estimated from prevalence of respective rrs sequences in clone libraries . however , sequence prevalence does not necessarily reflect actual abundance of the represented bacteria in the microbiome because of biases associated with pcr and cloning . we hypothesize that the population sizes of uncultured bacteria can be quantified using specific qpcr , and the quantitative information can complement the results of rrs clone libraries and help gauge the importance of uncultured bacteria . in this study , we tested this hypothesis by recovering full - length rrs sequences from select uncultured bacteria and then quantifying their abundance in fractionated rumen samples of sheep fed hay only or hay plus corn . four ruminally cannulated sheep were divided into two groups of two sheep each and used in the feeding experiment that was set up in a crossover design with two periods of three weeks each . during the first period , one group was fed 100% orchardgrass hay , while the other group was fed a combination of 70% orchardgrass hay and 30% corn . during the second period , the sheep were fed once daily for 21 days prior to ruminal sample collection , which took place 6 hrs after feeding . sample collection and fractionation ( adhering or ad versus liquid or lq ) the dna quality was evaluated using agarose gel ( 1.0% ) electrophoresis , and dna yield was quantified using the quant - it kit ( invitrogen corporation , carlsbad , calif , usa ) . in a previous study , a number of otus were defined from novel partial rrs sequences ( approximat 600 bp from the 3 end corresponding to 9001,540 of the e. coli rrs gene ) recovered from fractionated rumen samples . some of these downstream partial sequences either have no close match in the rdp database or only match sequences of bacteria never reported in the rumen . one specific reverse primer was designed using primer premier 5.0 ( premier biosoft int'l , palo alto , calif , usa ) for each of 25 otus defined from the downstream partial sequences . the specificity of the primers was verified by in silico analysis against sequences in the rdp database using the probe match function . this otu - specific reverse primer ( table 1 ) was paired with bacterial primer 27f ( table 2 ) in pcr to recover the upstream partial sequence . the pcr reactions and cloning were done as described previously , except for an optimized annealing temperature at 54c . the partial sequences recovered from each clone library were assembled using bioedit to form the upstream partial sequence ( > 1000 bp from the 5 end corresponding to 81006 or beyond of the e. coli rrs gene ) . this upstream partial sequence and the corresponding downstream partial sequence recovered previously were assembled into a full - length gene sequence using bioedit . the full - length sequences were subjected to vigorous chimera analysis using four different programs : the rdp chimera check ( http://rdp.cme.msu.edu/ ) , the bellerophon ( http://greengenes.lbl.gov/ ) , the pintail program of bioinformatics - toolkit ( http://www.bioinformatics-toolkit.org/web-pintail/ ) , and the mallard . the full - length sequences were compared to rdp sequences and classified using the classifier program . a neighbor - joining tree based on the full - length sequences and their most similar sequences was constructed using the neighbor joining method at rdp . the full - length sequences obtained in this study were deposited in genbank ( accession numbers gu120110 , gu120113 , gu120120 , gu120121 , gu120128 , gu120129 , and gu120131-gu120137 ) . one qpcr standard was prepared for each species , genus , group , or otu of the uncultured bacteria to be quantified . the standard for f. succinogenes , r. albus , and prevotella was prepared through pcr using the bacterial primers 27f and 1525r ( table 2 ) and the genomic dna of f. succinogenes s85 , r. albus 8 , and prevotella ruminicola 23 , respectively . due to the lack of strains in our laboratory , a sample - derived standard was prepared for genus butyrivibrio , r. amylophilus , r. flavefaciens , and s. ruminantium , total bacteria , and total archaea using the respective specific pcr primer set ( table 2 ) and a composite dna sample pooled from all the metagenomic dna to be quantified as described previously . one sample - derived standard for each of the uncultured bacterial otus was prepared similarly but with pcr using primer 530f ( table 2 ) and the respective specific reverse primer for each of the full - length rrs sequences ( table 1 ) . each standard was serially diluted ( 1 : 10 ) immediately before the qpcr assays , and the concentrations ranged from 10 to 10 copies per reaction . qpcr was carried out using respective specific primers ( table 2 ) and a stratagene mx3000 machine ( la jolla , calif , usa ) . total bacteria was quantified using the taqman assay , while the other species , groups or uncultured bacterial otus were quantified using sybr green - based qpcr . the pcr conditions were the same as those used previously , except for the annealing temperature that was optimized in this study ( see table 2 ) . each of the uncultured bacterial otus was quantified using the respective otu - specific reverse primer ( table 1 ) and bacterial primer 530f ( table 2 ) similarly as for the cultured bacteria but with a primer annealing temperature at 54c . to minimize variations , the qpcr assay for each bacterium , species , or group was done in triplicates for both the standards and the metagenomic dna samples using the same master mix and the same pcr plate . absolute abundance was calculated as rrs copied per g metagenomic dna , while relative abundance was expressed as percent of total bacterial rrs copies . the absolute abundance was not expressed as rrs gene copies / g or ml of sample because ( i ) the solid and the liquid fractions have different sample matrices , ( ii ) not all adhering bacteria can be detached or recovered from the solid digesta particles , and ( iii ) the two types of diets probably resulted in solid digesta particles containing different contents of plant content materials ( nonmicrobial ) . then , the mean was calculated from the four samples ( two animals by two periods ) of each fraction and each diet . the fraction- and diet - based data of abundance were analyzed using one - way analysis of variance ( anova ) using graphpad prism 5 ( graphpad software , san diego , calif , usa ) and the means were compared using one - way anova with tukey 's multiple comparison test . significant difference was declared at p 0.05 , while tendency was declared at p 0.10 . twenty - five reverse primers were designed and used in retrieving upstream partial sequences , but only 12 each were allowed for identical upstream partial sequences from the clones that were sequenced . the remaining 13 primers generated 2 - 3 very similar but different upstream partial sequences ( data not shown ) . the full - length sequences were assigned to genus ( the lowest taxonomic rank of the new bergey 's taxonomy of prokaryotes used in the rdp database ) or higher taxa ( figure 2 ) . the increased sequence length allowed taxonomic assignment with a greater confidence for all the sequences and to genus for ad - h1 - 89 - 3 , ad - c2 - 43 - 3 , ad - c1 - 74 - 3 , lq - c1 - 28 - 3 , and lq - c2 - 58 - 2 . six full - length sequences remained to be assigned to a genus ( i.e. , lq - c2 - 16 - 3 and ad - h2 - 89 - 1 ) , family ( i.e. , lq - h1 - 18 - 2 , ad - h1 - 53 - 2 , and ad - h1 - 75 - 1 ) , or order ( i.e. , ad - h2 - 90 - 2 ) ( figure 2 ) . seven of the full - length sequences each are very similar ( 99% sequence identity ) to sequences also recovered from the rumen by other researchers ( based on blastn analysis and genbank records ) , including lq - h1 - 18 - 2 ( 17 sequences ) , lq - h2 - 71 - 3 ( 9 sequences ) , ad - h1 - 14 - 1 ( 45 sequences ) , lq - c1 - 28 - 3 ( 7 sequences ) , lq - c2 - 16 - 3 ( 2 sequences ) , ad - h1 - 53 - 2 ( 1 sequence ) , and ad - h2 - 90 - 2 ( 1 sequence ) . because none of these novel bacteria can be classified to existing species or genus , they were referred to bacterial otus . these otus , especially otus ad - h1 - 14 - 1 and lq - h1 - 18 - 2 , may represent bacteria common in the rumen . the remaining six full - length sequences shared no more than 97% sequence identity with any of the sequences in the rdp or the genbank . total bacteria did not differ in abundance between the two diets or between the two fractions , while the archaeal abundance tended to be lower ( p = 0.067 ) in the h - ad sample than in the other three samples ( table 3 ) . of the three major known cellulolytic species , r. albus and r. flavefaciens were more abundant than f. succinogenes in all the samples ( table 3 ) , a finding consistent with some previous studies ( e.g. , [ 26 , 27 ] ) but contradictory to other studies ( e.g. , [ 28 , 29 ] ) . f. succinogenes tended to be more abundant in the adhering fraction and in the hay - fed sheep , reflecting its ability to adhere to fiber particles in the rumen . the abundance of the two ruminococcus species , especially relative to total bacteria , was numerically higher in the adhering fraction of hay - fed sheep . overall , the abundance of each of these three cellulolytic species was similar between the two diets and between the two fractions . genus butyrivibrio was significantly more abundant in the hay - fed sheep than in the hay : corn - fed counterparts , but its abundance did not differ between the two ruminal fractions within the same dietary group ( table 3 ) . of the known species and genera quantified , genus prevotella was the most predominant , accounting for about 27% of the total bacteria in the hay - fed sheep and more than 50% in the hay : corn - fed sheep ( table 3 ) . r. amylophilus was found in relatively high abundance in the adherent fraction of the sheep fed the hay : corn diet , corresponding to its ability to utilize starch . s. ruminantium and m. multacida are closely related species within family veillonellaceae . since the primers used in this study amplify both species this group of bacteria was less abundant in the adhering fraction of the hay - fed sheep than in the liquid fraction of the hay : corn - fed sheep . these results are in general agreement with the ability of these two species to utilize sugars and lactate . the abundance of otus ad - h1 - 14 - 1 ( classified to genus acetivibrio ) , lq - c2 - 16 - 3 ( classified to ruminococcaceae ) , and ad - h2 - 90 - 2 ( classified only to class clostridia ) ranged from 10 to 10 copies of rrs genes/g metagenomic dna , corresponding to about 0.11 to 1.2% of total bacteria ( table 3 ) . these abundances were lower than that of the genus prevotella , comparable to that of the two ruminococcus species and the genus butyrivibrio , but higher than that of f. succinogenes , r. amylophilus , or s. ruminantium and m. multacida combined . these three otus did not differ in abundance between the two fractions in the hay - fed sheep , but appeared to be numerically more abundant in the adhering fraction than in the liquid fraction of the hay : corn - fed sheep . otus lq - c2 - 58 - 2 ( classified to genus alloculum ) and ad - h1 - 75 - 1 ( classified only to order clostridiales ) were slightly less abundant than the other three otus mentioned above . otu lq - c2 - 58 - 2 was significantly more abundant in the adhering fraction than in the liquid fraction of the hay : corn - fed sheep and tended to be more abundant in the liquid fraction of hay - fed sheep . overall , otus ad - h1 - 14 - 1 , ad - h2 - 90 - 2 , and ad - h1 - 75 - 1 were more abundant in the hay - fed sheep than in the hay : corn - fed sheep , whereas otus lq - c2 - 16 - 3 and lq - c2 - 58 - 2 had comparable abundance between the two feeding groups . due to cost and time restraint , partial rrs gene sequences are typically determined in most studies that examined the diversity and species richness of various microbiome samples . as demonstrated in this study , however , full - length rrs sequences improve upon partial sequences in classification of rrs sequences , in both confidence and low taxa that are more informative . although this is expected , the results of this study demonstrated the extent and aspects that full - length rrs sequences can improve over partial rrs sequences . conceivably , full - length high - quality rrs sequences are also important in assigning candidate taxa ( incertae sedis ) that do not have cultured representatives . it should be noted that 13 of the 25 reverse primers designed in this study did not allow for retrieval of a single upstream partial sequence . given that these reverse primers did not have any match in rdp or genbank ( data not shown ) , this might be explained by the fact that the downstream regions ( v6v9 ) of the rrs genes are more conserved than the upstream regions [ 30 , 31 ] . all the full - length sequences determined in this study represented uncultured ruminal bacterial otus that can not assigned to existing species or genera . classification to a genus helped with inference of possible functions of these bacterial otus , such as otus ad - h1 - 14 - 1 ( classified to acetivibrio ) , ad - c1 - 74 - 3 ( classified to anaerovorax ) , and lq - c1 - 28 - 3 ( roseburia ) . in addition to 45 nearly identical sequences , otus ad - h1 - 14 - 1 is 98.8% identical to the sequence of a new strain , r-25 ( accession number of its rrs sequence : ab239489 ) , which was recently isolated from an enriched culture of sheep rumen . this strain was shown to be short rod or coccus shaped , to adhere to orchardgrass hay , and to have activities of carboxymethylcellulase , xylanase , and -l - arabinofuranosidase . strain r-25 reached a relative abundances of 0.98% and 0.64% of total bacteria in the solid and the liquid fractions of rumen samples collected from sheep , which is comparable to that of otu ad - h1 - 14 - 1 in the sheep rumen sampled in this present study ( table 3 ) . acetivibrio is a genus that contains only two recognized cellulolytic species ( i.e. , a. cellulolyticus and a. cellulosolvens ) . however , the high prevalence of otu ad - h1 - 14 - 1 sequences recovered from the rumen and the relatively high abundance of ad - h1 - 14 - 1 determined in the hay - fed sheep than in the hay : corn - fed sheep ( table 3 ) suggest that otu ad - h1 - 14 - 1 , together with strain r-25 , may represent an important species of fibrolytic ruminal bacteria in the genus acetivibrio . in this study , we quantified the populations of five uncultured bacteria classified to known genera ( i.e. , otus lq - c2 - 58 - 2 and ad - h1 - 14 - 1 ) , family ( i.e. , otu lq - c2 - 16 - 3 ) , order ( otu ad - h1 - 75 - 1 ) , or class ( otu ad - h2 - 90 - 2 ) in the phylum firmicutes ( figure 2 ) . these uncultured bacteria had abundance comparable to or greater than that of known species or genera ( except the genus prevotella ) of bacteria that are perceived important to rumen functions . for example , otu ad - h1 - 14 - 1 may be one important group of bacteria participating in fiber digestion in the rumen . additionally , otu lq - c2 - 58 - 2 was classified to genus allobaculum within the class erysipelotrichi , a class of firmicutes poorly represented by sequences of rumen origin . alloculum is a new genus represented by a single species , a. stercoricanis , whose type strain was initially isolated from canine feces and was shown to utilize several sugars , including glucose , fructose , maltose , and cellubiose . otu lq - c2 - 58 - 2 might represent a group of scavenger utilizing sugars in the rumen . although the specific functions of these uncultured bacteria remain to be determined , their relatedness with known taxa and their abundance suggest that some of them may play as important role in rumen function as some of the well - characterized bacteria . the abundance of a bacterial group in an environment reflects its ability to adapt to the conditions and compete for the nutrients available therein and signifies its importance to the overall functions of the microbiome . as mentioned above , sequence frequencies in rrs gene clone libraries are often used in assessing the relative abundance of the bacteria represented , but the validity of such correlation is uncertain due to bias inherent to pcr and cloning . in this study , we examined the above validity by comparing the frequency of five downstream partial sequences that were recovered previously in clone libraries and the relative abundance ( % of total bacteria ) of the corresponding full - length sequences quantified by the specific qpcr assays . in the clone libraries , sequence ad - h1 - 75 - 1 had a frequency of 2.1% , while the other four sequences had a frequency of 1.0% , in the fractions from which these sequences were recovered . the frequencies of all these sequences were greater than their relative abundance determined in this study , especially ad - h1 - 75 - 1 ( table 3 ) , suggesting that these sequences were over represented in the rrs gene clone libraries and their frequency in the clone libraries would overestimate their abundance in the rumen . more studies involving multiple rrs gene clone libraries constructed using different pcr primers and from different samples are needed to verify if sequence frequency in rrs gene clone libraries generally overestimates relative abundance of the bacteria represented . nevertheless , caution should be exercised in estimating bacterial abundance from sequence frequency in rrs gene clone libraries . as demonstrated in this study , actual abundance and population dynamics of uncultured bacteria should be quantified using specific qpcr so their ecology and importance to the microbiome can be inferred more accurately .

the objective of this study was to assess the importance of select cultured and uncultured bacteria in the rumen by quantifying their populations and the effect of diets and ruminal fractions . full - length 16s rrna gene ( rrs ) sequences were recovered from rumen samples using specific primers designed from partial sequences recovered previously . five uncultured bacterial operational taxonomic units ( otus ) were quantified using specific quantitative pcr ( qpcr ) in fractionated ruminal samples from sheep fed either hay alone or hay plus corn . species fibrobacter succinogenes , ruminococcus albus , r. flavefaciens , ruminobacter amylophilus , selenomonas ruminantium , and mitsuokella multacida and genera butyrivibrio and prevotella were also quantified as comparison . the full - length rrs sequence improved taxonomic assignments of partial rrs sequences . genus prevotella had the greatest abundance . of the three major cultured cellulolytic species , r. flavefaciens was most abundant , followed by r. albus and f. succinogenes . the five uncultured bacterial otus , classified to genus acetivibrio , genus allobaculum , family ruminococcaceae , order clostridiales , or class clostridia , had abundance comparable to that of the above species of genera except prevotella . corn supplementation and fractions affected distribution of the rumen bacteria , but to a limited extent . when compared to the qpcr data , sequence frequencies in the rrs clone libraries tended to overestimate the abundance of the bacteria represented . this study showed that abundance and population dynamics of uncultured bacteria can be quantified by specific qpcr , which complements the results of rrs clone libraries . this study also revealed that some uncultured bacteria might be as important as some of the well - characterized bacteria in the rumen . the approach used should be applicable to assess the abundance and potential importance of uncultured bacteria in other environments .

1. Introduction 2. Materials and Methods 3. Results 4. Discussion

the most frequent benign paediatric soft tissue tumours in the head and neck are hemangiomas . a 6-year - old girl presented with a painless , progressive growing left neck mass , first noticed about 1 month earlier . ultrasonography revealed a homogeneous , hypovascular , hyperechogenic mass next to the submandibular gland . on mri , the soft tissue lesion was seen to be localized in the left parapharyngeal space , extending into the submandibular space , having a mass effect on the oro- and nasopharynx . the lesion showed an overall hyperintense signal on t1- and t2-weighted images , similar to the signal intensities of the subcutaneous fat , with streaky hypointensities ( fig . histological examination showed an adipose lesion , fitting with the overall t2 and t1 hyperintense aspect , divided into lobules by fibrous septa , compatible with the streaky hypointensities . figure 1axial plain t1-weighted image ( a ) and coronal gadolinium - enhanced t1-weighted image ( b ) . a sharply demarcated , spontaneously hyperintense soft tissue mass ( arrowheads ) is seen in the prestyloid compartment of the left parapharyngeal space , displacing the surrounding structures , and extending into the submandibular space . axial plain t1-weighted image ( a ) and coronal gadolinium - enhanced t1-weighted image ( b ) . a sharply demarcated , spontaneously hyperintense soft tissue mass ( arrowheads ) is seen in the prestyloid compartment of the left parapharyngeal space , displacing the surrounding structures , and extending into the submandibular space . a 6-month - old girl presented with a painless , progressive growing left neck mass with a diameter of approximately 4 cm , detected 2 months earlier . on computed tomography ( ct ) the mass had a peripheral fatty rim and higher density in the centre in which some enhancement was visible ( fig . 2a ) . on mri , the t1-weighted images showed a hyperintense peripheral rim , compatible with fat , and a hypointense centre , which showed intense enhancement after administration of gadolinium ( fig . histological examination confirmed the diagnosis of lipoblastoma , showing a lobulated fatty tumour , partially consisting of mature adipocytes and lipoblasts , while the central part of the lesion contained fibrous tissue and vascular elements . figure 2(a ) axial contrast - enhanced ct image . a large mass lesion is seen in the left side of the neck ( arrowheads ) , largely consisting out of fatty tissue . the mass contains a central tissue portion of higher density ( asterisk ) ; a vessel - like structure is seen running through the mass ( arrow ) . ( b , c ) coronal plain ( b ) and gadolinium - enhanced fat - saturated ( c ) t1-weighted images confirm the fatty nature of the peripheral tumour rim ( arrows ) ; the largest part of the central portion shows enhancement . ( a ) axial contrast - enhanced ct image . a large mass lesion is seen in the left side of the neck ( arrowheads ) , largely consisting out of fatty tissue . the mass contains a central tissue portion of higher density ( asterisk ) ; a vessel - like structure is seen running through the mass ( arrow ) . ( b , c ) coronal plain ( b ) and gadolinium - enhanced fat - saturated ( c ) t1-weighted images confirm the fatty nature of the peripheral tumour rim ( arrows ) ; the largest part of the central portion shows enhancement . an 18-month - old boy presented with bronchitis and a painless mass posterior in the neck . this mass was initially considered to correspond to an adenopathy ; however , the lesion showed slow progressive enlargement over a period of 6 weeks . there were no other symptoms , the clinical examination was within normal limits , and no abnormal laboratory findings . ultrasonography revealed a heterogeneous mainly hyperechogenic , hypovascular mass , with a diameter of about 4 cm , just below the trapezius muscle . on ct , the lesion appeared as a well - circumscribed , lobulated mass in the paraspinal muscles , showing an overall low attenuation , similar to fat , with some intralesional septations ( fig . after surgical resection , histological examination showed an adipose tumour with an overall lobular structure , adipocytes of varying size and multiple lipoblasts . between the adipocytes , a few scarce myxoid fields and numerous small blood vessels a well - delineated mass lesion ( arrows ) , located in the paraspinal muscles , showing fat density is seen . within the lesion , a well - delineated mass lesion ( arrows ) , located in the paraspinal muscles , showing fat density is seen . within the lesion , a 6-year - old girl presented with a painless , progressive growing left neck mass , first noticed about 1 month earlier . ultrasonography revealed a homogeneous , hypovascular , hyperechogenic mass next to the submandibular gland . on mri , the soft tissue lesion was seen to be localized in the left parapharyngeal space , extending into the submandibular space , having a mass effect on the oro- and nasopharynx . the lesion showed an overall hyperintense signal on t1- and t2-weighted images , similar to the signal intensities of the subcutaneous fat , with streaky hypointensities ( fig . histological examination showed an adipose lesion , fitting with the overall t2 and t1 hyperintense aspect , divided into lobules by fibrous septa , compatible with the streaky hypointensities . figure 1axial plain t1-weighted image ( a ) and coronal gadolinium - enhanced t1-weighted image ( b ) . a sharply demarcated , spontaneously hyperintense soft tissue mass ( arrowheads ) is seen in the prestyloid compartment of the left parapharyngeal space , displacing the surrounding structures , and extending into the submandibular space . axial plain t1-weighted image ( a ) and coronal gadolinium - enhanced t1-weighted image ( b ) . a sharply demarcated , spontaneously hyperintense soft tissue mass ( arrowheads ) is seen in the prestyloid compartment of the left parapharyngeal space , displacing the surrounding structures , and extending into the submandibular space . a 6-month - old girl presented with a painless , progressive growing left neck mass with a diameter of approximately 4 cm , detected 2 months earlier . on computed tomography ( ct ) the mass had a peripheral fatty rim and higher density in the centre in which some enhancement was visible ( fig . 2a ) . on mri , the t1-weighted images showed a hyperintense peripheral rim , compatible with fat , and a hypointense centre , which showed intense enhancement after administration of gadolinium ( fig . histological examination confirmed the diagnosis of lipoblastoma , showing a lobulated fatty tumour , partially consisting of mature adipocytes and lipoblasts , while the central part of the lesion contained fibrous tissue and vascular elements . a large mass lesion is seen in the left side of the neck ( arrowheads ) , largely consisting out of fatty tissue . the mass contains a central tissue portion of higher density ( asterisk ) ; a vessel - like structure is seen running through the mass ( arrow ) . ( b , c ) coronal plain ( b ) and gadolinium - enhanced fat - saturated ( c ) t1-weighted images confirm the fatty nature of the peripheral tumour rim ( arrows ) ; the largest part of the central portion shows enhancement . ( a ) axial contrast - enhanced ct image . a large mass lesion is seen in the left side of the neck ( arrowheads ) , largely consisting out of fatty tissue . the mass contains a central tissue portion of higher density ( asterisk ) ; a vessel - like structure is seen running through the mass ( arrow ) . ( b , c ) coronal plain ( b ) and gadolinium - enhanced fat - saturated ( c ) t1-weighted images confirm the fatty nature of the peripheral tumour rim ( arrows ) ; the largest part of the central portion shows enhancement . an 18-month - old boy presented with bronchitis and a painless mass posterior in the neck . this mass was initially considered to correspond to an adenopathy ; however , the lesion showed slow progressive enlargement over a period of 6 weeks . there were no other symptoms , the clinical examination was within normal limits , and no abnormal laboratory findings . ultrasonography revealed a heterogeneous mainly hyperechogenic , hypovascular mass , with a diameter of about 4 cm , just below the trapezius muscle . on ct , the lesion appeared as a well - circumscribed , lobulated mass in the paraspinal muscles , showing an overall low attenuation , similar to fat , with some intralesional septations ( fig . after surgical resection , histological examination showed an adipose tumour with an overall lobular structure , adipocytes of varying size and multiple lipoblasts . between the adipocytes , a few scarce myxoid fields and numerous small blood vessels figure 3axial and coronal contrast - enhanced ct image . a well - delineated mass lesion ( arrows ) , located in the paraspinal muscles , showing fat density is seen . within the lesion , a well - delineated mass lesion ( arrows ) , located in the paraspinal muscles , showing fat density is seen . within the lesion , lipoblastoma is a rare , benign , rapidly growing tumour of infancy and early childhood that arises from embryonal white fat , accounting for up to 30% of adipocytic tumours in children . in contrast , true lipomas ( accounting for two - thirds of adipocytic tumours in children ) consist of mature adipocytes identical to those in normal fat , and do not display the rapid growth rate . lipoblastoma is categorized into two types : the circumscribed lipoblastoma ( approximately 70% of cases ) , a superficial and encapsulated lesion , and diffuse lipoblastomatosis ( about 30% of cases ) , a deeply located , poorly circumscribed lesion with infiltrative growth pattern that may affect surrounding muscle structures . lipoblastoma occurs almost exclusively in infants and children , and is usually diagnosed within the first 3 years of life , the median age of onset being 1 year . the site of origin is most often in the limbs , followed by the trunk , the retroperitoneum , and the head and neck . within this last region , other uncommon sites include the mediastinum , heart , lung , mesentery , omentum , scrotum , labia , axillary , inguinal and perineal regions . the most common presenting symptom is a painless , progressively growing mass if localized superficially . other symptoms are related to the location and size or mass effect of the lesion . airway obstruction and respiratory symptoms have been described in patients with pleural , mediastinal , pulmonary , and lower neck lipoblastomas . gastrointestinal symptoms , such as emesis , diarrhoea , anorexia and abdominal pain occur in patients with mesenteric or retroperitoneal lipoblastomas . depending on the location , lipoblastoma appears as a well - defined soft tissue mass , often with lobular appearance and showing internal septations . the imaging appearance of lipoblastoma depends on the proportion of fat relative to the amount of myxocollagenous stroma . fat in lipoblastoma appears as hyperechogenic areas on ultrasonographs , areas of low attenuation on ct images and signal intensity identical to that of subcutaneous adipose tissue ( high signal intensity on t1- and t2- weighted images ) . the myxoid components are hypoechoic on ultrasonographs , have low attenuation on ct images ( but less hypodense than fat ) and on mri have low signal intensities on t1-weighted images and high signal intensities on t2-weighted images ; contrast enhancement of these areas reflects the rich capillary network . histologically , the lesions are composed of immature fat cells ( lipoblasts ) in varying stages of maturity , mesenchymal cells , a plexiform capillary network , myxoid stroma and mature adipocytes organized in lobules by fibrous septa . cytogenic and molecular genetic analysis is useful to differentiate lipoblastoma from myxoid liposarcoma and atypical lipomatous tumour : lipoblastoma shows a characteristic rearrangement of the long arm of chromosome 8 ( 8q11 - 13 ) affecting plag1 , myxoid liposarcoma , a t(12;16)(q13;p11 ) translocation , and atypical lipomatous tumour amplification of the mdm2/cdk4 genes on 12q . the differential diagnosis of this fat - containing tumour includes liposarcoma , lipoma , teratoma , dermoid cyst , hibernoma and involuting hemangioma . most teratomas and dermoid cysts contain calcifications or cystic areas in addition to soft tissue and fatty elements . . masses consisting entirely of fat are diagnostic for lipoma ; a few thin septa may be present , possibly enhancing . a fat - rich lipoblastoma may have a similar appearance , however , in such a case , the clinical history of a progressive growing mass would serve to differentiate a fat - rich lipoblastoma from a lipoma . involuting hemangiomas may include a small amount of fat , but have a characteristic clinical history ; hemangiomas undergo a proliferation phase and an involuting phase . the proliferation phase is characterized by rapid growth in the first months of life , stabilizing in size at about 910 months of age . the involuting phase then continues slowly for the next several years , during which the hemangioma is replaced by fibrofatty tissue ; usually this process is completed by 710 years of age . hibernomas are mostly seen in the 3rd to 4th decade of life ; often these lesions have typical prominent branching and serpentine high- and low - flow vascular structures . lipoblastoma can not be distinguished from myxoid liposarcoma on imaging . however , the age of the patient is vital ; liposarcomas are extraordinarily rare in patients less than 10 years of age . histology can differentiate on the basis of architectural changes and cytogenetic analysis as described above . thus , on imaging , a lesion containing fat in a young child ( less than 2 years old ) , even with prominent or predominant non - lipomatous components , is nearly always a lipoblastoma . although recurrence rates after surgery vary between 9% and 25% , and this is largely associated with the infiltrative lipoblastomatosis , maturation into lipoma and spontaneous resolution may occur . neck lipoblastoma is a rare childhood tumour , usually presenting as a progressive painless swelling , rarely causing airway obstruction or nerve compression . although the ratio of fat to myxocollagenous tissue in the tumour is variable , the diagnosis can be suggested in most cases based on the imaging characteristics . recommended treatment is complete surgical excision , if possible ; subtotal , non - mutilating surgery seems to be acceptable .

abstractlipoblastoma is a rare benign tumour arising from embryonic white fat . the tumours occur primarily in infancy and early childhood and usually arise from the limbs and the trunk , but neck involvement is rare . we report three cases of head and neck lipoblastoma . in all cases , imaging showed a well - delineated , fat - containing tumour . after surgical resection , the outcome of these patients was uneventful .

Introduction Case report Case 1 Case 2 Case 3 Discussion

the deinococcus - thermus phylum constitutes one of the major bacterial evolutionary lineages [ 1 , 2 ] . at present , the genome sequence data of 6 genera ( 13 organisms ) belonging to this phylum are available in the kyoto encyclopedia of genes and genomes ( kegg ) database . two pathways for lysine biosynthesis have been described , namely , the -aminoadipate ( aaa ) pathway and the diaminopimelate ( dap ) pathway . , a gene cluster was found for lysine biosynthesis not through the dap pathway but through the aaa pathway [ 68 ] . although deinococcus radiodurans has genes homologous to the t. thermophilus lysine biosynthetic genes , these genes are scattered on the genome . in addition , the d. radiodurans aspartate kinase that catalyzes the phosphorylation of l - aspartate ( the first reaction in the dap pathway ) is structurally and phylogenetically very different from that of t. thermophilus . recent studies have shown that the genome signatures of these 2 bacteria are different , supporting the theory that deinococcus species acquired genes from various other bacteria to survive different kinds of environmental stresses , whereas thermus species have acquired genes from thermophilic bacteria to adapt to high - temperature environments . the distribution of lysine biosynthetic genes in the deinococcus - thermus phylum has not been clearly described . in this study , we compared the distribution of the genes for lysine biosynthesis between 13 organisms ( d. deserti , d. geothermalis , d. maricopensis , d. proteolyticus , d. radiodurans , marinithermus hydrothermalis , meiothermus ruber , m. silvanus , oceanithermus profundus , t. scotoductus , t. thermophilus hb8 , t. thermophilus hb27 , and truepera radiovictrix ) . we analyzed the distribution of each of the following 10 enzymes related to lysine biosynthesis through the aaa pathway in the deinococcus - thermus phylum : -aminoadipate aminotransferase , homoisocitrate dehydrogenase , lysw--l - lysine aminotransferase , lysw--l - lysine hydrolase , lysw--l--aminoadipate kinase , lysw--l--aminoadipyl-6-phosphate reductase , -aminoadipate - lysw ligase lysx , lysu , lyst , and homocitrate synthase . in addition , we analyzed the distribution of each of the following 6 enzymes related to lysine biosynthesis through the dap pathway : aspartate kinase , aspartate - semialdehyde dehydrogenase , dihydrodipicolinate synthase , dihydrodipicolinate reductase , ll - diaminopimelate aminotransferase , and diaminopimelate decarboxylase . homologous genes were selected on the basis of blastp search results by using each t. thermophilus enzyme for lysine biosynthesis through the aaa pathway and each d. proteolyticus enzyme for lysine biosynthesis through the dap pathway . multiple alignments were obtained using 20 amino acid sequences , with the highest to the 20th highest score by the blastp result . the -distributed rate was considered , and the number of discrete categories was 3 . genes homologous to the t. thermophilus genes for lysine biosynthesis through the aaa pathway were found to be widely distributed in bacteria belonging to the deinococcus - thermus phylum , except for d. proteolyticus ( table 1 ) . among the 13 organisms examined , marinithermus , oceanithermus , and truepera have the largest gene cluster , containing 8 lysine biosynthetic genes ( table 1 ) . in each phylogenetic analysis of the 10 enzymes , lysine biosynthetic genes of the deinococcus - thermus phylum were found to have a common ancestor ( see in supplementary material figures s1s10 available online at doi:10.1155/2012/745931 ) . we hypothesize that a common ancestor of the deinococcus - thermus phylum biosynthesized lysine through the aaa pathway . in contrast , the distribution of genes for lysine biosynthesis through the dap pathway was found to be limited in the deinococcus - thermus phylum ( table 2 ) . thus , ll - diaminopimelate aminotransferase and dihydrodipicolinate reductase were identified in no bacteria other than d. proteolyticus ( table 2 ) . this observation supports our hypothesis that a common ancestor of the deinococcus - thermus phylum biosynthesized lysine not through the dap pathway , but through the aaa pathway . interestingly , d. proteolyticus was found to have the genes for lysine biosynthesis through the dap pathway ( table 2 ) . d. proteolyticus has 2 diaminopimelate decarboxylases , namely , deipro 0627 and deipro 1375 ( table 2 ) , which are structurally different from each other . because deipro 1375 forms a gene cluster with other genes for lysine biosynthesis through the dap pathway , we used deipro 1375 as a query sequence in the blastp search . each phylogenetic tree based on diaminopimelate decarboxylase ( figure 1 ) , ll - diaminopimelate aminotransferase ( figure 2 ) , dihydrodipicolinate synthase ( figure 3 ) , and dihydrodipicolinate reductase ( figure 4 ) showed that the d. proteolyticus enzyme is closely related to that of the genera kytococcus ( a member of actinobacteria ) and spirochaeta ( a member of spirochaetes ) ( figures 14 ) . the 3 phyla actinobacteria , deinococcus - thermus , and spirochaetes do not form a monophyletic lineage in the phylogenetic tree , as based on genomewide comparative studies . in addition , the 4 genes encoding diaminopimelate decarboxylase , ll - diaminopimelate aminotransferase , dihydrodipicolinate synthase , and dihydrodipicolinate reductase are clustered in each genus ( figures 14 ) . thus , these findings strongly suggested that a dna fragment including the 4 d. proteolyticus genes was horizontally transferred from a phylogenetically distant organism . this horizontal transfer event may have induced the loss of the genes for lysine biosynthesis through the aaa pathway in d. proteolyticus .

thermus thermophilus biosynthesizes lysine through the -aminoadipate ( aaa ) pathway : this observation was the first discovery of lysine biosynthesis through the aaa pathway in archaea and bacteria . genes homologous to the t. thermophilus lysine biosynthetic genes are widely distributed in bacteria of the deinococcus - thermus phylum . our phylogenetic analyses strongly suggest that a common ancestor of the deinococcus - thermus phylum had the ancestral genes for bacterial lysine biosynthesis through the aaa pathway . in addition , our findings suggest that the ancestor lacked genes for lysine biosynthesis through the diaminopimelate ( dap ) pathway . interestingly , deinococcus proteolyticus does not have the genes for lysine biosynthesis through the aaa pathway but does have the genes for lysine biosynthesis through the dap pathway . phylogenetic analyses of d. proteolyticus lysine biosynthetic genes showed that the key gene cluster for the dap pathway was transferred horizontally from a phylogenetically distant organism .

1. Introduction 2. Methods 3. Results and Discussion

the motion of a point electric charge in flat spacetime was the subject of active investigation since the early work of lorentz , abrahams , and poincar , until dirac produced a proper relativistic derivation of the equations of motion in 1938 . ( the field s early history is well related in . ) in 1960 dewitt and brehme generalized dirac s result to curved spacetimes , and their calculation was corrected by hobbs several years later . in 1997 the motion of a point mass in a curved background spacetime was investigated by mino , sasaki , and tanaka , who derived an expression for the particle s acceleration ( which is not zero unless the particle is a test mass ) ; the same equations of motion were later obtained by quinn and wald using an axiomatic approach . the case of a point scalar charge was finally considered by quinn in 2000 , and this led to the realization that the mass of a scalar particle is not necessarily a constant of the motion . this article reviews the achievements described in the preceding paragraph ; it is concerned with the motion of a point scalar charge q , a point electric charge e , and a point mass m in a specified background spacetime with metric g. these particles carry with them fields that behave as outgoing radiation in the wave zone . the radiation removes energy and angular momentum from the particle , which then undergoes a radiation reaction its world line can not be simply a geodesic of the background spacetime . the particle s motion is affected by the near - zone field which acts directly on the particle and produces a self - force . in curved spacetime the self - force contains a radiation - reaction component that is directly associated with dissipative effects , but it contains also a conservative component that is not associated with energy or angular - momentum transport . the self - force is proportional to q in the case of a scalar charge , proportional to e in the case of an electric charge , and proportional to m in the case of a point mass . in this review i derive the equations that govern the motion of a point particle in a curved background spacetime . the presentation is entirely self - contained , and all relevant materials are developed ab initio . the reader , however , is assumed to have a solid grasp of differential geometry and a deep understanding of general relativity . the reader is also assumed to have unlimited stamina , for the road to the equations of motion is a long one . one must first assimilate the basic theory of bitensors ( section 2 ) , then apply the theory to construct convenient coordinate systems to chart a neighbourhood of the particle s world line ( section 3 ) . one must next formulate a theory of green s functions in curved spacetimes ( section 4 ) , and finally calculate the scalar , electromagnetic , and gravitational fields near the world line and figure out how they should act on the particle ( section 5 ) . the review is very long , but the payoff , i hope , will be commensurate . in this introductory section this should help the reader get oriented and acquainted with some of the ideas and some of the notation . enjoy ! let us first consider the relatively simple and well - understood case of a point electric charge e moving in flat spacetime [ 52 , 30 , 56 , 47 ] . the charge produces an electromagnetic vector potential a that satisfies the wave equation 1\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square { a^\alpha } = - 4\pi { j^\alpha}$$\end{document } together with the lorenz gauge condition a = 0 . the vector j is the charge s current density , which is formally written in terms of a four - dimensional dirac functional supported on the charge s world line : the density is zero everywhere , except at the particle s position where it is infinite . for concreteness we will imagine that the particle moves around a centre ( perhaps another charge , which is taken to be fixed ) and that it emits outgoing radiation . we expect that the charge will undergo a radiation reaction and that it will spiral down toward the centre . this effect must be accounted for by the equations of motion , and these must therefore include the action of the charge s own field , which is the only available agent that could be responsible for the radiation reaction . we seek to determine this self - force acting on the particle . an immediate difficulty presents itself : the vector potential , and also the electromagnetic field tensor , diverge on the particle s world line , because the field of a point charge is necessarily infinite at the charge s position . this behaviour makes it most difficult to decide how the field is supposed to act on the particle . i note first that the situation considered here , in which the radiation is propagating outward and the charge is spiraling inward , breaks the time - reversal invariance of maxwell s theory . a specific time direction was adopted when , among all possible solutions to the wave equation , we chose \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{{\rm{ret}}}^\alpha$\end{document } , the retarded solution , as the physically - relevant solution . choosing instead the advanced solution \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{{\rm{adv}}}^\alpha$\end{document } would produce a time - reversed picture in which the radiation is propagating inward and the charge is spiraling outward . alternatively , choosing the linear superposition 2\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a_{\rm{s}}^\alpha = { 1 \over 2}(a_{{\rm{ret}}}^\alpha + a_{{\rm{adv}}}^\alpha)$$\end{document } would restore time - reversal invariance : outgoing and incoming radiation would be present in equal amounts , there would be no net loss nor gain of energy by the system , and the charge would not undergo any radiation reaction . in equation s stands for symmetric , as the vector potential depends symmetrically upon future and past . my second key observation is that while the potential of equation ( 2 ) does not exert a force on the charged particle , it is just as singular as the retarded potential in the vicinity of the world line . this follows from the fact that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{{\rm{ret}}}^\alpha , a_{{\rm{adv}}}^\alpha$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{\rm{s}}^\alpha$\end{document } all satisfy equation ( 1 ) , whose source term is infinite on the world line . so while the wave - zone behaviours of these solutions are very different ( with the retarded solution describing outgoing waves , the advanced solution describing incoming waves , and the symmetric solution describing standing waves ) , the three vector potentials share the same singular behaviour near the world line all three electromagnetic fields are dominated by the particle s coulomb field and the different asymptotic conditions make no difference close to the particle . symmetric. because \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{\rm{s}}^\alpha$\end{document } is just as singular as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{{\rm{ret}}}^\alpha$\end{document } , removing it from the retarded solution gives rise to a potential that is well behaved in a neighbourhood of the world line . and because \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{\rm{s}}^\alpha$\end{document } is known not to affect the motion of the charged particle , this new potential must be entirely responsible for the radiation reaction . we therefore introduce the new potential 3\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a_{\rm{r}}^\alpha = a_{{\rm{ret}}}^\alpha - a_{\rm{s}}^\alpha = { 1 \over 2}(a_{{\rm{ret}}}^\alpha - a_{{\rm{adv}}}^\alpha)$$\end{document } and postulate that it , and it alone , exerts a force on the particle . the subscript r stands for regular , because \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{\rm{r}}^\alpha$\end{document } is nonsingular on the world line . this property can be directly inferred from the fact that the regular potential satisfies the homogeneous version of equation ( 1 ) , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\square a_{\rm{r}}^\alpha = 0$\end{document } ; there is no singular source to produce a singular behaviour on the world line . since \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{\rm{r}}^\alpha$\end{document } satisfies the homogeneous wave equation , it can be thought of as a free radiation field , and the subscript r could also stand for radiative. the self - action of the charge s own field is now clarified : a singular potential \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{\rm{s}}^\alpha$\end{document } can be removed from the retarded potential and shown not to affect the motion of the particle . ( establishing this last statement requires a careful analysis that is presented in the bulk of the paper ; what really happens is that the singular field contributes to the particle s inertia and renormalizes its mass . ) what remains is a well - behaved potential \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{\rm{r}}^\alpha$\end{document } that must be solely responsible for the radiation reaction . from the radiative potential we form an electromagnetic field tensor \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{\alpha \beta}^{\rm{r } } = { \partial \beta}a_\alpha ^{\rm{r}}$\end{document } , and we take the particle s equations of motion to be 4\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$m{a_\mu } = f_\mu ^{{\rm{ext } } } + ef_{\mu \nu}^{\rm{r}}{u^\nu},$$\end{document } where u = dz / d is the charge s four - velocity ( z( ) gives the description of the world line and is proper time ) , a = du / d its acceleration , m its ( renormalized ) mass , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{{\rm{ext}}}^\mu$\end{document } an external force also acting on the particle . calculation of the radiative field yields the more concrete expression 5\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$m{a^\mu } = f_{{\rm{ext}}}^\mu + { { 2{e^2 } } \over { 3m}}(\delta _ \nu ^\mu + { u^\mu}{u_\nu}){{df_{{\rm{ext}}}^\nu } \over { d\tau}},$$\end{document } in which the second - term is the self - force that is responsible for the radiation reaction . we observe that the self - force is proportional to e , it is orthogonal to the four - velocity , and it depends on the rate of change of the external force . this is the result that was first derived by dirac 1 . to see how equation ( 5 ) can eventually be generalized to curved spacetimes , i introduce a new layer of mathematical formalism and show that the decomposition of the retarded potential into symmetric - singular and regular - radiative pieces can be performed at the level of the green s functions associated with equation ( 1 ) . the retarded solution to the wave equation can be expressed as 6\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a_{{\rm{ref}}}^\alpha ( x ) = \int { g_{+ \beta{\prime}}^\alpha ( x , x{\prime}){j^{\beta{\prime}}}(x{\prime})dv{\prime}}$$\end{document } in terms of the retarded green s function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{+ { \beta { \prime}}}^\alpha ( x,{x{\prime } } ) = \delta _ { { \beta { \prime}}}^\alpha \delta ( t - { t{\prime } } - \vert x - { x{\prime}}\vert)/\vert x - { x{\prime}}\vert$\end{document}. here x = ( t , x ) is an arbitrary field point , x = ( t , x ) is a source point , and dv dx ; tensors at x are identified with unprimed indices , while primed indices refer to tensors at x. similarly , the advanced solution can be expressed as 7\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a_{{\rm{adv}}}^\alpha ( x ) = \int { g_{- \beta{\prime}}^\alpha ( x , x{\prime}){j^{\beta{\prime}}}(x{\prime})dv{\prime}}$$\end{document } in terms of the advanced green s function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{- { \beta \prime}}^\alpha ( x,{x\prime } ) = \delta _ { { \beta \prime}}^\alpha \delta ( t - { t\prime } + \vert x - { x\prime}\vert)/\vert x - { x\prime}\vert$\end{document}. the retarded green s function is zero whenever x lies outside of the future light cone of x , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{+ { \beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } is infinite at these points . on the other hand , the advanced green s function is zero whenever x lies outside of the past light cone of x , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{- { \beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } is infinite at these points . the retarded and advanced green s functions satisfy the reciprocity relation 8\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{\beta \prime \alpha}^ - ( x\prime , x ) = g_{\alpha \beta \prime}^ + ( x , x\prime);$$\end{document } this states that the retarded green s function becomes the advanced green s function ( and vice versa ) when x and x are interchanged . from the retarded and advanced green s functions we can define a singular green s function by 9\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{s}}\beta \prime}^{\;\alpha}(x , x\prime ) = { 1 \over 2}[g_{+ \beta \prime}^{\;\alpha}(x , x\prime ) + g_{- \beta \prime}^{\;\alpha}(x , x\prime)]$$\end{document } and a radiative green s function by 10\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{r}}\beta \prime}^{\;\alpha}(x , x\prime ) = g_{{+}\beta \prime}^{\;\alpha}(x , x\prime ) - g_{{\rm{s}}\beta \prime}^{\;\alpha}(x , x\prime ) = { 1 \over 2}[g_{+ \beta \prime}^{\;\alpha}(x , x\prime ) - g_{- \beta \prime}^{\;\alpha}(x , x\prime)].$$\end{document } by virtue of equation ( 8) the singular green s function is symmetric in its indices and arguments : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{{\beta { \prime}}\alpha}^{\rm{s}}({x{\prime}},x ) = g_{\alpha { \beta { \prime}}}^{\rm{s}}(x,{x{\prime}})$\end{document}. the radiative green s function , on the other hand , is antisymmetric . the potential 11\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a_{\rm{s}}^\alpha ( x ) = \int { g_{{\rm{s}}\beta{\prime}}^\alpha ( x , x{\prime}){j^{\beta{\prime}}}(x{\prime})dv{\prime}}$$\end{document } satisfies the wave equation of equation ( 1 ) and is singular on the world line , while 12\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a_{\rm{r}}^\alpha ( x ) = \int { g_{{\rm{r}}\beta{\prime}}^\alpha ( x , x{\prime}){j^{\beta{\prime}}}(x{\prime})dv{\prime}}$$\end{document } satisfies the homogeneous equation a = 0 and is well behaved on the world line . equation ( 6 ) implies that the retarded potential at x is generated by a single event in spacetime : the intersection of the world line and the past light cone of x ( see figure 1 ) . i shall call this the retarded point associated with x and denote it z(u ) ; u is the retarded time , the value of the proper - time parameter at the retarded point . similarly we find that the advanced potential of equation ( 7 ) is generated by the intersection of the world line and the future light cone of the field point x. i shall call this the advanced point associated with x and denote it z(u ) ; v is the advanced time , the value of the proper - time parameter at the advanced point . figure 1 in flat spacetime , the retarded potential at x depends on the particle s state of motion at the retarded point z(u ) on the world line ; the advanced potential depends on the state of motion at the advanced point z(v ) . in flat spacetime , the retarded potential at x depends on the particle s state of motion at the retarded point z(u ) on the world line ; the advanced potential depends on the state of motion at the advanced point z(v ) . in a curved spacetime with metric g the wave equation for the vector potential becomes 13\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square { a^\alpha } - { r^\alpha}_\beta { a^\beta } = - 4\pi { j^\alpha},$$\end{document } where = g is the covariant wave operator and r is the spacetime s ricci tensor ; the lorenz gauge conditions becomes a = 0 , and denotes covariant differentiation . retarded and advanced green s functions can be defined for this equation , and solutions to equation ( 13 ) take the same form as in equations ( 6 ) and ( 7 ) , except that dv now stands for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt { - g({x{\prime } } ) } { d^4}{x{\prime}}$\end{document}. the causal structure of the green s functions is richer in curved spacetime : while in flat spacetime the retarded green s function has support only on the future light cone of x , in curved spacetime its support extends inside the light cone as well ; \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{+ { \beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } is therefore nonzero when x i(x ) , which denotes the chronological future of x. this property reflects the fact that in curved spacetime , electromagnetic waves propagate not just at the speed of light , but at all speeds smaller than or equal to the speed of light ; the delay is caused by an interaction between the radiation and the spacetime curvature . a direct implication of this property is that the retarded potential at x is now generated by the point charge during its entire history prior to the retarded time u associated with x : the potential depends on the particle s state of motion for all times u ( see figure 2 ) . figure 2 in curved spacetime , the retarded potential at x depends on the particle s history before the retarded time u ; the advanced potential depends on the particle s history after the advanced time . in curved spacetime , the retarded potential at x depends on the particle s history before the retarded time u ; the advanced potential depends on the particle s history after the advanced time . similar statements can be made about the advanced green s function and the advanced solution to the wave equation . while in flat spacetime the advanced green s function has support only on the past light cone of x , in curved spacetime its support extends inside the light cone , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{- { \beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } is nonzero when x i(x ) , which denotes the chronological past of x. this implies that the advanced potential at x is generated by the point charge during its entire future history following the advanced time v associated with x : the potential depends on the particle s state of motion for all times . the physically relevant solution to equation ( 13 ) is obviously the retarded potential \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{{\rm{ret}}}^\alpha ( x)$\end{document } , and as in flat spacetime , this diverges on the world line . the cause of this singular behaviour is still the pointlike nature of the source , and the presence of spacetime curvature does not change the fact that the potential diverges at the position of the particle . once more this behaviour makes it difficult to figure out how the retarded field is supposed to act on the particle and determine its motion . as in flat spacetime we shall attempt to decompose the retarded solution into a singular part that exerts no force , and a smooth radiative part that produces the entire self - force . to decompose the retarded green s function into singular and radiative parts is not a straightforward task in curved spacetime . the flat - spacetime definition for the singular green s function , equation ( 9 ) , can not be adopted without modification : while the combination half - retarded plus half - advanced green s functions does have the property of being symmetric , and while the resulting vector potential would be a solution to equation ( 13 ) , this candidate for the singular green s function would produce a self - force with an unacceptable dependence on the particle s future history . for suppose that we made this choice . then the radiative green s function would be given by the combination half - retarded minus half - advanced green s functions , just as in flat spacetime . the resulting radiative potential would satisfy the homogeneous wave equation , and it would be smooth on the world line , but it would also depend on the particle s entire history , both past ( through the retarded green s function ) and future ( through the advanced green s function ) . more precisely stated , we would find that the radiative potential at x depends on the particle s state of motion at all times outside the interval u < < v ; in the limit where x approaches the world line , this interval shrinks to nothing , and we would find that the radiative potential is generated by the complete history of the particle . a self - force constructed from this potential would be highly noncausal , and we are compelled to reject these definitions for the singular and radiative green s functions . the proper definitions were identified by detweiler and whiting , who proposed the following generalization to equation ( 9 ) : 14\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{s}}\beta \prime}^{\;\alpha}(x , x\prime ) = { 1 \over 2}[g_{+ \beta \prime}^{\;\alpha}(x , x\prime ) + g_{- \beta \prime}^{\;\alpha}(x , x\prime ) - h_{\;\;\beta \prime}^\alpha ( x , x\prime)].$$\end{document } the two - point function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } is introduced specifically to cure the pathology described in the preceding paragraph . it is symmetric in its indices and arguments , so that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{\alpha { \beta { \prime}}}^{\rm{s}}(x,{x{\prime}})$\end{document } will be also ( since the retarded and advanced green s functions are still linked by a reciprocity relation ) ; and it is a solution to the homogeneous wave equation , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\square{h^\alpha}_{{\beta { \prime}}}(x,{x{\prime } } ) - { r^\alpha}_\gamma ( x){h^\gamma}_{{\beta { \prime}}}(x,{x{\prime } } ) = 0$\end{document } , so that the singular , retarded , and advanced green s functions will all satisfy the same wave equation . furthermore , and this is its key property , the two - point function is defined to agree with the advanced green s function when x is in the chronological past of x : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${x{\prime}}:{h^\alpha}_{{\beta { \prime}}}(x,{x{\prime } } ) = g_{- { \beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } when x i(x ) . this ensures that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{{\rm{s}}{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } vanishes when x is in the chronological past of x. in fact , reciprocity implies that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } will also agree with the retarded green s function when x is in the chronological future of x , and it follows that the symmetric green s function vanishes also when x is in the chronological future of x. the potential \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{\rm{s}}^\alpha ( x)$\end{document } constructed from the singular green s function can now be seen to depend on the particle s state of motion at times restricted to the interval u v ( see figure 3 ) . because this potential satisfies equation ( 13 ) , it is just as singular as the retarded potential in the vicinity of the world line . and because the singular green s function is symmetric in its arguments , the singular potential can be shown to exert no force on the charged particle . ( this requires a lengthy analysis that will be presented in the bulk of the paper . ) figure 3 in curved spacetime , the singular potential at x depends on the particle s history during the interval u v ; for the radiative potential the relevant interval is < v. in curved spacetime , the singular potential at x depends on the particle s history during the interval u v ; for the radiative potential the relevant interval is < v. the detweiler - whiting definition for the radiative green s function is then 15\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{r}}\beta \prime}^{\;\alpha}(x , x\prime ) = g_{+ \beta \prime}^{\;\alpha}(x , x\prime ) - g_{{\rm{s}}\beta \prime}^{\;\alpha}(x , x\prime ) = { 1 \over 2}[g_{+ \beta \prime}^{\;\alpha}(x , x\prime ) - g_{- \beta \prime}^{\;\alpha}(x , x\prime ) + h_{\;\;\beta \prime}^\alpha ( x , x\prime)].$$\end{document } the potential \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{\rm{r}}^\alpha ( x)$\end{document } constructed from this depends on the particle s state of motion at all times prior to the advanced time v : v. because this potential satisfies the homogeneous wave equation , it is well behaved on the world line and its action on the point charge is well defined . and because the singular potential \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{\rm{s}}^\alpha ( x)$\end{document } can be shown to exert no force on the particle , we conclude that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a_{\rm{r}}^\alpha ( x)$\end{document } alone is responsible for the self - force . from the radiative potential we form an electromagnetic field tensor \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{\alpha \beta}^{\rm{r } } = { \nabla _ a}a_\beta ^{\rm{r } } - { \nabla _ \beta}a_\alpha ^{\rm{r}}$\end{document } , and the curved - spacetime generalization to equation ( 4 ) is 16\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$m{a_\mu } = f_\mu ^{{\rm{ext } } } + ef_{\mu \nu}^{\rm{r}}{u^\nu},$$\end{document } where u = dz / d is again the charge s four - velocity , but a = du / d is now its covariant acceleration . to flesh out the ideas contained in the preceding section 1.4 i add yet another layer of mathematical formalism and construct a convenient coordinate system to chart a neighbourhood of the particle s world line . in the next section 1.6 i will display explicit expressions for the retarded , singular , and radiative fields of a point electric charge . its tangent vector is u = dz / d and its acceleration is a = du / d ; we shall also encounter \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\dot a}^\mu } \equiv d{a^\mu}/d\tau$\end{document}. on we erect an orthonormal basis that consists of the four - velocity u and three spatial vectors \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_a^\mu$\end{document } labelled by a frame index a = ( 1 , 2 , 3 ) . these vectors satisfy the relations guu = 1 , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\mu \nu}}{u^\mu}e_a^\nu = 0$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\mu \nu}}e_a^\mu e_b^\nu = { \delta _ { ab}}$\end{document}. we take the spatial vectors to be fermi - walker transported on the world line : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$de_a^\mu / d\tau = { a_a}{u^\mu}$\end{document } , where 17\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a_a}(\tau ) = { a_\mu}e_a^\mu$$\end{document } are frame components of the acceleration vector ; it is easy to show that fermi - walker transport preserves the orthonormality of the basis vectors . an example was already given in equation ( 17 ) but we shall also encounter frame components of the riemann tensor , 18\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{a0b0}}(\tau ) = { r_{\mu \lambda \nu \rho}}e_a^\mu { u^\lambda}e_b^\nu { u^\rho},\quad \quad { r_{a0bc}}(\tau ) = { r_{\mu \lambda \nu \rho}}e_a^\mu { u^\lambda}e_b^\nu e_c^\rho , \;\;\quad { r_{abcd}}(\tau ) = { r_{\mu \lambda \nu \rho}}e_a^\mu e_b^\lambda e_c^\nu e_d^\rho , $ $ \end{document } as well as frame components of the ricci tensor , 19\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{00}}(\tau ) = { r_{\mu \lambda}}{u^\mu}{u^\nu},\quad \quad { r_{a0}}(\tau ) = { r_{\mu \nu}}e_a^\mu { u^\nu},\quad \quad { r_{ab}}(\tau ) = { r_{\mu \nu}}e_a^\mu e_b^\nu.$$\end{document } we shall use ab = diag(1 , 1 , 1 ) and its inverse = diag(1 , 1 , 1 ) to lower and raise frame indices , respectively . consider a point x in a neighbourhood of the world line . we assume that x is sufficiently close to the world line that a unique geodesic links x to any neighbouring point z on . the two - point function (x , z ) , known as synge s world function , is numerically equal to half the squared geodesic distance between z and x ; it is positive if x and z are spacelike related , negative if they are timelike related , and (x , z ) is zero if x and z are linked by a null geodesic . we denote its gradient /z by (x , z ) , and gives a meaningful notion of a separation vector ( pointing from z to x ) . to construct a coordinate system in this neighbourhood z(u ) on which is linked to x by a future - directed null geodesic ( this geodesic is directed from x to x ) ; i shall refer to x as the retarded point associated with x , and u will be called the retarded time . to tensors at x we assign indices , , ; this will distinguish them from tensors at a generic point z( ) on the world line , to which we have assigned indices , , . we have (x , x ) = 0 , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$- { \sigma ^{{\alpha { \prime}}}}(x,{x{\prime}})$\end{document } is a null vector that can be interpreted as the separation between x and x. the retarded coordinates of the point x are ( u , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^a}$\end{document } ) , where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^a } = - e_{{\alpha { \prime}}}^a{\sigma ^{{\alpha { \prime}}}}$\end{document } are the frame components of the separation vector . the invariant quantity 20\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$r \equiv \sqrt { { \delta _ { ab}}{{\hat x}^a}{{\hat x}^b } } = { u_{\alpha\prime}}{\sigma ^{\alpha\prime}}$$\end{document } is an affine parameter on the null geodesic that links x to x ; it can be loosely interpreted as the time delay between x and x as measured by an observer moving with the particle . this therefore gives a meaningful notion of distance between x and the retarded point , and i shall call r the retarded distance between x and the world line . the unit vector 21\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\omega ^a } = { \hat x^a}/r$$\end{document } is constant on the null geodesic that links x to x. because is a different constant on each null geodesic that emanates from x , keeping u fixed and varying produces a congruence of null geodesics that generate the future light cone of the point x ( the congruence is hypersurface orthogonal ) . each light cone can thus be labelled by its retarded time u , each generator on a given light cone can be labelled by its direction vector , and each point on a given generator can be labelled by its retarded distance r. we therefore have a good coordinate system in a neighbourhood of . figure 4retarded coordinates of a point x relative to a world line . the retarded time u selects a particular null cone , the unit vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega ^a } \equiv { { \hat x}^a}/r$\end{document } selects a particular generator of this null cone , and the retarded distance r selects a particular point on this generator . retarded coordinates of a point x relative to a world line . the retarded time u selects a particular null cone , the unit vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega ^a } \equiv { { \hat x}^a}/r$\end{document } selects a particular generator of this null cone , and the retarded distance r selects a particular point on this generator . to tensors at x we assign indices , , . these tensors will be decomposed in a tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } that is constructed as follows : given x we locate its associated retarded point x on the world line , as well as the null geodesic that links these two points ; we then take the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{\alpha \prime}},e_a^{\alpha \prime})$\end{document } at x and parallel transport it to x along the null geodesic to obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document}. the retarded solution to equation ( 13 ) is 22\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^\alpha}(x ) = e\int\nolimits_\gamma { g_{+ \mu}^\alpha ( x , z ) } { u^\mu}d\tau,$$\end{document } where the integration is over the world line of the point electric charge . because the retarded solution is the physically relevant solution to the wave equation , it will not be necessary to put a label ret on the vector potential . from the vector potential we form the electromagnetic field tensor f , which we decompose in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } introduced at the end of section 1.5 . we then express the frame components of the field tensor in retarded coordinates , in the form of an expansion in powers of r. this gives 23\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{f_{a0}}(u , r,{\omega ^a } ) \equiv { f_{\alpha \beta}}(x)e_a^\alpha ( x)e_0^\beta ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\{\quad \quad \quad \quad \quad = { e \over { { r^2}}}{\omega _ a } - { e \over r}({a_a } - { a_b}{\omega ^b}{\omega _ a } ) + { 1 \over 3}e{r_{b0c0}}{\omega ^b}{\omega ^c}{\omega _ a } - { 1 \over 6}e(5{r_{a0b0}}{\omega ^b } + { r_{ab0c}}{\omega ^b}{\omega ^c } ) } \\{\quad \quad \quad \quad \quad \quad + { 1 \over { 12}}e(5{r_{00 } } + { r_{bc}}{\omega ^b}{\omega ^c } + r){\omega _ a } + { 1 \over 3}e{r_{a0 } } - { 1 \over 6}e{r_{ab}}{\omega ^b } + f_{a0}^{{\rm{tail } } } + { \mathcal o}(r),\quad \quad \quad } \\\end{array}$$\end{document } 24\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{f_{ab}}(u , r,{\omega ^a } ) \equiv { f_{\alpha \beta}}(x)e_a^\alpha ( x)e_b^\beta ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \;\ ; } \\{\quad \quad \quad \quad \quad = { e \over r}({a_a}{\omega _ a } - { \omega _ a}{a_b } ) + { 1 \over 2}e({r_{a0bc } } - { r_{b0ac } } + { r_{a0c0}}{\omega _ b } - { \omega _ a}{r_{b0c0}}){\omega ^c } } \\{\quad \quad \quad \quad \quad \quad - { 1 \over 2}e({r_{a0}}{\omega _ b } - { \omega _ a}{r_{b0 } } ) + f_{ab}^{{\rm{tail } } } + { \mathcal o}(r),\quad \quad \quad \quad \quad \quad \quad \quad \;\;\ ; } \\\end{array}$$\end{document } where 25\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f_{a0}^{{\rm{tail } } } = f_{\alpha \prime \beta \prime}^{{\rm{tail}}}(x\prime)e_a^{\alpha \prime}{u^{\beta \prime}},\quad \quad f_{ab}^{{\rm{tail } } } = f_{\alpha \prime \beta \prime}^{{\rm{tail}}}(x\prime)e_a^{\alpha \prime}e_b^{\beta \prime}$$\end{document } are the frame components of the tail part of the field , which is given by 26\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f_{\alpha{\prime}\beta{\prime}}^{{\rm{tail}}}(x{\prime } ) = 2e\int\nolimits_{- \infty}^{{u^ - } } { { \nabla _ { [ \alpha{\prime}}}{g_{+ \beta{\prime}]\mu}}(x{\prime},z){u^\mu}d\tau.}$$\end{document } in these expressions , all tensors ( or their frame components ) are evaluated at the retarded point x = z(u ) associated with x ; for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_a } \equiv { a_a}(u ) \equiv { a_{{\alpha { \prime}}}}e_a^\alpha$\end{document}. the tail part of the electromagnetic field tensor is written as an integral over the portion of the world line that corresponds to the interval < u u 0 ; this represents the past history of the particle . the integral is cut short at u to avoid the singular behaviour of the retarded green s function when z( ) coincides with x ; the portion of the green s function involved in the tail integral is smooth , and the singularity at coincidence is completely accounted for by the other terms in equations ( 23 ) and ( 24 ) . the expansion of f(x ) near the world line does indeed reveal many singular terms . we first recognize terms that diverge when r 0 ; for example the coulomb field fa0 diverges as r when we approach the world line . but there are also terms that , though they stay bounded in the limit , possess a directional ambiguity at r = 0 ; for example fab contains a term proportional to ra0bc whose limit depends on the direction of approach . this singularity structure is perfectly reproduced by the singular field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{\alpha \beta}^{\rm{s}}$\end{document } obtained from the potential 27\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a_{\rm{s}}^\alpha ( x ) = e\int\nolimits_\gamma { g_{{\rm{s}}\mu}^\alpha ( x , z){u^\mu}d\tau,}$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{s}}}_\mu ^\alpha ( x , z)$\end{document } is the singular green s function of equation ( 14 ) . near the world line the singular field is given by 28\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{f_{a0}^{\rm{s}}(u , r,{\omega ^a } ) \equiv f_{\alpha \beta}^{\rm{s}}(x)e_a^\alpha ( x)e_0^\beta ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { \quad \quad \quad \quad \quad = { e \over { { r^2}}}{\omega _ a } - { e \over r}({a_a } - { a_b}{\omega ^b}{\omega _ a } ) - { 2 \over 3}e{{\dot a}_a } + { 1 \over 3}e{r_{b0c0}}{\omega ^b}{\omega ^c}{\omega _ a } - { 1 \over 6}e(5{r_{a0b0}}{\omega ^b } + { r_{ab0c}}{\omega ^b}{\omega ^c } ) } \\ { \quad \quad \quad \quad \quad \quad + { 1 \over { 12}}e\;(5{r_{00 } } + { r_{bc}}{\omega ^b}{\omega ^c } + r)\;{\omega _ a } - { 1 \over 6}e{r_{ab}}{\omega ^b } + { \mathcal o}(r),\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ \end{array}$$\end{document } 29\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{f_{ab}^{\rm{s}}(u , r,{\omega ^a } ) \equiv f_{\alpha \beta}^{\rm{s}}(x)e_a^\alpha ( x)e_b^\beta ( x)\quad \quad \quad \quad \quad \quad \;\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \;\ ; } \\{= { e \over r}({a_a}{\omega _ b } - { \omega _ a}{a_b } ) + { 1 \over 2}e\;({r_{a0bc } } - { r_{b0ac } } + { r_{a0c0}}{\omega _ b } - { \omega _ a}{r_{b0c0}}){\omega ^c } } \\{\quad \quad \quad \quad \quad \quad - { 1 \over 2}e\;({r_{a0}}{\omega _ b } - { \omega _ a}{r_{b0 } } ) + { \mathcal o}(r)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\end{array}$$\end{document } comparison of these expressions with equations ( 23 ) and ( 24 ) does indeed reveal that all singular terms are shared by both fields . the difference between the retarded and singular fields defines the radiative field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{\alpha \beta}^{\rm{r}}(x)$\end{document}. its frame components are 30\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f_{a0}^{\rm{r } } = { 2 \over 3}e{\dot a_a } + { 1 \over 3}e{r_{a0 } } + f_{a0}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } 31\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f_{ab}^{\rm{r } } = f_{ab}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } and at x the radiative field becomes 32\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f_{\alpha{\prime}\beta{\prime}}^{\rm{r } } = 2e{u_{[\alpha{\prime}}}({g_{\beta{\prime}]\gamma{\prime } } } + { u_{\beta{\prime}]}}{u_{\gamma{\prime}}})\left({{2 \over 3}{{\dot a}^{\gamma{\prime } } } + { 1 \over 3}{r^{\gamma{\prime}}}_{\delta{\prime}}{u^{\delta{\prime } } } } \right ) + f_{\alpha{\prime}\beta{\prime}}^{{\rm{tail}}},$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\dot a}^{{\gamma { \prime } } } } = d{a^{{\gamma { \prime}}}}/d\tau$\end{document } is the rate of change of the acceleration vector , and where the tail term was given by equation ( 26 ) . we see that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{\alpha \beta}^{\rm{r}}(x)$\end{document } is a smooth tensor field , even on the world line . i have argued in section 1.4 that the self - force acting on a point electric charge is produced by the radiative field , and that the charge s equations of motion should take the form of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m{a_\mu } = f_\mu ^{{\rm{ext } } } + ef_{\mu \nu}^{\rm{r}}{u^\nu}$\end{document } , where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_\mu ^{{\rm{ext}}}$\end{document } is an external force also acting on the particle . substituting equation ( 32 ) gives 33\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$m{a^\mu } = f_{{\rm{ext}}}^\mu + { e^2}({\delta ^\mu}_\nu + { u^\mu}{u_\nu})\left({{2 \over { 3m}}{{df_{{\rm{ext}}}^\nu } \over { d\tau } } + { 1 \over 3}{r^\nu}_\lambda { u^\lambda } } \right ) + 2{e^2}{u_\nu}\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla ^{[\mu}}g_{+ \lambda{\prime}}^{\nu ] } ( z(\tau),z(\tau{\prime})){u^{\lambda{\prime}}}d\tau{\prime},}$$\end{document } in which all tensors are evaluated at z( ) , the current position of the particle on the world line . the primed indices in the tail integral refer to a point z( ) which represents a prior position ; the integration is cut short at = 0 to avoid the singular behaviour of the retarded green s function at coincidence . to get equation ( 33 ) i have reduced the order of the differential equation by replacing with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${m^{- 1}}\dot f_{{\rm{ext}}}^\nu$\end{document } on the right - hand side ; this procedure was explained at the end of section 1.2 . equation ( 33 ) is the result that was first derived by dewitt and brehme and later corrected by hobbs . ( the original equation did not include the ricci - tensor term . ) in flat spacetime the ricci tensor is zero , the tail integral disappears ( because the green s function vanishes everywhere within the domain of integration ) , and equation ( 33 ) reduces to dirac s result of equation ( 5 ) . in curved spacetime the self - force does not vanish even when the electric charge is moving freely , in the absence of an external force : it is then given by the tail integral , which represents radiation emitted earlier and coming back to the particle after interacting with the spacetime curvature . this delayed action implies that , in general , the self - force is nonlocal in time : it depends not only on the current state of motion of the particle , but also on its past history . lest this behaviour should seem mysterious , it may help to keep in mind that the physical process that leads to equation ( 33 ) is simply an interaction between the charge and a free electromagnetic field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{\alpha \beta}^{\rm{r}}$\end{document } ; it is this field that carries the information about the charge s past . the dynamics of a point scalar charge can be formulated in a way that stays fairly close to the electromagnetic theory . the particle s charge q produces a scalar field (x ) , which satisfies a wave equation 34\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - \xi r)\phi = - 4\pi \mu$$\end{document } that is very similar to equation ( 13 ) . here , r is the spacetime s ricci scalar , and is an arbitrary coupling constant ; the scalar charge density (x ) is given by a four - dimensional dirac functional supported on the particle s world line . the retarded solution to the wave equation is 35\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi ( x ) = q\int\nolimits_\gamma { { g _ + } ( x , z)d\tau,}$$\end{document } where g+(x , z ) is the retarded green s function associated with equation ( 34 ) . the field exerts a force on the particle , whose equations of motion are 36\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$m{a^\mu } = q({g^{\mu \nu } } + { u^\mu}{u^\nu}){\nabla _ \nu}\phi,$$\end{document } where m is the particle s mass ; this equation is very similar to the lorentz - force law . but the dynamics of a scalar charge comes with a twist : if equations ( 34 ) and ( 36 ) are to follow from a variational principle , the particle s mass should not be expected to be a constant of the motion . it is found instead to satisfy the differential equation 37\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{dm } \over { d\tau } } = - q{u^\mu}{\nabla _ \mu}\phi,$$\end{document } and in general m will vary with proper time . this phenomenon is linked to the fact that a scalar field has zero spin : the particle can radiate monopole waves and the radiated energy can come at the expense of the rest mass . the scalar field of equation ( 35 ) diverges on the world line , and its singular part s(x ) must be removed before equations ( 36 ) and ( 37 ) can be evaluated . this procedure produces the radiative field r(x ) , and it is this field ( which satisfies the homogeneous wave equation ) that gives rise to a self - force . the gradient of the radiative field takes the form of 38\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\nabla _ \mu}{\phi _ { \rm{r } } } = - { 1 \over { 12}}(1 - 6\xi)qr{u_\mu } + q({g_{\mu \nu } } + { u_\mu}{u_\nu})\left({{1 \over 3}{{\dot a}^\nu } + { 1 \over 6}{r^\nu}_\lambda { u^\lambda } } \right ) + \phi _ \mu ^{{\rm{tail}}}$$\end{document } when it is evaluated of the world line . the last term is the tail integral 39\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi _ \mu ^{{\rm{tail } } } = q\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla _ \mu}{g _ + } ( z(\tau),z(\tau{\prime } ) ) } \,d\tau{\prime},$$\end{document } and this brings the dependence on the particle s past . substitution of equation ( 38 ) into equations ( 36 ) and ( 37 ) gives the equations of motion of a point scalar charge . ( at this stage i introduce an external force \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{{\rm{ext}}}^\mu$\end{document } and reduce the order of the differential equation . ) the acceleration is given by 40\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$m{a^\mu } = f_{{\rm{ext}}}^\mu + { q^2}({\delta ^\mu}_\nu + { u^\mu}{u_\nu})\left [ { { 1 \over { 3m}}{{df_{{\rm{ext}}}^\nu } \over { d\tau } } + { 1 \over 6}{r^\nu}_\lambda { u^\lambda } + \int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla ^\nu}{g _ + } ( z(\tau),z(\tau{\prime}))\;d\tau{\prime } } } \right],$$\end{document } and the mass changes according to 41\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{dm } \over { d\tau } } = - { 1 \over { 12}}(1 - 6\xi){q^2}r - { q^2}{u^\mu}\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla _ \mu}{g _ + } ( z(\tau),z(\tau{\prime}))\;d\tau{\prime}}.$$\end{document } these equations were first derived by quinn 2 . in flat spacetime the ricci - tensor term and the tail integral disappear , and equation ( 40 ) takes the form of equation ( 5 ) with q/(3 m ) replacing the factor of 2e/(3 m ) . in this simple case equation ( 41 ) reduces to dm / d = 0 and the mass is in fact a constant . this property remains true in a conformally - flat spacetime when the wave equation is conformally invariant ( = 1/6 ) : in this case the green s function possesses only a light - cone part , and the right - hand side of equation ( 41 ) vanishes . in generic situations the case of a point mass moving in a specified background spacetime presents itself with a serious conceptual challenge , as the fundamental equations of the theory are nonlinear and the very notion of a point mass is somewhat misguided . nevertheless , to the extent that the perturbation h(x ) created by the point mass can be considered to be small , the problem can be formulated in close analogy with what was presented before . we take the metric g of the background spacetime to be a solution of the einstein field equations in vacuum . we describe the gravitational perturbation produced by a point particle of mass m in terms of trace - reversed potentials defined by 42\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma _ { \alpha \beta } } = { h_{\alpha \beta } } - { 1 \over 2}({g^{\gamma \delta}}{h_{\gamma \delta}}){g_{\alpha \beta}},$$\end{document } where h is the difference between g , the actual metric of the perturbed spacetime , and g. the potentials satisfy the wave equation 43\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square { \gamma ^{\alpha \beta } } + 2r_{\gamma \;\delta}^{\alpha \;\beta}{\gamma ^{\gamma \delta } } = - 16\pi { t^{\alpha \beta}}$$\end{document } together with the lorenz gauge condition \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\gamma ^{\alpha \beta}}_{;\beta } = 0$\end{document}. here and below , covariant differentiation refers to a connection that is compatible with the background metric , = g is the wave operator for the background spacetime , and t is the stress - energy tensor of the point mass ; this is given by a dirac distribution supported on the particle s world line . the retarded solution is 44\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma ^{\alpha \beta}}(x ) = 4m\int\nolimits_\gamma { g _ + ^{\alpha \beta}(x , z){u^\mu}{u^\nu}d\tau,}$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g _ { + \;\mu \nu } ^{\alpha \beta } ( x , z)$\end{document } is the retarded green s function associated with equation ( 43 ) . equations of motion for the point mass can be obtained by formally demanding that the motion be geodesic in the perturbed spacetime with metric g = g + h. after a mapping to the background spacetime , the equations of motion take the form of 45\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^\mu } = - { 1 \over 2}({g^{\mu \nu } } + { u^\mu}{u^\nu})(2{h_{\nu \lambda ; \rho } } - { h_{\lambda \rho ; \nu}}){u^\lambda}{u^\rho}.$$\end{document } the acceleration is thus proportional to m ; in the test - mass limit the world line of the particle is a geodesic of the background spacetime . we now remove \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha \beta}^{\rm{s}}(x)$\end{document } from the retarded perturbation and postulate that it is the radiative field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha \beta}^{\rm{s}}(x)$\end{document } that should act on the particle . ( note that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \alpha \beta}^{\rm{s}}$\end{document } satisfies the same wave equation as the retarded potentials , but that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \alpha \beta}^{\rm{r}}$\end{document } is a free gravitational field that satisfies the homogeneous wave equation . ) on the world line we have 46\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h_{\mu \nu ; \lambda}^{\rm{r } } = - 4m\left({{u_{(\mu}}{r_{\nu)\rho \lambda \xi } } + { r_{\mu \rho \nu { \xi ^u}\lambda } } } \right){u^\rho}{u^\xi } + h_{\mu \nu \lambda}^{{\rm{tail}}},$$\end{document } where the tail term is given by 47\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h_{\mu \nu \lambda}^{{\rm{tail } } } = 4m\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla _ \;\;\rho \mu \prime \nu \prime}^{\;\;\rho } } \right ) } \;(z(\tau),z(\tau \prime))\;{u^{\mu \prime}}{u^{\nu \prime}}d\tau \prime .$$\end{document } when equation ( 46 ) is substituted into equation ( 45 ) we find that the terms that involve the riemann tensor cancel out , and we are left with 48\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^\mu } = - { 1 \over 2}({g^{\mu \nu } } + { u^\mu}{u^\nu})(2h_{\nu \lambda \rho}^{{\rm{tail } } } - h_{\lambda \rho \nu}^{{\rm{tail}}}){u^\lambda}{u^\rho}.$$\end{document } only the tail integral appears in the final form of the equations of motion . it involves the current position z( ) of the particle , at which all tensors with unprimed indices are evaluated , as well as all prior positions z( ) , at which tensors with primed indices are evaluated . as before the integral is cut short at = 0 to avoid the singular behaviour of the retarded green s function at coincidence . the equations of motion of equation ( 48 ) were first derived by mino , sasaki , and tanaka , and then reproduced with a different analysis by quinn and wald . detweiler and whiting have contributed the compelling interpretation that the motion is actually geodesic in a spacetime with metric \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\rm{g}}_{\alpha \beta } } = { g_{\alpha \beta } } + { h_{\alpha \beta}}$\end{document}. this metric satisfies the einstein field equations in vacuum and is perfectly smooth on the world line . this spacetime can thus be viewed as the background spacetime perturbed by a free gravitational wave produced by the particle at an earlier stage of its history . while equation ( 48 ) does indeed give the correct equations of motion for a small mass m moving in a background spacetime with metric g , the derivation outlined here leaves much to be desired to what extent should we trust an analysis based on the existence of a point mass ? fortunately , mino , sasaki , and tanaka gave two different derivations of their result , and the second derivation was concerned not with the motion of a point mass , but with the motion of a small nonrotating black hole . in this alternative derivation of the misataquwa equations , the metric of the black hole perturbed by the tidal gravitational field of the external universe is matched to the metric of the background spacetime perturbed by the moving black hole . demanding that this metric be a solution to the vacuum field equations determines the motion of the black hole : it must move according to equation ( 48 ) . this alternative derivation is entirely free of conceptual and technical pitfalls , and we conclude that the misataquwa equations can be trusted to describe the motion of any gravitating body in a curved background spacetime ( so long as the body s internal structure can be ignored ) . it is important to understand that unlike equations ( 33 ) and ( 40 ) , which are true tensorial equations , equation ( 48 ) reflects a specific choice of coordinate system and its form would not be preserved under a coordinate transformation . in other words , the misataquwa equations are not gauge invariant , and they depend upon the lorenz gauge condition \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\gamma ^{\alpha \beta}}_{;\beta } = 0$\end{document}. barack and ori have shown that under a coordinate transformation of the form x x + , where x are the coordinates of the background spacetime and is a smooth vector field of order m , the particle s acceleration changes according to a a + a[ ] , where 49\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a{[\xi ] ^\mu } = ( { \delta ^\mu}_\nu + { u^\mu}{u_\nu})\left({{{{d^2}{\xi ^\nu } } \over { d{\tau ^2 } } } + { r^\nu}_{\rho \omega \lambda}{u^\rho}{\xi ^\omega}{u^\lambda } } \right)$$\end{document } is the gauge acceleration ; \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${d^2}{\xi ^\nu}/d{\tau ^2 } = { ( { \xi ^\nu}_{;\mu}{u^\mu})_{;\rho}}{u^\rho}$\end{document } is the second covariant derivative of in the direction of the world line . this implies that the particle s acceleration can be altered at will by a gauge transformation ; could even be chosen so as to produce a = 0 , making the motion geodesic after all . this observation provides a dramatic illustration of the following point : the misataquwa equations of motion are not gauge invariant and they can not by themselves produce a meaningful answer to a well - posed physical question ; to obtain such answers it shall always be necessary to combine the equations of motion with the metric perturbation h so as to form gauge - invariant quantities that will correspond to direct observables . this point is very important and can not be over - emphasized . to concretely evaluate the self - force , whether it be for a scalar charge , an electric charge , or a point mass , is a difficult undertaking . the difficulty resides mostly with the computation of the retarded green s function for the spacetime under consideration . because green s functions are known for a very limited number of spacetimes , the self - force has so far been evaluated in a rather limited number of situations . the first evaluation of the electromagnetic self - force was carried out by dewitt and dewitt for a charge moving freely in a weakly - curved spacetime characterized by a newtonian potential 1 . ( this condition must be imposed globally , and requires the spacetime to contain a matter distribution . ) in this context the right - hand side of equation ( 33 ) reduces to the tail integral , since there is no external force acting on the charge . they found the spatial components of the self - force to be given by 50\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${f_{{\rm{em } } } } = { e^2}{m \over { { r^3}}}\hat r + { 2 \over 3}{e^2}{{dg } \over { dt}},$$\end{document } where m is the total mass contained in the spacetime , r = x is the distance from the centre of mass , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\hat r = x / r$\end{document } , and g = is the newtonian gravitational field . ( in these expressions the bold - faced symbols represent vectors in three - dimensional flat space . ) the first term on the right - hand side of equation ( 50 ) is a conservative correction to the newtonian force mg . the second term is the standard radiation - reaction force ; although it comes from the tail integral , this is the same result that would be obtained in flat spacetime if an external force mg were acting on the particle . a similar expression was obtained by pfenning and poisson for the case of a scalar charge . here 51\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${f_{{\rm{scalar } } } } = 2\xi { q^2}{m \over { { r^3}}}\hat r + { 1 \over 3}{q^2}{{dg } \over { dt}},$$\end{document } where is the coupling of the scalar field to the spacetime curvature ; the conservative term disappears when the field is minimally coupled . pfenning and poisson also computed the gravitational self - force acting on a massive particle moving in a weakly curved spacetime . the expression they obtained is in complete agreement ( within its domain of validity ) with the standard post - newtonian equations of motion . the force required to hold an electric charge in place in a schwarzschild spacetime was computed , without approximations , by smith and will . as measured by a free - falling observer momentarily at rest at the position of the charge , the total force is 52\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f = { { mm } \over { { r^2}}}{\left({1 - { { 2 m } \over r } } \right)^{- 1/2 } } - { e^2}{m \over { { r^3}}},$$\end{document } and it is directed in the radial direction . here , m is the mass of the charge , m is the mass of the black hole , and r is the charge s radial coordinate ( the expression is valid in schwarzschild coordinates ) . the first term on the right - hand side of equation ( 52 ) is the force required to keep a neutral test particle stationary in a schwarzschild spacetime ; the second term is the negative of the electromagnetic self - force , and its expression agrees with the weak - field result of equation ( 50 ) . this result is not incompatible with equation ( 51 ) , even for nonminimal coupling , because the computation of the weak - field self - force requires the presence of matter , while wiseman s scalar charge lives in a purely vacuum spacetime . the intriguing phenomenon of mass loss by a scalar charge was studied by burko , harte , and poisson in the simple context of a particle at rest in an expanding universe . for the special cases of a de sitter cosmology , or a spatially - flat matter - dominated universe , the retarded green s function could be computed , and the action of the scalar field on the particle determined , without approximations . in de sitter spacetime the particle is found to radiate all of its rest mass into monopole scalar waves . in the matter - dominated cosmology this happens only if the charge of the particle is sufficiently large ; for smaller charges the particle first loses a fraction of its mass , but then regains it eventually . in recent years a large effort has been devoted to the elaboration of a practical method to compute the ( scalar , electromagnetic , and gravitational ) self - force in the schwarzschild spacetime . this work originated with barack and ori and was pursued by barack [ 2 , 3 ] until it was put in its definitive form by barack , mino , nakano , ori , and sasaki [ 6 , 9 , 11 , 38 ] . the idea is to take advantage of the spherical symmetry of the schwarzschild solution by decomposing the retarded green s function g+(x , x ) into spherical - harmonic modes which can be computed individually . ( to be concrete i refer here to the scalar case , but the method works just as well for the electromagnetic and gravitational cases . ) from the mode - decomposition of the green s function one obtains a mode - decomposition of the field gradient , and from this subtracts a mode - decomposition of the singular field s , for which a local expression is known . this results in the radiative field r decomposed into modes , and since this field is well behaved on the world line , it can be directly evaluated at the position of the particle by summing over all modes . ( this sum converges because the radiative field is smooth ; the mode sums for the retarded or singular fields , on the other hand , do not converge . ) an extension of this method to the kerr spacetime has recently been presented [ 44 , 34 , 10 ] , and mino has devised a surprisingly simple prescription to calculate the time - averaged evolution of a generic orbit around a kerr black hole . burko computed the self - force acting on an electric charge in circular motion in flat spacetime , as well as on a scalar and electric charge kept stationary in a schwarzschild spacetime , in a spacetime that contains a spherical matter shell ( burko , liu , and soren ) , and in a kerr spacetime ( burko and liu ) . burko also computed the scalar self - force acting on a particle in circular motion around a schwarzschild black hole , a calculation that was recently revisited by detweiler , messaritaki , and whiting . barack and burko considered the case of a particle falling radially into a schwarzschild black hole , and evaluated the scalar self - force acting on such a particle ; lousto and barack and lousto , on the other hand , calculated the gravitational self - force . the main body of the review begins in section 2 with a description of the general theory of bitensors , the name designating tensorial functions of two points in spacetime . i introduce synge s world function (x , x ) and its derivatives in section 2.1 , the parallel propagator \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\alpha { \prime}}}(x,{x{\prime}})$\end{document } in section 2.3 , and the van vleck determinant (x , x ) in section 2.5 . an important portion of the theory ( covered in sections 2.2 and 2.4 ) is concerned with the expansion of bitensors when x is very close to x ; expansions such as those displayed in equations ( 23 ) and ( 24 ) are based on these techniques . the presentation in section 2 borrows heavily from synge s book and the article by dewitt and brehme . these two sources use different conventions for the riemann tensor , and i have adopted synge s conventions ( which agree with those of misner , thorne , and wheeler ) . the reader is therefore warned that formulae derived in section 2 may look superficially different from what can be found in dewitt and brehme . in section 3 i introduce a number of coordinate systems that play an important role in later parts of the review . as a warmup exercise i first construct ( in section 3.1 ) riemann normal coordinates in a neighbourhood of a reference point x. i then move on ( in section 3.2 ) to fermi normal coordinates , which are defined in a neighbourhood of a world line . the retarded coordinates , which are also based at a world line and which were briefly introduced in section 1.5 , are covered systematically in section 3.3 . the relationship between fermi and retarded coordinates is worked out in section 3.4 , which also locates the advanced point z( ) associated with a field point x. the presentation in section 3 borrows heavily from synge s book . in fact , i am much indebted to synge for initiating the construction of retarded coordinates in a neighbourhood of a world line . i have implemented his program quite differently ( synge was interested in a large neighbourhood of the world line in a weakly curved spacetime , while i am interested in a small neighbourhood in a strongly curved spacetime ) , but the idea is originally his . in section 4 i review the theory of green s functions for ( scalar , vectorial , and tensorial ) wave equations in curved spacetime . i begin in section 4.1 with a pedagogical introduction to the retarded and advanced green s functions for a massive scalar field in flat spacetime ; in this simple context the all - important hadamard decomposition of the green s function into light - cone and tail parts can be displayed explicitly . the invariant dirac functional is defined in section 4.2 along with its restrictions on the past and future null cones of a reference point x. the retarded , advanced , singular , and radiative green s functions for the scalar wave equation are introduced in section 4.3 . in sections 4.4 and 4.5 i cover the vectorial and tensorial wave equations , respectively . the presentation in section 4 is based partly on the paper by dewitt and brehme , but it is inspired mostly by friedlander s book . the reader should be warned that in one important aspect , my notation differs from the notation of dewitt and brehme : while they denote the tail part of the green s function by v(x , x ) , i have taken the liberty of eliminating the silly minus sign and i call it instead + v(x , x ) . the reader should also note that all my green s functions are normalized in the same way , with a factor of 4 multiplying a four - dimensional dirac functional of the right - hand side of the wave equation . ( the gravitational green s function is sometimes normalized with a 16 on the right - hand side . ) in section 5 i compute the retarded , singular , and radiative fields associated with a point scalar charge ( section 5.1 ) , a point electric charge ( section 5.2 ) , and a point mass ( section 5.3 ) . the first type of derivation was outlined previously : i follow detweiler and whiting and postulate that only the radiative field exerts a force on the particle . in the second type of derivation i take guidance from quinn and wald and postulate that the net force exerted on a point particle is given by an average of the retarded field over a surface of constant proper distance orthogonal to the world line this rest - frame average is easily carried out in fermi normal coordinates . the averaged field is still infinite on the world line , but the divergence points in the direction of the acceleration vector and it can thus be removed by mass renormalization . such calculations show that while the singular field does not affect the motion of the particle , it nonetheless contributes to its inertia . in section 5.4 i present an alternative derivation of the misataquwa equations of motion based on the method of matched asymptotic expansions [ 35 , 31 , 58 , 19 , 1 , 20 ] ; the derivation applies to a small nonrotating black hole instead of a point mass . the ideas behind this derivation were contained in the original paper by mino , sasaki , and tanaka , but the implementation given here , which involves the retarded coordinates of section 3.3 and displays explicitly the transformation between external and internal coordinates , is original work . i use geometrized units and adopt the notations and conventions of misner , thorne , and wheeler . in this and the following sections we will construct a number of bitensors , tensorial functions of two points in spacetime . the first is x , to which we refer as the base point , and to which we assign indices , , etc . the second is x , to which we refer as the field point , and to which we assign indices , , etc . we assume that x belongs to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}({x{\prime}})$\end{document } , the normal convex neighbourhood of x ; this is the set of points that are linked to x by a unique geodesic . the geodesic that links x to x is described by relations z( ) in which is an affine parameter that ranges from 0 to 1 ; we have z(0 ) x and z(1 ) x. to an arbitrary point z on the geodesic we assign indices , , etc . the vector t = dz / d is tangent to the geodesic , and it obeys the geodesic equation dt / d = 0 . the situation is illustrated in figure 5 . figure 5the base point x , the field point x , and the geodesic that links them . the geodesic is described by parametric relations z( ) , and t = dz / d is its tangent vector . the base point x , the field point x , and the geodesic that links them . the geodesic is described by parametric relations z( ) , and t = dz / d is its tangent vector . synge s world function is a scalar function of the base point x and the field point x. it is defined by 53\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\sigma ( x , x{\prime } ) = { 1 \over 2}({\lambda _ 1 } - { \lambda _ 0})\int\nolimits_{{\lambda _ 0}}^{{\lambda _ 1 } } { { g_{\mu \nu}}(z){t^\mu}{t^\nu}d\lambda,}$$\end{document } and the integral is evaluated on the geodesic that links x to x. you may notice that is invariant under a constant rescaling of the affine parameter , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\lambda \rightarrow \bar \lambda = a\lambda + b$\end{document } , where a and b are constants . by virtue of the geodesic equation , if the geodesic is timelike , then can be set equal to the proper time , which implies that = 1 and = ( ) . if the geodesic is spacelike , then can be set equal to the proper distance s , which implies that = 1 and = (s ) quite generally , therefore , the world function is half the squared geodesic distance between the points x and x. in flat spacetime , the geodesic linking x to x is a straight line , and = (x x)(x x ) in lorentzian coordinates . the world function (x , x ) can be differentiated with respect to either argument . we let = /x be its partial derivative with respect to x , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ { \alpha \prime } } = \partial \sigma /\partial { x^{\alpha \prime}}$\end{document } its partial derivative with respect to x. it is clear that behaves as a dual vector with respect to tensorial operations carried out at x , but as a scalar with respect to operations carried out x. similarly , is a scalar at x but a dual vector at x. we let be the covariant derivative of with respect to x ; this is a rank-2 tensor at x and a scalar at x. because is a scalar at x , we have that this tensor is symmetric : = . similarly , we let \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ { \alpha { \beta { \prime } } } } \equiv { \partial _ { { \beta { \prime}}}}{\sigma _ \alpha } = { \partial ^2}\sigma/\partial { x^{{\beta { \prime}}}}\partial { x^\alpha}$\end{document } be the partial derivative of with respect to x ; this is a dual vector both at x and x. we can also define \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ { { \alpha { \prime}}\beta } } \equiv { \partial _ \beta}{\sigma _ { { \alpha { \prime } } } } = { \partial ^2}\sigma/\partial { x^\beta}\partial { x^{{\alpha { \prime}}}}$\end{document } to be the partial derivative of with respect to x. because partial derivatives commute , these bitensors are equal : = . finally , we let \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ { { \alpha { \prime}}{\beta { \prime } } } } \equiv { \nabla _ { { \beta { \prime}}}}{\sigma _ { { \alpha { \prime}}}}$\end{document } be the covariant derivative of with respect to x ; this is a symmetric rank-2 tensor at x and a scalar at x. the notation is easily extended to any number of derivatives . for example , we let , which is a rank-3 tensor at x and a dual vector at x. this bitensor is symmetric in the pair of indices and , but not in the pairs and , nor and . because is here an ordinary partial derivative with respect to x , the bitensor is symmetric in any pair of indices involving . the ordering of the primed index relative to the unprimed indices is therefore irrelevant : the same bitensor can be written as or or , making sure that the ordering of the unprimed indices is not altered . (x , x ) satisfy the property 54\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\omega _ { \ldots ; \beta \alpha{\prime } \ldots } } = { \omega _ { \ldots ; \alpha{\prime}\beta \ldots}},$$\end{document } in which stands for any combination of primed and unprimed indices . ; with respect to the pair and . this is most easily done by adopting fermi normal coordinates ( see section 3.2 ) adapted to the geodesic , and setting the connection to zero both at x and x. in these coordinates , the bitensor ; is the partial derivative of with respect to x , and ; is obtained by taking an additional partial derivative with respect to x. these two operations commute , and equation ( 54 ) then follows by further differentiation with respect to either x or x. the message of equation ( 54 ) , when applied to derivatives of the world function , is that while the ordering of the primed and unprimed indices relative to themselves is important , their ordering with respect to each other is arbitrary . for example , = = . we can compute by examining how varies when the field point x moves . we let the new field point be x + x , and (x + x , x ) (x , x ) is the corresponding variation of the world function . we let + be the unique geodesic that links x + x to x ; it is described by relations z( ) + z( ) , in which the affine parameter is scaled in such a way that it runs from 0 to 1 also on the new geodesic . working to first order in the variations , equation ( 53 ) implies \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta \sigma = \delta \lambda \int\nolimits_{{\lambda _ 0}}^{{\lambda _ 1 } } { \left({{g_{\mu \nu}}{{\dot z}^\mu}\delta { { \dot z}^\nu } + { 1 \over 2}{g_{\mu \nu , \lambda}}{{\dot z}^\mu}{{\dot z}^\nu}\;\delta { z^\lambda } } \right)d\lambda,}$$\end{document } where = 1 0 , an overdot indicates differentiation with respect to , and the metric and its derivatives are evaluated on . integrating the first term by parts gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta \sigma = \delta \lambda [ { g_{\mu \nu}}{\dot z^\mu}\delta { z^\nu}]_{{\lambda _ 0}}^{{\lambda _ 1 } } - \delta \lambda \int\nolimits_{{\lambda _ 0}}^{{\lambda _ 1 } } { ( { g_{\mu \nu}}{{\ddot z}^\nu } + { \gamma _ { \mu \nu \lambda}}{{\dot z}^\nu}{{\dot z}^\lambda } + { \gamma _ { \mu \nu \lambda}}{{\dot z}^\nu}{{\dot z}^\lambda})\;\delta { z^\mu}d\lambda.}$$\end{document } the integral vanishes because z( ) satisfies the geodesic equation . we are left with = gtx , or 55\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\sigma _ \alpha}(x , x{\prime } ) = ( { \lambda _ 1 } - { \lambda _ 0}){g_{\alpha \beta}}{t^\beta},$$\end{document } in which the metric and the tangent vector are both evaluated at x. apart from a factor , we see that (x , x ) is equal to the geodesic s tangent vector at x. if in equation ( 55 ) we replace x by a generic point z( ) on , and if we correspondingly replace 1 by , we obtain (z , x ) = ( 0)t ; we therefore see that (z , x ) is a rescaled tangent vector on the geodesic . a virtually identical calculation reveals how varies under a change of base point x. here the variation of the geodesic is such that z(0 ) = x and z(1 ) = x = 0 , and we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\delta \sigma = - \delta \lambda { g_{{\alpha { \prime}}{\beta { \prime}}}}{t^{{\alpha { \prime}}}}\delta { x^{{\beta { \prime}}}}$\end{document}. this shows that 56\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\sigma _ { \alpha{\prime}}}(x , x{\prime } ) = - ( { \lambda _ 1 } - { \lambda _ 0}){g_{\alpha{\prime}\beta{\prime}}}{t^{\beta{\prime}}},$$\end{document } in which the metric and the tangent vector are both evaluated at x. apart from a factor , we see that ( x , x ) is minus the geodesic s tangent vector at x. it is interesting to compute the norm of . according to equation ( 55 ) we have g = ( )gtt = ( ). according to equation ( 53 ) , this is equal to 2. we have obtained 57\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^{\alpha \beta}}{\sigma _ \alpha}{\sigma _ \beta } = 2\sigma,$$\end{document } and similarly 58\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^{\alpha{\prime}\beta{\prime}}}{\sigma _ { \alpha{\prime}}}{\sigma _ { \beta{\prime } } } = 2\sigma.$$\end{document } these important relations will be the starting point of many computations to be described below . we note that in flat spacetime , = (x x ) and = (x x ) in lorentzian coordinates . from this it follows that = = = = , and finally , g = 4 = g . if the base point x is kept fixed , can be considered to be an ordinary scalar function of x. according to equation ( 57 ) , this function is a solution to the nonlinear differential equation g = . suppose that we are presented with such a scalar field . an additional differentiation of the defining equation reveals that the vector satisfies 59\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\sigma ^\alpha}_{;\beta}{\sigma ^\beta } = { \sigma ^\alpha},$$\end{document } which is the geodesic equation in a non - affine parameterization . the geodesics are timelike where < 0 , they are spacelike where > 0 , and they are null where = 0 . here , the vector 60\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u^\alpha } = { { { \sigma ^\alpha } } \over { \vert 2\sigma { \vert^{1/2}}}}$$\end{document } is a normalized tangent vector that satisfies the geodesic equation in affine - parameter form : u;u = 0 . the parameter is then proper time . if t denotes the original parameterization of the geodesics , we have that dt / d = 2 , and we see that the original parameterization is singular at = 0 . in the affine parameterization , the expansion of the congruence is calculated to be 61\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\theta = { { { \theta ^{\ast } } } \over { \vert 2\sigma { \vert ^{1/2}}}},\quad \quad { \theta ^{\ast } } = { \sigma ^\alpha}_{;\alpha } - 1,$$\end{document } where t = ( v)(d / dt)(v ) is the expansion in the original parameterization ( v is the congruence s cross - sectional volume ) . while t is well behaved in the limit 0 ( we shall see below that t 3 ) , we have that . this means that the point x at which = 0 is a caustic of the congruence : all geodesics emanate from this point . these considerations , which all follow from a postulated relation g = , are clearly compatible with our preceding explicit construction of the world function . it is useful to determine the limiting behaviour of the bitensors as x approaches x. we introduce the notation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left [ { \omega \ldots } \right ] = \mathop { \lim } \limits_{x \to x ' } \;\omega \ldots \left ( { x , x ' } \right ) = \;\text{a}\;\text{tensor}\;\text{at}\;x'$$\end{document } to designate the limit of any bitensor (x , x ) as x approaches x ; this is called the coincidence limit of the bitensor . we assume that the coincidence limit is a unique tensorial function of the base point x , independent of the direction in which the limit is taken . in other words , if the limit is computed by letting 0 after evaluating ( z , x ) as a function of on a specified geodesic , it is assumed that the answer does not depend on the choice of geodesic . from equations ( 53 , 55 , 56 ) we already have 62\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[\sigma ] = 0,\quad \quad [ { \sigma _ \alpha } ] = [ { \sigma _ { \alpha{\prime } } } ] = 0.$$\end{document } additional results are obtained by repeated differentiation of the relations ( 57 ) and ( 58 ) . for example , equation ( 57 ) implies = g = , or ( g )t = 0 after using equation ( 55 ) . from the assumption stated in the preceding paragraph , becomes independent of t in the limit x x , and we arrive at [ ] = g. by very similar calculations we obtain all other coincidence limits for the second derivatives of the world function . the results are 63\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{\sigma _ { \alpha \beta } } ] = [ { \sigma _ { \alpha{\prime}\beta{\prime } } } ] = { g_{\alpha{\prime}\beta{\prime}}},\quad \quad [ { \sigma _ { \alpha \beta{\prime } } } ] = [ { \sigma _ { \alpha{\prime}\beta } } ] = - { g_{\alpha{\prime}\beta{\prime}}}.$$\end{document } from these relations we infer that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{\sigma ^\alpha}_\alpha ] = 4$\end{document } , so that [ t ] = 3 , where t was defined in equation ( 61 ) . to generate coincidence limits of bitensors involving primed indices , it is efficient to invoke synge s rule , 64\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left [ { \sigma \ldots \alpha ' } \right ] = { \left [ { \sigma \ldots } \right]_{;\alpha ' } } - \left [ { \sigma \ldots \alpha } \right],$$\end{document } in which designates any combination of primed and unprimed indices ; this rule will be established below . for example , according to synge s rule we have [ ] = [ ]; [ ] , and since the coincidence limit of is zero , this gives us [ ] = [ ] = g , as was stated in equation ( 63 ) . similarly , [ ] = [ ]; [ ] = [ ] = g. the results of equation ( 63 ) can thus all be generated from the known result for [ ] . the coincidence limits of equation ( 63 ) were derived from the relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ \alpha } = { \sigma ^\delta}_\alpha { \sigma _ \delta}$\end{document}. we now differentiate this twice more and obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ { \alpha \beta \gamma } } = { \sigma ^\delta}_{\alpha \beta \gamma}{\sigma _ \delta } + { \sigma ^\delta}_{\alpha \beta}{\sigma _ { \delta \gamma } } + { \sigma ^\delta}_{\alpha \gamma}{\sigma _ { \delta \beta } } + { \sigma ^\delta}_\alpha { \sigma _ { \delta \beta \gamma}}$\end{document}. at coincidence we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{\sigma _ { \alpha \beta \gamma } } ] = [ { \sigma ^\delta}_{\alpha \beta}]{g_{\delta{\prime}\gamma{\prime } } } + [ { \sigma ^\delta}_{\alpha \gamma}]{g_{\delta{\prime}\beta{\prime } } } + { \delta ^{\delta{\prime}}}_{\alpha{\prime}}[{\sigma _ { \delta \beta \gamma}}],$$\end{document } or [ ] + [ ] = 0 if we recognize that the operations of raising or lowering indices and taking the limit x x commute . noting the symmetries of , this gives us [ ] + [ ] = 0 , or \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$2[{\sigma _ { \alpha \beta \gamma } } ] - [ { r^\delta}_{\alpha \beta \gamma}{\sigma _ \delta } ] = 0,\,{\rm{or}}\,{\rm{2[}}{\sigma _ { \alpha \beta \gamma } } ] = { r^{{\delta { \prime}}}}_{{\alpha { \prime}}{\beta { \prime}}{\gamma { \prime}}}[{\sigma _ { { \delta { \prime}}}}]$\end{document}. since the last factor is zero , we arrive at 65\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{\sigma _ { \alpha \beta \gamma } } ] = [ { \sigma _ { \alpha \beta \gamma{\prime } } } ] = [ { \sigma _ { \alpha \beta{\prime}\gamma{\prime } } } ] = [ { \sigma _ { \alpha{\prime}\beta{\prime}\gamma{\prime } } } ] = 0.$$\end{document } the last three results were derived from [ ] = 0 by employing synge s rule . we now differentiate the relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ \alpha } = { \sigma ^\delta}_\alpha { \sigma _ \delta}$\end{document } three times and obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\sigma _ { \alpha \beta \gamma \delta } } = { \sigma ^\epsilon}_{\alpha \beta \gamma \delta}{\sigma _ \epsilon } + { \sigma ^\epsilon}_{\alpha \beta \gamma}{\sigma _ { \epsilon \delta } } + { \sigma ^\epsilon}_{\alpha \beta \delta}{\sigma _ { \epsilon \gamma } } + { \sigma ^\epsilon}_{\alpha \gamma \delta}{\sigma _ { \epsilon \beta } } + { \sigma ^\epsilon}_{\alpha \beta}{\sigma _ { \epsilon \gamma \delta } } + { \sigma ^\epsilon}_{\alpha \gamma}{\sigma _ { \epsilon \beta \delta } } + { \sigma ^\epsilon}_{\alpha \delta}{\sigma _ { \epsilon \beta \gamma } } + { \sigma ^\epsilon}_\alpha { \sigma _ { \epsilon \beta \gamma \delta}}.$$\end{document } at coincidence this reduces to [ ] + [ ] + [ ] = 0 . to simplify the third term we differentiate ricci s identity \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ { \alpha \gamma \beta } } = { \sigma _ { \alpha \beta \gamma } } - { r^\epsilon}_{\alpha \beta \gamma}{\sigma _ \epsilon}$\end{document } with respect to x and then take the coincidence limit . this gives us \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{\sigma _ { \alpha \gamma \beta \delta } } ] = [ { \sigma _ { \alpha \beta \gamma \delta } } ] + { r_{{\alpha { \prime}}{\delta { \prime}}{\beta { \prime}}{\gamma { \prime}}}}$\end{document}. the same manipulations on the second term give \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{\sigma _ { \alpha \delta \beta \gamma } } ] = [ { \sigma _ { \alpha \beta \delta \gamma } } ] + { r_{{\alpha { \prime}}{\gamma { \prime}}{\beta { \prime}}{\delta { \prime}}}}$\end{document}. using the identity \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ { \alpha \beta \delta \gamma } } = { \sigma _ { \alpha \beta \gamma \delta } } - { r^\epsilon}_{\alpha \gamma \delta}{\sigma _ { \epsilon \beta } } - { r^\epsilon}_{\beta \gamma \delta}{\sigma _ { \alpha \epsilon}}$\end{document } and the symmetries of the riemann tensor , it is then easy to show that [ ] = [ ] . gathering the results , we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$3[{\sigma _ { \alpha \beta \gamma \delta } } ] + { r_{{\alpha { \prime}}{\gamma { \prime}}{\beta { \prime}}{\delta { \prime } } } } + { r_{{\alpha { \prime}}{\delta { \prime}}{\beta { \prime}}{\gamma { \prime } } } } = 0$\end{document } , and synge s rule allows us to generalize this to any combination of primed and unprimed indices . our final results are 66\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { \;\;\;\;[{\sigma _ { \alpha \beta \gamma \delta } } ] = - { 1 \over 3}({r_{\alpha{\prime}\beta{\prime}\gamma{\prime}\delta{\prime } } } + { r_{\alpha{\prime}\delta{\prime}\beta{\prime}\gamma{\prime } } } ) } , \\ { \;\;\;[{\sigma _ { \alpha \beta \gamma \delta{\prime } } } ] = { 1 \over 3}({r_{\alpha{\prime}\gamma{\prime}\beta{\prime}\delta{\prime } } } + { r_{\alpha{\prime}\delta{\prime}\beta{\prime}\gamma{\prime}}})},\;\ ; \\ { \;[{\sigma _ { \alpha \beta{\prime}\gamma{\prime}\delta{\prime } } } ] = - { 1 \over 3}({r_{\alpha{\prime}\gamma{\prime}\beta{\prime}\delta{\prime } } } + { r_{\alpha{\prime}\delta{\prime}\beta{\prime}\gamma{\prime } } } ) } , \\ { \;[{\sigma _ { \alpha \beta{\prime}\gamma{\prime}\delta{\prime } } } ] = - { 1 \over 3}({r_{\alpha{\prime}\beta{\prime}\gamma{\prime}\delta{\prime } } } + { r_{\alpha{\prime}\gamma{\prime}\beta{\prime}\delta{\prime } } } ) } , \\ { [ { \sigma _ { \alpha{\prime}\beta{\prime}\gamma{\prime}\delta{\prime } } } ] = - { 1 \over 3}({r_{\alpha{\prime}\gamma{\prime}\beta{\prime}\delta{\prime } } } + { r_{\alpha{\prime}\delta{\prime}\beta{\prime}\gamma{\prime}}})}. \\ \end{array}$$\end{document } we begin with any bitensor ab(x , x ) in which a = is a multi - index that represents any number of unprimed indices , and b = a multi - index that represents any number of primed indices . ( it does not matter whether the primed and unprimed indices are segregated or mixed . ) on the geodesic that links x to x we introduce an ordinary tensor p(z ) where m is a multi - index that contains the same number of indices as a. this tensor is arbitrary , but we assume that it is parallel transported on ; this means that it satisfies p;t = 0 at x. similarly , we introduce an ordinary tensor q(z ) in which n contains the same number of indices as b. this tensor is arbitrary , but we assume that it is parallel transported on ; at x it satisfies \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${q^{{b{\prime}}}}_{;{\alpha { \prime}}}{t^{{\alpha { \prime } } } } = 0$\end{document}. with , p , and q we form a biscalar h ( x , x ) defined by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h(x , x{\prime } ) = { \omega _ { ab{\prime}}}(x , x{\prime}){p^a}(x){q^{b{\prime}}}(x{\prime}).$$\end{document } having specified the geodesic that links x to x , we can consider h to be a function of 0 and 1 . if 1 is not much larger than 0 ( so that x is not far from x ) , we can express h(1 , 0 ) as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h({\lambda _ 1},{\lambda _ 0 } ) = h({\lambda _ 0},{\lambda _ 0 } ) + ( { \lambda _ 1 } - { \lambda _ 0}){\left . { { { \partial h } \over { \partial { \lambda _ 1 } } } } \right\vert_{{\lambda _ 1 } = { \lambda _ 0 } } } + \ldots$$\end{document } alternatively , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h({\lambda _ 1},{\lambda _ 0 } ) = h({\lambda _ 1},{\lambda _ 1 } ) - ( { \lambda _ 1 } - { \lambda _ 0}){\left . { { { \partial h } \over { \partial { \lambda _ 0 } } } } \right\vert_{{\lambda _ 0 } = { \lambda _ 1 } } } + \ldots,$$\end{document } and these two expressions give \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${d \over { d{\lambda _ 0}}}h({\lambda _ 0},{\lambda _ 0 } ) = { \left . { { { \partial h } \over { \partial { \lambda _ 0 } } } } \right\vert_{{\lambda _ 0 } = { \lambda _ 1 } } } + { \left . { { { \partial h } \over { \partial { \lambda _ 1 } } } } \right\vert_{{\lambda _ 1 } = { \lambda _ 0}}},$$\end{document } because the left - hand side is the limit of [ h(1 , 1 ) h(0 , 0)]/(1 0 ) when 1 0 . the partial derivative of h with respect to 0 is equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega _ { a{b{\prime}};{\alpha { \prime}}}}{t^{{\alpha { \prime}}}}{p^a}{q^{{b{\prime}}}}$\end{document } , and in the limit this becomes \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{\omega _ { a{b{\prime}};{\alpha { \prime}}}}]{t^{{\alpha { \prime}}}}{p^{{a{\prime}}}}{q^{{b{\prime}}}}$\end{document}. similarly , the partial derivative of h with respect to 1 is ab;tpq , and in the limit 1 0 this becomes [ ab;]tp q. finally , h(0 , 0 ) = [ ab]pq , and its derivative with respect to 0 is [ ab];t p q. gathering the results we find that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left\{{{{[{\omega _ { ab{\prime}}}]}_{;\alpha{\prime } } } - [ { \omega _ { ab{\prime};\alpha{\prime } } } ] - [ { \omega _ { ab{\prime};\alpha } } ] } \right\}{t^{\alpha{\prime}}}{p^{a{\prime}}}{q^{b{\prime } } } = 0,$$\end{document } and the final statement of synge s rule , 67\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${[{\omega _ { ab{\prime}}}]_{;\alpha{\prime } } } = [ { \omega _ { ab{\prime};\alpha{\prime } } } ] + [ { \omega _ { ab{\prime};\alpha}}],$$\end{document } follows from the fact that the tensors p and q , and the direction of the selected geodesic , are all arbitrary . equation ( 67 ) reduces to equation ( 64 ) when is substituted in place of ab. on the geodesic that links x to x we introduce an orthonormal basis \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{\rm{a}}^\mu ( z)$\end{document } that is parallel transported on the geodesic . the frame indices3 a , b , , run from 0 to 3 , and the frame vectors satisfy 68\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\mu \nu}}e_{\rm{a}}^\mu e_{\rm{b}}^\mu = { \eta _ { { \rm{ab}}}},\quad \quad { { de_{\rm{a}}^\mu } \over { d\lambda } } = 0,$$\end{document } where ab = diag(1 , 1 , 1 , 1 ) is the minkowski metric ( which we shall use to raise and lower frame indices ) . we have the completeness relations 69\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^{\mu \nu } } = { \eta ^{{\rm{ab}}}}e_{\rm{a}}^\mu e_{\rm{b}}^\nu,$$\end{document } and we define a dual tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_\mu ^{\rm{a}}(z)$\end{document } by 70\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$e_\mu ^{\rm{a } } = { \eta ^{{\rm{ab}}}}{g_{\mu \nu}}e_{\rm{b}}^\nu;$$\end{document } this is also parallel transported on . in terms of the dual tetrad the completeness relations take the form 71\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\mu \nu } } = { \eta _ { { \rm{ab}}}}e_\mu ^{\rm{a}}e_\nu ^{\rm{b}},$$\end{document } and it is easy to show that the tetrad and its dual satisfy \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_\mu ^{\rm{a}}e_{\rm{b}}^\mu = { \delta ^{\rm{a}}}_{\rm{b}}$\end{document}. equations ( 68 , 69 , 70 , 71 ) hold everywhere on . in particular , with an appropriate change of notation they hold at x and x ; for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\alpha \beta } } = { \eta _ { { \rm{ab}}}}e_\alpha ^{\rm{a}}e_\beta ^{\rm{b}}$\end{document } is the metric at x. any vector field a(z ) on can be decomposed in the basis \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{\rm{a}}^\mu : { a^\mu } = { a^{\rm{a}}}e_{\rm{a}}^\mu$\end{document } , and the vector s frame components are given by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^{\rm{a } } } = { a^\mu}e_\mu ^{\rm{a}}$\end{document}. if a is parallel transported on the geodesic , then the coefficients a are constants . the vector at x can then be expressed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^\alpha } = ( { a^{{\alpha { \prime}}}}e_{{\alpha { \prime}}}^{\rm{a}})e_{\rm{a}}^\alpha$\end{document } , or 72\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^\alpha}(x ) = { g^\alpha}_{\alpha{\prime}}(x , x{\prime}){a^{\alpha{\prime}}}(x{\prime}),\quad \quad { g^\alpha}_{\alpha{\prime}}(x , x{\prime } ) \equiv e_{\rm{a}}^\alpha ( x)e_{\alpha{\prime}}^{\rm{a}}(x{\prime}).$$\end{document } the object \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\alpha { \prime } } } = e_{\rm{a}}^\alpha e_{{\alpha { \prime}}}^{\rm{a}}$\end{document } is the parallel propagator : it takes a vector at x and parallel - transports it to x along the unique geodesic that links these points . similarly , we find that 73\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^{\alpha{\prime}}}(x{\prime } ) = { g^{\alpha{\prime}}}_\alpha ( x{\prime},x){a^\alpha}(x),\quad \quad { g^{\alpha{\prime}}}_\alpha ( x{\prime},x ) \equiv e_{\rm{a}}^{\alpha{\prime}}(x{\prime})e_\alpha ^{\rm{a}}(x),$$\end{document } and we see that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{{\alpha { \prime}}}}_\alpha = e_{\rm{a}}^{{\alpha { \prime}}}e_\alpha ^{\rm{a}}$\end{document } performs the inverse operation : it takes a vector at x and parallel - transports it back to x. clearly , 74\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^\alpha}_{\alpha{\prime}}{g^{\alpha{\prime}}}_\beta = { \delta ^\alpha}_\beta , \quad \quad { g^{\alpha{\prime}}}_\alpha { g^\alpha}_{\beta{\prime } } = { \delta ^{\alpha{\prime}}}_{\beta{\prime}},$$\end{document } and these relations formally express the fact that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{{\alpha { \prime}}}}_\alpha$\end{document } is the inverse of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\alpha { \prime}}}$\end{document}. the relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\alpha { \prime } } } = e_{\rm{a}}^\alpha e_{{\alpha { \prime}}}^{\rm{a}}$\end{document } can also be expressed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_\alpha}^{{\alpha { \prime } } } = e_\alpha ^{\rm{a}}e_{\rm{a}}^{{\alpha { \prime}}}$\end{document } , and this reveals that 75\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_\alpha}^{\alpha{\prime}}(x , x{\prime } ) = { g^{\alpha{\prime}}}_\alpha = { g^{\alpha{\prime}}}_\alpha ( x , x{\prime}),\quad \quad { g_{\alpha{\prime}}}^\alpha ( x , x{\prime } ) = { g^\alpha}_{\alpha{\prime}}(x , x{\prime}).$$\end{document } the ordering of the indices , and the ordering of the arguments , are therefore arbitrary . the action of the parallel propagator on tensors of arbitrary ranks is easy to figure out . for example , suppose that the dual vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${p_\mu } = { p_a}e_\mu ^a$\end{document } is parallel transported on . then the frame components \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${p_{\rm{a } } } = { p_\mu}e_{\rm{a}}^\mu$\end{document } are constants , and the dual vector at x can be expressed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${p_\alpha } = ( { p_{{\alpha { \prime}}}}e_{\rm{a}}^{{\alpha { \prime}}})e_{\rm{a}}^\alpha$\end{document } , or 76\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${p_\alpha}(x ) = { g^{\alpha{\prime}}}_\alpha ( x{\prime},x){p_{\alpha{\prime}}}(x{\prime}).$$\end{document } it is therefore the inverse propagator \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{{\alpha { \prime}}}}_\alpha$\end{document } that takes a dual vector at x and parallel - transports it to x. as another example , it is easy to show that a tensor \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^{\alpha \beta}}$\end{document } at x obtained by parallel transport from x must be given by 77\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^{\alpha \beta}}(x ) = { g^\alpha}_{\alpha{\prime}}(x , x{\prime}){g^\beta}_{\beta{\prime}}(x , x{\prime}){a^{\alpha{\prime}\beta{\prime}}}(x{\prime}).$$\end{document } here we need two occurrences of the parallel propagator , one for each tensorial index . because the metric tensor is covariantly constant , it is automatically parallel transported on , and a special case of equation ( 77 ) is therefore \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\alpha \beta } } = { g^{{\alpha { \prime}}}}_\alpha { g^{{\beta { \prime}}}}_\beta { g_{{\alpha { \prime}}{\beta { \prime}}}}$\end{document}. because the basis vectors are parallel transported on , they satisfy \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{{\rm{a;}}\beta}^\alpha { \sigma ^\beta } = 0$\end{document } at x and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{{\rm{a;}}{\beta { \prime}}}^{{\alpha { \prime}}}{\sigma ^{{\beta { \prime } } } } = 0$\end{document } at x. this immediately implies that the parallel propagators must satisfy 78\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^\alpha}_{\alpha{\prime};\beta}{\sigma ^\beta } = { g^\alpha}_{\alpha{\prime};\beta{\prime}}{\sigma ^{\beta{\prime } } } = 0,\quad \quad { g^{\alpha{\prime}}}_{\alpha ; \beta}{\sigma ^\beta } = { g^{\alpha{\prime}}}_{\alpha ; \beta{\prime}}{\sigma ^{\beta{\prime } } } = 0.$$\end{document } another useful property of the parallel propagator follows from the fact that if t = dz / d is tangent to the geodesic connecting x to x , then \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${t^\alpha } = { g^\alpha}_{{\alpha { \prime}}}{t^{{\alpha { \prime}}}}$\end{document}. using equations ( 55 ) and ( 56 ) , this observation gives us the relations 79\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\sigma _ \alpha } = - { g^{\alpha{\prime}}}_\alpha { \sigma _ { \alpha{\prime}}},\quad \quad { \sigma _ { \alpha{\prime } } } = - { g^\alpha}_{\alpha{\prime}}{\sigma _ \alpha}.$$\end{document } equation ( 72 ) and the completeness relations of equations ( 69 ) or ( 71 ) imply that 80\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left [ { { g^\alpha}_{\beta{\prime } } } \right ] = { \delta ^{\alpha{\prime}}}_{\beta{\prime}}.$$\end{document } other coincidence limits are obtained by differentiation of equations ( 78 ) . for example , the relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\beta { \prime}};\gamma}{\sigma ^\gamma } = 0$\end{document } implies \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\beta { \prime}};\gamma \delta}{\sigma ^\gamma } + { g^\alpha}_{{\beta { \prime}};\gamma}{\sigma ^\gamma}_\delta = 0$\end{document } , and at coincidence we have 81\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left [ { { g^\alpha}_{\beta{\prime};\gamma } } \right ] = \left [ { { g^\alpha}_{\beta{\prime};\gamma{\prime } } } \right ] = 0;$$\end{document } the second result was obtained by applying synge s rule on the first result . further differentiation gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^\alpha}_{\beta{\prime};\gamma \delta \epsilon}{\sigma ^\gamma } + { g^\alpha}_{\beta{\prime};\gamma \delta}{\sigma ^\gamma}_\epsilon + { g^\alpha}_{\beta{\prime};\gamma \epsilon}{\sigma ^\gamma}_\delta + { g^\alpha}_{\beta{\prime};\gamma}{\sigma ^\gamma}_{\delta \epsilon } = 0,$$\end{document } and at coincidence we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{g^\alpha}_{{\beta { \prime}};\gamma \delta } ] + [ { g^\alpha}_{{\beta { \prime}};\delta \gamma } ] = 0$\end{document } , or \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$2[{g^\alpha}_{{\beta { \prime}};\gamma \delta } ] + { r^{{\alpha { \prime}}}}_{{\beta { \prime}}{\gamma { \prime}}{\delta { \prime } } } = 0$\end{document}. the coincidence limit for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\beta { \prime}};\gamma { \delta { \prime } } } = { g^\alpha}_{{\beta { \prime}};{\delta { \prime}}\gamma}$\end{document } can then be obtained from synge s rule , and an additional application of the rule gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{g^\alpha}_{{\beta { \prime}};{\gamma { \prime}}{\delta { \prime}}}]$\end{document}. our results are 82\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { \left [ { { g^\alpha}_{\beta{\prime};\gamma \delta } } \right ] = - { 1 \over 2}{r^{\alpha{\prime}}}_{\beta{\prime}\gamma{\prime}\delta{\prime } } , } & { \left [ { { g^\alpha}_{\beta{\prime};\gamma \delta{\prime } } } \right ] = { 1 \over 2}{r^{\alpha{\prime}}}_{\beta{\prime}\gamma{\prime}\delta{\prime } } } , \\ { \left [ { { g^\alpha}_{\beta{\prime};\gamma{\prime}\delta } } \right ] = - { 1 \over 2}{r^{\alpha{\prime}}}_{\beta{\prime}\gamma{\prime}\delta{\prime } } , } & { \left [ { { g^\alpha}_{\beta{\prime};\gamma{\prime}\delta{\prime } } } \right ] = { 1 \over 2}{r^{\alpha{\prime}}}_{\beta{\prime}\gamma{\prime}\delta{\prime}}}. \\ \end{array}$$\end{document } we would like to express a bitensor ( x , x ) near coincidence as an expansion in powers of ( x , x ) , the closest analogue in curved spacetime to the flat - spacetime quantity ( x x ) . for concreteness we shall consider the case of rank-2 bitensor , and for the moment we will assume that the bitensor s indices all refer to the base point x. the expansion we seek is of the form 83\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\omega _ { \alpha{\prime}\beta{\prime}}}(x , x{\prime } ) = { a_{\alpha{\prime}\beta{\prime } } } + { a_{\alpha{\prime}\beta{\prime}\gamma{\prime}}}{\sigma ^{\gamma{\prime } } } + { 1 \over 2}{a_{\alpha{\prime}\beta{\prime}\gamma{\prime}\delta{\prime}}}{\sigma ^{\gamma{\prime}}}{\sigma ^{\delta{\prime } } } + \mathcal{o}({\epsilon ^3}),$$\end{document } in which the expansion coefficients a , a , and a are all ordinary tensors at x ; this last tensor is symmetric in the pair of indices and , and measures the size of a typical component of . to find the expansion coefficients we differentiate equation ( 83 ) repeatedly and take coincidence limits . equation ( 83 ) immediately implies \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{\omega _ { { \alpha { \prime}}{\beta { \prime } } } } ] = { a_{{\alpha { \prime}}{\beta { \prime}}}}$\end{document}. after one differentiation we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega _ { { \alpha { \prime}}{\beta { \prime}};{\gamma { \prime } } } } = { a_{{\alpha { \prime}}{\beta { \prime}};{\gamma { \prime } } } } + { a_{{\alpha { \prime}}{\beta { \prime}}{\epsilon { \prime}};{\gamma { \prime}}}}{\sigma ^{{\epsilon { \prime } } } } + { a_{{\alpha { \prime}}{\beta { \prime}}{\epsilon { \prime}}}}{\sigma ^{{\epsilon { \prime}}}}_{{\gamma { \prime}}}{1 \over 2}{a_{{\alpha { \prime}}{\beta { \prime}}{\epsilon { \prime}}{\iota { \prime}};{\gamma { \prime}}}}{\sigma ^{{\epsilon { \prime}}}}{\sigma ^{{\iota { \prime } } } } + { a_{{\alpha { \prime}}{\beta { \prime}}{\epsilon { \prime}}{\iota { \prime}}}}{\sigma ^{{\epsilon { \prime}}}}{\sigma ^{{\iota { \prime}}}}_{{\gamma { \prime } } } + o({\epsilon ^2})$\end{document } , and at coincidence this reduces to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{\omega _ { { \alpha { \prime}}{\beta { \prime}};{\gamma { \prime } } } } ] = { a_{{\alpha { \prime}}{\beta { \prime}};{\gamma { \prime } } } } + { a_{{\alpha { \prime}}{\beta { \prime}}{\gamma { \prime}}}}$\end{document}. taking the coincidence limit after two differentiations yields \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{\omega _ { { \alpha { \prime}}{\beta { \prime}};{\gamma { \prime}}{\delta { \prime } } } } ] = { a_{{\alpha { \prime}}{\beta { \prime}};{\gamma { \prime}}{\delta { \prime } } } } + { a_{{\alpha { \prime}}{\beta { \prime}}{\gamma { \prime}};{\delta { \prime } } } } + { a_{{\alpha { \prime}}{\beta { \prime}}{\delta { \prime}};{\gamma { \prime } } } } + { a_{{\alpha { \prime}}{\beta { \prime}}{\gamma { \prime}}{\delta { \prime}}}}$\end{document}. the expansion coefficients are therefore 84\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{a_{\alpha \prime \beta \prime } } = [ { \omega _ { \alpha \prime \beta \prime}}],\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { { a_{\alpha \prime \beta \prime \gamma \prime } } = [ { \omega _ { \alpha \prime \beta \prime ; \gamma \prime } } ] - { a_{\alpha \prime \beta \prime ; \gamma \prime}},\quad \quad \quad \quad \quad \quad \quad \quad } \\ { { a_{\alpha \prime \beta \prime \gamma \prime \delta \prime } } = [ { \omega _ { \alpha \prime \beta \prime ; \gamma \prime \delta \prime } } ] - { a_{\alpha \prime \beta \prime ; \gamma \prime \delta \prime } } - { a_{\alpha \prime \beta \prime \gamma \prime ; \delta \prime } } - { a_{\alpha \prime \beta \prime \delta \prime ; \gamma \prime}}. } \\ \end{array}$$\end{document } these results are to be substituted into equation ( 83 ) , and this gives us (x , x ) to second order in . suppose now that the bitensor is , with one index referring to x and the other to x. the previous procedure can be applied directly if we introduce an auxiliary bitensor \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\tilde \omega}_{{\alpha { \prime}}{\beta { \prime } } } } \equiv { g^\beta}_{{\beta { \prime}}}{\omega _ { { \alpha { \prime}}\beta}}$\end{document } whose indices all refer to the point x. then \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\tilde \omega}_{{\alpha { \prime}}{\beta { \prime}}}}$\end{document } can be expanded as in equation ( 83 ) , and the original bitensor is reconstructed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega _ { { \alpha { \prime}}\beta } } \equiv { g^{{\beta { \prime}}}}_\beta { { \tilde \omega}_{{\alpha { \prime}}{\beta { \prime}}}}$\end{document } , or 85\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\omega _ { \alpha{\prime}\beta{\prime}}}(x , x{\prime } ) = { g^{\beta{\prime}}}_\beta \left({{b_{\alpha{\prime}\beta{\prime } } } + { b_{\alpha{\prime}\beta{\prime}\gamma{\prime}}}{\sigma ^{\gamma{\prime } } } + { 1 \over 2}{b_{\alpha{\prime}\beta{\prime}\gamma{\prime}\delta{\prime}}}{\sigma ^{\gamma{\prime}}}{\sigma ^{\delta{\prime } } } } \right ) + \mathcal{o}({\epsilon ^3}).$$\end{document } the expansion coefficients can be obtained from the coincidence limits of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\tilde \omega}_{{\alpha { \prime}}{\beta { \prime}}}}$\end{document } and its derivatives . it is convenient , however , to express them directly in terms of the original bitensor by substituting the relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\tilde \omega}_{{\alpha { \prime}}{\beta { \prime } } } } = { g^\beta}_{{\beta { \prime}}}{\omega _ { { \alpha { \prime}}\beta}}$\end{document } and its derivatives . after using the results of equation ( 80 , 81 , 82 ) we find 86\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{b_{\alpha \prime \beta \prime } } = [ { \omega _ { \alpha \prime \beta}}],\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \ ; } \\ { { b_{\alpha \prime \beta \prime \gamma \prime } } = [ { \omega _ { \alpha \prime \beta ; \gamma \prime } } ] - { b_{\alpha \prime \beta \prime ; \gamma \prime}},\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\{{b_{\alpha \prime \beta \prime \gamma \prime \delta \prime } } = [ { \omega _ { \alpha \prime \beta ; \gamma \prime \delta \prime } } ] + { 1 \over 2}{b_{\alpha \prime \epsilon \prime}}r_{\;\;\beta \prime \gamma \prime \delta \prime}^{\epsilon \prime } - { b_{\alpha \prime \beta \prime ; \gamma \prime \delta \prime } } - { b_{\alpha \prime \beta \prime \gamma \prime ; \delta \prime } } - { b_{\alpha \prime \beta \prime \delta \prime ; \gamma \prime}}.\ ; } \\ \end{array}$$\end{document } the only difference with respect to equation ( 85 ) is the presence of a riemann - tensor term in b. suppose finally that the bitensor to be expanded is , whose indices all refer to x. much as we did before , we introduce an auxiliary bitensor \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\tilde \omega}_{{\alpha { \prime}}{\beta { \prime } } } } \equiv { g^\beta}_{{\beta { \prime}}}{\omega _ { { \alpha { \prime}}\beta}}$\end{document } whose indices all refer to x , we expand \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\tilde \omega}_{{\alpha { \prime}}{\beta { \prime}}}}$\end{document } as in equation ( 83 ) , and we then reconstruct the original bitensor . this gives us 87\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\omega _ { \alpha \beta}}(x , x{\prime } ) = { g^{\alpha{\prime}}}_\alpha { g^{\beta{\prime}}}_\beta \left({{c_{\alpha{\prime}\beta{\prime } } } + { c_{\alpha{\prime}\beta{\prime}\gamma{\prime}}}{\sigma ^{\gamma{\prime } } } + { 1 \over 2}{c_{\alpha{\prime}\beta{\prime}\gamma{\prime}\delta{\prime}}}{\sigma ^{\gamma{\prime}}}{\sigma ^{\delta{\prime } } } } \right ) + \mathcal{o}({\epsilon ^3}),$$\end{document } and the expansion coefficients are now \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{c_{\alpha \prime \beta \prime } } = [ { \omega _ { \alpha \beta}}],\;\;\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\ { { c_{\alpha \prime \beta \prime \gamma \prime } } = [ { \omega _ { \alpha \beta ; \gamma \prime } } ] - { c_{\alpha \prime \beta \prime ; \gamma \prime}},\;\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\ { { c_{\alpha \prime \beta \prime \gamma \prime \delta \prime } } = [ { \omega _ { \alpha \beta ; \gamma \prime \delta \prime } } ] + { 1 \over 2}{c_{\alpha \prime \epsilon \prime}}r_{\;\;\beta \prime \gamma \prime \delta \prime}^{\epsilon \prime } + { 1 \over 2}{c_{\epsilon \prime \beta \prime}}r_{\;\;\alpha \prime \gamma \prime \delta \prime}^{\epsilon \prime } - { c_{\alpha \prime \beta \prime ; \gamma \prime \delta \prime } } - { c_{\alpha \prime \beta \prime \gamma \prime ; \delta \prime } } - { c_{\alpha \prime \beta \prime \delta \prime ; \gamma \prime}}.}\\\end{array}$$\end{document } this differs from equation ( 86 ) by the presence of an additional riemann - tensor term in c. we now apply the general expansion method developed in the preceding section 2.4.1 to the bitensors , , and . in the first instance we have a = g , a = 0 , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_{{\alpha { \prime}}{\beta { \prime}}{\gamma { \prime}}{\delta { \prime } } } } = - { 1 \over 3}({r_{{\alpha { \prime}}{\gamma { \prime}}{\beta { \prime}}{\delta { \prime } } } } + { r_{{\alpha { \prime}}{\delta { \prime}}{\beta { \prime}}{\gamma { \prime}}}})$\end{document}. in the second instance we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${b_{{\alpha { \prime}}{\beta { \prime } } } } = - { g_{{\alpha { \prime}}{\beta { \prime}}}},{b_{{\alpha { \prime}}{\beta { \prime}}{\gamma { \prime } } } } = 0$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${b_{{\alpha { \prime}}{\beta { \prime}}{\gamma { \prime}}{\delta { \prime } } } } = - { 1 \over 3}({r_{{\beta { \prime}}{\alpha { \prime}}{\gamma { \prime}}{\delta { \prime } } } } + { r_{{\beta { \prime}}{\gamma { \prime}}{\alpha { \prime}}{\delta { \prime } } } } ) - { 1 \over 2}{r_{{\alpha { \prime}}{\beta { \prime}}{\gamma { \prime}}{\delta { \prime } } } } = { 1 \over 3}{r_{{\alpha { \prime}}{\delta { \prime}}{\beta { \prime}}{\gamma { \prime } } } } - { 1 \over 6}{r_{{\alpha { \prime}}{\beta { \prime}}{\gamma { \prime}}{\delta { \prime}}}}$\end{document}. in the third instance we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${c_{{\alpha { \prime}}{\beta { \prime } } } } = { g_{{\alpha { \prime}}{\beta { \prime}}}},{c_{{\alpha { \prime}}{\beta { \prime}}{\gamma { \prime } } } } = 0$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${c_{{\alpha { \prime}}{\beta { \prime}}{\gamma { \prime}}{\delta { \prime } } } } = - { 1 \over 3}({r_{{\alpha { \prime}}{\gamma { \prime}}{\beta { \prime}}{\delta { \prime } } } } + { r_{{\alpha { \prime}}{\delta { \prime}}{\beta { \prime}}{\gamma { \prime}}}})$\end{document}. this gives us the expansions 88\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\sigma _ { \alpha{\prime}\beta{\prime } } } = { g_{\alpha{\prime}\beta{\prime } } } - { 1 \over 3}{r_{\alpha{\prime}\gamma{\prime}\beta{\prime}\delta{\prime}}}{\sigma ^{\gamma{\prime}}}{\sigma ^{\delta{\prime } } } + \mathcal{o}({\epsilon ^3}),$$\end{document } 89\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\sigma _ { \alpha{\prime}\beta } } = - { g^{\beta{\prime}}}_\beta \left({{g_{\alpha{\prime}\beta{\prime } } } + { 1 \over 6}{r_{\alpha{\prime}\gamma{\prime}\beta{\prime}\delta{\prime}}}{\sigma ^{\gamma{\prime}}}{\sigma ^{\delta{\prime } } } } \right ) + \mathcal{o}({\epsilon ^3}),$$\end{document } 90\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\sigma _ { \alpha \beta } } = { g^{\alpha{\prime}}}_\alpha { g^{\beta{\prime}}}_\beta \left({{g_{\alpha{\prime}\beta{\prime } } } - { 1 \over 3}{r_{\alpha{\prime}\gamma{\prime}\beta{\prime}\delta{\prime}}}{\sigma ^{\gamma{\prime}}}{\sigma ^{\delta{\prime } } } } \right ) + \mathcal{o}({\epsilon ^3}).$$\end{document } taking the trace of the last equation returns \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma ^\alpha}_\alpha = 4 - { 1 \over 3}{r_{{\gamma { \prime}}{\delta { \prime}}}}{\sigma ^{{\gamma { \prime}}}}{\sigma ^{{\delta { \prime } } } } + o({\epsilon ^3})$\end{document } , or 91\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\theta ^\ast } = 3 - { 1 \over 3}{r_{\alpha{\prime}\beta{\prime}}}{\sigma ^{\alpha{\prime}}}{\sigma ^{\beta{\prime } } } + \mathcal{o}({\epsilon ^3}),$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\theta ^{\ast } } \equiv { \sigma ^\alpha}_\alpha - 1$\end{document } was shown in section 2.1.4 to describe the expansion of the congruence of geodesics that emanate from x. equation ( 91 ) reveals that timelike geodesics are focused if the ricci tensor is nonzero and the strong energy condition holds : when r > 0 we see that t is smaller than 3 , the value it would take in flat spacetime . in particular , it can be adapted to give expansions of the first derivatives of the parallel propagator . the expansions 92\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^\alpha}_{\beta{\prime};\gamma{\prime } } = { 1 \over 2}{g^\alpha}_{\alpha{\prime}}{r^{\alpha{\prime}}}_{\beta{\prime}\gamma{\prime}\delta{\prime}}{\sigma ^{\delta{\prime } } } + \mathcal{o}({\epsilon ^2}),\quad \quad { g^\alpha}_{\beta{\prime};\gamma } = { 1 \over 2}{g^\alpha}_{\alpha{\prime}}{g^{\gamma{\prime}}}_\gamma { r^{\alpha{\prime}}}_{\beta{\prime}\gamma{\prime}\delta{\prime}}{\sigma ^{\delta{\prime } } } + \mathcal{o}({\epsilon ^2})$$\end{document } and thus easy to establish , and they will be needed in section 4 of this review . suppose that we wish to express a rank-2 tensor a at a point x in terms of its values ( and that of its covariant derivatives ) at a neighbouring point x. the tensor can be written as an expansion in powers of ( x , x ) , and in this case we have 93\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a_{\alpha \beta}}(x ) = { g^{\alpha{\prime}}}_\alpha { g^{\beta{\prime}}}_\beta \left({{a_{\alpha{\prime}\beta{\prime } } } - { a_{\alpha{\prime}\beta{\prime};\gamma{\prime}}}{\sigma ^{\gamma{\prime } } } + { 1 \over 2}{a_{\alpha{\prime}\beta{\prime};\gamma{\prime}\delta{\prime}}}{\sigma ^{\gamma{\prime}}}{\sigma ^{\delta{\prime } } } } \right ) + \mathcal{o}({\epsilon ^3}).$$\end{document } if the tensor field is parallel transported on the geodesic that links x to x , then equation ( 93 ) reduces to equation ( 77 ) . the extension of this formula to tensors of other ranks is obvious . to derive this result we express a(z ) , the restriction of the tensor field on , in terms of its tetrad components \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_{{\rm{ab}}}}(\lambda ) = { a_{\mu \nu}}e_{\rm{a}}^\mu e_{\rm{b}}^\nu$\end{document}. recall from section 2.3.1 that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{\rm{a}}^\mu$\end{document } is an orthonormal basis that is parallel transported on ; recall also that the affine parameter ranges from 0 ( its value at x ) to 1 ( its value at x ) . we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_{{\alpha { \prime}}{\beta { \prime}}}}({x{\prime } } ) = { a_{{\rm{ab}}}}({\lambda _ 0})e_{{\alpha { \prime}}}^{\rm{a}}e_{{\beta { \prime}}}^{\rm{b}}{a_{\alpha \beta}}(x ) = { a_{{\rm{ab}}}}({\lambda _ 1})e_\alpha ^{\rm{a}}e_\beta ^{\rm{b}}$\end{document } , and aab(1 ) can be expressed in terms of quantities at = 0 by straightforward taylor expansion . since , for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$({\lambda _ 1 } - { \lambda _ 0}){\left . { { { d{a_{{\rm{ab } } } } } \over { d\lambda } } } \right\vert_{{\lambda _ 0 } } } = { \left . { ( { \lambda _ 1 } - { \lambda _ 0}){{({a_{\mu \nu}}e_{\rm{a}}^\mu e_{\rm{b}}^\nu)}_{;\lambda}}{t^\lambda } } \right\vert_{{\lambda _ 0 } } } = { \left . { ( { \lambda _ 1 } - { \lambda _ 0}){a_{\mu \nu ; \lambda}}e_{\rm{a}}^\mu e_{\rm{b}}^\nu { t^\lambda } } \right\vert_{{\lambda _ 0 } } } = - { a_{\alpha{\prime}\beta{\prime}\gamma{\prime}}}e_{\rm{a}}^{\alpha{\prime}}e_{\rm{b}}^{\beta{\prime}}{\sigma ^{\gamma{\prime}}},$$\end{document } where we have used equation ( 56 ) , we arrive at equation ( 93 ) after involving equation ( 73 ) . the van vleck biscalar (x , x ) is defined by 94\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta ( x , x{\prime } ) \equiv \det \left [ { { \delta ^{\alpha{\prime}}}_{\beta{\prime}}(x , x{\prime } ) } \right],\quad \quad { \delta ^{\alpha{\prime}}}_{\beta{\prime}}(x , x{\prime } ) \equiv - { g^{\alpha{\prime}}}_\alpha ( x{\prime},x){\sigma ^\alpha}_{\beta{\prime}}(x , x{\prime}).$$\end{document } as we shall show below , it can also be expressed as 95\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta ( x , x{\prime } ) \equiv { { \det [ - { \sigma _ { \alpha \beta{\prime}}}(x , x{\prime } ) ] } \over { \sqrt { - g } \sqrt { - g{\prime}}}},$$\end{document } where g is the metric determinant at x and g the metric determinant at x. equations ( 63 ) and ( 80 ) imply that at coincidence , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{\delta ^{{\alpha { \prime}}}}_{{\beta { \prime } } } ] = { \delta ^{{\alpha { \prime}}}}_{{\beta { \prime}}}$\end{document } and [ ] = 1 . equation ( 89 ) , on the other hand , implies that near coincidence 96\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\delta ^{\alpha{\prime}}}_{\beta{\prime } } = { \delta ^{\alpha{\prime}}}_{\beta{\prime } } + { 1 \over 6}{r^{\alpha{\prime}}}_{\gamma{\prime}\beta{\prime}\delta{\prime}}{\sigma ^{\gamma{\prime}}}{\sigma ^{\delta{\prime } } } + \mathcal{o}({\epsilon ^3}),$$\end{document } so that 97\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta = 1 + { 1 \over 6}{r_{\alpha{\prime}\beta{\prime}}}{\sigma ^{\alpha{\prime}}}{\sigma ^{\beta{\prime } } } + \mathcal{o}({\epsilon ^3}).$$\end{document } this last result follows from the fact that for a small matrix a , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\det ( 1 + a ) = 1 + { \rm{tr(}}a{\rm { ) + { \mathcal o}(}}{a^2})$\end{document}. we shall prove below that the van vleck determinant satisfies the differential equation 98\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${1 \over \delta}{(\delta { \sigma ^\alpha})_{;\alpha } } = 4,$$\end{document } which can also be written as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\ln \delta){,_\alpha}{\sigma ^\alpha } = 4 - { \sigma ^\alpha}_\alpha$\end{document } or 99\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${d \over { d{\lambda ^{\ast}}}}(\ln \delta ) = 3 - { \theta ^{\ast}}$$\end{document } in the notation introduced in section 2.1.4 . equation ( 99 ) reveals that the behaviour of the van vleck determinant is governed by the expansion of the congruence of geodesics that emanate from x. if t < 3 , then the congruence expands less rapidly than it would in flat spacetime , and increases along the geodesics . if , on the other hand , t > 3 , then the congruence expands more rapidly than it would in flat spacetime , and decreases along the geodesics . thus , > 1 indicates that the geodesics are undergoing focusing , while < 1 indicates that the geodesics are undergoing defocusing . the connection between the van vleck determinant and the strong energy condition is well illustrated by equation ( 97 ) : the sign of 1 near x is determined by the sign of r . to show that equation ( 95 ) follows from equation ( 94 ) we rewrite the completeness relations at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{\alpha \beta } } = { \eta ^{{\rm{ab}}}}e_{\rm{a}}^\alpha e_{\rm{b}}^\beta$\end{document } , in the matrix form g = ee , where e denotes the 4 4 matrix whose entries correspond to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{\rm{a}}^\alpha$\end{document}. ( in this translation we put tensor and frame indices on equal footing . ) with e denoting the determinant of this matrix , we have 1/g = e , or \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e = 1/\sqrt { - g}$\end{document}. similarly , we rewrite the completeness relations at x , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{{\alpha { \prime}}{\beta { \prime } } } } = { \eta ^{{\rm{ab}}}}e_{\rm{a}}^{{\alpha { \prime}}}e_{\rm{b}}^{{\beta { \prime}}}$\end{document } , in the matrix form g = ee , where e is the matrix corresponding to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{\rm{a}}^{{\alpha { \prime}}}$\end{document}. with e denoting its determinant , we have 1/g = e , or \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${e{\prime } } = 1/\sqrt { - { g{\prime}}}$\end{document}. now , the parallel propagator is defined by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\alpha { \prime } } } = { \eta ^{{\rm{ab}}}}{g_{{a{\prime}}{\beta { \prime}}}}e_{\rm{a}}^\alpha e_{\rm{b}}^{{\beta { \prime}}}$\end{document } , and the matrix form of this equation is = eeg. the determinant of the parallel propagator is therefore \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\hat g = - e{e{\prime}}{g{\prime } } = \sqrt { - { g{\prime}}}/\sqrt { - g}$\end{document}. so we have 100\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\det [ { g^\alpha}_{\alpha{\prime } } ] = { { \sqrt { - g{\prime } } } \over { \sqrt { - g{\prime}}}},\quad \quad \det \left [ { { g^\alpha}_{\alpha{\prime } } } \right ] = { { \sqrt { - g } } \over { \sqrt { - g}}},$$\end{document } and equation ( 95 ) follows from the fact that the matrix form of equation ( 94 ) is = g , where is the matrix corresponding to . to establish equation ( 98 ) we differentiate the relation = twice and obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ { \alpha { \beta { \prime } } } } = { \sigma ^\gamma}_{^\alpha}{\sigma _ { \gamma { \beta { \prime } } } } + { \sigma ^\gamma}{\sigma _ { \gamma \alpha { \beta { \prime}}}}$\end{document}. if we replace the last factor by and multiply both sides by g we find \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta _ { \beta { \prime}}^{\alpha { \prime } } = - { g^{\alpha { \prime}\alpha}}({\sigma ^\gamma}_\alpha { \sigma _ { \gamma \beta { \prime } } } + { \sigma ^\gamma}{\sigma _ { \alpha \beta { \prime}\gamma}}).$$\end{document } in this expression we make the substitution \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ { \alpha { \beta { \prime } } } } = - { g_{\alpha { \alpha { \prime}}}}{\delta ^{{\alpha { \prime}}}}_{{\beta { \prime}}}$\end{document } , which follows directly from equation ( 94 ) . this gives us 101\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\delta ^{\alpha { \prime}}}_{\beta { \prime } } = { g^{\alpha { \prime}}}_\alpha { g^\gamma}_{\gamma { \prime}}{\sigma ^\alpha}_\gamma { \delta ^{\gamma { \prime}}}_{\beta { \prime } } + { \delta ^{\alpha { \prime}}}_{\beta { \prime};\gamma}{\sigma ^\gamma},$$\end{document } where we have used equation ( 78 ) . at this stage we introduce an inverse \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${({\delta ^{- 1}})^{{\alpha { \prime}}}}_{{\beta { \prime}}}$\end{document } to the van vleck bitensor , defined by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\delta ^{{\alpha { \prime}}}}_{{\beta { \prime}}}{({\delta ^{- 1}})^{{\beta { \prime}}}}_{{\gamma { \prime } } } = { \delta ^{{\alpha { \prime}}}}_{{\gamma { \prime}}}$\end{document}. after multiplying both sides of equation ( 101 ) by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${({\delta ^{- 1}})^{{\beta { \prime}}}}_{{\gamma { \prime}}}$\end{document } we find \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\delta ^{\alpha { \prime}}}_{\beta { \prime } } = { g^{\alpha { \prime}}}_\alpha { g^\beta}_{\beta { \prime}}{\sigma ^\alpha}_\beta + { ( { \delta ^{- 1}})^{\gamma { \prime}}}_{\beta { \prime}}{\delta ^{\alpha { \prime}}}_{\gamma { \prime};\gamma}{\sigma ^\gamma},$$\end{document } and taking the trace of this equation yields \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$4 = { \sigma ^\alpha}_\alpha + { ( { \delta ^{- 1}})^{\beta { \prime}}}_{\alpha { \prime}}{\delta ^{\alpha { \prime}}}_{\beta { \prime};\gamma}{\sigma ^\gamma}.$$\end{document } we now recall the identity ln det m = tr(mm ) , which relates the variation of a determinant to the variation of the matrix elements . it implies , in particular , that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${({\delta ^{- 1}})^{{\beta { \prime}}}}_{{\alpha { \prime}}}{\delta ^{{\alpha { \prime}}}}_{{\beta { \prime}};\gamma } = { ( \ln \delta)_{,\gamma}}$\end{document } , and we finally obtain 102\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$4 = { \sigma ^\alpha}_\alpha + { ( \ln \delta)_,}_\alpha { \sigma ^\alpha},$$\end{document } which is equivalent to equation ( 98 ) or equation ( 99 ) . given a fixed base point x and a tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{\rm{a}}^{{\alpha { \prime}}}({x{\prime}})$\end{document } , we assign to a neighbouring point x the four coordinates 103\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\hat x^{\rm{a } } } = - e_{\alpha { \prime}}^{\rm{a}}(x{\prime}){\sigma ^{\alpha { \prime}}}(x,\;x{\prime}),$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{{\alpha { \prime}}}^{\rm{a } } = { \eta ^{{\rm{ab}}}}{g_{{\alpha { \prime}}{\beta { \prime}}}}e_{\rm{b}}^{{\beta { \prime}}}$\end{document } is the dual tetrad attached to x. the new coordinates \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^{\rm{a}}}$\end{document } are called riemann normal coordinates ( rnc ) , and they are such that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\eta _ { { \rm{ab}}}}{{\hat x}^{\rm{a}}}{{\hat x}^{\rm{b } } } = { \eta _ { { \rm{ab}}}}e_{{\alpha { \prime}}}^{\rm{a}}e_{{\beta { \prime}}}^{\rm{b}}{\sigma ^{{\alpha { \prime}}}}{\sigma ^{{\beta { \prime } } } } = { g_{{\alpha { \prime}}{\beta { \prime}}}}{\sigma ^{{\alpha { \prime}}}}{\sigma ^{{\beta { \prime}}}}$\end{document } , or 104\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ { { \rm{ab}}}}{\hat x^{\rm{a}}}{\hat x^{\rm{b } } } = 2\sigma ( x,\;x{\prime}).$$\end{document } thus , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\eta _ { { \rm{ab}}}}{{\hat x}^{\rm{a}}}{{\hat x}^{\rm{b}}}$\end{document } is the squared geodesic distance between x and the base point x. it is obvious that x is at the origin of the rnc , where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^{\rm{a } } } = 0$\end{document}. if we move the point x to x + x , the new coordinates change to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^{\rm{a } } } + \delta { { \hat x}^{\rm{a } } } = - e_{{\alpha { \prime}}}^{\rm{a}}{\sigma ^{{\alpha { \prime}}}}(x + \delta x,{x{\prime } } ) = { { \hat x}^{\rm{a } } } - e_{{\alpha { \prime}}}^{\rm{a}}{\sigma ^{{\alpha { \prime}}}}_\beta \delta { x^\beta}$\end{document } , so that 105\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d{\hat x^{\rm{a } } } = - e_{\alpha { \prime}}^{\rm{a}}{\sigma ^{\alpha { \prime}}}_\beta d{x^\beta}.$$\end{document } the coordinate transformation is therefore determined by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\partial { { \hat x}^{\rm{a}}}/\partial { x^\beta } = - e_{{\alpha { \prime}}}^{\rm{a}}{\sigma ^{{\alpha { \prime}}}}_\beta$\end{document } , and at coincidence we have 106\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left [ { { { \partial { { \hat x}^{\rm{a } } } } \over { \partial { x^\alpha } } } } \right ] = e_{\alpha { \prime}}^{\rm{a}},\quad \left [ { { { \partial { x^\alpha } } \over { \partial { { \hat x}^{\rm{a } } } } } } \right ] = e_{\rm{a}}^{\alpha { \prime}};$$\end{document } the second result follows from the identities \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{{\alpha { \prime}}}^{\rm{a}}e_{\rm{b}}^{{\alpha { \prime } } } = { \delta ^{\rm{a}}}_{\rm{b}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{\rm{a}}^{{\alpha { \prime}}}e_{{\beta { \prime}}}^{\rm{a } } = { \delta ^{{\alpha { \prime}}}}_{{\beta { \prime}}}$\end{document}. it is interesting to note that the jacobian of the transformation of equation ( 105 ) , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$j \equiv \det ( \partial { { \hat x}^{\rm{a}}}/\partial { x^\beta})$\end{document } , is given by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$j = \sqrt { - g } \delta ( x,{x{\prime}})$\end{document } , where g is the determinant of the metric in the original coordinates , and (x , x ) is the van vleck determinant of equation ( 95 ) . this result follows simply by writing the coordinate transformation in the form \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\partial { { \hat x}^{\rm{a}}}/\partial { x^\beta } = - { \eta ^{{\rm{ab}}}}e_{\rm{b}}^{{\alpha { \prime}}}{\sigma _ { { \alpha { \prime}}\beta}}$\end{document } and computing the product of the determinants . it allows us to deduce that in the rnc , the determinant of the metric is given by 107\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\sqrt { - g({\rm{rnc } } ) } = { 1 \over { \delta ( x,\;x{\prime})}}.$$\end{document } it is easy to show that the geodesics emanating from x are straight lines in the rnc . the proper volume of a small comoving region is then equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$dv = { \delta ^{- 1}}{d^4}\hat x$\end{document } , and this is smaller than the flat - spacetime value of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${d^4}\hat x$\end{document } if > 1 , that is , if the geodesics are focused by the spacetime curvature . we now would like to invert equation ( 105 ) in order to express the line element \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d{s^2 } = { g_{\alpha \beta}}d{x^\alpha}d{x^\beta}$\end{document } in terms of the displacements \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d{{\hat x}^{\rm{a}}}$\end{document}. we shall do this approximately , by working in a small neighbourhood of x. we recall the expansion of equation ( 89 ) , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\sigma ^{\alpha { \prime}}}_\beta = - { g^{\beta { \prime}}}_\beta \left({{\delta ^{\alpha { \prime}}}_{\beta { \prime } } + { 1 \over 6}{r^{\alpha { \prime}}}_{\gamma { \prime}\beta { \prime}\delta { \prime}}{\sigma ^{\gamma { \prime}}}{\sigma ^{\delta { \prime } } } } \right ) + \mathcal{o}({\epsilon ^3}),$$\end{document } and in this we substitute the frame decomposition of the riemann tensor , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r^{{\alpha { \prime}}}}_{{\gamma { \prime}}{\beta { \prime}}{\delta { \prime } } } = { r^{\rm{a}}}_{{\rm{cbd}}}e_{\rm{a}}^{{\alpha { \prime}}}e_{{\gamma { \prime}}}^ce_{{\beta { \prime}}}^{\rm{b}}e_{{\delta { \prime}}}^{\rm{d}}$\end{document } , and the tetrad decomposition of the parallel propagator , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{{\beta { \prime}}}}_\beta = e_{\rm{b}}^\beta e_\beta ^{\rm{b}}$\end{document } , where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{{\alpha { \prime}}}^{\rm{a } } = { \eta ^{{\rm{ab}}}}{g_{{\alpha { \prime}}{\beta { \prime}}}}e_{\rm{b}}^{{\beta { \prime}}}$\end{document } is the dual tetrad at x obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_{{\beta { \prime}}}^{\rm{b}}({x{\prime}})$\end{document}. after some algebra we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\sigma ^{\alpha { \prime}}}_\beta = - e_{\rm{a}}^{\alpha { \prime}}e_\beta ^{\rm{a } } - { 1 \over 6}{r^{\rm{a}}}_{{\rm{cbd}}}e_{\rm{a}}^{\alpha { \prime}}e_\beta ^{\rm{b}}{\hat x^{\rm{c}}}{\hat x^{\rm{d } } } + \mathcal{o}({\epsilon ^3}),$$\end{document } where we have used equation ( 103 ) . substituting this into equation ( 105 ) yields 108\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d{\hat x^{\rm{a } } } = \left [ { { \delta ^{\rm{a}}}_{\rm{b } } + { 1 \over 6}{r^{\rm{a}}}_{{\rm{cbd}}}{{\hat x}^{\rm{c}}}{{\hat x}^{\rm{d } } } + \mathcal{o}({x^3 } ) } \right]e_\beta ^{\rm{b}}d{x^\beta},$$\end{document } and this is easily inverted to give 109\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$e_\alpha ^{\rm{a}}d{x^\alpha } = \left [ { { \delta ^{\rm{a}}}_{\rm{b } } - { 1 \over 6}{r^{\rm{a}}}_{{\rm{cbd}}}{{\hat x}^{\rm{c}}}{{\hat x}^{\rm{d } } } + \mathcal{o}({x^3 } ) } \right]d{\hat x^{\rm{b}}}.$$\end{document } this is the desired approximate inversion of equation ( 105 ) . it is useful to note that equation ( 109 ) , when specialized from the arbitrary coordinates \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${x^\alpha}\,{\rm{to}}\,{{\hat x}^{\rm{a}}}$\end{document } , gives us the components of the dual tetrad at x in the rnc . we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d{s^2 } = { g_{\alpha \beta}}d{x^\alpha}d{x^\beta } = ( { \eta _ { { \rm{ab}}}}e_\alpha ^{\rm{a}}e_\beta ^{\rm{b}})\;d{x^\alpha}d{x^\beta } = { \eta _ { { \rm{ab}}}}(e_\alpha ^{\rm{a}}d{x^\alpha})(e_\beta ^{\rm{b}}d{x^\beta})$\end{document } , and in this we substitute equation ( 109 ) . the final result is \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d{s^2 } = { g_{{\rm{ab}}}}d{\hat x^{\rm{a}}}d{\hat x^{\rm{b}}}$\end{document } , with 110\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{{\rm{ab } } } } = { \eta _ { { \rm{ab } } } } - { 1 \over 3}{r_{{\rm{acbd}}}}{\hat x^{\rm{c}}}{\hat x^{\rm{d } } } + \mathcal{o}({x^3}).$$\end{document } the quantities racbd appearing in equation ( 110 ) are the frame components of the riemann tensor evaluated at the base point x , 111\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{{\rm{acbd } } } } = { r_{\alpha { \prime}\gamma { \prime}\beta { \prime}\delta { \prime}}}\;e_{\rm{a}}^{\alpha { \prime}}e_{\rm{c}}^{\gamma { \prime}}e_{\rm{b}}^{\beta { \prime}}e_{\rm{d}}^{\delta { \prime}},$$\end{document } and these are independent of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^{\rm{a}}}$\end{document}. they are also , by virtue of equation ( 106 ) , the components of the ( base - point ) riemann tensor in the rnc , because equation ( 111 ) can also be expressed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{{\rm{acdb } } } } = { r_{\alpha { \prime}\gamma { \prime}\beta { \prime}\delta { \prime}}}\;\left [ { { { \partial { x^\alpha } } \over { \partial { { \hat x}^{\rm{a } } } } } } \right]\left [ { { { \partial { x^\gamma } } \over { \partial { { \hat x}^{\rm{c } } } } } } \right]\left [ { { { \partial { x^\beta } } \over { \partial { { \hat x}^{\rm{b } } } } } } \right]\left [ { { { \partial { x^\delta } } \over { \partial { { \hat x}^{\rm{d } } } } } } \right],$$\end{document } which is the standard transformation law for tensor components . it is obvious from equation ( 110 ) that gab(x ) = ab and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\gamma ^{\rm{a}}}_{{\rm{bc}}}({x{\prime } } ) = 0$\end{document } , where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\gamma ^{\rm{a}}}_{{\rm{bc } } } = - { 1 \over 3}({r^{\rm{a}}}_{{\rm{bcd } } } + { r^{\rm{a}}}_{{\rm{cbd}}}){{\hat x}^{\rm{d } } } + { \mathcal o}({x^2})$\end{document } is the connection compatible with the metric gab . let be a timelike curve described by parametric relations z( ) in which is proper time . let u = dz / d be the curve s normalized tangent vector , and let = du / d be its acceleration vector . a vector field v is said to be fermi - walker transported on if it is a solution to the differential equation 112\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{d{v^\mu } } \over { d\tau } } = ( { v_\nu}{a^\nu})\;{u^\mu } - ( { v_\nu}{u^\nu})\;{a^\mu}.$$\end{document } notice that this reduces to parallel transport if a = 0 and is a geodesic . the operation of fermi - walker ( fw ) transport satisfies two important properties . the first is that u is automatically fw transported along ; this follows at once from equation ( 112 ) and the fact that u is orthogonal to . the second is that if the vectors v and w are both fw transported along , then their inner product vw is constant on : d(vw)/d = 0 ; this also follows immediately from equation ( 112 ) . let \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar z}$\end{document } be an arbitrary reference point on . at this point we erect an orthonormal tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{\bar \mu}},e_a^{\bar \mu})$\end{document } where , contrary to former usage , the frame index a runs from 1 to 3 . we then propagate each frame vector on by fw transport ; this guarantees that the tetrad remains orthonormal everywhere on . at a generic point z( ) we have 113\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{de_a^\mu } \over { d\tau } } = ( { a_\nu}e_a^\nu)\;{u^\mu},\quad \quad { g_{\mu \nu}}{u^\mu}{u^\nu } = - 1,\quad \quad { g_{\mu \nu}}e_a^\mu { u^\nu } = 0,\quad \quad { g_{\mu \nu}}e_a^\mu e_b^\nu = { \delta _ { ab}}.$$\end{document } from the tetrad on we define a dual tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_\mu ^0,e_\mu ^a)$\end{document } by the relations 114\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$e_\mu ^0 = - \;{u_{\mu}},\quad \quad e_\mu ^a = { \delta ^{ab}}{g_{\mu \nu}}e_b^\nu;$$\end{document } this is also fw transported on . the tetrad and its dual give rise to the completeness relations 115\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^{\mu \nu } } = - { u^\mu}{u^\nu } + { \delta ^{ab}}e_a^\mu e_b^\nu , \quad \quad { g_{\mu \nu } } = - e_\mu ^0e_\nu ^0 + { \delta _ { ab}}e_\mu ^ae_\nu ^b.$$\end{document } to construct the fermi normal coordinates ( fnc ) of a point x in the normal convex neighbourhood of , we locate the unique spacelike geodesic that passes through x and intersects orthogonally . we denote the intersection point by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document } , with t denoting the value of the proper - time parameter at this point . to tensors at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } we assign indices \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar \alpha , \bar \beta$\end{document } and so on . the fnc of x are defined by 116\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\hat x^0 } = t,\quad \quad { \hat x^a } = - e_{\bar \alpha}^a(\bar x){\sigma ^{\bar \alpha}}(x,\bar x),\quad \quad { \sigma _ { \bar \alpha}}(x,\bar x){u^{\bar \alpha}}(x ) = 0;$$\end{document } the last statement determines \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } from the requirement that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$- { \sigma ^{\vec \alpha}}$\end{document } , the vector tangent to at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } , be orthogonal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^{\bar \alpha}}$\end{document } , the vector tangent to . from the definition of the fnc and the completeness relations of equation ( 115 ) it follows that 117\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s^2 } \equiv { \delta _ { ab}}{\hat x^a}{\hat x^b } = 2\sigma ( x,\;\bar x),$$\end{document } so that s is the spatial distance between \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } and x along the geodesic . this statement gives an immediate meaning to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^a}$\end{document } , the spatial fermi normal coordinates ; and the time coordinate \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^0}$\end{document } is simply proper time at the intersection point \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document}. the situation is illustrated in figure 6 . figure 6fermi normal coordinates of a point x relative to a world line . the time coordinate t selects a particular point on the word line , and the disk represents the set of spacelike geodesics that intersect orthogonally at z(t ) . the unit vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega ^a } \equiv { { \hat x}^a}/s$\end{document } selects a particular geodesic among this set , and the spatial distance s selects a particular point on this geodesic . fermi normal coordinates of a point x relative to a world line . the time coordinate t selects a particular point on the word line , and the disk represents the set of spacelike geodesics that intersect orthogonally at z(t ) . the unit vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega ^a } \equiv { { \hat x}^a}/s$\end{document } selects a particular geodesic among this set , and the spatial distance s selects a particular point on this geodesic . suppose that x is moved to x + x . this typically induces a change in the spacelike geodesic , which moves to + , and a corresponding change in the intersection point \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } , which moves to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$x\prime\prime \equiv \bar x + \delta \bar x$\end{document } , with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\delta { x^{\bar \alpha } } = { u^{\bar \alpha}}\delta t$\end{document}. the fnc of the new point are then \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^0}(x + \delta x ) = t + \delta t$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^a}(x + \delta x ) = - e_{^{{\alpha ^{{\prime\prime}}}}}^a({x^{{\prime\prime}}}){\sigma ^{{\alpha ^{{\prime\prime}}}}}(x + \delta x,{x^{{\prime\prime}}})$\end{document } , with x determined by (x + x , x)u ( x ) = 0 . expanding these relations to first order in the displacements , and simplifying using equations ( 113 ) , yields 118\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$dt = \mu { \sigma _ { \bar \alpha \beta}}{u^{\bar \alpha}}d{x^\beta},\quad \quad d{\hat x^a } = - e_{\bar \alpha}^a\left({{\sigma ^{\bar \alpha}}_\beta + \mu { \sigma ^{\bar \alpha}}_{\bar \beta}{u^{\bar \beta}}{\sigma _ { \beta \bar \gamma}}{u^{\bar \gamma } } } \right)d{x^\beta},$$\end{document } where is determined by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mu ^{- 1 } } = - ( { \sigma _ { \bar \alpha \bar \beta}}{u^{\bar \alpha}}{u^{\bar \beta } } + { \sigma _ { \bar \alpha}}{a^{\bar \alpha}})$\end{document}. the relations of equation ( 118 ) can be expressed as expansions in powers of s , the spatial distance from \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } to x. for this we use the expansions of equations ( 88 ) and ( 89 ) , in which we substitute \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma ^{\bar \alpha } } = - e_a^{\bar \alpha}{{\hat x}^a}$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{\bar \alpha}}_\alpha = { u^{\bar \alpha}}\bar e_\alpha ^0 + e_a^{\bar \alpha}\bar e_\alpha ^a$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_\alpha ^0,\bar e_\alpha ^a)$\end{document } is a dual tetrad at x obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(- { u_{\bar \alpha}},e_{\bar \alpha}^a)$\end{document } on the spacelike geodesic . after some algebra we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\mu ^{- 1 } } = 1 + { a_a}{\hat x^a } + { 1 \over 3}{r_{0c0d}}{\hat x^c}{\hat x^d } + \mathcal{o}({s^3}),$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_a}(t ) \equiv { a_{\bar \alpha}}e_a^{\bar \alpha}$\end{document } are frame components of the acceleration vector , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{0c0d}}(t ) \equiv { r_{\bar \alpha \bar \gamma \bar \beta}}{u^{\bar \alpha}}e_c^{\bar \gamma}{u^{\bar \beta}}e_d^{\bar \delta}$\end{document } are frame components of the riemann tensor evaluated on . this last result is easily inverted to give \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\mu = 1 - { a_a}{\hat x^a } + { ( { a_a}{\hat x^a})^2 } - { 1 \over 3}{r_{0c0d}}{\hat x^c}{\hat x^d } + \mathcal{o}({s^3}).$$\end{document } proceeding similarly for the other relations of equation ( 118 ) , we obtain 119\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$dt = \left [ { 1 - { a_a}{{\hat x}^a } + { { ( { a_a}{{\hat x}^a})}^2 } - { 1 \over 2}{r_{0c0d}}{{\hat x}^c}{{\hat x}^d } + \mathcal{o}({s^3 } ) } \right]\left({\bar e_\beta ^0d{x^\beta } } \right ) + \left [ { - { 1 \over 6}{r_{0cbd}}{{\hat x}^c}{{\hat x}^d } + \mathcal{o}({s^3 } ) } \right]\left({\bar e_\beta ^bd{x^\beta } } \right)$$\end{document } and 120\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d{\hat x^a } = \left [ { { 1 \over 2}{r^a}_{c0d}{{\hat x}^c}{{\hat x}^d } + \mathcal{o}({s^3 } ) } \right]\left({\bar e_\beta ^0d{x^\beta } } \right ) + \left [ { { \delta ^a}_b + { 1 \over 6}{r^a}_{cbd}{{\hat x}^c}{{\hat x}^d } + \mathcal{o}({s^3 } ) } \right]\left({\bar e_\beta ^bd{x^\beta } } \right),$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{ac0d}}(t ) \equiv { r_{\bar \alpha \bar \gamma \bar \beta \bar \delta}}e_a^{\bar \alpha}e_c^{\bar \gamma}{u^{\bar \beta}}e_d^{\bar \delta}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{acbd}}(t ) \equiv { r_{\bar \alpha \bar \gamma \bar \beta \bar \delta}}e_a^{\bar \alpha}e_c^{\bar \gamma}e_b^{\bar \beta}e_d^{\bar \delta}$\end{document } are additional frame components of the riemann tensor evaluated on . ( note that frame indices are raised with . ) as a special case of equations ( 119 ) and ( 120 ) we find that 121\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\left . { \,{{\partial t } \over { \partial { x^\alpha } } } } \right\vert _ \gamma } = - { u_{\bar \alpha}},\quad \quad { \left . { \,{{\partial { { \hat x}^a } } \over { \partial { x^\alpha } } } } \right\vert _ \gamma } = e_{\bar \alpha}^a,$$\end{document } because in the limit \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$x \rightarrow \bar x$\end{document } the dual tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_\alpha ^0,\bar e_\alpha ^a)$\end{document } at x coincides with the dual tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(- { u_{\bar \alpha}},e_{\bar \alpha}^a)$\end{document } at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document}. it follows that on , the transformation matrix between the original coordinates x and the fnc \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(t,{{\hat x}^a})$\end{document } is formed by the fermi - walker transported tetrad : 122\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\left . { \,{{\partial { x^\alpha } } \over { \partial t } } } \right\vert_\gamma } = { u^{\bar \alpha}},\quad \quad { \left . { \,{{\partial { x^\alpha } } \over { \partial { { \hat x}^a } } } } \right\vert_\gamma } = e_a^{\bar \alpha}.$$\end{document } this implies that the frame components of the acceleration vector aa(t ) are also the components of the acceleration vector in the fnc ; orthogonality between \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^{\bar \alpha}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^{\bar \alpha}}$\end{document } means that a0 = 0 . similarly , r0c0d(t ) , r0cbd(t ) , and racbd(t ) are the components of the riemann tensor ( evaluated on ) in the fermi normal coordinates . inversion of equations ( 119 ) and ( 120 ) gives 123\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\bar e_\alpha ^0d{x^\alpha } = \left [ { 1 + { a_a}{{\hat x}^a } + { 1 \over 2}{r_{0c0d}}{{\hat x}^c}{{\hat x}^d } + \mathcal{o}({s^3 } ) } \right]dt + \left [ { { 1 \over 6}{r_{0cbd}}{{\hat x}^c}{{\hat x}^d } + \mathcal{o}({s^3 } ) } \right]d{\hat x^b}$$\end{document } and 124\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\bar e_\alpha ^0d{x^\alpha } = \left [ { { \delta ^a}_b - { 1 \over 6}{r^a}_{cbd}{{\hat x}^c}{{\hat x}^d } + o({s^3 } ) } \right]d{\hat x^b } + \left [ { - { 1 \over 2}{r^a}_{c0d}{{\hat x}^c}{{\hat x}^d } + o({s^3 } ) } \right]dt.$$\end{document } these relations , when specialized to the fnc , give the components of the dual tetrad at x. they can also be used to compute the metric at x , after invoking the completeness relations \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\alpha \beta } } = - \bar e_\alpha ^0\bar e_\beta ^0 + { \delta _ { ab}}\bar e_\alpha ^a\bar e_\beta ^b$\end{document}. this gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d{s^2 } = { g_{tt}}d{t^2 } + 2{g_{ta}}dtd{\hat x^a } + { g_{ab}}d{\hat x^a}d{\hat x^b},$$\end{document } with 125\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{tt } } = - \left [ { 1 + 2{a_a}{{\hat x}^a } + { { ( { a_a}{{\hat x}^a})}^2 } + { r_{0c0d}}{{\hat x}^c}{{\hat x}^d } + \mathcal{o}({s^3 } ) } \right],$$\end{document } 126\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ta } } = - { 2 \over 3}{r_{0cad}}{\hat x^c}{\hat x^d } + \mathcal{o}({s^3}),$$\end{document } 127\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ab } } = { \delta _ { ab } } - { 1 \over 3}{r_{acbd}}{\hat x^c}{\hat x^d } + \mathcal{o}({s^3}).$$\end{document } this is the metric near in the fermi normal coordinates . recall that aa(t ) are the components of the acceleration vector of the timelike curve described by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^a } = 0$\end{document } while r0c0d(t ) , r0cbd(t ) , and racbd(t ) are the components of the riemann tensor evaluated on . notice that on , the metric of equations ( 125 , 126 , 127 ) reduces to gtt = 1 and gab = ab . on the other hand , the nonvanishing christoffel symbols ( on ) are \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\gamma ^a}_{ta } = { \gamma ^a}_{tt } = { a_a}$\end{document } ; these are zero ( and the fnc enforce local flatness on the entire curve ) when is a geodesic . the form of the metric can be simplified if the ricci tensor vanishes on the world line : 128\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{\mu \nu}}(z ) = 0.$$\end{document } in such circumstances , a transformation from the fermi normal coordinates \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(t,{{\hat x}^a})$\end{document } to the thorne - hartle coordinates \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(t,{{\hat y}^a})$\end{document } brings the metric to the form 129\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{tt } } = - \left [ { 1 + 2{a_a}{{\hat y}^a } + { { ( { a_a}{{\hat y}^a})}^2 } + { r_{0c0d}}{{\hat y}^c}{{\hat y}^d } + \mathcal{o}({s^3 } ) } \right],$$\end{document } 130\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ta } } = - { 2 \over 3}{r_{0cad}}{\hat y^c}{\hat y^d } + \mathcal{o}({s^3}),$$\end{document } 131\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ab } } = { \delta _ { ab}}(1 - { r_{0c0d}}{\hat y^c}{\hat y^d } ) + \mathcal{o}({s^3}).$$\end{document } we see that the transformation leaves gtt and gta unchanged , but that it diagonalizes gab . this metric was first displayed in and the coordinate transformation was later produced by zhang . the key to the simplification comes from equation ( 128 ) , which dramatically reduces the number of independent components of the riemann tensor . in particular , equation ( 128 ) implies that the frame components racbd of the riemann tensor are completely determined by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}_{ab } } \equiv { r_{0a0b}}$\end{document } , which in this special case is a symmetric - tracefree tensor . to prove this we invoke the completeness relations of equation ( 115 ) and take frame components of equation ( 128 ) this produces the three independent equations \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\delta ^{cd}}{r_{acbd } } = { \mathcal{e}_{ab}},\quad \quad { \delta ^{cd}}{r_{0cad } } = 0,\quad \quad { \delta ^{cd}}{\mathcal{e}_{cd } } = 0,$$\end{document } the last of which states that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}_{ab}}$\end{document } has a vanishing trace . taking the trace of the first equation gives racbd = 0 , and this implies that racbd has five independent components . since this is also the number of independent components of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}_{ab}}$\end{document } , we see that the first equation can be inverted racbd can be expressed in terms of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}_{ab}}$\end{document}. a complete listing of the relevant relations is \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{1212 } } = { { \mathcal e}_{11 } } + { { \mathcal e}_{22 } } = - { { \mathcal e}_{33}},{r_{1213 } } = { { \mathcal e}_{23}},{r_{1223 } } = - { { \mathcal e}_{13}},{r_{1313 } } = { { \mathcal e}_{11 } } + { { \mathcal e}_{33 } } = - { { \mathcal e}_{22}},\,{r_{1323 } } = { { \mathcal e}_{12}}$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{2323 } } = { { \mathcal e}_{22 } } + { { \mathcal e}_{33 } } = - { { \mathcal e}_{11}}$\end{document}. these are summarized by 132\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{acbd } } = { \delta _ { ab}}{\mathcal{e}_{cd } } + { \delta _ { cd}}{\mathcal{e}_{ab } } - { \delta _ { ad}}{\mathcal{e}_{bc } } - { \delta _ { bc}}{\mathcal{e}_{ad}},$$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}_{ab } } \equiv { r_{0a0b}}$\end{document } satisfies \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\delta ^{ab}}{{\mathcal e}_{ab } } = 0$\end{document}. we may also note that the relation r0cad = 0 , together with the usual symmetries of the riemann tensor , imply that r0cad too possesses five independent components . these may thus be related to another symmetric - tracefree tensor \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal b}_{ab}}$\end{document}. we take the independent components to be \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{0112 } } \equiv - { { \mathcal b}_{13}},\,{r_{0113 } } \equiv { { \mathcal b}_{12}},\,{r_{0123 } } \equiv - { { \mathcal b}_{11}},\,{r_{0212 } } \equiv - { { \mathcal b}_{23}}$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{0213 } } \equiv { { \mathcal b}_{22}}$\end{document } , and it is easy to see that all other components can be expressed in terms of these . for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{0223 } } = - { r_{0113 } } = - { { \mathcal b}_{12}},\,{r_{0312 } } = - { r_{0123 } } + { r_{0213 } } = { { \mathcal b}_{11 } } + { { \mathcal b}_{22 } } = - { { \mathcal b}_{33}},\,{r_{0313 } } = - { r_{0212 } } = { { \mathcal b}_{23}}$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{0323 } } = { r_{0112 } } = - { { \mathcal b}_{13}}$\end{document}. these relations are summarized by 133\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{0abc } } = - { \varepsilon _ { bcd}}{\mathcal{b}^d}_a,$$\end{document } where abc is the three - dimensional permutation symbol . the inverse relation is \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal b}^a}_b = { 1 \over 2}{{\mathcal e}^{acd}}{r_{0bcd}}$\end{document}. substitution of equation ( 132 ) into equation ( 127 ) gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ab } } = { \delta _ { ab}}\left({1 - { 1 \over 3}{\mathcal{e}_{cd}}{{\hat x}^c}{{\hat x}^d } } \right ) - { 1 \over 3}({\hat x_c}{\hat x^c}){\mathcal{e}_{ab } } + { 1 \over 3}{\hat x_a}{\mathcal{e}_{bc}}{\hat x^c } + { 1 \over 3}{\hat x_b}{\mathcal{e}_{ac}}{\hat x^c } + \mathcal{o}({s^3}),$$\end{document } and we have not yet achieved the simple form of equation ( 131 ) . the missing step is the transformation from the fnc \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^a}$\end{document } to the thorne - hartle coordinates . this is given by 134\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\hat y^a } = { \hat x^a } + { \xi ^a},\quad \quad { \xi ^a } = - { 1 \over 6}({\hat x_c}{\hat x^c}){\mathcal{e}_{ab}}{\hat x^b } + { 1 \over 3}{\hat x_a}{\mathcal{e}_{bc}}{\hat x^b}{\hat x^c } + \mathcal{o}({s^4}).$$\end{document } it is easy to see that this transformation affects neither gtt nor gta at orders s and s. the remaining components of the metric , however , transform according to gab(thc ) = gab(fnc ) a;b b;a , where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\xi _ { a;b } } = { 1 \over 3}{\delta _ { ab}}{\mathcal{e}_{cd}}{\hat x^c}{\hat x^d } - { 1 \over 6}({\hat x_c}{\hat x^c}){\mathcal{e}_{ab } } - { 1 \over 3}{\mathcal{e}_{ac}}{\hat x^c}{\hat x_b } + { 2 \over 3}{\hat x_a}{\mathcal{e}_{bc}}{\hat x^c } + \mathcal{o}({s^3}).$$\end{document } it follows that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{ab}^{{\rm{thc } } } = { \delta _ { ab}}(1 - { { \mathcal e}_{cd}}{{\hat y}^c}{{\hat y}^d } ) + { \mathcal o}({{\hat y}^3})$\end{document } , which is just the same statement as in equation ( 131 ) . alternative expressions for the components of the thorne - hartle metric are 135\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{tt } } = - \left [ { 1 + 2{a_a}{{\hat y}^a } + { { ( { a_a}{{\hat y}^a})}^2 } + { e_{ab}}{{\hat y}^a}{{\hat y}^b } + \mathcal{o}({s^3 } ) } \right],$$\end{document } 136\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ta } } = - { 2 \over 3}{\varepsilon _ { abc}}{\mathcal{b}^b}_d{\hat y^c}{\hat y^d } + \mathcal{o}({s^3}),$$\end{document } 137\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ab } } = { \delta _ { ab}}(1 - { \mathcal{e}_{cd}}{\hat y^c}{\hat y^d } ) + \mathcal{o}({s^3}).$$\end{document } we introduce the same geometrical elements as in section 3.2 : we have a timelike curve described by relations z( ) , its normalized tangent vector u = dz / d , and its acceleration vector a = du / d. we also have an orthonormal triad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_a^\mu$\end{document } that is transported on the world line according to 138\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{de_a^\mu } \over { d\tau } } = { a_a}{u^\mu } + { \omega _ a}^be_b^\mu,$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_a}(\tau ) = { a_\mu}e_a^\mu$\end{document } are the frame components of the acceleration vector and ab( ) = ba( ) is a prescribed rotation tensor . here the triad is not fermi - walker transported : for added generality we allow the spatial vectors to rotate as they are transported on the world line . while ab will be set to zero in most sections of this paper , the freedom to perform such a rotation can be useful and will be exploited in section 5.4 . it is easy to check that equation ( 138 ) is compatible with the requirement that the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^\mu},e_a^\mu)$\end{document } be orthonormal everywhere on . finally , we have a dual tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_\mu ^0,e_\mu ^a)$\end{document } , with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_\mu ^0 = { \delta ^{ab}}{g_{\mu \nu}}e_b^\nu$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_\mu ^a = { \delta ^{ab}}{g_{\mu \nu}}e_b^\nu$\end{document}. the tetrad and its dual give rise to the completeness relations 139\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^{\mu \nu } } = - { u^\mu}{u^\nu } + { \delta ^{ab}}e_a^\mu e_b^\nu , \quad \quad { g_{\mu \nu } } = - e_\mu ^0e_\nu ^0 + { \delta _ { ab}}e_\mu ^ae_\nu ^b,$$\end{document } which are the same as in equation ( 115 ) . the fermi normal coordinates of section 3.2 were constructed on the basis of a spacelike geodesic connecting a field point x to the world line . the retarded coordinates are based instead on a null geodesic going from the world line to the field point . we thus let x be within the normal convex neighbourhood of , be the unique future - directed null geodesic that goes from the world line to x , and x = z(u ) be the point at which intersects the world line , with u denoting the value of the proper - time parameter at this point . from the tetrad at x we obtain another tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } at x by parallel transport on . by raising the frame index and lowering the vectorial index we also obtain a dual tetrad at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$x : e_\alpha ^0 = - { g_{\alpha \beta}}e_0^\beta$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_\alpha ^a = { \delta ^{ab}}{g_{\alpha \beta}}e_b^\beta$\end{document}. the metric at x can be then be expressed as 140\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\alpha \beta } } = - e_\alpha ^0e_\beta ^0 + { \delta _ { ab}}e_\alpha ^ae_\beta ^b,$$\end{document } and the parallel propagator from x to x is given by 141\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^\alpha}_{\alpha { \prime}}(x,\;x{\prime } ) = - e_0^\alpha { u_{\alpha { \prime } } } + e_a^\alpha e_{\alpha { \prime}}^a,\quad \quad { g^{\alpha { \prime}}}_\alpha ( x{\prime},\;x ) = { u^{\alpha { \prime}}}e_\alpha ^0 + e_a^{\alpha { \prime}}e_\alpha ^a.$$\end{document } the quasi - cartesian version of the retarded coordinates are defined by 142\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\hat x^0 } = u,\quad \quad { \hat x^a } = - e_{\alpha { \prime}}^a(x{\prime}){\sigma ^{\alpha { \prime}}}(x,\;x{\prime}),\quad \quad \sigma ( x,\;x{\prime } ) = 0;$$\end{document } the last statement indicates that x and x are linked by a null geodesic . from the fact that is a null vector we obtain 143\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$r \equiv { ( { \delta _ { ab}}{\hat x^a}{\hat x^b})^{1/2 } } = { u_{\alpha { \prime}}}{\sigma ^{\alpha { \prime}}},$$\end{document } and r is a positive quantity by virtue of the fact that is a future - directed null geodesic this makes past - directed . in flat spacetime , = ( x x ) , and in a lorentz frame that is momentarily comoving with the world line , r = t t > 0 ; with the speed of light set equal to unity , r is also the spatial distance between x and x as measured in this frame . in curved spacetime , the quantity r = u can still be called the retarded distance between the point x and the world line . another consequence of equation ( 142 ) is that 144\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\sigma ^{\alpha { \prime } } } = - r\left({{u^{\alpha { \prime } } } + { \omega ^a}e_a^{\alpha { \prime } } } \right),$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega ^a } \equiv { { \hat x}^a}/r$\end{document } is a spatial vector that satisfies ab = 1 . a straightforward calculation reveals that under a displacement of the point x , the retarded coordinates change according to 145\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$du = - { k_\alpha}d{x^\alpha},\quad \quad d{\hat x^a } = - \left({r{a^a } - { \omega ^a}_b{{\hat x}^b } + e_{\alpha { \prime}}^a{\sigma ^{\alpha { \prime}}}_{\beta { \prime}}{u^{\beta { \prime } } } } \right)du - e_{\alpha { \prime}}^a{\sigma ^{\alpha { \prime}}}_\beta d{x^\beta},$$\end{document } where k = /r is a future - directed null vector at x that is tangent to the geodesic . to obtain these results we must keep in mind that a displacement of x typically induces a simultaneous displacement of x because the new points x + x and x + x must also be linked by a null geodesic . we therefore have 0 = (x + x , x + x ) = x + x , and the first relation of equation ( 145 ) follows from the fact that a displacement along the world line is described by x = u u . if we keep x linked to x by the relation (x , x ) = 0 , then the quantity 146\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$r(x ) = { \sigma _ { \alpha { \prime}}}(x,\;x{\prime}){u^{\alpha { \prime}}}(x{\prime})$$\end{document } can be viewed as an ordinary scalar field defined in a neighbourhood of . we can compute the gradient of r by finding how r changes under a displacement of x ( which again induces a displacement of x ) . the result is 147\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\partial _ \beta}r = - \left({{\sigma _ { \alpha { \prime}}}{a^{\alpha { \prime } } } + { \sigma _ { \alpha { \prime}\beta { \prime}}}{u^{\alpha { \prime}}}{u^{\beta { \prime } } } } \right){k_\beta } + { \sigma _ { \alpha { \prime}\beta}}{u^{\alpha { \prime}}}.$$\end{document } similarly , we can view 148\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${k^\alpha}(x ) = { { { \sigma ^\alpha}(x,\;x{\prime } ) } \over { r(x)}}$$\end{document } as an ordinary vector field , which is tangent to the congruence of null geodesics that emanate from x. it is easy to check that this vector satisfies the identities 149\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\sigma _ { \alpha \beta}}{k^\beta } = { k_\alpha},\quad \quad { \sigma _ { \alpha { \prime}\beta}}{k^\beta } = { { { \sigma _ { \alpha { \prime } } } } \over r},$$\end{document } from which we also obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ { { \alpha { \prime}}\beta}}{u^{{\alpha { \prime}}}}{k^\beta } = 1$\end{document}. from this last result and equation ( 147 ) we deduce the important relation 150\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${k^\alpha}{\partial _ \alpha}r = 1.$$\end{document } in addition , combining the general statement \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma ^\alpha } = - { g^\alpha}_{{\alpha { \prime}}}{\sigma ^{{\alpha { \prime}}}}$\end{document } ( cf . equation ( 79 ) ) with equation ( 144 ) gives 151\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${k^\alpha } = { g^\alpha}_{\alpha { \prime}}\left({{u^{\alpha { \prime } } } + { \omega ^a}e_a^{\alpha { \prime } } } \right);$$\end{document } the vector at x is therefore obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^{{\alpha { \prime } } } } + { \omega ^a}e_a^{{\alpha { \prime}}}$\end{document } on . from this and equation ( 141 ) we get the alternative expression 152\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${k^\alpha } = e_0^\alpha + { \omega ^a}e_a^\alpha,$$\end{document } which confirms that k is a future - directed null vector field ( recall that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega ^a } = { { \hat x}^a}/r$\end{document } is a unit vector ) . the covariant derivative of k can be computed by finding how the vector changes under a displacement of x. ( it is in fact easier to first calculate how rk changes , and then substitute our previous expression for r . ) the result is 153\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$r{k_{\alpha ; \beta } } = { \sigma _ { \alpha \beta } } - { k_\alpha}{\sigma _ { \beta \gamma { \prime}}}{u^{\gamma { \prime } } } - { k_\beta}{\sigma _ { \alpha \gamma { \prime}}}{u^{\gamma { \prime } } } + \left({{\sigma _ { \alpha { \prime}}}{a^{\alpha { \prime } } } + { \sigma _ { \alpha { \prime}\beta { \prime}}}{u^{\alpha { \prime}}}{u^{\beta { \prime } } } } \right){k_\alpha}{k_\beta}.$$\end{document } from this we infer that k satisfies the geodesic equation in affine - parameter form , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${k^\alpha}_{;\beta}{k^\beta } = 0$\end{document } , and equation ( 150 ) informs us that the affine parameter is in fact r. a displacement along a member of the congruence is therefore given by dx = k dr . specializing to retarded coordinates , and using equations ( 145 ) and ( 149 ) , we find that this statement becomes du = 0 and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d{{\hat x}^a } = ( { { \hat x}^a}/r)dr$\end{document } , which integrate to u = const and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^a } = r{\omega ^a}$\end{document } , respectively , with still denoting a constant unit vector . we have found that the congruence of null geodesics emanating from x is described by 154\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$u = { \rm{const}}.,\quad \quad { \hat x^a } = r{\omega ^a}({\theta ^a})$$\end{document } in the retarded coordinates . here , the two angles ( a = 1 , 2 ) serve to parameterize the unit vector , which is independent of r. equation ( 153 ) also implies that the expansion of the congruence is given by 155\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\theta = { k^\alpha}_{;\alpha } = { { { \sigma ^\alpha}_\alpha - 2 } \over r}.$$\end{document } using the expansion for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma ^\alpha}_\alpha$\end{document } given by equation ( 91 ) , we find that this becomes \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r\theta = 2 - { 1 \over 3}{r_{{\alpha { \prime}}{\beta { \prime}}}}{\sigma ^{{\alpha { \prime}}}}{\sigma ^{{\beta { \prime } } } } + { \mathcal o}({r^3})$\end{document } , or 156\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$r\theta = 2 - { 1 \over 3}{r^2}({r_{00 } } + 2{r_{0a}}{\omega ^a } + { r_{ab}}{\omega ^a}{\omega ^b } ) + \mathcal{o}({r^3})$$\end{document } after using equation ( 144 ) . here , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{00 } } = { r_{{\alpha { \prime}}{\beta { \prime}}}}{u^{{\alpha { \prime}}}}{u^{{\beta { \prime}}}},\,{r_{0a } } = { r_{{\alpha { \prime}}{\beta { \prime}}}}{u^{{\alpha { \prime}}}}e_a^{{\beta { \prime}}}$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{ab } } = { r_{{\alpha { \prime}}{\beta { \prime}}}}e_a^{{\alpha { \prime}}}e_b^{{\beta { \prime}}}$\end{document } are the frame components of the ricci tensor evaluated at x. this result confirms that the congruence is singular at r = 0 , because diverges as 2/r in this limit ; the caustic coincides with the point x. finally , we infer from equation ( 153 ) that k is hypersurface orthogonal . this , together with the property that k satisfies the geodesic equation in affine - parameter form , implies that there exists a scalar field u(x ) such that 157\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${k_\alpha } = - { \partial _ \alpha}u.$$\end{document } this scalar field was already identified in equation ( 145 ) : it is numerically equal to the propertime parameter of the world line at x. we conclude that the geodesics to which k is tangent are the generators of the null cone u = const as equation ( 154 ) indicates , a specific generator is selected by choosing a direction ( which can be parameterized by two angles ) , and r is an affine parameter on each generator . the geometrical meaning of the retarded coordinates is now completely clear ; it is illustrated in figure 7 . figure 7retarded coordinates ofa point x relative to a world line . the retarded time u selects a particular null cone , the unit vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega ^a } \equiv { { \hat x}^a}/r$\end{document } selects a particular generator of this null cone , and the retarded distance r selects a particular point on this generator . retarded coordinates ofa point x relative to a world line . the retarded time u selects a particular null cone , the unit vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega ^a } \equiv { { \hat x}^a}/r$\end{document } selects a particular generator of this null cone , and the retarded distance r selects a particular point on this generator . the metric at x in the retarded coordinates will be expressed in terms of frame components of vectors and tensors evaluated on the world line . for example , if a is the acceleration vector at x , then as we have seen , 158\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a_a}(u ) = { a_{\alpha { \prime}}}e_a^{\alpha { \prime}}$$\end{document } are the frame components of the acceleration at proper time u. similarly , 159\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { r_{a0b0}}(u ) = { r_{\alpha { \prime}\gamma { \prime}\beta { \prime}\delta { \prime}}}e_a^{\alpha { \prime}}{u^{\gamma { \prime}}}e_b^{\beta { \prime}}{u^{\delta { \prime } } } } , \\ { { r_{a0bd}}(u ) = { r_{\alpha { \prime}\gamma { \prime}\beta { \prime}\delta { \prime}}}e_a^{\alpha { \prime}}{u^{\gamma { \prime}}}e_b^{\beta { \prime}}u_d^{\delta { \prime } } } , \\ { { r_{acbd}}(u ) = { r_{\alpha { \prime}\gamma { \prime}\beta { \prime}\delta { \prime}}}e_a^{\alpha { \prime}}e_c^{\gamma { \prime}}e_b^{\beta { \prime}}u_d^{\delta { \prime } } } \\ \end{array}$$\end{document } are the frame components of the riemann tensor evaluated on . from these we form the useful combinations 160\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_{ab}}(u,\;{\theta ^a } ) = { r_{a0b0 } } + { r_{a0bc}}{\omega ^c } + { r_{b0ac}}{\omega ^c } + { r_{acbd}}{\omega ^c}{\omega ^d } = { s_{ba}},$$\end{document } 161\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_{ab}}(u,\;{\theta ^a } ) = { s_{ab}}{\omega ^b } = { r_{a0b0}}{\omega ^b } - { r_{ab0c}}{\omega ^b}{\omega ^c},$$\end{document } 162\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$s(u,\;{\theta ^a } ) = { s_a}{\omega ^a } = { r_{a0b0}}{\omega ^a}{\omega ^b},$$\end{document } in which the quantities \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega ^a } \equiv { { \hat x}^a}/r$\end{document } depend on the angles only they are independent of u and r. we have previously introduced the frame components of the ricci tensor in equation ( 156 ) . the identity 163\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{00 } } + 2{r_{0a}}{\omega ^a } + { r_{ab}}{\omega ^a}{\omega ^b } = { \delta ^{ab}}{s_{ab } } - s$$\end{document } follows easily from equations ( 160 , 161 , 162 ) and the definition of the ricci tensor . in section 3.2 we saw that the frame components of a given tensor were also the components of this tensor ( evaluated on the world line ) in the fermi normal coordinates . we should not expect this property to be true also in the case of the retarded coordinates : the frame components of a tensor are not to be identified with the components of this tensor in the retarded coordinates . the reason is that the retarded coordinates are in fact singular on the world line . as we shall see , they give rise to a metric that possesses a directional ambiguity at r = 0 . ( this can easily be seen in minkowski spacetime by performing the coordinate transformation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$u = t - \sqrt { { x^2 } + { y^2 } + { z^2}})$\end{document } components of tensors are therefore not defined on the world line , although they are perfectly well defined for r 0 . frame components , on the other hand , are well defined both off and on the world line , and working with them will eliminate any difficulty associated with the singular nature of the retarded coordinates . the changes in the quasi - cartesian retarded coordinates under a displacement of x are given by equation ( 145 ) . in these we substitute the standard expansions for and , as given by equations ( 88 ) and ( 89 ) , as well as equations ( 144 ) and ( 151 ) . after a straightforward ( but fairly lengthy ) calculation , we obtain the following expressions for the coordinate displacements : 164\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$du = \left({e_\alpha ^0d{x^\alpha } } \right ) - { \omega _ a}\left({e_\alpha ^bd{x^\alpha } } \right),$$\end{document } 165\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{d{{\hat x}^a } = - \left [ { r{a^a } - r{\omega ^a}_b{\omega ^b } + { 1 \over 2}{r^2}{s^a } + { \mathcal o}({r^3 } ) } \right](e_\alpha ^0d{x^\alpha})\quad \quad \quad \quad \quad \quad \quad \quad \ ; } \\{\quad \quad \ ; + \left [ { \delta _ { \;\;b}^a + \left({r{a^a } - r{\omega ^a}_c{\omega ^c } + { 1 \over 3}{r^2}{s^a } } \right){\omega _ b } + { 1 \over 6}{r^2}{s^a}_b + { \mathcal o}({r^3 } ) } \right](e_\alpha ^bd{x^\alpha}){. } } \\\end{array}$$\end{document } notice that the result for du is exact , but that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d{{\hat x}^a}$\end{document } is expressed as an expansion in powers of r. these results can also be expressed in the form of gradients of the retarded coordinates : 166\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\partial _ \alpha}u = e_\alpha ^0 - { \omega _ a}e_\alpha ^a,$$\end{document } 167\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{\partial _ \alpha}{{\hat x}^a } = - \left [ { r{a^a } - r{\omega ^a}_b{\omega ^b } + { 1 \over 2}{r^2}{s^a } + { \mathcal o}({r^3 } ) } \right]e_\alpha ^0\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \;\;\ ; } \\{+ \left [ { { \delta ^a}_b + \left({r{a^a } - r{\omega ^a}_c{\omega ^c } + { 1 \over 3}{r^2}{s^a } } \right){\omega _ b } + { 1 \over 6}{r^2}{s^a}_b + { \mathcal o}({r^3 } ) } \right]e_\alpha ^b . } \\\end{array}$$\end{document } notice that equation ( 166 ) follows immediately from equations ( 152 ) and ( 157 ) . from equation ( 167 ) and the identity \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\partial _ we also infer 168\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\partial _ \alpha}r = - \left [ { r{a_a}{\omega ^a } + { 1 \over 2}{r^2}s + \mathcal{o}({r^3 } ) } \right]e_\alpha ^0 + \left [ { \left({1 + r{a_b}{\omega ^b } + { 1 \over 3}{r^2}s } \right){\omega _ a } + { 1 \over 6}{r^2}{s_a } + \mathcal{o}({r^3 } ) } \right]e_\alpha ^a,$$\end{document } where we have used the facts that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${s_a } = { s_{ab}}{\omega ^b}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$s = { s_a}{\omega ^a}$\end{document } ; these last results were derived in equations ( 161 ) and ( 162 ) . it may be checked that equation ( 168 ) agrees with equation ( 147 ) . it is straightforward ( but fairly tedious ) to invert the relations of equations ( 164 ) and ( 165 ) and solve for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_\alpha ^0d{x^a}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_\alpha ^ad{x^\alpha}$\end{document}. the results are 169\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$e_\alpha ^0d{x^\alpha } = \left [ { 1 + r{a_a}{\omega ^a } + { 1 \over 2}{r^2}s + \mathcal{o}({r^3 } ) } \right]du + \left [ { \left({1 + { 1 \over 6}{r^2}s } \right){\omega _ a } - { 1 \over 6}{r^2}{s_a } + \mathcal{o}({r^3 } ) } \right]d{\hat x^a},$$\end{document } 170\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$e_\alpha ^ad{x^\alpha } = \left [ { r({a^a } - { \omega ^a}_b{\omega ^b } ) + { 1 \over 2}{r^2}{s^a } + \mathcal{o}({r^3 } ) } \right]du + \left [ { { \delta ^a}_b - { 1 \over 6}{r^2}{s^a}_b + { 1 \over 6}{r^2}{s^a}{\omega _ b } + \mathcal{o}({r^3 } ) } \right]d{\hat x^b}.$$\end{document } these relations , when specialized to the retarded coordinates , give us the components of the dual tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_\alpha ^0,e_\alpha ^a)$\end{document } at x. the metric is then computed by using the completeness relations of equation ( 140 ) . we find \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d{s^2 } = { g_{uu}}d{u^2 } + 2{g_{ua}}dud{\hat x^a } + { g_{ab}}d{\hat x^a}d{\hat x^b},$$\end{document } with 171\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{uu } } = - { ( 1 + r{a_a}{\omega ^a})^2 } + { r^2}({a_a } - { \omega _ { ab}}{\omega ^b})({a^a } - { \omega ^a}_c{\omega ^c } ) - { r^2}s + \mathcal{o}({r^3}),$$\end{document } 172\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ua } } = - \left({1 + r{a_b}{\omega ^b } + { 2 \over 3}{r^2}s } \right){\omega _ a } + r({a_a } - { \omega _ { ab}}{\omega ^b } ) + { 2 \over 3}{r^2}{s_a } + \mathcal{o}({r^3}),$$\end{document } 173\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ab } } = { \delta _ { ab } } - \left({1 + { 1 \over 3}{r^2}s } \right){\omega _ a}{\omega _ b } - { 1 \over 3}{r^2}{s_{ab } } + { 1 \over 3}{r^2}({s_a}{\omega _ b } + { \omega _ a}{s_b } ) + \mathcal{o}({r^3}).$$\end{document } we see ( as was pointed out in section 3.3.4 ) that the metric possesses a directional ambiguity on the world line : the metric at r = 0 still depends on the vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega ^a } = { { \hat x}^a}/r$\end{document } that specifies the direction to the point x. the retarded coordinates are therefore singular on the world line , and tensor components can not be defined on . by setting sab = sa = s = 0 in equations ( 171 , 172 , 173 ) we obtain the metric of flat spacetime in the retarded coordinates . this we express as 174\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{\eta _ { uu } } = - { { ( 1 + r{a_a}{\omega ^a})}^2 } + { r^2}({a_a } - { \omega _ { ab}}{\omega ^b})({a^a } - { \omega ^a}_c{\omega ^c}),\;\ ; } \\ { { \eta _ { ua } } = - ( 1 + r{a_b}{\omega ^b})\;{\omega _ a } + r({a_a } - { \omega _ { ab}}{\omega ^b}),\quad \quad \quad \quad \quad } \\{{\eta _ { ab } } = { \delta _ { ab } } - { \omega _ a}{\omega _ b}.\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } in spite of the directional ambiguity , the metric of flat spacetime has a unit determinant everywhere , and it is easily inverted : 175\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta ^{uu } } = 0,\quad \quad { \eta ^{ua } } = - { \omega ^a},\quad \quad { \eta ^{ab } } = { \delta ^{ab } } + r({a^a } - { \omega ^a}_c{\omega ^c}){\omega ^b } + r{\omega ^a}({a^b } - { \omega ^b}_c{\omega ^c}).$$\end{document } the inverse metric also is ambiguous on the world line . to invert the curved - spacetime metric of equations ( 171 , 172 , 173 ) we express it as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\alpha \beta } } = { \eta _ { \alpha \beta } } + { h_{\alpha \beta } } + { \mathcal o}({r^3})$\end{document } and treat \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h_{\alpha \beta } } = { \mathcal o}({r^2})$\end{document } as a perturbation . the inverse metric is then \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{\alpha \beta } } = { \eta ^{\alpha \beta } } - { \eta ^{\alpha \gamma}}{\eta ^{\beta \delta}}{h_{\gamma \delta } } + { \mathcal o}({r^3})$\end{document } , or 176\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^{uu } } = 0,$$\end{document } 177\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^{ua } } = - { \omega ^a},$$\end{document } 178\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^{ab } } = { \delta ^{ab } } + r({a^a } - { \omega ^a}_c{\omega ^c}){\omega ^b } + r{\omega ^a}({a^b } - { \omega ^b}_c{\omega ^c } ) + { 1 \over 3}{r^2}{s^{ab } } + { 1 \over 3}{r^2}({s^a}{\omega ^b } + { \omega ^a}{s^b } ) + \mathcal{o}({r^3}).$$\end{document } the results for g and g are exact , and they follow from the general relations g(du)(du ) = 0 and g(u)(r ) = 1 that are derived from equations ( 150 ) and ( 157 ) . the metric determinant is computed from \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt { - g } = 1 + { 1 \over 2}{\eta ^{\alpha \beta}}{h_{\alpha \beta } } + { \mathcal o}({r^3})$\end{document } , which gives 179\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\sqrt { - g } = 1 - { 1 \over 6}{r^2}({\delta ^{ab}}{s_{ab } } - s ) + \mathcal{o}({r^3 } ) = 1 - { 1 \over 6}{r^2}({r_{00 } } + 2{r_{0a}}{\omega ^a } + { r_{ab}}{\omega ^a}{\omega ^b } ) + \mathcal{o}({r^3}),$$\end{document } where we have substituted the identity of equation ( 163 ) . comparison with equation ( 156 ) then gives us the interesting relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt { - g } = { 1 \over 2}r\theta + { \mathcal o}({r^3})$\end{document } , where is the expansion of the generators of the null cones u = const . because the vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega ^a } = { { \hat x}^a}/r$\end{document } satisfies ab = 1 , it can be parameterized by two angles . a canonical choice for the parameterization is = ( sin cos , sin sin , cos ) . it is then convenient to perform a coordinate transformation from \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^a}$\end{document } to ( r , ) , using the relations \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^a } = r{\omega ^a}({\theta ^a})$\end{document}. ( recall from section 3.3.3 that the angles are constant on the generators of the null cones u = const . , and that r is an affine parameter on these generators . the relations \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^a } = r{\omega ^a}$\end{document } therefore describe the behaviour of the generators . ) the differential form of the coordinate transformation is 180\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d{\hat x^a } = { \omega ^a}dr + r\omega _ a^ad{\theta ^a},$$\end{document } where the transformation matrix 181\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\omega _ a^a \equiv { { \partial { \omega ^a } } \over { \partial { \theta ^a}}}$$\end{document } satisfies the identity \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega _ a}\omega _ a^a = 0$\end{document}. we introduce the quantities 182\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\omega _ { ab } } = { \delta _ { ab}}\omega _ a^a\omega _ b^b,$$\end{document } which act as a ( nonphysical ) metric in the subspace spanned by the angular coordinates . in the canonical parameterization , ab = diag(1 , sin ) we use the inverse of ab , denoted , to raise upper - case latin indices . we then define the new object 183\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\omega _ = { \delta _ { ab}}{\omega ^{ab}}\omega _ b^b$$\end{document } which satisfies the identities 184\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\omega _ a^a\omega _ b^a = \delta _ b^a,\quad \quad \omega _ a^a\omega _ b^a = { \delta ^a}_b - { \omega ^a}{\omega _ b}.$$\end{document } the second result follows from the fact that both sides are simultaneously symmetric in and b , orthogonal to a and , and have the same trace . from the preceding results we establish that the transformation from \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^a}\,{\rm{to}}\,{\rm{(}}r,{\theta ^a})$\end{document } to ( r , ) is accomplished by 185\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\partial { { \hat x}^a } } \over { \partial r } } = { \omega ^a},\quad \quad { { \partial { { \hat x}^a } } \over { \partial { \theta ^a } } } = r\omega _ a^a,$$\end{document } while the transformation from ( r , ) to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(r,{\theta ^a})$\end{document } is accomplished by 186\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\partial r } \over { \partial { { \hat x}^a } } } = { \omega _ a},\quad \quad { { \partial { \theta ^a } } \over { \partial { { \hat x}^a } } } = { 1 \over r}\omega _ a^a.$$\end{document } with these transformation rules it is easy to show that in the angular coordinates , the metric takes the form of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d{s^2 } = { g_{uu}}d{u^2 } + 2{g_{ur}}dudr + 2{g_{ua}}dud{\theta ^a } + { g_{ab}}d{\theta ^a}d{\theta ^b},$$\end{document } with 187\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{uu } } = - { ( 1 + r{a_a}{\omega ^a})^2 } + { r^2}({a_a } - { \omega _ { ab}}{\omega ^b})({a^a } - { \omega ^a}_c{\omega ^c } ) - { r^2}s + \mathcal{o}({r^3}),$$\end{document } 188\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ur } } = - 1,$$\end{document } 189\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ua } } = r\left [ { r({a_a } - { \omega _ { ab}}{\omega ^b } ) + { 2 \over 3}{r^2}{s_a } + \mathcal{o}({r^3 } ) } \right]\omega _ a^a,$$\end{document } 190\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ab } } = { r^2}\left [ { { \omega _ { ab } } - { 1 \over 3}{r^2}{s_{ab}}\omega _ a^a\omega _ b^b + \mathcal{o}({r^3 } ) } \right].$$\end{document } the results gru = 1 , grr = 0 , and gra = 0 are exact , and they follow from the fact that in the retarded coordinates , k dx = du and k = r . the nonvanishing components of the inverse metric are 191\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^{ur } } = - 1,$$\end{document } 192\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^{rr } } = 1 + 2r{a_a}{\omega ^a } + { r^2}s + \mathcal{o}({r^3}),$$\end{document } 193\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^{ra } } = { 1 \over r}\left [ { r({a^a } - { \omega ^a}_b{\omega ^b } ) + { 2 \over 3}{r^2}{s^a } + \mathcal{o}({r^3 } ) } \right]\omega _ a^a,$$\end{document } 194\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g^{ab } } = { 1 \over { { r^2}}}\left [ { { \omega ^{ab } } + { 1 \over 3}{r^2}{s^{ab}}\omega _ a^a\omega _ b^b + \mathcal{o}({r^3 } ) } \right].$$\end{document } the results g = 0 , g = 1 , and g = 0 are exact , and they follow from the same reasoning as before . finally , we note that in the angular coordinates , the metric determinant is given by 195\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\sqrt { - g } = { r^2}\sqrt \omega \left [ { 1 - { 1 \over 6}{r^2}({r_{00 } } + 2{r_{0a}}{\omega ^a } + { r_{ab}}{\omega ^a}{\omega ^b } ) + \mathcal{o}({r^3 } ) } \right],$$\end{document } where is the determinant of ab ; in the canonical parameterization , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt \omega = \sin \theta$\end{document}. in this section we specialize our previous results to a situation where is a geodesic on which the ricci tensor vanishes . we therefore set a = 0 = r everywhere on , and for simplicity we also set ab to zero . we have seen in section 3.2.6 that when the ricci tensor vanishes on , all frame components of the riemann tensor can be expressed in terms of the symmetric - tracefree tensors \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}_{ab}}(u)$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal b}_{ab}}(u)$\end{document}. the relations are \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{a0b0 } } = { { \mathcal e}_{ab}},\,{r_{a0bc } } = { \epsilon _ { bcd}}{{\mathcal b}^d}_a$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{acbd } } = { \delta _ { ab}}{{\mathcal e}_{cd } } + { \delta _ { cd}}{{\mathcal e}_{ab } } - { \delta _ { ad}}{{\mathcal e}_{bc } } - { \delta _ { bc}}{{\mathcal e}_{ad}}$\end{document}. these can be substituted into equations ( 160 , 161 , 162 ) to give 196\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_{ab}}(u,{\theta ^a } ) = 2{\mathcal{e}_{ab } } - { \omega _ a}{\mathcal{e}_{bc}}{\omega ^c } - { \omega _ b}{\mathcal{e}_{ac}}{\omega ^c } + { \delta _ { ab}}{\mathcal{e}_{bc}}{\omega ^c}{\omega ^d } + { \varepsilon _ { acd}}{\omega ^c}{\mathcal{b}^d}_b + { \varepsilon _ { bcd}}{\omega ^c}{\mathcal{b}^d}_a,$$\end{document } 197\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_a}(u,{\theta ^a } ) = { \mathcal{e}_{ab}}{\omega ^b } + { \varepsilon _ { abc}}{\omega ^b}{\mathcal{b}^c}_d{\omega ^d},$$\end{document } 198\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$s(u,{\theta ^a } ) = { \mathcal{e}_{ab}}{\omega ^a}{\omega ^b}.$$\end{document } in these expressions the dependence on retarded time u is contained in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}_{ab}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal b}_{ab}}$\end{document } , while the angular dependence is encoded in the unit vector . it is convenient to introduce the irreducible quantities 199\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\mathcal{e}^{\ast } } = { \mathcal{e}_{ab}}{\omega ^a}{\omega ^b},$$\end{document } 200\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\mathcal{e}_a^{\ast } = ( { \delta _ a}^b - { \omega _ a}{\omega ^b}){\mathcal{e}_{bc}}{\omega ^c},$$\end{document } 201\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\mathcal{e}_{ab}^{\ast } = 2{\mathcal{e}_{ab } } - 2{\omega _ a}{\mathcal{e}_{bc}}{\omega ^c } - 2{\omega _ b}{\mathcal{e}_{ac}}{\omega ^c } + ( { \delta _ { ab } } + { \omega _ a}{\omega _ b})\mathcal{e}^{\ast},$$\end{document } 202\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\mathcal{b}_{a}^{\ast } = { \epsilon _ { abc}}{\omega ^b}{\mathcal{b}^c}_d{\omega ^d},$$\end{document } 203\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\mathcal{b}_{ab}^{\ast } = { \epsilon _ { acd}}{\omega ^c}{\mathcal{b}^d}_e({\delta ^e}_b - { \omega ^e}{\omega _ b } ) + { \epsilon _ { bcd}}{\omega ^c}{\mathcal{b}^d}_e({\delta ^e}_a - { \omega ^e}{\omega _ a}).$$\end{document } these are all orthogonal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega ^a}:{\mathcal e}_a^{\ast}{\omega ^a } = { \mathcal b}_a^{\ast}{\omega ^a } = 0$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal e}_{ab}^{\ast}{\omega ^b } = { \mathcal b}_{ab}^{\ast}{\omega ^b } = 0$\end{document}. in terms of these equations ( 196 , 197 , 198 ) become 204\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_{ab } } = \mathcal{e}_{ab}^{\ast } + { \omega _ a}\mathcal{e}_b^{\ast } + \mathcal{e}_a^{\ast}{\omega _ b } + { \omega _ a}{\omega _ b}\mathcal{e}^{\ast } + \mathcal{b}_{ab}^{\ast } + { \omega _ a}\mathcal{b}_b^{\ast } + \mathcal{b}_a^{\ast}{\omega _ b},$$\end{document } 205\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_a } = \mathcal{e}_a^{\ast } + { \omega _ a}\mathcal{e}^{\ast } + \mathcal{b}_a^{\ast},$$\end{document } 206\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$s = \mathcal{e}^{\ast}.$$\end{document } when equations ( 204 , 205 , 206 ) are substituted into the metric tensor of equations ( 171 , 172 , 173 ) in which aa and ab are both set equal to zero we obtain the compact expressions 207\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{uu } } = - 1 - { r^2}\mathcal{e}^{\ast } + \mathcal{o}({r^3}),$$\end{document } 208\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ua } } = - { \omega _ a } + { 2 \over 3}{r^2}(\mathcal{e}_a^{\ast } + \mathcal{b}_a^{\ast } ) + \mathcal{o}({r^3}),$$\end{document } 209\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ab } } = { \delta _ { ab } } - { \omega _ a}{\omega _ b } - { 1 \over 3}{r^2}(\mathcal{e}_{ab}^{\ast } + \mathcal{b}_{ab}^{\ast } ) + \mathcal{o}({r^3}).$$\end{document } the metric becomes 210\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{uu } } = - 1 - { r^2}\mathcal{e}^{\ast } + \mathcal{o}({r^3}),$$\end{document } 211\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ur } } = - 1,$$\end{document } 212\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ua } } = { 2 \over 3}{r^3}(\mathcal{e}_a^{\ast } + \mathcal{b}_a^{\ast } ) + \mathcal{o}({r^4}),$$\end{document } 213\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ab } } = { r^2}{\omega _ { ab } } - { 1 \over 3}{r^4}(\mathcal{e}_{ab}^{\ast } + \mathcal{b}_{ab}^{\ast } ) + \mathcal{o}({r^5})$$\end{document } after transforming to angular coordinates using the rules of equation ( 185 ) . here we have introduced the projections 214\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\mathcal{e}_a^{\ast } \equiv \mathcal{e}_a^{\ast}\omega _ a^a = { \mathcal{e}_{ab}}\omega _ a^a{\omega ^b},$$\end{document } 215\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\mathcal{e}_{ab}^{\ast } \equiv \mathcal{e}_{ab}^{\ast}\omega _ a^a\omega _ b^b = 2{\mathcal{e}_{ab}}\omega _ a^a\omega _ b^b + \mathcal{e}^{\ast}{\omega _ { ab}},$$\end{document } 216\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\mathcal{b}_a^{\ast } \equiv \mathcal{b}_a^{\ast}\omega _ a^a = { \epsilon _ { abc}}\omega _ a^a{\omega ^b}{\mathcal{b}^c}_d{\omega ^d},$$\end{document } 217\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\mathcal{b}_{ab}^{\ast } \equiv \mathcal{b}_{ab}^{\ast}\omega _ a^a\omega _ b^b = 2{\epsilon _ { acd}}{\omega ^c}{\mathcal{b}^d}_b{\omega ^a}_{(a}\omega _ { b)}^b.$$\end{document } it may be noted that the inverse relations are \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal e}_a^{\ast } = { \mathcal e}_a^{\ast}\omega _ b^b$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal b}_{ab}^{\ast } = { \mathcal b}_{ab}^{\ast}\omega _ b^b$\end{document } , where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\omega _ a^a$\end{document } was introduced in equation ( 183 ) . a point x in the normal convex neighbourhood of a world line can be assigned a set of fermi normal coordinates ( as in section 3.2 ) , or it can be assigned a set of retarded coordinates ( see section 3.3 ) . these coordinate systems can obviously be related to one another , and our first task in this section ( which will occupy us in sections 3.4.1 , 3.4.2 , and 3.4.3 ) will be to derive the transformation rules . the fermi normal coordinates of x refer to a point \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document } on that is related to x by a spacelike geodesic that intersects orthogonally ( see figure 8) . we refer to this point as x s simultaneous point , and to tensors at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } we assign indices \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar \alpha}$\end{document } , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar \beta}$\end{document } etc . we let ( t , s ) be the fermi normal coordinates of x , with t denoting the value of s proper - time parameter at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x , s = \sqrt { 2\sigma ( x,\bar x)}$\end{document } representing the proper distance from \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } to x along the spacelike geodesic , and denoting a unit vector ( ab = 1 ) that determines the direction of the geodesic . the fermi normal coordinates are defined by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal s}{\omega ^a } = - e_{\bar \alpha}^a{\sigma ^{\bar \alpha}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma _ { \bar \alpha}}{u^{\bar \alpha } } = 0$\end{document}. finally , we denote by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } , the tetrad at x that is obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{\bar \alpha}},\bar e_a^{\bar \alpha})$\end{document } on the spacelike geodesic . figure 8the retarded , simultaneous , and advanced points on a world line . the retarded point x the simultaneous point \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document } is linked to x by a spacelike geodesic that intersects orthogonally . the advanced point x = is linked to x by a past - directed null geodesic . the retarded , simultaneous , and advanced points on a world line . the retarded point x the simultaneous point \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document } is linked to x by a spacelike geodesic that intersects orthogonally . the advanced point x = is linked to x by a past - directed null geodesic . the retarded coordinates of x refer to a point x z(u ) on that is linked to x by a future - directed null geodesic ( see figure 8) . we refer to this point as x s retarded point , and to tensors at x we assign indices , , etc . we let ( u , r ) be the retarded coordinates of x , with u denoting the value of s proper - time parameter at x , r = u representing the affine - parameter distance from x to x along the null geodesic , and denoting a unit vector ( ab = 1 ) that determines the direction of the geodesic . the retarded coordinates are defined by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal s}{\omega ^a } = - e_{\bar \alpha}^a{\sigma ^{\bar \alpha}}$\end{document } and (x , x ) = 0 . finally , we denote by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } the tetrad at x that is obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{\bar \alpha}},e_a^{\bar \alpha})$\end{document } on the null geodesic . the reader not interested in following the details of this discussion can be informed that our results concerning the transformation from the retarded coordinates ( u , r , ) to the fermi normal coordinates ( t , s , ) are contained in equations ( 218 , 219 , 220 ) below;our results concerning the transformation from the fermi normal coordinates ( t , s , ) to the retarded coordinates ( u , r , ) are contained in equations ( 221 , 222 , 223);the decomposition of each member of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } is given in retarded coordinates by equations ( 224 ) and ( 225 ) ; andthe decomposition of each member of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } is given in fermi normal coordinates by equations ( 226 ) and ( 227 ) . our results concerning the transformation from the retarded coordinates ( u , r , ) to the fermi normal coordinates ( t , s , ) are contained in equations ( 218 , 219 , 220 ) below ; our results concerning the transformation from the fermi normal coordinates ( t , s , ) to the retarded coordinates ( u , r , ) are contained in equations ( 221 , 222 , 223 ) ; the decomposition of each member of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } is given in retarded coordinates by equations ( 224 ) and ( 225 ) ; and the decomposition of each member of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } is given in fermi normal coordinates by equations ( 226 ) and ( 227 ) . our final task will be to define , along with the retarded and simultaneous points , an advanced point x on the world line ( see figure 8) . we shall set ab = 0 , where ab is the rotation tensor defined by equation ( 138 ) the tetrad vectors \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_a^\mu$\end{document } will be assumed to be fermi - walker transported on . quantities at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv x(t)$\end{document } can be related to quantities at x z(u ) by taylor expansion along the world line . to implement this strategy we must first find an expression for t u. ( although we use the same notation , this should not be confused with the van vleck determinant introduced in section 2.5 . ) consider the function p( ) of the proper - time parameter defined by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\rho ( \tau ) = { \sigma _ \mu}(x , z(\tau)){u^\mu}(\tau),$$\end{document } in which x is kept fixed and in which z( ) is an arbitrary point on the world line . we have that p(u ) = r and p(t ) = 0 , and can ultimately be obtained by expressing p(t ) as p(u + ) and expanding in powers of . formally , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$p(t ) = p(u ) + \dot p(u)\delta + { 1 \over 2}\ddot p(u){\delta ^2 } + { 1 \over 6}{p^{(3)}}(u){\delta ^3 } + \mathcal{o}({\delta ^4}),$$\end{document } where overdots ( or a number within brackets ) indicate repeated differentiation with respect to . we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{\dot p(u ) = { \sigma _ { \alpha \prime \beta \prime}}{u^{\alpha \prime}}{u^{\beta \prime } } + { \sigma _ { \alpha \prime}}{a^{{a\prime}}},\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \;\ ; } \\ { \ddot p(u ) = { \sigma _ { \alpha \prime \beta \prime}}_{\gamma \prime}{u^{\alpha \prime}}{u^{\beta \prime}}{u^{\gamma \prime } } + 3{\sigma _ { \alpha \prime \beta \prime}}{u^{\alpha \prime}}{a^{\beta \prime } } + { \sigma _ { \alpha \prime}}{{\dot a}^{\alpha \prime}},\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { { p^{(3)}}(u ) = { \sigma _ { \alpha \prime \beta \prime}}_{\gamma \prime \delta \prime}{u^{\alpha \prime}}{u^{\beta \prime}}{u^{\gamma \prime}}{u^{\delta \prime } } + { \sigma _ { \alpha \prime \beta \prime}}_{\gamma \prime}\left({5{a^{\alpha \prime}}{u^{\beta \prime}}{u^{\gamma \prime } } + { u^{\alpha \prime}}{u^{\beta \prime}}{u^{\gamma \prime } } } \right ) + { \sigma _ { \alpha \prime \beta \prime}}\left({3{a^{\alpha \prime}}{a^{\beta \prime } } + 4{u^{\alpha \prime}}{{\dot a}^{\beta \prime } } } \right ) + { \sigma _ { \alpha \prime}}{{\ddot a}^{\alpha \prime } } , } \\ \end{array}$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^\mu } = d{u^\mu}/d\tau , \ , { { \dot \alpha}^\mu } = d{a^\mu}/d\tau$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\ddot a}^\mu } = d{{\dot a}^\mu}/d\tau$\end{document}. we now express all of this in retarded coordinates by invoking the expansion of equation ( 88 ) for ( as well as additional expansions for the higher derivatives of the world function , obtained by further differentiation of this result ) and the relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma ^{{\alpha { \prime } } } } = - r({u^{{\alpha { \prime } } } } + { \omega ^a}e_a^{{\alpha { \prime}}})$\end{document } first derived in equation ( 144 ) . with a degree of accuracy sufficient for our purposes we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{\dot p(u ) = - \left [ { 1 + r{a_a}{\omega ^a } + { 1 \over 3}{r^2}s + { \mathcal o}({r^3 } ) } \right ] , } \\{\ddot p(u ) = - r({{\dot a}_0 } + { { \dot a}_a}{\omega ^a } ) + { \mathcal o}({r^2}),\quad \quad \quad } \\{{p^{(3)}}(u ) = { { \dot a}_0 } + { \mathcal o}(r),\quad \quad \quad \quad \quad \quad \quad \quad \quad } \\\end{array}$$\end{document } where s = ra0b0 was first introduced in equation ( 162 ) , and where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\dot a}_0 } \equiv { { \dot a}_{{\alpha { \prime}}}}{u^{{\alpha { \prime}}}},\,\,{{\dot a}_a } \equiv { { \dot a}_{{\alpha { \prime}}}}e_a^{{\alpha { \prime}}}$\end{document } are the frame components of the covariant derivative of the acceleration vector . to arrive at these results we made use of the identityaa + au= 0 that follows from the fact that a is orthogonal to u. notice that there is no distinction between the two possible interpretations a daa / d and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\dot a}_a } \equiv { { \dot a}_\mu}e_a^\mu$\end{document } for the quantity a( ) ; their equality follows at once from the substitution of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$de_a^\mu / d\tau = { a_a}{u^\mu}$\end{document } ( which states that the basis vectors are fermi - walker transported on the world line ) into the identity \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d{a_a}/d\tau = d({a_\nu}e_a^\nu)/d\tau$\end{document}. collecting our results we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$r = \left [ { 1 + r{a_a}{\omega ^a } + { 1 \over 3}{r^2}s + \mathcal{o}({r^3 } ) } \right]\delta + { 1 \over 2}r[{\dot a_0 } + { \dot a_a}{\omega ^a } + \mathcal{o}(r)]{\delta ^2 } - { 1 \over 6}[{\dot a_0 } + \mathcal{o}(r)]{\delta ^3 } + \mathcal{o}({\delta ^4}),$$\end{document } which can readily be solved for t u expressed as an expansion in powers of r. the final result is 218\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$t = u + r\left\{{1 - r{a_a}(u){\omega ^a } + { r^2}{{[{a_a}(u){\omega ^a}]}^2 } - { 1 \over 3}{r^2}{{\dot a}_0}(u ) - { 1 \over 2}{r^2}{{\dot a}_a}(u){\omega ^a } - { 1 \over 3}{r^2}{r_{a0b0}}(u){\omega ^a}{\omega ^b } + \mathcal{o}({r^3 } ) } \right\},$$\end{document } where we show explicitly that all frame components are evaluated at the retarded point z(u ) . to obtain relations between the spatial coordinates we consider the functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${p_a}(\tau ) = - { \sigma _ \mu}(x , z(\tau))e_a^\mu ( \tau),$$\end{document } in which x is fixed and z( ) is an arbitrary point on . we have that the retarded coordinates are given by r = p(u ) , while the fermi coordinates are given instead by s = p(t ) = p(u + ) . this last expression can be expanded in powers of , producing \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$s{\omega ^a } = { p^a}(u ) + { \dot p^a}(u)\delta + { 1 \over 2}{\ddot p^a}(u){\delta ^2 } + { 1 \over 6}{p^{a(3)}}(u){\delta ^3 } + \mathcal{o}({\delta ^4}),$$\end{document } with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{{\dot p}_a}(u ) = - { \sigma _ { \alpha \prime \beta \prime}}e_a^{\alpha \prime}{u^{\beta \prime } } - \left({{\sigma _ { \alpha \prime}}{u^{\alpha \prime } } } \right)\left({{a_{\beta \prime}}e_a^{\beta \prime } } \right)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\ { = - r{a_a } - { 1 \over 3}{r^2}{s_a } + { \mathcal o}({r^3}),\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \;\;\;}\\ { { { \ddot p}_a}(u ) = - { \sigma _ { \alpha \prime \beta \prime \gamma \prime}}e_a^{\alpha \prime}{u^{\beta \prime}}{u^{\gamma \prime } } - \left({2{\sigma _ { \alpha \prime \beta \prime}}{u^{\alpha \prime}}{u^{\beta \prime } } + { \sigma _ { \alpha \prime}}{a^{\alpha \prime } } } \right)\left({{a_{\gamma \prime}}e_a^{\gamma \prime } } \right ) - { \sigma _ { \alpha \prime \beta \prime}}e_a^{\alpha \prime}{a^{\beta \prime } } - \left({{\sigma _ { \alpha \prime}}{u^{\alpha \prime } } } \right)\left({{{\dot a}_{\beta \prime}}e_a^{\beta \prime } } \right)}\\ { = ( 1 + r{a_b}{\omega ^b}){a_a } - r{{\dot a}_a } + { 1 \over 3}r{r_{a0b0}}{\omega ^b } + { \mathcal o}({r^2}),\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\ { p_a^{(3)}(u ) = - { \sigma _ { \alpha \prime \beta \prime \gamma \prime \delta \prime}}e_a^{\alpha \prime}{u^{\beta \prime}}{u^{\gamma \prime}}{u^{\delta \prime}}\;\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \;}\\ { - \left({3{\sigma _ { \alpha \prime \beta \prime \gamma \prime}}{u^{\alpha \prime}}{u^{\beta \prime}}{u^{\gamma \prime } } + 6{\sigma _ { \alpha \prime \beta \prime}}{u^{\alpha \prime}}{a^{\beta \prime } } + { \sigma _ { \alpha \prime}}{{\dot a}^{\alpha \prime } } + { \sigma _ { \alpha \prime}}{u^{\alpha \prime}}{{\dot a}_{\beta \prime}}{u^{\beta \prime } } } \right)\left({{a_{\delta \prime}}e_a^{\delta \prime } } \right)\quad \quad \quad \;\;}\\ { - { \sigma _ { \alpha \prime \beta \prime \gamma \prime}}e_a^{\alpha \prime}\left({2{a^{\beta \prime}}{u^{\gamma \prime } } + { u^{\beta \prime}}{a^{\gamma \prime } } } \right ) - \left({3{\sigma _ { \alpha \prime \beta \prime}}{u^{\alpha \prime}}{u^{\beta \prime } } + 2{\sigma _ { \alpha \prime}}{a^{\alpha \prime } } } \right)\left({{{\dot a}_{\gamma \prime}}e_a^{\gamma \prime } } \right ) - { \sigma _ { \alpha \prime \beta \prime}}e_a^{\alpha \prime}{{\dot a}^{\beta \prime}}}\\ { - \left({{\sigma _ { \alpha \prime}}{u^{\alpha \prime } } } \right)\left({{{\ddot a}_{\beta \prime}}e_a^{\beta \prime } } \right)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\ { = 2{{\dot a}_a } + { \mathcal o}(r).\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } to arrive at these results we have used the same expansions as before and re - introduced sa = ra0b0 rab0c , as it was first defined in equation ( 161 ) . collecting our results we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{s{\omega ^a } = r{\omega ^a } - r\left [ { { a^a } + { 1 \over 3}r{s^a } + { \mathcal o}({r^2 } ) } \right]\delta + { 1 \over 2}\left [ { ( 1 + r{a_b}{\omega ^b}){a^a } - r{{\dot a}^a } + { 1 \over 3}r{r^a}_{0b0}{\omega ^b } + { \mathcal o}({r^2 } ) } \right]{\delta ^2}}\\{+ { 1 \over 3}[{{\dot a}^a } + { \mathcal o}(r)]{\delta ^3 } + { \mathcal o}({\delta ^4}),\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } which becomes 219\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$s{\omega ^a } = r\left\{{{\omega ^a } - { 1 \over 2}r[1 - r{a_b}(u){\omega ^b}]{a^a}(u ) - { 1 \over 6}{r^2}{{\dot a}^a}(u ) - { 1 \over 6}{r^2}{r^a}_{0b0}(u){\omega ^b } + { 1 \over 3}{r^2}r_{b0c}^a(u){\omega ^b}{\omega ^c } + \mathcal{o}({r^3 } ) } \right\}$$\end{document } after substituting equation ( 218 ) for t u. from squaring equation ( 219 ) and using the identity ab = 1 we can also deduce 220\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$s = r\left\{{1 - { 1 \over 2}r{a_a}(u){\omega ^a } + { 3 \over 8}{r^2}{{\left [ { { a_a}(u){\omega ^a } } \right]}^2 } - { 1 \over 8}{r^2}{{\dot a}_0}(u ) - { 1 \over 6}{r^2}{{\dot a}_a}(u){\omega ^a } - { 1 \over 6}{r^2}{r_{a0b0}}(u){\omega ^a}{\omega ^b } + \mathcal{o}({r^3 } ) } \right\}$$\end{document } for the spatial distance between x and z(t ) . the techniques developed in the preceding section 3.4.2 can easily be adapted to the task of relating the retarded coordinates of x to its fermi normal coordinates . here we use \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document } as the reference point and express all quantities at x z(u ) as taylor expansions about = t. we begin by considering the function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\sigma ( \tau ) = \sigma ( x , z(\tau))$$\end{document } of the proper - time parameter on . we have that (t ) = s and (u ) = 0 , and t u is now obtained by expressing (u ) as (t ) and expanding in powers of . using the fact that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\dot \sigma ( \tau ) = p(\tau)$\end{document } , we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\sigma ( u ) = \sigma ( t ) - p(t)\delta + { 1 \over 2}\dot p(t){\delta ^2 } - { 1 \over 6}\ddot p(t){\delta ^3 } + { 1 \over { 24}}{p^{(3)}}(t){\delta ^4 } + \mathcal{o}({\delta ^5}).$$\end{document } expressions for the derivatives of p( ) evaluated at = t can be constructed from results derived previously in section 3.4.1 : it suffices to replace all primed indices by barred indices and then substitute the relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma ^{\bar \alpha } } = - { \mathcal s}{\omega ^a}e_a^{\bar \alpha}$\end{document } that follows immediately from equation ( 116 ) . this gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { \dot p(t ) = - \left [ { 1 + s{a_a}{\omega ^a } + { 1 \over 3}{s^2}{r_{a0b0}}{\omega ^a}{\omega ^b } + \mathcal{o}({s^3 } ) } \right ] , } \\ { \ddot p(t ) = - s{{\dot a}_a}{\omega ^a } + \mathcal{o}({s^2}),}\quad\quad\quad\quad\quad\quad\quad\quad\quad \\ { { p^{(3)}}(t ) = { { \dot a}_0 } + \mathcal{o}(s),}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\ ; \\ \end{array}$$\end{document } and then \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s^2 } = \left [ { 1 + s{a_a}{\omega ^a } + { 1 \over 3}{s^2}{r_{a0b0}}{\omega ^a}{\omega ^b } + \mathcal{o}({s^3 } ) } \right]{\delta ^2 } - { 1 \over 3}s[{\dot a_a}{\omega ^a } + \mathcal{o}(s)]{\delta ^3 } - { 1 \over { 12}}[{\dot a_0 } + \mathcal{o}(s)]{\delta ^4 } + \mathcal{o}({\delta ^5})$$\end{document } after recalling that p(t ) = 0 . solving for as an expansion in powers of s returns 221\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$u = t - s\left\{{1 - { 1 \over 2}s{a_a}(t){\omega ^a } + { 3 \over 8}{s^2}{{[{a_a}(t){\omega ^a}]}^2 } + { 1 \over { 24}}{s^2}{{\dot a}_0}(t ) + { 1 \over 6}{s^2}{{\dot a}_a}(t){\omega ^a } - { 1 \over 6}{s^2}{r_{a0b0}}(t){\omega ^a}{\omega ^b } + \mathcal{o}({s^3 } ) } \right\},$$\end{document } in which we emphasize that all frame components are evaluated at the simultaneous point z(t ) . an expression for r = p(u ) can be obtained by expanding p(t ) in powers of . we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$r = - \dot p(t)\delta + { 1 \over 2}\ddot p(t){\delta ^2 } - { 1 \over 6}{p^{(3)}}(t){\delta ^3 } + \mathcal{o}({\delta ^4}),$$\end{document } and substitution of our previous results gives 222\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$r = s\left\{{1 + { 1 \over 2}s{a_a}(t){\omega ^a } - { 1 \over 8}{s^2}{{[{a_a}(t){\omega ^a}]}^2 } - { 1 \over 8}{s^2}{{\dot a}_0}(t ) - { 1 \over 3}{s^2}{{\dot a}_a}(t){\omega ^a } + { 1 \over 6}{s^2}{r_{a0b0}}(t){\omega ^a}{\omega ^b } + \mathcal{o}({s^3 } ) } \right\}$$\end{document } for the retarded distance between x and z(u ) . finally , the retarded coordinates r = p(u ) can be related to the fermi coordinates by expanding p(t ) in powers of , so that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$r{\omega ^a } = { p^a}(t ) - { \dot p^a}(t)\delta + { 1 \over 2}{\ddot p^a}(t){\delta ^2 } - { 1 \over 6}{p^{a(3)}}(t){\delta ^3 } + \mathcal{o}({\delta ^4}).$$\end{document } results from the preceding section 3.4.2 can again be imported with mild alterations , and we find \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \dot p}_a}(t ) = { 1 \over 3}{s^2}{r_{ab0c}}{\omega ^b}{\omega ^c } + \mathcal{o}({s^3})},\quad\quad\quad\quad\quad \\ { { { \ddot p}_a}(t ) = ( 1 + s{a_b}{\omega ^b}){a_a } + { 1 \over 3}s{r_{a0b0}}{\omega ^b } + \mathcal{o}({s^2 } ) } , \\ { p_a^{(3)}(t ) = 2{{\dot a}_a}(t ) + \mathcal{o}(s)}.\quad\quad\quad\quad\quad\quad\quad\quad\quad \\ \end{array}$$\end{document}. this , together with equation ( 221 ) , gives 223\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$r{\omega ^a } = s\left\{{{\omega ^a } + { 1 \over 2}s{a^a}(t ) - { 1 \over 3}{s^2}{{\dot a}^a}(t ) - { 1 \over 3}{s^2}r_{\;\;b0c}^a(t){\omega ^b}{\omega ^c } + { 1 \over 6}{s^2}r_{\;\;0b0}^a(t){\omega ^b } + \mathcal{o}({s^3 } ) } \right\}.$$\end{document } it may be checked that squaring this equation and using the identity ab = 1 returns the same result as equation ( 222 ) . recall that we have constructed two sets of basis vectors at x. the first set is the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } that is obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{\bar \alpha}},e_a^{\bar \alpha})$\end{document } on the spacelike geodesic that links x to the simultaneous point \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document}. the second set is the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } that is obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{\bar \alpha}},e_a^{\bar \alpha})$\end{document } on the null geodesic that links x to the retarded point x since each tetrad forms a complete set of basis vectors , each member of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } can be decomposed in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } , and correspondingly , each member of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } can be decomposed in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document}. these decompositions are worked out in this section . for this purpose we shall consider the functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${p^\alpha}(\tau ) = g_{\;\mu}^\alpha ( x , z(\tau)){u^\mu}(\tau),\quad \;p_a^\alpha ( \tau ) = g_{\;\;\mu}^\alpha ( x , z(\tau))e_a^\mu ( \tau),$$\end{document } in which x is a fixed point in a neighbourhood of , z( ) is an arbitrary point on the world line , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_\mu ( x , z)$\end{document } is the parallel propagator on the unique geodesic that links x to z. we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar e_0^\alpha = { p^\alpha}(t),\bar e_a^\alpha = p_a^\alpha ( t),\,e_0^\alpha = { p^\alpha}(u)$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_a^\alpha = p_a^\alpha ( u)$\end{document}. we begin with the decomposition of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } , associated with the retarded point z(u ) . this decomposition will be expressed in the retarded coordinates as an expansion in powers of r. as in section 3.2.1 we express quantities at z(t ) in terms of quantities at z(u ) by expanding in powers of t u. we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\bar e_0^\alpha = { p^\alpha}(u ) + { \dot p^\alpha}(u)\delta + { 1 \over 2}{\ddot p^\alpha}(u){\delta ^2 } + \mathcal{o}({\delta ^3}),$$\end{document } with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{{\dot p}^\alpha}(u ) = g_{\;\;\alpha \prime ; \beta \prime}^\alpha { u^{\alpha \prime}}{u^{\beta \prime } } + g_{\;\;\alpha \prime}^\alpha { a^{\alpha \prime}}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{= \left [ { { a^a } + { 1 \over 2}rr_{\;\;0b0}^a{\omega ^b } + { \mathcal o}({r^2 } ) } \right]e_a^\alpha , \quad \quad \quad \quad \;\;\;}\\{{{\ddot p}^\alpha}(u ) = g_{\;\;\alpha \prime ; \beta \prime \gamma \prime}^\alpha { u^{\alpha \prime}}{u^{\beta \prime}}{u^{\gamma \prime } } + g_{\;\;\alpha \prime ; \beta \prime}^\alpha \left({2{a^{\alpha \prime}}{u^{\beta \prime } } + { u^{\alpha \prime}}{a^{\beta \prime } } } \right ) + g_{\;\;\alpha \prime}^\alpha { { \dot a}^{\alpha \prime}}\;}\\{= [ - { { \dot a}_0 } + { \mathcal o}(r)]e_0^\alpha + [ { { \dot a}^a } + { \mathcal o}(r)]e_a^\alpha , \quad \quad \quad \quad \;}\\\end{array}$$\end{document } , where we have used the expansions of equation ( 92 ) as well as the decompositions of equation ( 141 ) . collecting these results and substituting equation ( 218 ) for yields 224\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\bar e_0^\alpha = \left [ { 1 - { 1 \over 2}{r^2}{{\dot a}_0}(u ) + \mathcal{o}({r^3 } ) } \right]e_0^\alpha + \left [ { r(1 - { a_b}{\omega ^b}){a^a}(u ) + { 1 \over 2}{r^2}{{\dot a}^a}(u ) + { 1 \over 2}{r^2}r_{\;\;0b0}^a(u){\omega ^b } + \mathcal{o}({r^3 } ) } \right]e_a^\alpha.$$\end{document } similarly , we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\bar e_a^\alpha = p_a^\alpha ( u ) + \dot p_a^\alpha ( u)\delta + { 1 \over 2}\ddot p_a^\alpha ( u){\delta ^2 } + \mathcal{o}({\delta ^3}),$$\end{document } with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { \dot p_a^\alpha ( u ) = g_{{\alpha { \prime}};{\beta { \prime}}}^\alpha e_a^{{\alpha { \prime}}}{u^{{\beta { \prime } } } } + \left({g_{{\alpha { \prime}}}^\alpha { u^{{\alpha { \prime } } } } } \right)\left({{a_{{\beta { \prime}}}}e_a^{{\beta { \prime } } } } \right)}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \\ { = \left [ { { a_a } + { 1 \over 2}r{r_{a0b0}}{\omega ^b } + \mathcal{o}({r^2 } ) } \right]e_0^\alpha + \left [ { - { 1 \over 2}rr_{\;\;a0c}^b{\omega ^c } + \mathcal{o}({r^2 } ) } \right]e_b^\alpha},\quad\quad\quad\quad\quad\quad\quad\;\ ; \\ { \ddot p_a^\alpha ( u ) = g_{\;\;{\alpha { \prime}};{\beta { \prime}}{\gamma { \prime}}}^\alpha e_a^{{\alpha { \prime}}}{u^{{\beta { \prime}}}}{u^{{\gamma { \prime } } } } + g_{\;\;{\alpha { \prime}};{\beta { \prime}}}^\alpha \left({2{u^{{\alpha { \prime}}}}{u^{{\beta { \prime}}}}{a_{{\gamma { \prime}}}}e_a^{{\gamma { \prime } } } + e_a^{{\alpha { \prime}}}{a^{{\beta { \prime } } } } } \right ) + \left({g_{\;\;{\alpha { \prime}}}^\alpha { a^{{\alpha { \prime } } } } } \right)\left({{a_{{\beta { \prime}}}}e_a^{{\beta { \prime } } } } \right ) + \left({g_{\;\;{\alpha { \prime}}}^\alpha { u^{{\alpha { \prime } } } } } \right)\left({{{\dot a}_{{\beta { \prime}}}}e_a^{{\beta { \prime } } } } \right ) } \;\;\;\\ { \quad \quad \;\ ; = [ { { \dot a}_a } + \mathcal{o}(r)]e_0^\alpha + [ { a_a}{a^b } + \mathcal{o}(r)]e_b^\alpha } , \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\;\\ \end{array}$$\end{document } and all this gives 225\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { \bar e_a^\alpha = \left [ { \delta _ { \;\;a}^b + { 1 \over 2}{r^2}{a^b}(u){a_a}(u ) - { 1 \over 2}{r^2}r_{\;\;\;a0c}^b(u){\omega ^c } + \mathcal{o}({r^3 } ) } \right]e_b^\alpha}\quad \quad \quad \quad \quad \\ { \quad \quad + \left [ { r(1 - r{a_b}{\omega ^b}){a_a}(u ) + { 1 \over 2}{r^2}{{\dot a}_a}(u ) + { 1 \over 2}{r^2}{r_{a0b0}}(u){\omega ^b } + \mathcal{o}({r^3 } ) } \right]e_0^\alpha}. \\ \end{array}$$\end{document } we now turn to the decomposition of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } associated with the simultaneous point z(t ) . this decomposition will be expressed in the fermi normal coordinates as an expansion in powers of s. here , as in section 3.2.2 , we shall express quantities at z(u ) in terms of quantities at z(t ) . we begin with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$e_0^\alpha = { p^\alpha}(t ) - { \dot p^\alpha}(t)\delta + { 1 \over 2}{\ddot p^\alpha}(t){\delta ^2 } + \mathcal{o}({\delta ^3}),$$\end{document } and we evaluate the derivatives of p( ) at = t. to accomplish this we rely on our previous results ( replacing primed indices with barred indices ) , on the expansions of equation ( 92 ) , and on the decomposition of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{\bar \alpha}(x,\bar x)$\end{document } in the tetrads at x and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document}. this gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \dot p}^\alpha}(t ) = \left [ { { a^a } + { 1 \over 2}sr_{\;\;0b0}^a{\omega ^b } + \mathcal{o}({s^2 } ) } \right]\bar e_a^\alpha } , \quad\\ { { { \ddot p}^\alpha}(t ) = [ - { { \dot a}_0 } + \mathcal{o}(s)]\bar e_0^\alpha + [ { { \dot a}^a } + \mathcal{o}(s)]\bar e_a^\alpha } , \\ \end{array}$$\end{document } and we finally obtain 226\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$e_0^\alpha = \left [ { 1 - { 1 \over 2}{s^2}{{\dot a}_0}(t ) + \mathcal{o}({s^3 } ) } \right]\bar e_0^\alpha + \left [ { - s\left({1 - { 1 \over 2}s{a_b}{\omega ^b } } \right){a^a}(t ) + { 1 \over 2}{s^2}{{\dot a}^a}(t ) - { 1 \over 2}{s^2}r_{\;\;0b0}^a(t){\omega ^b } + \mathcal{o}({s^3 } ) } \right]\bar e_a^\alpha.$$\end{document } similarly , we write \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$e_a^\alpha = p_a^\alpha ( t ) - \dot p_a^\alpha ( t)\delta + { 1 \over 2}\ddot p_a^\alpha ( t){\delta ^2 } + \mathcal{o}({\delta ^3}),$$\end{document } in which we substitute \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { \quad \dot p_a^\alpha = \left [ { { a_a } + { 1 \over 2}s{r_{a0b0}}{\omega ^b } + \mathcal{o}({s^2 } ) } \right]\bar e_0^\alpha + \left [ { - { 1 \over 2}sr_{\;\;a0c}^b{\omega ^c } + \mathcal{o}({s^2 } ) } \right]\bar e_b^\alpha } , \\ { \ddot p_a^\alpha ( t ) = [ { { \dot a}_a } + \mathcal{o}(s)]\bar e_0^\alpha + [ { a_a}{a^b } + \mathcal{o}(s)]\bar e_b^\alpha } , \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \end{array}$$\end{document } as well as equation ( 221 ) for t u. our final result is 227\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { e_a^\alpha = \left [ { \delta _ { \;a}^b + { 1 \over 2}{s^2}{a^b}(t){a_a}(t ) + { 1 \over 2}{s^2}r_{\;\;a0c}^b(t){\omega ^c } + \mathcal{o}({s^3 } ) } \right]\bar e_b^\alpha}\quad \quad\quad \quad\quad \quad\quad \quad \\ { + \left [ { - s\left({1 - { 1 \over 2}s{a_b}{\omega ^b } } \right){a_a}(t ) + { 1 \over 2}{s^2}{{\dot a}_a}(t ) - { 1 \over 2}{s^2}{r_{a0b0}}(u){\omega ^b } + \mathcal{o}({s^3 } ) } \right]\bar e_0^\alpha}. \\ \end{array}$$\end{document } it will prove convenient to introduce on the world line , along with the retarded and simultaneous points , an advanced point associated with the field point x. the advanced point will be denoted x z(v ) , with v denoting the value of the proper - time parameter at x ; to tensors at this point we assign indices , , etc . the advanced point is linked to x by a past - directed null geodesic ( refer back to figure 8) , and it can be located by solving (x , x ) = 0 together with the requirement that ( x , x ) be a future - directed null vector . the affine - parameter distance between x and x along the null geodesic is given by 228\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{{\rm{adv } } } } = - { \sigma _ { { \alpha { \prime\prime}}}}{u^{{\alpha { \prime\prime}}}},$$\end{document } and we shall call this the advanced distance between x and the world line . notice that radv is a positive quantity . we wish first to find an expression for v in terms of the retarded coordinates of x. for this purpose we define v u and re - introduce the function ( ) = (x , z( ) ) first considered in section 3.4.2 . we have that (v ) = (u ) = 0 , and can ultimately be obtained by expressing (v ) as (u + ) and expanding in powers of . recalling that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\dot \sigma ( \tau ) = p(\tau)$\end{document } , we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\sigma ( v ) = \sigma ( u ) + p(u){\delta { \prime } } + { 1 \over 2}\dot p(u){\delta ^{\prime 2 } } + { 1 \over 6}\ddot p(u){\delta ^{\prime 3 } } + { 1 \over { 24}}{p^{(3)}}(u){\delta ^{\prime 4 } } + \mathcal{o}({\delta ^{\prime 5}}).$$\end{document } using the expressions for the derivatives of p( ) that were first obtained in section 3.4.1 , we write this as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$r = { 1 \over 2}\left [ { 1 + r{a_a}{\omega ^a } + { 1 \over 3}{r^2}s + \mathcal{o}({r^3 } ) } \right]{\delta { \prime } } + { 1 \over 6}r[{\dot a_0 } + { \dot a_a}{\omega ^a } + \mathcal{o}(r)]{\delta ^{\prime 2 } } - { 1 \over { 24}}[{\dot a_0 } + \mathcal{o}(r)]{\delta ^{\prime 3 } } + \mathcal{o}({\delta ^{\prime 4}}).$$\end{document } solving for as an expansion in powers of r , we obtain 229\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$v = u + 2r\left\{{1 - r{a_a}(u){\omega ^a } + { r^2}{{[{a_a}(u){\omega ^a}]}^2 } - { 1 \over 3}{r^2}{{\dot a}_0}(u ) - { 2 \over 3}{r^2}{{\dot a}_a}(u){\omega ^a } - { 1 \over 3}{r^2}{r_{a0b0}}(u){\omega ^a}{\omega ^b } + \mathcal{o}({r^3 } ) } \right\},$$\end{document } in which all frame components are evaluated at the retarded point z(u ) . our next task is to derive an expression for the advanced distance radv . for this purpose we observe that radv = p(v ) = p(u + ) , which we can expand in powers of v u. this gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{{\rm{adv } } } } = - r + \left [ { 1 + r{a_a}{\omega ^a } + { 1 \over 3}{r^2}s + \mathcal{o}({r^3 } ) } \right]{\delta { \prime } } + { 1 \over 2}r[{\dot a_0 } + { \dot a_a}{\omega ^a } + \mathcal{o}(r)]{\delta ^{\prime 2 } } - { 1 \over 6}[{\dot a_0 } + \mathcal{o}(r)]{\delta ^{\prime 3 } } + \mathcal{o}({\delta ^{\prime 4}}).$$\end{document } which then becomes \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{{\rm{adv } } } } = - p(u ) - \dot p(u){\delta { \prime } } - { 1 \over 2}\ddot p(u){\delta ^{\prime 2 } } - { 1 \over 6}{p^{(3)}}(u){\delta ^{\prime 3 } } + \mathcal{o}({\delta ^{\prime 4}}),$$\end{document } after substituting equation ( 229 ) for and witnessing a number of cancellations , we arrive at the simple expression 230\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{{\rm{adv } } } } = r\left [ { 1 + { 2 \over 3}{r^2}{{\dot a}_a}(u){\omega ^a } + \mathcal{o}({r^3 } ) } \right].$$\end{document } from equations ( 166 ) , ( 167 ) , and ( 229 ) we deduce that the gradient of the advanced time v is given by 231\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\partial _ \alpha}v = [ 1 - 2r{a_a}{\omega ^a } + \mathcal{o}({r^2})]e_\alpha ^0 + [ { \omega _ a } - 2r{a_a } + \mathcal{o}({r^2})]e_\alpha ^a,$$\end{document } where the expansion in powers of r was truncated to a sufficient number of terms . similarly , equations ( 167 , 168 , 230 ) imply that the gradient of the advanced distance is given by 232\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { \partial _ \alpha}{r_{{\rm{adv } } } } = \left [ { \left({1 + r{a_b}{\omega ^b } + { 4 \over 3}{r^2}{{\dot a}_b}{\omega ^b } + { 1 \over 3}{r^2}s } \right){\omega _ a } + { 2 \over 3}{r^2}{{\dot a}_a } + { 1 \over 6}{r^2}{s_a } + \mathcal{o}({r^3 } ) } \right]e_\alpha ^a } \\ { + \left [ { - r{a_a}{\omega ^a } - { 1 \over 2}{r^2}s + \mathcal{o}({r^3 } ) } \right]e_\alpha ^0},\quad \quad \quad \quad \quad \quad \quad \quad \quad\quad\\ \end{array}$$\end{document } where sa and s were first introduced in equations ( 161 ) and ( 162 ) , respectively . we emphasize that in equations ( 231 ) and ( 232 ) , all frame components are evaluated at the retarded point z(u ) . to prepare the way for our discussion of green s functions in curved spacetime , we consider first the slightly nontrivial case of a massive scalar field (x ) in flat spacetime . this field satisfies the wave equation 233\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - { k^2})\phi ( x ) = - 4\pi \mu ( x),$$\end{document } where = is the wave operator , (x ) a prescribed source , and where the mass parameter k has a dimension of inverse length . we seek a green s function g(x , x ) such that a solution to equation ( 233 ) can be expressed as 234\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi ( x ) = \int g ( x , x{\prime})\mu ( x{\prime}){d^4}x{\prime},$$\end{document } where the integration is over all of minkowski spacetime . the relevant wave equation for the green s function is 235\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - { k^2})g(x , x{\prime } ) = - 4\pi { \delta _ 4}(x - x{\prime}),$$\end{document } where 4(x x ) = (t t)(x x)(y y)(z z ) is a four - dimensional dirac distribution in flat spacetime . two types of green s functions will be of particular interest : the retarded green s function , a solution to equation ( 235 ) with the property that it vanishes if x is in the past of x , and the advanced green s function , which vanishes when x is in the future of x. to solve equation ( 235 ) we use lorentz invariance and the fact that the spacetime is homogeneous to argue that the retarded and advanced green s functions must be given by expressions of the form 236\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{{\rm{ret}}}}(x , x{\prime } ) = \theta ( t - t{\prime})g(\sigma),\quad \quad { g_{{\rm{adv}}}}(x , x{\prime } ) = \theta ( t{\prime } - t)g(\sigma),$$\end{document } where = (x x)(x x ) is synge s world function in flat spacetime , and where g( ) is a function to be determined . for the remainder of this section we set x = 0 without loss of generality . the dirac functional on the right - hand side of equation ( 235 ) is a highly singular quantity , and we can avoid dealing with it by integrating the equation over a small four - volume v that contains x 0 this volume is bounded by a closed hypersurface v . after using gauss theorem on the first term of equation ( 235 ) , we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\oint\nolimits_{\partial v } { { g^{;\alpha}}d{\sigma _ \alpha } - { k^2}\int\nolimits_v g } \;dv = - 4\pi$\end{document } , where d is a surface element on v . assuming that the integral of g over v goes to zero in the limit v 0 , we have 237\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\lim \limits_{v \rightarrow 0 } \oint\nolimits_{\partial v } { { g^{;\alpha } } } d{\sigma _ \alpha } = - 4\pi.$$\end{document } it should be emphasized that the four - volume v must contain the point x. to examine equation ( 237 ) we introduce coordinates ( w , , , ) defined by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$t = w\cos \chi , \quad \quad x = w\sin \chi \sin \theta \cos \phi , \quad \quad y = w\sin \chi \sin \theta \sin \phi , \quad \quad z = w\sin \chi \cos \theta,$$\end{document } and we let v be a surface of constant w. the metric of flat spacetime is given by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d{s^2 } = - \cos 2\chi d{w^2 } + 2w\sin 2\chi \;dw\;d\chi + { w^2}\cos 2\chi \;d{\chi ^2 } + { w^2}{\sin ^2}\chi \;d{\omega ^2}$$\end{document } in the new coordinates , where d = d + sind notice that w is a timelike coordinate when cos2 > 0 , and that is then a spacelike coordinate ; the roles are reversed when cos 2 < 0 . straightforward computations reveal that in these coordinates = w cos 2 , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt { - g } = { w^3}{\sin ^2}\chi \sin \theta$\end{document } , g = cos2 , g = w sin , g = w cos , and the only nonvanishing component of the surface element is dw = w sin d d , where d = sin d d.to calculate the gradient of the green s function we express it as g = (t)g( ) = (w cos )g(w cos2 ) , with the upper ( lower ) sign belonging to the retarded ( advanced ) green s function . calculation gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{;\alpha}}d{\sigma _ \alpha } = \theta ( \pm \cos \chi){w^4}{\sin ^2}\chi { g{\prime}}(\sigma)\,d\chi \,d\omega$\end{document } , with a prime indicating differentiation with respect to it should be noted that derivatives of the step function do not appear in this expression . integration of gd with respect to d is immediate , and we find that equation ( 237 ) reduces to 238\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\lim\limits_{w \rightarrow 0}\int\nolimits_0^\pi \theta ( \pm \cos \chi){w^4}{\sin ^2}\chi g{\prime}(\sigma)d\chi = - 1.$$\end{document } for the retarded green s function , the step function restricts the domain of integration to 0 < < /2 in which increases from w to w . changing the variable of integration from to transforms equation ( 238 ) into 239\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\lim\limits_{\epsilon \rightarrow 0}\epsilon \int\nolimits_{- \epsilon}^\epsilon w ( \sigma/\epsilon)g{\prime}(\sigma)d\sigma = - 1,\quad \quad w(\xi ) \equiv \sqrt { { { 1 + \xi } \over { 1 - \xi}}},$$\end{document } where w . for the advanced green s function , the domain of integration is /2 < < , in which decreases from w to w . changing the variable of integration from to also produces equation ( 239 ) . we have seen that equation ( 239 ) properly encodes the influence of the singular source term on both the retarded and advanced green s function . the function g( ) that enters into the expressions of equation ( 236 ) must therefore be such that equation ( 239 ) is satisfied . it follows immediately that g( ) must be a singular function , because for a smooth function the integral of equation ( 239 ) would be of order , and the left - hand side of equation ( 239 ) could never be made equal to 1 . the singularity , however , must be integrable , and this leads us to assume that g( ) must be made out of dirac -functions and derivatives . we make the ansatz 240\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g(\sigma ) = v(\sigma)\theta ( - \sigma ) + a\delta ( \sigma ) + b\delta { \prime}(\sigma ) + c\delta { \prime\prime}(\sigma ) + \ldots,$$\end{document } where v( ) is a smooth function , and a , b , c , are constants . the first term represents a function supported within the past and future light cones of x 0 ; we exclude a term proportional to ( ) for reasons of causality . it is sufficient to take the coefficients in front of the -functions to be constants . to see this we invoke the distributional identities 241\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\sigma \delta ( \sigma ) = 0\quad \rightarrow \quad \sigma \delta { \prime}(\sigma ) + \delta ( \sigma ) = 0\quad \rightarrow \quad \sigma \delta { \prime\prime}(\sigma ) + 2\delta { \prime}(\sigma ) = 0\quad \rightarrow \quad \ldots,$$\end{document } from which it follows that ( ) = ( ) = = 0 . a term like f( ) ( ) is then distribution - ally equal to f(0 ) ( ) , while a term like f( ) ( ) is distributionally equal to f(0 ) ( ) f(0)( ) , and a term like f( ) ( ) is distributionally equal to f(0)( ) 2f(0)( ) + 2f(0 ) ( ) ; here f( ) is an arbitrary test function . summing over such terms , we recover an expression of the form of equation ( 241 ) , and there is no need to make a , b , c , functions of . differentiation of equation ( 240 ) and substitution into equation ( 239 ) yields \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\epsilon \int\nolimits_{- \epsilon}^\epsilon { w(\sigma/\epsilon)g{\prime}(\sigma)d\sigma = \epsilon \left [ { \int\nolimits_{- \epsilon}^\epsilon { v{\prime } } ( \sigma)w(\sigma/\epsilon)d\sigma - v(0)w(0 ) - { a \over \epsilon}\dot w(0 ) + { b \over { { e^2}}}\ddot w(0 ) - { c \over { { e^3}}}{w^{(3)}}(0 ) + \ldots } \right]},$$\end{document } where overdots ( or a number within brackets ) indicate repeated differentiation with respect to / the limit 0 exists if and only if b = c = = 0 in the limit we must then have a(0 ) = 1 , which implies a = 1 . we conclude that g( ) must have the form of 242\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g(\sigma ) = \delta ( \sigma ) + v(\sigma)\theta ( - \sigma),$$\end{document } with v( ) being a smooth function that can not be determined from equation ( 239 ) alone . to determine v( ) because the singular structure of the green s function is now under control , we can safely set x x 0 in the forthcoming operations . this means that the equation to solve is in fact ( k)g( ) = 0 , the homogeneous version of equation ( 235 ) . we have g = g , g = g + g , and g = 2g + 4g , so that green s equation reduces to the ordinary differential equation 243\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$2\sigma g{\prime\prime } + 4g{\prime } - { k^2}g = 0.$$\end{document } if we substitute equation ( 242 ) into this we get \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$- ( 2v + { k^2})\delta ( \sigma ) + ( 2\sigma v{\prime\prime } + 4v{\prime } - { k^2}v)\theta ( - \sigma ) = 0,$$\end{document } where we have used the identities of equation ( 241 ) . the left - hand side will vanish as a distribution if we set 244\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$2\sigma v{\prime\prime } + 4v{\prime } - { k^2}v = 0,\quad \quad v(0 ) = - { 1 \over 2}{k^2}.$$\end{document } these equations determine v( ) uniquely , even in the absence of a second boundary condition at = 0 , because the differential equation is singular at = 0 and v is known to be smooth . to solve equation ( 244 ) we let v = f(z)/z , with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$z \equiv k\sqrt { - 2\sigma}$\end{document}. this gives rise to bessel s equation for the new function f : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${z^2}{f_{zz } } + z{f_z } + ( { z^2 } - 1)f = 0.$$\end{document } the solution that is well behaved near z = 0 is f = aj1(z ) , where a is a constant to be determined . we have that j1(z ) z for small values of z , and it follows that v a/2 . from equation ( 244 ) so we have found that the only acceptable solution to equation ( 244 ) is 245\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$v(\sigma ) = - { k \over { \sqrt { - 2\sigma}}}{j_1}(k\sqrt { - 2\sigma}).$$\end{document } to summarize , the retarded and advanced solutions to equation ( 235 ) are given by equation ( 236 ) with g( ) given by equation ( 242 ) and v( ) given by equation ( 245 ) . the techniques developed previously to find green s functions for the scalar wave equation are limited to flat spacetime , and they would not be very useful for curved spacetimes . to pursue this generalization we do so in this section , and in the next we shall use them to recover our previous results . let +(x , ) be a generalized step function , defined to be one if x is in the future of the spacelike hypersurface , and defined to be zero otherwise . similarly , define (x , ) 1 +(x , ) to be one if x is in the past of the spacelike hypersurface , and zero otherwise . then define the light - cone step functions 246\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\theta _ \pm}(- \sigma ) = { \theta _ \pm}(x,\sigma)\theta ( - \sigma),\quad \quad x{\prime } \in \sigma,$$\end{document } so that +( ) is one if x is an element of i(x ) , the chronological future of x , and zero otherwise , and ( ) is one if x is an element of i(x ) , the chronological past of x , and zero otherwise ; the choice of hypersurface is immaterial so long as is spacelike and contains the reference point x. notice that +( ) + ( ) = ( ) define also the light - cone dirac functionals 247\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\delta _ \pm}(\sigma ) = { \theta _ \pm}(x,\sigma)\delta ( \sigma),\quad \quad x{\prime } \in \sigma,$$\end{document } so that +( ) , when viewed as a function of x , is supported on the future light cone of x , while ( ) is supported on its past light cone . in equations ( 246 ) and ( 247 ) , is the world function for flat spacetime ; it is negative if x and x are timelike related , and positive if they are spacelike related . the distributions ( ) and ( ) are not defined at x = x and they can not be differentiated there . this pathology can be avoided if we shift by a small positive quantity . we can therefore use the distributions ( ) and ( + ) in some sensitive computations , and then take the limit 0 . notice that the equation + = 0 describes a two - branch hyperboloid that is located just within the light cone of the reference point x. the hyperboloid does not include x , and +(x , ) is one everywhere on its future branch , while (x , ) is one everywhere on its past branch . these factors , therefore , become invisible to differential operators . for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\theta _ + { \prime}(- \sigma - \epsilon ) = { \theta _ + } ( x,\sigma){\theta { \prime}}(- \sigma - \epsilon ) = - { \theta _ + } ( x,\sigma)\delta ( \sigma + \epsilon ) = - { \delta _ + } ( \sigma + \epsilon)$\end{document}. this manipulation shows that after the shift from to + , the distributions of equations ( 246 ) and ( 247 ) can be straightforwardly differentiated with respect to . in the next paragraphs we shall establish the distributional identities 248\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\lim \limits_{\epsilon \rightarrow 0 + } \epsilon \delta _ \pm ( \sigma + \epsilon ) = 0,$$\end{document } 249\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\lim\limits_{\epsilon \rightarrow 0 + } \epsilon \delta _ \pm { \prime}(\sigma + \epsilon ) = 0,$$\end{document } 250\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\lim\limits_{\epsilon \rightarrow 0 + } \epsilon \delta _ \pm ^{{\prime\prime}}(\sigma + \epsilon ) = 2\pi { \delta _ 4}(x - x{\prime})$$\end{document } in four - dimensional flat spacetime . these will be used in the next section 4.1.6 to recover the green s functions for the scalar wave equation , and they will be generalized to curved spacetime in section 4.2 . the derivation of equations ( 248 , 249 , 250 ) relies on a master distributional identity , formulated in three - dimensional flat space : 251\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\lim\limits_{\epsilon \rightarrow { 0^ + } } { \epsilon \over { { r^5 } } } = { { 2\pi } \over 3}{\delta _ 3}(x),\quad r \equiv \sqrt { { r^2 } + 2\epsilon},$$\end{document } with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r \equiv \vert x\vert \equiv \sqrt { { x^2 } + { y^2 } + { z^2}}$\end{document}. this follows from yet another identity , r = 43(x ) , in which we write the left - hand side as lim=0 + r ; since r is nonsingular at x = 0 , it can be straightforwardly differentiated , and the result is r = 6/r from which equation ( 251 ) follows . to prove equation ( 248 ) we must show that ( + ) vanishes as a distribution in the limit 0 . for this we must prove that a functional of the form \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a _ \pm}\left [ f \right ] = \lim\limits_{\epsilon \rightarrow { 0^ + } } \int { \epsilon { \delta _ \pm}(\sigma + \epsilon ) } f(x)\,{d^4}x,$$\end{document } where f(x ) = f(t , x ) is a smooth test function , vanishes for all such functions f. our first task will be to find a more convenient expression for ( + ) . once more we set x = 0 ( without loss of generality ) and we note that 2( + ) = t + r + 2 = (t r)(t + r ) where we have used equation ( 251 ) . it follows that 252\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\delta _ \pm}(\sigma + \epsilon ) = { { \delta ( t \mp r ) } \over r},$$\end{document } and from this we find \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a _ \pm}[f ] = \underset{\epsilon \rightarrow { 0^ + } } { \lim}\int { \epsilon { { f(\pm r , x ) } \over r}{d^3}x } = \underset{\epsilon \rightarrow { 0^ + } } { \lim}\int { { \epsilon \over { { r^5}}}{r^4}f(\pm r , x)\,{d^3}x } = { { 2\pi } \over 3}\int { { \delta _ 3}(x){r^4}f(\pm r , x)\,{d^3}x } = 0,$$\end{document } which establishes equation ( 248 ) . we must show that a functional of the form \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${b _ \pm}\left [ f \right ] = \lim\limits_{\epsilon \rightarrow { 0^ + } } \int { \epsilon { { \delta { \prime } } _ \pm}(\sigma + \epsilon)f(x)\,{d^4}x}$$\end{document } vanishes for all test functions f. we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{b _ \pm}[f ] = \underset { \epsilon \rightarrow { 0^ + } } { \lim } \epsilon { d \over { d\epsilon}}\int { { \delta _ \pm}(\sigma + \epsilon)f(x)\,{d^4}x = \underset { \epsilon \rightarrow { 0^ + } } { \lim } \epsilon { d \over { d\epsilon}}\int { { { f(\pm r , x ) } \over r}\,{d^3}x = \underset { \epsilon \rightarrow { 0^ + } } { \lim } \epsilon \int { \left({\pm { { \dot f } \over { { r^2 } } } - { f \over { { r^3 } } } } \right)\,\,{d^3}x } } } } \\{= \underset { \epsilon \rightarrow { 0^ + } } { \lim } \int { { \epsilon \over { { r^5}}}\left({\pm { r^3}\dot f - { r^2}f } \right ) } \,\,{d^3}x = { { 2\pi } \over 3}\int { { \delta _ 3}(x)\left({\pm { r^3}\dot f - { r^2}f } \right)\,\,{d^3}x\;\;\;\quad \quad \quad \quad \quad \quad } } \\{= 0,\;\;\;\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \;\ ; } \\\end{array}$$\end{document } and the identity of equation ( 249 ) is proved . in these manipulations we have let an overdot indicate partial differentiation with respect to t , and we have used r/ = 1/r . to establish equation ( 250 ) we consider the functional \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${c _ \pm}[f ] = \lim\limits_{\epsilon \rightarrow { 0^ + } } \int { \epsilon { { \delta { \prime\prime } } _ \pm } } ( \sigma + \epsilon)f(x)\,{d^4}x,$$\end{document } and show that it evaluates to 2f(0 , 0 ) . we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{c _ \pm}[f ] = \underset { \epsilon \rightarrow { 0^ + } } { \lim } \epsilon { { { d^2 } } \over { d{\epsilon ^2}}}\int { { \delta _ \pm}(\sigma + \epsilon)f(x)\,{d^4}x = \underset { \epsilon \rightarrow { 0^ + } } { \lim } \epsilon { { { d^2 } } \over { d{\epsilon ^2}}}\int { { { f(\pm r , x ) } \over r}\,{d^3}x\quad \quad\quad \quad \quad \quad}}}\\{= \underset { \epsilon \rightarrow { 0^ + } } { \lim } \epsilon \,\int { \left({{{\ddot f } \over { { r^3 } } } \mp 3{{\dot f } \over { { r^4 } } } + 3{f \over { { r^5 } } } } \right)\,{d^3}x = 2\pi \,\int { { \delta _ 3}(x)\,\left({{1 \over 3}{r^2}\ddot f \pm r\,\dot f + f } \right)\,{d^3}x}}}\\{= 2\pi f(0,0),\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } as required . this proves that equation ( 250 ) holds as a distributional identity in four - dimensional flat spacetime . the retarded and advanced green s functions for the scalar wave equation are now defined as the limit of the functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g _ \pm ^\epsilon ( x,{x{\prime}})\,{\rm{as}}\,\epsilon \rightarrow { { \rm{0}}^ + } $ \end{document}. for these we make the ansatz 253\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g _ \pm ^\epsilon ( x , x{\prime } ) = { \delta _ \pm}(\sigma + \epsilon ) + v(\sigma){\theta _ \pm}(- \sigma - \epsilon),$$\end{document } and we shall prove that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g _ \pm ^\epsilon ( x,{x{\prime}})$\end{document } satisfies equation ( 235 ) in the limit . we recall that the distributions and were defined in the preceding section 4.1.5 , and we assume that v( ) is a smooth function of (x , x ) = (x x)(x x ) ; because this function is smooth , it is not necessary to evaluate v at + in equation ( 253 ) . we recall also that + and + are nonzero when x is in the future of x , while and are nonzero when x is in the past of x. we will therefore prove that the retarded and advanced green s functions are of the form 254\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{{\rm{ret}}}}(x , x{\prime } ) = \lim\limits_{\epsilon \rightarrow { 0^ + } } \,g _ + ^\epsilon ( x , x{\prime } ) = { 0 _ + } ( x,\sigma)\,[\delta ( \sigma ) + v(\sigma)\theta ( - \sigma)]$$\end{document } and 255\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{{\rm{adv}}}}(x , x{\prime } ) = \lim\limits_{\epsilon \rightarrow { 0^ + } } \,g _ - ^\epsilon ( x , x{\prime } ) = { 0 _ -}(x,\sigma)\,[\delta ( \sigma ) + v(\sigma)\theta ( - \sigma)],$$\end{document } where is a spacelike hypersurface that contains x. we will also determine the form of the function v( ) . the functions that appear in equation ( 253 ) can be straightforwardly differentiated . the manipulations are similar to what was done in section 4.1.4 , and dropping all labels , we obtain ( k ) g = 2g + 4g kg , with a prime indicating differentiation with respect to . from equation ( 253 ) we obtain g = v + v and g = v 2v + v. the identities of equation ( 241 ) can be expressed as ( + )( + ) = ( + ) and ( + )( + ) = 2( + ) , and combining this with our previous results gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{(\square - { k^2})g _ \pm ^\epsilon(x , x\prime ) = ( - 2v - { k^2}){\delta _ \pm}(\sigma + \epsilon ) + ( 2\sigma { v^{\prime \prime } } + 4v\prime - { k^2}v){\theta _ \pm}(- \sigma - \epsilon)\quad \quad \quad \quad \quad}\\{- 2\epsilon{\delta ^{\prime \prime } } _ \pm ( \sigma + \epsilon ) + 2v\epsilon\delta { \prime _ \pm}(\sigma + \epsilon ) + 4v\prime \epsilon{\delta _ \pm}(\delta + \epsilon).}\\\end{array}$$\end{document } according to equation ( 248 , 249 , 250 ) , the last two terms on the right - hand side disappear in the limit 0 , and the third term becomes 44(x x ) . provided that the first two terms vanish also , we recover ( k)g(x x ) = 44(x x ) . in the limit , as required . thus , the limit of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g _ \pm ^\epsilon ( x,{x{\prime}})$\end{document } as 0 will indeed satisfy green s equation provided that v( ) is a solution to 256\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$2\sigma v{\prime\prime } + 4v{\prime } - { k^2}v = 0,\quad v(0 ) = - { 1 \over 2}{k^2};$$\end{document } these are the same statements as in equation ( 244 ) . the solution to these equations was produced in equation ( 245 ) , 257\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$v(\sigma ) = - { k \over { \sqrt { - 2\sigma}}}\,{j_1}\,(k\sqrt { - 2\sigma}),$$\end{document } and this completely determines the green s functions of equations ( 254 ) and ( 255 ) . the distributions introduced in section 4.1.5 can also be defined in a four - dimensional spacetime with metric g. here we produce the relevant generalizations of the results derived in that section . we first introduce 4(x , x ) , an invariant dirac functional in a four - dimensional curved spacetime . this is defined by the relations 258\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\int\nolimits_v { f(x){\delta _ 4}(x , x{\prime})\sqrt { - g } \,{d^4}x } = f(x{\prime}),\quad \int\nolimits_{v{\prime } } { f(x{\prime}){\delta _ 4}(x , x{\prime})\sqrt { - g{\prime } } \,{d^4}x{\prime } = f(x),}$$\end{document } where f(x ) is a smooth test function , v any four - dimensional region that contains x , and v any four - dimensional region that contains x. these relations imply that 4(x , x ) is symmetric in its arguments , and it is easy to see that 259\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\delta _ 4}(x , x{\prime } ) = { { { \delta _ 4}(x - x{\prime } ) } \over { \sqrt { - g } } } = { { { \delta _ 4}(x - x{\prime } ) } \over { \sqrt { - g{\prime } } } } = { ( gg{\prime})^{- 1/4}}{\delta _ 4}(x - x{\prime}),$$\end{document } where 4(x x ) = (x x ) (x x ) (x x ) (x x ) is the ordinary ( coordinate ) four - dimensional dirac functional . the relations of equation ( 259 ) are all equivalent because f(x ) 4(x , x ) = f(x ) 4(x , x ) is a distributional identity ; the last form is manifestly symmetric in x and x. the invariant dirac distribution satisfies the identities 260\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}{c } } { \omega \ldots \left ( { x , x ' } \right){\delta _ 4}\left ( { x , x ' } \right ) = \left [ { \omega \ldots } \right]{\delta _ 4}\left ( { x , x ' } \right ) , } \\ { { { \left ( { { g^\alpha } _ { \alpha ' } \left ( { x , x ' } \right){\delta _ 4}\left ( { x , x ' } \right ) } \right)}_{;\alpha } } = - { \partial _ { \alpha ' } } { \delta _ 4}\left ( { x , x ' } \right),\;\;\;\;\;\;\;\;\;\;\;\;\;{{\left ( { { g^{\alpha ' } } _ \alpha \left ( { x',x } \right){\delta _ 4}\left ( { x , x ' } \right ) } \right)}_{;\alpha ' } } = - { \partial _ \alpha } { \delta _ 4}\left ( { x , x ' } \right ) , } \end{array}$$\end{document } where ( x , x ) is any bitensor and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\alpha { \prime}}}(x,{x{\prime}}),{g^{{\alpha { \prime}}}}_\alpha ( x,{x{\prime}})$\end{document } are parallel propagators . the second and third identities are established by showing that integration against a test function f(x ) gives the same result from both sides . for example , the first of the equations ( 258 ) implies \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\int\nolimits_v { f(x){\partial _ { \alpha { \prime}}}{\delta _ 4}(x , x{\prime})\sqrt { - g } \,{d^4}x = { \partial _ { \alpha { \prime}}}f(x{\prime}),}$$\end{document } and on the other hand , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$- \int\nolimits_v { f(x)\,({g^\alpha}_{\alpha { \prime}}{\delta _ 4}{{(x , x{\prime})}_{;\alpha}}\sqrt { - g } } \,{d^4}x = - \oint\nolimits_{\partial v } { f(x){g^\alpha}_{\alpha { \prime } } } \,{\delta _ 4}(x , x{\prime})d{\sigma _ a } + [ { f_{,\alpha}}{g^\alpha}_{\alpha { \prime } } ] = { \partial _ { \alpha { \prime}}}f(x{\prime}),$$\end{document } which establishes the second identity of equation ( 260 ) . notice that in these manipulations , the integrations involve scalar functions of the coordinates x ; the fact that these functions are also vectors with respect to x does not invalidate the procedure . the third identity of equation ( 260 ) is proved in a similar way . for the remainder of section 4.2 we assume that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$x\ , \in { \mathcal n}({x{\prime}})$\end{document } , so that a unique geodesic links these two points . we then let (x , x ) be the curved spacetime world function , and we define light - cone step functions by 261\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\theta _ \pm}(- \sigma ) = { \theta _ \pm}(x,\sigma)\theta ( - \sigma),\quad x{\prime } \in \sigma,$$\end{document } where +(x , ) is one if x is in the future of the spacelike hypersurface and zero otherwise , and (x , ) = 1 +(x , ) . these are immediate generalizations to curved spacetime of the objects defined in flat spacetime by equation ( 246 ) . we have that +( ) is one if x is an element of i(x ) , the chronological future of x , and zero otherwise , and ( ) is one if x is an element of i(x ) , the chronological past of x , and zero otherwise . we define the curved - spacetime version of the light - cone dirac functionals by 262\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\delta _ \pm}(\sigma ) = { \theta _ \pm}(x,\sigma)\delta ( \sigma),\quad x{\prime } \in \sigma,$$\end{document } an immediate generalization of equation ( 247 ) . we have that +( ) , when viewed as a function of x , is supported on the future light cone of x , while ( ) is supported on its past light cone . we also have +( ) + ( ) = ( ) , and we recall that a is negative if x and x are timelike related , and positive if they are spacelike related . for the same reasons as those mentioned in section 4.1.5 , it is sometimes convenient to shift the argument of the step and -functions from to + , where is a small positive quantity . with this shift , the light - cone distributions can be straightforwardly differentiated with respect to . for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\delta _ \pm}(\sigma + \epsilon ) = - \theta _ \pm { \prime}(- \sigma - \epsilon)$\end{document } , with a prime indicating differentiation with respect to . we now prove that the identities of equation ( 248 , 249 , 250 ) generalize to 263\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\lim\limits_{\epsilon \rightarrow { 0^ + } } \,\epsilon { \delta _ \pm}(\sigma + \epsilon ) = 0,$$\end{document } 264\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\lim\limits_{\epsilon \rightarrow { 0^ + } } \,\epsilon { \delta { \prime } _ \pm}(\sigma + \epsilon ) = 0,$$\end{document } 265\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\lim\limits_{\epsilon \rightarrow { 0^ + } } \,\epsilon { \delta { \prime\prime } _ \pm}(\sigma + \epsilon ) = 2\pi { \delta _ 4}(x , x{\prime})$$\end{document } in a four - dimensional curved spacetime ; the only differences lie with the definition of the world function and the fact that it is the invariant dirac functional that appears in equation ( 265 ) . to establish these identities in curved spacetime we use the fact that they hold in flat spacetime as was shown in section 4.1.5 and that they are scalar relations that must be valid in any coordinate system if they are found to hold in one . let us then examine equations ( 263 , 264 ) in the riemann normal coordinates of section 3.1 ; these are denoted \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\hat x^\alpha}$\end{document } and are based at x. we have that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sigma ( x,{x{\prime } } ) = { 1 \over 2}{\eta _ { \alpha \beta}}{\hat x^\alpha}{\hat x^\beta}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\delta _ 4}(x,{x{\prime } } ) = \delta ( x,{x{\prime}}){\delta _ 4}(x - { x{\prime } } ) = { \delta _ 4}(x - { x{\prime}})$\end{document } where (x , x ) is the van vleck determinant , whose coincidence limit is unity . in riemann normal coordinates , therefore , equations ( 263 , 264 , 265 ) take exactly the same form as equations ( 248 , 264 , 250 ) . because the identities are true in flat spacetime , they must be true also in curved spacetime ( in riemann normal coordinates based at x ) ; and because these are scalar relations , they must be valid in any coordinate system . we consider a massless scalar field ( x ) in a curved spacetime with metric g. the field satisfies the wave equation 266\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - \xi r)\phi ( x ) = - 4\pi \mu ( x),$$\end{document } where = g is the wave operator , r the ricci scalar , an arbitrary coupling constant , and (x ) is a prescribed source . we seek a green s function g(x , x ) such that a solution to equation ( 266 ) can be expressed as 267\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi ( x ) = \int { g(x , x{\prime})\mu ( x{\prime})\sqrt { - g{\prime } } \,{d^4}x{\prime}},$$\end{document } where the integration is over the entire spacetime . the wave equation for the green s function is 268\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - \xi r)g(x , x{\prime } ) = - 4\pi { \delta _ 4}(x , x{\prime}),$$\end{document } where 4(x , x ) is the invariant dirac functional introduced in section 4.2.1 . it is easy to verify that the field defined by equation ( 267 ) is truly a solution to equation ( 266 ) . we let g+(x , x ) be the retarded solution to equation ( 268 ) , and g(x , x ) be the advanced solution ; when viewed as functions of x , g+ ( x , x ) is nonzero in the causal future of x , while g ( x , x ) is nonzero in its causal past . we assume that the retarded and advanced green s functions exist as distributions and can be defined globally in the entire spacetime . assuming throughout this section that x is restricted to the normal convex neighbourhood of x , we make the ansatz 269\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g _ \pm}(x , x{\prime } ) = u(x , x{\prime}){\delta _ \pm}(- \sigma),$$\end{document } where u(x , x ) and v(x , x ) are smooth biscalars ; the fact that the spacetime is no longer homogeneous means that these functions can not depend on alone . before we substitute the green s functions of equation ( 269 ) into the differential equation of equation ( 268 ) , we proceed as in section 4.1.6 and shift by the small positive quantity . we shall therefore consider the distributions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g _ \pm ^\epsilon ( x , x{\prime } ) = u(x , x{\prime}){\delta _ \pm}(\sigma + \epsilon ) + v(x , x{\prime}){\theta _ \pm}(- \theta - \epsilon),$$\end{document } and later recover the green s functions by taking the limit 0 . differentiation of these objects is straightforward , and in the following manipulations we will repeatedly use the relation = 2 satisfied by the world function . we will also use the distributional identities \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sigma { \delta _ \pm}(\sigma + \epsilon ) = - \epsilon { \delta _ \pm}(\sigma + \epsilon),\,\sigma \delta _ \pm { \prime}(\sigma + \epsilon ) = - { \delta _ \pm}(\sigma + \epsilon ) - \epsilon \delta _ \pm { \prime}(\sigma + \epsilon)$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sigma \delta _ \pm ^{{\prime\prime}}(\sigma + \epsilon ) = - 2{\delta { \prime}}(\sigma + \epsilon ) - \epsilon { \delta ^{{\prime\prime}}}(\sigma + \epsilon)$\end{document}. after a routine calculation we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{(\square - \xi r)g _ \pm ^\epsilon = - 2\epsilon \delta \prime { \prime _ \pm}(\sigma + \epsilon)u + 2\epsilon \delta { \prime _ \pm}(\sigma + \epsilon)v + \delta { \prime _ \pm}(\sigma + \epsilon)\,\{2{u_{,\alpha}}{\sigma ^\alpha } + ( { \sigma ^\alpha}_\alpha - 4)u\ } \quad \quad \quad \quad \quad \quad \quad}\\ { + { \delta _ \pm}(\sigma + \epsilon)\,\{- 2{v_{,\alpha}}{\sigma ^\alpha } + ( 2 - { \sigma ^\alpha}_\alpha)v + ( \square - \xi r)u\ } + { \theta _ \pm}(- \sigma - \epsilon)\,\{(\square - \xi r)v\ } , } \\ \end{array}$$\end{document } which becomes 270\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{(\square - \xi r){g _ \pm } = - 4\pi { \delta _ 4}(x , x\prime)u + \delta { \prime _ \pm}(\sigma)\,\{2{u_{,\alpha}}{\sigma ^\alpha } + ( { \sigma ^\alpha}_\alpha - 4)u\ } \;\;\quad \quad \quad \;\quad \quad \quad \quad \quad \quad \quad \quad}\\{+ \,{\delta _ \pm}(\sigma)\,\{- 2{v_{,\alpha}}{\sigma ^\alpha } + ( 2 - { \sigma ^\alpha}_\alpha)v + ( \square- \xi r)u\ } + { \theta _ \pm}(\sigma)\,\{(\square- \xi r)v\}}\\\end{array}$$\end{document } in the limit 0 , after using the identities of equations ( 263 , 264 , 265 ) . according to equation ( 268 ) , the right - hand side of equation ( 270 ) should be equal to 44(x , x ) . this immediately gives us the coincidence condition 271\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[u ] = 1$$\end{document } for the biscalar u(x , x ) . to eliminate the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\delta _ \pm { \prime}$\end{document } term we make its coefficient vanish : 272\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$2{u_{,\alpha}}{\sigma ^\alpha } + ( { \sigma ^\alpha}_\alpha - 4)u = 0.$$\end{document } as we shall now prove , these two equations determine u(x , x ) uniquely . recall from section 2.1.3 that is a vector at x that is tangent to the unique geodesic that connects x to x. this geodesic is affinely parameterized by and a displacement along is described by dx = ( /)d. the first term of equation ( 272 ) therefore represents the rate of change of u(x , x ) along , and this can be expressed as 2 du / d. for the second term we recall from section 2.5.1 the differential equation (); = 4 satisfied by (x , x ) , the van vleck determinant . this gives us \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma ^\alpha}_\alpha - 4 = { \delta ^{- 1}}{\delta _ { , \alpha}}{\sigma ^\alpha } = { \delta ^{- 1}}\lambda d\delta / d\lambda$\end{document } and equation ( 272 ) becomes \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\lambda { d \over { d\lambda}}\,\,(2\,\ln u - \ln \delta ) = 0.$$\end{document } it follows that u/ is constant on , and it must therefore be equal to its value at the starting point x : u/ = [ u/ ] = 1 , by virtue of equation ( 271 ) and the property [ ] = 1 of the van vleck determinant . since this statement must be true for all geodesics that emanate from x , we have found that the unique solution to equations ( 271 ) and ( 272 ) is 273\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$u(x , x{\prime } ) = { \delta ^{1/2}}(x , x{\prime}).$$\end{document } we must still consider the remaining terms in equation ( 270 ) . the term can be eliminated by demanding that its coefficient vanish when = 0 . this , however , does not constrain its value away from the light cone , and we thus obtain information about v=0 only . denoting this by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\check v}(x,{x{\prime}})$\end{document } the restriction of v(x , x ) on the light cone (x , x ) = 0 we have 274\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\left . { { { \check v}_{,\alpha}}{\sigma ^\alpha } + { 1 \over 2}({\sigma ^\alpha}_\alpha - 2)\,\check v = { 1 \over 2}(\square - \xi r)\,u } \right\vert_{\sigma = 0}},$$\end{document } where we indicate that the right - hand side also must be restricted to the light cone . the first term of equation ( 274 ) can be expressed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\lambda d{\check v}/d\lambda$\end{document } , and this equation can be integrated along any null geodesic that generates the null cone (x , x ) = 0 . for these integrations to be well posed , however , we must provide initial values at x = x. as we shall now see , these can be inferred from equation ( 274 ) and the fact that v(x , x ) must be smooth at coincidence . equations ( 97 ) and ( 273 ) imply that near coincidence , u(x , x ) admits the expansion 275\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$u = 1 + { 1 \over { 12}}{r_{\alpha { \prime}\beta { \prime}}}{\sigma ^{\alpha { \prime}}}{\sigma ^{\beta { \prime } } } + \mathcal{o}({\lambda ^3}),$$\end{document } where r is the ricci tensor at x and is the affine - parameter distance to x ( which can be either on or off the light cone ) . differentiation of this relation gives 276\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{,\alpha } } = - { 1 \over 6}{g^{\alpha { \prime}}}_\alpha { r_{\alpha { \prime}\beta { \prime } } } + \mathcal{o}({\lambda ^2}),\quad { u_{,\alpha { \prime } } } = { 1 \over 6}{r_{\alpha { \prime}\beta { \prime}}}{\sigma ^{\beta { \prime } } } + \mathcal{o}({\lambda ^2}),$$\end{document } and eventually , 277\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[\square u ] = { 1 \over 6}r(x{\prime}).$$\end{document } using also \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{\alpha ^\alpha}_\alpha ] = 4$\end{document } we find that the coincidence limit of equation ( 274 ) gives 278\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[v ] = { 1 \over { 12}}(1 - 6\xi)\,r(x{\prime}),$$\end{document } and this provides the initial values required for the integration of equation ( 274 ) on the null cone . equations ( 274 ) and ( 278 ) give us a means to construct \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\check v}(x,{x\prime})$\end{document } , the restriction of v(x , x ) on the null cone (x , x ) = 0 . these values can then be used as characteristic data for the wave equation 279\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - \xi r)v(x , x{\prime } ) = 0,$$\end{document } which is obtained by elimination of the term in equation ( 270 ) . while this certainly does not constitute a practical method to compute the biscalar v(x , x ) , these considerations show that v(x , x ) exists and is unique . to summarize : we have shown that with u(x , x ) given by equation ( 273 ) and v(x , x ) determined uniquely by the wave equation of equation ( 279 ) and the characteristic data constructed with equations ( 274 ) and ( 278 ) , the retarded and advanced green s functions of equation ( 269 ) do indeed satisfy equation ( 268 ) . it should be emphasized that the construction provided in this section is restricted to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}({x{\prime}})$\end{document } , the normal convex neighbourhood of the reference point x. we shall now establish the following reciprocity relation between the ( globally defined ) retarded and advanced green s functions : 280\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g _ -}(x{\prime},x ) = { g _ + } ( x , x{\prime}).$$\end{document } before we get to the proof we observe that by virtue of equation ( 280 ) , the biscalar v(x , x ) must be symmetric in its arguments , 281\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$v(x{\prime},x ) = v(x , x{\prime})$$\end{document } to go from equation ( 280 ) to equation ( 281 ) we need simply note that if \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$x \in { \mathcal n}({x{\prime}})$\end{document } and belongs to i(x ) , then g+(x , x ) = v(x , x ) and g(x , x ) = v(x , x ) . to prove the reciprocity relation we invoke the identities \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g _ + } ( x , x{\prime})(\square - \xi r){g _ -}(x , x{\prime\prime } ) = - 4\pi { g _ + } ( x , x{\prime}){\delta _ 4}(x , x{\prime\prime})$$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g _ -}(x , x{\prime\prime})(\square - \xi r){g _ + } ( x , x{\prime } ) = - 4\pi { g _ -}(x , x{\prime\prime}){\delta _ 4}(x , x{\prime}),$$\end{document } and take their difference . on the left - hand side we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { g _ + } ( x , x{\prime})\square{g _ -}(x , x{\prime\prime } ) - { g _ -}(x , x{\prime\prime})\square{g _ + } ( x , x{\prime } ) = } \quad \quad \quad\quad \quad \quad\quad \quad \quad\\ { { \nabla _ \alpha}({g _ + } ( x , x{\prime}){\nabla ^\alpha}{g _ -}(x , x{\prime\prime } ) - { g _ -}(x , x{\prime\prime}){\nabla ^\alpha}{g _ + } ( x , x{\prime } ) ) } , \\ \end{array}$$\end{document } while the right - hand side gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$- 4\pi ( { g _ + } ( x , x{\prime}){\delta _ 4}(x , x{\prime\prime } ) - { g _ -}(x , x{\prime\prime}){\delta _ 4}(x , x{\prime})).$$\end{document } integrating both sides over a large four - dimensional region v that contains both x and x , we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\oint\nolimits_{\partial v } { ( { g _ + } ( x , x{\prime}){\nabla ^\alpha}{g _ + } ( x , x{\prime\prime } ) - { g _ -}(x - x{\prime\prime}){\nabla ^\alpha}{g _ + } ( x , x{\prime}))\,\,d{\sigma _ \alpha } = - 4\pi ( { g _ + } ( x{\prime\prime},x{\prime } ) - { g _ -}(x{\prime},x{\prime\prime})),}$$\end{document } where v is the boundary of v. assuming that the green s functions fall off sufficiently rapidly at infinity ( in the limit v ; this statement imposes some restriction on the spacetime s asymptotic structure ) , we have that the left - hand side of the equation evaluates to zero in the limit . this gives us the statement g+(x , x ) = g(x , x ) , which is just equation ( 280 ) with x replacing x. suppose that the values for a scalar field (x ) and its normal derivative n(x ) are known on a spacelike hypersurface . suppose also that the scalar field satisfies the homogeneous wave equation 282\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - \xi r)\phi ( x ) = 0.$$\end{document } then the value of the field at a point x in the future of is given by kirchhoff s formula , 283\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi ( x ) = - { 1 \over { 4\pi}}\int\nolimits_\sigma { \left({{g _ + } ( x , x{\prime}){\nabla ^{\alpha { \prime}}}\phi ( x{\prime } ) - \phi ( x{\prime}){\nabla ^{\alpha { \prime}}}{g _ + } ( x , x{\prime } ) } \right)\,\,d{\sigma _ { \alpha { \prime}}},}$$\end{document } where d is the surface element on . if n is the future - directed unit normal , then d = ndv , with dv denoting the invariant volume element on ; notice that d is past directed . to establish this result we start with the equations \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g _ -}(x{\prime},x)(\square{\prime } - \xi r{\prime})\phi ( x{\prime } ) = 0,\quad \phi ( x{\prime})(\square{\prime } - \xi r{\prime}){g _ -}(x{\prime},x ) = - 4\pi { \delta _ 4}(x{\prime},x)\phi ( x{\prime}),$$\end{document } in which x and x refer to arbitrary points in spacetime . taking their difference gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\nabla _ { \alpha { \prime}}}\left({{g _ -}(x{\prime},x){\nabla ^{\alpha { \prime}}}\phi ( x{\prime } ) - \phi ( x{\prime}){\nabla ^{\alpha { \prime}}}{g _ -}(x{\prime},x ) } \right ) = 4\pi { \delta _ 4}(x{\prime},x)\phi ( x{\prime}),$$\end{document } and this we integrate over a four - dimensional region v that is bounded in the past by the hyper - surface . we suppose that v contains x and we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\oint\nolimits_{\partial v } { \left({{g _ -}(x{\prime},x){\nabla ^{\alpha { \prime}}}\phi ( x{\prime } ) - \phi ( x{\prime})\,{\nabla ^{\alpha { \prime}}}{g _ -}(x{\prime},x ) } \right)\,\,d{\sigma _ { \alpha { \prime } } } = 4\pi \phi ( x),}$$\end{document } where d is the outward - directed surface element on the boundary v . assuming that the green s function falls off sufficiently rapidly into the future , we have that the only contribution to the hypersurface integral is the one that comes from . since the surface element on points in the direction opposite to the outward - directed surface element on v , we must change the sign of the left - hand side to be consistent with the convention adopted previously . with this change we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi ( x ) = - { 1 \over { 4\pi}}\oint\nolimits_{\partial v } { \left({{g _ -}(x{\prime},x){\nabla ^{\alpha { \prime}}}\phi ( x{\prime } ) - \phi ( x{\prime}){\nabla ^{\alpha { \prime}}}{g _ -}(x{\prime},x ) } \right)\,\,d{\sigma _ { \alpha { \prime}}},}$$\end{document } which is the same as equation ( 283 ) if we take into account the reciprocity relation of equation ( 280 ) . in section 5 of this review we will compute the retarded field of a moving scalar charge , and we will analyze its singularity structure near the world line ; this will be part of our effort to understand the effect of the field on the particle s motion . the retarded solution to the scalar wave equation is the physically relevant solution because it properly incorporates outgoing - wave boundary conditions at infinity the advanced solution would come instead with incoming - wave boundary conditions . the retarded field is singular on the world line because a point particle produces a coulomb field that diverges at the particle s position . in view of this singular behaviour , it is a subtle matter to describe the field s action on the particle , and to formulate meaningful equations of motion . when facing this problem in flat spacetime ( recall the discussion of section 1.3 ) , it is convenient to decompose the retarded green s function g+(x , x ) into a singular green s function gs(x , x ) g+(x , x ) + g(x , x ) and a radiative green s function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{r}}}(x,{x{\prime } } ) \equiv { 1 \over 2}[{g _ + } ( x,{x{\prime } } ) - { g _ -}(x,{x{\prime}})]$\end{document}. the singular green s function takes its name from the fact that it produces a field with the same singularity structure as the retarded solution : the diverging field near the particle is insensitive to the boundary conditions imposed at infinity . we note also that gs(x , x ) satisfies the same wave equation as the retarded green s function ( with a dirac functional as a source ) , and that by virtue of the reciprocity relations , it is symmetric in its arguments . the radiative green s function , on the other hand , takes its name from the fact that it satisfies the homogeneous wave equation , without the dirac functional on the right - hand side ; it produces a field that is smooth on the world line of the moving scalar charge . because the singular green s function is symmetric in its argument , it does not distinguish between past and future , and it produces a field that contains equal amounts of outgoing and incoming radiation the singular solution describes standing waves at infinity . removing gs(x , x ) from the retarded green s function will therefore have the effect of removing the singular behaviour of the field without affecting the motion of the particle . the motion is not affected because it is intimately tied to the boundary conditions : if the waves are outgoing , the particle loses energy to the radiation and its motion is affected ; if the waves are incoming , the particle gains energy from the radiation and its motion is affected differently . with equal amounts of outgoing and incoming radiation , the particle neither loses nor gains energy and its interaction with the scalar field can not affect its motion . thus , subtracting gs(x , x ) from the retarded green s function eliminates the singular part of the field without affecting the motion of the scalar charge . the subtraction leaves behind the radiative green s function , which produces a field that is smooth on the world line ; it is this field that will govern the motion of the particle . the action of this field is well defined , and it properly encodes the outgoing - wave boundary conditions : the particle will lose energy to the radiation . in this section we attempt a decomposition of the curved - spacetime retarded green s function into singular and radiative green s functions . the flat - spacetime relations will have to be amended , however , because of the fact that in a curved spacetime , the advanced green s function is generally nonzero when x is in the chronological future of x. this implies that the value of the advanced field at x depends on events x that will unfold in the future ; this dependence would be inherited by the radiative field ( which acts on the particle and determines its motion ) if the naive definition gr(x , x ) g+(x , x ) g(x , x ) were to be adopted . instead , we shall follow detweiler and whiting and introduce a singular green s function with the properties sc.s1 : gs(x , x ) satisfies the inhomogeneous scalar wave equation , 284\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - \xi r){g_{\rm{s}}}(x , x{\prime } ) = - 4\pi { \delta _ 4}(x , x{\prime});$$\end{document}sc.s2 : gs(x , x ) is symmetric in its arguments , 285\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{s}}}(x{\prime},x ) = { g_{\rm{s}}}(x , x{\prime});$$\end{document}sc.s3 : gs(x , x ) vanishes if x is in the chronological past or future of x , 286\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{s}}}(x , x{\prime } ) = 0\quad { \rm{when}}\,x \in { i^ \pm}(x{\prime}).$$\end{document } properties sc.s1 and sc.s2 ensure that the singular green s function will properly reproduce the singular behaviour of the retarded solution without distinguishing between past and future ; and as we shall see , property sc.s3 ensures that the support of the radiative green s function will not include the chronological future of x. sc.s1 : gs(x , x ) satisfies the inhomogeneous scalar wave equation , 284\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - \xi r){g_{\rm{s}}}(x , x{\prime } ) = - 4\pi { \delta _ 4}(x , x{\prime});$$\end{document } sc.s2 : gs(x , x ) is symmetric in its arguments , 285\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{s}}}(x{\prime},x ) = { g_{\rm{s}}}(x , x{\prime});$$\end{document } sc.s3 : gs(x , x ) vanishes if x is in the chronological past or future of x , 286\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{s}}}(x , x{\prime } ) = 0\quad { \rm{when}}\,x \in { i^ \pm}(x{\prime}).$$\end{document } the radiative green s function is then defined by 287\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{r}}}(x , x{\prime } ) = { g _ + } ( x , x{\prime } ) - { g_{\rm{s}}}(x , x{\prime}),$$\end{document } where g+ ( x , x ) is the retarded green s function . this comes with the properties sc.r1 : gr(x , x ) satisfies the homogeneous wave equation , 288\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - \xi r){g_{\rm{r}}}(x , x{\prime } ) = 0;$$\end{document}sc.r2 : gr(x , x ) agrees with the retarded green s function if x is in the chronological future of 289\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{r}}}(x , x{\prime } ) = { g _ + } ( x , x{\prime})\quad { \rm{when}}\,x \in { i^ + } ( x{\prime});$$\end{document}sc.r3 : gr(x , x ) vanishes if x is in the chronological past of x , 290\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{r}}}(x , x{\prime } ) = 0\quad { \rm{when}}\,x \in { i^ -}(x{\prime}).$$\end{document } property sc.r1 follows directly from equation ( 287 ) and property sc.s1 of the singular green s function . properties sc.r2 and sc.r3 follow from property sc.s3 and the fact that the retarded green s function vanishes if x is in past of x. the properties of the radiative green s function ensure that the corresponding radiative field will be smooth at the world line , and will depend only on the past history of the scalar charge . sc.r1 : gr(x , x ) satisfies the homogeneous wave equation , 288\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - \xi r){g_{\rm{r}}}(x , x{\prime } ) = 0;$$\end{document } sc.r2 : gr(x , x ) agrees with the retarded green s function if x is in the chronological future of 289\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{r}}}(x , x{\prime } ) = { g _ + } ( x , x{\prime})\quad { \rm{when}}\,x \in { i^ + } ( x{\prime});$$\end{document } sc.r3 : gr(x , x ) vanishes if x is in the chronological past of x , 290\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{r}}}(x , x{\prime } ) = 0\quad { \rm{when}}\,x \in { i^ -}(x{\prime}).$$\end{document } we must still show that such singular and radiative green s functions can be constructed . this relies on the existence of a two - point function h(x , x ) that would possess the properties sc.h1 : h(x , x ) satisfies the homogeneous wave equation , 291\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - \xi r)h(x , x{\prime } ) = 0;$$\end{document}sc.h2 : h(x , x ) is symmetric in its arguments , 292\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h(x{\prime},x ) = h(x , x{\prime});$$\end{document}sc.h3 : h(x , x ) agrees with the retarded green s function if x is in the chronological future of 293\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h(x , x{\prime } ) = { g _ + } ( x , x{\prime})\quad { \rm{when}}\,x \in { i^ + } ( x{\prime});$$\end{document}sc.h4 : h(x , x ) agrees with the advanced green s function if x is in the chronological past of 294\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h(x , x{\prime } ) = { g _ -}(x , x{\prime})\quad { \rm{when}}\,x \in { i^ -}(x{\prime}).$$\end{document } with a biscalar h(x , x ) satisfying these relations , a singular green s function defined by 295\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{s}}}(x , x{\prime } ) = { 1 \over 2}[{g _ + } ( x , x{\prime } ) + { g _ -}(x , x{\prime } ) - h(x , x{\prime})]$$\end{document } will satisfy all the properties listed previously : property sc.s1 comes as a consequence of property sc.h1 and the fact that both the advanced and the retarded green s functions are solutions to the inhomogeneous wave equation , property sc.s2 follows directly from property sc.h2 and the definition of equation ( 295 ) , and property sc.s3 comes as a consequence of properties sc.h3 , property sc.h4 and the properties of the retarded and advanced green s functions . sc.h1 : h(x , x ) satisfies the homogeneous wave equation , 291\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - \xi r)h(x , x{\prime } ) = 0;$$\end{document } sc.h2 : h(x , x ) is symmetric in its arguments , 292\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h(x{\prime},x ) = h(x , x{\prime});$$\end{document } sc.h3 : h(x , x ) agrees with the retarded green s function if x is in the chronological future of 293\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h(x , x{\prime } ) = { g _ + } ( x , x{\prime})\quad { \rm{when}}\,x \in { i^ + } ( x{\prime});$$\end{document } sc.h4 : h(x , x ) agrees with the advanced green s function if x is in the chronological past of 294\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h(x , x{\prime } ) = { g _ -}(x , x{\prime})\quad { \rm{when}}\,x \in { i^ -}(x{\prime}).$$\end{document } the question is now : does such a function h(x , x ) exist ? we will see that h(x , x ) is guaranteed to exist in the local convex neighbourhood of x , where it is equal to v(x , x ) . and in section 4.3.6 we will see that there exist particular spacetimes for which h(x , x ) can be defined globally . to satisfy all of properties sc.h4 , sc.h2 , sc.h3 , and sc.h4 might seem a tall order , but it should be possible . we first note that property sc.h4 is not independent from the rest : it follows from property sc.h2 , property sc.h3 , and the reciprocity relation ( 280 ) satisfied by the retarded and advanced green s functions . then h(x , x ) = h(x , x ) by property sc.h2 , and by property sc.h3 this is equal to g+(x , x ) . but by the reciprocity relation this is also equal to g(x , x ) , and we have obtained property sc.h4 . alternatively , and this shall be our point of view in the next paragraph , we can think of property sc.h3 as following from properties sc.h2 and sc.h4 . because h(x , x ) satisfies the homogeneous wave equation ( property sc.h1 ) , it can be given the kirkhoff representation of equation ( 283 ) : if is a spacelike hypersurface in the past of both x and x , then \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h(x , x{\prime } ) = - { 1 \over { 4\pi}}\int\nolimits_\sigma { \left({{g _ + } ( x , x{\prime\prime}){\nabla ^{\alpha { \prime\prime}}}h(x{\prime\prime},x{\prime } ) - h(x{\prime\prime},x{\prime})\,{\nabla ^{\alpha { \prime\prime}}}{g _ + } ( x , x{\prime\prime } ) } \right)\,\,d{\sigma _ { \alpha { \prime\prime}}},}$$\end{document } where d is a surface element on . the hypersurface can be partitioned into two segments , (x ) and (x ) , with (x ) denoting the intersection of with i(x ) . to enforce property sc.h4 it suffices to choose for h(x , x ) initial data on (x ) that agree with the initial data for the advanced green s function ; because both functions satisfy the homogeneous wave equation in i(x ) , the agreement will be preserved in all of the domain of dependence of (x ) . the data on (x ) is still free , and it should be possible to choose it so as to make h(x , x ) symmetric . assuming that this can be done , we see that property sc.h2 is enforced and we conclude that the properties sc.h1 when x is restricted to the normal convex neighbourhood of x , properties sc.h1 , sc.h2 , sc.h3 , and sc.h4 imply that 296\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h(x , x{\prime } ) = v(x , x{\prime});$$\end{document } it should be stressed here that while h(x , x ) is assumed to be defined globally in the entire spacetime , the existence of v(x , x ) is limited to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}({x{\prime}})$\end{document}. with equations ( 269 ) and ( 295 ) we find that the singular green s function is given explicitly by 297\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{s}}}(x , x{\prime } ) = { 1 \over 2}u(x , x{\prime})\delta ( \sigma ) - { 1 \over 2}v(x , x{\prime})\theta ( \sigma)$$\end{document } in the normal convex neighbourhood . equation ( 297 ) shows very clearly that the singular green s function does not distinguish between past and future ( property sc.s2 ) , and that its support excludes i(x ) in which ( ) = 0 ( property sc.s3 ) . from equation ( 287 ) we get an analogous expression for the radiative green s function : 298\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{r}}}(x , x{\prime } ) = { 1 \over 2}u(x , x{\prime})[{\delta _ + } ( \sigma ) - { \delta _ -}(\sigma ) ] + v(x , x{\prime})\,\left [ { { \theta _ + } ( - \sigma ) + { 1 \over 2}\theta ( \sigma ) } \right].$$\end{document } this reveals directly that the radiative green s function coincides with g+(x , x ) in i(x ) , in which ( ) = 0 and + ( ) = 1 ( property sc.r2 ) , and that its support does not include i(x ) , in which ( ) = +( ) = 0 ( property sc.r3 ) . to illustrate the general theory outlined in the previous sections 4.3.1 , 4.3.2 , 4.3.3 , 4.3.4 , and 4.3.5 , we consider here the specific case of a minimally - coupled ( = 0 ) scalar field in a cosmological spacetime with metric 299\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d{s^2 } = { a^2}(\eta)(- d{\eta ^2 } + d{x^2 } + d{y^2 } + d{z^2}),$$\end{document } where a( ) is the scale factor expressed in terms of conformal time . for concreteness we take the universe to be matter dominated , so that a( ) = c , where c is a constant . this spacetime is one of the very few for which green s functions can be explicitly constructed . the calculation presented here was first carried out by burko , harte , and poisson ; it can be extended to other cosmologies . to solve green s equation g(x , x ) = 44(x , x ) we first introduce a reduced green s function g(x , x ) defined by 300\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g(x , x{\prime } ) = { { g(x , x{\prime } ) } \over { a(\eta)a(\eta { \prime})}}.$$\end{document } substitution yields 301\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left({- { { { \partial ^2 } } \over { \partial { \eta ^2 } } } + { \nabla ^2 } + { 2 \over { { \eta ^2 } } } } \right)g(x , x{\prime } ) = - 4\pi \delta ( \eta - \eta { \prime}){\delta _ 3}(x - x{\prime}),$$\end{document } where x = ( x , y , z ) is a vector in three - dimensional flat space , and is the laplacian operator in this space . we next expand g(x , x ) in terms of plane - wave solutions to laplace s equation , 302\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g(x , x{\prime } ) = { 1 \over { { { ( 2\pi)}^3}}}\int { \tilde g(\eta , \eta { \prime};k){e^{ik \cdot ( x - x{\prime})}}{d^3}k},$$\end{document } and we substitute this back into equation ( 301 ) . the result , after also fourier transforming 3(x x ) , is an ordinary differential equation for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\tilde g(\eta , { \eta { \prime}};k)$\end{document } 303\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left({{{{d^2 } } \over { d{\eta ^2 } } } + { k^2 } - { 2 \over { { \eta ^2 } } } } \right)\tilde g = 4\pi \delta ( \eta - \eta { \prime}),$$\end{document } where k = k k. to generate the retarded green s function we set 304\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\tilde g + ( \eta , \eta { \prime};k ) = \theta ( \eta - \eta { \prime})\hat g(\eta , \eta { \prime};k),$$\end{document } in which we indicate that depends only on the modulus of the vector k. to generate the advanced green s function we would set instead \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\tilde g - ( \eta , { \eta { \prime}};k ) = \theta ( { \eta { \prime } } - \eta)\hat g(\eta , { \eta { \prime}};k)$\end{document}. the following manipulations will refer specifically to the retarded green s function ; they are easily adapted to the case of the advanced green s function . substitution of equation ( 304 ) into equation ( 303 ) reveals that must satisfy the homogeneous equation 305\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left({{{{d^2 } } \over { d{\eta ^2 } } } + { k^2 } - { 2 \over { { \eta ^2 } } } } \right)\hat g = 0,$$\end{document } together with the boundary conditions 306\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\hat g(\eta = \eta { \prime};k ) = 0,\quad \quad { { d\hat g } \over { d\eta}}(\eta = \eta { \prime};k ) = 4\pi.$$\end{document } inserting equation ( 304 ) into equation ( 302 ) and integrating over the angular variables associated with the vector k yields 307\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g + ( x , x{\prime } ) = { { \theta ( \delta \eta ) } \over { 2{\pi ^2}r}}\int\nolimits_0^\infty { \hat g(\eta , \eta { \prime};k)k\sin ( kr)dk},$$\end{document } where and r x x . equation ( 305 ) has sin(k ) + ( k ) cos(k ) as linearly independent solutions , and ( , ; k ) must be given by a linear superposition . the coefficients can be functions of , and after imposing equations ( 306 ) we find that the appropriate combination is 308\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\hat g(\eta , \eta { \prime};k ) = { { 4\pi } \over k}\left [ { \left({1 + { 1 \over { { k^2}\eta \eta { \prime } } } } \right)\sin ( k\delta \eta ) - { { \delta \eta } \over { k\eta \eta { \prime}}}\cos ( k\delta \eta ) } \right].$$\end{document } substituting this into equation ( 307 ) and using the identity \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(2/\pi)\int\nolimits_0^\infty { \sin ( \omega x)\sin ( \omega { x{\prime}})d\omega = \delta ( x - { x{\prime } } ) - \delta ( x + { x{\prime}})}$\end{document } yields \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g _ + } ( x , x{\prime } ) = { { \delta ( \delta \eta - r ) } \over r } + { { \theta ( \delta \eta ) } \over { \eta \eta { \prime}}}{2 \over \pi}\int\nolimits_0^\infty { { 1 \over k}\sin ( k\delta \eta)\cos ( kr)dk}$$\end{document } after integration by parts . the integral evaluates to ( r ) . we have arrived at 309\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g _ + } ( x , x{\prime } ) = { { \delta ( \eta - \eta { \prime } - \vert x - x{\prime}\vert ) } \over { \vert x - x{\prime}\vert } } + { { \theta ( \eta - \eta { \prime } - \vert x - x{\prime}\vert ) } \over { \eta \eta { \prime}}}$$\end{document } for our final expression for the retarded green s function . the advanced green s function is given instead by 310\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g _ -}(x , x{\prime } ) = { { \delta ( \eta - \eta { \prime } + \vert x - x{\prime}\vert ) } \over { \vert x - x{\prime}\vert } } + { { \theta ( - \eta + \eta { \prime } - \vert x - x{\prime}\vert ) } \over { \eta \eta { \prime}}}.$$\end{document } the distributions g(x , x ) are solutions to the reduced green s equation of equation ( 301 ) . the actual green s functions are obtained by substituting equations ( 309 ) and ( 310 ) into equation ( 300 ) . we note that the support of the retarded green s function is given by x x while the support of the advanced green s function is given by x x it may be verified that the symmetric two - point function 311\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h(x , x{\prime } ) = { 1 \over { \eta \eta { \prime}}}$$\end{document } satisfies all of the properties sc.hl , sc.h2 , sc.h3 , and sc.h4 listed in section 4.3.5 ; it may thus be used to define singular and radiative green s functions . according to equation ( 295 ) the singular green s function is given by 312\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { g_{\rm{s}}}(x , x{\prime } ) = { 1 \over { 2\vert x - x{\prime}\vert}}[\delta ( \eta - \eta { \prime } - \vert x - x{\prime}\vert ) + \delta ( \eta - \eta { \prime } + \vert x - x{\prime}\vert)]}\quad \quad \quad \quad \\ { + { 1 \over { 2\eta \eta { \prime}}}[\theta ( \eta - \eta { \prime } - \vert x - x{\prime}\vert ) - \theta ( \eta - \eta { \prime } + \vert x - x{\prime}\vert ) ] } , \\ \end{array}$$\end{document } and its support is limited to the interval x x x x according to equation ( 287 ) the radiative green s function is given by 313\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { g_{\rm{r}}}(x , x{\prime } ) = { 1 \over { 2\vert x - x{\prime}\vert}}[\delta ( \eta - \eta { \prime } - \vert x - x{\prime}\vert ) - \delta ( \eta - \eta { \prime } + \vert x - x{\prime}\vert ) ] } \quad \quad \quad \quad\\ { + { 1 \over { 2\eta \eta { \prime}}}[\theta ( \eta - \eta { \prime } - \vert x - x{\prime}\vert ) + \theta ( \eta - \eta { \prime } + \vert x - x{\prime}\vert ) ] } ; \\ \end{array}$$\end{document } its support is given by x x and for x x the radiative green s function agrees with the retarded green s function . as a final observation we note that for this cosmological spacetime , the normal convex neighbourhood of any point x consists of the whole spacetime manifold ( which excludes the cosmological singularity at a = 0 ) . the hadamard construction of the green s functions is therefore valid globally , a fact that is immediately revealed by equations ( 309 ) and ( 310 ) . the electromagnetic field tensor f = a a is expressed in terms of a vector potential a. in the lorenz gauge a = 0 , the vector potential satisfies the wave equation 314\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square{a^\alpha } - { r^\alpha}_\beta { a^\beta } = - 4\pi { j^\alpha},$$\end{document } where = g is the wave operator , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r^\alpha}_\beta$\end{document } the ricci tensor , and j a prescribed current density . the solution to the wave equation is written as 315\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^\alpha}(x ) = \int { { g^\alpha}_{\beta { \prime}}(x , x{\prime}){j^{\beta { \prime}}}(x{\prime } ) } \sqrt { - g{\prime } } { d^4}x{\prime},$$\end{document } in terms of a green s function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } that satisfies 316\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square{g^\alpha}_{\beta { \prime}}(x , x{\prime } ) - { r^\alpha}_\beta ( x){g^\beta}_{\beta { \prime}}(x , x{\prime } ) = - 4\pi { g^\alpha}_{\beta { \prime}}(x , x{\prime}){\delta _ 4}(x , x{\prime}),$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } is a parallel propagator and 4(x , x ) an invariant dirac distribution . the parallel propagator is inserted on the right - hand side of equation ( 316 ) to keep the index structure of the equation consistent from side to side ; because \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\beta { \prime}}}(x,{x{\prime}}){\delta _ 4}(x,{x{\prime}})$\end{document } is distributionally equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{g^\alpha}_{{\beta { \prime}}}]{\delta _ 4}(x,{x{\prime } } ) = { \delta ^{{\alpha { \prime}}}}_{^{{\beta { \prime}}}}{\delta _ 4}(x,{x{\prime}})$\end{document } , it could have been replaced by either \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\delta ^{{\alpha { \prime}}}}_{{\beta { \prime}}}$\end{document } or \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\delta ^\alpha}_\beta$\end{document}. it is easy to check that by virtue of equation ( 316 ) , the vector potential of equation ( 315 ) satisfies the wave equation of equation ( 314 ) . we will assume that the retarded green s function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{+ \beta}^\alpha ( x,{x{\prime}})$\end{document } , which is nonzero if x is in the causal future of x , and the advanced green s function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{- { \beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } , which is nonzero if x is in the causal past of x , exist as distributions and can be defined globally in the entire spacetime . assuming throughout this section that x is in the normal convex neighbourhood of x , we make the ansatz 317\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{\pm \beta { \prime}}^{\,\alpha}(x , x{\prime } ) = { u^\alpha}_{\beta { \prime}}(x , x{\prime}){\delta _ \pm}(\sigma ) + { v^\alpha}_{\beta { \prime}}(x , x{\prime}){\theta _ \pm}(- \sigma),$$\end{document } where ( ) , ( ) are the light - cone distributions introduced in section 4.2.2 , and where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^\alpha}_{{\beta { \prime}}}(x,{x{\prime}}),\,{v^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } are smooth bitensors . to conveniently manipulate the green s functions we shift by a small positive quantity . the green s functions are then recovered by the taking the limit of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{\pm \,\,\,\,\,\beta { \prime}}^{\epsilon \,\,\,\alpha}(x , x{\prime } ) \equiv { u^\alpha}_{\beta { \prime}}(x , x{\prime}){\delta _ \pm}(\sigma + \epsilon ) + { v^\alpha}_{\beta { \prime}}(x , x{\prime}){\theta _ when we substitute this into the left - hand side of equation ( 316 ) and then take the limit , we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{\square g_{\pm \beta \prime}^{\,\,\alpha } - r_{\;\;\beta}^\alpha g_{\pm \beta \prime}^{\,\,\beta } = - 4\pi { \delta _ 4}(x , x\prime)u_{\;\;\beta \prime}^\alpha + \delta { \prime _ \pm}(\sigma)\{2u_{\;\;\beta \prime ; \gamma}^\alpha { \sigma ^\gamma } + ( \sigma _ { \;\;\gamma}^\gamma - 4)u_{\;\;\beta \prime}^\alpha \ } \quad \quad \quad \quad \quad \quad \quad \quad}\\{+ { \delta _ \pm}(\sigma)\left\{{- 2v_{\;\;\beta \prime ; \gamma}^\alpha { \sigma ^\gamma } + ( 2 - { \sigma ^\gamma}_\gamma)v_{\;\;\beta \prime}^\alpha + \square { u^\alpha}_{\beta \prime } - r_\beta ^\alpha u_{\beta \prime}^\beta } \right\ } } \quad \\{+ { \theta _ \pm}(- \sigma)\left\{{\square v_{\beta \prime}^\alpha - r_\beta ^\alpha v_{\beta \prime}^\beta } \right\}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } after a routine computation similar to the one presented at the beginning of section 4.3.2 . comparison with equation ( 316 ) returns the equations 318\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{u^\alpha}_{\beta { \prime } } ] = [ { g^\alpha}_{\beta { \prime } } ] = { \delta ^{\alpha { \prime}}}_{\beta { \prime}}$$\end{document } and 319\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$2{u^\alpha}_{\beta { \prime};\gamma}{\sigma ^\gamma } + ( { \sigma ^\gamma}_\gamma - 4){u^\alpha}_{\beta { \prime } } = 0$$\end{document } that determine \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document};the equation 320\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over v } ^\alpha}_{\beta { \prime};\gamma}{\sigma ^\gamma } + { 1 \over 2}({\sigma ^\gamma}_\gamma - 2){\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over v } ^\alpha}_{\beta { \prime } } = { 1 \over 2}{\left . { \left({\square{u^\alpha}_{\beta { \prime } } - { r^\alpha}_\beta { u^\beta}_{\beta { \prime } } } \right ) } \right\vert _ { \sigma = 0}}$$\end{document } that determines \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\check v}^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } , the restriction of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$v_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } on the light cone (x , x ) = 0 ; andthe wave equation 321\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square{v^\alpha}_{\beta { \prime } } - { r^\alpha}_\beta { v^\beta}_{\beta { \prime } } = 0$$\end{document } that determines \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$v_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } inside the light cone . the equations 318\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{u^\alpha}_{\beta { \prime } } ] = [ { g^\alpha}_{\beta { \prime } } ] = { \delta ^{\alpha { \prime}}}_{\beta { \prime}}$$\end{document } and 319\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$2{u^\alpha}_{\beta { \prime};\gamma}{\sigma ^\gamma } + ( { \sigma ^\gamma}_\gamma - 4){u^\alpha}_{\beta { \prime } } = 0$$\end{document } that determine \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } ; the equation 320\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over v } ^\alpha}_{\beta { \prime};\gamma}{\sigma ^\gamma } + { 1 \over 2}({\sigma ^\gamma}_\gamma - 2){\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over v } ^\alpha}_{\beta { \prime } } = { 1 \over 2}{\left . { \left({\square{u^\alpha}_{\beta { \prime } } - { r^\alpha}_\beta { u^\beta}_{\beta { \prime } } } \right ) } \right\vert _ { \sigma = 0}}$$\end{document } that determines \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\check v}^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } , the restriction of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$v_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } on the light cone (x , x ) = 0 ; and the wave equation 321\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square{v^\alpha}_{\beta { \prime } } - { r^\alpha}_\beta { v^\beta}_{\beta { \prime } } = 0$$\end{document } that determines \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$v_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } inside the light cone . equation ( 319 ) can be integrated along the unique geodesic that links x to x. the initial conditions are provided by equation ( 318 ) , and if we set \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$u_{{\beta { \prime}}}^\alpha ( x,{x{\prime } } ) = { g^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})u(x,{x{\prime}})$\end{document } , we find that these equations reduce to equations ( 272 ) and ( 271 ) , respectively . according to equation ( 273 ) , then , we have 322\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u^\alpha}_{\beta { \prime}}(x , x{\prime } ) = { g^\alpha}_{\beta { \prime}}(x , x{\prime}){\delta ^{1/2}}(x , x{\prime}),$$\end{document } which reduces to 323\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u^\alpha}_{\beta { \prime } } = { g^\alpha}_{\beta { \prime}}\left({1 + { 1 \over { 12}}{r_{\gamma { \prime}\delta { \prime}}}{\sigma ^{\gamma { \prime}}}{\sigma ^{\delta { \prime } } } + \mathcal{o}({\lambda ^3 } ) } \right)$$\end{document } near coincidence , with denoting the affine - parameter distance between x and x. differentiation of this relation gives 324\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u^\alpha}_{\beta { \prime};\gamma } = { 1 \over 2}{g^{\gamma { \prime}}}_\gamma \left({{g^\alpha}_{\alpha { \prime}}{r^{\alpha { \prime}}}_{\beta { \prime}\gamma { \prime}\delta { \prime } } - { 1 \over 3}{g^\alpha}_{\beta { \prime}}{r_{\gamma { \prime}\delta { \prime } } } } \right){\sigma ^{\delta { \prime } } } + \mathcal{o}({\lambda ^2}),$$\end{document } 325\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u^\alpha}_{\beta { \prime};\gamma { \prime } } = { 1 \over 2}\left({{g^\alpha}_{\alpha { \prime}}{r^{\alpha { \prime}}}_{\beta { \prime}\gamma { \prime}\delta { \prime } } + { 1 \over 3}{g^\alpha}_{\beta { \prime}}{r_{\gamma { \prime}\delta { \prime } } } } \right){\sigma ^{\delta { \prime } } } + \mathcal{o}({\lambda ^2}),$$\end{document } and eventually , 326\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[\square{u^\alpha}_{\beta { \prime } } ] = { 1 \over 6}{\delta ^{\alpha { \prime}}}_{\beta { \prime}}r(x{\prime}).$$\end{document } similarly , equation ( 320 ) can be integrated along each null geodesic that generates the null cone (x , x ) = 0 . the initial values are obtained by taking the coincidence limit of this equation , using equations ( 318 ) , ( 326 ) , and the additional relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{\sigma ^\gamma}_\gamma ] = 4$\end{document } we arrive at 327\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{v^\alpha}_{\beta { \prime } } ] = { 1 \over 2}\left({{r^{\alpha { \prime}}}_{\beta { \prime } } - { 1 \over 6}{\delta ^{\alpha { \prime}}}_{\beta { \prime}}r{\prime } } \right).$$\end{document } with the characteristic data obtained by integrating equation ( 320 ) , the wave equation of equation ( 321 ) admits a unique solution . to summarize , the retarded and advanced electromagnetic green s functions are given by equation ( 317 ) with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } given by equation ( 322 ) and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$v_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } determined by equation ( 321 ) and the characteristic data constructed with equations ( 320 ) and ( 327 ) . it should be emphasized that the construction provided in this section is restricted to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}({x{\prime}})$\end{document } , the normal convex neighbourhood of the reference point x. like their scalar counterparts , the ( globally defined ) electromagnetic green s functions satisfy a reciprocity relation , the statement of which is 328\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{\beta { \prime}\alpha}^ - ( x , x{\prime } ) = g_{\alpha \beta { \prime}}^ + ( x , x{\prime}).$$\end{document } the derivation of equation ( 328 ) is virtually identical to what was presented in section 4.3.3 , and we shall not present the details . it suffices to mention that it is based on the identities \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{\alpha \beta { \prime}}^ + ( x , x{\prime})\left({\square g_{- \gamma{\prime\prime}}^{\,\,\alpha}(x , x{\prime\prime } ) - { r^\alpha}_\gamma g_{- \gamma{\prime\prime}}^{\,\,\gamma}(x , x{\prime\prime } ) } \right ) = - 4\pi g_{\alpha \beta { \prime}}^ + ( x , x{\prime}){g^\alpha}_{\gamma{\prime\prime}}(x , x{\prime\prime}){\delta _ 4}(x , x{\prime\prime})$$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{\alpha \gamma{\prime\prime}}^ - ( x , x{\prime\prime})\left({\square g_{+ \beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) - { r^\alpha}_\gamma g_{+ \beta { \prime}}^{\,\,\gamma}(x , x{\prime } ) } \right ) = - 4\pi g_{\alpha \gamma{\prime\prime}}^ - ( x , x{\prime\prime}){g^\alpha}_{\beta { \prime}}(x , x{\prime}){\delta _ 4}(x , x{\prime}).$$\end{document } a direct consequence of the reciprocity relation is 329\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${v_{\beta { \prime}\alpha}}(x , x{\prime } ) = { v_{\alpha { \prime}\beta}}(x , x{\prime}),$$\end{document } the statement that the bitensor \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${v_{\alpha { \beta { \prime}}}}(x,{x{\prime}})$\end{document } is symmetric in its indices and arguments . suppose that a(x ) satisfies the homogeneous version of equation ( 314 ) and that initial values \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^{{\alpha { \prime}}}}({x{\prime}}),{n^{{\beta { \prime}}}}{\nabla _ { { \beta { \prime}}}}{a^{{\alpha { \prime}}}}({x{\prime}})$\end{document } are specified on a spacelike hypersurface . then the value of the potential at a point x in the future of is given by 330\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^\alpha}(x ) = - { 1 \over { 4\pi}}\int\nolimits_\sigma { \left({g_{+ \beta { \prime}}^{\,\,\alpha}(x , x{\prime}){\nabla ^{\gamma { \prime}}}{a^{\beta { \prime}}}(x{\prime } ) - { a^{\beta { \prime}}}(x{\prime}){\nabla ^{\gamma { \prime}}}g_{+ \beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) } \right ) } d{\sigma _ { \gamma { \prime}}},$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d{\sigma _ { { \gamma { \prime } } } } = - { n_{{\gamma { \prime}}}}dv$\end{document } is a surface element on \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sigma ; { n_{{\gamma { \prime}}}}$\end{document } is the future - directed unit normal and dv is the invariant volume element on the hypersurface . the derivation of equation ( 330 ) is virtually identical to what was presented in section 4.3.4 . the treatment here parallels closely what was presented in section 4.3.5 , and the reader is referred to that section for a more complete discussion . we begin by introducing the bitensor \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } with properties em.h1 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } satisfies the homogeneous wave equation , 331\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square{h^\alpha}_{\beta { \prime}}(x , x{\prime } ) - { r^\alpha}_\beta ( x){h^\beta}_{\beta { \prime}}(x , x{\prime } ) = 0;$$\end{document}em.h2 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } is symmetric in its indices and arguments , 332\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h_{\beta { \prime}\alpha}}(x{\prime},x ) = { h_{\alpha \beta { \prime}}}(x , x{\prime});$$\end{document}em.h3 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } agrees with the retarded green s function if x is in the chronological future of x , 333\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h^\alpha}_{\beta { \prime}}(x , x{\prime } ) = g_{+ \beta { \prime}}^{\,\,\alpha}(x , x{\prime})\quad \quad { \rm{when}}\,x \in { i^ + } ( x{\prime});$$\end{document}em.h4 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } agrees with the advanced green s function if x is in the chronological past of x , 334\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h^\alpha}_{\beta { \prime}}(x , x{\prime } ) = g_{- \beta { \prime}}^{\,\,\alpha}(x , x{\prime})\quad \quad { \rm{when}}\,x \in { i^ -}(x{\prime}).$$\end{document } it is easy to prove that property em.h4 follows from property em.h2 , property em.h3 , and the reciprocity relation ( 328 ) satisfied by the retarded and advanced green s functions . that such a bitensor exists can be argued along the same lines as those presented in section 4.3.5 . em.h1 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } satisfies the homogeneous wave equation , 331\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square{h^\alpha}_{\beta { \prime}}(x , x{\prime } ) - { r^\alpha}_\beta ( x){h^\beta}_{\beta { \prime}}(x , x{\prime } ) = 0;$$\end{document } em.h2 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } is symmetric in its indices and arguments , 332\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h_{\beta { \prime}\alpha}}(x{\prime},x ) = { h_{\alpha \beta { \prime}}}(x , x{\prime});$$\end{document } em.h3 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } agrees with the retarded green s function if x is in the chronological future of x , 333\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h^\alpha}_{\beta { \prime}}(x , x{\prime } ) = g_{+ \beta { \prime}}^{\,\,\alpha}(x , x{\prime})\quad \quad { \rm{when}}\,x \in { i^ + } ( x{\prime});$$\end{document } em.h4 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } agrees with the advanced green s function if x is in the chronological past of x , 334\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h^\alpha}_{\beta { \prime}}(x , x{\prime } ) = g_{- \beta { \prime}}^{\,\,\alpha}(x , x{\prime})\quad \quad { \rm{when}}\,x \in { i^ -}(x{\prime}).$$\end{document } equipped with the bitensor \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^\alpha}_{{\beta { \prime}}}(x,{x{\prime}})$\end{document } we define the singular green s function to be 335\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{s}}\beta { \rm{{\prime}}}}^{\,\,\alpha}(x , x{\prime } ) = { 1 \over 2}[g_{+ \beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) + g_{- \beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) - { h^\alpha}_{\beta { \prime}}(x , x{\prime})].$$\end{document } this comes with the properties em.s1 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{s}}}_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } satisfies the inhomogeneous wave equation , 336\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square g_{{\rm{s}}\beta { \rm{{\prime}}}}^{\,\,\alpha}(x , x{\prime } ) - { r^\alpha}_\beta ( x)g_{{\rm{s}}\beta { \rm{{\prime}}}}^{\,\,\beta}(x , x{\prime } ) = - 4\pi { g^\alpha}_{\beta { \prime}}(x , x{\prime}){\delta _ 4}(x , x{\prime});$$\end{document}em.s2 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{s}}}_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } is symmetric in its indices and arguments , 337\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{\beta { \prime}\alpha}^{\rm{s}}(x , x{\prime } ) = g_{\alpha \beta { \prime}}^{\rm{s}}(x , x{\prime});$$\end{document}em.s3 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{s}}}_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } vanishes if x is in the chronological past or future of x , 338\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{s}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) = 0\quad \quad { \rm{when}}\,x \in { i^ \pm}(x{\prime}).$$\end{document } these can be established as consequences of properties em.h1 , em.h2 , em.h3 , and em.h4 , and the properties of the retarded and advanced green s functions . em.s1 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{s}}}_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } satisfies the inhomogeneous wave equation , 336\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square g_{{\rm{s}}\beta { \rm{{\prime}}}}^{\,\,\alpha}(x , x{\prime } ) - { r^\alpha}_\beta ( x)g_{{\rm{s}}\beta { \rm{{\prime}}}}^{\,\,\beta}(x , x{\prime } ) = - 4\pi { g^\alpha}_{\beta { \prime}}(x , x{\prime}){\delta _ 4}(x , x{\prime});$$\end{document } em.s2 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{s}}}_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } is symmetric in its indices and arguments , 337\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{\beta { \prime}\alpha}^{\rm{s}}(x , x{\prime } ) = g_{\alpha \beta { \prime}}^{\rm{s}}(x , x{\prime});$$\end{document } em.s3 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{s}}}_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } vanishes if x is in the chronological past or future of x , 338\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{s}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) = 0\quad \quad { \rm{when}}\,x \in { i^ \pm}(x{\prime}).$$\end{document } the radiative green s function is then defined by 339\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{r}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) = g_{{\rm{+}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) - g_{{\rm{s}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime}),$$\end{document } and it comes with the properties em.r1 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{r}}}_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } satisfies the homogeneous wave equation , 340\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square g_{{\rm{r}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) - { r^\alpha}_\beta ( x)g_{{\rm{r}}\beta { \prime}}^{\,\,\beta}(x , x{\prime } ) = 0;$$\end{document}em.r2 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{r}}}_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } agrees with the retarded green s function if x is in the chronological future of x 341\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{r}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) = g_{{\rm{+}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime})\quad \quad { \rm{when}}\,x \in { i^ + } ( x{\prime});$$\end{document}em.r3 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{r}}}_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } vanishes if x is in the chronological past of x , 342\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{r}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) = 0\quad \quad { \rm{when}}\,x \in { i^ -}(x{\prime}).$$\end{document } those follow immediately from properties em.s1 , em.s2 , and em.s3 and the properties of the retarded green s function . em.r1 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{r}}}_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } satisfies the homogeneous wave equation , 340\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square g_{{\rm{r}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) - { r^\alpha}_\beta ( x)g_{{\rm{r}}\beta { \prime}}^{\,\,\beta}(x , x{\prime } ) = 0;$$\end{document } em.r2 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{r}}}_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } agrees with the retarded green s function if x is in the chronological future of x 341\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{r}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) = g_{{\rm{+}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime})\quad \quad { \rm{when}}\,x \in { i^ + } ( x{\prime});$$\end{document } em.r3 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\rm{r}}}_{{\beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } vanishes if x is in the chronological past of x , 342\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{r}}\beta { \prime}}^{\,\,\alpha}(x , x{\prime } ) = 0\quad \quad { \rm{when}}\,x \in { i^ -}(x{\prime}).$$\end{document } when x is restricted to the normal convex neighbourhood of x , we have the explicit relations 343\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h^\alpha}_{\beta { \prime}}(x , x{\prime } ) = { v^\alpha}_{\beta { \prime}}(x , x{\prime}),$$\end{document } 344\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{s}}\beta { \rm{{\prime}}}}^{\,\,\alpha}(x , x{\prime } ) = { 1 \over 2}{u^\alpha}_{\beta { \prime}}(x , x{\prime})\delta ( \sigma ) - { 1 \over 2}{v^\alpha}_{\beta { \prime}}(x , x{\prime})\theta ( \sigma),$$\end{document } 345\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{r\beta ' } ^\alpha \left ( { x , x ' } \right ) = \frac{1}{2}{u^\alpha } _ { \beta ' } \left ( { x , x ' } \right)\left [ { { \delta _ + } \left ( \sigma \right ) - { \delta _ - } \left ( \sigma \right ) } \right ] + v_{\beta ' } ^\alpha \left ( { x , x ' } \right)\left [ { { \theta _ + } \left ( { - \sigma } \right ) + \frac{1}{2}\theta ( \sigma ) } \right].$$\end{document } from these we see clearly that the singular green s function does not distinguish between past and future ( property em.s2 ) , and that its support excludes i(x ) ( property em.s3 ) . we see also that the radiative green s function coincides with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{+ { \beta { \prime}}}^\alpha ( x,{x{\prime}})$\end{document } in i(x ) ( property em.r2 ) , and that its support does not include i(x ) ( property em.r3 ) . we are given a background spacetime for which the metric g satisfies the einstein field equations in vacuum . we then perturb the metric from g to 346\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\bf{g}}_{\alpha \beta } } = { g_{\alpha \beta } } + h_{\alpha \beta}.$$\end{document } the metric perturbation h is assumed to be small , and when working out the einstein field equations to be satisfied by the new metric g , we work consistently to first order in h. to simplify the expressions we use the trace - reversed potentials defined by 347\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma _ { \alpha \beta } } = { h_{\alpha \beta } } - { 1 \over 2}({g^{\gamma \delta}}{h_{\gamma \delta}}){g_{\alpha \beta}},$$\end{document } and we impose the lorenz gauge condition , 348\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma ^{\alpha \beta}}_{;\beta } = 0.$$\end{document } in this equation , and in all others below , indices are raised and lowered with the background metric g.similarly , the connection involved in equation ( 348 ) , and in all other equations below , is the one that is compatible with the background metric . if t is the perturbing stress - energy tensor , then by virtue of the linearized einstein field equations the perturbation field obeys the wave equation 349\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square{\gamma ^{\alpha \beta } } + 2r_{\gamma \,\,\delta}^{\,\,\alpha \,\,\beta}{\gamma ^{\gamma \delta } } = - 16\pi { t^{\alpha \beta}},$$\end{document } in which = g is the wave operator and r the riemann tensor . in first - order perturbation theory , the stress - energy tensor must be conserved in the background spacetime : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${t^{\alpha \beta}}_{;\beta } = 0$\end{document}. the solution to the wave equation is written as 350\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma ^{\alpha \beta}}(x ) = 4\int { { g^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime}){t^{\gamma { \prime}\delta { \prime}}}(x{\prime})\sqrt { - g{\prime } } { d^4}x{\prime}},$$\end{document } in terms of a green s function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{\alpha \beta}}_{{\gamma { \prime}}{\delta { \prime}}}(x,{x{\prime}})$\end{document } that satisfies 351\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square { g^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) + 2{r_\gamma}{^\alpha _ \delta}^\beta ( x){g^{\gamma \delta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) = - 4\pi g_{\gamma { \prime}}^{(\alpha}(x , x{\prime})g_{\delta { \prime}}^{\beta)}(x , x{\prime}){\delta _ 4}(x , x{\prime}),$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_{{\gamma { \prime}}}(x,{x{\prime}})$\end{document } is a parallel propagator and 4(x , x ) an invariant dirac functional . the parallel propagators are inserted on the right - hand side of equation ( 351 ) to keep the index structure of the equation consistent from side to side ; in particular , both sides of the equation are symmetric in and , and in and . it is easy to check that by virtue of equation ( 351 ) , the perturbation field of equation ( 350 ) satisfies the wave equation of equation ( 349 ) . once is known , the metric perturbation can be reconstructed from the relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h_{\alpha \beta } } = { \gamma _ { \alpha \beta } } - { 1 \over 2}({g^{\gamma \delta}}{\gamma _ { \gamma \delta}}){g_{\alpha \beta}}$\end{document}. we will assume that the retarded green s function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g { { _ + ^{\alpha \beta } } _ { \gamma ' \delta ' } } ( x , x')$\end{document } , which is nonzero if x is in the causal future of x , and the advanced green s function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g { { _ + ^{\alpha \beta } } _ { \gamma ' \delta ' } } ( x , x')$\end{document } , which is nonzero if x is in the causal past of x , exist as distributions and can be defined globally in the entire background spacetime . assuming throughout this section that x is in the normal convex neighbourhood of x , we make the ansatz 352\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$gg { { _ + ^{\alpha \beta } } _ { \gamma ' \delta ' } } ( x , x ' ) = { u^{\alpha \beta } } _ { \gamma ' \delta ' } ( x , x'){\delta _ \pm } ( \sigma ) + v { { _ + ^{\alpha \beta } } _ { \gamma ' \delta ' } } ( x , x'){\theta _ \pm } ( - \sigma ) , $ $ \end{document } where ( ) , ( ) are the light - cone distributions introduced in section 4.2.2 , and where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^\alpha}_{{\gamma { \prime}}{\delta { \prime}}}^\beta ( x,{x{\prime}}),\,{v^\alpha}_{{\gamma { \prime}}{\delta { \prime}}}^\beta ( x,{x{\prime}})$\end{document } are smooth bitensors . to conveniently manipulate the green s functions we shift by a small positive quantity . the green s functions are then recovered by the taking the limit of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g _ { \pm \;\;\;\gamma ' \delta ' } ^{\epsilon\;\alpha \beta } ( x , x ' ) = u_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x'){\delta _ \pm } ( \sigma + \epsilon ) + v_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x'){\theta _ when we substitute this into the left - hand side of equation ( 351 ) and then take the limit , we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{\square g_{\pm \gamma \prime \delta \prime}^{\;\alpha \beta } + 2r_{\gamma \;\;\delta}^{\alpha \;\;\beta}g_{\pm \;\gamma \prime \delta \prime}^{\;\gamma \delta } = - 4\pi { \delta _ 4}(x , x\prime)u_{\;\;\gamma \prime \delta \prime}^{\alpha \beta } + \delta { \prime _ \pm}(\sigma)\left\{{2u_{\;\;\gamma \prime \delta \prime ; \gamma}^{\alpha \beta}{\sigma ^\gamma } + ( { \sigma ^\gamma}_\gamma - 4)u_{\;\;\;\gamma \prime \delta \prime}^{\alpha \beta } } \right\}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\{+ { \delta _ \pm}(\sigma)\left\{{- 2v_{\;\;\gamma \prime \delta \prime ; \gamma}^{\alpha \beta}{\sigma ^\gamma } + ( 2 - { \sigma ^\gamma}_\gamma)v_{\;\;\;\;\gamma \prime \delta \prime}^{\alpha \beta } + \square u_{\;\;\;\gamma \prime \delta \prime}^{\alpha \beta } + 2r_{\gamma \;\;\delta}^{\alpha \;\;\beta}u_{\;\;\gamma \prime \delta \prime}^{\gamma \delta } } \right\}\quad } \\{+ { \theta _ \pm}(- \sigma)\left\{{\square v_{\;\;\;\gamma \prime \delta \prime}^{\alpha \beta } + 2r_{\gamma \;\;\delta}^{\alpha \;\;\beta}v_{\;\;\gamma \prime \delta \prime}^{\alpha \beta } } \right\}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ \end{array}$$\end{document } after a routine computation similar to the one presented at the beginning of section 4.3.2 . comparison with equation ( 351 ) returns the equations 353\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left [ { { u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime } } } \right ] = \left [ { g_{\gamma { \prime}}^{(\alpha}g_{\delta { \prime}}^{\beta ) } } \right ] = { \delta ^{(\alpha { \prime}}}_{\gamma { \prime}}{\delta ^{\beta { \prime})}}_{\delta { \prime}}$$\end{document } and 354\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$2{u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime};\gamma}{\sigma ^\gamma } + ( { \sigma ^\gamma}_\gamma - 4){u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime } } = 0$$\end{document } that determine \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^\alpha}_{{\gamma { \prime}}{\delta { \prime}}}^\beta ( x,{x{\prime}})$\end{document};the equation 355\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\check{v}_{\;\;\gamma \prime \delta \prime ; \gamma}^{\alpha \beta}{\sigma ^\gamma } + { 1 \over 2}(\sigma _ { \;\;\gamma}^\gamma - 2)\check{v}_{\;\;\;\;\gamma \prime \delta \prime}^{\alpha \beta } = { \left . { { 1 \over 2}\left({\square u_{\;\;\gamma \prime \delta \prime}^{\alpha \beta } + 2r_{\gamma \;\;\delta}^{\alpha \;\;\beta}u_{\;\;\gamma \prime \delta \prime}^{\gamma \delta } } \right ) } \right\vert_{\sigma = 0}}$$\end{document } that determines \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{v } } _ { \;\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } , the restriction of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${v^\alpha}_{{\gamma { \prime}}{\delta { \prime}}}^\beta ( x,{x{\prime}})$\end{document } on the light cone (x , x ) = 0 ; andthe wave equation 356\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square { v^{\alpha \beta}}_{\gamma { \prime}\delta { \prime } } + 2{r_\gamma}{^\alpha _ \delta}^\beta { v^{\gamma \delta}}_{\gamma { \prime}\delta { \prime } } = 0$$\end{document } that determines \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${v^\alpha}_{{\gamma { \prime}}{\delta { \prime}}}^\beta ( x,{x{\prime}})$\end{document } inside the light cone . the equations 353\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left [ { { u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime } } } \right ] = \left [ { g_{\gamma { \prime}}^{(\alpha}g_{\delta { \prime}}^{\beta ) } } \right ] = { \delta ^{(\alpha { \prime}}}_{\gamma { \prime}}{\delta ^{\beta { \prime})}}_{\delta { \prime}}$$\end{document } and 354\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$2{u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime};\gamma}{\sigma ^\gamma } + ( { \sigma ^\gamma}_\gamma - 4){u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime } } = 0$$\end{document } that determine \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^\alpha}_{{\gamma { \prime}}{\delta { \prime}}}^\beta ( x,{x{\prime}})$\end{document } ; the equation 355\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\check{v}_{\;\;\gamma \prime \delta \prime ; \gamma}^{\alpha \beta}{\sigma ^\gamma } + { 1 \over 2}(\sigma _ { \;\;\gamma}^\gamma - 2)\check{v}_{\;\;\;\;\gamma \prime \delta \prime}^{\alpha \beta } = { \left . { { 1 \over 2}\left({\square u_{\;\;\gamma \prime \delta \prime}^{\alpha \beta } + 2r_{\gamma \;\;\delta}^{\alpha \;\;\beta}u_{\;\;\gamma \prime \delta \prime}^{\gamma \delta } } \right ) } \right\vert_{\sigma = 0}}$$\end{document } that determines \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{v } } _ { \;\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } , the restriction of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${v^\alpha}_{{\gamma { \prime}}{\delta { \prime}}}^\beta ( x,{x{\prime}})$\end{document } on the light cone (x , x ) = 0 ; and the wave equation 356\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square { v^{\alpha \beta}}_{\gamma { \prime}\delta { \prime } } + 2{r_\gamma}{^\alpha _ \delta}^\beta { v^{\gamma \delta}}_{\gamma { \prime}\delta { \prime } } = 0$$\end{document } that determines \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${v^\alpha}_{{\gamma { \prime}}{\delta { \prime}}}^\beta ( x,{x{\prime}})$\end{document } inside the light cone . equation ( 354 ) can be integrated along the unique geodesic that links x to x. the initial conditions are provided by equation ( 353 ) , and if we set \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^\alpha}_{{\gamma { \prime}}{\delta { \prime}}}^\beta ( x,{x{\prime } } ) = g_{{\gamma { \prime}}}^{(\alpha}g_{{\delta { \prime}}}^{\beta)}u(x,{x{\prime}})$\end{document } , we find that these equations reduce to equations ( 272 ) and ( 271 ) , respectively . according to equation ( 273 ) , then , we have 357\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) = g_{\gamma { \prime}}^{(\alpha}(x , x{\prime})g_{\delta { \prime}}^{\beta)}(x , x{\prime}){\delta ^{1/2}}(x , x{\prime}),$$\end{document } which reduces to 358\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime } } = g_{\gamma { \prime}}^{(\alpha}g_{\delta { \prime}}^{\beta)}(1 + \mathcal{o}({\lambda ^3}))$$\end{document } near coincidence , with denoting the affine - parameter distance between x and x ; there is no term of order because , by assumption , the background ricci tensor vanishes at x ( as it does in the entire spacetime ) . differentiation of this relation gives 359\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime};\varepsilon } = { 1 \over 2}g_{\alpha { \prime}}^{(\alpha}g_{\beta { \prime}}^{\beta)}{g^{\varepsilon { \prime}}}_\varepsilon \left({{r^{\alpha { \prime}}}_{\gamma { \prime}\varepsilon { \prime}\iota { \prime}}{\delta ^{\beta { \prime}}}_{\delta { \prime } } + { r^{\alpha { \prime}}}_{\delta { \prime}\varepsilon { \prime}\iota { \prime}}{\delta ^{\beta { \prime}}}_{\gamma { \prime } } } \right){\sigma ^{\iota { \prime } } } + \mathcal{o}({\lambda ^2}),$$\end{document } 360\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime};\varepsilon } = { 1 \over 2}g_{\alpha { \prime}}^{(\alpha}g_{\beta { \prime}}^{\beta)}\left({{r^{\alpha { \prime}}}_{\gamma { \prime}\varepsilon { \prime}\iota { \prime}}{\delta ^{\beta { \prime}}}_{\delta { \prime } } + { r^{\alpha { \prime}}}_{\delta { \prime}\varepsilon { \prime}\iota { \prime}}{\delta ^{\beta { \prime}}}_{\gamma { \prime } } } \right){\sigma ^{\iota { \prime } } } + \mathcal{o}({\lambda ^2}),$$\end{document } and eventually , 361\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left [ { \square { u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime } } } \right ] = 0;$$\end{document } this last result follows from the fact that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{u^\alpha}_{{\gamma { \prime}}{\delta { \prime}};\epsilon \iota}^\beta ] $ \end{document } is antisymmetric in the last pair of indices . similarly , equation ( 355 ) can be integrated along each null geodesic that generates the null cone (x , x ) = 0 . the initial values are obtained by taking the coincidence limit of this equation , using equations ( 353 ) , ( 361 ) , and the additional relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{\sigma ^\gamma}_\gamma ] = 4$\end{document}. we arrive at 362\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left [ { { v^{\alpha \beta}}_{\gamma { \prime}\delta { \prime } } } \right]{1 \over 2}\left({{r_{\gamma { \prime}}}{{^{\alpha { \prime}}}_{\delta { \prime}}}^{\beta { \prime } } + { r_{\gamma { \prime}}}{{^{\beta { \prime}}}_{\delta { \prime}}}^{\alpha { \prime } } } \right).$$\end{document } with the characteristic data obtained by integrating equation ( 355 ) , the wave equation of equation ( 356 ) admits a unique solution . to summarize , the retarded and advanced gravitational green s functions are given by equation ( 352 ) with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^\alpha}_{{\gamma { \prime}}{\delta { \prime}}}^\beta ( x,{x{\prime}})$\end{document } given by equation ( 357 ) and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${v^\alpha}_{{\gamma { \prime}}{\delta { \prime}}}^\beta ( x,{x{\prime}})$\end{document } determined by equation ( 356 ) , and the characteristic data constructed with equations ( 355 ) and ( 362 ) . it should be emphasized that the construction provided in this section is restricted to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}({x{\prime}})$\end{document } , the normal convex neighbourhood of the reference point x. the ( globally defined ) gravitational green s functions satisfy the reciprocity relation 363\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{\gamma { \prime}\delta { \prime}\alpha \beta}^ - ( x , x{\prime } ) = g_{\alpha \beta \gamma { \prime}\delta { \prime}}^ + ( x , x{\prime}).$$\end{document } the derivation of this result is virtually identical to what was presented in sections 4.3.3 and 4.4.3 . a direct consequence of the reciprocity relation is the statement 364\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${v_{\gamma { \prime}\delta { \prime}\alpha \beta}}(x , x{\prime } ) = { v_{\alpha \beta \gamma { \prime}\delta { \prime}}}(x , x{\prime}).$$\end{document } the kirchhoff representation for the trace - reversed gravitational perturbation is formulated as follows . suppose that (x ) satisfies the homogeneous version of equation ( 349 ) and that initial values \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\gamma ^{{\alpha { \prime}}{\beta { \prime}}}}({x{\prime}}),\,{n^{{\gamma { \prime}}}}{\nabla _ { { \gamma { \prime}}}}{\gamma ^{{\alpha { \prime}}{\beta { \prime}}}}({x{\prime}})$\end{document } are specified on a spacelike hypersurface . then the value of the perturbation field at a point x in the future of is given by 365\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma ^{\alpha \beta}}(x ) = - { 1 \over { 4\pi}}\int\nolimits_\sigma { \left({{g _ + } { { ^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime}){\nabla ^{\varepsilon { \prime}}}{\gamma ^{\gamma { \prime}\delta { \prime}}}(x{\prime } ) - { \gamma ^{\gamma { \prime}\delta { \prime}}}(x{\prime}){\nabla ^{\varepsilon { \prime}}}{g _ + } { { ^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) } \right)d{\sigma _ { \varepsilon { \prime}}},}$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d{\sigma _ { { \epsilon { \prime } } } } = - { n_{{\epsilon { \prime}}}}dv$\end{document } is a surface element on ; \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sigma ; { n_{{\gamma { \prime}}}}$\end{document } is the future - directed unit normal and dv is the invariant volume element on the hypersurface . the derivation of equation ( 365 ) is virtually identical to what was presented in sections 4.3.4 and 4.4.3 . we shall now construct singular and radiative green s functions for the linearized gravitational field . we begin by introducing the bitensor \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^{\alpha \beta}}_{{\gamma { \prime}}{\delta { \prime}}}(x,{x{\prime}})$\end{document } with properties gr.h1 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^{\alpha \beta}}_{{\gamma { \prime}}{\delta { \prime}}}(x,{x{\prime}})$\end{document } satisfies the homogeneous wave equation , 366\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square { h^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) + 2{r_\gamma}{^\alpha _ \delta}^\beta ( x){h^{\gamma \delta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) = 0;$$\end{document}gr.h2 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^{\alpha \beta}}_{{\gamma { \prime}}{\delta { \prime}}}(x,{x{\prime}})$\end{document } is symmetric in its indices and arguments , 367\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h_{\gamma { \prime}\delta { \prime}\alpha \beta}}(x , x{\prime } ) = { h_{\alpha \beta \gamma { \prime}\delta { \prime}}}(x , x{\prime});$$\end{document}gr.h3 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^{\alpha \beta}}_{{\gamma { \prime}}{\delta { \prime}}}(x,{x{\prime}})$\end{document } agrees with the retarded green s function if x is in the chronological future of x , 368\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) = { g^{\alpha \beta}}_{+ \gamma { \prime}\delta { \prime}}(x , x{\prime})\quad \quad { \rm{when}}\;x \in { i^ + } ( x{\prime});$$\end{document}gr.h4 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^{\alpha \beta}}_{{\gamma { \prime}}{\delta { \prime}}}(x,{x{\prime}})$\end{document } agrees with the advanced green s function if x is in the chronological past of x , 369\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) = { g^{\alpha \beta}}_{- \gamma { \prime}\delta { \prime}}(x , x{\prime})\quad \quad { \rm{when}}\;x \in { i^ -}(x{\prime}).$$\end{document } it is easy to prove that property gr.h4 follows from property gr.h2 , property gr.h3 , and the reciprocity relation ( 363 ) satisfied by the retarded and advanced green s functions . that such a bitensor exists can be argued along the same lines as those presented in section 4.3.5 . gr.h1 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^{\alpha \beta}}_{{\gamma { \prime}}{\delta { \prime}}}(x,{x{\prime}})$\end{document } satisfies the homogeneous wave equation , 366\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square { h^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) + 2{r_\gamma}{^\alpha _ \delta}^\beta ( x){h^{\gamma \delta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) = 0;$$\end{document } gr.h2 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^{\alpha \beta}}_{{\gamma { \prime}}{\delta { \prime}}}(x,{x{\prime}})$\end{document } is symmetric in its indices and arguments , 367\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h_{\gamma { \prime}\delta { \prime}\alpha \beta}}(x , x{\prime } ) = { h_{\alpha \beta \gamma { \prime}\delta { \prime}}}(x , x{\prime});$$\end{document } gr.h3 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^{\alpha \beta}}_{{\gamma { \prime}}{\delta { \prime}}}(x,{x{\prime}})$\end{document } agrees with the retarded green s function if x is in the chronological future of x , 368\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) = { g^{\alpha \beta}}_{+ \gamma { \prime}\delta { \prime}}(x , x{\prime})\quad \quad { \rm{when}}\;x \in { i^ + } ( x{\prime});$$\end{document } gr.h4 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^{\alpha \beta}}_{{\gamma { \prime}}{\delta { \prime}}}(x,{x{\prime}})$\end{document } agrees with the advanced green s function if x is in the chronological past of x , 369\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) = { g^{\alpha \beta}}_{- \gamma { \prime}\delta { \prime}}(x , x{\prime})\quad \quad { \rm{when}}\;x \in { i^ -}(x{\prime}).$$\end{document } equipped with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^{\alpha \beta}}_{{\gamma { \prime}}{\delta { \prime}}}(x,{x{\prime}})$\end{document } we define the singular green s function to be 370\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{s}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) = { 1 \over 2}\left [ { { g_{\rm{+}}}{{^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) + { g_{\rm{-}}}{{^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) - { h^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) } \right].$$\end{document } this comes with the properties gr.s1 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_s}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } satisfies the inhomogeneous wave equation , 371\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square { g_{\rm{s}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) + 2{r_\gamma}{^\alpha _ \delta}^\beta ( x){g_{\rm{s}}}{^{\gamma \delta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) = - 4\pi { g^{(\alpha}}_{\gamma { \prime}}(x , x{\prime})g_{\delta { \prime}}^{\beta)}(x , x{\prime}){\delta _ 4}(x , x{\prime});$$\end{document}gr.s2 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_s}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } is symmetric in its indices and arguments , 372\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{\gamma { \prime}\delta { \prime}\alpha \beta}^{\rm{s}}(x , x{\prime } ) = g_{\alpha \beta \gamma { \prime}\delta { \prime}}^{\rm{s}}(x , x{\prime});$$\end{document}gr.s3 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_s}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } vanishes if x is in the chronological past or future of x , 373\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{s}}\;\;\gamma { \prime}\delta { \prime}\alpha \beta}^{\alpha \beta}(x , x{\prime } ) = 0\quad \quad { \rm{when}}\;x \in { i^ \pm}(x{\prime}).$$\end{document } these can be established as consequences of properties gr.h1 , gr.h2 , gr.h3 , and gr.h4 , and the properties of the retarded and advanced green s functions . gr.s1 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_s}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } satisfies the inhomogeneous wave equation , 371\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square { g_{\rm{s}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) + 2{r_\gamma}{^\alpha _ \delta}^\beta ( x){g_{\rm{s}}}{^{\gamma \delta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) = - 4\pi { g^{(\alpha}}_{\gamma { \prime}}(x , x{\prime})g_{\delta { \prime}}^{\beta)}(x , x{\prime}){\delta _ 4}(x , x{\prime});$$\end{document } gr.s2 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_s}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } is symmetric in its indices and arguments , 372\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{\gamma { \prime}\delta { \prime}\alpha \beta}^{\rm{s}}(x , x{\prime } ) = g_{\alpha \beta \gamma { \prime}\delta { \prime}}^{\rm{s}}(x , x{\prime});$$\end{document } gr.s3 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_s}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } vanishes if x is in the chronological past or future of x , 373\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{s}}\;\;\gamma { \prime}\delta { \prime}\alpha \beta}^{\alpha \beta}(x , x{\prime } ) = 0\quad \quad { \rm{when}}\;x \in { i^ \pm}(x{\prime}).$$\end{document } the radiative green s function is then defined by 374\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$g_{{\rm{r}}\;\;\gamma { \prime}\delta { \prime}\alpha \beta}^{\alpha \beta}(x , x{\prime } ) = { g _ + } { ^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) - { g_{\rm{s}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime}),$$\end{document } and it comes with the properties gr.r1 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_r}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } satisfies the homogeneous wave equation , 375\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square { g_{\rm{r}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) + 2{r_\gamma}{^\alpha _ \delta}^\beta ( x){g_{\rm{r}}}{^{\gamma \delta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) = 0;$$\end{document}gr.r2 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_r}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } agrees with the retarded green s function if x is in the chronological future of x , 376\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{r}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) = { g_{\rm{+}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime})\quad \quad { \rm{when}}\;x \in { i^ + } ( x{\prime});$$\end{document}gr.r3 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_r}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } vanishes if x is in the chronological past of x , 377\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{r}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) = 0\quad \quad { \rm{when}}\;x \in { i^ -}(x{\prime}).$$\end{document } those follow immediately from properties gr.s1 , gr.s2 , and gr.s3 , and the properties of the retarded green s function . gr.r1 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_r}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } satisfies the homogeneous wave equation , 375\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square { g_{\rm{r}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) + 2{r_\gamma}{^\alpha _ \delta}^\beta ( x){g_{\rm{r}}}{^{\gamma \delta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) = 0;$$\end{document } gr.r2 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_r}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } agrees with the retarded green s function if x is in the chronological future of x , 376\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{r}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) = { g_{\rm{+}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime})\quad \quad { \rm{when}}\;x \in { i^ + } ( x{\prime});$$\end{document } gr.r3 : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_r}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } vanishes if x is in the chronological past of x , 377\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{r}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) = 0\quad \quad { \rm{when}}\;x \in { i^ -}(x{\prime}).$$\end{document } when x is restricted to the normal convex neighbourhood of x , we have the explicit relations 378\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime } ) = { v^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime}),$$\end{document } 379\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{s}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) = { 1 \over 2}{u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime})\gamma ( \sigma ) - { 1 \over 2}{v^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime})\theta ( \sigma),$$\end{document } 380\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\rm{r}}}{^{\alpha \beta}_{\gamma { \prime}\delta { \prime}}}(x , x{\prime } ) = { 1 \over 2}{u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime})[{\delta _ + } ( \sigma ) - { \delta _ -}(\sigma ) ] + { v^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime})\left [ { { \theta _ + } ( - \sigma ) + { 1 \over 2}\theta ( \sigma ) } \right].$$\end{document } from these we see clearly that the singular green s function does not distinguish between past and future ( property gr.s2 ) , and that its support excludes i(x ) ( property gr.s3 ) . we see also that the radiative green s function coincides with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_+}_{\;\;\gamma ' \delta ' } ^{\alpha \beta } ( x , x')$\end{document } in i(x ) ( property gr.r2 ) , and that its support does not include i(x ) ( property gr.r3 ) . a point particle carries a scalar charge q and moves on a world line described by relations z( ) , in which is an arbitrary parameter . the particle generates a scalar potential (x ) and a field (x ) (x ) . the dynamics of the entire system is governed by the action 381\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$s = { s_{{\rm{field } } } } + { s_{{\rm{partial } } } } + { s_{{\rm{interaction}}}},$$\end{document } where sfield is an action functional for a free scalar field in a spacetime with metric g , sparticle is the action of a free particle moving on a world line in this spacetime , and sinteraction is an interaction term that couples the field to the particle . the field action is given by 382\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_{{\rm{field } } } } = - { 1 \over { 8\pi}}\int { ( { g^{\alpha \beta}}{\phi _ \alpha}{\phi _ \beta } + \xi r{\phi ^2})\sqrt { - g } { d^4}x,}$$\end{document } where the integration is over all of spacetime ; the field is coupled to the ricci scalar r by an arbitrary constant . the particle action is 383\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_{{\rm{partial } } } } = - { m_0}\int\nolimits_\gamma { d\tau},$$\end{document } where m0 is the bare mass of the particle and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d\tau = \sqrt { - { g_{\mu \nu}}(z){{\dot z}^\mu}{{\dot z}^\nu } } d\lambda$\end{document } is the differential of proper time along the world line ; we use an overdot on z( ) to indicate differentiation with respect to the parameter . finally , the interaction term is given by 384\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_{{\rm{interaction } } } } = q\int\nolimits_\gamma { \phi ( z)d\tau = q } \int { \phi ( x){\delta _ 4}(x , z)\sqrt { - g } { d^4}xd\tau}.$$\end{document } notice that both sparticle and sinteraction are invariant under a reparameterization ( ) of the world line . demanding that the total action be stationary under a variation (x ) of the field configuration yields the wave equation 385\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(\square - \xi r)\phi ( x ) = - 4\pi \mu ( x)$$\end{document } for the scalar potential , with a charge density (x ) defined by 386\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\mu ( x ) = q\int\nolimits_\gamma { { \delta _ 4}(x , z)d\tau}.$$\end{document } these equations determine the field (x ) once the motion of the scalar charge is specified . on the other hand , demanding that the total action be stationary under a variation ( z( ) of the world line yields the equations of motion for the scalar charge , 387\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$m(\tau){{d{u^\mu } } \over { d\tau } } = q({g^{\mu \nu } } + { u^\mu}{u^\nu}){\phi _ \nu}(z).$$\end{document } we have here adopted as the parameter on the world line , and introduced the four - velocity u( ) dz / d. the dynamical mass that appears in equation ( 387 ) is defined by m( ) = m0 q(z ) , which can also be written in differential form as 388\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{dm } \over { d\tau } } = - q{\phi _ \mu}(z){u^\mu}.$$\end{document } it should be clear that equations ( 387 ) and ( 388 ) are valid only in a formal sense , because the scalar potential obtained from equations ( 385 ) and ( 386 ) diverges on the world line . before we can make sense of these equations we have to analyze the field s singularity structure near the world line . the retarded solution to equation ( 385 ) is \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\phi ( x ) = \int { g _ + } ( x,{x{\prime}})\mu ( { x{\prime}})\sqrt { { g{\prime } } } { d^4}{x{\prime}}$\end{document } , where g+(x , x ) is the retarded green s function introduced in section 4.3 . after substitution of equation ( 386 ) we obtain 389\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi ( x ) = q\int\nolimits_\gamma { { g _ + } ( x , z)d\tau},$$\end{document } in which z( ) gives the description of the world line . because the retarded green s function is defined globally in the entire spacetime , equation ( 389 ) applies to any field point x. we now specialize equation ( 389 ) to a point x near the world line ( see figure 9 ) . we let \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } be the normal convex neighbourhood of this point , and we assume that the world line traverses \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document}. let < be the value of the proper - time parameter at which enters \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } from the past , and let > be its value when the world line leaves \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document}. then equation ( 389 ) can be broken down into the three integrals \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi ( x ) = q\int\nolimits_{- \infty}^{{\tau _ < } } { { g _ + } ( x , z)d\tau + q } \int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { { g _ + } ( x , z)d\tau + q } \int\nolimits_{{\tau _ > } } ^\infty { { g _ + } ( x , z)d\tau.}$$\end{document } the third integration vanishes because x is then in the past of z( ) , and g+(x , z ) = 0 . for the second integration , x is the normal convex neighbourhood of z( ) , and the retarded green s function can be expressed in the hadamard form produced in section 4.3.2 . this gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { { g _ + } ( x , z)d\tau = } \int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { u(x , z){\delta _ + } ( \sigma)d\tau + } \int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { v(x , z){\theta _ + } ( - \sigma)d\tau,}$$\end{document } and to evaluate this we refer back to section 3.3 and let x z(u ) be the retarded point associated with x ; these points are related by (x , x ) = 0 and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r \equiv { \sigma _ { { \alpha { \prime}}}}{u^{{\alpha { \prime}}}}$\end{document } is the retarded distance between x and the world line . we resume the index convention of section 3.3 : to tensors at x we assign indices , , etc . ; to tensors at x we assign indices , , etc . ; and to tensors at a generic point z( ) on the world line we assign indices , , etc . figure 9the region within the dashed boundary represents the normal convex neighbourhood of the point x. the world line enters the neighbourhood at proper time < and exits at proper time >. also shown are the retarded point z(u ) and the advanced point z(v ) . the region within the dashed boundary represents the normal convex neighbourhood of the point x. the world line enters the neighbourhood at proper time < and exits at proper time >. also shown are the retarded point z(u ) and the advanced point z(v ) . to perform the first integration we change variables from to , noticing that a increases as z( ) passes through x. the change of on the world line is given by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d\sigma \equiv \sigma ( x , z + dz ) - \sigma ( x , z ) = { \sigma _ \mu}{u^\mu}d\tau$\end{document } , and we find that the first integral evaluates to u(x , z)/(u ) with z identified with x. the second integration is cut off at = u by the step function , and we obtain our final expression for the retarded potential of a point scalar charge : 390\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi ( x ) = { q \over r}u(x , x{\prime } ) + q\int\nolimits_{{\tau _ < } } ^u { v(x , z)d\tau + q } \int\nolimits_{- \infty}^{{\tau _ < } } { { g _ + } ( x , z)d\tau.}$$\end{document } this expression applies to a point x sufficiently close to the world line that there exists a nonempty intersection between \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } and . when we differentiate the potential of equation ( 390 ) we must keep in mind that a variation in x induces a variation in x because the new points x + and x + x must also be linked by a null geodesic you may refer back to section 3.3.2 for a detailed discussion . this means , for example , that the total variation of u(x , x ) is \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\delta u = u(x + \delta x,{x{\prime } } + \delta { x{\prime } } ) - u(x,{x{\prime } } ) = { u_{;\alpha}}\delta { x^\alpha } + { u_{;{\alpha { \prime}}}}{u^{{\alpha { \prime}}}}\delta u$\end{document}. the gradient of the scalar potential is therefore given by 391\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\phi _ \alpha}(x ) = - { q \over { { r^2}}}u(x , x{\prime}){\partial _ \alpha}r + { q \over r}{u_{;\alpha}}(x , x{\prime } ) + { q \over r}{u_{;\alpha { \prime}}}(x , x{\prime}){u^{\alpha { \prime}}}{\partial _ \alpha}u + qv(x , x{\prime}){\partial _ \alpha}u + \phi _ \alpha ^{{\rm{tail}}}(x),$$\end{document } where the tail integral is defined by 392\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { \phi _ \alpha ^{{\rm{tail}}}(x ) = q\int\nolimits_{{\tau _ < } } ^u { { \nabla _ \alpha}v(x , z)d\tau + q } \int\nolimits_{- \infty}^{{\tau _ < } } { { \nabla _ \alpha}{g _ + } ( x , z)d\tau } } \\ { = q\int\nolimits_{- \infty}^{{u^ - } } { { \nabla _ \alpha}{g _ + } ( x , z)d\tau . } \quad\quad\quad\quad\;\;}\\ \end{array}$$\end{document } in the second form of the definition we integrate g+(x , z ) from = to almost = u , but we cut the integration short at = u = u 0 to avoid the singular behaviour of the retarded green s function at = 0 . this limiting procedure gives rise to the first form of the definition , with the advantage that the integral need not be broken down into contributions that refer to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } and its complement , respectively . we shall now expand (x ) in powers of r , and express the results in terms of the retarded coordinates ( u , r , ) introduced in section 3.3 . it will be convenient to decompose (x ) in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } that is obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{{\alpha { \prime}}}},e_a^{{\alpha { \prime}}})$\end{document } on the null geodesic that links x to x z(u ) ; this construction is detailed in section 3.3 . note that throughout this section we set ab = 0 , where ab is the rotation tensor defined by equation ( 138 ) : the tetrad vectors are taken to be fermi - walker transported on . the expansion relies on equation ( 166 ) for u , equation ( 168 ) for r , and we shall need 393\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$u(x , x{\prime } ) = 1 + { 1 \over { 12}}{r^2}({r_{00 } } + 2{r_{0a}}{\omega ^a } + { r_{ab}}{\omega ^a}{\omega ^b } ) + \mathcal{o}({r^3}),$$\end{document } which follows from equation ( 275 ) and the relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma ^{{\alpha { \prime } } } } = - r({u^{{\alpha { \prime } } } } + { \omega ^a}e_a^{{\alpha { \prime}}})$\end{document } first encountered in equation ( 144 ) ; recall that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{00}}(u ) = { r_{\alpha { \prime}\beta { \prime}}}{u^{\alpha { \prime}}}{u^{\beta { \prime}}},\quad \quad { r_{0a}}(u ) = { r_{\alpha { \prime}\beta { \prime}}}{u^{\alpha { \prime}}}e_a^{\beta { \prime}},\quad \quad { r_{ab}}(u ) = { r_{\alpha { \prime}\beta { \prime}}}e_a^{\alpha { \prime}}e_b^{\beta { \prime}}$$\end{document } are frame components of the ricci tensor evaluated at x. we shall also need the expansions 394\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{;\alpha}}(x , x{\prime } ) = { 1 \over 6}r{g^{\alpha { \prime}}}_\alpha ( { r_{\alpha { \prime}0 } } + { r_{\alpha { \prime}b}}{\omega ^b } ) + \mathcal{o}({r^2})$$\end{document } and 395\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{;\alpha { \prime}}}(x , x{\prime}){u^{\alpha { \prime } } } = - { 1 \over 6}r({r_{00 } } + { r_{0a}}{\omega ^a } ) + \mathcal{o}({r^2}),$$\end{document } which follow from equations ( 276 ) ; recall from equation ( 141 ) that the parallel propagator can be expressed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{{\alpha { \prime}}}}_\alpha = { u^{{\alpha { \prime}}}}e_\alpha ^0 + e_a^{{\alpha { \prime}}}e_\alpha ^a$\end{document}. and finally , we shall need 396\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$v(x , x{\prime } ) = { 1 \over { 12}}(1 - 6\xi)r + \mathcal{o}(r),$$\end{document } a relation that was first established in equation ( 278 ) ; here r r(u ) is the ricci scalar evaluated at x. collecting all these results gives 397\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { \phi _ 0}(u , r,{\omega ^a } ) = { \phi _ \alpha}(x)e_0^\alpha ( x ) } \quad \quad \quad \quad \quad\quad \quad \quad \quad \quad\quad \quad \quad \quad \quad\quad \quad \quad \quad \quad\;\;\\ { = { q \over r}{a_a}{\omega ^a } + { 1 \over 2}q{r_{a0b0}}{\omega ^a}{\omega ^b } + { 1 \over { 12}}(1 - 6\xi)qr + \phi _ 0^{{\rm{tail } } } + \mathcal{o}(r ) } , \\ \end{array}$$\end{document } 398\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{\phi _ a}(u , r,{\omega ^a } ) \equiv { \phi _ \alpha}(x)e_a^\alpha ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{= - { q \over { { r^2}}}{\omega _ a } - { q \over r}{a_b}{\omega ^b}{\omega _ a } - { 1 \over 3}q{r_{b0c0}}{\omega ^b}{\omega ^c}{\omega _ a } - { 1 \over 6}q({r_{a0b0}}{\omega ^b } - { r_{ab0c}}{\omega ^b}{\omega ^c})\quad}\\{+ { 1 \over { 12}}q[{r_{00 } } - { r_{bc}}{\omega ^b}{\omega ^c } - ( 1 - 6\xi)r]{\omega _ a } + { 1 \over 6}q({r_{a0 } } + { r_{ab}}{\omega ^b } ) + \phi _ a^{{\rm{tail } } } + { \mathcal o}(r),\;}\\\end{array}$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_a } = { a_{{\alpha { \prime}}}}e_a^{{\alpha { \prime}}}$\end{document } are the frame components of the acceleration vector , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{a0b0}}(u ) = { r_{\alpha { \prime}\gamma { \prime}\beta { \prime}\delta { \prime}}}e_a^{\alpha { \prime}}{u^{\gamma { \prime}}}e_b^{\beta { \prime}}{u^{\delta { \prime}}},$$\end{document } are frame components of the riemann tensor evaluated at x , and 399\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi _ 0^{{\rm{tail}}}(u ) = \phi _ { \alpha { \prime}}^{{\rm{tail}}}(x{\prime}){u^{\alpha { \prime}}},\quad \quad \phi _ a^{{\rm{tail}}}(u ) = \phi _ { \alpha { \prime}}^{{\rm{tail}}}(x{\prime})e_a^{\alpha { \prime}}$$\end{document } are the frame components of the tail integral evaluated at x. equations ( 397 ) and ( 398 ) show clearly that (x ) is singular on the world line : the field diverges as r when r 0 , and many of the terms that stay bounded in the limit depend on and therefore possess a directional ambiguity at r = 0 . the gradient of the scalar potential can also be expressed in the fermi normal coordinates of section 3.2 . to effect this translation we make \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document } the new reference point on the world line . we resume here the notation of section 3.4 and assign indices \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar \alpha , \ , \bar \beta$\end{document } , to tensors at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document}. the fermi normal coordinates are denoted ( t , s , ) , and we let \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } be the tetrad at x that is obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{\bar \alpha}},e_a^{\bar \alpha})$\end{document } on the spacelike geodesic that links x to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document}. our first task is to decompose (x ) in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } , thereby defining \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\bar \phi}_0 } \equiv { \phi _ \alpha}\bar e_0^\alpha$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\bar \phi}_a } \equiv { \phi _ \alpha}\bar e_a^\alpha$\end{document } for this purpose we use equations ( 224 , 225 ) and ( 397 , 398 ) to obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{{\bar \phi}_0 } = [ 1 + { \mathcal o}({r^2})]{\phi _ 0 } + \left [ { r(1 - { a_b}{\omega ^b}){a^a } + { 1 \over 2}{r^2}{{\dot a}^a } + { 1 \over 2}{r^2}r_{\;\;0b0}^a{\omega ^b } + { \mathcal o}({r^3 } ) } \right]{\phi _ a}}\\{= - { 1 \over 2}q{{\dot a}_a}{\omega ^a } + { 1 \over { 12}}(1 - 6\xi)qr + \bar \phi _ 0^{{\rm{tail } } } + { \mathcal o}(r)\quad \quad \quad \quad \quad \quad \quad \quad \;}\\\end{array}$$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{{\bar \phi}_a } = \left [ { { \delta ^b}_a + { 1 \over 2}{r^2}{a^b}{a_a } - { 1 \over 2}{r^2}r_{\;\;a0c}^b{\omega ^c } + { \mathcal o}({r^3 } ) } \right]{\phi _ b } + [ r{a_a } + { \mathcal o}({r^2})]{\phi _ 0}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{= - { q \over { { r^2}}}{\omega _ a } - { q \over r}{a_b}{\omega ^b}{\omega _ a } + { 1 \over 2}q{a_b}{\omega ^b}{a_a } - { 1 \over 3}q{r_{b0c0}}{\omega ^b}{\omega ^c}{\omega _ a } - { 1 \over 6}q{r_{a0b0}}{\omega ^b } - { 1 \over 3}q{r_{ab0c}}{\omega ^a}{\omega ^c}}\\{+ { 1 \over { 12}}q[{r_{00 } } - { r_{bc}}{\omega ^b}{\omega ^c } - ( 1 - 6\xi)r]{\omega _ a } + { 1 \over 6}q({r_{a0 } } + { r_{ab}}{\omega ^b } ) + \bar \phi _ a^{{\rm{tail } } } + { \mathcal o}(r),\quad \quad \quad \quad \quad}\\\end{array}$$\end{document } where all frame components are still evaluated at x , except for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar \phi _ 0^{{\rm{tail}}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar \phi _ a^{{\rm{tail}}}$\end{document } which are evaluated at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document}. we must still translate these results into the fermi normal coordinates ( t , s , ) . for this we involve equations ( 221 , 222 , 223 ) , from which we deduce , for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{1 \over { { r^2}}}{\omega _ a } = { 1 \over { { s^2}}}{\omega _ a } + { 1 \over { 2s}}{a_a } - { 3 \over { 2s}}{a_b}{\omega ^b}{\omega _ a } - { 3 \over 4}{a_b}{\omega ^b}{a_a } + { { 15 } \over 8}{{({a_b}{\omega ^b})}^2}{\omega _ a } + { 3 \over 8}{{\dot a}_0}{\omega _ a } - { 1 \over 3}{{\dot a}_a}}\\{+ { { \dot a}_b}{\omega ^b}{\omega _ a } + { 1 \over 6}{r_{a0b0}}{\omega ^b } - { 1 \over 2}{r_{b0c0}}{\omega ^b}{\omega ^c}{\omega _ a } - { 1 \over 3}{r_{ab0c}}{\omega ^b}{\omega ^c } + { \mathcal o}(s)\quad}\\\end{array}$$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${1 \over r}{a_b}{\omega ^b}{\omega _ a } = { 1 \over s}{a_b}{\omega ^b}{\omega _ a } + { 1 \over 2}{a_b}{\omega ^b}{a_a } - { 3 \over 2}{({a_b}{\omega ^b})^2}{\omega _ a } - { 1 \over 2}{\dot a_0}{\omega _ a } - { \dot a_b}{\omega ^b}{\omega _ a } + \mathcal{o}(s),$$\end{document } in which all frame components ( on the right - hand side of these relations ) are now evaluated at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } ; to obtain the second relation we expressed aa(u ) as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_a}(t ) - { \mathcal s}{{\dot a}_a}(t ) + { \mathcal o}({{\mathcal s}^2})$\end{document } , since according to equation ( 221 ) , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$u = t - s + { \mathcal o}({{\mathcal s}^2})$\end{document}. collecting these results yields 400\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{{\bar \phi}_0}(t , s,{\omega ^a } ) \equiv { \phi _ \alpha}(x)e_0^{- \alpha}(x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{= - { 1 \over 2}q{{\dot a}_a}{\omega ^a } + { 1 \over { 12}}(1 - 6\xi)qr + \bar \phi _ 0^{{\rm{tail } } } + { \mathcal o}(s),}\\\end{array}$$\end{document } 401\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{{\bar \phi}_a}(t , s,{\omega ^a } ) \equiv { \phi _ \alpha}(x)\bar e_a^\alpha ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{\ , = - { q \over { { s^2}}}{\omega _ a } - { q \over { 2s}}({a_a } - { a_b}{\omega ^b}{\omega _ a } ) + { 3 \over 4}q{a_b}{\omega ^b}{a_a } - { 3 \over 8}q{{({a_b}{\omega ^b})}^2}{\omega _ a } + { 1 \over 8}q{{\dot a}_0}{\omega _ a } + { 1 \over 3}q{{\dot a}_a}}\\{- { 1 \over 3}q{r_{a0b0}}{\omega ^b } + { 1 \over 6}q{r_{b0c0}}{\omega ^b}{\omega ^c}{\omega _ a } + { 1 \over { 12}}q[{r_{00 } } - { r_{bc}}{\omega ^b}{\omega ^c } - ( 1 - 6\xi)r]\,{\omega _ a}\quad}\\{\ , + { 1 \over 6}q({r_{a0 } } + { r_{ab}}{\omega ^b } ) + \bar \phi _ a^{{\rm{tail } } } + { \mathcal o}(s).\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } in these expressions , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_a}(t ) = { a_{\bar \alpha}}e_a^{\bar \alpha}$\end{document } are the frame components of the acceleration vector evaluated at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x,\,{{\dot a}_0}(t ) = { { \dot a}_{\bar \alpha}}{u^{\bar \alpha}}$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\dot a}_a}(t ) = { { \dot a}_{\bar \alpha}}e_a^{\bar \alpha}$\end{document } are frame components of its covariant derivative , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{a0b0}}(t ) = { r_{\bar \alpha \bar \gamma \bar \beta \bar \delta}}e_a^{\bar \alpha}{u^{\bar \gamma}}e_b^{\bar \beta}{u^{\bar \delta}}$\end{document } are frame components of the riemann tensor evaluated at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{00}}(t ) = { r_{\bar \alpha \bar \beta}}{u^{\bar \alpha}}{u^{\bar \beta}},\quad { r_{0a}}(t ) = { r_{\bar \alpha \bar \beta}}{u^{\bar \alpha}}e_a^{\bar \beta},\quad { r_{ab}}(t ) = { r_{\bar \alpha \bar \beta}}e_a^{\bar \alpha}e_b^{\bar \beta}$$\end{document } are frame components of the ricci tensor , and r(t ) is the ricci scalar evaluated at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document}. finally , we have that 402\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\bar \phi _ 0^{{\rm{tail}}}(t ) = \bar \phi _ { \bar \alpha}^{{\rm{tail}}}(\bar x){u^{\bar \alpha}},\quad \bar \phi _ a^{{\rm{tail}}}(t ) = \phi _ { \bar \alpha}^{{\rm{tail}}}(\bar x)e_a^{\bar \alpha}$$\end{document } are the frame components of the tail integral see equation ( 392 ) evaluated at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\,\bar x \equiv z(t)$\end{document}. we shall now compute the averages of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\bar \phi}_0}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\bar \phi}_a}$\end{document } over s(t , s ) , a two - surface of constant t and s ; these will represent the mean value of the field at a fixed proper distance away from the world line , as measured in a reference frame that is momentarily comoving with the particle . the two - surface is charted by angles ( a = 1 , 2 ) and it is described , in the fermi normal coordinates , by the parametric relations \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\hat x}^a } = { \mathcal s}{\omega ^a}({\theta ^a})$\end{document } ; canonical choice of parameterization is = ( sin cos sin sin , cos ) . introducing the transformation matrices \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\omega _ \equiv \partial { \omega ^a}/\partial { \theta ^a}$\end{document } , we find from equation ( 127 ) that the induced metric on s(t , s ) is given by 403\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d{s^2 } = { s^2}\left [ { { \omega _ { ab } } - { 1 \over 3}{s^2}{r_{ab } } + \mathcal{o}({s^3 } ) } \right]\,\,d{\theta ^a}d{\theta ^b},$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\omega _ { ab } } \equiv { \delta _ { ab}}\omega _ a^a\omega _ b^b$\end{document } is the metric of the unit two - sphere , and where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{ab } } \equiv { r_{acbd}}\omega _ a^a{\omega ^c}\omega _ b^b{\omega ^d}$\end{document } depends on t and the angles . from this we infer that the element of surface area is given by 404\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d\mathcal{a } = { s^2}\left [ { 1 - { 1 \over 6}{s^2}{r^c}_{acb}(t){\omega ^a}{\omega ^b } + \mathcal{o}({s^3 } ) } \right]\,\,d\omega,$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d\omega = \sqrt { \det [ { \omega _ { ab } } ] } { d^2}\theta$\end{document } is an element of solid angle in the canonical parameterization , d = sin dd. integration of equation ( 404 ) produces the total surface area of s(t , s ) , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal a } = 4\pi { { \mathcal s}^2}[1 - { 1 \over { 18}}{{\mathcal s}^2}{r^{ab}}_{ab } + { \mathcal o}({{\mathcal s}^3})]$\end{document}. the averaged fields are defined by 405\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left\langle { { { \bar \phi}_0 } } \right\rangle \,(t , s ) = { 1 \over \mathcal{a}}\oint\nolimits_{s(t , s ) } { { { \bar \phi}_0 } } ( t , s,{\theta ^a})\,d\mathcal{a},\quad \left\langle { { { \bar \phi}_a } } \right\rangle \,(t , s ) = { 1 \over \mathcal{a}}\oint\nolimits_{s(t , s ) } { { { \bar \phi}_a } } ( t , s,{\theta ^a})\,d\mathcal{a},$$\end{document } where the quantities to be integrated are scalar functions of the fermi normal coordinates . the results 406\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${1 \over { 4\pi}}\oint { { \omega ^a}d\omega } = 0,\quad { 1 \over { 4\pi}}\oint { { \omega ^a}{\omega ^b}d\omega } = { 1 \over 3}{\delta ^{ab}},\quad { 1 \over { 4\pi}}\oint { { \omega ^a}{\omega ^b}{\omega ^c}d\omega } = 0,$$\end{document } are easy to establish , and we obtain 407\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left\langle { { { \bar \phi}_0 } } \right\rangle = { 1 \over { 12}}(1 - 6\xi)qr + \bar \phi _ 0^{{\rm{tail } } } + \mathcal{o}(s),$$\end{document } 408\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left\langle { { { \bar \phi}_a } } \right\rangle = - { q \over { 3s}}{a_a } + { 1 \over 3}q{\dot a_a } + { 1 \over 6}q{r_{a0 } } + \bar \phi _ a^{{\rm{tail } } } + \mathcal{o}(s).$$\end{document } the averaged field is still singular on the world line . regardless , we shall take the formal limit s 0 of the expressions displayed in equations ( 407 ) and ( 408 ) . in the limit the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } reduces to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{\bar \alpha}},\bar e_a^{\bar \alpha})$\end{document } , and we can reconstruct the field at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } by invoking the completeness relations \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\delta ^{\bar \alpha}}_{\bar \beta } = - { u^{\bar \alpha}}{u_{\bar \beta } } + e_a^{\bar \alpha}e_\beta ^a$\end{document}. we thus obtain 409\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left\langle { { \phi _ { \bar \alpha } } } \right\rangle = \lim\limits_{s \rightarrow 0 } \left({- { q \over { 3s } } } \right)\,{a_{\bar \alpha } } - { 1 \over { 12}}(1 - 6\xi)qr{u_{\bar \alpha } } + q({g_{\bar \alpha \bar \beta } } + { u_{\bar \alpha}}{u_{\bar \beta}})\,\left({{1 \over 3}{{\dot a}^{\bar \beta } } + { 1 \over 6}{r^{\bar \beta}}_{\bar \gamma}{u^{\bar \gamma } } } \right ) + \phi _ { \bar \alpha}^{{\rm{tail}}},$$\end{document } where the tail integral can be copied from equation ( 392 ) , 410\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi _ { \bar \alpha}^{{\rm{tail}}}(\bar x ) = q\int\nolimits_{- \infty}^{{t^ - } } { { \nabla _ { \bar \alpha}}{g _ + } ( \bar x , z)\,d\tau}.$$\end{document } the tensors appearing in equation ( 409 ) a refer to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document } , which now stands for an arbitrary point on the world ine . the singular potential 411\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\phi ^{\rm{s}}}(x ) = q\int\nolimits_\gamma { { g_{\rm{s}}}(x , z)\,d\tau}$$\end{document } is the ( unphysical ) solution to equations ( 385 ) and ( 386 ) that is obtained by adopting the singular green s function of equation ( 295 ) instead of the retarded green s function . as we shall see , the resulting singular field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\phi _ \alpha ^{\rm{s}}(x)$\end{document } reproduces the singular behaviour of the retarded solution ; the difference , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\phi _ \alpha ^{\rm{s}}(x)$\end{document } , is smooth on the world line . to evaluate the integral of equation ( 411 ) we assume once more that x is sufficiently close to that the world line traverses \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } ( refer back to figure 9 ) . as before we let < and > be the values of the proper - time parameter at which enters and leaves \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } , respectively . then equation ( 411 ) can be broken down into the three integrals , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\phi ^{\rm{s}}}(x ) = q\int\nolimits_{- \infty}^{{\tau _ < } } { { g_{\rm{s}}}(x , z)\,d\tau + q } \,\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { { g_{\rm{s}}}(x , z)\,d\tau + q } \,\int\nolimits_{{\tau _ > } } ^\infty { { g_{\rm{s}}}(x , z)\,d\tau}.$$\end{document } the first integration vanishes because x is then in the chronological future of z( ) , and gs(x , z ) = 0 by equation ( 286 ) . similarly , the third integration vanishes because x is then in the chronological past of z( ) . for the second integration , x is the normal convex neighbourhood of z( ) , the singular green s function can be expressed in the hadamard form of equation ( 297 ) , and we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { { g_{\rm{s}}}(x , z)\,d\tau = { 1 \over 2 } } \,\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { u(x , z){\delta _ + } ( \sigma)\,d\tau + { 1 \over 2}\,\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { u(x , z){\delta _ -}(\sigma)\,d\tau - { 1 \over 2}\,\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { v(x , z)\theta ( \sigma)\,d\tau}}}.$$\end{document } to evaluate these we re - introduce the retarded point x z(v ) be the advanced point associated with x ; we recall from section 3.4.4 that these points are related by (x , x ) = 0 and that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{{\rm{adv } } } } \equiv - { \sigma _ { { \alpha ^{{\prime\prime}}}}}{u^{{\alpha ^{{\prime\prime}}}}}$\end{document } is the advanced distance between x and the world line . to perform the first integration we change variables from to , noticing that increases as z( ) passes through x ; the integral evaluates to u(x , x)/r . we do the same for the second integration , but we notice now that decreases as z( ) passes through x ; the integral evaluates to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$u(x,{x^{{\prime\prime}}})/{r_{{\rm{adv}}}}$\end{document } the third integration is restricted to the interval u v by the step function , and we obtain our final expression for the singular potential of a point scalar charge : 412\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\phi ^{\rm{s}}}(x ) = { q \over { 2r}}u(x , x{\prime } ) + { q \over { 2{r_{{\rm{adv}}}}}}u(x , x{\prime\prime } ) - { 1 \over 2}q\int\nolimits_u^v { v(x , z)\,d\tau}.$$\end{document } we observe that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\phi ^{\rm{s}}}(x)$\end{document } depends on the state of motion of the scalar charge between the retarded time u and the advanced time v ; contrary to what was found in section 5.1.2 for the retarded potential , there is no dependence on the particle s remote past . we use the techniques of section 5.1.3 to differentiate the potential of equation ( 412 ) . we find 413\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{\phi _ \alpha}r - { q \over { 2{r_{{\rm{adv}}}}^2}}u(x , x\prime \prime){\partial _ \alpha}{r_{{\rm{adv } } } } + { q \over { 2r}}{u_{;\alpha}}(x , x\prime ) + { q \over { 2r}}{u_{;\alpha \prime}}(x , x\prime){u^{\alpha \prime}}{\partial _ \alpha}u\quad \quad \quad \quad}\\{+ { q \over { 2{r_{{\rm{adv}}}}}}{u_{;\alpha}}(x , x\prime \prime ) + { q \over { 2{r_{{\rm{adv}}}}}}{u_{;\alpha \prime \prime}}(x , x\prime \prime){u^{\alpha \prime \prime}}{\partial _ \alpha}v + { 1 \over 2}qv(x , x\prime){\partial _ \alpha}u - { 1 \over 2}qv(x , x\prime \prime){\partial _ \alpha}v}\\{- { 1 \over 2}q\,\int\nolimits_u^v { { \nabla _ \alpha}v(x , z)\,d\tau } , \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } and we would like to express this as an expansion in powers of r. for this we shall rely on results already established in section 5.1.3 , as well as additional expansions that will involve the advanced point x. those we develop now . we recall first that a relation between retarded and advanced times was worked out in equation ( 229 ) , that an expression for the advanced distance was displayed in equation ( 230 ) , and that equations ( 231 ) and ( 232 ) give expansions for v and radv , respectively . to derive an expansion for u(x , x ) we follow the general method of section 3.4.4 and define a function u( ) u(x , z( ) ) of the proper - time parameter on . we have that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$u(x , x{\prime\prime } ) \equiv u(v ) = u(u + \delta { \prime } ) = u(u ) + \dot u(u)\delta { \prime } + { 1 \over 2}\ddot u(u){\delta { \prime}^2 } + o({\delta { \prime}^3}),$$\end{document } where overdots indicate differentiation with respect to , and where v u. the leading term u(u ) u(x , x ) was worked out in equation ( 393 ) , and the derivatives of u( ) are given by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\dot u(u ) = { u_{;\alpha { \prime}}}{u^{\alpha { \prime } } } = - { 1 \over 6}r({r_{00 } } + { r_{0a}}{\omega ^a } ) + \mathcal{o}({r^2})$$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\ddot u(u ) = { u_{;\alpha { \prime}\beta { \prime}}}{u^{\alpha { \prime}}}{u^{\beta { \prime } } } + { u_{;\alpha { \prime}}}{a^{\alpha { \prime } } } = { 1 \over 6}{r_{00 } } + \mathcal{o}(r),$$\end{document } according to equations ( 395 ) and ( 276 ) . combining these results together with equation ( 229 ) for gives 414\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$u(x , x{\prime\prime } ) = 1 + { 1 \over { 12}}{r^2}({r_{00 } } - 2{r_{0a}}{\omega ^a } + { r_{ab}}{\omega ^a}{\omega ^b } ) + \mathcal{o}({r^3}),$$\end{document } which should be compared with equation ( 393 ) . it should be emphasized that in equation ( 414 ) and all equations below , the frame components of the ricci tensor are evaluated at the retarded point x the preceding computation gives us also an expansion for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{;{\alpha ^{{\prime\prime}}}}}{u^{{\alpha ^{{\prime\prime } } } } } \equiv \dot u(\upsilon ) = \dot u(u ) + \ddot u(u){\delta { \prime } } + { \mathcal o}({\delta ^{{\prime}2}})$\end{document}. this becomes 415\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{;\alpha { \prime\prime}}}(x , x{\prime\prime}){u^{\alpha { \prime\prime } } } = { 1 \over 6}r({r_{00 } } - { r_{0a}}{\omega ^a } ) + \mathcal{o}({r^2}),$$\end{document } which should be compared with equation ( 395 ) . u;(x , z( ) ) and express u;(x , x ) as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_\alpha}(\upsilon ) = { u_\alpha}(u ) + { { \dot u}_\alpha}(u){\delta { \prime } } + { \mathcal o}({\delta ^{{\prime}2}})$\end{document } the leading term u(u ) u;(x , x ) was computed in equation ( 394 ) , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\dot u_\alpha}(u ) = { u_{;\alpha \beta { \prime}}}{u^{\beta { \prime } } } = - { 1 \over 6}{g^{\alpha { \prime}}}_\alpha { r_{\alpha { \prime}0 } } + \mathcal{o}(r)$$\end{document } follows from equation ( 276 ) . combining these results together with equation ( 229 ) for gives 416\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{;\alpha}}(x , x{\prime\prime } ) = - { 1 \over 6}r{g^{\alpha { \prime}}}_\alpha ( { r_{\alpha { \prime}0 } } - { r_{\alpha { \prime}b}}{\omega ^b } ) + \mathcal{o}({r^2}),$$\end{document } and this should be compared with equation ( 394 ) . the last expansion we shall need is 417\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$v(x , x{\prime\prime } ) = { 1 \over { 12}}(1 - 6\xi)\,r + \mathcal{o}(r),$$\end{document } which follows at once from equation ( 396 ) and the fact that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$v(x,{x^{{\prime\prime } } } ) - v(x,{x{\prime } } ) = { \mathcal o}(r)$\end{document } ; the ricci scalar is evaluated at the retarded point x. it is now a straightforward ( but tedious ) matter to substitute these expansions ( all of them ! ) into equation ( 413 ) and obtain the projections of the singular field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\phi _ \alpha ^{\rm{s}}(x)$\end{document } in the same tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } that was employed in section 5.1.3 . this gives 418\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{\phi _ 0^{\rm{s}}(u , r,{\omega ^a } ) \equiv \phi _ \alpha ^{\rm{s}}(x)e_0^\alpha ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\{= { q \over r}{a_a}{\omega ^a } + { 1 \over 2}q{r_{a0b0}}{\omega ^a}{\omega ^b } + { \mathcal o}(r ) , } \\\end{array}$$\end{document } 419\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{\phi _ a^{\rm{s}}(u , r,{\omega ^a } ) \equiv \phi _ \alpha ^{\rm{s}}(x)e_a^\alpha ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \;\ ; } \\{= - { q \over { { r^2}}}{\omega _ a } - { q \over r}{a_b}{\omega ^b}{\omega _ a } - { 1 \over 3}q{{\dot a}_a } - { 1 \over 3}q{r_{b0c0}}{\omega ^b}{\omega ^c}{\omega _ a } - { 1 \over 6}q({r_{a0b0}}{\omega ^b } - { r_{ab0c}}{\omega ^b}{\omega ^c } ) } \\{+ { 1 \over { 12}}q\,[{r_{00 } } - { r_{bc}}{\omega ^b}{\omega ^c } - ( 1 - 6\xi)r]\,\,{\omega _ a } + { 1 \over 6}q{r_{ab}}{\omega ^b},\quad \quad \quad \quad \quad \quad \quad \quad \quad } \\\end{array}$$\end{document } in which all frame components are evaluated at the retarded point x comparison of these expressions with equations ( 397 ) and ( 398 ) reveals that the retarded and singular fields share the same singularity structure . the difference between the retarded field of equations ( 397 , 398 ) and the singular field of equations ( 418 , 419 ) defines the radiative field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\phi _ \alpha ^{\rm{r}}(x)$\end{document}. its tetrad components are 420\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi _ 0^{\rm{r } } = { 1 \over { 12}}(1 - 6\xi)qr + \phi _ 0^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } 421\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi _ a^{\rm{r } } = { 1 \over 3}q{\dot a_a } + { 1 \over 6}q{r_{a0 } } + \phi _ a^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } and we see that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\phi _ there is therefore no obstacle in evaluating the radiative field directly at x = x , where the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } becomes \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{{\alpha { \prime}}}},e_a^{{\alpha { \prime}}})$\end{document}. reconstructing the field at x from its frame components , we obtain 422\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi _ { \alpha { \prime}}^{\rm{r}}(x{\prime } ) = - { 1 \over { 12}}(1 - 6\xi)qr{u_{\alpha { \prime } } } + q({g_{\alpha { \prime}\beta { \prime } } } + { u_{\alpha { \prime}\beta { \prime}}})\,\left({{1 \over 3}{{\dot a}^{\beta { \prime } } } + { 1 \over 6}{r^{\beta { \prime}}}_{\gamma { \prime}}{u^{\gamma { \prime } } } } \right ) + \phi _ { \alpha { \prime}}^{{\rm{tail}}},$$\end{document } where the tail term can be copied from equation ( 392 ) , 423\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\phi _ { \alpha { \prime}}^{{\rm{tail}}}(x{\prime } ) = q\int\nolimits_{- \infty}^{{u^ - } } { { \nabla _ { \alpha { \prime}}}{g _ + } ( x{\prime},z)\,d\tau}.$$\end{document } the tensors appearing in equation ( 422 ) all refer to the retarded point x z(u ) , which now stands for an arbitrary point on the world line . the retarded field (x ) of a point scalar charge is singular on the world line , and this behaviour makes it difficult to understand how the field is supposed to act on the particle and affect its motion . the field s singularity structure was analyzed in sections 5.1.3 and 5.1.4 , and in section 5.1.5 it was shown to originate from the singular field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\phi _ \alpha ^{\rm{s}}(x)$\end{document } ; the radiative field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\phi _ \alpha ^{\rm{r}}(x ) = { \phi _ \alpha}(x ) - \phi _ \alpha ^{\rm{s}}(x)$\end{document } was then shown to be smooth on the world line . to make sense of the retarded field s action on the particle we temporarily model the scalar charge not as a point particle , but as a small hollow shell that appears spherical when observed in a reference frame that is momentarily comoving with the particle ; the shell s radius is s0 in fermi normal coordinates , and it is independent of the angles contained in the unit vector . the net force acting at proper time on this hollow shell is the average of q( , s0 , ) over the surface of the shell . this was worked out at the end of section 5.1.4 , and ignoring terms that disappear in the limit s0 0 , we obtain 424\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$q\left\langle { { \phi _ \mu } } \right\rangle = - ( \delta m){a_\mu } - { 1 \over { 12}}(1 - 6\xi){q^2}r{u_\mu } + { q^2}({g_{\mu \nu } } + { u_\mu}{u_\nu})\,\left({{1 \over 3}{{\dot a}^\nu } + { 1 \over 6}{r^\nu}_\lambda { u^\lambda } } \right ) + q\phi _ \mu ^{{\rm{tail}}},$$\end{document } where 425\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta m \equiv \lim\limits_{{s_0 } \rightarrow 0 } { { { q^2 } } \over { 3{s_0}}}$$\end{document } is for ally a divergent quantity and 426\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$q\phi _ \mu ^{{\rm{tail } } } = { q^2}\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla _ \mu}{g _ + } ( z(\tau),z(\tau { \prime } ) ) } \,d\tau { \prime}$$\end{document } is the tail part of the force ; all tensors in equation ( 424 ) are evaluated at an arbitrary point z( ) on the world line . substituting equations ( 424 ) and ( 426 ) into equation ( 387 ) gives rise to the equations of motion 427\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(m + \delta m){a^\mu } = { q^2}({\delta ^\mu}_\nu + { u^\mu}{u_\nu})\,\left [ { { 1 \over 3}{{\dot a}^\nu } + { 1 \over 6}{r^\nu}_\lambda { u^\lambda } + \int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla ^\nu}{g _ + } ( z(\tau),z(\tau { \prime}))\,\,d\tau { \prime } } } \right]$$\end{document } for the scalar charge , with m m0 q(z ) denoting the ( also formally divergent ) dynamical mass of the particle . we see that m and m combine in equation ( 427 ) to form the particle s observed mass mobs , which is taken to be finite and to give a true measure of the particle s inertia . all diverging quantities have thus disappeared into the process of mass renormalization . substituting equations ( 424 ) and ( 426 ) into equation ( 388 ) , in which we replace m by mobs = m + m , returns an expression for the rate of change of the observed mass , 428\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{d{m_{{\rm{obs } } } } } \over { d\tau } } = - { 1 \over { 12}}(1 - 6\xi){q^2}r - { q^2}{u^\mu}\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla _ \mu}{g _ + } ( z(\tau ) } , z(\tau { \prime}))\,\,d\tau { \prime}.$$\end{document } that the observed mass is not conserved is a remarkable property of the dynamics of a scalar charge in a curved spacetime . physically , this corresponds to the fact that in a spacetime with a time - dependent metric , a scalar charge radiates monopole waves and the radiated energy comes at the expense of the particle s inertial mass . apart from the term proportional to m , the averaged field of equation ( 424 ) has exactly the same form as the radiative field of equation ( 422 ) , which we re - express as 429\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$q\phi _ \mu ^{\rm{r } } = - { 1 \over { 12}}(1 - 6\xi){q^2}r{u_\mu } + { q^2}({g_{\mu \nu } } + { u_\mu}{u_\nu})\,\left({{1 \over 3}{{\dot a}^\nu } + { 1 \over 6}{r^\nu}_\lambda { u^\lambda } } \right ) + q\phi _ \mu ^{{\rm{tail}}}.$$\end{document } the force acting on the point particle can therefore be thought of as originating from the ( smooth ) radiative field , while the singular field simply contributes to the particle s inertia . after mass renormalization , equations ( 427 ) and ( 428 ) are equivalent to the statements 430\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$m{a^\mu } = q\,({g^{\mu \nu } } + { u^\mu}{u^\nu})\,\phi _ \nu ^{\rm{r}}(z),\quad { { dm } \over { d\tau } } = - q{u^\mu}\phi _ \mu ^{\rm{r}}(z),$$\end{document } where we have dropped the superfluous label obs on the particle s observed mass . another argument in support of the claim that the motion of the particle should be affected by the radiative field the equations of motion displayed in equations ( 427 ) and ( 428 ) are third - order differential equations for the functions z( ) . it is well known that such a system of equations admits many unphysical solutions , such as runaway situations in which the particle s acceleration increases exponentially with , even in the absence of any external force [ 25 , 30 , 47 ] . and indeed , our equations of motion do not yet incorporate an external force which presumably is mostly responsible for the particle s acceleration . both defects can be cured in one stroke . we shall take the point of view , the only admissible one in a classical treatment , that a point particle is merely an idealization for an extended object whose internal structure the details of its charge distribution can be considered to be irrelevant . this view automatically implies that our equations are meant to provide only an approximate description of the object s motion . it can then be shown [ 47 , 26 ] that within the context of this approximation , it is consistent to replace , on the right - hand side of the equations of motion , any occurrence of the acceleration vector by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{{\rm{ext}}}^\mu / m$\end{document } , where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{{\rm{ext}}}^\mu$\end{document } is the external force acting on the particle . because \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{{\rm{ext}}}^\mu$\end{document } is a prescribed quantity , differentiation of the external force does not produce higher derivatives of the functions z( ) , and the equations of motion are properly of second order . we shall therefore write , in the final analysis , the equations of motion in the form 431\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$m{{d{u^\mu } } \over { d\tau } } = f_{{\rm{ext}}}^\mu + { q^2}({\delta ^\mu}_\nu + { u^\mu}{u_\nu})\,\left [ { { 1 \over { 3m}}{{df_{{\rm{ext}}}^\nu } \over { d\tau } } + { 1 \over 6}{r^\nu}_\lambda { u^\lambda } + \int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla ^\nu}{g _ + } ( z(\tau),z(\tau { \prime}))\,d\tau { \prime } } } \right]$$\end{document } and 432\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{dm } \over { d\tau } } = - { 1 \over { 12}}(1 - 6\xi){q^2}r - { q^2}{u^\mu}\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla _ \mu}{g _ + } ( z(\tau),z(\tau { \prime}))\,d\tau { \prime}},$$\end{document } where m denotes the observed inertial mass of the scalar charge , and where all tensors are evaluated at z( ) . we recall that the tail integration must be cut short at = 0 to avoid the singular behaviour of the retarded green s function at coincidence ; this procedure was justified at the beginning of section 5.1.3 . equations ( 431 ) and ( 432 ) were first derived by theodore c. quinn in 2000 . in his paper quinn also establishes that the total work done by the scalar self - force matches the amount of energy radiated away by the particle . a point particle carries an electric charge e and moves on a world line described by relations z( ) , in which is an arbitrary parameter . the particle generates a vector potential a(x ) and an electromagnetic field f(x ) = a a. the dynamics of the entire system is governed by the action 433\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$s = { s_{{\rm{field } } } } + { s_{{\rm{particle } } } } + { s_{{\rm interaction}}},$$\end{document } where sfie1d is an action functional for a free electromagnetic field in a spacetime with metric g , spartic1e is the action of a free particle moving on a world line in this spacetime , and sinteraction is an interaction term that couples the field to the particle . the field action is given by 434\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_{{\rm{field } } } } = - { 1 \over { 16\pi}}\int { { f_{\alpha \beta}}{f^{\alpha \beta}}\sqrt { - g } \,{d^4}x},$$\end{document } where the integration is over all of spacetime . the particle action is 435\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_{{\rm{particle } } } } = - m\,\int\nolimits_\gamma { d\tau},$$\end{document } where m is the bare mass of the particle and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d\tau = \sqrt { - { g_{\mu \nu}}(z){{\dot z}^\mu}{{\dot z}^\nu } } d\lambda$\end{document } is the differential of proper time along the world line ; we use an overdot to indicate differentiation with respect to the parameter . finally , the interaction term is given by 436\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_{{\rm{interaction } } } } = e\,\int\nolimits_\gamma { { a_\mu}(z){{\dot z}^\mu}\,d\lambda = e\,\int { a_\alpha}(x)g_{\;\;\mu}^\alpha ( x , z){{\dot z}^\mu}{\delta _ 4}(x , z)\sqrt { - g } \,{d^4}xd\lambda .}$$\end{document } notice that both spartic1e and sinteraction are invariant under a reparameterization ( ) of the world line . demanding that the total action be stationary under a variation a(x ) of the vector potential yields maxwell s equations 437\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${f^{\alpha \beta}}_{;\beta } = 4\pi { j^\alpha}$$\end{document } with a current density j(x ) defined by 438\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${j^\alpha}(x ) = e\,\int\nolimits_\gamma { { g^\alpha}_\mu ( x , z){{\dot z}^\mu}{\delta _ 4}(x , z)\,d\lambda.}$$\end{document } these equations determine the electromagnetic field f , once the motion of the electric charge is specified . on the other hand , demanding that the total action be stationary under a variation z( ) of the world line yields the equations of motion for the electric charge , 439\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$m{{d{u^\mu } } \over { d\tau } } = e{f^\mu}_\nu ( z){u^\nu}.$$\end{document } we have adopted as the parameter on the world line , and introduced the four - velocity u( ) dz / d. the electromagnetic field f is invariant under a gauge transformation of the form a a + , in which (x ) is an arbitrary scalar function . this function can always be chosen so that the vector potential satisfies the lorenz gauge condition , 440\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\nabla _ \alpha}{a^\alpha } = 0.$$\end{document } under this condition the maxwell equations of equation ( 437 ) reduce to a wave equation for the vector potential , 441\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\square{a^\alpha } - { r^\alpha}_\beta { a^\beta } = - 4\pi { j^\alpha},$$\end{document } where = g is the wave operator and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r^\alpha}_\beta$\end{document } is the ricci tensor . having adopted as the parameter on the world line , we can re - express the current density of equation ( 438 ) as 442\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${j^\alpha}(x ) = e\,\int\nolimits_\gamma { { g^\alpha}_\mu ( x , z){u^\mu}{\delta _ 4}(x , z)\,d\tau,}$$\end{document } and we shall use equations ( 441 ) and ( 442 ) to determine the electromagnetic field of a point electric charge . the motion of the particle is in principle determined by equation ( 439 ) , but because the vector potential obtained from equation ( 441 ) is singular on the world line , these equations have only formal validity . before we can make sense of them we will have to analyze the field s singularity structure near the world line . the calculations to be carried out parallel closely those presented in section 5.1 for the case of a scalar charge ; the details will therefore be kept to a minimum and the reader is referred to section 5.1 for additional information . the retarded solution to equation ( 441 ) is \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^\alpha}(x ) = \int g_{+ { \beta { \prime}}}^\alpha ( x,{x{\prime}}){j^{{\beta { \prime}}}}({x{\prime}})\sqrt { { g{\prime } } } { d^4}{x{\prime}}$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{+ \beta}^\alpha ( x,{x{\prime}})$\end{document } is the retarded green s function introduced in section 4.4 . after substitution of equation ( 442 ) we obtain 443\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^\alpha}(x ) = e\,\int\nolimits_\gamma { g_{+ \mu}^\alpha ( x , z){u^\mu}d\tau,}$$\end{document } in which z( ) gives the description of the world line and u( ) = dz / d. because the retarded green s function is defined globally in the entire spacetime , equation ( 443 ) applies to any field point x. we now specialize equation ( 443 ) to a point x close to the world line . we let \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } be the normal convex neighbourhood of this point , and we assume that the world line traverses \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } ( refer back to figure 9 ) . as in section 5.1.2 we let < and > be the values of the proper - time parameter at which enters and leaves \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } , respectively . then equation ( 443 ) can be expressed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^\alpha}(x ) = e\,\int\nolimits_{- \infty}^{{\tau _ < } } { g_{+ \mu}^\alpha ( x , z){u^\mu}d\tau + e\ , } \,\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { g_{+ \mu}^\alpha ( x , z){u^\mu}d\tau + e\ , } \int\nolimits_{{\tau _ > } } ^\infty { g_{+ \mu}^\alpha ( x , z){u^\mu}d\tau}.$$\end{document } the third integration vanishes because x is then in the past of z( ) , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{+ \mu}^\alpha ( x , z ) = 0$\end{document}. for the second integration , x is the normal convex neighbourhood of z( ) , and the retarded green s function can be expressed in the hadamard form produced in section 4.4.2 . this gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { g_{+ \mu}^\alpha ( x , z){u^\mu}d\tau = \int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { u_\mu ^\alpha ( x , z){u^\mu}{\delta _ + } ( \sigma)\,d\tau + \int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { v_\mu ^\alpha ( x , z){u^\mu}{\theta _ + } ( - \sigma)\,d\tau , } \ , } \,}$$\end{document } and to evaluate this we let x z(u ) be the retarded point associated with x ; these points are related by (x , x ) = 0 and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r \equiv { \sigma _ { { \alpha { \prime}}}}{u^{{\alpha { \prime}}}}$\end{document } is the retarded distance between x and the world line . to perform the first integration we change variables from to , noticing that increases as z( ) passes through x ; the integral evaluates to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^\alpha}_{{\beta { \prime}}}{u^{{\beta { \prime}}}}/r$\end{document}. the second integration is cut off at = u by the step function , and we obtain our final expression for the vector potential of a point electric charge : 444\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^\alpha}(x ) = { e \over r}{u^\alpha}_{\beta { \prime}}(x , x{\prime}){u^{\beta { \prime } } } + e\,\int\nolimits_{{\tau _ < } } ^u { v_\mu ^\alpha ( x , z){u^\mu}d\tau + e\ , } \int\nolimits_{- \infty}^{{\tau _ > } } { g_{+ \mu}^\alpha ( x , z){u^\mu}d\tau.}$$\end{document } this expression applies to a point x sufficiently close to the world line that there exists a nonempty intersection between \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } and . when we differentiate the vector potential of equation ( 444 ) we must keep in mind that a variation in x induces a variation in x , because the new points x + x and x + x must also be linked by a null geodesic . taking this into account , we find that the gradient of the vector potential is given by 445\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{\nabla _ \beta}{a_\alpha}(x ) = \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{\quad \ , - { e \over { { r^2}}}{u_{\alpha \beta \prime}}{u^{\beta \prime}}{\partial _ \beta}r + { e \over r}{u_{\alpha \beta \prime ; \beta}}{u^{\beta \prime } } + { e \over r}\left({{u_{\alpha \beta \prime ; \gamma \prime}}{u^{\beta \prime}}{u^{\gamma \prime } } + { u_{\alpha \beta \prime}}{a^{\beta \prime } } } \right)\,{\partial _ \beta}u + e{v_{\alpha \beta \prime}}{u^{\beta \prime}}{\partial _ \beta}u + a_{\alpha \beta}^{{\rm{tail}}}(x),}\\\end{array}$$\end{document } where the tail integral is defined by 446\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{a_{\alpha \beta}^{{\rm{tail}}}(x ) = e\,\int\nolimits_{\tau < } ^u { { \nabla _ \beta}{v_{\alpha \mu}}(x , z ) } { u^\mu}\,d\tau + e\,\int\nolimits_{- \infty}^{{\tau _ < } } { { \nabla _ \beta}{g_{+ \alpha \mu}}(x , z){u^\mu}\,d\tau}}\\{= e\,\int\nolimits_{- \infty}^{{u^ - } } { { \nabla _ \beta}{g_{+ \alpha \mu}}(x , z ) } { u^\mu}\,d\tau .\quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } the second form of the definition , in which we integrate the gradient of the retarded green s function from = to = u u 0 to avoid the singular behaviour of the retarded green s function at = 0 , is equivalent to the first form . we shall now expand f = a a in powers of r , and express the result in terms of the retarded coordinates ( u , r , ) introduced in section 3.3 . it will be convenient to decompose the electromagnetic field in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } that is obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{{\alpha \prime}}},e_a^{{\alpha \prime}})$\end{document } on the null geodesic that links x to x z(u ) ; this construction is detailed in section 3.3 . note that throughout this section we set ab = 0 , where ab is the rotation tensor defined by equation ( 138 ) : the tetrad vectors \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_a^{{\alpha \prime}}$\end{document } are taken to be fermi - walker transported on . we recall from equation ( 141 ) that the parallel propagator can be expressed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{{\alpha \prime}}}_\alpha = { u^{{\alpha \prime}}}e_\alpha ^0 + e_a^{{\alpha \prime}}e_\alpha ^a$\end{document}. the expansion relies on equation ( 166 ) for u , equation ( 168 ) for r , and we shall need 447\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \prime}}}{u^{\beta { \prime } } } = { g^{\alpha { \prime}}}_\alpha \left [ { { u_{\alpha { \prime } } } + { 1 \over { 12}}{r^2}({r_{00 } } + 2{r_{0a}}{\omega ^a } + { r_{ab}}{\omega ^a}{\omega ^b})\,{u_{\alpha { \prime } } } + \mathcal{o}({r^3 } ) } \right],$$\end{document } which follows from equation ( 323 ) and the relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma ^{{\alpha \prime } } } = - r({u^{{\alpha \prime } } } + { \omega ^\alpha}e_a^{{\alpha \prime}})$\end{document } first encountered in equation ( 144 ) . we shall also need the expansions 448\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \prime};\beta}}{u^{\beta { \prime } } } = - { 1 \over 2}r{g^{\alpha { \prime}}}_\alpha { g^{\beta { \prime}}}_\beta \left [ { { r_{\alpha { \prime}0\beta { \prime}0 } } + { r_{\alpha { \prime}0\beta { \prime}c}}{\omega ^c } - { 1 \over 3}({r_{\beta { \prime}0 } } + { r_{\beta { \prime}c}}{\omega ^c}){u_{\alpha { \prime } } } + \mathcal{o}(r ) } \right]$$\end{document } and 449\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \prime};\gamma { \prime}}}{u^{\beta { \prime}}}{u^{\gamma { \prime } } } + { u_{\alpha \beta { \prime}}}{a^{\beta { \prime } } } = { g^{\alpha { \prime}}}_\alpha \left [ { { a_{\alpha { \prime } } } + { 1 \over 2}r{r_{\alpha { \prime}0b0}}{\omega ^b } - { 1 \over 6}r\,({r_{00 } } + { r_{0b}}{\omega ^b})\,{u_{\alpha { \prime } } } + \mathrm{o}({r^2 } ) } \right]$$\end{document } that follow from equations ( 323 , 324 , 325 ) . and finally , we shall need 450\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${v_{\alpha \beta { \prime}}}{u^{\beta { \prime } } } = - { 1 \over 2}{g^{\alpha { \prime}}}_\alpha \left [ { { r_{\alpha { \prime}0 } } - { 1 \over 6}r{u_{\alpha { \prime } } } + \mathcal{o}(r ) } \right],$$\end{document } a relation that was first established in equation ( 327 ) . collecting all these results gives 451\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{f_{a0}}(u , r,{\omega ^a } ) \equiv { f_{\alpha \beta}}(x)e_a^\alpha ( x)e_0^\beta ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{= { e \over { { r^2}}}{\omega _ a } - { e \over r}({a_a } - { a_b}{\omega ^b}{\omega _ a } ) + { 1 \over 3}e{r_{b0c0}}{\omega ^b}{\omega ^c}{\omega _ a } - { 1 \over 6}e(5{r_{a0b0}}{\omega ^b } + { r_{ab0c}}{\omega ^b}{\omega ^c})}\\{+ { 1 \over { 12}}e(5{r_{00 } } + { r_{bc}}{\omega ^b}{\omega ^c } + r){\omega _ a } + { 1 \over 3}e{r_{a0 } } - { 1 \over 6}e{r_{ab}}{\omega ^b } + f_{a0}^{{\rm{tail } } } + { \mathcal o}(r),\quad \quad \quad}\\\end{array}$$\end{document } 452\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{f_{ab}}(u , r,{\omega ^a } ) \equiv { f_{\alpha \beta}}(x)e_a^\alpha ( x)e_b^\beta ( x)\;\;\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{= { e \over r}({a_a}{\omega _ b } - { \omega _ a}{a_b } ) + { 1 \over 2}e({r_{a0bc } } - { r_{b0ac } } + { r_{a0c0}}{\omega _ b } - { \omega _ a}{r_{b0c0}}){\omega ^c}}\\{- { 1 \over 2}e({r_{a0}}{\omega _ b } - { \omega _ a}{r_{b0 } } ) + f_{ab}^{{\rm{tail } } } + { \mathcal o}(r),\quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } where 453\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f_{a0}^{{\rm{tail } } } = f_{\alpha { \prime}\beta { \prime}}^{{\rm{tail}}}(x{\prime})e_a^{\alpha { \prime}}{u^{\beta { \prime}}},\quad \quad f_{ab}^{{\rm{tail } } } = f_{\alpha { \prime}\beta { \prime}}^{{\rm{tail}}}(x{\prime})e_a^{\alpha { \prime}}e_b^{\beta { \prime}}$$\end{document } are the frame components of the tail integral ; this is obtained from equation ( 446 ) evaluated at x : 454\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f_{\alpha { \prime}\beta { \prime}}^{{\rm{tail}}}(x{\prime } ) = 2e\int\nolimits_{- \infty}^{{u^ - } } { { \nabla _ { [ \alpha { \prime}}}{g_{+ \beta { \prime}]\mu}}(x{\prime},z){u^u}d\tau}.$$\end{document } it should be emphasized that in equations ( 451 ) and ( 452 ) , all frame components are evaluated at the retarded point x z(u ) associated with x ; for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_a } \equiv { a_a}(u ) \equiv { a_{{\alpha \prime}}}e_a^{{\alpha \prime}}$\end{document}. it is clear from these equations that the electromagnetic field f(x ) is singular on the world line . we now wish to express the electromagnetic field in the fermi normal coordinates of section 3.2 ; as before those will be denoted ( t , s , ) . the translation will be carried out as in section 5.1.4 , and we will decompose the field in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } that is obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{\bar \alpha}},e_a^{\bar \alpha})$\end{document } on the spacelike geodesic that links x to the simultaneous point \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document}. our first task is to decompose f(x ) in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${f_{\alpha \beta}}(x)$\end{document } , thereby defining \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\bar f}_{a0 } } = { f_{\alpha \beta}}\bar e_a^\alpha \bar e_0^\beta$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\bar f}_{ab } } = { f_{\alpha \beta}}\bar e_a^\alpha \bar e_b^\beta$\end{document}. for this purpose we use equations ( 224 , 225 ) and ( 451 , 452 ) to obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{{\bar f}_{a0 } } = { e \over { { r^2}}}{\omega _ a } - { e \over r}({a_a } - { a_b}{\omega ^b}{\omega _ a } ) + { 1 \over 2}e{a_b}{\omega ^b}{a_a } + { 1 \over 2}e{{\dot a}_0}{\omega _ a } - { 5 \over 6}e{r_{a0b0}}{\omega ^b } + { 1 \over 3}e{r_{b0c0}}{\omega ^b}{\omega ^c}{\omega _ a}\quad \quad \quad}\\{+ { 1 \over 3}e{r_{ab0c}}{\omega ^b}{\omega ^c } + { 1 \over { 12}}e(5{r_{00 } } + { r_{bc}}{\omega ^b}{\omega ^c } + r){\omega _ a } + { 1 \over 3}e{r_{a0 } } - { 1 \over 6}e{r_{ab}}{\omega ^b } + \bar f_{a0}^{{\rm{tail } } } + { \mathcal o}(r)}\\\end{array}$$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\bar f_{ab } } = { 1 \over 2}e({\omega _ a}{\dot a_b } - { \dot a_a}{\omega _ b } ) + { 1 \over 2}e({r_{a0bc } } - { r_{b0ac}}){\omega ^c } - { 1 \over 2}e({r_{a0}}{\omega _ b } - { \omega _ a}{r_{b0 } } ) + \bar f_{ab}^{{\rm{tail } } } + { \mathcal o}(r),$$\end{document } where all frame components are still evaluated at x , except for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\bar f_{a0}^{{\rm{tail } } } = f_{\bar \alpha \bar \beta}^{{\rm{tail}}}(\bar x)e_a^{\bar \alpha}{u^{\bar \beta}},\quad \quad \bar f_{ab}^{{\rm{tail } } } \equiv f_{\bar \alpha \bar \beta}^{{\rm{tail}}}(\bar x)e_a^{\bar \alpha}e_b^{\bar \beta},$$\end{document } which are evaluated at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document}. we must still translate these results into the fermi normal coordinates ( t , s , ) . for this we involve equations ( 221 , 222 , 223 ) , and we recycle some computations that were first carried out in section 5.1.4 . after some algebra , we arrive at 455\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{{\bar f}_{a0}}(t , s,{\omega ^a } ) \equiv { f_{\alpha \beta}}(x)\bar e_a^\alpha ( x)\bar e_0^\beta ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{= { e \over { { s^2}}}{\omega _ a } - { e \over { 2s}}({a_a } + { a_b}{\omega ^b}{\omega _ a } ) + { 3 \over 4}e{a_b}{\omega ^b}{a_a } + { 3 \over 8}e{{({a_b}{\omega ^b})}^2}{\omega _ a } + { 3 \over 8}e{{\dot a}_0}{\omega _ a } + { 2 \over 3}e{{\dot a}_a}}\\{\quad - { 2 \over 3}e{r_{a0b0}}{\omega ^b } - { 1 \over 6}e{r_{b0c0}}{\omega ^b}{\omega ^c}{\omega _ a } + { 1 \over { 12}}e(5{r_{00 } } + { r_{bc}}{\omega ^b}{\omega ^c } + r){\omega _ a}\quad \quad \quad \quad}\\{+ { 1 \over 3}e{r_{a0 } } - { 1 \over 6}e{r_{ab}}{\omega ^b } + \bar f_{a0}^{{\rm{tail } } } + { \mathcal o}(s),\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } 456\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{{\bar f}_{ab}}(t , s,{\omega ^a } ) \equiv { f_{\alpha \beta}}(x)\bar e_a^\alpha ( x)\bar e_b^\beta ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\ { = { 1 \over 2}e({\omega _ a}{{\dot a}_b } - { { \dot a}_b}{\omega _ b } ) + { 1 \over 2}e({r_{a0bc } } - { r_{b0ac}}){\omega ^c } - { 1 \over 2}e({r_{a0}}{\omega _ b } - { \omega _ a}{r_{b0 } } ) + \bar f_{ab}^{{\rm{tail } } } + { \mathcal o}(s),}\\ \end{array}$$\end{document } where all frame components are now evaluated at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document } for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_a } \equiv { a_a}(t ) \equiv { a_{\bar \alpha}}e_a^{\bar \alpha}$\end{document}. our next task is to compute the averages of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\bar f}_{a0}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\bar f}_{ab}}$\end{document } over s(t , s ) , a two - surface of constant t and s. these are defined by 457\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\langle { \bar f_{a0}}\rangle ( t , s ) = { 1 \over \mathcal{a}}\oint\nolimits_{s(t , s ) } { { { \bar f}_{a0}}(t , s,{\omega ^a})d\mathcal{a},\quad \quad \langle { { \bar f}_{ab}}\rangle ( t , s ) = { 1 \over \mathcal{a}}\oint\nolimits_{s(t , s ) } { { { \bar f}_{ab}}(t , s,{\omega ^a})d\mathcal{a}}},$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d{\mathcal a}$\end{document } is the element of surface area on s(t , s ) , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal a } = \oint { d{\mathcal a}}$\end{document}. using the methods developed in section 5.1.4 , we find 458\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\langle { \bar f_{a0}}\rangle = - { { 2e } \over { 3s}}{a_a } + { 2 \over 3}e{\dot a_a } + { 1 \over 3}e{r_{a0 } } + \bar f_{a0}^{{\rm{tail } } } + \mathcal{o}(s),$$\end{document } 459\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\langle { \bar f_{ab}}\rangle = \bar f_{ab}^{{\rm{tail } } } + \mathcal{o}(s).$$\end{document } the averaged field is singular on the world line , but we nevertheless take the formal limit s 0 of the expressions displayed in equations ( 458 ) and ( 459 ) . in the limit the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } becomes \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{\bar \alpha}},e_a^{\bar \alpha})$\end{document } , and we can easily reconstruct the field at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } from its frame components . we thus obtain 460\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\langle { f_{\bar \alpha \bar \beta}}\rangle = \underset { s \rightarrow 0 } { \lim } \left({- { { 4e } \over { 3s } } } \right){u_{\left [ { \bar \alpha } \right.}}{a_{\left . { \bar \beta } \right ] } } + 2e{u_{\left [ { \bar \alpha } \right.}}\left({{g_{\left . { \bar \beta } \right]}}{u_{\bar \gamma } } } \right)\left({{2 \over 3}{{\dot a}^{\bar \gamma } } + { 1 \over 3}{r^{\bar \gamma}}_{\bar \delta}{u^{\bar \delta } } } \right ) + f_{\bar \alpha \bar \beta}^{{\rm{tail}}},$$\end{document } where the tail term can be copied from equation ( 454 ) , 461\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f_{\bar \alpha \bar \beta}^{{\rm{tail}}}(\bar x ) = 2e\int\nolimits_{- \infty}^{{t^ - } } { { \nabla _ { \left [ { \bar \alpha } \right.}}{g_{\left . { + \bar \beta } \right]\mu}}(\bar x , z){u^\mu}d\tau } .$$\end{document } the tensors appearing in equation ( 460 ) all refer to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document } , which now stands for an arbitrary point on the world line . the singular vector potential 462\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a_{\rm{s}}^\alpha ( x ) = e\int\nolimits_\gamma { g_{{\rm{s}}\,\mu}^{\,\,\alpha}(x , z){u^\mu}d\tau}$$\end{document } is the ( unphysical ) solution to equations ( 441 ) and ( 442 ) that is obtained by adopting the singular green s function of equation ( 335 ) instead of the retarded green s function . we will see that the singular field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{\alpha \beta}^{\rm{s}}$\end{document } reproduces the singular behaviour of the retarded solution , and that the difference , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{\alpha \beta}^{\rm{r } } = { f_{\alpha \beta } } - f_{\alpha \beta}^{\rm{s}}$\end{document } is smooth on the world line . to evaluate the integral of equation ( 462 ) we assume once more that x is sufficiently close to that the world line traverses \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } ( refer back to figure 9 ) . as before we let < and > be the values of the proper - time parameter at which enters and leaves \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } , respectively . then equation ( 462 ) becomes \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a_{\rm{s}}^\alpha ( x ) = e\int\nolimits_{- \infty}^{{\tau _ < } } { g_{{\rm{s}}\,\mu}^{\,\,\alpha}(x , z){u^\mu}d\tau } + e\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { g_{{\rm{s}}\,\mu}^{\,\,\alpha}(x , z){u^\mu}d\tau } + e\int\nolimits_{{\tau _ > } } ^\infty { g_{{\rm{s}}\,\mu}^{\,\,\alpha}(x , z){u^\mu}d\tau}.$$\end{document } the first integration vanishes because x is then in the chronological future of z( ) , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{s\mu}^{\,\,\alpha}(x , z ) = 0$\end{document } by equation ( 338 ) . similarly , the third integration vanishes because x is then in the chronological past of z( ) . for the second integration , x is the normal convex neighbourhood of z( ) , the singular green s function can be expressed in the hadamard form of equation ( 344 ) , and we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { g_{{\rm{s}}\,\mu}^{\,\,\alpha}(x , z){u^\mu}d\tau = \quad \quad \quad \quad \quad}}\\{\quad \quad \quad { 1 \over 2}\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { { u}_{\;\;\mu}^\alpha ( x , z){u^\mu}{\delta _ + } ( \sigma)d\tau + { 1 \over 2}\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { { u}_{\;\;\mu}^\alpha ( x , z){u^\mu}{\delta _ -}(\sigma)d\tau - { 1 \over 2}\int\nolimits_{{\tau _ < } } ^{{\tau _ > } } { { v}_{\;\;\mu}^\alpha ( x , z){u^\mu}\theta ( \sigma)d\tau } } } .}\\ \end{array}$$\end{document } to evaluate these we let x z(u ) and x z(v ) be the retarded and advanced points associated with x , respectively . to perform the first integration we change variables from to a , noticing that increases as z( ) passes through x ; the integral evaluates to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^\alpha}_{{\beta \prime}}{u^{{\beta \prime}}}/r$\end{document}. we do the same for the second integration , but we notice now that decreases as z( ) passes through x ; the integral evaluates to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u^\alpha}_{{\beta ^{\prime \prime}}}{u^{{\beta ^{\prime \prime}}}}/{r_{{\rm{adv}}}}$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{{\rm{adv } } } } \equiv - { \sigma _ { { \alpha ^{\prime \prime}}}}{u^\alpha}^{\prime \prime}$\end{document } is the advanced distance between x and the world line . the third integration is restricted to the interval u v by the step function , and we obtain the expression 463\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a_{\rm{s}}^\alpha ( x ) = { e \over { 2r}}{u^\alpha}_{\beta { \prime}}{u^{\beta { \prime } } } + { e \over { 2{r_{{\rm{adv}}}}}}{u^\alpha}_{\beta{\prime\prime}}{u^{\beta{\prime\prime } } } - { 1 \over 2}e\int\nolimits_u^v { { v^\alpha}_\mu ( x , z){u^\mu}d\tau}$$\end{document } for the singular vector potential . differentiation of equation ( 463 ) yields 464\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{\nabla _ \beta}a_\alpha ^{\rm{s}}(x ) = - { e \over { 2{r^2}}}{u_{\alpha \beta \prime}}{u^{\beta \prime}}{\partial _ \beta}r - { e \over { 2{r_{{\rm{adv}}}}^2}}{u_{\alpha \beta \prime \prime}}{u^{\beta \prime \prime}}{\partial _ \beta}{r_{{\rm{adv } } } } + { e \over { 2r}}{u_{\alpha \beta \prime ; \beta}}{u^{\beta \prime}}\quad \quad \quad \quad}\\{+ { e \over { 2r}}\left({{u_{\alpha \beta \prime ; \gamma \prime}}{u^{\beta \prime}}{u^{\gamma \prime } } + { u_{\alpha \beta \prime}}{a^{\beta \prime } } } \right){\partial _ \beta}u + { e \over { 2{r_{{\rm{adv}}}}}}{u_{\alpha \beta \prime \prime ; \beta}}{u^{\beta \prime \prime}}\quad}\\{+ { e \over { 2{r_{{\rm{adv}}}}}}\left({{u_{\alpha \beta \prime \prime ; \gamma \prime \prime}}{u^{\beta \prime \prime}}{u^{\gamma \prime \prime } } + { u_{\alpha \beta \prime \prime}}{a^{\beta \prime \prime } } } \right){\partial _ \beta}v + { 1 \over 2}e{v_{\alpha \beta \prime}}{u^{\beta \prime}}{\partial _ \beta}u}\\ { \ , - { 1 \over 2}e{v_{\alpha \beta \prime \prime}}{u^{\beta \prime \prime}}{\partial _ \beta}v - { 1 \over 2}e\int\nolimits_u^v { { \nabla _ \beta}{v_{\alpha \mu}}(x , z){u^\mu}d\tau } , \quad \quad \quad \quad}\\ \end{array}$$\end{document } and we would like to express this as an expansion in powers of r. for this we will rely on results already established in section 5.2.3 , as well as additional expansions that will involve the advanced point x. we recall that a relation between retarded and advanced times was worked out in equation ( 229 ) , that an expression for the advanced distance was displayed in equation ( 230 ) , and that equations ( 231 ) and ( 232 ) give expansions for v and radv , respectively . to derive an expansion for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{\alpha { \beta { \prime \prime}}}}{u^{{\beta ^{\prime \prime}}}}$\end{document } we follow the general method of section 3.4.4 and introduce the functions u( ) u(x , z)u . we have that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \prime\prime}}}{u^{\beta { \prime\prime } } } \equiv { u_\alpha}(v ) = { u_\alpha}(u ) + { \dot u_\alpha}(u)\delta { \prime } + { 1 \over 2}{\ddot u_\alpha}(u){\delta ^{{\prime}2 } } + o({\delta ^{{\prime}3}}),$$\end{document } where overdots indicate differentiation with respect to , and v u. the leading term \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_\alpha}(u ) \equiv { u_{\alpha { \beta \prime}}}{u^{{\beta \prime}}}$\end{document } was worked out in equation ( 447 ) , and the derivatives of u( ) are given by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\dot u_\alpha}(u ) = { u_{\alpha \beta { \prime};\gamma { \prime}}}{u^{\beta { \prime}}}{u^{\gamma { \prime } } } + { u_{\alpha \beta { \prime}}}{a^{\beta { \prime } } } = { g^{\alpha { \prime}}}_\alpha \left [ { { a_{\alpha { \prime } } } + { 1 \over 2}r{r_{\alpha { \prime}0b0}}{\omega ^b } - { 1 \over 6}r({r_{00 } } + { r_{0b}}{\omega ^b}){u_{\alpha { \prime } } } + \mathcal{o}({r^2 } ) } \right]$$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\ddot u_\alpha}(u ) = { u_{\alpha \beta { \prime};\gamma { \prime}\delta { \prime}}}{u^{\beta { \prime}}}{u^{\gamma { \prime}}}{u^{\delta { \prime } } } + { u_{\alpha \beta { \prime};\gamma { \prime}}}\left({2{a^{\beta { \prime}}}{u^{\gamma { \prime } } } + { u^{\beta { \prime}}}{a^{\gamma { \prime } } } } \right ) + { u_{\alpha \beta { \prime}}}{\dot a^{\beta { \prime } } } = { g^{\alpha { \prime}}}_\alpha \left [ { { { \dot a}_{\alpha { \prime } } } + { 1 \over 6}{r_{00}}{u_{\alpha { \prime } } } + \mathcal{o}(r ) } \right],$$\end{document } according to equations ( 449 ) and ( 325 ) . combining these results together with equation ( 229 ) for gives 465\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{u_{\alpha \beta \prime \prime}}{u^{\beta \prime \prime } } = g_\alpha ^{\alpha \prime}\left [ { { u_{\alpha \prime } } + 2r(1 - r{a_b}{\omega ^b}){a_{\alpha \prime } } + 2{r^2}{{\dot a}_{\alpha \prime } } + { r^2}{r_{\alpha \prime 0b0}}{\omega ^b}\quad \quad \quad \quad \quad \quad \quad } \right.}\\ { \left . { + { 1 \over { 12}}{r^2}({r_{00 } } - 2{r_{0a}}{\omega ^a } + { r_{ab}}{\omega ^a}{\omega ^b}){u_{\alpha \prime } } + { \mathcal o}({r^3 } ) } \right],}\\\end{array}$$\end{document } which should be compared with equation ( 447 ) . it should be emphasized that in equation ( 465 ) and all equations below , all frame components are evaluated at the retarded point x , and not at the advanced point . the preceding computation gives us also an expansion for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \prime\prime};\gamma { \prime\prime}}}{u^{\beta { \prime\prime}}}{u^{\gamma { \prime\prime } } } + { u_{\alpha \beta { \prime\prime}}}{a^{\beta { \prime\prime } } } \equiv { \dot u_\alpha}(v ) = { \dot u_\alpha}(u ) + { \ddot u_\alpha}(u)\delta { \prime } + \mathcal{o}({\delta ^{{\prime}2}}),$$\end{document } which becomes 466\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta{\prime\prime};\gamma{\prime\prime}}}{u^{\beta{\prime\prime}}}{u^{\gamma{\prime\prime } } } + { u_{\alpha \beta{\prime\prime}}}{a^{\beta{\prime\prime } } } = { g^{\alpha { \prime}}}_\alpha \left [ { { a_{\alpha { \prime } } } + 2r\dot a_{\alpha { \prime } } + { 1 \over 2}r{r_{\alpha { \prime}0b0}}{\omega ^b } + { 1 \over 6}r({r_{00 } } - { r_{0b}}{\omega ^b}){u_{\alpha { \prime } } } + \mathcal{o}({r^2 } ) } \right],$$\end{document } and which should be compared with equation ( 449 ) . we proceed similarly to derive an expansion for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{\alpha { \beta ^{\prime \prime}};\beta}}{u^{{\beta ^{\prime \prime}}}}$\end{document}. here we introduce the functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{\alpha \beta}}(\tau ) \equiv { u_{\alpha \mu}}_{;\beta}{u^\mu}$\end{document } and express \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{\alpha { \beta ^{\prime \prime}};\beta}}{u^{{\beta ^{\prime \prime}}}}$\end{document } as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\delta \prime } \equiv v - u$\end{document } the leading term \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_\alpha}(u ) \equiv { u_{\alpha { \beta \prime}}}{u^{{\beta \prime}}}$\end{document } was computed in equation ( 448 ) , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\dot u_{\alpha \beta}}(u ) = { u_{\alpha \beta { \prime};\beta \gamma { \prime}}}{u^{\beta { \prime}}}{u^{\gamma { \prime } } } + { u_{\alpha \beta { \prime};\beta}}{a^{\beta { \prime } } } = { 1 \over 2}{g^{\alpha { \prime}}}_\alpha { g^{\beta { \prime}}}_\beta \left [ { { r_{\alpha { \prime}0\beta { \prime}0 } } - { 1 \over 3}{u_{\alpha { \prime}}}{r_{\beta { \prime}0 } } + \mathcal{o}(r ) } \right]$$\end{document } follows from equation ( 324 ) . combining these results together with equation ( 229 ) for gives 467\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta{\prime\prime};\beta}}{u^{\beta { \prime\prime } } } = { 1 \over 2}r{g^{\alpha { \prime}}}_\alpha { g^{\beta { \prime}}}_\beta \left [ { { r_{\alpha { \prime}0\beta { \prime}0 } } - { r_{\alpha { \prime}0\beta { \prime}c}}{\omega ^c } - { 1 \over 3}({r_{\beta { \prime}0 } } - { r_{\beta { \prime}c}}{\omega ^c}){u_{\alpha { \prime } } } + \mathcal{o}(r ) } \right],$$\end{document } and this should be compared with equation ( 448 ) . the last expansion we shall need is 468\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${v_{\alpha \beta{\prime\prime}}}{u^{\beta{\prime\prime } } } = - { 1 \over 2}{g^{\alpha { \prime}}}_\alpha \left [ { { r_{\alpha { \prime}0 } } - { 1 \over 6}r{u_{\alpha { \prime } } } + \mathcal{o}(r ) } \right],$$\end{document } which follows at once from equation ( 450 ) . it is now a straightforward ( but still tedious ) matter to substitute these expansions into equation ( 464 ) to obtain the projections of the singular electromagnetic field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{\alpha \beta}^{\rm{s } } = { \nabla _ \alpha}a_\beta ^{\rm{s } } - { \nabla _ \beta}a_\alpha ^{\rm{s}}$\end{document } in the same tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } that was employed in section 5.2.3 . this gives 469\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{f_{a{\rm{0}}}^{\rm{s}}(u , r,{\omega ^a } ) \equiv f_{\alpha \beta}^{\rm{s}}(x)e_a^\alpha ( x)e_0^\beta ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{= { e \over { { r^2}}}{\omega _ a } - { e \over r}({a_a } - { a_b}{\omega ^b}{\omega _ b } ) - { 2 \over 3}e{{\dot a}_a } + { 1 \over 3}e{r_{b0c0}}{\omega ^b}{\omega ^c}{\omega _ a } - { 1 \over 6}e(5{r_{a0b0}}{\omega ^b } + { r_{ab0c}}{\omega ^b}{\omega ^c})}\\{+ { 1 \over { 12}}e(5{r_{00 } } + { r_{bc}}{\omega ^b}{\omega ^c } + r){\omega _ a } - { 1 \over 6}e{r_{ab}}{\omega ^b } + { \mathcal o}(r),\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\\end{array}$$\end{document } 470\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{f_{ab}^{\rm{s}}(u , r,{\omega ^a } ) \equiv f_{\alpha \beta}^{\rm{s}}(x)e_a^\alpha ( x)e_b^\beta ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{= { e \over r}({a_a}{\omega _ b } - { \omega _ a}{a_b } ) + { 1 \over 2}e({r_{a0bc } } - { r_{b0ac } } + { r_{a0c0}}{\omega _ b } - { \omega _ a}{r_{b0c0}}){\omega ^c}}\\{- { 1 \over 2}e({r_{a0}}{\omega _ b } - { \omega _ a}{r_{b0 } } ) + { \mathcal o}(r),\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } in which all frame components are evaluated at the retarded point x. comparison of these expressions with equations ( 451 ) and ( 452 ) reveals that the retarded and singular fields share the same singularity structure . the difference between the retarded field of equations ( 451 , 452 ) and the singular field of equations ( 469 , 470 ) defines the radiative field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{\alpha \beta}^{\rm{r}}(x)$\end{document}. its tetrad components are 471\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f_{a0}^{\rm{r } } = { 2 \over 3}e{\dot a_a } + { 1 \over 3}e{r_{a0 } } + f_{a0}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } 472\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f_{ab}^{\rm{r } } = f_{ab}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } and we see that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{\alpha \beta}^{\rm{r}}$\end{document } is a smooth tensor field on the world line . there is therefore no obstacle in evaluating the radiative field directly at x = x , where the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } becomes \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{{\alpha \prime}}},e_a^{{\alpha \prime}})$\end{document}. reconstructing the field at x from its frame components , we obtain 473\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f_{\alpha { \prime}\beta { \prime}}^{\rm{r}}(x{\prime } ) = 2e{u_{[\alpha { \prime}}}({g_{\beta { \prime}]\gamma { \prime } } } + { u_{\beta { \prime}]}}{u_{\gamma { \prime}}})\left({{2 \over 3}{{\dot a}^{\gamma { \prime } } } + { 1 \over 3}{r^{\gamma { \prime}}}_{\delta { \prime}}{u^{\delta { \prime } } } } \right ) + f_{\alpha { \prime}\beta { \prime}}^{{\rm{tail}}},$$\end{document } where the tail term can be copied from equation ( 454 ) , 474\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$f_{\alpha { \prime}\beta { \prime}}^{{\rm{tail}}}(x{\prime } ) = 2e\int\nolimits_{- \infty}^{{u^ - } } { { \nabla _ { [ \alpha { \prime}}}{g_{+ \beta { \prime}]\mu}}(x{\prime},z){u^\mu}d\tau.}$$\end{document } the tensors appearing in equation ( 473 ) all refer to the retarded point x z(u ) , which now stands for an arbitrary point on the world line . the retarded field f of a point electric charge is singular on the world line , and this behaviour makes it difficult to understand how the field is supposed to act on the particle and exert a force . the field s singularity structure was analyzed in sections 5.2.3 and 5.2.4 , and in section 5.2.5 it was shown to originate from the singular field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \alpha \beta ; \gamma}^{\rm{s}}$\end{document } ; the radiative field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \alpha \beta ; \gamma}^{\rm{r}}$\end{document } was then shown to be smooth on the world line . to make sense of the retarded field s action on the particle we follow the discussion of section 5.1.6 and temporarily picture the electric charge as a spherical hollow shell ; the shell s radius is s0 in fermi normal coordinates , and it is independent of the angles contained in the unit vector . the net force acting at proper time on this shell is proportional to the average of f( , s0 , ) over the shell s surface . this was worked out at the end of section 5.2.4 , and ignoring terms that disappear in the limit s0 0 , we obtain 475\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$e\langle { f_{\mu \nu}}\rangle { u^\nu } = - ( \delta m){a_\mu } + { e^2}({g_{\mu \nu } } + { u_\mu}{u_\nu})\left({{2 \over 3}{{\dot a}^\nu } + { 1 \over 3}{r^\nu}_\lambda { u^\lambda } } \right ) + ef_{\mu \nu}^{{\rm{tail}}}{u^\nu},$$\end{document } where 476\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta m \equiv { \lim\limits_{{s_0 } \rightarrow 0}}{{2{e^2 } } \over { 3{s_0}}}$$\end{document } is formally a divergent quantity and 477\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$ef_{\mu \nu}^{{\rm{tail}}}{u^\nu } = 2{e^2}{u^\nu}\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla _ { [ \mu}}{g_{+ \nu ] \lambda { \prime}}}(z(\tau),z(\tau { \prime})){u^{\lambda { \prime}}}d\tau { \prime}}$$\end{document } is the tail part of the force ; all tensors in equation ( 475 ) are evaluated at an arbitrary point z( ) on the world line . substituting equations ( 475 ) and ( 477 ) into equation ( 439 ) gives rise to the equations of motion for the electric charge 478\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(m + \delta m){a^\mu } = { e^2}({\delta ^\mu}_\nu + { u^\mu}{u_\nu})\left({{2 \over 3}{{\dot a}^\nu } + { 1 \over 3}{r^\nu}_\lambda { u^\lambda } } \right ) + 2{e^2}{u_\nu}\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla ^{[\mu}}g_{+ \lambda { \prime}}^{\nu ] } ( z(\tau),z(\tau { \prime})){u^{\lambda { \prime}}}d\tau { \prime},}$$\end{document } with m denoting the ( also formally divergent ) bare mass of the particle . we see that m and m combine in equation ( 478 ) to form the particle s observed mass mobs , which is finite and gives a true measure of the particle s inertia . apart from the term proportional to m , the averaged force of equation ( 475 ) has exactly the same form as the force that arises from the radiative field of equation ( 473 ) , which we express as 479\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$ef_{\mu \nu}^{\rm{r}}{u^\nu } = { e^2}({g_{\mu \nu } } + { u_\mu}{u_\nu})\left({{2 \over 3}{{\dot a}^\nu } + { 1 \over 3}{r^\nu}_\mu { u^\lambda } } \right ) + ef_{\mu \nu}^{{\rm{tail}}}{u^\nu}.$$\end{document } the force acting on the point particle can therefore be thought of as originating from the ( smooth ) radiative field , while the singular field simply contributes to the particle s inertia . after mass renormalization , equation ( 478 ) is equivalent to the statement 480\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$m{a_\mu } = ef_{\mu \nu}^{\rm{r}}(z){u^\nu},$$\end{document } where we have dropped the superfluous label obs on the particle s observed mass . for the final expression of the equations of motion we follow the discussion of section 5.1.6 and allow an external force \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{{\rm{ext}}}^\mu$\end{document } to act on the particle , and we replace , on the right - hand side of the equations , the acceleration vector by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f_{{\rm{ext}}}^\mu / m$\end{document}. this produces 481\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$m{{d{u^\mu } } \over { d\tau } } = f_{{\rm{ext}}}^\mu + { e^2}({\delta ^\mu}_\nu + { u^\mu}{u_\nu})\left({{2 \over { 3m}}{{df_{{\rm{ext}}}^\nu } \over { d\tau } } + { 1 \over 3}{r^\nu}_\lambda { u^\lambda } } \right ) + 2{e^2}{u_\nu}\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla ^{[\mu}}g_{+ \lambda { \prime}}^{\nu ] } ( z(\tau),z(\tau { \prime } ) ) } { u^{\lambda { \prime}}}d\tau { \prime},$$\end{document } in which m denotes the observed inertial mass of the electric charge and all tensors are evaluated at z( ) , the current position of the particle on the world line ; the primed indices in the tail integral refer to the point z( ) , which represents a prior position . we recall that the integration must be cut short at = 0 to avoid the singular behaviour of the retarded green s function at coincidence ; this procedure was justified at the beginning of section 5.2.3 . equation ( 481 ) was first derived ( without the ricci - tensor term ) by bryce s. dewitt and robert w. brehme in 1960 , and then corrected by j.m . an alternative derivation was produced by theodore c. quinn and robert m. wald in 1997 . in a subsequent publication , quinn and wald proved that the total work done by the electromagnetic self - force matches the energy radiated away by the particle . in this section we consider the motion of a point particle of mass m subjected to its own gravitational field . the particle moves on a world line in a curved spacetime whose background metric g is assumed to be a vacuum solution to the einstein field equations . we shall suppose that m is small , so that the perturbation h created by the particle can also be considered to be small ; it will obey a linear wave equation in the background spacetime . this linearization of the field equations will allow us to fit the problem of determining the motion of a point mass within the framework developed in sections 5.1 and 5.2 , and we shall obtain the equations of motion by following the same general line of reasoning . we shall find that is not a geodesic of the background spacetime because h acts on the particle and induces an acceleration of order m ; the motion is geodesic in the test - mass limit only . our discussion in this first section is largely formal : as in sections 5.1.1 and 5.2.1 we insert the point particle in the background spacetime and ignore the fact that the field it produces is singular on the world line . to make sense of the formal equations of motion will be our goal in the following sections 5.3.2 , 5.3.3 , 5.3.4 , 5.3.5 , 5.3.6 , and 5.3.7 . the problem of determining the motion of a small mass in a background spacetime will be reconsidered in section 5.4 from a different and more satisfying premise : there the small body will be modeled as a black hole instead of as a point particle , and the singular behaviour of the perturbation will automatically be eliminated . let a point particle of mass m move on a world line in a curved spacetime with metric g this is the total metric of the perturbed spacetime , and it depends on m as well as all other relevant parameters . at a later stage of the discussion part h that is proportional to m. the world line is described by relations z( ) in which is an arbitrary parameter this will later be identified with proper time in the background spacetime . in this and the following sections we will use sans - serif symbols to denote tensors that refer to the perturbed spacetime ; tensors in the background spacetime will be denoted , as usual , by italic symbols . the particle s action functional is 482\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_{{\rm{particle } } } } = - m\int\nolimits_\gamma { \sqrt { - { g_{\mu \nu}}{{\dot z}^\mu}{{\dot z}^\nu } } d\lambda,}$$\end{document } where = dz / d is tangent to the world line and the metric is evaluated at z. we assume that the particle provides the only source of matter in the spacetime an explanation will be provided at the end of this section so that the einstein field equations take the form of 483\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{g}}^{\alpha \beta } } = 8\pi { { \rm{t}}^{\alpha \beta}},$$\end{document } where g is the einstein tensor constructed from g and 484\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{t}}^{\alpha \beta}}(x ) = m\int\nolimits_\gamma { { { { { \rm{g}}^\alpha}_\mu ( x , z){{\rm{g}}^\beta}_\nu ( x , z){{\dot z}^\mu}{{\dot z}^\nu } } \over { \sqrt { - { { \rm{g}}_{\mu \nu}}{{\dot z}^\mu}{{\dot z}^\nu}}}}{\delta _ 4}(x , z)d\lambda}$$\end{document } is the particle s stress - energy tensor , obtained by functional differentiation of spartic1e with respect to g(x ) ; the parallel propagators appear naturally by expressing g as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\alpha}_\mu { g^\beta}_\nu { g_{\alpha \beta}}$\end{document}. on a formal level the metric g is obtained by solving the einstein field equations , and the world line is determined by solving the equations of energy - momentum conservation , which follow from the field equations . from equations ( 81 , 260 , 484 ) we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\nabla _ \beta}{{\rm{t}}^{\alpha \beta } } = m\int\nolimits_\gamma { { d \over { d\lambda}}\left({{{{{\rm{g}}^\alpha}_\mu { { \dot z}^\mu } } \over { \sqrt { - { { \rm{g}}_{\mu \nu}}{{\dot z}^\mu}{{\dot z}^\nu } } } } } \right){\delta _ 4}(x , z)d\lambda,}$$\end{document } and additional manipulations reduce this to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\nabla _ \beta}{{\rm{t}}^{\alpha \beta } } = m\int\nolimits_\gamma { { { { { \rm{g}}^\alpha}_\mu } \over { \sqrt { - { { \rm{g}}_{\mu \nu}}{{\dot z}^\mu}{{\dot z}^\nu}}}}\left({{{{\rm{d}}{{\dot z}^\mu } } \over { d\lambda } } - { \rm{k}}{{\dot z}^\mu } } \right){\delta _ 4}(x , z)d\lambda,}$$\end{document } where d / d is the covariant acceleration and k is a scalar field on the world line . energy - momentum conservation therefore produces the geodesic equation 485\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{{\rm{d}}{{\dot z}^\mu } } \over { d\lambda } } = { \rm{k}}{\dot z^\mu},$$\end{document } and 486\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{k } } \equiv { 1 \over { \sqrt { - { { \rm{g}}_{\mu \nu}}{{\dot z}^\mu}{{\dot z}^\nu}}}}{d \over { d\lambda}}\sqrt { - { { \rm{g}}_{\mu \nu}}{{\dot z}^\mu}{{\dot z}^\nu}}$$\end{document } measures the failure of to be an affine parameter on the geodesic . at this stage we begin treating m as a formal expansion parameter , and we write 487\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{g}}_{\alpha \beta } } = { g_{\alpha \beta } } + { h_{\alpha \beta}}\mathcal{o}({m^2}),$$\end{document } with g denoting the m 0 limit of the total metric g , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h_{\alpha \beta } } = { \mathcal o}(m)$\end{document } the first - order correction . we shall refer to g as the metric of the background spacetime and to h as the perturbation produced by the particle . we similarly write 488\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{g}}^{\alpha \beta}}[{\rm{g } } ] = { g^{\alpha \beta}}[g ] + { h^{\alpha \beta}}[g;h ] + \mathcal{o}({m^2})$$\end{document } for the einstein tensor , and 489\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{t}}^{\alpha \beta } } = { t^{\alpha \beta } } + \mathcal{o}({m^2})$$\end{document } for the particle s stress - energy tensor . the leading term t(x ) describes the stress - energy tensor of a test particle of mass m that moves on a world line in a background spacetime with metric g. if we choose to be proper time as measured in this spacetime , then equation ( 484 ) implies 490\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${t^{\alpha \beta}}(x ) = m\int\nolimits_\gamma { { g^\alpha}_\mu ( x , z){g^\beta}_\nu ( x , z){u^\mu}{u^\nu}{\delta _ 4}(x , z)d\tau,}$$\end{document } where u( ) = dz / d is the particle s four - velocity . we have already stated that the particle is the only source of matter in the spacetime , and the metric g must therefore be a solution to the vacuum field equations : g[g ] = 0 . equations ( 483 , 488 , ( 489 ) then imply h[g ; h ] = 8t , in which both sides of the equation are of order m. to simplify the expression of the first - order correction to the einstein tensor we introduce the trace - reversed gravitational potentials 491\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma _ { \alpha \beta } } = { h_{\alpha \beta } } - { 1 \over 2}({g^{\gamma \delta}}{h_{\gamma \delta}}){g_{\alpha \beta}},$$\end{document } and we impose the lorenz gauge condition 492\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma ^{\alpha \beta}}_{;\beta } = 0.$$\end{document } here and below it is understood that indices are lowered and raised with the background metric and its inverse , respectively , and that covariant differentiation refers to a connection that is compatible with g. we then have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h^{\alpha \beta } } = - { 1 \over 2}(\square{\gamma ^{\alpha \beta } } + 2r_{\gamma \;\delta}^{\alpha \;\beta}{\gamma ^{\gamma \delta}})$\end{document } , and equation ( 483 ) reduces to 493\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\square\gamma ^{\alpha \beta } } + 2r_{\gamma \;\delta}^{\alpha \;\beta}{\gamma ^{\gamma \delta } } = - 16\pi { t^{\alpha \beta}},$$\end{document } where = g is the wave operator and t is defined by equation ( 490 ) . we have here a linear wave equation for the potentials , and this equation can be placed on an equal footing with equation ( 385 ) for the potential associated with a point scalar charge , and equation ( 441 ) for the vector potential a associated with a point electric charge . the equations of motion for the point mass are obtained by substituting the expansion of equation ( 487 ) into equations ( 485 ) and ( 486 ) . the perturbed connection is easily computed to be \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\gamma ^\alpha}_{\beta \gamma } + { 1 \over 2}({h^\alpha}_{\beta ; \gamma } + { h^\alpha}_{\gamma ; \beta } - { h_{\beta \gamma}}^{;\alpha})$\end{document } and this leads to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{{\rm{d}}{{\dot z}^\mu } } \over { d\tau } } = { { d{u^\mu } } \over { d\tau } } + { 1 \over 2}\left({h_{\nu ; \lambda}^\mu + h_{\lambda ; \nu}^\mu - { h_{\nu \lambda}}^{;\mu } } \right){u^\nu}{u^\lambda } + \mathcal{o}({m^2}),$$\end{document } having once more selected proper time ( as measured in the background spacetime ) as the parameter on the world line . on the other hand , equation ( 486 ) gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{k } } = - { 1 \over 2}{h_{\nu \lambda ; \rho}}{u^\nu}{u^\lambda}{u^\rho } - { h_{\nu \lambda}}{u^\nu}{u^\lambda } + \mathcal{o}({m^2}),$$\end{document } where a = du / d is the particle s acceleration vector . since it is clear that the acceleration will be of order m , the second term can be discarded and we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{d{u^\mu } } \over { d\tau } } = - { 1 \over 2}\left({h_{\nu ; \lambda}^\mu + h_{\lambda ; \nu}^\mu - { h_{\nu \lambda}}^{;\mu } + { u^\mu}{h_{\nu \lambda ; \rho}}{u^\rho } } \right){u^\nu}{u^\lambda}\mathcal{o}({m^2}).$$\end{document } keeping the error term implicit , we shall express this in the equivalent form 494\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{d{u^\mu } } \over { d\tau } } = - { 1 \over 2}({g^{\mu \nu } } + { u^\mu}{u^\nu})(2{h_{\nu \lambda ; \rho } } - { h_{\lambda \rho ; \nu}}){u^\lambda}{u^\rho},$$\end{document } which emphasizes the fact that the acceleration is orthogonal to the four - velocity . it should be clear that equation ( 494 ) is valid only in a formal sense , because the potentials obtained from equations ( 493 ) diverge on the world line . the nonlinearity of the einstein field equations makes this problem even worse here than for the scalar and electromagnetic cases , because the singular behaviour of the perturbation might render meaningless a formal expansion of g in powers of m. ignoring this issue for the time being ( we shall return to it in section 5.4 ) , we will proceed as in sections 5.1 and 5.2 and attempt , with a careful analysis of the field s singularity structure , to make sense of these equations . to conclude this section i should explain why it is desirable to restrict our discussion to spacetimes that contain no matter except for the point particle . suppose , in contradiction with this assumption , that the background spacetime contains a distribution of matter around which the particle is moving . notice that we are still assuming that the particle moves in a region of spacetime in which there is no matter ; the issue is whether we can allow for a distribution of matter somewhere else . ) suppose also that the matter distribution is described by a collection of matter fields . then the field equations satisfied by the matter have the schematic form e[ ; g ] = 0 , and the metric is determined by the einstein field equations g[g ] = 8m [ ; g ] , in which m[ ; g ] stands for the matter s stress - energy tensor . we now insert the point particle in the spacetime , and recognize that this displaces the background solution ( , g ) to a new solution ( + , g + g ) . the perturbations are determined by the coupled set of equations e[ + ; g + g ] = 0 and g[g + g ] = 8m[ + ; g + g ] + 8t[g ] . after linearization these take the form of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${e_{\psi}}\cdot\delta \psi + { e_g}\cdot\delta g = 0,\quad { g_g}\cdot\delta g = 8\pi ( { m_\psi}\cdot\delta \psi + { m_g}\cdot\delta g + t),$$\end{document } where e , eg , m , and mg are suitable differential operators acting on the perturbations . this is a coupled set of partial differential equations for the perturbations and g . these equations are linear , but they are much more difficult to deal with than the single equation for g that was obtained in the vacuum case . and although it is still possible to solve the coupled set of equations via a green s function technique , the degree of difficulty is such that we will not attempt this here . we shall , therefore , continue to restrict our attention to the case of a point particle moving in a vacuum ( globally ricci - flat ) background spacetime . the retarded solution to equation ( 493 ) is \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\gamma ^{\alpha \beta}}(x ) = 4\int { g_{+ \,\,\,\,{\gamma \prime}{\delta \prime}}^{\,\,\alpha \beta } } ( x,{x\prime}){t^{{\gamma \prime}{\delta \prime}}}({x\prime})\sqrt { - { g\prime } } { d^4}{x\prime}$\end{document } , where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{+ \,\,\,\,{\gamma \prime}{\delta \prime}}^{\,\,\alpha \beta}(x,{x\prime})$\end{document } is the retarded green s function introduced in section 4.5 . after substitution of the stress - energy tensor of equation ( 490 ) we obtain 495\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma ^{\alpha \beta}}(x ) = 4m\int\nolimits_\gamma { g_{+ \mu \nu}^{\alpha \beta}(x , z){u^\mu}{u^\nu}d\tau,}$$\end{document } in which z( ) gives the description of the world line and u = dz / d. because the retarded green s function is defined globally in the entire background spacetime , equation ( 495 ) describes the gravitational perturbation created by the particle at any point x in that spacetime . for a more concrete expression we must take x to be in a neighbourhood of the world line . the following manipulations follow closely those performed in section 5.1.2 for the case of a scalar charge , and in section 5.2.2 for the case of an electric charge . because these manipulations are by now familiar first , for the purposes of computing (x ) to first order in m , it is sufficient to take the world line to be a geodesic of the background spacetime : the deviations from geodesic motion that we are in the process of calculating are themselves of order m and would affect (x ) at order m only . we shall therefore be allowed to set 496\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^\mu } = 0 = { \dot a^\mu}$$\end{document } in our computations . second , because we take g to be a solution to the vacuum field equations , we are also allowed to set 497\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${r_{\mu \nu}}(z ) = 0$$\end{document } in our computations . with the understanding that x is close to the world line ( refer back to figure 9 ) , we substitute the hadamard construction of equation ( 352 ) into equation ( 495 ) and integrate over the portion of that is contained in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document}. the result is 498\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma ^{\alpha \beta}}(x ) = { { 4 m } \over r}{u^{\alpha \beta}}_{\gamma { \prime}\delta { \prime}}(x , x{\prime}){u^{\gamma { \prime}}}{u^{\delta { \prime } } } + 4m\int\nolimits_{{\tau _ < } } ^u { { v^{\alpha \beta}}_{\mu \nu}(x , z){u^\mu}{u^\nu}d\tau + 4 m } \int\nolimits_{- \infty}^{{\tau _ < } } { g_{+ \mu \nu}^{\alpha \beta}(x , z){u^\mu}{u^\nu}d\tau,}$$\end{document } in which primed indices refer to the retarded point x z(u ) associated with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r \equiv { \sigma _ { { \alpha \prime}}}{u^{{\alpha \prime}}}$\end{document } is the retarded distance from x to x , and < is the proper time at which enters \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal n}(x)$\end{document } from the past . in the following sections 5.3.3 , 5.3.4 , 5.3.5 , 5.3.6 , and 5.3.7 , we shall refer to (x ) as the gravitational potentials at x produced by a particle of mass m moving on the world line , and to ;(x ) as the gravitational field at x. to compute this is our next task . keeping in mind that x and x are related by (x , x ) = 0 , a straightforward computation reveals that the covariant derivatives of the gravitational potentials are given by 499\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{\gamma _ { \alpha \beta ; \gamma}}(x ) = - { { 4 m } \over 2}{u_{\alpha \beta \alpha \prime \beta \prime}}{u^{\alpha \prime}}{u^{\beta \prime}}{\partial _ \gamma}r + { { 4 m } \over r}{u_{\alpha \beta \alpha \prime \beta \prime ; \gamma}}{u^{\alpha \prime}}{u^{\beta \prime } } + { { 4 m } \over r}{u_{\alpha \beta \alpha \prime \beta \prime ; \gamma \prime}}{u^{\alpha \prime}}{u^{\beta \prime}}{u^{\gamma \prime}}{\partial _ _ \gamma}u + \gamma _ { \alpha \beta \gamma}^{{\rm{tail}}}(x),\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } where the tail integral is defined by 500\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{\gamma _ { \alpha \beta \gamma}^{{\rm{tail } } } = 4m\int\nolimits_{{\tau _ < } } ^u { { \nabla _ \gamma}{v_{\alpha \beta \mu \nu}}(x , z){u^\mu}{u^\nu}d\tau + 4 m } \int\nolimits_{- \infty}^{{\tau _ < } } { { \nabla _ \gamma}{g_{+ \alpha \beta \mu \nu}}(x , z){u^\mu}{u^\nu}d\tau}}\\{= 4m\int\nolimits_{- \infty}^{{u^ - } } { { \nabla _ \gamma}{g_{+ \alpha \beta \mu \nu}}(x , z){u^\mu}{u^\nu}d\tau .\quad \quad \quad \quad \quad \quad \quad \quad \quad}}\\\end{array}$$\end{document } the second form of the definition , in which the integration is cut short at = u u 0 to avoid the singular behaviour of the retarded green s function at = 0 , is equivalent to the first form . we wish to express ;(x ) in the retarded coordinates of section 3.3 , as an expansion in powers of r. for this purpose we decompose the field in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } that is obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{{\alpha \prime}}},e_a^{{\alpha \prime}})$\end{document } on the null geodesic that links x to x ; this construction is detailed in section 3.3 . note that throughout this section we set ab = 0 , where ab is the rotation tensor defined by equation ( 138 ) : the tetrad vectors \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_a^{{\alpha \prime}}$\end{document } are taken to be parallel transported on . we recall from equation ( 141 ) that the parallel propagator can be expressed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^{{\alpha \prime}}}_\alpha = { u^{{\alpha \prime}}}e_\alpha ^0 + e_a^{{\alpha \prime}}e_\alpha ^a$\end{document}. the expansion relies on equation ( 166 ) for u and equation ( 168 ) for r , both specialized to the case of geodesic motio , aa = 0 . we shall also need 501\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \alpha { \prime}}{\beta { \prime}}}}{u^{{\alpha { \prime}}}}{u^{{\beta { \prime } } } } = { g^{{\alpha { \prime}}}}{}_{(\alpha}{g^{{\beta { \prime}}}}_{\beta)}[{u_{{\alpha { \prime}}}}{u_{{\beta { \prime } } } } + \mathcal{o}({r^3})],$$\end{document } which follows from equation ( 358 ) , 502\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \alpha { \prime}}{\beta { \prime}};\gamma}}{u^{{\alpha { \prime}}}}{u^{{\beta { \prime } } } } = { g^{{\alpha { \prime}}}}{}_{(\alpha}{g^{{\beta { \prime}}}}_{\beta)}{g^{{\gamma { \prime}}}}_\gamma [ - r({r_{{\alpha { \prime}}0{\gamma { \prime}}0 } } + { r_{{\alpha { \prime}}0{\gamma { \prime}}d}}{\omega ^d}){u_{{\beta { \prime } } } } + \mathcal{o}({r^2})],$$\end{document } 503\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \alpha { \prime}}{\beta { \prime}};{\gamma { \prime}}}}{u^{{\alpha { \prime}}}}{u^{{\beta { \prime}}}}{u^{{\gamma { \prime } } } } = { g^{{\alpha { \prime}}}}{}_{(\alpha}{g^{{\beta { \prime}}}}_{\beta)}[r{r_{{\alpha { \prime}}0d0 } } + { \omega ^d}{u_{{\beta { \prime } } } } + \mathcal{o}({r^2})],$$\end{document } which follow from equations ( 359 ) and ( 360 ) , respectively , as well as the relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma ^{{\alpha \prime } } } = - r({u^{{\alpha \prime } } } + { \omega ^\alpha}e_a^{{\alpha \prime}})$\end{document } first encountered in equation ( 144 ) . and finally , we shall need 504\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${v_{\alpha \beta { \alpha { \prime}}{\beta { \prime}}}}{u^{{\alpha { \prime}}}}{u^{{\beta { \prime } } } } = { g^{{\alpha { \prime}}}}{}_{(\alpha}{g^{{\beta { \prime}}}}_{\beta)}[{r_{{\alpha { \prime}}0{\beta { \prime}}0 } } + \mathcal{o}(r)],$$\end{document } which follows from equation ( 362 ) . making these substitutions in equation ( 484 ) and projecting against various members of the tetrad gives 505\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma _ { 000}}(u , r,{\omega ^a } ) \equiv { \gamma _ { \alpha \beta ; \gamma}}(x)e_0^\alpha ( x)e_0^\beta ( x)e_0^\gamma ( x ) = 2m{r_{a0b0}}{\omega ^a}{\omega ^b } + \gamma _ { 000}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } 506\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma _ { 0b0}}(u , r,{\omega ^a } ) \equiv { \gamma _ { \alpha \beta ; \gamma}}(x)e_0^\alpha ( x)e_b^\beta ( x)e_0^\gamma ( x ) = - 4m{r_{b0c0}}{\omega ^c } + \gamma _ { 0b0}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } 507\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma _ { ab0}}(u , r,{\omega ^a } ) \equiv { \gamma _ { \alpha \beta ; \gamma}}(x)e_a^\alpha ( x)e_b^\beta ( x)e_0^\gamma ( x ) = 4m{r_{a0b0 } } + \gamma _ { ab0}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } 508\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{\gamma _ { 00c}}(u , r,{\omega ^a } ) \equiv { \gamma _ { \alpha \beta ; \gamma}}(x)e_0^\alpha ( x)e_0^\beta ( x)e_c^\gamma ( x)\quad \quad \quad \quad \;\;\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\ { = - 4m\left [ { \left({{1 \over { { r^2 } } } + { 1 \over 3}{r_{a0b0}}{\omega ^a}{\omega ^b } } \right){\omega _ c } + { 1 \over 6}{r_{c0b0}}{\omega ^b } - { 1 \over 6}{r_{ca0b}}{\omega ^a}{\omega ^b } } \right ] + \gamma _ { 00c}^{{\rm{tail } } } + { \mathcal o}(r),}\\\end{array}$$\end{document } 509\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{\gamma _ { 0bc}}(u , r,{\omega ^a } ) \equiv { \gamma _ { \alpha \beta ; \gamma}}(x)e_0^\alpha ( x)e_b^\beta ( x)e_c^\gamma ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\ { = 2m({r_{b0c0 } } + { r_{b0cd}}{\omega ^d } + { r_{b0d0}}{\omega ^d}{\omega _ c } ) + \gamma _ { 0bc}^{{\rm{tail } } } + { \mathcal o}(r),}\\\end{array}$$\end{document } 510\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma _ { abc}}(u , r,{\omega ^a } ) \equiv { \gamma _ { \alpha \beta ; \gamma}}(x)e_a^\alpha ( x)e_b^\beta ( x)e_c^\gamma ( x ) = - 4m{r_{a0b0}}{\omega _ c } + \gamma _ { abc}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } where , for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{a0b0}}(u ) = { r_{{\alpha \prime}{\gamma \prime}{\beta \prime}{\delta \prime}}}e_a^{{\alpha \prime}}{u^\gamma}\prime e_b^{{\beta \prime}}{u^{{\delta \prime}}}$\end{document } are frame components of the riemann tensor evaluated at x z(u ) . we have also introduced the frame components of the tail part of the gravitational field , which are obtained from equation ( 500 ) evaluated at x instead of x ; for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { 000}^{{\rm{tail } } } = { u^{{\alpha \prime}}}{u^{{\beta \prime}}}{u^{{\gamma \prime}}}\gamma _ { { \alpha \prime}{\beta \prime}{\gamma \prime}}^{{\rm{tail}}}({x\prime})$\end{document}. we may note here that while 00c is the only component of the gravitational field that diverges when r 0 , the other components are nevertheless singular because of their dependence on the unit vector ; the only exception is ab0 , which is smooth . the translation of the results contained in equations ( 505 , 506 , 507 , 508 , 509 , 510 ) into the fermi normal coordinates of section 3.2 proceeds as in sections 5.1.4 and 5.2.4 , but is simplified by the fact that here the world line can be taken to be a geodesic . we may thus set \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_a } = { { \dot a}_0 } = { { \dot a}_a } = 0$\end{document } in equations ( 224 ) and ( 225 ) that relate the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } , as well as in equations ( 221 , 222 , 223 ) that relate the fermi normal coordinates ( t , s , ) to the retarded coordinates . we recall that the fermi normal coordinates refer to a point \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document } on the world line that is linked to x by a spacelike geodesic that intersects orthogonally . the translated results are 511\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\bar \gamma _ { 000}}(t , s,{\omega ^a } ) \equiv { \gamma _ { \alpha \beta ; \gamma}}(x)\bar e_0^\alpha ( x)\bar e_0^\beta ( x)\bar e_0^\gamma ( x ) = \bar \gamma _ { 000}^{{\rm{tail } } } + \mathcal{o}(s),$$\end{document } 512\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\bar \gamma _ { 0b0}}(t , s,{\omega ^a } ) \equiv { \gamma _ { \alpha \beta ; \gamma}}(x)\bar e_0^\alpha ( x)\bar e_b^\beta ( x)\bar e_0^\gamma ( x ) = - 4m{r_{b0c0}}{\omega ^c } + \bar \gamma _ { 0b0}^{{\rm{tail } } } + \mathcal{o}(s),$$\end{document } 513\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\bar \gamma _ { ab0}}(t , s,{\omega ^a } ) \equiv { \gamma _ { \alpha \beta ; \gamma}}(x)\bar e_a^\alpha ( x)\bar e_b^\beta ( x)\bar e_0^\gamma ( x ) = 4m{r_{a0b0 } } + \bar \gamma _ { ab0}^{{\rm{tail } } } + \mathcal{o}(s),$$\end{document } 514\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}{c } } { { { \bar \gamma } _ { 00c}}(t , s,{\omega ^a } ) \equiv { \gamma _ { \alpha \beta ; \gamma } } ( x)\bar e_0^\alpha ( x)\bar e_0^\beta ( x)\bar e_c^\gamma ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { = - 4m\left [ { \left ( { \frac{1}{{{s^2 } } } - \frac{1}{6}{r_{a0b0}}{\omega ^a}{\omega ^b } } \right){\omega _ c } + \frac{1}{3}{r_{c0b0}}{\omega ^b } } \right ] + \bar \gamma _ { 00c}^{{\text{tail } } } + \mathcal{o}(s ) , } \end{array}$$\end{document } 515\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\bar \gamma _ { 0bc}}(t , s,{\omega ^a } ) \equiv { \gamma _ { \alpha \beta ; \gamma}}(x)\bar e_0^\alpha ( x)\bar e_b^\beta ( x)\bar e_c^\gamma ( x ) = 2m({r_{b0c0 } } + { r_{b0cd}}{\omega ^d } ) + \bar \gamma _ { 0bc}^{{\rm{tail } } } + \mathcal{o}(s),$$\end{document } 516\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\bar \gamma _ { abc}}(t , s,{\omega ^a } ) \equiv { \gamma _ { \alpha \beta ; \gamma}}(x)\bar e_a^\alpha ( x)\bar e_b^\beta ( x)\bar e_c^\gamma ( x ) = - 4m{r_{a0b0}}{\omega _ c } + \bar \gamma _ { abc}^{{\rm{tail } } } + \mathcal{o}(s),$$\end{document } where all frame components are now evaluated at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } instead of x. it is then a simple matter to average these results over a two - surface of constant t and s. using the area element of equation ( 404 ) and definitions analogous to those of equation ( 405 ) , we obtain 517\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left\langle { { { \bar \gamma}_{000 } } } \right\rangle = \bar \gamma _ { 000}^{{\rm{tail } } } + \mathcal{o}(s),$$\end{document } 518\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left\langle { { { \bar \gamma}_{0b0 } } } \right\rangle = \bar \gamma _ { 0b0}^{{\rm{tail } } } + \mathcal{o}(s),$$\end{document } 519\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left\langle { { { \bar \gamma}_{ab0 } } } \right\rangle = 4m{r_{a0b0 } } + \bar \gamma _ { ab0}^{{\rm{tail } } } + \mathcal{o}(s),$$\end{document } 520\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left\langle { { { \bar \gamma}_{00c } } } \right\rangle = \bar \gamma _ { 00c}^{{\rm{tail } } } + \mathcal{o}(s),$$\end{document } 521\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left\langle { { { \bar \gamma}_{0bc } } } \right\rangle = 2m{r_{b0c0 } } + \bar \gamma _ { 0bc}^{{\rm{tail } } } + \mathcal{o}(s),$$\end{document } 522\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left\langle { { { \bar \gamma}_{abc } } } \right\rangle = \bar \gamma _ { abc}^{{\rm{tail } } } + \mathcal{o}(s).$$\end{document } the averaged gravitational field is smooth in the limit s 0 , in which the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\bar e_0^\alpha , \bar e_a^\alpha)$\end{document } coincides with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{\bar \alpha}},e_a^{\bar \alpha})$\end{document } reconstructing the field at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x}$\end{document } from its frame components gives 523\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\left\langle { { \gamma _ { \bar \alpha \bar \beta ; \bar \gamma } } } \right\rangle = - 4m\left({u{}_{(\bar \alpha}{r_{\bar \beta)\bar \delta \bar \gamma \bar \epsilon } } + { r_{\bar \alpha \bar \delta \bar \beta \bar \epsilon}}{u_{\bar \gamma } } } \right){u^{\bar \delta}}{u^{\bar \epsilon } } + \gamma _ { \bar \alpha \bar \beta \bar \gamma}^{{\rm{tail}}},$$\end{document } where the tail term can be copied from equation ( 500 ) , 524\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { \bar \alpha \bar \beta \bar \gamma}^{{\rm{tail}}}(\bar x ) = 4m\int\nolimits_{- \infty}^{{t^ - } } { { \nabla _ { \bar \gamma}}{g_{+ \bar \alpha \bar \beta \mu \nu}}(\bar x , z){u^\mu}{u^\nu}d\tau.}$$\end{document } the tensors that appear in equation ( 523 ) all refer to the simultaneous point \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar x \equiv z(t)$\end{document } , which can now be treated as an arbitrary point on the world line . the singular gravitational potentials 525\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { \rm{s}}^{\alpha \beta}(x ) = 4m\int\nolimits_\gamma { g_{{\rm{s}}\;\;\mu \nu}^{\;\;\alpha \beta}(x , z){u^\mu}{u^\nu}d\tau}$$\end{document } are solutions to the wave equation of equation ( 493 ) ; the singular green s function was introduced in section 4.5.4 . we will see that the singular field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \alpha \beta ; \gamma}^{\rm{s}}$\end{document } reproduces the singular behaviour of the retarded solution near the world line , and that the difference , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \alpha \beta ; \gamma}^{\rm{r } } = { \gamma _ { \alpha \beta ; \gamma } } - \gamma _ { \alpha \beta ; \gamma}^{\rm{s}}$\end{document } , is smooth on the world line . to evaluate the integral of equation ( 525 ) we take x to be close to the world line ( see figure 9 ) , and we invoke equation ( 373 ) as well as the hadamard construction of equation ( 379 ) . this gives 526\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { \rm{s}}^{\alpha \beta}(x ) = { { 2 m } \over r}u_{\;\;{\gamma { \prime}}{\delta { \prime}}}^{\alpha \beta}{u^{{\gamma { \prime}}}}{u^{{\delta { \prime } } } } + { { 2 m } \over { { r_{{\rm{adv}}}}}}u_{\;\;{\gamma { \prime\prime}}{\delta { \prime\prime}}}^{\alpha \beta}{u^{{\gamma { \prime\prime}}}}{u^{{\delta { \prime\prime } } } } - 2m\int\nolimits_u^v { v_{\;\;\;\mu \nu}^{\alpha \beta}(x , z){u^\mu}{u^\nu}d\tau,}$$\end{document } where primed indices refer to the retarded point x z(u ) , double - primed indices refer to the advanced point x z(v ) , and where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r_{{\rm{adv } } } } \equiv - { \sigma _ { { \alpha ^{\prime \prime}}}}{u^\alpha}^{\prime \prime}$\end{document } is the advanced distance between x and the world line . differentiation of equation ( 526 ) yields 527\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{\gamma _ { \alpha \beta ; \gamma}^{\rm{s}}(x ) = - { { 2 m } \over { { r^2}}}{u_{\alpha \beta \alpha \prime \beta \prime}}{u^{\alpha \prime}}{u^{\beta \prime}}{\partial _ \gamma}r - { { 2 m } \over { { r_{{\rm{adv}}}}^2}}{u_{\alpha \beta \alpha \prime \prime \beta \prime \prime}}{u^{\alpha \prime \prime}}{u^{\beta \prime \prime}}{\partial _ \gamma}{r_{{\rm{adv } } } } + { { 2 m } \over r}{u_{\alpha \beta \alpha \prime \beta \prime ; \gamma}}{u^{\alpha \prime}}{u^{\beta \prime}}\quad \quad \quad \quad \quad \quad \quad } \\ { + { { 2 m } \over r}{u_{\alpha \beta \alpha \prime \beta \prime ; \gamma \prime}}{u^{\alpha \prime}}{u^{\beta \prime}}{u^{\gamma \prime}}{\partial _ \gamma}u + { { 2 m } \over { { r_{{\rm{adv}}}}}}{u_{\alpha \beta \alpha \prime \prime \beta \prime \prime ; \gamma}}{u^{\alpha \prime \prime}}{u^{\beta \prime \prime } } + { { 2 m } \over { { r_{{\rm{adv}}}}}}{u_{\alpha \beta \alpha \prime \prime \beta \prime \prime ; \gamma \prime \prime}}{u^{\alpha \prime \prime}}{u^{\beta \prime \prime}}{u^{\gamma \prime \prime}}{\partial _ \gamma}v } \\ { + 2m{v_{\alpha \beta \alpha \prime \beta \prime}}{u^{\alpha \prime}}{u^{\beta \prime}}{\partial _ \gamma}u - 2m{v_{\alpha \beta \alpha \prime \prime \beta \prime \prime}}{u^{\alpha \prime \prime}}{u^{\beta \prime \prime}}{\partial _ \gamma}v - 2m\int\nolimits_u^v { { \nabla _ \gamma}{v_{\alpha \beta \mu \nu}}(x , z){u^\mu}{u^\nu}d\tau } , \quad } \\ \\\end{array}$$\end{document } and we would like to express this as an expansion in powers of r. for this we will rely on results already established in section 5.3.3 , as well as additional expansions that will involve the advanced point x. we recall that a relation between retarded and advanced times was worked out in equation ( 229 ) , that an expression for the advanced distance was displayed in equation ( 230 ) , and that equations ( 231 ) and ( 232 ) give expansions for v and radv , respectively ; these results can be simplified by setting \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_a } = { { \dot a}_0 } = { { \dot a}_a } = 0$\end{document } which is appropriate in this computation . to derive an expansion for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{\alpha \beta { \alpha ^{\prime \prime}}{\beta ^{\prime \prime}}}}{u^{{\alpha ^{\prime \prime}}}}{u^{{\beta ^{\prime \prime}}}}$\end{document } we follow the general method of section 3.4.4 and introduce the functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{\alpha \beta}}(\tau ) \equiv { u_{\alpha \beta \mu \nu}}(x , z){u^\mu}{u^\nu}$\end{document } we have that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \alpha { \prime\prime}}{\beta { \prime\prime}}}}{u^{{\alpha { \prime\prime}}}}{u^{{\beta { \prime\prime } } } } \equiv { u_{\alpha \beta}}(v ) = { u_{\alpha \beta}}(u ) + { \dot u_{\alpha \beta}}(u){\delta { \prime } } + { 1 \over 2}{\ddot u_{\alpha \beta}}(u){\delta ^{\prime 2 } } + o({\delta ^{\prime 3}}),$$\end{document } where overdots indicate differentiation with respect to and v u. the leading term \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{\alpha \beta}}(u ) \equiv { u_{\alpha \beta { \alpha \prime}{\beta \prime}}}{u^{{\alpha \prime}}}{u^{{\beta \prime}}}$\end{document } was worked out in equation ( 501 ) , and the derivatives of u( ) are given by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\dot u_{\alpha \beta}}(u ) = { u_{\alpha \beta { \alpha { \prime}}{\beta { \prime}};{\gamma { \prime}}}}{u^{{\alpha { \prime}}}}{u^{{\beta { \prime}}}}{u^{{\gamma { \prime } } } } = { g^{{\alpha { \prime}}}}{}_{(\alpha}{g^{{\beta { \prime}}}}_{\beta)}[r{r_{{\alpha { \prime}}0d0}}{\omega ^d}{u_{{\beta { \prime } } } } + \mathcal{o}({r^2})]$$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\ddot u_{\alpha \beta}}(u ) = { u_{\alpha \beta { \alpha { \prime}}{\beta { \prime}};{\gamma { \prime}}{\delta { \prime}}}}{u^{{\alpha { \prime}}}}{u^{{\beta { \prime}}}}{u^{{\gamma { \prime}}}}{u^{{\delta { \prime } } } } = \mathcal{o}(r),$$\end{document } according to equations ( 503 ) and ( 360 ) . combining these results together with equation ( 229 ) for gives 528\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \alpha { \prime\prime}}{\beta { \prime\prime}}}}{u^{{\alpha { \prime\prime}}}}{u^{{\beta { \prime\prime } } } } = { g^{{\alpha { \prime}}}}{}_{(\alpha}g_{\;\;\beta)}^{{\beta { \prime}}}[{u_{{\alpha { \prime}}}}{u_{{\beta { \prime } } } } + 2{r^2}{r_{{\alpha { \prime}}0d0}}{\omega ^d}{u_{{\beta { \prime } } } } + \mathcal{o}({r^3})],$$\end{document } which should be compared with equation ( 501 ) . it should be emphasized that in equation ( 528 ) and all equations below , all frame components are evaluated at the retarded point x , and not at the advanced point . the preceding computation gives us also an expansion for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \alpha { \prime\prime}}{\beta { \prime\prime}};{\gamma { \prime\prime}}}}{u^{{\alpha { \prime}}}}{u^{{\beta { \prime\prime}}}}{u^{{\gamma { \prime\prime } } } } = { \dot u_{\alpha \beta}}(u ) + { \ddot u_{\alpha \beta}}(u){\delta { \prime } } + \mathcal{o}({\delta ^{\prime 2}}),$$\end{document } which becomes 529\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \alpha { \prime\prime}}{\beta { \prime\prime}};{\gamma { \prime\prime}}}}{u^{{\alpha { \prime\prime}}}}{u^{{\beta { \prime\prime}}}}{u^{{\gamma { \prime\prime } } } } = { g^{{\alpha { \prime}}}}{}_{(\alpha}g_{\;\;\beta)}^{{\beta { \prime}}}[r{r_{{\alpha { \prime}}0d0}}{\omega ^d}{u_{{\beta { \prime } } } } + \mathcal{o}({r^2})],$$\end{document } and which is identical to equation ( 503 ) . we proceed similarly to obtain an expansion for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{\alpha \beta { \alpha ^{\prime \prime}}{\beta ^{\prime \prime}};\gamma}}{u^{{\alpha ^{\prime \prime}}}}{u^{{\beta ^{\prime \prime}}}}$\end{document}. here we introduce the functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{\alpha \beta \gamma}}(\tau ) \equiv { u_{\alpha \beta \mu \nu ; \gamma}}{u^\mu}{u^\nu}$\end{document } and express \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{\alpha \beta { \alpha ^{\prime \prime}}{\beta ^{\prime \prime}};\gamma}}{u^{{\alpha ^{\prime \prime}}}}{u^{{\beta ^{\prime \prime}}}}$\end{document } as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{\alpha \beta \gamma}}(v ) = { u_{\alpha \beta \gamma}}(u ) + { { \dot u}_{\alpha \beta \gamma}}(u){\delta \prime } + { \mathcal o}({\delta \prime}^2)$\end{document}. the leading term \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${u_{\alpha \beta \gamma}}(u ) \equiv { u_{\alpha \beta { \alpha \prime}{\beta \prime};\gamma}}{u^{{\alpha \prime}}}{u^{{\beta \prime}}}$\end{document } was computed in equation ( 502 ) , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\dot u_{\alpha \beta \gamma}}(u ) = { u_{\alpha \beta { \alpha { \prime}}{\beta { \prime}};\gamma { \gamma { \prime}}}}{u^{{\alpha { \prime}}}}{u^{{\beta { \prime}}}}{u^{{\gamma { \prime } } } } = { g^{{\alpha { \prime}}}}{}_{(\alpha}g_{\;\;\beta)}^{{\beta { \prime}}}g_{\;\;\gamma}^{{\gamma { \prime}}}[{r_{{\alpha { \prime}}0{\gamma { \prime}}0}}{u_{{\beta { \prime } } } } + \mathcal{o}({r^2})]$$\end{document } follows from equation ( 359 ) . combining these results together with equation ( 229 ) for gives 530\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \alpha { \prime\prime}}{\beta { \prime\prime}};\gamma}}{u^{{\alpha { \prime\prime}}}}{u^{{\beta { \prime\prime } } } } = { g^{{\alpha { \prime}}}}{}_{(\alpha}g_{\;\;\beta)}^{{\beta { \prime}}}g_{\;\;\gamma}^{{\gamma { \prime}}}[r({r_{{\alpha { \prime}}0{\gamma { \prime}}0 } } - { r_{{\alpha { \prime}}0{\gamma { \prime}}d}}{\omega ^d}){u_{{\beta { \prime } } } } + \mathcal{o}({r^2})],$$\end{document } and this should be compared with equation ( 502 ) . the last expansion we shall need is 531\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_{\alpha \beta { \alpha { \prime\prime}}{\beta { \prime\prime}}}}{u^{{\alpha { \prime\prime}}}}{u^{{\beta { \prime\prime } } } } = { g^{{\alpha { \prime}}}}{}_{(\alpha}g_{\;\;\beta)}^{{\beta { \prime}}}[{r_{{\alpha { \prime}}0{\beta { \prime}}0 } } + \mathcal{o}(r)],$$\end{document } which is identical to equation ( 504 ) . we obtain the frame components of the singular gravitational field by substituting these expansions into equation ( 527 ) and projecting against the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document}. after some algebra we arrive at 532\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { 000}^{\rm{s}}(u , r,{\omega ^a } ) \equiv \gamma _ { \alpha \beta ; \gamma}^{\rm{s}}(x)e_0^\alpha ( x)e_0^\beta ( x)e_0^\gamma ( x ) = 2m{r_{a0b0}}{\omega ^a}{\omega ^b}\mathcal{o}(r),$$\end{document } 533\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { 0b0}^{\rm{s}}(u , r,{\omega ^a } ) \equiv \gamma _ { \alpha \beta ; \gamma}^{\rm{s}}(x)e_0^\alpha ( x)e_b^\beta ( x)e_0^\gamma ( x ) = - 4m{r_{b0c0}}{\omega ^c } + \mathcal{o}(r),$$\end{document } 534\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { ab0}^{\rm{s}}(u , r,{\omega ^a } ) \equiv \gamma _ { \alpha \beta ; \gamma}^{\rm{s}}(x)e_a^\alpha ( x)e_b^\beta ( x)e_0^\gamma ( x ) = \mathcal{o}(r),$$\end{document } 535\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{\gamma _ { 00c}^{\rm{s}}(u , r,{\omega ^a } ) \equiv \gamma _ { \alpha \beta ; \gamma}^{\rm{s}}(x)e_0^\alpha ( x)e_0^\beta ( x)e_c^\gamma ( x)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{= - 4m\left [ { \left({{1 \over { { r^2 } } } + { 1 \over 3}{r_{a0b0}}{\omega ^a}{\omega ^b } } \right){\omega _ c } + { 1 \over 6}{r_{c0b0}}{\omega ^b } - { 1 \over 6}{r_{ca0b}}{\omega ^a}{\omega ^b } } \right ] + { \mathcal o}(r),}\\\end{array}$$\end{document } 536\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { 0bc}^{\rm{s}}(u , r,{\omega ^a } ) \equiv \gamma _ { \alpha \beta ; \gamma}^{\rm{s}}(x)e_0^\alpha ( x)e_b^\beta ( x)e_c^\gamma ( x ) = 2m({r_{b0cd}}{\omega ^d } + { r_{b0d0}}{\omega ^a}{\omega _ c } ) + \mathcal{o}(r),$$\end{document } 537\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { abc}^{\rm{s}}(u , r,{\omega ^a } ) \equiv \gamma _ { \alpha \beta ; \gamma}^{\rm{s}}(x)e_a^\alpha ( x)e_b^\beta ( x)e_c^\gamma ( x ) = - 4m{r_{a0b0}}{\omega _ c } + \mathcal{o}(r),$$\end{document } in which all frame components are evaluated at the retarded point x. comparison of these expressions with equations ( 505 , 506 , 507 , 508 , 509 , 510 ) reveals identical singularity structures for the retarded and singular gravitational fields . the difference between the retarded field of equations ( 505 , 506 , 507 , 508 , 509 , 510 ) and the singular field of equations ( 532 , 533 , 534 , 535 , 536 , 537 ) defines the radiative gravitational field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \alpha \beta ; \gamma}^{\rm{r}}$\end{document } its tetrad components are 538\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { 000}^{\rm{r } } = \gamma _ { 000}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } 539\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { 0b0}^{\rm{r } } = \gamma _ { 0b0}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } 540\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { ab0}^{\rm{r } } = 4m{r_{a0b0 } } + \gamma _ { ab0}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } 541\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { 00c}^{\rm{r } } = \gamma _ { 00c}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } 542\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { 0bc}^{\rm{r } } = 2m{r_{b0c0 } } + \gamma _ { 0bc}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } 543\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { abc}^{\rm{r } } = \gamma _ { abc}^{{\rm{tail } } } + \mathcal{o}(r),$$\end{document } and we see that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \alpha \beta ; \gamma}^{\rm{r}}$\end{document } is smooth in the limit r 0 . we may therefore evaluate the radiative field directly at x = x , where the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(e_0^\alpha , e_a^\alpha)$\end{document } coincides with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({u^{{\alpha \prime}}},e_a^{{\alpha \prime}})$\end{document}. after reconstructing the field at x from its frame components , we obtain 544\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { { \alpha { \prime}}{\beta { \prime}};{\gamma { \prime}}}^{\rm{r}}({x{\prime } } ) = - 4m(u{}_{({\alpha { \prime}}}{r_{{\beta { \prime}}){\delta { \prime}}{\gamma { \prime}}{\epsilon { \prime } } } } + { r_{{\alpha { \prime}}{\delta { \prime}}{\gamma { \prime}}{\epsilon { \prime}}}}{u_{{\gamma { \prime}}}}){u^{{\delta { \prime}}}}{u^{{\epsilon { \prime } } } } + \gamma _ { { \alpha { \prime}}{\beta { \prime}}{\gamma { \prime}}}^{{\rm{tail}}},$$\end{document } where the tail term can be copied from equation ( 500 ) , 545\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { { \alpha { \prime}}{\beta { \prime}}{\gamma { \prime}}}^{{\rm{tail}}}({x{\prime } } ) = 4m\int\nolimits_{- \infty}^{{u^ - } } { { \nabla _ { { \gamma { \prime}}}}{g_{+ { \alpha { \prime}}{\beta { \prime}}\mu \nu}}({x{\prime}},z){u^\mu}{u^\nu}d\tau}.$$\end{document } the tensors that appear in equation ( 545 ) all refer to the retarded point x z(u ) which can now be treated as an arbitrary point on the world line . the retarded gravitational field ; of a point particle is singular on the world line , and this behaviour makes it difficult to understand how the field is supposed to act on the particle and influence its motion . the field s singularity structure was analyzed in sections 5.3.3 and 5.3.4 , and in section 5.3.5 it was shown to originate from the singular field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \alpha \beta ; \gamma}^{\rm{s}}$\end{document } ; the radiative field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \alpha \beta ; \gamma}^{\rm{r}}$\end{document } was then shown to be smooth on the world line . to make sense of the retarded field s action on the particle we can follow the discussions of section 5.1.6 and 5.2.6 and postulate that the self gravitational field of the point particle is either ; as worked out in equation ( 523 ) , or \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \mu \nu ; \lambda}^{\rm{r}}$\end{document } as worked out in equation ( 544 ) . these regularized fields are both given by 546\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { \mu \nu ; \lambda}^{{\rm{reg } } } = - 4m(u{}_{(\mu}{r_{\nu)\rho \lambda \xi } } + { r_{\mu \rho \nu \xi}}{u_\lambda}){u^\rho}{u^\xi } + \gamma _ { \mu \nu \lambda}^{{\rm{tail}}}$$\end{document } and 547\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { \mu \nu \lambda}^{{\rm{tail } } } = 4m\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla _ \lambda}{g_{+ \mu \nu { \mu { \prime}}{\nu { \prime}}}}(z(\tau),(z({\tau { \prime}})){u^{{\mu { \prime}}}}{u^{{\nu { \prime}}}}d{\tau { \prime}},}$$\end{document } in which all tensors are now evaluated at an arbitrary point z( ) on the world line . the actual gravitational perturbation h is obtained by inverting equation ( 491 ) , which leads to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h_{\mu \nu ; \lambda } } = { \gamma _ { \mu \nu ; \gamma } } - { 1 \over 2}{g_{\mu \nu}}{\gamma ^\rho}_{\rho ; \lambda}$\end{document}. substituting equation ( 546 ) yields 548\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h_{\mu \nu ; \lambda}^{{\rm{reg } } } = - 4m(u{}_{(\mu}{r_{\nu)\rho \lambda \xi } } + { r_{\mu \rho \nu \xi}}{u_\lambda}){u^\rho}{u^\xi } + h_{\mu \nu \lambda}^{{\rm{tail}}},$$\end{document } where the tail term is given by the trace - reversed counterpart to equation ( 547 ) : 549\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h_{\mu \nu \lambda}^{{\rm{tail } } } = 4m\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla _ \lambda}\left({{g_{+ \mu \nu { \mu { \prime}}{\nu { \prime } } } } - { 1 \over 2}{g_{\mu \nu}}g_{+ \;\;\rho { \mu { \prime}}{\nu { \prime}}}^{\;\;\;\rho } } \right)(z(\tau),z({\tau { \prime}})){u^{{\mu { \prime}}}}{u^{{\nu { \prime}}}}d{\tau { \prime}}.}$$\end{document } when this regularized field is substituted into equation ( 494 ) , we find that the terms that depend on the riemann tensor cancel out , and we are left with 550\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{d{u^\mu } } \over { d\tau } } = - { 1 \over 2}({g^{\mu \nu } } + { u^\mu}{u^\nu})(2h_{\nu \lambda \rho}^{{\rm{tail } } } - h_{\lambda \rho \nu}^{{\rm{tail}}}){u^\lambda}{u^\rho}.$$\end{document } we see that only the tail term is involved in the final form of the equations of motion . the tail integral of equation ( 549 ) involves the current position z( ) of the particle , at which all tensors with unprimed indices are evaluated , as well as all prior positions z( ) , at which all tensors with primed indices are evaluated . the tail integral is cut short at = 0 to avoid the singular behaviour of the retarded green s function at coincidence ; this limiting procedure was justified at the beginning of section 5.3.3 . equation ( 550 ) was first derived by yasushi mino , misao sasaki , and takahiro tanaka in 1997 . ( an incomplete treatment had been given previously by morette - dewitt and ging . ) an alternative derivation was then produced , also in 1997 , by theodore c. quinn and robert m. wald . it should be noted that equation ( 550 ) is formally equivalent to the statement that the point particle moves on a geodesic in a spacetime with metric \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\alpha \beta } } + h_{\alpha \beta}^{\rm{r}}$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha \beta}^{\rm{r}}$\end{document } is the radiative metric perturbation obtained by trace - reversal of the potentials \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \alpha \beta}^{\rm{r } } \equiv { \gamma _ { \alpha \beta } } - \gamma _ { \alpha \beta}^{\rm{s}}$\end{document } ; this perturbed metric is smooth on the world line , and it is a solution to the vacuum field equations . this elegant interpretation of the misataquwa equations was proposed in 2002 by steven detweiler and bernard f. whiting . quinn and wald have shown that under some conditions , the total work done by the gravitational self - force is equal to the energy radiated ( in gravitational waves ) by the particle . the equations of motion derived in the preceding section 5.3.6 refer to a specific choice of gauge for the metric perturbation h produced by a point particle of mass m. we indeed recall that back at equation ( 492 ) we imposed the lorenz gauge condition \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\gamma ^{\alpha \beta}}_{;\beta } = 0$\end{document } on the gravitational potentials \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\gamma _ { \alpha \beta } } \equiv { h_{\alpha \beta } } - { 1 \over 2}({g^{\gamma \delta}}{h_{\gamma \delta}}){g_{\alpha \beta}}$\end{document}. by virtue of this condition we found that the potentials satisfy the wave equation of equation ( 493 ) in a background spacetime with metric g. the hyperbolic nature of this equation allowed us to identify the retarded solution as the physically relevant solution , and the equations of motion were obtained by removing the singular part of the retarded field . once the equations of motion have been formulated , however , the freedom of performing a gauge transformation ( either away from the lorenz gauge , or within the class of lorenz gauges ) should be explored . a gauge transformation will affect the form of the equations of motion : these must depend on the choice of coordinates , and there is no reason to expect equation ( 550 ) to be invariant under a gauge transformation . our purpose in this section is to work out how the equations of motion change under such a transformation . we introduce a coordinate transformation of the form 551\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${x^\alpha } \rightarrow { x^\alpha } + { \xi ^\alpha},$$\end{document } where x are the coordinates of the background spacetime , and is a vector field that we take to be of order m. we assume that is smooth in a neighbourhood of the world line . the coordinate transformation changes the background metric according to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\alpha \beta } } \rightarrow { g_{\alpha \beta } } - { \xi _ { \alpha ; \beta } } - { \xi _ { \beta ; \alpha } } + \mathcal{o}({m^2}),$$\end{document } and this change can be interpreted as a gauge transformation of the metric perturbation created by the moving particle : 552\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h_{\alpha \beta } } \rightarrow { h_{\alpha \beta } } - { \xi _ { \alpha ; \beta } } - { \xi _ { \beta ; \alpha}}.$$\end{document } this , in turn , produces a change in the particle s acceleration , 553\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^\mu } \rightarrow { a^\mu } + a{[\xi ] ^\mu},$$\end{document } where a is the acceleration of equation ( 550 ) and a[ ] is the gauge acceleration generated by the vector field . to compute the gauge acceleration we substitute equation ( 552 ) into equation ( 494 ) , and we simplify the result by invoking ricci s identity , ; ; = r , and the fact that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^\mu } = { \mathcal o}(m)$\end{document}. the final expression is 554\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a{[\xi ] ^\mu } = ( { \delta ^\mu}_\nu + { u^\mu}{u_\nu})\left({{{{d^2}{\xi ^\nu } } \over { d{\tau ^2 } } } + r_{\rho \omega \lambda}^\nu { u^\rho}{\xi ^\omega}{u^\lambda } } \right),$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${d^2}{\xi ^\nu}/d{\tau ^2 } = ( { \xi ^\nu}_{;\mu}{u^\mu}){;_\rho}{u^\rho}$\end{document } is the second covariant derivative of in the direction of the world line . the expression within the large brackets is familiar from the equation of geodesic deviation , which states that this quantity vanishes if is a deviation vector between two neighbouring geodesics . equation ( 553 ) , with a[ ] given by equation ( 554 ) , is therefore a generalized version of this statement . the derivation of the misataquwa equations of motion presented in section 5.3 was framed within the paradigm introduced in sections 5.1 and 5.2 to describe the motion of a point scalar charge , and a point electric charge , respectively . while this paradigm is well suited to fields that satisfy linear wave equations , it is not the best conceptual starting point in the nonlinear context of general relativity . the linearization of the einstein field equations with respect to the small parameter m did allow us to use the same mathematical techniques as in sections 5.1 and 5.2 , but the validity of the perturbative method must be critically examined when the gravitational potentials are allowed to be singular . so while equation ( 550 ) does indeed give the correct equations of motion when m is small , its previous derivation leaves much to be desired . in this section the point mass will be replaced by a nonrotating black hole , and the perturbation s singular behaviour on the world line will be replaced by a well - behaved metric at the event horizon . we will use the powerful technique of matched asymptotic expansions [ 35 , 31 , 58 , 19 , 1 , 20 ] . the problem presents itself with a clean separation of length scales , and the method relies entirely on this . on the one hand we have the length scale associated with the small black hole , which is set by its mass m. on the other hand we have the length scale associated with the background spacetime in which the black hole moves , which is set by the radius of curvature \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal r}$\end{document } ; formally this is defined so that a typical component of the background spacetime s riemann tensor is equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$1/{{\mathcal r}^2}$\end{document } up to a numerical factor of order unity . we demand that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m/{\mathcal r } \ll 1$\end{document}. as before we assume that the background spacetime contains no matter , so that its metric is a solution to the einstein field equations in vacuum . for example , suppose that our small black hole of mass m is on an orbit of radius b around another black hole of mass m. then \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal r } \sim b\sqrt { b / m } > b$\end{document } and we take m to be much smaller than the orbital separation . notice that the time scale over which the background geometry changes is of the order of the orbital period \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$b\sqrt { b / m } \sim{\mathcal r}$\end{document } , so that this does not constitute a separate scale . similarly , the inhomogeneity scale the length scale over which the riemann tensor of the background spacetime changes is of order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$b\sim { \mathcal r}\sqrt { m / b } < { \mathcal r}$\end{document } and also does not constitute an independent scale . ( in this discussion we have considered b / m to be of order unity , so as to represent a strong - field , fast - motion situation . ) let r be a meaningful measure of distance from the small black hole , and let us consider a region of spacetime defined by r < ri , where ri is a constant that is much smaller than \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal r}$\end{document}. this inequality defines a narrow world tube that surrounds the small black hole , and we shall call this region the internal zone ( see figure 10 ) . in the internal zone the gravitational field is dominated by the black hole , and the metric can be expressed as 555\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{g}}({\rm{internal}}\;{\rm{zone } } ) = g({\rm{black}}\;{\rm{hole } } ) + { h_1}/\mathcal{r } + { h_2}/{\mathcal{r}^2 } + \ldots,$$\end{document } where g(black hole ) is the metric of a nonrotating black hole in isolation ( as given by the unperturbed schwarzschild solution ) , while h1 and h2 are corrections associated with the conditions in the external universe . the metric of equation ( 555 ) represents a black hole that is distorted by the tidal gravitational field of the external universe , and h1 , h2 are functions of m and the spacetime coordinates that can be obtained by solving the einstein field equations . they must be such that the spacetime possesses a regular event horizon near r = 2 m , and such that g(internal zone ) agrees with the metric of the external universe the metric of the background spacetime in the absence of the black hole when r m. as we shall see in section 5.4.2 , h1 actually vanishes and the small correction \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h_2}/{{\mathcal r}^2}$\end{document } can be obtained by employing the well - developed tools of black - hole perturbation theory [ 51 , 59 , 63 ] . figure 10a black hole , represented by the black disk , is immersed in a background spacetime . the internal zone extends from r = 0 to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r = { r_i } \ll { \mathcal r}$\end{document } , while the external zone extends from r = re m to r = . when \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m \ll { \mathcal r}$\end{document } there exists a buffer zone that extends from r = re to r = ri . in the buffer zone m / r and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r/{\mathcal r}$\end{document } are both small . a black hole , represented by the black disk , is immersed in a background spacetime . the internal zone extends from r = 0 to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r = { r_i } \ll { \mathcal r}$\end{document } , while the external zone extends from r = re m to r = . when \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m \ll { \mathcal r}$\end{document } there exists a buffer zone that extends from r = re to r = ri . in the buffer zone m / r and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r/{\mathcal r}$\end{document } are both small . consider now a region of spacetime defined by r > re , where re is a constant that is much larger than m ; this region will be called the external zone ( see figure 10 ) . in the external zone the gravitational field is dominated by the conditions in the external universe , and the metric can be expressed as 556\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{g}}({\rm{external}}\;{\rm{zone } } ) = g({\rm{background}}\;{\rm{spacetime } } ) + m{h_1 } + { m^2}{h_2 } + \ldots,$$\end{document } where g(background spacetime ) is the unperturbed metric of the background spacetime in which the black hole is moving , while h1 and h2 are corrections associated with the hole s presence ; these are functions of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal r}$\end{document } and the spacetime coordinates that can be obtained by solving the einstein field equations . we shall truncate equation ( 556 ) to first order in m , and mh1 will be calculated in section 5.4.3 by linearizing the field equations about the metric of the background spacetime . in the external zone the perturbation associated with the presence of a black hole can not be distinguished from the perturbation produced by a point particle of the same mass , and mh1 will therefore be obtained by solving equation ( 493 ) in the background spacetime . the metric g(external zone ) returned by the procedure described in the preceding paragraph is a functional of a world line that represents the motion of the small black hole in the background spacetime . our goal is to obtain a description of this world line , in the form of equations of motion to be satisfied by the black hole ; these equations will be formulated in the background spacetime . it is important to understand that fundamentally , exists only as an external - zone construct : it is only in the external zone that the black hole can be thought of as moving on a world line ; in the internal zone the black hole is revealed as an extended object and the notion of a world line describing its motion is no longer meaningful . equations ( 555 ) and ( 556 ) give two different expressions for the metric of the same spacetime ; the first is valid in the internal zone \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r < { r_i } \ll { \mathcal r}$\end{document } , while the second is valid in the external zone r > re m. the fact that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal r } \gg m$\end{document } allows us to define a buffer zone in which r is restricted to the interval re < r < ri . in the buffer zone r is simultaneously much larger than m and much smaller than \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal r}$\end{document } a typical value might be \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt { m{\mathcal r}}$\end{document } and equations ( 555 , 556 ) are simultaneously valid . since the two metrics are the same up to a diffeomorphism , these expressions must agree . and since g(external zone ) is a functional of a world line while g(internal zone ) contains no such information , matching the metrics necessarily determines the motion of the small black hole in the background spacetime . what we have here is a beautiful implementation of the general observation that the motion of self - gravitating bodies is determined by the einstein field equations . it is not difficult to recognize that the metrics of equations ( 555 , 556 ) can be matched in the buffer zone . when r m in the internal zone , the metric of the unperturbed black hole can be expanded as g(black hole ) = m / r m / r , where is the metric of flat spacetime ( in asymptotically inertial coordinates ) and the symbol means and a term of the form . on the other hand , dimensional analysis dictates that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h_1}/{\mathcal r}$\end{document } be of the form \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r/{\mathcal r } \oplus m/{\mathcal r } \oplus { m^2}/\left({r{\mathcal r } } \right ) \oplus \ldots$\end{document } while \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h_2}/{{\mathcal r}^2}$\end{document } should be expressed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${r^2}/{{\mathcal r}^2 } \oplus mr/{{\mathcal r}^2 } \oplus { m^2}/{{\mathcal r}^2 } \oplus \ldots$\end{document}. altogether we obtain 557\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{\rm{g}}({\rm{buffer}}\;{\rm{zone } } ) = \eta \oplus m / r \oplus { m^2}/{r^2 } \oplus \ldots \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{\oplus \;r/{\mathcal r } \oplus m/{\mathcal r } \oplus { m^2}/(r{\mathcal r } ) \oplus \ldots \quad}\\{\oplus \;{r^2}/{{\mathcal r}^2 } \oplus mr/{{\mathcal r}^2 } \oplus { m^2}/{{\mathcal r}^2 } \oplus \ldots}\\{\oplus \ldots \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } for the buffer - zone metric . if instead we approach the buffer zone from the opposite side , letting r be much smaller than \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal r}$\end{document } in the external zone , we have that the metric of the background spacetime can be expressed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g\left({{\rm{background}}\,{\rm{spacetime } } } \right ) = \eta \oplus r/{\mathcal r } \oplus { r^2}/{{\mathcal r}^2 } \oplus \ldots$\end{document } , where the expansion now uses world - line based coordinates such as the fermi normal coordinates of section 3.2 or the retarded coordinates of section 3.3 . on dimensional grounds we also have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m{h_1 } = m / r \oplus m/{\mathcal r } \oplus mr/{{\mathcal r}^2 } \oplus \ldots$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${m^2}{h_2 } = { m^2}/{r^2 } \oplus { m^2}/\left({r{\mathcal r } } \right ) \oplus { m^2}/{{\mathcal r}^2 } \oplus \ldots$\end{document}. altogether this gives 558\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{\rm{g}}({\rm{buffer}}\;{\rm{zone } } ) = \eta \oplus r/{\mathcal r } \oplus { r^2}/{{\mathcal r}^2 } \oplus \ldots \quad \;\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{\oplus \;m / r \oplus m/{\mathcal r } \oplus mr/{{\mathcal r}^2 } \oplus \ldots \quad \quad \quad}\\{\oplus \;{m^2}/{r^2 } \oplus { m^2}/(r{\mathcal r } ) \oplus { m^2}/{{\mathcal r}^2 } \oplus \ldots \;\;}\\{\oplus \ldots \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\\end{array}$$\end{document } for the buffer - zone metric . apart from a different ordering of terms , the metrics of equations ( 557 ) and ( 558 ) have identical forms . matching the metrics of equations ( 555 ) and ( 556 ) in the buffer zone can be carried out in practice only after performing a transformation from the external coordinates used to express g(external zone ) to the internal coordinates employed for g(internal zone ) . the details of this coordinate transformation will be described in section 5.4.4 , and the end result of matching the misataquwa equations of motion will be revealed in section 5.4.5 . to flesh out the ideas contained in the previous section 5.4.1 we first calculate the internal - zone metric and replace equation ( 555 ) by a more concrete expression . we recall that the internal zone is defined by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r < { r_i } \ll { \mathcal r}$\end{document } where r is a suitable measure of distance from the black hole . we begin by expressing g(black hole ) , the schwarzschild metric of an isolated black hole of mass m , in terms of retarded eddington - finkelstein coordinates \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\left({\bar u,\,\bar r,\,{{\bar \theta}^a } } \right)$\end{document } where is retarded time , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar r$\end{document } the usual areal radius , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar \theta ^a } = \left({\bar \theta , \ , \bar \phi } \right)$\end{document } are two angles spanning the two - spheres of constant and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar r$\end{document}. the metric is given by 559\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d{s^2 } = - f\;d{\bar u^2 } - 2d\bar ud\bar r + { r^2}d{\bar \omega ^2},\quad \quad f = 1 - { { 2 m } \over { \bar r}},$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d{\bar \omega ^2 } = { \bar \omega _ { ab}}d{\bar \theta ^a}d{\bar \theta ^b } = d{\bar \theta ^2 } + { \sin ^2}\bar \theta d{\bar \phi ^2}$\end{document } is the line element on the unit two - sphere . in the limit r m this metric achieves the asymptotic values \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{\bar u\bar u } } \rightarrow - 1,\quad \quad { g_{\bar u\bar r } } = - 1,\quad \quad { g_{\bar u\bar a } } = 0,\quad \quad { g_{\bar a\bar b } } = { r^2}{\bar \omega _ { ab}};$$\end{document } these are appropriate for a black hole immersed in a flat spacetime charted by retarded coordinates . the corrections h1 and h2 in equation ( 555 ) encode the information that our black hole is not isolated but in fact immersed in an external universe whose metric becomes g(background spacetime ) asymptotically . in the internal zone the metric of the background spacetime can be expanded in powers of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar r/{\mathcal r}$\end{document } and expressed in a form that can be directly imported from section 3.3 . if we assume for the moment that the world line \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar r = 0$\end{document } has no acceleration in the background spacetime ( a statement that will be justified shortly ) , then the asymptotic values of g(internal zone ) must be given by equations ( 210 , 211 , 212 , 213 ) : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{{\rm{g}}_{\bar u\bar u } } \rightarrow - 1 - { r^2}{{\overline { \mathcal e}}^ \ast } + { \mathcal o}({r^3}/{{\mathcal r}^3}),\quad \quad } & { { { \rm{g}}_{\bar u\bar r } } = - 1,\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \;}\\{{{\rm{g}}_{\bar u\bar a } } \rightarrow { 2 \over 3}{{\bar r}^3}(\overline { \mathcal e } _ a^ \ast + \bar { \mathcal b}_a^ \ast ) + { \mathcal o}({{\bar r}^4}/{{\mathcal r}^3 } ) , } & { \quad { { \rm{g}}_{\bar a\bar b } } \rightarrow { { \bar r}^2}{{\bar \omega}_{ab } } - { 1 \over 3}{{\bar r}^4}(\overline { \mathcal e } _ { ab}^ \ast + \bar { \mathcal b}_{ab}^ \ast ) + { \mathcal o}({{\bar r}^5}/{{\mathcal r}^3}),}\\\end{array}$$\end{document } where 560\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\overline{\mathcal{e } } ^{\ast } } = { \mathcal{e}_{ab}}{\bar \omega ^a}{\bar \omega ^b},\quad \quad \overline{\mathcal{e } } _ a^{\ast } = { \mathcal{e}_{ab}}\bar \omega _ a^a{\bar \omega ^b},\quad \quad \overline{\mathcal{e } } _ { ab}^{\ast } = 2{\mathcal{e}_{ab}}\bar \omega _ a^a\bar \omega _ b^b + { \overline{\mathcal{e } } ^{\ast}}{\bar \omega _ { ab}}$$\end{document } and 561\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\overline{\mathcal{b}}_a^{\ast } = { \varepsilon _ { abc}}\bar \omega _ a^a{\bar \omega ^b}{\mathcal{b}^c}_d{\bar \omega ^d},\quad \quad \overline{\mathcal{b}}_{ab}^{\ast } = 2{\varepsilon _ { acd}}{\bar \omega ^c}{\mathcal{b}^d}_b\bar \omega _ a^{(a}\bar \omega _ recall that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar \omega ^a } = \left({\sin \bar \theta \cos \bar \phi , \ , \sin \bar \theta \sin \bar \phi , \ , \cos \theta } \right)$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar \omega _ a^a = \partial { \bar \omega ^a}/\partial { \bar \theta ^a}$\end{document}. apart from an angular dependence made explicit by these relations , the tidal fields depend on through the frame components \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal e}ab \equiv { r_{a0b0 } } = { \mathcal o}\left({1/{{\mathcal r}^2 } } \right)$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal b}^a}_b \equiv { 1 \over 2}{\varepsilon ^{acd}}{r_{0bcd } } = { \mathcal o}\left({1/{{\mathcal r}^2 } } \right)$\end{document } of the riemann tensor . ( this is the riemann tensor of the background spacetime evaluated at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar r = 0$\end{document}. ) notice that we have incorporated the fact that the ricci tensor vanishes at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar r = 0:$\end{document } the black hole moves in a vacuum spacetime . the modified asymptotic values lead us to the following ansatz for the internal - zone metric : 562\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{g}}_{\bar u\bar u } } = - f[1 + { \bar r^2}{e_1}(\bar r){\overline{\mathcal{e } } ^{\ast } } ] + \mathcal{o}({r^3}/{\mathcal{r}^3}),$$\end{document } 563\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{g}}_{\bar u\bar r } } = - 1,$$\end{document } 564\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{g}}_{\bar u\bar a } } = { 2 \over 3}{\bar r^3}[{e_2}(r)\overline{\mathcal{e } } _ a^{\ast } + { b_2}(\bar r)\overline{\mathcal{b}}_a^{\ast } ] + \mathcal{o}({\bar r^4}/{\mathcal{r}^3}),$$\end{document } 565\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{g}}_{\bar a\bar b } } = { \bar r^2}{\bar \omega _ { ab } } - { 1 \over 3}{\bar r^4}[{e_3}(\bar r)\overline{\mathcal{e } } _ { ab}^{\ast } + { b_3}(\bar r)\overline{\mathcal{b}}_{ab}^{\ast } ] + \mathcal{o}({\bar r^5}/{\mathcal{r}^3}).$$\end{document } the five unknown functions e1 , e2 , e3 , b2 , and b3 can all be determined by solving the einstein field equations ; they must all approach unity when r m and be well - behaved at r = 2 m ( so that the tidally distorted black hole will have a nonsingular event horizon ) . it is clear from equations ( 562 , 563 , 564 , 565 ) that the assumed deviation of g(internal zone ) with respect to g(black hole ) scales as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$1/{{\mathcal r}^2}$\end{document}. it is therefore of the form of equation ( 555 ) with h1 = 0 . the fact that h1 vanishes comes as a consequence of our previous assumption that the world line \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar r = 0$\end{document } has a zero acceleration in the background spacetime ; a nonzero acceleration of order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$1/{\mathcal r}$\end{document } would bring terms of order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$1/{\mathcal r}$\end{document } to the metric , and h1 would then be nonzero . as i shall explain in the next paragraph ( and you might also refer back to the discussion of section 5.3.7 ) , the reason is simply that it reflects a choice of coordinate system : setting the acceleration to zero amounts to adopting a specific and convenient gauge condition . this gauge differs from the lorenz gauge adopted in section 5.3 , and it will be our choice in this section only ; in the following section 5.4.3 we will return to the lorenz gauge , and the acceleration will be seen to return to its standard misataquwa expression . inspection of equations ( 560 ) and ( 561 ) reveals that the angular dependence of the metric perturbation is generated entirely by scalar , vectorial , and tensorial spherical harmonics of degree = 2 . in particular , h2 contains no = 0 and = 1 modes , and this statement reflects a choice of gauge condition . zerilli has shown that a perturbation of the schwarzschild spacetime with = 0 corresponds to a shift in the mass parameter . as thorne and hartle have shown , a black hole interacting with its environment will undergo a change of mass , but this effect is of order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${m^3}/{{\mathcal r}^2}$\end{document } and thus beyond the level of accuracy of our calculations . there is therefore no need to include \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ell = 0$\end{document } terms in h2 . similarly , it was shown by zerilli that odd - parity perturbations of degree = 1 correspond to a shift in the black hole s angular - momentum parameters . as thorne and hartle have shown , a change of angular momentum is quadratic in the hole s angular momentum , and we can ignore this effect when dealing with a nonrotating black hole . there is therefore no need to include odd - parity , = 1 terms in h2 . finally , zerilli has shown that in a vacuum spacetime , even - parity perturbations of degree = 1 correspond to a change of coordinate system these modes are pure gauge . since we have the freedom to adopt any gauge condition , we can exclude even - parity , = 1 terms from the perturbed metric . this leads us to equations ( 562 , 563 , 564 , 565 ) , which contain only = 2 perturbation modes ; the even - parity modes are contained in those terms that involve \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}_{ab}}$\end{document } , while the odd - parity modes are associated with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal b}_{ab}}$\end{document}. the perturbed metric contains also higher multipoles , but those come at a higher order in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$1/{\mathcal r}$\end{document } ; for example , the terms of order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$1/{{\mathcal r}^3}$\end{document } include = 3 modes . we conclude that equations ( 562 , 563 , 564 , 565 ) is a sufficiently general ansatz for the perturbed metric in the internal zone . there remains the task of finding the functions e1 , e2 , e3 , b2 , and b3 . for this it is sufficient to take , say , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}_{12 } } = { { \mathcal e}_{21}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal b}_{12 } } = { { \mathcal b}_{21}}$\end{document } as the only nonvanishing components of the tidal fields ab and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal b}_{ab}}$\end{document}. and since the equations for even - parity and odd - parity perturbations decouple , each case can be considered separately . including only even - parity perturbations , equations ( 562)(565 ) become \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{{\rm{g}}_{\bar u\bar u } } = - f(1 + { { \bar r}^2}{e_1}{{\mathcal e}_{12}}{{\sin}^2}\bar \theta \sin 2\bar \phi),\;\quad \quad \quad \quad \quad \quad } & { { { \rm{g}}_{\bar u\bar r } } = - 1,\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad}\\{{{\rm{g}}_{\bar u\bar \theta } } = { 2 \over 3}{{\bar r}^3}{e_2}{{\mathcal e}_{12}}\sin \bar \theta \cos \bar \theta \sin 2\bar \phi , \quad \quad \quad \quad \quad \quad \quad } & { { { \rm{g}}_{\bar u\bar \phi } } = { 2 \over 3}{{\bar r}^3}{e_2}{{\mathcal e}_{12}}{{\sin}^2}\bar \theta \cos 2\bar \phi , \quad \quad \quad}\\{{{\rm{g}}_{\bar \theta \bar \theta } } = { { \bar r}^2 } - { 1 \over 3}{{\bar r}^4}{e_3}{{\mathcal e}_{12}}(1 + { { \cos}^2}\bar \theta)\sin 2\bar \phi , \quad \quad \quad \quad \quad } & { { { \rm{g}}_{\bar \theta \bar \phi } } = - { 2 \over 3}{{\bar r}^4}{e_3}{{\mathcal e}_{12}}\sin \bar \theta \cos \bar \theta \cos 2\bar \phi , } \\{{{\rm{g}}_{\bar \phi \bar \phi } } = { { \bar r}^2}{{\sin}^2}\bar \theta + { 1 \over 3}{{\bar r}^4}{e_3}{{\mathcal e}_{12}}{{\sin}^2}\bar \theta ( 1 + { { \cos}^2}\bar \theta)\sin 2\bar \phi . } & { } \\\end{array}$$\end{document } this metric is then substituted into the vacuum einstein field equations , g = 0 . calculating the einstein tensor is simplified by linearizing with respect to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}_{12}}$\end{document } and discarding its derivatives with respect to : since the time scale over which \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}_{ab}}$\end{document } changes is of order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal r}$\end{document } , the ratio between temporal and spatial derivatives is of order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\bar r/{\mathcal r}$\end{document } and therefore small in the internal zone ; the temporal derivatives can be consistently neglected . the field equations produce ordinary differential equations to be satisfied by the functions e1 , e2 , and e3 . those are easily decoupled , and demanding that the functions all approach unity as r and be well - behaved at r = 2 m yields the unique solutions 566\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${e_1}(\bar r ) = { e_2}(\bar r ) = f,\quad \quad { e_3}(\bar r ) = 1 - { { 2{m^2 } } \over { { { \bar r}^2}}}.$$\end{document } switching now to odd - parity perturbations , equations ( 562 , 563 , 564 , 565 ) become \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c}{{{\rm{g}}_{\bar u\bar u } } = - f\quad \quad { { \rm{g}}_{\bar u\bar r } } = - 1,\quad \quad { { \rm{g}}_{\bar u\bar \theta } } = - { 2 \over 3}{{\bar r}^3}{b_2}{{\mathcal b}_{12}}\sin \bar \theta \cos 2\bar \phi , \quad \quad { { \rm{g}}_{\bar u\bar \phi } } = { 2 \over 3}{{\bar r}^3}{b_2}{{\mathcal b}_{12}}{{\sin}^2}\bar \theta \cos \bar \theta \sin 2\bar \phi , } \\{{{\rm{g}}_{\bar \theta \bar \theta } } = { { \bar r}^2 } + { 2 \over 3}{{\bar r}^4}{b_3}{{\mathcal b}_{12}}\cos \bar \theta \cos 2\bar \phi , \quad \quad { { \rm{g}}_{\bar \theta \bar \phi } } = - { 1 \over 3}{{\bar r}^4}{b_3}{{\mathcal b}_{12}}\sin \bar \theta ( 1 + { { \cos}^2}\bar \theta)\sin 2\bar \phi , \quad \quad}\\{{{\rm{g}}_{\bar \phi \bar \phi } } = { { \bar r}^2}{{\sin}^2}\bar \theta - { 2 \over 3}{{\bar r}^4}{b_3}{{\mathcal b}_{12}}{{\sin}^2}\bar \theta \cos \bar \theta \cos 2\bar \phi .\quad \quad}\\\end{array}$$\end{document } following the same procedure , we arrive at 567\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${b_2}(\bar r ) = f,\quad \quad { b_3}(\bar r ) = 1.$$\end{document } substituting equations ( 566 ) and ( 567 ) into equations ( 562 , 563 , 564 , 565 ) returns our final expression for the metric in the internal zone . it shall prove convenient to transform g(internal zone ) from the quasi - spherical coordinates \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\left({\bar r,\,{{\bar \theta}^a } } \right)$\end{document } to a set of quasi - cartesian coordinates \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\bar x^a } = \bar r{\bar \omega ^a}\left({{{\bar \theta}^a } } \right)$\end{document}. the transformation rules are worked out in section 3.3.7 and further illustrated in section 3.3.8 . this gives 568\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{g}}_{\bar u\bar u } } = - f(1 + { \bar r^2}f{\overline{\mathcal{e } } ^{\ast } } ) + \mathcal{o}({\bar r^3}/{\mathcal{r}^3}),$$\end{document } 569\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{g}}_{\bar u\bar a } } = - { \bar \omega _ a } + { 2 \over 3}{\bar r^2}f(\overline{\mathcal{e } } _ a^{\ast } + \overline{\mathcal{b}}_a^{\ast } ) + \mathcal{o}({r^3}/{\mathcal{r}^3}),$$\end{document } 570\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{g}}_{\bar a\bar b } } = { \delta _ { ab } } - { \bar \omega _ a}{\bar \omega _ b } - { 1 \over 3}{r^2}\left({1 - 2{{{m^2 } } \over { { { \bar r}^2 } } } } \right)\overline{\mathcal{e } } _ { ab}^{\ast } - { 1 \over 3}{\bar r^2}\overline{\mathcal{b}}_{ab}^{\ast } + \mathcal{o}({r^3}/{\mathcal{r}^3}),$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$f = 1 - 2m/\bar r$\end{document } and where the tidal fields 571\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\overline{\mathcal{e } } ^{\ast } } = { \mathcal{e}_{ab}}{\bar \omega ^a}{\bar \omega ^b},$$\end{document } 572\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\overline{\mathcal{e } } _ a^{\ast } = ( \delta _ a^b - { \bar \omega _ a}{\bar \omega ^b}){\mathcal{e}_{bc}}{\bar \omega ^c},$$\end{document } 573\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\overline{\mathcal{e } } _ { ab}^{\ast } = 2{\mathcal{e}_{ab } } - 2{\bar \omega _ a}{\mathcal{e}_{bc}}{\bar \omega ^c } - 2{\bar \omega _ b}{\mathcal{e}_{ac}}{\bar \omega ^c } + ( { \delta _ { ab } } + { \bar \omega _ a}{\bar \omega _ b}){\overline{\mathcal{e } } ^{\ast}},$$\end{document } 574\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\overline{\mathcal{b}}_a^{\ast } = { \varepsilon _ { abc}}{\bar \omega ^b}\mathcal{b}_d^c{\bar \omega ^d},$$\end{document } 575\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\overline{\mathcal{b}}_{ab}^{\ast } = { \varepsilon _ { acd}}{\bar \omega ^c}\mathcal{b}_e^d(\delta _ b^e - { \bar \omega ^e}{\bar \omega _ b } ) + { \varepsilon _ { bcd}}{\bar \omega ^c}\mathcal{b}_e^d(\delta _ a^e - { \bar \omega ^e}{\bar \omega _ a})$$\end{document } were first introduced in section 3.3.8 . the metric of equations ( 568 , 569 , 570 ) represents the spacetime geometry of a black hole immersed in an external universe and distorted by its tidal gravitational fields . we next move on to the external zone and seek to replace equation ( 556 ) by a more concrete expression ; recall that the external zone is defined by m re < r. as was pointed out in section 5.4.1 , in the external zone the gravitational perturbation associated with the presence of a black hole can not be distinguished from the perturbation produced by a point particle of the same mass ; it can therefore be obtained by solving equation ( 493 ) in a background spacetime with metric g(background spacetime ) . the external - zone metric is decomposed as 576\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{g}}_{\alpha \beta } } = { g_{\alpha \beta } } + { h_{\alpha \beta}},$$\end{document } where g is the metric of the background spacetime and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${h_{\alpha \beta } } = { \mathcal o}\left(m \right)$\end{document } is the perturbation ; we shall work consistently to first order in m and systematically discard all terms of higher order . we relate h to trace - reversed potentials , 577\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h_{\alpha \beta } } = { \gamma _ { \alpha \beta } } - { 1 \over 2}({g^{\gamma \delta}}{\gamma _ { \gamma \delta}}){g_{\alpha \beta}},$$\end{document } and solving the linearized field equations produces 578\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma _ { \alpha \beta}}(x ) = 4m\int\nolimits_\gamma { { g_{+ \alpha \beta \mu \nu } } } ( x,\;z){u^\mu}{u^\nu}d\tau,$$\end{document } where z( ) gives the description of the world line , is proper time in the background spacetime , u = dz / d is the four - velocity , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$g_{+ \,\mu \nu}^{\,\alpha \beta}\left({x,\,z } \right)$\end{document } is the retarded green s function associated with equation ( 493 ) ; the potentials of equation ( 578 ) satisfy the lorenz - gauge condition \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\gamma ^{\alpha \beta}}_{;\beta } = 0$\end{document}. as was pointed out in section 5.4.1 , ( and therefore h ) are functionals of a world line that will be determined by matching g(external zone ) to g(internal zone ) . we now place ourselves in the buffer zone ( where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m \ll r \ll { \mathcal r}$\end{document } and where the matching will take place ) and work toward expressing g(external zone ) as an expansion in powers of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r/{\mathcal r}$\end{document}. for this purpose we will adopt the retarded coordinates ( u , r ) of section 3.3 and rely on the machinery developed there . we have seen in section 3.3.8 that if the world line is a geodesic , if the vectors \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e_a^\mu$\end{document } are parallel transported on the world line , and if the ricci tensor vanishes on , then the metric takes the form given by equations ( 207 , 208 , 209 ) . this form , however , is too restrictive for our purposes : we must allow to have an acceleration , and allow the basis vectors to be transported in the most general way compatible with their orthonormality property ; this transport law is given by equation ( 138 ) , 579\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{de_a^\mu } \over { d\tau } } = { a_a}{u^\mu } + \omega _ a^be_b^\mu,$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a_a}\left(\tau \right ) = { a_\mu}e_a^\mu$\end{document } are the frame components of the acceleration vector a = du / d , and ab( ) = ba( ) is a rotation tensor to be determined . anticipating that aa and ab will both be proportional to m , we express the metric of the background spacetime as 580\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{uu } } = - 1 - 2r{a_a}{\omega ^a } - { r^2}{\mathcal{e}^{\ast } } + \mathcal{o}({r^3}/{\mathcal{r}^3}),$$\end{document } 581\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ua } } = - { \omega _ a } + r(\delta _ a^b - { \omega _ a}{\omega ^b}){a_b } - r{\omega _ { ab}}{\omega ^b } + { 2 \over 3}{r^2}(\mathcal{e}_a^{\ast } + \mathcal{b}_a^{\ast } ) + \mathcal{o}({r^3}/{\mathcal{r}^3}),$$\end{document } 582\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${g_{ab } } = { \delta _ { ab } } - { \omega _ a}{\omega _ b } - { 1 \over 3}{r^2}(\mathcal{e}_{ab}^{\ast } + \mathcal{b}_{ab}^{\ast } ) + \mathcal{o}({r^3}/{\mathcal{r}^3}),$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}^{\ast}},\,{\mathcal e}_a^{\ast},\,{\mathcal e}_{ab}^{\ast},\,{\mathcal b}_a^{\ast}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal b}_{ab}^{\ast}$\end{document } are the tidal gravitational fields first introduced in section 3.3.8 . the metric of equations ( 580 , 581 , 582 ) is obtained from the general form of equations ( 171 , 172 , 173 ) by neglecting quadratic terms in aa and ab and specializing to a zero ricci tensor . to express the perturbation h as an expansion in powers of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r/{\mathcal r}$\end{document } we first go back to equation ( 498 ) and rewrite it in the form 583\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma _ { \alpha \beta}}(x ) = { { 4 m } \over r}{u_{\alpha \beta \gamma { \prime}\delta { \prime}}}(x,\;x{\prime}){u^{\gamma { \prime}}}{u^{\delta { \prime } } } + \gamma _ { \alpha \beta}^{{\rm{tai}}}(x),$$\end{document } in which primed indices refer to the retarded point x z(u ) associated with x , and 584\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { \gamma _ { \alpha \beta}^{{\rm{tail}}}(x ) = 4m\int\nolimits_{{\tau _ < } } ^u { { v_{\alpha \beta \mu \nu } } } ( x,\;z){u^\mu}{u^\nu}\;d\tau + 4m\int\nolimits_{- \infty}^{{\tau _ < } } { { g_{+ \alpha \beta \mu \nu } } } ( x,\;z){u^\mu}{u^\nu}\;d\tau } \\ { \equiv 4m\int\nolimits_{- \infty}^{{u^ - } } { { g_{+ \alpha \beta \mu \nu } } } ( x,\;z){u^\mu}{u^\nu}\;d\tau \quad \quad \quad \quad \quad \quad \quad \;\;\ , } \\ \end{array}$$\end{document } is the tail part of the gravitational potentials ( recall that < is the proper time at which enters x s normal convex neighbourhood from the past ) . we next expand the first term on the right - hand side of equation ( 583 ) with the help of equation ( 501 ) , and the tail term is expanded using equation ( 93 ) in which we substitute equation ( 504 ) and the familiar relation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\sigma ^{\alpha { \prime } } } = - r\left({{u^{\alpha { \prime } } } + { \omega ^a}e_a^{\alpha { \prime } } } \right)$\end{document}. this gives 585\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\gamma _ { \alpha \beta}}(x ) = { g^{\alpha { \prime}}}_\alpha { g^{\beta { \prime}}}_\beta \left [ { { { 4 m } \over r}{u_{\alpha { \prime}}}{u_{\beta { \prime } } } + \gamma _ { \alpha \beta}^{{\rm{tail}}},\ ; + r\gamma _ { \alpha \beta { \prime}\gamma { \prime}}^{{\rm{tail}}}\left({{u^{\gamma { \prime } } } + { \omega ^c}e_c^{\gamma { \prime } } } \right ) + \mathcal{o}(m{r^2}/{\mathcal{r}^3 } ) } \right],$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\gamma _ { \alpha { \prime}\beta { \prime}}^{{\rm{tail}}}$\end{document } is the tensor of equation ( 584 ) evaluated at x , and where 586\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\gamma _ { \alpha { \prime}\beta { \prime}\gamma { \prime}}^{{\rm{tail}}}(x{\prime } ) = 4m\int\nolimits_{- \infty}^{{u^ - } } { { \nabla _ { \gamma { \prime } } } } { g_{+ \alpha { \prime}\beta { \prime}\mu \nu}}(x{\prime},\;z){u^\mu}{u^\nu}d\tau$$\end{document } was first defined by equation ( 545 ) . at this stage we introduce the trace - reversed fields 587\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h_{\alpha { \prime}\beta { \prime}}^{{\rm{tail}}}\;(x{\prime } ) = 4m\int\nolimits_{- \infty}^{{u^ - } } { \left({{g_{+ \alpha { \prime}\beta { \prime}\mu \nu } } - { 1 \over 2}{g_{\alpha { \prime}\beta { \prime}}}g_{+ \;\delta \mu \nu}^{\;\;\delta { \prime } } } \right)(x{\prime},\;z ) } { u^\mu}{u^\nu}d\tau,$$\end{document } 588\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h_{\alpha { \prime}\beta { \prime}\gamma { \prime}}^{{\rm{tail}}}\;(x{\prime } ) = 4m\int\nolimits_{- \infty}^{{u^ - } } { { \nabla _ { \gamma { \prime } } } } \left({{g_{+ \alpha { \prime}\beta { \prime}\mu \nu } } - { 1 \over 2}{g_{\alpha { \prime}\beta { \prime}}}g_{+ \;\delta { \prime}\mu \nu}^{\;\delta { \prime } } } \right)(x{\prime},\;z){u^\mu}{u^\nu}d\tau$$\end{document } and recognize that the metric perturbation obtained from equations ( 577 ) and ( 585 ) is 589\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h_{\alpha \beta}}(x ) = { g^{\alpha { \prime}}}_\alpha { g^{\beta { \prime}}}_\beta \left [ { { { 2 m } \over r}(2{u_{\alpha { \prime}}}{u_{\beta { \prime } } } + { g_{\alpha { \prime}\beta { \prime } } } ) + h_{\alpha { \prime}\beta}^{{\rm{tail } } } , + rh_{\alpha { \prime}\beta { \prime}\gamma { \prime}}^{{\rm{tail}}}\left({{u^{\gamma { \prime } } } + { \omega ^c}e_c^{\gamma { \prime } } } \right ) + \mathcal{o}(m{r^2}/{\mathcal{r}^3 } ) } \right].$$\end{document } this is the desired expansion of the metric perturbation in powers of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r/{\mathcal r}$\end{document}. our next task will be to calculate the components of this tensor in the retarded coordinates ( u , r ) . the first step of this computation is to decompose h in the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\left({e_0^\alpha , \ , e_a^\alpha } \right)$\end{document } that is obtained by parallel transport of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\left({{u^{\alpha { \prime}}},\,e_a^{\alpha { \prime } } } \right)$\end{document } on the null geodesic that links x to its corresponding retarded point x the projections are 590\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h_{00}}(u,\;r,\;{\omega ^a } ) \equiv { h_{\alpha \beta}}e_0^\alpha e_0^\beta = { { 2 m } \over r } + h_{00}^{{\rm{tail}}}(u ) + r[h_{000}^{{\rm{tail}}}(u ) + h_{00c}^{{\rm{tail}}}(u){\omega ^c } ] + \mathcal{o}(m{r^2}/{\mathcal{r}^3}),$$\end{document } 591\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h_{0b}}(u,\;r,\;{\omega ^a } ) \equiv { h_{\alpha \beta}}e_0^\alpha e_b^\beta = h_{0b}^{{\rm{tail}}}(u ) + r[h_{0b0}^{{\rm{tail}}}(u ) + h_{0bc}^{{\rm{tail}}}(u){\omega ^c } ] + \mathcal{o}(m{r^2}/{\mathcal{r}^3}),$$\end{document } 592\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h_{ab}}(u,\;r,\;{\omega ^a } ) \equiv { h_{\alpha \beta}}e_a^\alpha e_b^\beta = { { 2 m } \over r}{\delta _ { ab } } + h_{ab}^{{\rm{tail}}}(u ) + r[h_{ab0}^{{\rm{tail}}}(u ) + h_{abc}^{{\rm{tail}}}(u){\omega ^c } ] + \mathcal{o}(m{r^2}/{\mathcal{r}^3});$$\end{document } on the right - hand side we have the frame components of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha { \prime}\beta { \prime}}^{{\rm{tail}}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha { \prime}\beta { \prime}\gamma { \prime}}^{{\rm{tail}}}$\end{document } taken with respect to the tetrad \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\left({{u^{\alpha { \prime}}},\,e_a^{\alpha { \prime } } } \right)$\end{document } ; these are functions of retarded time u only . the perturbation is now expressed as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h_{\alpha \beta } } = { h_{00}}e_\alpha ^0e_\beta ^0 + { h_{0b}}(e_\alpha ^0e_\beta ^b + e_\alpha ^be_\beta ^0 ) + { h_{ab}}e_\alpha ^ae_\beta ^b,$$\end{document } and its components are obtained by involving equations ( 169 ) and ( 170 ) , which list the components of the tetrad vectors in the retarded coordinates ; this is the second ( and longest ) step of the computation . noting that aa and ab can both be set equal to zero in these equations ( because they would produce negligible terms of order m in h ) , and that sab , sa , and s can all be expressed in terms of the tidal fields \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal e}^{\ast}},\,{\mathcal e}_a^{\ast},\,{\mathcal e}_{ab}^{\ast},\,{\mathcal b}_a^{\ast}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal b}_{ab}^{\ast}$\end{document } using equations ( 204 , 205 , 206 ) , we arrive at 593\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${h_{uu } } = { { 2 m } \over r } + h_{00}^{{\rm{tail } } } + r(2m{\mathcal{e}^{\ast } } + h_{000}^{{\rm{tail } } } + h_{00a}^{{\rm{tail}}}{\omega ^a } ) + \mathcal{o}(m{r^2}/{\mathcal{r}^3}),$$\end{document } 594\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { h_{ua } } = { { 2 m } \over r}{\omega _ a } + h_{0a}^{{\rm{tail } } } + { \omega _ a}h_{00}^{{\rm{tail } } } + r\left [ { 2m{{\mathcal e}^ { \ast}}{\omega _ a } + { { 2 m } \over 3}({\mathcal e}_a^ { \ast } + { \mathcal b}_a^ { \ast } ) + h_{0a0}^{{\rm{tail } } } + { \omega _ a}h_{000}^{{\rm{tail } } } + h_{0ab}^{{\rm{tail}}}{\omega ^b } + { \omega _ a}h_{00b}^{{\rm{tail}}}{\omega ^b } } \right ] } \\ { + \;{\mathcal o}(m{r^2}/{{\mathcal r}^3}),\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ \end{array}$$\end{document } 595\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { h_{ab } } = { { 2 m } \over r}\;({\delta _ { ab } } + { \omega _ a}{\omega _ b } ) + { \omega _ a}{\omega _ b}h_{00}^{{\rm{tail } } } + { \omega _ a}h_{0b}^{{\rm{tail } } } + { \omega _ b}h_{0a}^{{\rm{tail } } } + h_{ab}^{{\rm{tail}}}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { + \;r\;\left [ { - { { 2 m } \over 3}({\mathcal e}_{ab}^ { \ast } + { \omega _ a}{\mathcal e}_b^ { \ast } + { \mathcal e}_a^ { \ast } { \omega _ b } + { \mathcal b}_{ab}^ { \ast } + { \omega _ a}{\mathcal b}_b^ { \ast } + { \omega _ b}{\mathcal b}_a^ { \ast } ) + { \omega _ a}{\omega _ b}\;(h_{000}^{{\rm{tail } } } + h_{00c}^{{\rm{tail}}}{\omega ^c})\quad \quad \;\;\ ; } \right . } \\ { + \left . { { \omega _ a}\;(h_{0b0}^{{\rm{tail } } } + h_{0bc}^{{\rm{tail}}}{\omega ^c } ) + { \omega _ b}\;(h_{0a0}^{{\rm{tail } } } + h_{0ac}^{{\rm{tail}}}{\omega ^c } ) + ( h_{ab0}^{{\rm{tail } } } + h_{abc}^{{\rm{tail}}}{\omega ^c } ) } \right ] + { \mathcal o}(m{r^2}/{{\mathcal r}^3 } ) . } \\ \end{array}$$\end{document } these are the coordinate components of the metric perturbation h in the retarded coordinates ( u , r ) , expressed in terms of frame components of the tail fields \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha { \prime}\beta { \prime}}^{{\rm{tails}}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha { \prime}\beta { \prime}\gamma { \prime}}^{{\rm{tails}}}$\end{document}. the perturbation is expanded in powers of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r/{\mathcal r}$\end{document } and it also involves the tidal gravitational fields of the background spacetime . the external - zone metric is obtained by adding g as given by equations ( 580 , 581 , 582 ) to h as given by equations ( 593 , 594 , 595 ) . the final result is 596\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \rm{g}}_{uu } } = - 1 - { r^2}{{\mathcal e}^ { \ast } } + { \mathcal o}({r^3}/{{\mathcal r}^3})\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \;\ ; } \\ { + { { 2 m } \over r } + h_{00}^{{\rm{tail } } } + r(2m{{\mathcal e}^ { \ast } } - 2{a_a}{\omega ^a } + h_{000}^{{\rm{tail } } } + h_{00a}^{{\rm{tail}}}{\omega ^a } ) + { \mathcal o}(m{r^2}/{{\mathcal r}^3 } ) , } \\ \end{array}$$\end{document } 597\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \rm{g}}_{ua } } = - { \omega _ a } + { 2 \over 3}{r^2}({\mathcal e}_a^ { \ast } + { \mathcal b}_a^ { \ast } ) + { \mathcal o}({r^3}/{{\mathcal r}^3})\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { + { { 2 m } \over r}{\omega _ a } + h_{0a}^{{\rm{tail } } } + { \omega _ a}h_{00}^{{\rm{tail}}}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { \quad \quad + r\left [ { 2m{{\mathcal e}^ { \ast}}{\omega _ a } + { { 2 m } \over 3}({\mathcal e}_a^ { \ast } + { \mathcal b}_a^ { \ast } ) + ( \delta _ a^b - { \omega _ a}{\omega ^b}){a_b } - { \omega _ { ab}}{\omega ^b } + h_{0a0}^{{\rm{tail } } } + { \omega _ a}h_{000}^{{\rm{tail } } } + h_{0ab}^{{\rm{tail}}}{\omega ^b } + { \omega _ a}h_{00b}^{{\rm{tail}}}{\omega ^b } } \right ] } \\ { \quad \quad + { \mathcal o}(m{r^2}/{{\mathcal r}^3}),\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ \end{array}$$\end{document } 598\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \rm{g}}_{ab } } = { \delta _ { ab } } - { \omega _ a}{\omega _ b } - { 1 \over 3}{r^2}({\mathcal e}_{ab}^ { \ast } + { \mathcal b}_{ab}^ { \ast } ) + { \mathcal o}({r^3}/{{\mathcal r}^3})\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { + { { 2 m } \over r}({\delta _ { ab } } + { \omega _ a}{\omega _ b } ) + { \omega _ a}{\omega _ b}h_{00}^{{\rm{tail } } } + { \omega _ a}h_{0b}^{{\rm{tail } } } + { \omega _ b}h_{0a}^{{\rm{tail } } } + h_{ab}^{{\rm{tail}}}\quad \quad \quad \quad \quad \quad \quad \quad } \\ { + r\left [ { - { { 2 m } \over 3}({\mathcal e}_{ab}^ { \ast } + { \omega _ a}{\mathcal e}_b^ { \ast } + { \mathcal e}_a^ { \ast } { \omega _ b } + { \mathcal b}_{ab}^ { \ast } + { \omega _ a}{\mathcal b}_b^ { \ast } + { \omega _ b}{\mathcal b}_a^ { \ast } ) + { \omega _ a}{\omega _ b}(h_{000}^{{\rm{tail } } } + h_{00c}^{{\rm{tail}}}{\omega ^c } ) } \right . } \\ { \quad \quad \left . { + { \omega _ a}(h_{0b0}^{{\rm{tail } } } + h_{0bc}^{{\rm{tail}}}{\omega ^c } ) + { \omega _ b}(h_{0a0}^{{\rm{tail } } } + h_{0ac}^{{\rm{tail}}}{\omega ^c } ) + ( h_{ab0}^{{\rm{tail } } } + h_{abc}^{{\rm{tail}}}{\omega ^c } ) } \right ] + { \mathcal o}(m{r^2}/{{\mathcal r}^3 } ) . } \\ \end{array}$$\end{document } because \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha { \prime}\beta { \prime}}^{{\rm{tails}}}$\end{document } is of order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m/{\mathcal r}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha { \prime}\beta { \prime}\gamma { \prime}}^{{\rm{tails}}}$\end{document } of order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m/{{\mathcal r}^2}$\end{document } we see that the metric possesses the buffer - zone form \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm g } = \eta \oplus { r^2}/{{\mathcal r}^2 } \oplus m / r \oplus m/{\mathcal r } \oplus mr/{{\mathcal r}^2}$\end{document } that was anticipated in equation ( 558 ) . notice that the expansion adopted here does not contain a term at order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$r/{\mathcal r}$\end{document } and presumes that aa and ab are both of order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m/{{\mathcal r}^2}$\end{document } ; this will be confirmed in section 5.4.5 . comparison of equations ( 568 , 569 , 570 ) and equations ( 596 , 597 , 598 ) reveals that the internal - zone and external - zone metrics do no match in the buffer zone . but as the metrics are expressed in two different coordinate systems , this mismatch is hardly surprising . a meaningful comparison of the two metrics must therefore come after a transformation from the external coordinates ( u , r ) to the internal coordinates \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\left({\bar u,\,\bar r{{\bar \omega}^a } } \right)$\end{document}. our task in this section is to construct this coordinate transformation . the first stage of the transformation , ( u , r ) ( u , r ) will be seen to remove unwanted terms of order m / r in g. the second stage , ( u , ra ) ( u,r ) , will remove all terms of order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m/{\mathcal r}$\end{document } in g. finally , the third stage \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\left({u{\prime\prime},\,r{\prime\prime}{{\omega { \prime\prime}}^a } } \right ) \rightarrow \left({\bar u,\,\bar r{{\bar \omega}^a } } \right)$\end{document } will produce the desired internal coordinates . the first stage of the coordinate transformation is 599\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$u{\prime } = u - 2m\ln r,$$\end{document } 600\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${x^{\prime a } } = \left({1 + { m \over r } } \right){x^a},$$\end{document } and it affects the metric at orders m / r and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$mr/{{\mathcal r}^2}$\end{document}. this transformation redefines the radial coordinate r r = r + m and incorporates in u the gravitational time delay contributed by the small mass m. after performing the coordinate transformation the metric becomes 601\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \rm{g}}_{u\prime u\prime } } = - 1 - { { r\prime}^2}{{{\mathcal e}\prime}^ { \ast } } + { \mathcal o}({{r\prime}^3}/{{\mathcal r}^3})\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { \quad \quad + { { 2 m } \over { r\prime } } + h_{00}^{{\rm{tail } } } + r\prime ( 4m{{{\mathcal e}\prime}^ { \ast } } - 2{a_a}{{\omega \prime}^a } + h_{000}^{{\rm{tail } } } + h_{00a}^{{\rm{tail}}}{{\omega \prime}^a } ) + { \mathcal o}(m{{r\prime}^2}/{{\mathcal r}^3 } ) , } \\ \end{array}$$\end{document } 602\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \rm{g}}_{u\prime a\prime } } = - { { \omega \prime}_a } + { 2 \over 3}{{r\prime}^2}({\mathcal e}\prime_a^ { \ast } + { \mathcal b}\prime_a^ { \ast } ) + { \mathcal o}({{r\prime}^3}/{{\mathcal r}^3})\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { + h_{0a}^{{\rm{tail } } } + { { \omega \prime}_a}h_{00}^{{\rm{tail}}}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { + r\prime\left [ { - { { 4 m } \over 3}({\mathcal e}\prime_a^ { \ast } + { \mathcal b}\prime_a^ { \ast } ) + ( \delta _ a^b - { { \omega \prime}_a}{{\omega \prime}^b}){a_b } - { \omega _ { ab}}{{\omega \prime}^b } + h_{0a0}^{{\rm{tail } } } + { { \omega \prime}_a}h_{000}^{{\rm{tail } } } + h_{0ab}^{{\rm{tail}}}{{\omega \prime}^b } + { { \omega \prime}_a}h_{00b}^{{\rm{tail}}}{{\omega \prime}^b } } \right ] } \\ { + { \mathcal o}(m{{r\prime}^2}/{{\mathcal r}^3}),\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ \end{array}$$\end{document } 603\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}{c } } { { g_{a'b ' } } = { \delta _ { ab } } - { { \omega ' } _ a}{{\omega ' } _ b } - \frac{1}{3}{{r'}^2}\left ( { { \mathcal{e}'}_{ab}^ * + { \mathcal{b}'}_{ab}^ * } \right ) + \mathcal{o}\left ( { { { r'}^3}/{\mathcal{r}^3 } } \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ ; } \\ { + \;{{\omega ' } _ a}{{\omega ' } _ b}h_{00}^{tail } + { { \omega ' } _ a}h_{0b}^{tail } + { { \omega ' } _ b}h_{0a}^{tail } + h_{ab}^{tail}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ ; } \\ { + \;r'\left [ { \frac{{2m}}{3}\left ( { { { \mathcal{e}'}_{ab } } + { { \omega ' } _ a}{\mathcal{e}'}_b^ * + { \mathcal{e}'}_a^*{{\omega ' } _ b } + { \mathcal{b}'}_{ab}^ * + { { \omega ' } _ a}{\mathcal{b}'}_b^ * + { { \omega ' } _ b}{\mathcal{b}'}_a^ * } \right ) } \right . + { { \omega ' } _ a}{{\omega ' } _ b}\left ( { h_{000}^{tail } + h_{00c}^{tail}{{\omega ' } ^c } } \right ) } \\ { \left . { + \omega ' \left ( { h_{0b0}^{tail } + h_{0bc}^{tail}{{\omega ' } ^c } } \right ) + { { \omega ' } _ b}\left ( { h_{0a0}^{tail } + h_{0ac}^{tail}\omega ' c } \right ) + \left ( { h_{ab0}^{tail } + h_{abc}^{tail}{{\omega ' } ^c } } \right ) } \right ] } \\ { + \mathcal{o}\left ( { m{{r'}^2}/{\mathcal{r}^3 } } \right).\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ ; } \end{array}$$\end{document } this metric matches g(internal zone ) at orders 1 , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{r{\prime}}^2}/{{\mathcal r}^2}$\end{document } , and m / r , but there is still a mismatch at orders \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m/{\mathcal r}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$mr{\prime}/{{\mathcal r}^2}$\end{document}. the second stage of the coordinate transformation is 604\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$u{\prime\prime } = u{\prime } - { 1 \over 2}\int\nolimits_{}^{u{\prime } } { h_{00}^{{\rm{tail } } } } ( u{\prime})du{\prime } - { 1 \over 2}r{\prime}[h_{00}^{{\rm{tail}}}(u{\prime } ) + 2h_{0a}^{{\rm{tail}}}(u{\prime}){\omega ^{\prime a } } + h_{ab}^{{\rm{tail}}}(u{\prime}){\omega ^{\prime a}}{\omega ^{\prime b}}],$$\end{document } 605\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$x_a{\prime\prime } = x_a{\prime } + { 1 \over 2}h_{ab}^{{\rm{tail}}}(u{\prime}){x^{\prime b}},$$\end{document } and it affects the metric at orders \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m/{\mathcal r}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$mr/{{\mathcal r}^2}$\end{document}. after performing this transformation the metric becomes 606\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \rm{g}}_{u{\prime}{\prime}u\prime \prime } } = - 1 - r{\prime}{\prime}^2{\mathcal e}{{\prime\prime}^\ast } + { \mathcal o}(r{\prime}{{\prime}^3}/{{\mathcal r}^3})\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \,\,\ , } \\ { \quad \quad \,\ , + { { 2 m } \over { r\prime \prime } } + r\prime \prime \left [ { 4m{\mathcal e}{\prime\prime}^\ast- 2\left({{a_a } - { 1 \over 2}h_{00a}^{{\rm{tail } } } + h_{0a0}^{{\rm{tail } } } } \right)\omega { \prime\prime}^a } \right ] + { \mathcal o}(mr{\prime\prime}^2/{{\mathcal r}^3 } ) , } \\ \end{array}$$\end{document } 607\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \rm{g}}_{u{\prime\prime } a{\prime\prime } } } = - \omega _ a^{\prime\prime } + { 2 \over 3}r{\prime\prime}^{2}({\mathcal e}_a^{{\prime\prime } { \ast } } + { \mathcal b}_a^{{\prime\prime } { \ast } } ) + { \mathcal o}(r{\prime\prime}^{3}/{{\mathcal r}^3})\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { + r{\prime\prime } \left [ { - { { 4 m } \over 3}({\mathcal e}_a^{{\prime\prime}{\ast } } + { \mathcal b}_a^{{\prime\prime } { \ast } } ) - 2m{{\mathcal e}_{ab}}\omega { \prime\prime}^{b } + ( \delta _ a^b - \omega _ a^{\prime\prime}\omega { \prime\prime}^{b})\left({{a_b } - { 1 \over 2}h_{00b}^{{\rm{tail } } } + h_{0b0}^{{\rm{tail } } } } \right ) - { \omega _ { ab}}\omega { \prime\prime}^{b } } \right . } \\ { \quad \left . { + { 1 \over 2}\omega _ a^{\prime\prime}h_{000}^{{\rm{tail } } } - { 1 \over 2}h_{ab0}^{{\rm{tail}}}\omega { \prime\prime}^{b } + h_{0ab}^{{\rm{tail}}}\omega { \prime\prime}^{b } + { 1 \over 2}({\delta _ a}^b + \omega _ a^{\prime\prime}\omega { \prime\prime}^{b})h_{00b}^{{\rm{tail } } } } \right ] + { \mathcal o}(mr{\prime\prime}^{2}/{{\mathcal r}^3 } ) , } \\ \end{array}$$\end{document } 608\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \rm{g}}_{a{\prime\prime}b{\prime\prime } } } = { \delta _ { ab } } - \omega _ a^{\prime\prime}\omega _ b^{\prime\prime } - { 1 \over 3}r{\prime\prime}^{2}({\mathcal e}_{ab}^{{\prime\prime } \ast } + { \mathcal b}_{ab}^{{\prime\prime } \ast } ) + { \mathcal o}(r{\prime\prime}^{3}/{{\mathcal r}^3})\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { + r{\prime\prime}\left [ { { { 2 m } \over 3}({\mathcal e}_{ab}^{{\prime\prime } \ast } + \omega _ a^{\prime\prime}{\mathcal e}_b^{{\prime\prime } \ast } + { \mathcal e}_a^{{\prime\prime } \ast}\omega _ b^{\prime\prime } + { \mathcal b}_{ab}^{{\prime\prime } \ast } + \omega _ a^{\prime\prime}{\mathcal b}_b^{{\prime\prime } \ast } + \omega _ b^{\prime\prime}{\mathcal b}_a^{{\prime\prime } \ast } ) + \omega _ a^{\prime\prime}\omega _ b^{\prime\prime}(h_{000}^{{\rm{tail } } } + h_{00c}^{{\rm{tail}}}\omega { \prime\prime}^{c})\quad } \right.\quad } \\ { \left . { \quad + \omega _ a^{\prime\prime}(h_{0b0}^{{\rm{tail } } } + h_{0bc}^{{\rm{tail}}}\omega { \prime\prime}^{c } ) + \omega _ b^{\prime\prime}(h_{0a0}^{{\rm{tail } } } + h_{0ac}^{{\rm{tail}}}\omega { \prime\prime}^{c } ) + ( h_{ab0}^{{\rm{tail } } } + h_{abc}^{{\rm{tail}}}\omega { \prime\prime}^{c } ) } \right]\quad \quad \quad \quad \,\,\,\quad } \\ { \quad \quad + { \mathcal o}(mr{\prime\prime}^{2}/{{\mathcal r}^3}){.}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ \end{array}$$\end{document } to arrive at these expressions we had to involve the relations 609\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${d \over { du{\prime\prime}}}h_{00}^{{\rm{tail } } } = h_{000}^{{\rm{tail}}},\quad \quad { d \over { du{\prime\prime}}}h_{0a}^{{\rm{tail } } } = h_{0a0}^{{\rm{tail}}},\quad \quad { d \over { du{\prime\prime}}}h_{ab}^{{\rm{tail } } } = 4m{\mathcal{e}_{ab } } + h_{ab0}^{{\rm{tail}}},$$\end{document } which are obtained by covariant differentiation of equation ( 587 ) with respect to u. the metric now matches g(internal zone ) at orders \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$1,\,{{r{\prime\prime}}^2}/{{\mathcal r}^2},\,m / r{\prime\prime}$\end{document } , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m/{\mathcal r}$\end{document } , but there is still a mismatch at order \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$mr{\prime\prime}/{{\mathcal r}^2}$\end{document}. the third and final stage of the coordinate transformation is 610\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\bar u = u{\prime\prime } - { 1 \over 4}{r^{\prime\prime 2}}[h_{000}^{{\rm{tail } } } + ( h_{00a}^{{\rm{tail } } } + 2h_{0a0}^{{\rm{tail}}}){\omega ^{\prime\prime a } } + ( h_{ab0}^{{\rm{tail } } } + 2h_{0ab}^{{\rm{tail}}}){\omega ^{\prime\prime a}}{\omega ^{\prime\prime b } } + h_{abc}^{{\rm{tail}}}{\omega ^{\prime\prime a}}{\omega ^{\prime\prime b}}{\omega ^{\prime\prime c}}],$$\end{document } 611\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \bar x}_a } = \left({1 + { m \over 3}r{\prime\prime}{{\mathcal e}_{bc}}{{\omega { \prime\prime}}^b}{{\omega { \prime\prime}}^c } } \right){{x{\prime\prime}}_a}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { \quad \quad + { 1 \over 2}{{r{\prime\prime}}^2}\left [ { - { 1 \over 2}h_{00a}^{{\rm{tail } } } + h_{0a0}^{{\rm{tail } } } + \left({h_{0ab}^{{\rm{tail } } } - h_{0ba}^{{\rm{tail } } } + h_{ab0}^{{\rm{tail } } } + { { 4 m } \over 3}{{\mathcal e}_{ab } } } \right){{\omega { \prime\prime}}^b } + ( { q_{abc } } - { q_{bca } } + { q_{cab}}){{\omega { \prime\prime}}^b}{{\omega { \prime\prime}}^c } } \right ] , } \\ \end{array}$$\end{document } where 612\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${q_{abc } } = { 1 \over 2}h_{abc}^{{\rm{tail } } } + { m \over 3}({\varepsilon _ { acd}}{\mathcal{b}^d}_b + { \varepsilon _ { bcd}}{\mathcal{b}^d}_a).$$\end{document } this transformation puts the metric in its final form 613\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \rm{g}}_{\bar u\bar u } } = - 1 - { { \bar r}^2}\bar { \mathcal e}^\ast + { \mathcal o}({{\bar r}^3}/{{\mathcal r}^3})\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { \quad \quad + { { 2 m } \over { \bar r } } + \bar r\left [ { 4m\overline { \mathcal e } ^\ast - 2\left({{a_a } - { 1 \over 2}h_{00a}^{{\rm{tail } } } + h_{0a0}^{{\rm{tail } } } } \right){{\bar \omega}^a } } \right ] + { \mathcal o}(m{{\bar r}^2}/{{\mathcal r}^3 } ) , } \\ \end{array}$$\end{document } 614\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}{c } } { { g_{\bar u\bar a } } = - { { \bar \omega } _ a } + \frac{2}{3}{{\bar r}^2}\left ( { \bar { \mathcal{e}}_a^ * + \bar { \mathcal{b}}_a^ * } \right ) + \mathcal{o}\left ( { { { \bar r}^3}/{\mathcal{r}^3 } } \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ ; } \\ { + \bar r\left [ { - \frac{{4m}}{a}\left ( { \bar { \mathcal{e}}_a^ * + \bar { \mathcal{b}}_a^ * } \right ) + \left ( { { \delta _ a}^b - { { \bar \omega } _ a}{{\bar \omega } ^b } } \right)\left ( { { a_b } - \frac{1}{2}h_{00b}^{tail } + h_{0b0}^{tail } } \right ) - \left ( { { \omega _ { ab } } - h_{0[ab]}^{tail } } \right){{\bar \omega } ^b } } \right ] } \\ { + \mathcal{o}\left ( { m{{\bar r}^2}/{\mathcal{r}^3 } } \right),\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ ; } \end{array}$$\end{document } 615\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\rm{g}}_{\bar a\bar b } } = { \delta _ { ab } } - { \bar \omega _ a}{\bar \omega _ b } - { 1 \over 3}{\bar r^2}(\overline{\mathcal{e } } _ { ab}^{\ast } + \overline{\mathcal{b}}_{ab}^{\ast } ) + \mathcal{o}({\bar r^3}/{\mathcal{r}^3 } ) + \mathcal{o}(m{\bar r^2}/{\mathcal{r}^3}).$$\end{document } except for the terms involving aa and ab , this metric is equal to g(internal zone ) as given by equations ( 568 , 569 , 570 ) linearized with respect to m. a precise match between g(external zone ) and g(internal zone ) is produced when we impose the relations 616\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a_a } = { 1 \over 2}h_{00a}^{{\rm{tail } } } - h_{0a0}^{{\rm{tail}}}$$\end{document } and 617\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\omega _ { ab } } = h_{0[ab]}^{{\rm{tail}}}.$$\end{document } while equation ( 616 ) tells us how the black hole moves in the background spacetime , equation ( 617 ) indicates that the vectors are not fermi - walker transported on the world line . the black hole s acceleration vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^\mu } = { a^a}e_a^\mu$\end{document } can be constructed from the frame components listed in equation ( 616 ) . a straightforward computation gives 618\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${a^\mu } = - { 1 \over 2}({g^{\mu \nu } } + { u^\mu}{u^\nu})(2h_{\nu \lambda \rho}^{{\rm{tail } } } - h_{\lambda \rho \nu}^{{\rm{tail}}}){u^\lambda}{u^\rho},$$\end{document } where the tail integral 619\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$h_{\mu \nu \lambda}^{{\rm{tail } } } = 4m\int\nolimits_{- \infty}^{{\tau ^ - } } { { \nabla _ \lambda } } { \rm{}}\left({{g_{+ \mu \nu { \mu \prime}{\nu \prime } } } - { 1 \over 2}{g_{\mu \nu}}{g _ + } { \;^\rho}_{\rho { \mu \prime}{\nu \prime}}\ , } \right)(z(\tau),\;z({\tau \prime})){u^{{\mu \prime}}}{u^{{\nu \prime}}}d{\tau \prime}$$\end{document } was previously defined by equation ( 588 ) . these are the misataquwa equations of motion , exactly as they were written down in equation ( 550 ) . while the initial derivation of this result was based upon formal manipulations of singular quantities , the present derivation involves only well - behaved fields and is free of any questionable aspect . such a derivation , based on matched asymptotic expansions , was first provided by yasushi mino , misao sasaki , and takahiro tanaka in 1997 . substituting equations ( 616 ) and ( 617 ) into equation ( 579 ) gives the following transport equation for the tetrad vectors : 620\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{de_a^\mu } \over { d\tau } } = - { 1 \over 2}{u^\mu}(2h_{\nu \lambda \rho}^{{\rm{tail } } } - h_{\nu \rho \lambda}^{{\rm{tail}}}){u^\nu}e_a^\lambda { u^\rho } + ( { g^{\mu \rho } } + { u^\mu}{u^\rho})h_{\nu [ \lambda \rho ] } ^{{\rm{tail}}}{u^\nu}e_a^\lambda.$$\end{document } this can also be written in the alternative form 621\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{de_a^\mu } \over { d\tau } } = - { 1 \over 2}({u^\mu}e_a^\lambda { u^\rho } + { g^{\mu \lambda}}e_a^\rho - { g^{\mu \rho}}e_a^\lambda){u^\nu}h_{\nu \lambda \rho}^{{\rm{tail}}}$$\end{document } that was first proposed by mino , sasaki , and tanaka . both equations state that in the background spacetime , the tetrad vectors are not fermi - walker transported on ; the rotation tensor is nonzero and given by equation ( 617 ) . i have presented a number of derivations of the equations that determine the motion of a point scalar charge q , a point electric charge e , and a point mass m in a specified background spacetime . in this concluding section i summarize these derivations , and identify their strengths and weaknesses . i also describe the challenges that lie ahead in the concrete evaluation of the self - forces , most especially in the gravitational case . for each of the three cases ( scalar , electromagnetic , and gravitational ) the first derivation is based on a spatial averaging of the retarded field , and the second is based on a decomposition of the retarded field into singular and radiative fields . in the gravitational case , a third derivation , based on matched asymptotic expansions , these derivations will be reviewed below , but i want first to explain why i have omitted to present a fourth derivation , based on energy - momentum conservation , in spite of the fact that historically , it is one of the most important . conservation of energy - momentum was used by dirac to derive the equations of motion of a point electric charge in flat spacetime , and the same method was adopted by dewitt and brehme in their generalization of dirac s work to curved spacetimes . this method was also one of the starting points of mino , sasaki , and tanaka in their calculation of the gravitational self - force . first , it is technically more difficult to implement than the methods presented in this review ( considerably longer computations are involved ) . second , it is difficult to endow this method with an adequate level of rigour , to the point that it is perhaps less convincing than the methods presented in this review . while the level of rigour achieved in flat spacetime is now quite satisfactory , i do not believe the same can be said of the generalization to curved spacetimes . the method is based on the conservation equation \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${t^{\alpha \beta}}_{;\beta } = 0$\end{document } , where the stress - energy tensor t includes a contribution from the particle and a contribution from the field ; the particle s contribution is a dirac functional on the world line , and the field s contribution diverges as 1/r near the world line . ( i am using retarded coordinates in this discussion . ) while in flat spacetime the differential statement of energy - momentum conservation can immediately be turned into an integral statement , the same is not true in a curved spacetime ( unless the spacetime possesses at least one killing vector ) . to proceed it is necessary to rewrite the conservation equation as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$0 = { g^\mu}_\alpha t_{\quad ; \beta}^{\alpha \beta } = { ( { g^\mu}_\alpha { t^{\alpha \beta}})_{;\beta } } - { g^\mu}_{\alpha ; \beta}{t^{\alpha \beta}},$$\end{document } where g(z , x ) is a parallel propagator from x to an arbitrary point z on the world line . integrating this equation over the interior of a world - tube segment that consists of a wall of constant r and two caps of constant u , we obtain \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$0 = \int\nolimits_{{\rm{wall } } } { { g^\mu}_\alpha { t^{\alpha \beta}}d{\sigma _ \beta } } + \int\nolimits_{{\rm{caps } } } { { g^\mu}_\alpha { t^{\alpha \beta}}d{\sigma _ \beta } } + \int\nolimits_{{\rm{interior } } } { { g^\mu}_{\alpha ; \beta}{t^{\alpha \beta}}dv,}$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d{\sigma _ \beta}$\end{document } is a three - dimensional surface element and dv an invariant , four - dimensional volume element . there is no obstacle in evaluating the wall integral , for which t reduces to the field s stress - energy tensor ; for a wall of radius r the integral scales as 1/r . the integrations over the caps , however , are problematic : while the particle s contribution to the stress - energy tensor is integrable , the integration over the field s contribution goes as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\int\nolimits_0^r { { { \left({r{\prime } } \right)}^{- 2}}dr{\prime}}$\end{document } and diverges . to properly regularize this integral requires great care , and the removal of all singular terms can be achieved by mass renormalization . this issue arises also in flat spacetime , and while it is plausible that the rigourous distributional methods presented in could be generalized to curved spacetimes , this remains to be done . more troublesome , however , is the interior integral , which does not appear in flat spacetime . because \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g^\mu}_{\alpha ; \beta}$\end{document } scales as r , this integral goes as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\int\nolimits_0^r { { { \left({r{\prime } } \right)}^{- 1}}dr{\prime}}$\end{document } and it also diverges , albeit less strongly than the caps integration . while simply discarding this integral produces the correct equations of motion , it would be desirable to go through a careful regularization of the interior integration , and provide a convincing reason to discard it altogether . to the best of my knowledge , this has not been done . to identify the strengths and weaknesses of the averaging method it is convenient to adopt the detweiler - whiting decomposition of the retarded field into singular and radiative pieces . for concreteness i shall focus my attention on the electromagnetic case , and write \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${f_{\alpha \beta } } = f_{\alpha \beta}^{\rm{s } } + f_{\alpha \beta}^{\rm{r}}.$$\end{document } recall that this decomposition is unambiguous , and that the retarded and singular fields share the same singularity structure near the world line . recall also that the retarded and singular fields satisfy the same field equations ( with a distributional current density on the right - hand side ) , but that the radiative field is sourcefree . to formulate equations of motion for the point charge we temporarily model it as a spherical hollow shell , and we obtain the net force acting on this object by averaging f over the shell s surface . ( the averaging is performed in the shell s rest frame , and the shell is spherical in the sense that its proper distance from the world line is the same in all directions . ) the averaged field is next evaluated on the world line , in the limit of a zero - radius shell . because the radiative field is smooth on the world line , this yields \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$e\langle { f_{\mu \nu}}\rangle { u^\nu } = e\langle f_{\mu \nu}^{\rm{s}}\rangle { u^\nu } + ef_{\mu \nu}^{\rm{r}}{u^\nu},$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$e\langle f_{\mu \nu}^{\rm{s}}\rangle { u^\nu } = - ( \delta m){a_\mu},\quad \quad \delta m = \lim\limits_{s \rightarrow 0 } \left({{2 \over 3}{{{e^2 } } \over s } } \right)$$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$ef_{\mu \nu}^{\rm{r}}{u^\nu } = { e^2}({g_{\mu \nu } } + { u_\mu}{u_\nu})\left({{2 \over 3}{{\dot a}^\nu } + { 1 \over 3}{r^\nu}_\lambda { u^\lambda } } \right ) + 2{e^2}{u^\nu}{\int\nolimits_{- \infty}^{{\tau ^ - } } \nabla _ { \left [ \mu \right.}}{g^ + } _ { \left . \nu \right]\lambda { \prime}}\;(z(\tau),\;z({\tau \prime})){u^{{\lambda \prime}}}d{\tau \prime}.$$\end{document } the equations of motion are then postulated to be ma = efu , where m is the particle s bare mass . with the preceding results we arrive at \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${m_{{\rm{obs}}}}{a_\mu } = ef_{\mu \nu}^{\rm{r}}{u^\nu}$\end{document } , where mobs m + m is the particle s observed ( renormalized ) inertial mass . the averaging method is sound , but it is not immune to criticism . a first source of criticism concerns the specifics of the averaging procedure , in particular , the choice of a spherical surface over any other conceivable shape . another source is a slight inconsistency of the method that gives rise to the famous 4/3 problem : the mass shift m is related to the shell s electrostatic energy \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$e = { e^2}/\left({2s } \right)$\end{document } by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\delta m = { 4 \over 3}e$\end{document } instead of the expected m = e. this problem is likely due to the fact that the field that is averaged over the surface of the shell is sourced by a point particle and not by the shell itself . it is plausible that a more careful treatment of the near - source field will eliminate both sources of criticism : we can expect that the field produced by an extended spherical object will give rise to a mass shift that equals the object s electrostatic energy , and the object s spherical shape would then fully justify a spherical averaging . ( considering other shapes might also be possible , but one would prefer to keep the object s structure simple and avoid introducing additional multipole moments . ) the averaging method is at the core of the approach followed by quinn and wald , who also average the retarded field over a spherical surface surrounding the particle . the detweiler - whiting decomposition of the retarded field becomes most powerful when it is combined with the detweiler - whiting axiom , which asserts that the singular field exerts no force on the particle ( it merely contributes to the particle s inertia ) ; the entire self - force arises from the action of the radiative field . this axiom , which is motivated by the symmetric nature of the singular field , and also its causal structure , gives rise to the equations of motion \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$m{a_\mu } = ef_{\mu \nu}^{\rm{r}}{u^\nu}$\end{document } , in agreement with the averaging method ( but with an implicit , instead of explicit , mass shift ) . in this picture , the particle simply interacts with a free radiative field ( whose origin can be traced to the particle s past ) , and the procedure of mass renormalization is sidestepped . in the scalar and electromagnetic cases , the picture of a particle interacting with a radiative field removes any tension between the nongeodesic motion of the charge and the principle of equivalence . in the gravitational case the detweiler - whiting axiom produces the statement that the point mass m moves on a geodesic in a spacetime whose metric \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\alpha \beta } } + h_{\alpha \beta}^{\rm{r}}$\end{document } is nonsingular and a solution to the vacuum field equations . this is a conceptually powerful , and elegant , formulation of the misataquwa equations of motion . the singular field exerts no force on the particle ( it merely contributes to the particle s inertia ) ; the entire self - force arises from the action of the radiative field . it is well known that in general relativity the motion of gravitating bodies is determined , along with the spacetime metric , by the einstein field equations ; the equations of motion are not separately imposed . this observation provides a means of deriving the misataquwa equations without having to rely on the fiction of a point mass . in the method of matched asymptotic expansions , the small body is taken to be a nonrotating black hole , and its metric perturbed by the tidal gravitational field of the external universe is matched to the metric of the external universe perturbed by the black hole . the equations of motion are then recovered by demanding that the metric be a valid solution to the vacuum field equations . this method , which was the second starting point of mino , sasaki , and tanaka , gives what is by far the most compelling derivation of the misataquwa equations . indeed , the method is entirely free of conceptual and technical pitfalls there are no singularities ( except deep inside the black hole ) and only retarded fields are employed . the introduction of a point mass in a nonlinear theory of gravitation would appear at first sight to be severely misguided . the derivation of the misataquwa equations of motion based on the method of matched asymptotic expansions does indeed show that results obtained on the basis of a point - particle description can be reliable , in spite of all their questionable aspects . this is a remarkable observation , and one that carries a lot of convenience : it is much easier to implement the point - mass description than to perform the matching of two metrics in two coordinate systems . the concrete evaluation of the scalar , electromagnetic , and gravitational self - forces is made challenging by the need to first obtain the relevant retarded green s function . successes achieved in the past were reviewed in section 1.10 , and here i want to describe the challenges that lie ahead . i will focus on the specific task of computing the gravitational self - force acting on a point mass that moves in a background kerr spacetime . this case is especially important because the motion of a small compact object around a massive ( galactic ) black hole is a promising source of low - frequency gravitational waves for the laser interferometer space antenna ( lisa ) ; to calculate these waves requires an accurate description of the motion , beyond the test - mass approximation which ignores the object s radiation reaction . the gravitational self - acceleration is given by the misataquwa expression , which i write in the form \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{d{u^\mu } } \over { d\tau } } = { a^\mu}[{h^{\rm{r } } } ] \equiv - { 1 \over 2}({g^{\mu \nu } } + { u^\mu}{u^\nu})(2h_{\nu \lambda ; \rho}^{\rm{r } } - h_{\lambda \rho ; \nu}^{\rm{r}}){u^\lambda}{u^\rho},$$\end{document } where \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha \beta}^{\rm{r}}$\end{document } is the radiative part of the metric perturbation . recall that this equation is equivalent to the statement that the small body moves on a geodesic of a spacetime with metric \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${g_{\alpha \beta } } + h_{\alpha \beta}^{\rm{r}}$\end{document}. here g is the kerr metric , and we wish to calculate a[h ] for a body moving in the kerr spacetime . this calculation is challenging and it involves a large number of steps . the first sequence of steps is concerned with the computation of the ( retarded ) metric perturbation h produced by a point particle moving on a specified geodesic of the kerr spacetime . a method for doing this was elaborated by lousto and whiting and ori , building on the pioneering work of teukolsky , chrzanowski , and wald . the procedure consists of solving the teukolsky equation for one of the newman - penrose quantities 0 and 4 ( which are complex components of the weyl tensor ) produced by the point particle;obtaining from 0 or 4 a related ( hertz ) potential by integrating an ordinary differential equation;applying to a number of differential operators to obtain the metric perturbation in a radiation gauge that differs from the lorenz gauge ; andperforming a gauge transformation from the radiation gauge to the lorenz gauge . it is well known that the teukolsky equation separates when 0 or 4 is expressed as a multipole expansion , summing over modes with ( spheroidal - harmonic ) indices l and m. in fact , the procedure outlined above relies heavily on this mode decomposition , and the metric perturbation returned at the end of the procedure is also expressed as a sum over modes \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha \beta}^l$\end{document}. ( for each l , m ranges from l to l , and summation of m over this range is henceforth understood . ) from these , mode contributions to the self - acceleration can be computed : a[hl ] is obtained from our preceding expression for the self - acceleration by substituting h in place of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha \beta}^{\rm{r}}$\end{document}. these mode contributions do not diverge on the world line , but a[hl ] is discontinuous at the radial position of the particle . the sum over modes , on the other hand , does not converge , because the bare acceleration ( constructed from the retarded field h ) is formally infinite . solving the teukolsky equation for one of the newman - penrose quantities 0 and 4 ( which are complex components of the weyl tensor ) produced by the point particle ; obtaining from 0 or 4 a related ( hertz ) potential by integrating an ordinary differential equation ; applying to a number of differential operators to obtain the metric perturbation in a radiation gauge that differs from the lorenz gauge ; and performing a gauge transformation from the radiation gauge to the lorenz gauge . the next sequence of steps is concerned with the regularization of each a[hl ] by removing the contribution from \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha \beta}^{\rm{s}}$\end{document } [ 6 , 7 , 9 , 11 , 38 , 21 ] . the singular field can be constructed locally in a neighbourhood of the particle , and then decomposed into modes of multipole order l. this gives rise to modes \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^\mu}\left [ { h_l^{\rm{s } } } \right]$\end{document } for the singular part of the self - acceleration ; these are also finite and discontinuous , and their sum over l also diverges . but the true modes \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^\mu}\left [ { h_l^{\rm{r } } } \right ] = { a^\mu}\left [ { { h_l } } \right ] - { a^\mu}\left [ { h_l^{\rm{s } } } \right]$\end{document } of the self - acceleration are continuous at the radial position of the particle , and their sum does converge to the particle s acceleration . ( it might be noted that obtaining a mode decomposition of the singular field involves providing an extension of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha \beta}^{\rm{s}}$\end{document } on a sphere of constant radial coordinate , and then integrating over the angular coordinates . the arbitrariness of the extension introduces ambiguities in each \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^\mu}\left [ { h_l^{\rm{s } } } \right]$\end{document } , but the ambiguity disappears after summing over l. ) the self - acceleration is thus obtained by first computing a[hl ] from the metric perturbation derived from 0 or 4 , then computing the counterterms \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^\mu}\left [ { h_l^{\rm{s } } } \right]$\end{document } by mode - decomposing the singular field , and finally summing over all \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${a^\mu}\left [ { h_l^{\rm{r } } } \right ] = { a^\mu}\left [ { { h_l } } \right ] - { a^\mu}\left [ { h_l^{\rm{s } } } \right]$\end{document}. this procedure is lengthy and involved , and thus far it has not been brought to completion , except for the special case of a particle falling radially toward a nonrotating black hole . in this regard it should be noted that the replacement of the central kerr black hole by a schwarzschild black hole simplifies the task considerably . in particular , because there exists a practical and well - developed formalism to describe the metric perturbations of a schwarzschild spacetime [ 51 , 59 , 63 ] , there is no necessity to rely on the teukolsky formalism and the complicated reconstruction of the metric variables . the reason is that the metric perturbations \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$h_{\alpha \beta}^l$\end{document } that can be recovered from 0 or 4 do not by themselves sum up to the complete gravitational perturbation produced by the moving particle . missing are the perturbations derived from the other newman - penrose quantities : 1 , 2 and 3 while 1 and 3 can always be set to zero by an appropriate choice of null tetrad , 2 contains such important physical information as the shifts in mass and angular - momentum parameters produced by the particle . because the mode decompositions of 0 and 4 start at l = 2 , we might colloquially say that what is missing from the above procedure are the it is not currently known how the procedure can be completed so as to incorporate all modes of the metric perturbations . specializing to a schwarzschild spacetime eliminates this difficulty , and in this context the low multipole modes have been studied for the special case of circular orbits [ 43 , 22 ] . in view of these many difficulties ( and i choose to stay silent on others , for example , the issue of relating metric perturbations in different gauges when the gauge transformation is singular on the world line ) , it is perhaps not too surprising that such a small number of concrete calculations have been presented to date . but progress in dealing with these difficulties has been steady , and the situation should change dramatically in the next few years . the successful computation of the gravitational self - force is not the end of the road . after the difficulties reviewed in the preceding section 5.5.5 have all been removed and the motion of the small body is finally calculated to order m , it will still be necessary to obtain gauge - invariant information associated with the body s corrected motion . because the misataquwa equations of motion are not by themselves gauge - invariant how this might be done , imagine that the small body is a pulsar , and that it emits light pulses at regular proper - time intervals . the motion of the pulsar around the central black hole modulates the pulse frequencies as measured at infinity , and information about the body s corrected motion is encoded in the times - of - arrival of the pulses . because these can be measured directly by a distant observer , they clearly constitute gauge - invariant information . but the times - of - arrival are determined not only by the pulsar s motion , but also by the propagation of radiation in the perturbed spacetime . this example shows that to obtain gauge - invariant information , one must properly combine the misataquwa equations of motion with the metric perturbations . in the context of the laser interferometer space antenna , the relevant observable is the instrument s response to a gravitational wave , which is determined by gauge - invariant waveforms , h+ and h to calculate these is the ultimate goal of this research programme , and the challenges that lie ahead go well beyond what i have described thus far . to obtain the waveforms it will be necessary to solve the einstein field equations to second order in perturbation theory . to understand this , schematically , one introduces a perturbation h that satisfies a wave equation h = t[z ] in the background spacetime , where t[z ] is the stress - energy tensor of the moving body , which is a functional of the world line z( ) . in first - order perturbation theory , the stress - energy tensor must be conserved in the background spacetime , and z( ) must describe a geodesic . it follows that in first - order perturbation theory , the waveforms constructed from the perturbation h contain no information about the body s corrected motion . the first - order perturbation , however , can be used to correct the motion , which is now described by the world line z( ) + z( ) . in a naive implementation of the self - force , one would now resolve the wave equation with a corrected stress - energy tensor , h = t[z + z ] , and the new waveforms constructed from h would then incorporate information about the corrected motion . in fact , to be consistent one would have to include all second - order terms in the wave equation , not just the ones that come from the corrected motion . schematically , the new wave equation would have the form of h = ( 1 + h)t[z + z ] + ( h ) , and this is much more difficult to solve than the naive problem ( if only because the source term is now much more singular than the distributional singularity contained in the stress - energy tensor ) . but provided one can find a way to make this second - order problem well posed , and provided one can solve it ( or at least the relevant part of it ) , the waveforms constructed from the second - order perturbation h will be gauge invariant . in this way , information about the body s corrected motion will have properly been incorporated into the gravitational waveforms .

this review is concerned with the motion of a point scalar charge , a point electric charge , and a point mass in a specified background spacetime . in each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone , and therefore removes energy from the particle . in the near zone the field acts on the particle and gives rise to a self - force that prevents the particle from moving on a geodesic of the background spacetime . the self - force contains both conservative and dissipative terms , and the latter are responsible for the radiation reaction . the work done by the self - force matches the energy radiated away by the particle.the field s action on the particle is difficult to calculate because of its singular nature : the field diverges at the position of the particle . but it is possible to isolate the field s singular part and show that it exerts no force on the particle its only effect is to contribute to the particle s inertia . what remains after subtraction is a smooth field that is fully responsible for the self - force . because this field satisfies a homogeneous wave equation , it can be thought of as a free ( radiative ) field that interacts with the particle ; it is this interaction that gives rise to the self-force.the mathematical tools required to derive the equations of motion of a point scalar charge , a point electric charge , and a point mass in a specified background spacetime are developed here from scratch . the review begins with a discussion of the basic theory of bitensors ( section 2 ) . it then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle s word line ( section 3 ) . it continues with a thorough discussion of green s functions in curved spacetime ( section 4 ) . the review concludes with a detailed derivation of each of the three equations of motion ( section 5 ) .

Introduction and Summary General Theory of Bitensors Coordinate Systems Greens Functions Motion of Point Particles

statin therapy has been well established as a cornerstone of cardiovascular prevention , and yet despite potent therapies for lowering lowdensity lipoprotein cholesterol ( ldlc ) , substantial residual risk remains.1 , 2 , 3 clinical and epidemiological studies have demonstrated that triglyceride ( tg ) elevation is an independent risk factor for increased cardiovascular ( cv ) events , and therefore may represent one contributive factor of residual cv risk beyond statin therapy.1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 more recently , elegant mendelian randomization studies have supported a causal role for tg in the pathogenesis of cardiovascular disease ( cvd ) , showing that elevated tg are not merely a risk marker , but rather a risk factor and thus potentially modifiable.3 despite the available data , an important question that remains is whether treatment of modest degrees of tg elevation would decrease cv events , in particular in patients already receiving ldlc lowering therapy with statins . prior cv outcome studies that administered therapies with tglowering effects ( niacin or fenofibrate ) on top of statin therapy did not reach their primary endpoints . nonetheless , these studies also did not prospectively enroll patients with elevated tg levels despite statin therapy,6 , 12 , 13 , 14 , 15 and subgroup analyses suggested possible benefits to tg lowering in patients with dyslipidemia.5 , 6 outcome studies of relatively low doses of prescription omega3 therapies in japan ( the japan epa lipid intervention study [ jelis])16 and italy ( gruppo italiano per lo studio della sopravvivenza nell'infarto miocardico [ gissi])17 , 18 have suggested that omega3 therapy may provide cv protection . however , these studies were performed in single countries prior to current treatment guidelines , and therefore provide supportive but not conclusive evidence of cv benefit . other more recent omega3 therapy outcome studies conducted in the presence of statins have been less encouraging , but these studies were characterized by evaluating nonhypertriglyceridemic patient populations ( eg , tg < 200 mg / dl ) and administering low doses of longchain omega3 fatty acids ( eg , eicosapentaenoic acid [ epa ] and/or docosoahexaenoic acid [ dha]).19 , 20 , 21 , 22 , 23 , 24 omega3 therapies , including epa , have been postulated to have cardioprotective effects such as beneficial changes to tg and other lipid and lipoprotein parameters ( eg , non highdensity lipoprotein cholesterol [ nonhdlc ] , apolipoprotein ciii ) , as well as other potential benefits beyond plasma lipid modification.19 , 25 , 26 , 27 , 28 , 29 , 30 icosapent ethyl ( vascepa ; amarin pharma inc . , bedminster , nj ) is a highly purified ethyl ester of epa , which has been reported to improve atherogenic dyslipidemia characterized by reductions in tg , tgrich lipoproteins , and factors involved in their metabolism , without raising ldlc.25 , 26 , 27 , 28 , 29 based on trials with tg lowering as the primary endpoint , this prescription therapy is currently approved for use in the united states by the us food and drug administration ( fda ) as an adjunct to diet to reduce tg levels in adult patients with severe hypertriglyceridemia ( 500 mg / dl).25 , 26 in this range of very elevated tg levels , reduction is considered to be clinically necessary to decrease the risk of pancreatitis . in addition to beneficial changes to tgrich lipoproteins and other plasma lipid markers , some clinical studies with higherdose epa also suggest beneficial effects on markers of oxidation and inflammation , coronary plaque characteristics , and major cv events.16 , 25 , 26 , 29 , 31 , 32 , 33 for example , in contrast to the fenofibrate and niacin studies , jelis found a 19% relative risk reduction in cv events in statintreated patients with relatively normal tg but a more pronounced 53% reduction in the subgroup with mixed dyslipidemia , specifically tg 150 mg / dl and hdlc < 40 mg / dl.4 , 16 although confirmation of these results is needed in western populations , the reduction of cv events with epa therapy in a patient population with relatively normal tg levels suggests that epa may have pleiotropic effects beyond plasmalipid modification . it is worth noting that the promising results from jelis occurred with a highpurity epa preparation dosed at 1.8 g / d in a japanese population , for whom the baseline epa levels are higher than in western populations due to greater dietary intake of marine omega3 fatty acids . icosapent ethyl 12week dosing at 4 g / d in a highrisk population similar to that within the reduction of cardiovascular events with icosapent ethyl intervention trial ( reduceit ) who had persistent elevations of tg after treatment with statins resulted in significant reductions in tg and atherogenic lipoproteins,26 , 27 , 28 as well as comparable plasma epa levels as the 1.8 g / d dosing group in jelis.34 therefore , a dose of 4 g / d was selected as the dose for further study . in this context , reduceit was designed to determine if treatment with icosapent ethyl 4 g / d vs placebo would reduce ischemic events in patients at increased cv risk already being treated with statins . reduceit ( nct01492361 ) is a phase 3b , international , multicenter , prospective , randomized , doubleblinded , placebocontrolled , parallelgroup trial of icosapent ethyl 4 g / d ( 2 g twice daily with food ) vs placebo ( figure ) . the main objective is to evaluate whether treatment with icosapent ethyl reduces ischemic events in patients at elevated cv risk concurrently treated with statins . inclusion and exclusion criteria are listed in table 1 and table 2 , respectively . men or women age 45 years with established cvd ( cv risk stratum 1 , table 1 ) or age 50 years with diabetes mellitus in combination with 1 additional risk factor for cvd ( cv risk stratum 2 , table 1 ) were eligible for inclusion . fasting tg levels 150 mg / dl and < 500 mg / dl were required . a study amendment was made during the early part of the trial , increasing the lower end of the fasting tg level from 150 mg / dl to 200 mg / dl , to increase enrollment of patients with more significant tg elevations . ldlc levels needed to be > 40 mg / dl and 100 mg / dl , with patients on stable statin therapy ( ezetimibe ) for 4 weeks prior to the ldlc and tg qualifying measurements for randomization . if patients met the inclusion criteria at visit 1 , they were asked to return for the randomization visit ( visit 2 ) and entered the treatment / followup period . patients who were not eligible at visit 1 but who became eligible in the next 28 days ( such as patients whose statin dose changed at visit 1 and/or needed to wash out prohibited medications ) may have returned for an optional second screening visit ( visit 1.1 ) . such patients entered a statin stabilization / medication washout period of 28 days prior to rescreening . patients who were eligible following screening / rescreening entered the treatment / followup period , with followup visits occurring at 4 months , 12 months , and annually thereafter . * a study amendment ( may 2013 ) was made , increasing the lower end of the fasting tg level from 150 mg / dl to 200 mg / dl to increase enrollment of patients with tg 200 mg / dl ; it is anticipated that mean and median qualifying tg levels will be > 200 mg / dl . eventdriven design : approximately 1612 primary efficacy events will be required during the study ; study duration will vary accordingly . abbreviations : cv , cardiovascular ; cvd , cardiovascular disease ; ldlc , lowdensity lipoprotein cholesterol ; mi , myocardial infarction ; reduceit , reduction of cardiovascular events with icosapent ethyl intervention trial ; t2 dm , type 2 diabetes mellitus ; tg , triglycerides . abbreviations : abi , anklebrachial index ; bp , blood pressure ; cad , coronary artery disease ; cr , creatinine ; crcl , creatinine clearance ; cv , cardiovascular ; cvd , cardiovascular disease ; dm , diabetes mellitus ; hdlc , highdensity lipoprotein cholesterol ; hscrp , highsensitivity creactive protein ; htn , hypertension ; ldlc , lowdensity lipoprotein cholesterol ; mi , myocardial infarction ; nsteacs , non stsegment elevation acute coronary syndrome ; pad , peripheral arterial disease ; tg , triglycerides . note : patients with dm and cvd as defined above are eligible based on the cvd requirements and will be counted under cv risk stratum 1 . only patients with dm and no documented cvd as defined above need 1 additional risk factor as listed , and they will be counted under cv risk stratum 2 . a study amendment ( may 2013 ) was made , increasing the lower end of the fasting tg level from 150 mg / dl to 200 mg / dl to increase enrollment of patients with tg 200 mg / dl ; it is anticipated that mean and median qualifying tg levels will be > 200 mg / dl . abbreviations : aids , acquired immunodeficiency syndrome ; apocii , apolipoprotein cii ; ck , creatine kinase ; crcl , creatinine clearance ; cvd , cardiovascular disease ; dbp , diastolic blood pressure ; hba1c , glycated hemoglobin ; hf , heart failure ; hiv , human immunodeficiency virus ; htn , hypertension ; ldlc , lowdensity lipoprotein cholesterol ; nyha , new york heart association ; om3 , omega3 ; pcsk9 , proprotein convertase subtilisin / kexin type 9 ; sbp , systolic blood pressure ; tg , triglyceride ; uln , upper limit of normal . the primary endpoint is a composite of cv death , nonfatal myocardial infarction ( mi ) , nonfatal stroke , coronary revascularization , or unstable angina . the key secondary endpoint is the composite of cv death , nonfatal mi , or nonfatal stroke . several other secondary , tertiary , and exploratory endpoints are being assessed ( table 3 ) , which were designed to provide additional insights into the potential effects of epa therapy on various outcomes and in distinct highrisk patient populations . abbreviations : apob , apolipoprotein b ; chf , coronary heart failure ; cv , cardiovascular ; dm , diabetes mellitus ; ecg , electrocardiography ; hdlc , highdensity lipoprotein cholesterol ; hscrp , highsensitivity creactive protein ; hstnt , highsensitivity troponin t ; htn , hypertension ; ldlc , lowdensity lipoprotein cholesterol ; mi , myocardial infarction ; non hdlc , non highdensity lipoprotein cholesterol ; pvd , peripheral vascular disease ; rlpc , remnant lipoprotein cholesterol ; tc , total cholesterol ; tg , triglycerides ; tia , transient ischemic attack ; ua , unstable angina ; vldlc , very lowdensity lipoprotein cholesterol . the first occurrence of any of these major adverse vascular events during the followup period of the study will be included in the incidence . for the secondary and tertiary endpoints that count a single event , the time from randomization to the first occurrence of this type of event will be counted for each patient . for secondary and tertiary endpoints that are composites of 2 types of events , the time from randomization to the first occurrence of any of the event types included in the composite the time from randomization to occurrence of the first and all recurrent major cv events defined as cv death , nonfatal mi ( including silent mi ) , nonfatal stroke , coronary revascularization , or ua determined to be caused by myocardial ischemia by invasive / noninvasive testing and requiring emergent hospitalization . including silent mi ; ecg will be performed annually for the detection of silent mi . composite endpoints include : composite of cv death , nonfatal mi ( including silent mi ) , nonfatal stroke , cardiac arrhythmia requiring hospitalization of 24 hours , or cardiac arrest ; composite of cv death , nonfatal mi ( including silent mi ) , nonelective coronary revascularizations ( defined as emergent or urgent classifications ) , or ua determined to be caused by myocardial ischemia by invasive / noninvasive testing and requiring emergent hospitalization ; composite of cv death , nonfatal mi ( including silent mi ) , nonelective coronary revascularizations ( defined as emergent or urgent classifications ) , ua determined to be caused by myocardial ischemia by invasive / noninvasive testing and requiring emergent hospitalization , nonfatal stroke , or pvd requiring intervention such as angioplasty , bypass surgery , or aneurysm repair ; and composite of cv death , nonfatal mi ( including silent mi ) , nonelective coronary revascularizations ( defined as emergent or urgent classifications ) , ua determined to be caused by myocardial ischemia by invasive / noninvasive testing and requiring emergent hospitalization , pvd requiring intervention , or cardiac arrhythmia requiring hospitalization of 24 hours . assessment of the relationship between baseline biomarker values and treatment effects within the primary and key secondary composite endpoints ; assessment of the effect of study drug on each marker ; and assessment of the relationship between postbaseline biomarker values and treatment effects within the primary and key secondary composite endpoints by including postbaseline biomarker values ( for example , at 4 months , or at 1 year ) as a covariate . therefore , 1612 events would be required to have approximately 90% power with a 1sided level of 2.5% and with 2 interim analyses . approximately 70% of randomized patients were to be in cv risk stratum 1 ( established cvd ) and approximately 30% of randomized patients were to be in cv risk stratum 2 ( highrisk primary prevention defined by diabetes mellitus and other risk factors ) . randomization was stratified by cv risk strata , ezetimibe use , and by geographical region . protocol amendment 1 ( may 2013 ) changed the lower limit of tg levels for entry into the trial from 150 mg / dl to 200 mg / dl , as a majority of the steering committee members felt that those were the patients most likely to benefit from tg lowering . protocol amendment 2 ( july 2016 ) designated the composite of hard major adverse cardiovascular events ( cv death , nonfatal mi , nonfatal stroke ) as the key secondary endpoint per suggestions from the fda with steering committee concordance . approximately 8000 patients have been randomized at approximately 470 centers worldwide ( see supporting information , appendix , in the online version of this article ) . follow up will continue in this eventdriven trial until approximately 1612 adjudicated primary efficacy endpoint events have occurred . this study is being conducted in accordance with a special protocol assessment agreement with the fda . despite cv risk reduction through potent ldlc lowering therapies such as statins , substantial residual cv risk remains . epidemiological , biological , and genetic studies have provided robust evidence of a strong association between elevated tg levels and higher rates of cv events.1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 furthermore , tg reduction lowers several inflammatory markers associated with cv risk , and subgroup and post hoc analyses of outcome studies suggest possible reductions in major cv events with tglowering therapy.3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 finally , studies administering higherdose epa suggest additional beneficial effects beyond lipidlowering that may be unique to epa relative to other tglowering therapies , such as beneficial changes in coronary plaque characteristics , which may lead to reductions in major cv events.4 , 16 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 however , randomized data from large outcome studies across broad populations regarding pharmacological tg lowering and effect on cv outcomes have been mixed ( table 4).1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 part of the reason may involve differences between the classes of drugs studied , such as fibrates , niacin , and omega3 fatty acids . even among omega3 fatty acid studies , there are marked differences with respect to the relatively low doses of omega3 administered and the ratio of epa to dha.16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 in addition , different tglowering therapies may exert differential effects across lipid profiles . for example , fibrates and dhacontaining omega3 fatty acid mixtures have been shown to increase ldlc , which in turn might adversely influence trial results . among outcome studies administering tglowering agents beyond statin therapy , only the jelis trial using pure epa demonstrated a significant reduction in cv events in patients with relatively normal tg levels.16 the subgroup data ( table 5 ) from the action to control cardiovascular risk in diabetes ( accord ) lipid,6 atherothrombosis intervention in metabolic syndrome with low hdl / high triglycerides and impact on global health outcomes ( aimhigh),5 and jelis4 trials further support a prospective study of epa in a broader patient population with hypertriglyceridemia , as exemplified in reduceit , as a potential addon to statin therapy to reduce residual cv risk . that the lipid changes in jelis were relatively modest ( ie , approximately a 5% tg reduction ) raises the possibility that other pleiotropic effects beyond lipid lowering may have also contributed to the reduction in cv risk.4 , 16 finally , any benefits to tglowering therapies may be most pronounced among statintreated patients in the higher range of tg elevation ( ie , 200 mg / dl),4 , 5 , 6 for whom randomized prospectively designed outcome studies have not been previously conducted prior to the reduceit study . cv outcome trials administering therapies that can be used for tg lowering abbreviations : accord , action to control cardiovascular risk in diabetes ; aimhigh , atherothrombosis intervention in metabolic syndrome with low hdl / high triglycerides : impact on global health outcomes ; ala , alphalinolenic acid ; alphaomega , study of omega3 fatty acids and coronary mortality ; bip , bezafibrate infarction prevention ; bl , baseline ; chd , coronary heart disease ; ci , confidence interval ; cv , cardiovascular ; cvd , cardiovascular disease ; dha , docosahexaenoic acid ; eos , end of study ; epa , eicosapentaenoic acid ; er , extended release ; feno , fenofibrate ; field , fenofibrate intervention and event lowering in diabetes ; gissip , gruppo italiano per lo studio della sopravvivenza nell'infarto miocardicoprevenzione ; gissihf , gruppo italiano per lo studio della sopravvivenza nell'infarto miocardicoheart failure ; hdlc , highdensity lipoprotein cholesterol ; hf , heart failure ; hps2thrive , heart protection study 2treatment of hdl to reduce the incidence of vascular events ; hr , hazard ratio ; jelis , japan epa lipid intervention study ; mace , major adverse cardiac events ; mi , myocardial infarction ; nyha , new york heart association ; oae , omega acid esters ; omega , effect of omega 3fatty acids on the reduction of sudden cardiac death after myocardial infarction ; or , odds ratio ; origin , outcome reduction with an initial glargine intervention ; pbo , placebo ; rrr , relative risk reduction ; scd , sudden cardiac death ; su.fol.om3 , supplmentation en folates et omega3 ; t2 dm , type 2 diabetes mellitus ; tc , total cholesterol ; tg , triglycerides ; vahit , veterans affairs cooperative studies program highdensity lipoprotein cholesterol intervention trial ; vit e , vitamin e. mean or median values are presented . subgroup analyses of patients with dyslipidemia from cv outcome trials administering tglowering therapies added to statin therapy vs statin monotherapy abbreviations : accord , action to control cardiovascular risk in diabetes ; aimhigh , atherothrombosis intervention in metabolic syndrome with low hdl / high triglycerides : impact on global health outcomes ; bl , baseline ; cv , cardiovascular ; epa , eicosapentaenoic acid ; er , extended release ; hdlc , highdensity lipoprotein cholesterol ; hps2thrive , heart protection study 2treatment of hdl to reduce the incidence of vascular events ; jelis , japan epa lipid intervention study ; mace , major adverse cardiac events ; tg , triglycerides . bolded values approached / achieved statistical significance . reduceit is designed to evaluate whether treating atrisk patients with highdose epa will lower the rates of important ischemic events beyond statin therapy . however , this trial alone will not validate whether lowering tg specifically in patients with elevated tg levels will result in lower rates of important ischemic events , because the effects of epa may be broader than tg reduction alone . several trials , including reduceit , are ongoing or planned to determine if different tglowering therapies in patients with elevated tg levels lower the rate of important ischemic events.35 , 36 , 37 , 38 the use of different therapeutic agents across these trials may in aggregate help us better understand the relative importance of tg lowering alone and may also help define which potential effects observed in reduceit might be uniquely attributable to epa therapy . several lines of data , including comparison of the jelis study results to those of fibrate and niacin outcome studies , suggest that epa may be differentiated from other tglowering agents as statin addon therapy , by potentially providing unique pleiotropic cardioprotective benefits in addition to tg lowering . other changes in the lipidlowering field may also affect the interpretation of the ongoing reduceit trial . for example , the proprotein convertase subtilisin / kexin type 9 inhibitors are being tested in large cv outcome trials of patients for whom ldlc control from statin ( ezetimibe ) therapy may be insufficient or poorly tolerated . if these ldlc lowering agents are found to be beneficial , epa therapy could potentially serve as a complementary approach to reduce residual cv risk even further , though this specific combination would not have been studied well in terms of incremental effects on cv events . importantly , residual cv risk remains high in patients with ldlc well controlled by statins , and many of these patients will likely need to be treated from multiple angles . the growing body of tgrelated evidence suggests that tgrich lipoproteins may be a causal factor in such residual risk . consequently , tg lowering represents a target of great interest to optimize further cv risk reduction beyond the ldlc lowering benefits attained with statin use . epaspecific studies suggest that epa may provide unique cv benefits through favorable effects on plasma lipid parameters , as well as on other pleiotropic pathways . a major remaining question is how to achieve cv risk reduction beyond the benefits realized from effective management of ldlc . for patients with persistently high tg levels despite statin therapy , an agent that improves atherogenic dyslipidemia without raising ldlc and provides other potentially pleiotropic benefits may improve cv outcomes . the addition of epa to statin therapy may thus provide additional cv benefit . the reduceit trial with highdose epa is designed to address this longstanding scientific gap and to provide physicians with this muchneeded information to guide clinical care of patients at high cv risk . dr . bhatt has served on advisory boards for cardax , elsevier practice update cardiology , medscape cardiology , and regado biosciences ; has served on the board of directors for boston va research institute and society of cardiovascular patient care ; has been chair of the american heart association quality oversight committee ; has served on data monitoring committees for duke clinical research institute , harvard clinical research institute , mayo clinic , and the population health research institute ; has received honoraria from the american college of cardiology ( senior associate editor , clinical trials and news , for acc.org ) , belvoir publications ( editor in chief , harvard heart letter ) , duke clinical research institute ( clinical trial steering committees ) , harvard clinical research institute ( clinical trial steering committee ) , hmp communications ( editor in chief , journal of invasive cardiology ) , journal of the american college of cardiology ( guest editor , associate editor ) , population health research institute ( clinical trial steering committee ) , slack publications ( chief medical editor , cardiology today 's intervention ) , society of cardiovascular patient care ( secretary / treasurer ) , and webmd ( cme steering committees ) ; has served as deputy editor of clinical cardiology , as chair of the ncdraction registry steering committee , and as chair of the va cart research and publications committee ; has received research funding from amarin ( for his role as chair of the steering committee and principal investigator of reduceit ) , amgen , astrazeneca , bristolmyers squibb , eisai , ethicon , forest laboratories , ischemix , lilly , medtronic , pfizer , roche , sanofiaventis , and the medicines company ; has received royalties from elsevier ( editor , cardiovascular intervention : a companion to braunwald 's heart disease ) ; has served as site coinvestigator for biotronik , boston scientific , and st . jude medical ; has served as a trustee of the american college of cardiology ; and reports unfunded research with flowco , plx pharma , and takeda . dr . steg has received research grants from merck , sanofi , and servier and has received speaking or consulting fees from amarin , amgen , astrazeneca , bayer , boehringer ingelheim , bristolmyers squibb , cslbehring , daiichisankyo , glaxosmithkline , janssen , lilly , merck , novartis , pfizer , regeneron , sanofi , servier , and the medicines company . dr . brinton has received speaking and/or consulting honoraria from alexion , amarin , amgen , aralez , arisaph , astrazeneca , janssen , kastle , kowa , merck , pts diagnostics , regeneron , and sanofiaventis and has received research funding from amarin ( for his role as steering committee member of reduceit ) and kowa ( for his role as steering committee member of prominent ) . jacobson has served as a consultant for amarin , amgen , astrazeneca , merck , regeneron , and sanofi and has done research for amgen and regeneron / sanofi . miller has served as a consultant for amarin , akcea , gemphire , and pfizer . dr . tardif has received research grants from amarin , astrazeneca , dalcor , eli lilly , esperion , merck , pfizer , sanofi , and servier ; has received honoraria from amarin , astrazeneca , dalcor , sanofi , and servier ; and holds equity ( modest position ) in dalcor . ballantyne discloses grant / research support ( all paid to the institution , not individual ) from amarin , amgen , eli lilly , esperion , ionis , novartis , pfizer , regeneron , sanofisynthelabo , the national institutes of health , the american heart association , and the american diabetes association , and has served as a consultant for amarin , amgen , astrazeneca , boehringer ingelheim , eli lilly , esperion , ionis , matinas biopharma inc , merck , novartis , pfizer , regeneron , and sanofisynthelabo .

residual cardiovascular risk persists despite statins , yet outcome studies of lipidtargeted therapies beyond lowdensity lipoprotein cholesterol ( ldlc ) have not demonstrated added benefit . triglyceride elevation is an independent risk factor for cardiovascular events . highdose eicosapentaenoic acid ( epa ) reduces triglyceriderich lipoproteins without raising ldlc . omega3s have postulated pleiotropic cardioprotective benefits beyond triglyceridelowering . to date , no large , multinational , randomized clinical trial has proved that lowering triglycerides on top of statin therapy improves cardiovascular outcomes . the reduction of cardiovascular events with icosapent ethyl intervention trial ( reduceit ; nct01492361 ) is a phase 3b randomized , doubleblinded , placebocontrolled trial of icosapent ethyl , a highly purified ethyl ester of epa , vs placebo . the main objective is to evaluate whether treatment with icosapent ethyl reduces ischemic events in statintreated patients with high triglycerides at elevated cardiovascular risk . reduceit enrolled men or women age 45 years with established cardiovascular disease or age 50 years with diabetes mellitus and 1 additional risk factor . randomization required fasting triglycerides 150 mg / dl and < 500 mg / dl and ldlc > 40 mg / dl and 100 mg / dl with stable statin ( ezetimibe ) 4 weeks prior to qualifying measurements . the primary endpoint is a composite of cardiovascular death , nonfatal myocardial infarction , nonfatal stroke , coronary revascularization , or unstable angina . the key secondary endpoint is the composite of cardiovascular death , nonfatal myocardial infarction , or nonfatal stroke . several secondary , tertiary , and exploratory endpoints will be assessed . approximately 8000 patients have been randomized at approximately 470 centers worldwide . followup will continue in this eventdriven trial until approximately 1612 adjudicated primaryefficacy endpoint events have occurred .

INTRODUCTION METHODS DISCUSSION CONCLUSION Supporting information Conflicts of Interest

studies have shown that laparoscopic cbd stone retrieval is as efficient and effective as endoscopic retrograde cholangiopancreatography ( ercp ) . usually , the transcystic approach is considered the first treatment of choice for laparoscopic cbd exploration because transcystic cbd exploration has more benefits than the choledochotomy approach . in the laparoscopic setting , it would be difficult for surgeons to manipulate the choledochoscope into the cbd from a small opening in the cystic duct . to overcome this shortcoming from april 2010 to june 2012 , 9 consecutive patients diagnosed with cholelithiasis and cbd stones were enrolled in this study . there were 2 men and 7 women , with a median age of 57 years ( range , 4371 years ) . the inclusion criteria were as follows : no upper abdominal surgical history , stones measuring < 5 mm , no intrahepatic duct stones , number of stones <3 , normal liver function test results , no jaundice , and normal leukocyte count . all the patients were fully informed about the characteristics of the procedure and its advantages over conventional choledochotomy exploration and 2-stage minimally invasive procedures . the patient was transferred to the operating room for laparoscopic management of gallbladder stones and cbd stones and placed in the supine position . at the time of general anesthesia , prophylactic antibiotic the first assistant , who was in charge of handing the laparoscope , stood at the surgeon 's left . the procedure was carried out using a 4-trocar cholecystectomy technique . instead of a 5-mm trocar , a 12-mm trocar was inserted about 3 cm from the right costal arch , at the midclavicular line ( figure 1 ) . after dissection of the calot triangle , the cystic artery and cystic duct came into view . once the cystic artery was transected , dissection of the gallbladder from its bed was begun at the fundus and continued to the body and infundibulum . while the gallbladder was dissected free from the liver connections , the fundus of the gallbladder was extracted via the 12-mm port incision carefully under laparoscopic vision ( figure 2 ) . after a small incision was made in the fundus of the gallbladder extracorporeally , a suction device was inserted into the gallbladder cavity , aspirating the bile juice . a flexible choledochoscope was introduced into the gallbladder through the opening in the fundus of the gallbladder and gently advanced toward the cystic duct under the guidance of both laparoscopic imaging and endoscopic imaging ( figure 3 ) . before introduction of the choledochoscope into the cbd , intraoperative cholangiography was performed to confirm the diagnosis of cbd stones and provide information about the number , size , and location of stones , as well as the anatomy of the cystic duct and cbd . in most situations , the cystic duct needs to be dilated by the choledochoscope itself or by a dilator for passage of the choledochoscope . by use of both endoscopic and laparoscopic imaging , the cbd was thoroughly examined , and the stones were retrieved under direct choledochoscopic vision ( figure 4 ) . finally , the cystic duct was closed with clips or surgitie ( covidien , mansfield , massachusetts ) , and the gallbladder , within a retrieval bag , was removed from the abdomen through the 12-mm port . liver function tests and assessments of the amylase level and leukocyte count were performed in patients postoperatively . successful transcystic cbd stone clearance was achieved in 7 of 9 patients , whereas treatment failure occurred in the other 2 patients . the reasons for failure were a narrow cystic duct in 1 patient and the cystic duct joining the cbd on the left side in the other patient . the duration of the operation in the 7 patients with successful transcystic cbd stone clearance was 126 minutes ( range , 96141 minutes ) . postoperative ercp was successfully performed in the 2 patients in whom failure occurred . no bile leakage , hemobilia , abdominal bleeding , or pancreatitis occurred in our series . transient epigastric colic pain occurred in 2 patients and was relieved by use of anisodamine . a transient increase in the amylase level was observed in 3 patients , and the amylase level returned to normal on postoperative day 3 without any treatment . the external drainage tube was removed 48 hours postoperatively in the absence of surgical complications . finally , the patients were discharged home on day 4 postoperatively once we were completely assured that the operation was successful and no complications had occurred . short - term follow - up ( median , 23 months ; range , 1640 months ) showed no recurrence of cbd stones by use of magnetic resonance cholangiography . in the era of minimally invasive surgery , various options for the treatment of cbd stones in patients with gallbladder stones are available , including ercp plus laparoscopic cholecystectomy , open surgery , and 1-stage laparoscopic cholecystectomy and cbd exploration . recent reports have shown that laparoscopic clearance of cbd stones is as efficient and effective as that with ercp and can avoid the potential complications of ercp , such as cholangitis , pancreatitis , duodenal perforation , and bile duct injury . so , laparoscopic cholecystectomy with simultaneous transcystic cbd exploration has gained wide acceptance for 1-stage laparoscopic management of cholecystochodocholithiasis . there are 2 types of laparoscopic cbd exploration : the transcystic approach and the choledochotomy approach . more and more surgeons prefer the transcystic approach to choledochotomy for cbd stone clearance because the transcystic approach can avoid an incision in the cbd wall . to carry out laparoscopic transcystic cbd exploration , a small incision has to be made in the cystic duct . the key step for successful transcystic cbd exploration is introduction of the choledochoscope into the cystic duct . in the laparoscopic setting , surgeons often confront difficulties in manipulating the choledochoscope into the small cystic duct through its partial opening . to overcome these shortcomings , we developed a novel transcystic approach that would facilitate introduction of the choledochoscope into the cystic duct and then its advancement into the cbd . a narrow cystic duct and the unfavorable anatomy of the junction of the cystic duct and cbd resulted in losing access to the cbd and were responsible for the failure of the novel transcystic approach . no difficulties were met in the process of retracting stones in the selected patients . except for 2 wound infections in the 12-mm port , no other complications were observed . we attributed the results to our inclusion criterion requiring stones to measure < 5 mm . in the future , we would expand this technique to acute inflammatory settings , impacted stones , or stones measuring > 5 mm . in a recent study , chiarugi et al showed that laparoscopic transcystic exploration for single - stage management of common duct stones and acute cholecystitis was a simple technique with a high yield of cbd clearance in the acute setting because the dissection of the calot triangle is facilitated by the edema . laparoscopic cbd exploration via a transcystic approach together with holmium laser lithotripsy can solve impacted or large solitary stones . laser lithotripsy can serve as an additional tool for the laparoscopic surgeon when confronted with impacted or large stones . laparoscopic cholecystectomy with simultaneous laparoscopic cbd exploration offers the advantage of avoiding an extra procedure and the potential complications of ercp . our results , along with other reports , have shown that single - stage laparoscopic cbd stone retrieval was feasible and efficient . our novel technique provides an alternative transcystic approach for single - stage laparoscopic cbd exploration . we believe that more and more cbd stones can be treated by the transcystic approach with advancements in equipment and surgical skill .

background and objectives : one - stage laparoscopic management for common bile duct stones in patients with gallbladder stones has gained wide acceptance . we developed a novel technique using a transcystic approach for common bile duct exploration as an alternative to the existing procedures.methods:from april 2010 to june 2012 , 9 consecutive patients diagnosed with cholelithiasis and common bile duct stones were enrolled in this study . the main inclusion criteria included no upper abdominal surgical history and the presence of a stone measuring < 5 mm . after the gallbladder was dissected free from the liver connections in a retrograde fashion , the fundus of the gallbladder was extracted via the port incision in the right epigastrium . the choledochoscope was inserted into the gallbladder through the small opening in the fundus of the gallbladder extracorporeally and was advanced toward the common bile duct via the cystic duct under the guidance of both laparoscopic imaging and endoscopic imaging . after stones were retrieved under direct choledochoscopic vision , a drainage tube was placed in the subhepatic space.results:of 9 patients , 7 had successful transcystic common bile duct stone clearance . a narrow cystic duct and the unfavorable anatomy of the junction of the cystic duct and common bile duct resulted in losing access to the common bile duct . no bile leakage , hemobilia , or pancreatitis occurred . wound infection occurred in 2 patients . transient epigastric colic pain occurred in 2 patients and was relieved by use of anisodamine . a transient increase in the amylase level was observed in 3 patients . short - term follow - up did not show any recurrence of common bile duct stones.conclusion:our novel transcystic approach to laparoscopic common bile duct exploration is feasible and efficient .

INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSION

the diabetes control and complications trial1 and the kumamoto study2 have shown that intensive insulin therapy and the resulting improvements in glycemic control reduce the incidence and delay the progression of microvascular complications . however , neutral protamine hagedorn ( nph ) insulin , which was used as basal insulin in these studies , has several limitations . of note , its duration of action is only 812 hours , with a peak in action occurring within 46 hours after subcutaneous administration , thus increasing the risk of hypoglycemia.37 indeed , some patients complain of hypoglycemia before dawn , necessitating a reduction in the nph insulin dose at bedtime . however , reducing the nph insulin dose at bedtime increases the blood glucose level in the morning . additionally , nph insulin is a suspension , which must be thoroughly resuspended before injection , and inadequate resuspension results in a very large day - to - day glycemic variability of action.8,9 therefore , to achieve tight glycemic control without increasing the risk of hypoglycemia , insulin preparations with a long duration of action and low day - to - day glycemic variability in terms of glucose - lowering action are needed . insulin glargine4,6,10 and insulin detemir5,7,11,12 are basal insulin analogs of the dissolution type that have flatter profiles and longer duration of action compared with nph insulin . however , there is controversy over which insulin analog has the longer and more stable action . therefore , in this study , the aim was to compare the glucose - lowering effect and glycemic stability of insulin glargine with those of insulin detemir using continuous glucose monitoring ( cgm ) . diabetic patients who were prescribed basal - bolus insulin therapy with nph insulin as basal insulin at bedtime for 1 year or more were enrolled in the study . patients who injected nph insulin two or more times per day , with proteinuria > 1.0 g / day , serum creatinine > 132 mol / l ( men ) or 106 mol / l ( women ) , abnormal aspartate aminotransferase/ alanine aminotransferase elevation ( > 3 the upper limit of normal ) , myocardial infarction or stroke within 6 months prior to study entry , or hba1c all patients received an explanation of the procedures and possible disadvantages of participating in the study and gave written informed consent prior to entry . this study was approved by the institutional review board of kitasato institute hospital and was performed in accordance with the declaration of helsinki . patients were randomized using a computer to either sequence a ( nph insulin was first switched to insulin glargine , then to insulin detemir ) or sequence b ( insulin detemir followed by insulin glargine ) . the patient s prior nph insulin was discontinued and replaced with the allocated long - acting insulin analog ( insulin glargine or insulin detemir ) . patients were asked to continue their other antihyperglycemic medications and to not change their dosage throughout the study . to compare insulin glargine with insulin detemir under the same conditions , the dose of the long - acting insulin analogs was the same as that of nph , and the doses of bolus insulin ( insulin lispro or insulin aspart ) were not changed . the cgm examination , of 72 hours in duration from 12 pm on day 1 to 12 pm on day 4 , was carried out at least 5 days after switching insulin . the study drugs were crossed over on the day when the first cgm examination ended . the cgm sensor ( cgms system gold ; medtronic , northridge , ca ) patients were instructed to measure their capillary blood glucose using finger sticks , at least four times per day ( at mealtimes and at bedtime ) . the outcomes of this study included determining the effectiveness of each type of insulin on glycemic control and glycemic variability . glycemic control was estimated as the mean blood glucose ( mbg ) , the area under the glucose curve above 7.8 or 10.0 mmol / l ( area under the curve [ auc]>7.8,10 ) , and the percentage of time above 7.8 or 10.0mmol / l ( t>7.8,10 ) . the auc was calculated using the trapezoidal method . intraday glycemic variability was assessed as the standard deviation ( sd ) and the mean amplitude of glycemic excursions ( mage ) . the sd around the mean glucose values is considered the gold standard assessment of intraday glycemic variability.13 mage , described by service et al,14 is probably more appropriate for selecting the major glucose swings that are calculated as the arithmetic mean of differences between consecutive peaks and nadirs , provided that the differences are greater than the sd around the mean values.13 day - to - day glycemic variability was assessed as the mean of daily difference ( modd ) . modd , described by molnar et al,15 is the mean of the absolute difference between glucose values taken on 2 consecutive days at the same time . hypoglycemia , which was defined as a sensor value of 3.9 mmol / l , was also calculated as a total time at 3.9 the differences between two insulin analogs were analyzed using the wilcoxon rank - sum test . spss software 14.0j ( spss japan inc , tokyo , japan ) was used for all statistical analyses . diabetic patients who were prescribed basal - bolus insulin therapy with nph insulin as basal insulin at bedtime for 1 year or more were enrolled in the study . patients who injected nph insulin two or more times per day , with proteinuria > 1.0 g / day , serum creatinine > 132 mol / l ( men ) or 106 mol / l ( women ) , abnormal aspartate aminotransferase/ alanine aminotransferase elevation ( > 3 the upper limit of normal ) , myocardial infarction or stroke within 6 months prior to study entry , or hba1c all patients received an explanation of the procedures and possible disadvantages of participating in the study and gave written informed consent prior to entry . this study was approved by the institutional review board of kitasato institute hospital and was performed in accordance with the declaration of helsinki . patients were randomized using a computer to either sequence a ( nph insulin was first switched to insulin glargine , then to insulin detemir ) or sequence b ( insulin detemir followed by insulin glargine ) . the patient s prior nph insulin was discontinued and replaced with the allocated long - acting insulin analog ( insulin glargine or insulin detemir ) . patients were asked to continue their other antihyperglycemic medications and to not change their dosage throughout the study . to compare insulin glargine with insulin detemir under the same conditions , the dose of the long - acting insulin analogs was the same as that of nph , and the doses of bolus insulin ( insulin lispro or insulin aspart ) were not changed . the cgm examination , of 72 hours in duration from 12 pm on day 1 to 12 pm on day 4 , was carried out at least 5 days after switching insulin . the study drugs were crossed over on the day when the first cgm examination ended . the cgm sensor ( cgms system gold ; medtronic , northridge , ca ) patients were instructed to measure their capillary blood glucose using finger sticks , at least four times per day ( at mealtimes and at bedtime ) . the outcomes of this study included determining the effectiveness of each type of insulin on glycemic control and glycemic variability . glycemic control was estimated as the mean blood glucose ( mbg ) , the area under the glucose curve above 7.8 or 10.0 mmol / l ( area under the curve [ auc]>7.8,10 ) , and the percentage of time above 7.8 or 10.0mmol / l ( t>7.8,10 ) . intraday glycemic variability was assessed as the standard deviation ( sd ) and the mean amplitude of glycemic excursions ( mage ) . the sd around the mean glucose values is considered the gold standard assessment of intraday glycemic variability.13 mage , described by service et al,14 is probably more appropriate for selecting the major glucose swings that are calculated as the arithmetic mean of differences between consecutive peaks and nadirs , provided that the differences are greater than the sd around the mean values.13 day - to - day glycemic variability was assessed as the mean of daily difference ( modd ) . modd , described by molnar et al,15 is the mean of the absolute difference between glucose values taken on 2 consecutive days at the same time . mmol / l , was also calculated as a total time at 3.9 mmol / l . the differences between two insulin analogs were analyzed using the wilcoxon rank - sum test . spss software 14.0j ( spss japan inc , tokyo , japan ) was used for all statistical analyses . a total of eleven japanese patients , six with type 1 and five with type 2 diabetes , were enrolled between may 2008 and june 2009 . because of an alert for insulin glargine issued by the european association for the study of diabetes,16 this study was discontinued and the available data was analyzed . two patients were excluded from analysis because of protocol violation ( misuse of nph ) . therefore , nine patients ( five in sequence a and four in sequence b ) completed the study . mbg , as calculated from cgm values , was significantly lower with insulin glargine than with insulin detemir ( 9.6 2.4 mmol / l versus 10.4 2.8 mmol / l , p = 0.038 ) ( type 1 : 11.0 2.5 mmol / l ; type 2 : 8.4 1.8 mmol / l versus 9.0 2.2 in addition , auc>10 and auc>7.8 were significantly lower with insulin glargine versus insulin detemir ( table 2 ) . the sd was significantly lower with insulin glargine than with insulin detemir . however , the mage value was not significantly different between the two insulin analogs ( table 3 ) . the modd value was significantly lower with insulin glargine than with insulin detemir ( 2.2 1.1 mmol / l vs 3.6 1.7 mmol / l , p = 0.011 ; figure 2 ) ( type 1 : 2.7 1.2 mmol / l vs 4.7 1.8 mmol / l ; type 2 : 1.8 0.9 mmol / l vs 2.7 0.9 mmol / l ) . there was no difference between the two insulin analogs in terms of the total hypoglycemic time . this lack of a difference remained even after separating the results according to daytime and nighttime values . a total of eleven japanese patients , six with type 1 and five with type 2 diabetes , were enrolled between may 2008 and june 2009 . because of an alert for insulin glargine issued by the european association for the study of diabetes,16 this study was discontinued and the available data was analyzed . two patients were excluded from analysis because of protocol violation ( misuse of nph ) . therefore , nine patients ( five in sequence a and four in sequence b ) completed the study . mbg , as calculated from cgm values , was significantly lower with insulin glargine than with insulin detemir ( 9.6 2.4 mmol / l versus 10.4 2.8 mmol / l , p = 0.038 ) ( type 1 : 11.0 2.5 mmol / l versus 12.2 2.7 mmol / l ; type 2 : 8.4 1.8 in addition , auc>10 and auc>7.8 were significantly lower with insulin glargine versus insulin detemir ( table 2 ) . the sd was significantly lower with insulin glargine than with insulin detemir . however , the mage value was not significantly different between the two insulin analogs ( table 3 ) . the modd value was significantly lower with insulin glargine than with insulin detemir ( 2.2 1.1 mmol / l vs 3.6 1.7 mmol / l , p = 0.011 ; figure 2 ) ( type 1 : 2.7 1.2 mmol / l vs 4.7 1.8 mmol / l ; type 2 : 1.8 0.9 mmol / l vs 2.7 0.9 mmol / l ) . there was no difference between the two insulin analogs in terms of the total hypoglycemic time . this lack of a difference remained even after separating the results according to daytime and nighttime values . in this study , the glucose - lowering effect and glucose stability of insulin glargine was compared with those of insulin detemir using cgm . glycemic control parameters , such as mbg , auc>10 , and auc>7.8 , were better with insulin glargine than with insulin detemir . the present study suggests that insulin glargine has a greater glucose - lowering effect than insulin detemir at the same dose . the difference in glucose - lowering effect can be compensated for by increasing the insulin dose but there might be a difference in the cost - effectiveness and hypoglycemic episode . because the same tendency was found in both type 1 and type 2 diabetes ( mbg in type 1 : insulin glargine , 11.0 2.5 mmol / l versus insulin detemir , 12.2 2.7 mmol / l ; type 2 : 8.4 1.8 mmol / l ) , to maintain statistical power , the two types of diabetes were not distinguished . these findings suggest that , if higher doses of insulin detemir are administered to achieve equivalent glycemic control to insulin glargine , the hypoglycemic time might increase . furthermore , the intraday and day - to - day glycemic variability of insulin glargine was compared with those of insulin detemir . the results of cgm revealed that sd and modd were lower with insulin glargine than with insulin detemir . these findings suggest that insulin glargine might have better glycemic variability compared with insulin detemir . it is expected that the risk of hypoglycemia is lower with insulin glargine than with insulin detemir , if the aim of treatment is near - normal glycemia . several previous studies have compared insulin glargine with insulin detemir.1729 three studies using insulin - clamp tests yielded very conflicting results.1719 heise et al reported that the same doses ( 0.4 u / kg ) of insulin glargine and insulin detemir are very similar in terms of the mean shape of their pharmacodynamic profiles and duration of action in patients with type 1 diabetes.17 they also reported that the day - to - day glycemic variability is lower with insulin detemir . klein et al reported a similar duration of action and lower day - to - day glycemic variability with insulin detemir versus insulin glargine in patients with type 2 diabetes ( 0.81.6 u / kg).18 by contrast , porcellati et al reported that 0.35 u / kg of insulin detemir has similar effects to the same dose of insulin glargine during the first 12 hours , and that the metabolic effects of insulin detemir are lower at 1224 hours.19 six clinical studies have compared insulin glargine with insulin detemir . in five studies , in which all patients or more than half of the patients were injected with insulin detemir twice daily , glycemic control was similar to that of once - daily insulin glargine.2024 the other study , in which the majority ( 87.4% ) of patients were injected with insulin detemir once a day , suggested inferiority of glycemic control for insulin detemir versus once - daily insulin glargine.25 these clinical studies clearly showed that , at similar daily doses , insulin detemir has a shorter action time and weaker action than insulin glargine . these findings are consistent with the results of the present study and with the results of a clamp study reported by porcellati et al.19 tone et al compared the day - to - day glycemic variability of insulin glargine with that of insulin detemir.26 however , cgm was not used and the study evaluated only fasting plasma glucose ; therefore , the study was inconclusive . however , king et al and wiesli et al have reported comparisons of insulin glargine with insulin detemir using cgm . although these studies concluded that once - daily insulin detemir provided 24-hour glycemic control similar to that of insulin glargine in patients with type 2 diabetes , did glycemic variability was not reported.2729 to the best of the present authors knowledge , the present study is the first to show that insulin glargine has better glycemic variability than insulin detemir based on cgm . first , because of the alert for insulin glargine , it was deemed inappropriate to continue enrolling patients to receive insulin glargine . therefore , the number of subjects enrolled was too small to reach a definitive conclusion and patients with type 1 and type 2 diabetes were combined . however , as shown in figure 2 , most of the patients had lower modd values with insulin glargine than with insulin detemir . in fact , our finding of lower modd was consistent after stratification for the type of diabetes ( insulin glargine versus insulin detemir , type 1 : 2.7 1.2 mmol / l versus 4.7 1.8 mmol / l ; type 2 : 1.8 0.9 second , the doses of basal insulin used in the present study were different from those used in the earlier clinical studies . the average basal insulin dose was 0.24 u / kg / day in this study ( type 1 : 0.22 u / kg / day ; type 2 : 0.26 u / kg / day ) , which was much lower than in earlier clinical studies ( insulin glargine : 0.33210.7525 u / kg / day ; insulin detemir : 0.40210.8223 u / kg / day ) . the doses of basal insulin used in our study are similar to those used in the japanese national phase iii program for insulin glargine for japanese patients with type 1 diabetes ( mean : 0.21 u / kg / day)30 and insulin detemir for japanese patients with type 1 or type 2 diabetes ( mean : 0.27 u / kg / day).31 therefore , the insulin dose in the present study appears to be appropriate for japanese patients . the results of the present study suggest that insulin glargine provides more effective and more stable glycemic control than insulin detemir . because this study was too small to make a final conclusion , however , large - scale studies are required to confirm these findings .

objective : this study aimed to compare the glucose - lowering effect and glycemic variability of insulin glargine with those of insulin detemir.material and methods : this was an open - label , single - center , randomized , two - way crossover study in patients with diabetes on basal - bolus insulin therapy , with neutral protamine hagedorn ( nph ) insulin as basal insulin . patients switched from nph insulin to a course either of insulin glargine followed by insulin detemir , or insulin detemir followed by insulin glargine , continuing the same dose of the prior bolus of insulin . to evaluate the glucose - lowering effect , daily glycemic profiles were recorded for 72 hours by continuous glucose monitoring ( cgm ) in an outpatient setting . the mean amplitude of glycemic excursions , standard deviation ( sd ) , and the mean of daily difference ( modd ) were used to assess intraday and day - to - day glycemic variability.results:eleven patients were enrolled and nine completed the study . mean blood glucose calculated from cgm values was significantly lower with insulin glargine compared with insulin detemir ( 9.6 2.4 mmol / l versus 10.4 2.8 mmol / l , p = 0.038 ) . the sd was significantly lower with insulin glargine versus insulin detemir ( 2.5 0.9 mmol / l vs 3.5 1.6 mmol / l , p = 0.011 ) . the modd value was significantly lower with insulin glargine than with insulin detemir ( 2.2 1.1 mmol / l vs 3.6 1.7 mmol / l , p = 0.011 ) . there was no significant difference between the two insulin analogs in terms of hypoglycemia.conclusion:this study suggests that insulin glargine leads to more effective and more stable glycemic control than the same dose of insulin detemir .

Introduction Material and methods Patients Design of the study Glycemic control Glycemic variability Hypoglycemia Statistical analysis Results Patient characteristics Glycemic control Glycemic variability Hypoglycemia Discussion Conclusion

it was estimated that there were 1,500,000 new cancer cases and approximately 560,000 deaths out of cancer in 2009 . chemotherapy is an important treatment option for patients with cancer , however chemotherapy drugs suffer from numerous problems including nonspecific uptake by healthy tissue , poor circulation times , and suboptimal accumulation in the tumor . often , a large percentage of cytotoxic drug administered to the patient does not reach the tumor environment , but rather is distributed throughout the body , resulting in the many toxic effects associated with chemotherapy and a narrowing of the drug 's therapeutic window . the delivery of chemotherapeutic drugs to tumors is still a major hurdle in the eradication of cancer , and the continual development of drug delivery technologies is vital to future breakthroughs in chemotherapy . polymer micelles offer a promising approach to achieving these goals due to their inherent ability to overcome multiple biological barriers , such as avoidance of the reticuloendothelial system ( res ) . due to their unique size range ( 20150 nm ) , micelles are able to avoid renal clearance ( typically less than 20 nm ) and uptake by the liver and spleen ( particles greater than 150 nm ) . these micelles can also preferentially accumulate in solid tumors via the enhanced permeation and retention ( epr ) effect [ 3 , 4 ] . the epr effect is a consequence of the disorganized nature of the tumor vasculature , which results in increased permeability of polymer therapeutics and drug retention at the tumor site . due to these promising aspects , a number of groups have developed various polymer micelle motifs , encapsulating a wide range of therapeutic classes [ 517 ] . colon cancer is the third most common cancer in men and women in most of the developed world . irinotecan , a topoisomerase i inhibitor , is approved in the clinic for colorectal cancer first - line therapy in combination with 5-fluorouracil / leucovorin / oxaliplatin ( folfox ) regimen or for monotherapy in second - line therapy following a failed folfox regimen . sn-38 , the active metabolite of irinotecan , is about 5001000 times more cytotoxic than irinotecan [ 1820 ] . although irinotecan has demonstrated clinical utility , it is highly inefficient in delivering active sn-38 to tumor tissue . studies in humans have shown that only three to four percent of the administered irinotecan is actually converted to sn-38 , which is reliant upon activating carboxylesterase enzymes localized in the liver and gastrointestinal tract . in addition , up to 95% of sn-38 is bound to circulating proteins such as albumin , which drastically reduces its bioavailability . irinotecan treatment also is accompanied by dose - limiting toxicities of grade 3 and 4 diarrhea and neutropenia . these limitations of irinotecan result in poor exposure of sn-38 to the tumor environment and severe side effects in the patient . a major limitation , however , of free sn-38 is that it is hydrophobic and is unable to be used as a free drug in the clinic . several groups have addressed the solubility problem of sn-38 by covalently attaching sn-38 to a polymer or peptide [ 2426 ] . in particular , a polymeric micellar formulation of sn-38 based on peo - poly ( glutamic acid ) block copolymers through chemical conjugation of sn-38 to the free carboxyl groups present on the poly ( glutamic acid ) backbone has been developed . this formulation , known as nk012 , as well as a peglyated sn-38 formulation ( ezn-2208 ) , is currently in clinical trials [ 27 , 28 ] . while polymer - drug conjugates effectively address solubility of hydrophobic drugs , this prodrug approach is dependent on enzymatic or chemical cleavage of the bond to release the active drug . to develop an encapsulated formulation of sn-38 , sn-38 was loaded into a polymer micelle , resulting in aqueous solubility of sn-38 without modification of the drug . this polymer micelle ( termed it-141 ) was evaluated for pharmacokinetics and antitumor activity compared to irinotecan . the data reported herein support it-141 as a promising new antineoplastic agent for the treatment of colorectal cancer . azido - poly(ethylene glycol)-t - butyl carbonate - amine ( n3-peg - nh - boc ) was prepared as described previously . n - carboxy anhydrides ( ncas ) were prepared according to previously published procedures [ 30 , 31 ] . n3-peg12k - nh - boc ( 150 g , 12.5 mmol ) was dissolved into 1 l of ch2cl2/difluoracetic acid ( dfa ) ( 70/30 ) and was allowed to stir at room temperature overnight . the product was precipitated twice in diethyl ether and was recovered as a white powder ( yield 90% ) : h nmr ( d6-dmso ) 7.77 ( 3h ) , 5.97 ( 1h ) , 3.833.21 ( 1050 h ) , 2.98 ( 2h ) ppm . n3-peg10k - nh3/dfa ( 95 g , 7.92 mmol ) was weighed into an oven - dried , 2 l - round - bottom flask and was left under vacuum for three hours before adding the nca . asp(obu ) nca ( 17.04 g , 79.2 mmol ) was added to the flask ; the flask was evacuated under reduced pressure , and subsequently backfilled with nitrogen gas . dry n - methylpyrrolidone ( nmp ) ( 560 ml ) was introduced by cannula , and the solution was heated to 60c . the reaction mixture was allowed to stir for 24 hours at 60c under nitrogen gas . then , d - leu nca ( 24.88 g , 158 mmol ) and tyr ( obzl ) nca ( 47.08 g , 158 mmol ) were dissolved under nitrogen gas into 360 ml of nmp into an oven - dried , round bottom flask , and the mixture was subsequently added to the polymerization reaction via a syringe . the solution was allowed to stir at 60c for another three days at which point the reaction was complete ( as determined by hplc ) . the solution was cooled to room temperature , and diisopropylethylamine ( dipea ) ( 10 ml ) , dimethylaminopyridine ( dmap ) ( 100 mg ) , and acetic anhydride ( 10 ml ) were added . the polymer was precipitated into diethyl ether ( 10 l ) and isolated by filtration . the solid was redissolved in dichloromethane ( 500 ml ) and precipitated into diethyl ether ( 10 l ) . the product was isolated by filtration and dried in vacuo to give the block copolymer as an off - white powder ( 134.6 g , yield = 73% ) : h nmr ( d6-dmso ) 8.437.62 ( 50h ) , 7.35 ( 100h ) , 7.1 ( 40h ) , 6.82 ( 40h ) , 4.96 ( 40h ) , 4.633.99 ( 50h ) , 3.743.2 ( 1500h ) , 3.062.6 ( 60h ) , 1.36 ( 90h ) , 1.270.47 ( 180 ) . n3-peg12 k - b - poly(asp(obu)10)-b - poly(tyr(obzl)20-co - d - leu20)-ac ( 134.6 g , 6.4 mmol ) was dissolved into 1000 ml of a solution of pentamethylbenzene ( pmb , 0.5 m ) in trifluoroacetic acid ( tfa ) . the solution was precipitated into a 10-fold excess of diethyl ether , and the solid was recovered by filtration . the polymer was redissolved into 800 ml of dichloromethane and precipitated into diethyl ether . an off - white polymer was obtained after drying the product overnight in vacuo ( 111.8 g , yield = 93% ) : h nmr ( d6-dmso ) 12.2 ( 10h ) , 9.1 ( 10h ) , 8.517.71 ( 50h ) , 6.96 ( 40h ) , 6.59 ( 40h ) , 4.693.96 ( 60h ) , 3.813.25 ( 1500h ) , 3.062.65 ( 60h ) , 1.00.43 ( 180 ) . h nmr ( d6-dmso ) 171.9 , 171 , 170.5 , 170.3 , 155.9 , 130.6 , 129.6 , 127.9 115.3 , 114.3 , 70.7 , 69.8 , 54.5 , 51.5 , 50 , 49.8 , 49.4 , 36.9 , 36 , 24.3 , 23.3 , 22.3 , 21.2 . ir ( atr ) 3290 , 2882 , 1733 , 1658 , 1342 , 1102 , 962 cm . sn-38-loaded micelles were prepared by dissolving 1 g of itp-101 in 200 ml of water and 100 mg of sn-38 in 8 ml of methanol and 16 ml of toluene . the water was mixed with a silverson lt4r shear mixer at 10,000 rpm at 4c , and the organic solution was added dropwise . the solution was mixed for 30 minutes , then the resulting emulsion gently stirred on a magnetic stir plate overnight , allowing the toluene to evaporate . the sn-38-loaded micelle solution was filtered through a 0.22 m pes filter , then lyophilized to give a slightly yellow powder . the hplc instrumentation consisted of a waters alliance separation module ( w2695 ) equipped with a lichrosphere select b ( 5 m ) , 250 4.6 mm column coupled with a waters multi - wavelength fluorescence detector ( w2475 ) with excitation at 355 nm and emission at 515 nm . mobile phase consisted of a 70 : 30 phosphate buffer ( 10 mm nah2po4 , 0.1% tea , ph 3.5)/acetonitrile . flow rate was isocratic at 0.8 ml / min . elution time for sn-38 was determined to be 11.6 minutes , while camptothecin internal standard was 4.2 minutes . particle sizes were determined using dynamic light scattering on a wyatt dynapro ( santa barbara , calif ) . micelle solutions were prepared at 1 mg / ml in filtered water and were centrifuged at 2,000 rpm to remove any dust prior to analysis . all cells were purchased from american type tissue collection ( atcc ) and maintained in the following media : rpmi 1640 with 10% fbs , 2 mm l - glutamine , and 100 units / ml penicillin / streptomycin ( lncap , pc-3 , mg-63 , bxpc-3 , mcf-7 , and bt-474 ) , dmem with 10% fbs , 2 mm l - glutamine and 100 units / ml penicillin / streptomycin ( mda - mb-453 , mda - mb-231 ) , f12k with 10% fbs , 2 mm l - glutamine and 100 units / ml penicillin / streptomycin ( a549 ) , and mccoy 's 5a with 10% fbs , 2 mm l - glutamine , and 100 units / ml penicillin / streptomycin ( ht-29 and hct116 ) . all media , fbs , and supplements were purchased from mediatech ( manassas , va ) or hyclone . female athymic nude mice weighing about 2025 g were obtained from charles river laboratories ( wilmington , mass ) . for assessing cytotoxicity , cancer cell lines the following day , when the cells were 50% confluent , the cells were treated with it-141 , free sn-38 , or irinotecan in complete growth medium . the drugs remained on the cells for 72 hours without media change . at this timepoint , cell viability was determined using the cell titer glo kit and measured using a luminescent plate reader ( bmg labtech , cary , nc ) . ht-29 cells were subcutaneously injected into the right flank of nude mice at a concentration of 5 million in 0.1 ml pbs . when the tumors were approximately 300 mm , mice were randomly divided into two groups of eight and injected with 30 mg / kg ( sn-38-equivalent ) of it-141 or 30 mg / kg irinotecan . injection occurred by a fast iv bolus into the tail vein in a volume of 0.2 ml . the delivery vehicle for it-141 was isotonic saline and acidified ( ph 3.5 ) isotonic saline for irinotecan . mouse blood was collected at timepoints of 5 minutes , 15 minutes , 1 hour , 4 hours , 12 hours , 24 hours , and 72 hours . plasma was processed for hplc analysis by protein precipitation in ice - cold , acidified methanol ( 10% perchloric acid / methanol ) with 100 ng / ml camptothecin as internal standard , at a ratio of 1 : 4 plasma to methanol . tumors were homogenized in 20 mm ammonium acetate , ph 3.5 and extracted in acidified methanol as described above . samples were vortexed for 10 minutes , centrifuged at 13,000 rpm for 10 minutes , and the supernatant was transferred to hplc vials for analysis . ht-29 cells were subcutaneously injected into the right flank of nude mice at a concentration of 5 million in 0.1 ml pbs . when the tumors were approximately 300 mm , mice were given both single and multidose ( q4d 3 , day 0 , 4 , 8) intravenous injections of it-141 at doses ranging from 1090 mg / kg . the mtd was defined as a dose that caused no greater than a 10% loss in body weight and no treatment - related deaths . ht-29 and hct-116 colon cancer cells were harvested and resuspended in sterile pbs at a concentration of 2 million ( ht-29 ) or 4 million ( hct-116 ) cells per 0.1 ml pbs and injected subcutaneously into the right flank of athymic nude mice . tumors were allowed to establish logarithmic growth ( 714 days ) , and the animals were randomly divided into six to eight mice per group . drug was administered by a fast bolus injection of 0.2 ml into the mouse tail vein on a schedule of q4d 3 . tumor volume was calculated according to the formula : v = ( short diameter)(long diameter)/2 . percent inhibition was calculated using the following formula : ( 1)100vgroupvgroup 0vctlvctl 0100 , where vgroup is the tumor volume on the final day of the study , vgroup 0 is the tumor volume of the group on day 0 , vctl is the tumor volume of the control group on the final day of the study , and vctl 0 is the tumor volume of the control group on day 0 . tumor regression was calculated using the following formula : ( 2 ) vgroup 0vgroup100100 , where vgroup is the tumor volume on the final day of the study and vgroup 0 is the tumor volume of the group on day 0 . statistical differences in tumor volume between groups were calculated using the student 's t - test using microsoft excel , whereby p < 0.05 was considered statistically significant . itp-101 is a triblock copolymer consisting of poly(ethylene glycol)-b - poly(aspartic acid)-b - poly(d - leucine - co - tyrosine ) . the hydrophobic amino acids provide a core region into which a hydrophobic drug can reside , and the amphiphilic peg block forms a protective corona around the micelle , giving the delivery system stealth - like properties to avoid protein opsonization and res uptake ( figure 1 ) . the use of both d and l stereoisomers of amino acids in the leucine / tyrosine core block disrupts the secondary structure of the polypeptide . replacing the rodlike helical nature of the polypeptide with the flexibility of a random coil the middle aspartic acid block allows for a hydrogen - bonding segment which can be further stabilized with the use of metal ions , an aspect that is not utilized for it-141 . it-141 was formulated using itp-101 with various concentrations of sn-38 , ranging from 1 to 14% ( w / w ) , achieving greater than 90% loading efficiency . formulations of it-141 reconstituted in water or saline resulted in a homogeneous solution free of precipitate for up to four days at room temperature , and the lyophilized powder is stable for months . following formulation , the aqueous solubility of sn-38 in it-141 was 30 mg / ml , which is about a 6,000-fold increase in solubility of sn-38 . . dynamic light scattering ( dls ) experiments demonstrated that the micelle size was approximately 130 nm , with a standard deviation of 6 nm . thus , the average size of it-141 falls within the desired range to avoid renal clearance ( above 20 nm ) and escape uptake by the res ( below 150 nm ) . zeta potential measurements from electrophoretic light scattering experiments demonstrated that the surface charge of the micelle is overall neutral , with a range of readings from 5 to 5 mv . the sensitivity of various cancer cell lines to free sn-38 , it-141 , and irinotecan was compared in a cytotoxicity assay . as shown in table 1 , both free sn-38 and it-141 were extremely potent , and the sensitivity of the cells to it-141 was similar to free sn-38 across the cell lines . certain cell lines ( pc-3 , mda - mb-231 , and bt-474 ) were insensitive to both free sn-38 and it-141 . to determine the mtd of it-141 , ht-29 tumor - bearing nude mice were given both single and multidose ( q4d 3 ) intravenous injections of it-141 . these studies demonstrated that the multidose mtd of it-141 in tumor - bearing animals was 45 mg / kg and single dose mtd was 60 mg / kg . using 30 mg / kg of it-141 as a safe dose , the pharmacokinetic ( pk ) profile and tumor accumulation of sn-38 delivered from it-141 then compared to irinotecan in nude mice bearing ht-29 tumors ( table 2 ) . mice receiving a single injection of 30 mg / kg it-141 achieved a significant improvement in sn-38 plasma concentration and exposure compared to 30 mg / kg of irinotecan ( figure 2(a ) , table 2 ) . the cmax for both groups was achieved by the first measured time point of 5 minutes , with > 200-fold higher sn-38 concentration in mice treated with it-141 ( 209 g / ml ) compared to irinotecan ( 1.0 g / ml ) . sn-38 exposure as measured by area under curve ( auc ) from irinotecan was 2.5 ghr / ml , while sn-38 exposure from it-141 was 13.8-fold greater at 34.6 ghr / ml . no data could be obtained for irinotecan plasma concentrations beyond 12 hours as the concentration fell below the limit of detection . the concentration of sn-38 in the tumor over time is plotted in figure 2(b ) . the tumor auc of it-141 was determined to be 16.4 gh / g , which was significantly higher than irinotecan at 1.9 gh / g . it-141 also had a 47-fold higher cmax in the tumor than irinotecan ( 9.4 g / ml versus 0.2 g / ml ) . based on the pharmacokinetic data , it was hypothesized that it-141 would show superior antitumor efficacy in colon cancer xenograft models compared to irinotecan . to test the antitumor efficacy of it-141 , ht-29 tumor - bearing mice were treated with either itp-101 alone at 300 mg / kg , irinotecan at 60 mg / kg , or it-141 at 30 mg / kg ( figure 3(a ) ) . treatment with irinotecan at 60 mg / kg , which is near its mtd on this dosing schedule , did not inhibit ht-29 tumor growth significantly compared to polymer alone [ 26 , 32 ] . however , treatment with it-141 at half the dose of irinotecan induced significant tumor regression by day 18 , ultimately resulting in complete inhibition of tumor growth compared to itp-101 control and 35% regression from initial tumor volume ( p = 0.002 ) . dose - ranging studies were then performed to determine if the antitumor efficacy of it-141 is dose dependent ( figure 3(b ) ) . ht-29 tumor - bearing mice were intravenously administered it-141 at doses of 1 , 5 , 10 , 15 , 30 , and 45 mg / kg via tail vein injection . treatment with 1 , 5 , or 10 mg / kg did not result in a statistically significant inhibition of tumor growth compared to control mice receiving only saline . by day 20 , treatment with 15 mg / kg it-141 resulted in a 54% inhibition of tumor growth , respectively , compared to mice treated with saline ( p = 0.028 ) . treatment with 30 and 45 mg / kg resulted in complete tumor growth inhibition compared to saline control , with tumor regression of 59 and 87% , respectively ( p = 0.005 for both ) . similar results were found using another colon cancer xenograft model , hct116 ( figure 3(c ) ) . in this model , a dose of 5 mg / kg resulted in a 59% inhibition of tumor growth ( p = 0.008 ) compared to the itp-101-treated group . treatment with it-141 at 15 and 30 mg / kg in this model resulted in complete inhibition of tumor growth compared to the itp-101 polymer control , with 15% and 51% regression , respectively ( p = 1.0 e and 8.1 ) . taken together , these data demonstrate that it-141 achieved significantly greater antitumor efficacy , compared to irinotecan , and dose - dependent tumor regression in two colorectal cancer xenograft models of colon cancer , with effective doses between 15 and 30 mg / kg . a final study was performed whereby it-141 formulations with different weight loadings of sn-38 were compared to each other . it-141 formulations were prepared with 11% ( it-141 - 11% ) and 4% ( it-141 - 4% ) sn-38 ( w / w ) , and equivalent doses of sn-38 were administered i.v . in an ht-29 colon cancer xenograft model ( figure 4 ) . there were no statistical differences in efficacy between the two formulations at either 30 mg / kg ( p = 0.292 ) , 15 mg / kg ( p = 0.119 ) , or 5 mg / kg ( p = 0.138 ) . these data demonstrate that the percent loading by weight of sn-38 into the micelles does not affect antitumor activity . in this report , a novel triblock copolymer was used to encapsulate and solubilize the hydrophobic drug , sn-38 , which is the active metabolite of irinotecan . although irinotecan is used in the clinic as a prodrug , its efficacy is reliant upon carboxylesterase enzymes localized in the liver and gastrointestinal tract for conversion to the active metabolite , sn-38 . irinotecan treatment is often followed by late - stage diarrhea with 24% grade 4 incidence and can require antidiarrheal premedication . this limits the dose of irinotecan that can be administered safely in subsequent administrations , thereby reducing response rates in these patients [ 34 , 35 ] . sn-38 is a potent cytotoxic compound that , by itself , can not be used in the clinic due to its extreme hydrophobicity . have effectively addressed the solubility problem of sn-38 by conjugating sn-38 to peg - poly(glutamic acid ) , forming a micelle called nk012 , which is currently in clinical trials . other nanocarriers for sn-38 have been developed involving conjugation of sn-38 to a polymer or peptide [ 24 , 25 ] . as an alternative approach to direct sn-38 conjugation , a novel triblock copolymer was used to encapsulate sn-38 into a polymer micelle , precluding the need to modify the drug and for cleavage of the bond to release the active drug . the itp-101 triblock copolymer was developed to efficiently encapsulate hydrophobic molecules and release them at the site of disease ( in the tumor ) without drug conjugation . encapsulation of sn-38 to create it-141 resulted in a 6,000-fold increase in solubility of sn-38 and a micelle size of 130 nm , which is ideal for accumulation in tumors due to the epr effect . in vitro , it-141 was found to possess potent cytotoxic activity , which was similar to that of free sn-38 but several fold more potent than irinotecan . cell lines that were resistant to killing by it-141 were also resistant to free sn-38 , which may indicate a natural insensitivity of these cell lines to inhibition of topoisomerase i. this could arise through alterations in the expression of , or mutations in , the gene encoding topoisomerase i or the activity of drug efflux pumps . it has been shown that the drug efflux pump abcg2 is overexpressed in cells resistant to sn-38 . the pharmacokinetic profile of it-141 demonstrated significant improvement in exposure and cmax for sn-38 , with a modest improvement in half - life , compared to sn-38 derived from irinotecan . importantly , the plasma auc from it-141 exposure was 14-fold higher than the sn-38 exposure from irinotecan administered at the same dose ( 34.6 ghr / ml versus 2.5 ghr / ml ) . similarly , it-141 demonstrated higher exposure in ht-29 tumors , as measured by auc , than irinotecan . the higher auc of it-141 in the tumor indicated that it would potentially be more efficacious than irinotecan in xenograft models . indeed , it-141 was found to be superior to irinotecan in an ht-29 xenograft model and was potent in dose - range finding studies in both ht-29 and hct-116 xenografts . in both models , tumor regression was observed at 30 mg / kg in the ht-29 model and 15 mg / kg in the hct116 model . during the development of it-141 , it was found that it-141 could be formulated with sn-38 with weight loadings in the range of 114% . different it-141 formulations were prepared with varying weight loadings of sn-38 and were evaluated in an ht-29 xenograft experiment . it was found that it-141 - 4% w / w had equivalent antitumor activity to it-141 - 11% w / w , demonstrating no differences in efficacy between these formulations . it can be speculated , therefore , that despite sn-38 loading differences between the micelle , equivalent or similar overall concentrations of sn-38 are being delivered to these tumors . in summary , it-141 is a novel sn-38-loaded polymer micelle with superior pharmacokinetics and antitumor activity compared to irinotecan . although irinotecan is effective in the clinic , the ability to deliver sn-38 could be a superior treatment option for many patients . it-141 increased the solubility of sn-38 by 6,000-fold and had a diameter of 130 nm . it-141 demonstrated superior pharmacokinetics to irinotecan and potent antitumor activity in ht-29 and hct-116 colorectal cancer xenograft models . in summary , it-141 is a promising new therapeutic agent for colorectal cancer that warrants clinical investigation .

polymer micelles are promising drug delivery vehicles for the delivery of anticancer agents to tumors . often , anticancer drugs display potent cytotoxic effects towards cancer cells but are too hydrophobic to be administered in the clinic as a free drug . to address this problem , a polymer micelle was designed using a triblock copolymer ( itp-101 ) that enables hydrophobic drugs to be encapsulated . an sn-38 encapsulated micelle , it-141 , was prepared that exhibited potent in vitro cytotoxicity against a wide array of cancer cell lines . in a mouse model , pharmacokinetic analysis revealed that it-141 had a much longer circulation time , plasma exposure , and tumor exposure compared to irinotecan . it-141 was also superior to irinotecan in terms of antitumor activity , exhibiting greater tumor inhibition in ht-29 and hct116 colorectal cancer xenograft models at half the dose of irinotecan . the antitumor effect of it-141 was dose - dependent and caused complete growth inhibition and tumor regression at well - tolerated doses . varying the specific concentration of sn-38 within the it-141 micelle had no detectible effect on this antitumor activity , indicating no differences in activity between different it-141 formulations . in summary , it-141 is a potent micelle - based chemotherapy that holds promise for the treatment of colorectal cancer .

1. Introduction 2. Materials and Methods 3. Results 4. Discussion 5. Conclusions

we do nt know that what the new anti - diabetic agents long - term or unknown rare side - effects are on patients . by the time , we will be experienced their rare or long - term side - effects together . in this case , we aim to make health care providers alert to focus on a possible side effect of sitagliptin that may lead to noncardiac pulmonary edema . the administration of oxygen therapy , inhalation of beta agonist and intravenous furosemide infusion was started quickly . during follow - up of the patient , his symptoms improved by the treatment . a 74-year - old male patient with type 2 diabetes mellitus admitted to the emergency department with the complaints of progressive breathlessness , dry cough and swollen lower extremities . he was taking acarbose 50 mg 3 times a day and telmisartan hydrochlorothiazide 80/12.5 mg once a day . his hba1c was not within the target range so sitagliptin was added to ongoing therapy . after 1 week of starting sitagliptin therapy even though the patient had not heart failure he applied to the emergency department with a complaint of dyspnea . in the admission he had severe dyspnea and lower extremity edema . physical examination revealed bibasilar lung crackles , + + /++ pretibial edema , arterial blood pressure of 120/80 mmhg , heart rate of 120 pulse / min and respiratory rate of 30/min . the rest of the physical examination was normal . in the emergency department the administration of oxygen therapy , inhalation of beta agonist and intravenous furosemide infusion was started quickly . chest x - ray revealed bibasilar pulmonary edema [ figure 1 ] . during follow - up of the patient , his symptoms improved by the treatment . fasting plasma glucose was 231 mg / dl and the remaining laboratory parameters were normal . cardiogenic or noncardiogenic pulmonary edema is a condition that is associated with high morbidity and mortality . acute respiratory distress syndrome , high altitude pulmonary edema , disseminated intravascular coagulopathy , smoke inhalation , head trauma , overwhelming sepsis , hypovolemia shock , near - drowning and many drugs ( ranging from illegal drugs such as heroin and cocaine to aspirin and chemotherapy drugs ) are known to cause noncardiac pulmonary edema . naranjo probability scale of our patient was seven and we thought that it was probably an adverse drug reaction . so we told the patient to stop taking sitagliptin and recalled him for re - evaluation after few days . previous study reported that another dipeptidyl peptidase 4 ( dpp-4 ) inhibitors saxagliptin increased the rate of hospitalization for diabetic patients with heart failure . furthermore , there is an ehealthme document which shows us that the sitagliptin is also one of the causes of noncardiac pulmonary edema . 17,872 people reported to have side effects when taking sitagliptin . among them , 7 people ( 0.04% ) have noncardiogenic pulmonary edema . our case and a previous study have shown that dpp-4 inhibitors may cause pulmonary edema . if a patient admit an emergency unit with severe dyspnea , the physician should ask if it is related with the sitagliptin or not .

a 74-year - old male patient with type 2 diabetes mellitus admitted to the emergency department with the complaints of progressive breathlessness , dry cough , and swollen lower extremities . our patient had type 2 diabetes mellitus and hypertension for 3 years . his hba1c was not within the target range so sitagliptin was added to on - going therapy . after 1 week of starting sitagliptin therapy , even though the patient had not heart failure he applied to the emergency department with a complaint of dyspnea . the cardiovascular safety and efficacy of many anti - hyperglycemic agents such as sitagliptin , saxagliptin are unclear . our case has shown that dipeptidyl peptidase 4 inhibitors may cause pulmonary edema . hence , it should be used with cautious , especially in patients with heart failure .

Introduction Case Report Discussion Conclusion

air pollution , a global problem being faced by both the developed nations and the developing ones , has been aggravated by developments that typically occur as countries become industrialized : growing cities , increased traffic , rapid economic development and industrialization , and high levels of energy consumption . motor vehicles account for 6070% of the pollution found in an urban environment [ 24 ] . it is estimated that vehicles account for 70% of co , 50% of hc , 3040% of nox , 30% of spm , and 10% of so2 of the total pollution load in the major metros of india , of which two - thirds are contributed by two wheelers alone [ 5 , 6 ] . besides the human and animal populations , this problem has drastic impacts on the local environment and causes extensive damage to vegetation including crops , fruit trees , medicinal plants , and ornamentals . plants being directly and constantly exposed to the pollutants ( both gaseous and particulates ) play a significant role as indicators and in mitigating the problem . they absorb , accumulate , and integrate the pollutants impinging on their foliar surface , acting as the sinks for various pollutants and thus mitigating the problem . the plants do not render this service to mankind without any serious implications ; in turn , they suffer from various deformities caused by the integrating pollutants and show diverse morphological , biochemical , anatomical , and physiological responses . thus , the plants can be used as both passive biomonitors and biomitigators in the urban environment to indicate the environmental quality and to attenuate the pollution level in a locality [ 7 , 8 ] . pollutants like so2 , o3 , and co2 have many harmful effects as they affect the physiological activities of the plants . they enhanced the production of reactive oxygen species like h2o2 which is very harmful to the metabolic activities of the plants . sulfur dioxide polluted regions showed the higher activities of peroxidase [ 10 , 11 ] . vehicular traffic is the main source of particulate air pollution in lucknow and these are the prime source of air pollution in urban areas . the number of different categories of vehicles registered with rto ( regional transport office ) , lucknow , is 12,09,745 on march 31 , 2011 , which is 9.23% higher over the last year . charbagh is the most polluted area in lucknow , says a report published by indian institute of toxicology research . the study carried out in three locations of the state capital showed that charbagh has the highest average level of respirable particulate matter ( rspm ) , sulfur dioxide , and oxides of nitrogen among all the locations . as per the national ambient air quality standards ( naaqs ) , charbagh had rspm of 253.66 with 23.62 and 58.42 micrograms per cubic meter of sulfur dioxide and oxides of nitrogen , respectively . the report cited the addition of 109,773 vehicles on the roads of lucknow as the chief reason for pollution and called for emergency attention of policy markers , researchers , and regulatory agencies . it has been investigated as an anti - inflammatory for preventing cell proliferation and for encouraging liver regrowth . due to its ephedrine content , it possesses psychostimulant properties , affecting the central nervous system and also the heart . catharanthus roseus l. , also known as periwinkle , is an important medicinal plant which belongs to family apocynaceae and is an important source of indole alkaloids which are present in all plant parts . periwinkle is used for the treatment of diabetes , fever , malaria , throat infections , and chest complaints . the physiologically important and antineoplastic alkaloids , namely , vincristine and vinblastine , are mainly present in the leaves , whereas antihypertensive alkaloids , such as ajmalicine , serpentine , and reserpine , are reported to be present in the roots . vincristine and vinblastine alkaloids are used in the treatment of various types of lymphoma and leukemia . these catharanthus alkaloids are also used for the treatment of both malignant and nonmalignant diseases and in platelet and platelet associated disorders . both plants are used as roadside plants as a green belt in cities . in view of plants ' role in the indication and abatement of air pollution , this study was carried out to assess the impact of automobile pollution on the plant metabolism and foliar surface configuration of plants growing along the roadsides in the urban locality in order to identify their role as the biomarkers of air pollution . for micromorphological and physiological studies , leaves of sida cordifolia l. ( flannel weed ) and catharanthus roseus l. ( periwinkle ) were collected from the botany department , lucknow university , which was found to be healthy and treated as control ( c ) and also the plants growing inside the talkatora ( industrial area p1 ) which has been taken as polluted site ( industrial area , p1 ) , charbagh , loco workshop , p2 , which has been taken as polluted site . for micromorphological evaluation , whole studies were carried out by comparing only one polluted site ( p2 ) with healthy site in the summer . the pieces of leaves were cut ( 1 1 cm ) and placed in maceration mixture ( conc . hno3 + h2cro3 in a ratio of 9 : 1 ) . scanning electron microscopy ( sem ) examination of values of both genera was carried out at the birbal sahni institute of paleobotany ( bsip ) , lucknow , india . for biochemical and physiological studies , both polluted sites ( p1 and p2 ) were taken into consideration in comparison to healthy site in both the summer and the winter . photosynthetic pigments in leaves were extracted in 80% acetone by the method of lichtenthaler et al . . the extract was centrifuged and read out at 480 and 510 nm for carotenoid , 645 and 663 nm for chlorophyll , and 655 and 666 for phaeophytin . the reaction mixture for enzyme assay contained 0.005 m hydrogen peroxide in 0.025 potassium phosphate buffer ph 7.0 and this was standardized against 0.1 n kmno4 . to 2 ml of 0.1 m phosphate buffer ph 6.0 , 0.01% h2o2 and 0.5% ( w / v ) p - phenylenediamine were added . the whole reaction was carried out at 25c and color intensity was read at 485 nm . the data has been presented in tables and figures and is the mean of the observations made in triplicate ( n = 3 ) along with the standard error and the least significant differences between mean values ( p 0.05 ) . the use of plants as monitors of air pollution has long been accepted since plants often are the initial indicators of air pollution . plants improve the quality of urban life due to their large leaf areas , relative to the ground on which they stand . depending on structural properties of their surface , they can act as biological absorbers or filters of pollutants . in this way , they remove huge quantities of gaseous pollutants and airborne particles , thus improving the quality of the environment . some plant species have been identified to be able to absorb , detoxify , and tolerate high levels of pollution . the foliar surface is the most important receptor of atmospheric pollutants where they cause several structural and biochemical changes . the present studies on the plants growing in loco area indicate that auto exhaust pollution brought appreciable changes in the number of epidermal cells and stomata per unit area . plants of both genera growing very close to the loco area showed an adverse effect on this number . in the present investigation , it has been observed that the stomatal and epidermal frequencies decline , resulting in the significant fall in stomatal index ( table 1 ) . size of epidermal cells and stomata was increased in polluted population . since differentiation of stomata mother cells requires division of epidermal cells , therefore , a decrease in the frequency of stomata should be normally accompanied by an increase in the size of epidermal cells . our results were in conformity with the findings of which studied the effect of environmental pollution on morphology and leaf epidermis of commelina bengalensis . results were the same ; stem length , leaf area , flower size , and fruit size showed a marked reduction in growth in the plants from the polluted area . length and density of trichome increased , while stomatal frequency values and the epidermal frequency decreased , in response to environmental pollution ( table 1 ) . lower foliar surface showed stomata with board aperture and large size trichome , while slit - like aperture of stomata was observed in polluted site plant in comparison to control ( figure 1 ) . it has been reported that air pollutants increase cell permeability by damaging the membrane integrity . pollutant induced increased cell permeability may cause a loss of water from the guard cells to make them flaccid , which result in stomatal closure . in catharanthus roseus l. stomata was observed on either side of mid vein on the upper surface of healthy population [ figure 2(a ) ] , but stomata on one side of mid vein [ figure 2(d ) ] was observed on the plants collected from highly polluted site . lower foliar surface showed stomata with thin walled marginal cells ( figure 2(b ) ) in healthy plants , while , in polluted population , there were thick walled marginal cells with occluded stomata ( figure 1(e ) ) observed . pal et al . studied sunken stomata and thick cuticles ; small and dense cells and suberised cell walls are in favor of reducing pollutant entry into leaves and cells . when the leaf samples of these plants were examined under sem , the following observations were recorded . sem micrographs of lower foliar surface of flannel weed showed sunken stomata with occluded stomatal pores . it was also observed that cuticle was ruptured at the edge of stomata to form a crypt - like structure ( figure 3 ) . in sem micrographs of periwinkle , upper foliar surface showed encrypted and sunken stomata , while lower foliar surface showed stomata with striations arising from subsidiary cells ( figure 3 ) . chlorophylls a and b both were found to be decreased in leaves of both plants collected from polluted site in comparison to plants collected from healthy site ( hs ) healthy site ( figure 4 ) . the concentration of chl a and chl b content in flannel weed in the summer at polluted site ( p1 ) was decreased up to 30% and 43% , while at polluted site 2 ( p2 ) it was found up to 55% and 71% in comparison to healthy site . in the winter , chlorophyll a was decreased to 43% and 71% at p1 and p2 , respectively . in the winter , chlorophyll b also showed a reduction of 52% and 59% at p1 and p2 , respectively , in comparison to healthy site . total chlorophyll was highly reduced at p2 in comparison to p1 in both seasons ( figure 4 ) . ratio of chl a and chl b was found to be increased in the summer at both sites . but in the winter , ratio of chl a and b was found to be increased ( 19% ) at p1 and decreased ( 29% ) at p2 in comparison to healthy site . in periwinkle , chl a was highly reduced in the winter at both p1 ( 43% ) and p2 ( 67% ) in comparison to healthy site , while in the summer it was decreased up to 15% and 31% at p1 and p2 sites in comparison to healthy site . in periwinkle , total chlorophyll was also reduced in plants collected from p1 and p2 in comparison to healthy site , and reduction was more pronounced in the winter . ratio of chl a and chl b was increased in both seasons at both sites except in the winter at p1 site where it was found to be decreased ( figure 4 ) . chlorophyll measurement is an important tool to evaluate the effect of air pollutants on plants as it plays an important role in plant metabolism , and any reduction in chlorophyll content corresponds directly to plant growth . leaf chlorophyll content , thus , can provide valuable information about physiological status of plants . pollutants like so2 entering the leaf sulfite affects the carbon fixation , ribulose biphosphate carboxylase , glycolate oxidase activity , and photophosphorylation . increasing level of air pollution in lucknow is a major contributor to the formation of dense fog and low day temperature in winters . suspended particle matter ( spm ) emitted by vehicles and in the air combines with the moisture content in the atmosphere to increase the density of the fog , which lasts for a longer period . the spm are present in the atmosphere in summers as well but do not pose much problem because moisture content in the atmosphere is very low . in monsoon season , the pollutants are cleared by rainfall . however , in winters , as temperatures come down due to icy winds coming to plains from the snow clad hills , the moisture content is condensed into fog . the presence of spm expedites the process of fog formation , leading to a drop in day temperatures and chilly weather . the fog thus formed bars penetration of sun rays leading to a fall in temperature during the daytime . a higher chlorophyll content was found in the monsoon season than in the summer and is the least in the winter ; it might be due to the high no2 concentration which increases the sensitivity of plant to winter stress as observed by swarnlata et al . . low - chlorophyll - content winter is due to the high pollution level , temperature stress , low sunlight intensity , and short photoperiod . present study revealed that chlorophyll content in both plants varies with the pollution status of the area ; that is , the higher the pollution level in the form of automobile exhaust the lower the chlorophyll content . studies [ 3 , 27 ] also suggest that high levels of automobile pollution decrease chlorophyll content in plants near roadsides . the reason for degradation of chlorophyll pigments can also be attributed to the action of so2 and no2 on the metabolism of chlorophyll ; both of these gases are the constituents of vehicular emissions . the reduction in the concentration of chlorophyll might have also been caused by the increase in chlorophyllase enzyme activities , which , in turn , affects the chlorophyll concentration in plants . , carotenoids were found to be reduced in both seasons at both sites in comparison to healthy site but phaeophytin was found to be increased ( figure 5 ) . in flannel weed , percentage decrease at p1 was marginally increased in the summer in comparison to the winter . at p2 carotenoids concentration was highly reduced ( up to 74% ) and the reduction was more pronounced in the summer . in periwinkle , carotenoids concentration was also reduced in both seasons and both sites . reduction was significantly high in the winter at p2 in comparison to healthy site ( figure 5 ) . agarwal and sharma have reported significant reduction in carotenoids in leaf samples collected from polluted environment . have also reported a reduction in carotenoids content in the plants of albizzia lebbek benth due to being exposed to coal smoke . carotenoids protect photosynthetic organisms from potentially harmful photooxidative processes and are essential structural components of the photosynthetic antenna and reaction center . the pheophytin concentration of plant leaves of both genera was found to be opposite that of chlorophyll concentration . higher level of pheophytin was found in the winter in both the plant species when the pollution level was high . in flannel weed and periwinkle , the highest concentration of phaeophytin was observed in the winter at p2 but the increase was more ( 202% ) pronounced in flannel weed ( figure 5 ) . it might be due to the breakdown of chlorophyll to pheophytin as suggested by rao and le blanc . it indicates the sensitivity of plants to the pollutants ; the higher the phaeophytin level in the plant is , the greater the sensitivity to air pollution is . the activity of cat at both sites in both seasons in flannel weed and periwinkle was found to be increased ( figure 6 ) . maximum increment in cat activity in flannel weed and periwinkle was 112% and 36% , which was observed at p2 site in the winter . in the summer , maximum ( 179% ) increment in cat activity was observed at p2 in flannel weed . peroxidase activity was more in the winter than in the summer at healthy site ( figure 6 ) . in the winter , the percentage increase in pod activity in flannel weed . in periwinkle pod activity was found to be 24% and 26% at p1 and 105% and 81% at p2 , respectively . in the summer , the percentage increase in pod activity in flannel weed and periwinkle was found to be 40% and 24% at p1 and 101% and 49% at p2 , respectively . antioxidative enzymes cat and pod are effective quenchers of reactive oxygen species ( ros ) and play an important role in the adaptation and ultimate survival of plants during periods of stress . as plants produce significant amount of antioxidants to prevent oxidative stress caused by photons and oxygen , they represent a potential source of new compounds with antioxidant activity . studies of karjalainen et al . suggested that pod is a specific indication of so2 and no2 pollution . in combination , so2 and basically , gaseous pollutants like so2 are taken up by stomata and solubilized in aqueous phase of the cell wall and can diffuse across the plasma membrane . peroxidases have a very important role as they may act as sulfite oxidases in the presence of monophenolics . relative water content ( rwc ) represents a useful indicator of the status of water balance of a plant , essentially because it expresses the absolute amount of water , that the plant requires to reach artificial full saturation ( gonzalez - vilar , 2001 ) . relative water content was found to be low in polluted plants in comparison to healthy plants ( figure 6 ) . more rwc of a leaf helps to maintain its physiological balance under stress condition of dust pollutants . the relative water content in the leaves of flannel weed at p1 showed reduction of 6% and 14% , while in periwinkle , the reduction was 15% and 27% at p2 in the summer in comparison to healthy site . significant reduction was observed in flannel weed ( 21% ) and in periwinkle ( 14% ) in the winter at p2 in comparison to healthy site ( figure 6 ) . it was observed that rwc declines more in sensitive species than that in tolerant ones , as reported by singh . it is evident from the above discussion that the pollutants such as spm , so2 , and no2 from automobile exhaust not only cause bad air quality conditions around nearby areas but also cause significant reduction in morphological and physiological parameters . present studies clearly indicate that the vehicular induced air pollution reduces the concentration of photosynthetic pigments ( chl a , chl b , carotenoid , and phaeophytin ) in both the species exposed to roadside pollution . the antioxidative enzymes ( catalase and peroxidase ) were found to be enhanced while relative water content was reduced . in micromorphological studies , there was a reduction in stomatal frequency , epidermal cell frequency , and stomatal index , while length and breadth of stomata and epidermal cells were found to be increased in both the species . marked alterations were observed both in the physiological status and in the foliar surface ultrastructural configuration of both periwinkle and flannel weed plants growing at highly polluted site in comparison to healthy site . therefore , these plant species may be used as biomarkers and mitigators of pollutants coming out of the automobile exhaust . significant changes were recorded in flannel weed in comparison to periwinkle in the studied parameters . it was noticed from the above result that periwinkle was found to be more tolerant compared to the flannel weed .

auto pollution is the by - product of our mechanized mobility , which adversely affects both plant and human life . however , plants growing in the urban locations provide a great respite to us from the brunt of auto pollution by absorbing the pollutants at their foliar surface . foliar surface configuration and biochemical changes in plant species , namely , sida cordifolia l. and catharanthus roseus l. grown at roadside ( polluted site 1 , talkatora ; polluted site 2 , charbagh ) in lucknow city and in the garden of the university campus , which has been taken as reference site , were investigated . it was observed that air pollution caused by auto exhaust showed marked alterations in photosynthetic pigments ( chlorophyll , carotenoid , and phaeophytin ) , and relative water content was reduced while antioxidative enzymes like catalase and peroxidase were found to be enhanced . the changes in the foliar configuration reveal marked alteration in epidermal traits , with decreased number of stomata , stomatal indices , and epidermal cells per unit area , while length and breadth of stomata and epidermal cells were found to be increased in leaves samples wich can be used as biomarkers of auto pollution .

1. Introduction 2. Materials and Methods 3. Result and Discussion

myiasis is defined by zumpt as the infestation of live human and vertebrate animals with dipterous larvae , which , at least for a certain period , feed on the host s dead or living tissue , liquid body - substances , or ingested food . traumatic myiasis is caused by fly larvae infesting pre - existing traumatic lesions or actively gaining access to tissues . fly species that cause traumatic myiasis can be divided into obligate or facultative ones according to the nature of the host - parasite association . obligate traumatic myiasis involves larvae that can only develop on living tissue , whereas in facultative myiasis the larvae can develop on both living and dead tissues . here , we describe a rare case of traumatic myiasis in a domestic cat ( felis catus l. , mammalia : felidae ) caused by an association of sarcophaga tibialis macquart ( diptera : sarcophagidae ) and lucilia sericata ( meigen ) ( diptera : calliphoridae ) . a 10-year old european shorthair cat , missing from home for about 3 days in august 2014 , was found near its home in the village of san martino ( ferrara province , italy ) with a large wound on the rump near the base of its tail , which was almost completely detached ( fig . the veterinaries assumed that the injury had been caused by a dog bite and found an extensive traumatic myiasis in the wound caused by a high number of diptera larvae ( fig . the veterinaries treating the cat collected 60 larvae ( all first or second instar ) , which were placed in plastic test tubes and immediately brought to the laboratory of urban ecology , department of life sciences and biotechnology , university of ferrara , for identification . the wound was washed with an antiseptic ( povidone - iodine ) , and ivermectin was administered subcutaneously . afterwards , the cat s tail was surgically amputated and during surgery the cat was drip - fed with physiological solution , a vitamin support , and a corticosteroid . after suturing the wound the cat was treated with broad - spectrum antibiotics ( streptomycin and penicillin ) . in the laboratory of urban ecology the larvae were divided into 2 groups : 15 of them were immediately fixed in 4% formaldehyde and the other 45 were reared in a plastic box containing 90 g of cow liver , at 25c , 50% relative humidity and a 16/8 ( l / d ) photoperiod . upon reaching the third instar , the larvae were again divided into 2 groups according to their length ( respectively 14.80.7 mm and 11.61.0 mm ) and aspect ( fig . morphological investigations were performed with a nikon smz 800 stereomicroscope ( nikon instruments europe , amsterdam , the netherlands ) and a nikon eclipse 80i optical microscope ( nikon instruments europe ) , both connected to a nikon digital sight ds - fil camera ( nikon instruments europe ) . the identification of s. tibialis was carried out by examination of adult males ( fig . 2c ) emerged from the first group of larvae , based mainly on aspects of the genitalia ( fig . the identification of the second species as l. sericata was carried out using the identification key of szpila and was based on morphology of adult males ( fig . 2e ) emerged from the second group of larvae , namely the bright yellow basicosta ( fig . 2f ) . all examined larvae and adults are deposited in the laboratory of urban ecology , department of life sciences and biotechnology , university of ferrara , ferrara ( italy ) . reports of myiasis in cats are uncommon , probably because they usually groom themselves carefully . in the present case , infestation by these 2 fly species was favoured by a deep and extensive wound that had weakened the cat , preventing it from properly grooming and cleaning its fur . cases of myiasis in humans and animals caused by an association of more than one diptera species have been reported in the literature . the species involved are chrysomya rufifacies ( macquart ) ( diptera : calliphoridae ) with chrysomya megacephala ( fabricius ) ( diptera : calliphoridae ) , sarcophaga ruficornis ( fabricius ) ( diptera : sarcophagidae ) with musca domestica ( linnaeus ) ( diptera : muscidae ) , and c. megacephala and chrysomya bezziana villeneuve ( diptera : calliphoridae ) with lucilia sp . ( diptera : calliphoridae ) . myiasis caused by s. tibialis in association with another species had been reported only once , by villeneuve with sarcophaga crassipalpis macquart ( diptera : sarcophagidae ) . l. sericata has been reported to cause myiasis in association with chrysomya albiceps wiedemann ( diptera : calliphoridae ) and wohlfahrtia magnifica ( schiner ) ( diptera : sarcophagidae ) . the case we report is the first of myiasis caused by an association of s. tibialis and l. sericata . s. tibialis is a thermophilic , heliophilic , and generally synanthropic species , probably indigenous to the afrotropical region and widespread in africa ( including the canary islands , madagascar , and the seychelles ) , central and southern europe , turkey , the chagos archipelago in the oriental region , and oceania . the species is widespread in italy , including sardinia and sicily . like most sarcophagidae , eggs laid in groups or together with larvae have been reported not to hatch . as in most flies , abasa reported that at 20 - 22c the development from first larval stage to adult lasts about 20 - 27 days , whereas aspoas stated that at 25c development from first instar to adult lasts 20 - 22 days . recently , villet et al . reported that the optimal temperature for development of this species ( based on lowest larval mortality ) is about 20c . in our study , females of s. tibialis and l. sericata were attracted by the smell released by the wound and subsequently deposited larvae and eggs on it . adults of s. tibialis are usually attracted by decaying matter such as carcasses and excrements , where larvae may or may not be laid . larvae of this species have been reared in the laboratory on liver , fish carrion , fresh bird meat , dead snails , and chopped grasshoppers [ 3,17 - 19 ] . only 2 well - documented cases of cutaneous human myiasis caused by s. tibialis were reported in the literature . both occurred in tripoli ( libya ) in 1913 , the first in may and the second in july . both cases were connected to poor sanitation and the myiasis was localized to the scalp . the first case involved a bedridden boy affected by peritoneal tuberculosis and tinea capitis , the second occurred in a little girl affected by tinea capitis , pediculosis , and pyoderma . according to these reports , onorato hypothesized a possible connection between tinea capitis and cutanous myiasis by s. tibialis . besides these 2 cases , there is a hint of another case of human traumatic myiasis in algeria mentioned by villeneuve , but without any further detail . also , patton and evans stated that s. tibialis is known to cause intestinal myiasis in europe , but they did not report any data on the number of cases and localities of occurrence therefore , the present case is the first record of s. tibialis causing myiasis in italy and is probably the first well - documented case of this kind in europe . on the other hand , l. sericata is a widely distributed agent of myiasis in temperate areas and a probable cosmopolite . in the united kingdom , south africa , and new zealand , l. sericata is a relevant agent of myiasis in sheep . adults are diurnal and commonly breed on carcasses , dirty or wet sheep fleece , garbage and manure ; they are also attracted by open wounds and lesions where conditions are such that the larvae can complete their development , causing myiases such as fly strike in sheep . females start to lay eggs 5 - 9 days after emerging from the puparium and within 3 weeks they lay 2,000 - 3,000 eggs in 9 - 10 batches . the larval developmental rate is strongly temperature - dependent : between 22c and 29c , development from egg to adult occurs in 13 - 19 days . in southern europe , l. sericata is considered a synanthropic species associated to houses and rural areas undergoing urbanization . together with calliphora vicina robineau - desvoidy ( diptera : calliphoridae ) and lucilia illustris meigen ( diptera : calliphoridae ) , l. sericata is among the 3 species characterizing urban and suburban areas in europe . in our report the cat contracted myiasis in san martino , a small country village about 4 km from the city of ferrara ( ferrara province , italy ) . myiasis caused by l. sericata has been reported in domestic cats in america , europe , and asia and may be traumatic [ 5,29 - 33 ] , gastrointestinal ( anal and rectal ) , urogenital ( vaginal , penile and perineal ) [ 30,35 - 37 ] , or ocular . our report is the first case of traumatic myiasis by l. sericata in a domestic cat in italy , albeit in association with s. tibialis . the only other case of myiasis by l. sericata in a domestic cat in italy was a rectal one , although cutaneous myiases by this species have been reported in sheep and dogs , and humans . the present results on the first case of myiasis caused by an association of s. tibialis and l. sericata and on the first case of myiasis by s. tibialis in italy were obtained through a close cooperation between veterinaries and entomologists . studies on the biology , distribution , and modes of infestation of diptera causing myiasis could largely benefit from similar collaborations . accurate and detailed information on the distribution of species of medical and veterinary interest is limited in italy . thus , the compilation of an infestation map should be a priority objective for veterinary interventions and for ecological and biological studies .

we describe here a rare case of traumatic myiasis occurred in august 2014 , caused by an association of 2 diptera species , sarcophaga tibialis macquart ( diptera : sarcophagidae ) and lucilia sericata ( meigen ) ( diptera : calliphoridae ) , in a domestic cat in northern italy . species identification was based on adult male morphology . the present case is the first report of s. tibialis as an agent of myiasis in italy , and also the first ever report of myiasis caused by an association of s. tibialis and l. sericata . the cat developed an extensive traumatic myiasis in a large wound on the rump , which was treated pharmacologically and surgically . the biology , ecology , and distribution of s. tibialis and l. sericata are also discussed . a literature review is provided on cases of myiasis caused by s. tibialis , and cases of myiasis by l. sericata involving cats worldwide and humans and animals in italy .

INTRODUCTION CASE DESCRIPTION DISCUSSION

in benin , 64% of the population has consumed once rabbit meat at least , and 95% of them appreciated it positively . thus , to supply the market with white meat , rabbits ' farms are installed in periurban areas . to promote optimal growth performance of rabbits , appropriate feeding strategy is necessary . fibres are one of the main components of rabbits ' diets ; because they play a key role in rabbit feeding by contributing to caecum activity for efficient digestion . moreover , demonstrated that particle size is a major factor of fibre digestibility in rabbits . crude fibre level in growing rabbits ' diet varies from 14 to 16% , whereas in reproductive rabbits ' diets that level is between 12 and 13% . unfortunately , the availability of forages , main sources of fibre is low in peri - urban areas , and farmers have difficulties to provide rabbits with grass . the processing of complete diets with optimal level of fibres is therefore suitable to efficiently feed rabbits . palm - press fibres contain about 86.2% of dry mater , 4% of crude proteins , 21% of fat , 0.31% of calcium , 0.13% of phosphate and 36.4% of crude fibre . palm - press fibres can be dried and pelleted to overcome the problems of poor keeping quality and bulkiness . palm - press fibres can be therefore included in complete diets of rabbits , rodents and ruminants . crude proteins and crude fibre digestibility decreases when the level of palm - press fibres exceeds 2530% in ruminants diet . the marketing of palm - press fibres for animal feeding will provide additional revenues to palm oil producers in developing countries . the objective of this study was to contribute to the valorization of palm - press fibres in growing rabbits feeding by evaluating its optimal level in diets . a total of 64 rabbits weaned at 35 days old were divided in 16 groups of 4 rabbits each . at the beginning of the experiment , the average live body weight of these rabbits of local breed reared in benin was 857.2 g. each group of 4 rabbits ( 2 males and 2 females ) was housed in a cage ( length width height : 80 50 30 cm ) . they contained , respectively , 0% ( f0 , control diet ) , 5% ( f5 ) , 10% ( f10 ) , and 15% ( f15 ) of palm press fibres ( table 1 ) . two cages of rabbits were randomly selected in each row . at the beginning of the experiment , similar ( p > 0.05 ) average live body weights of rabbits were recorded in f0 ( 858.1 g ) , f5 ( 836.3 g ) , f10 ( 880.0 g ) , and f15 ( 854.4 g ) dietary treatments . the experiment took six weeks and finished when rabbits were thirteen weeks old . at six weeks old , four starved rabbits ( 2 males and 2 female ) were slaughtered per diet for carcass study . the performances of rabbits were compared using each cage of four rabbits ( two males and two females ) as repetition . repetition effect and interaction between diets and repetitions were not significant ( p > 0.05 ) . thus , analyses were performed according to the model as follows : ( 1)yi=+fi+i , where yi is the observation for dependent variables ; is the general mean ; fi is the fixed effect of the feed ; i is the residual error . the daily feed intakes of rabbits fed with the four diets ( figure 1 ) were similar during the experiment ( p > 0.05 ) . on average , daily feed intakes were , respectively , 78.4 10.7 g ( f0 ) , 79.5 10.2 g ( f5 ) , 79.7 9.7 g ( f10 ) and 79.94 11.0 g ( f15 ) . in the sixth week of experiment ( 13 week old ) the feed intake decreased in all dietary treatments . the decrease of feed intake was more important when the level of crude fibre in diet is low as it was the case in f0 and f5 diets ( table 2 ) . the daily body weight gains ( table 3 ) were similar between diets ( p > 0.05 ) . thus , at the end of the experiment ( 77 days - old ) , the live body weights were not significantly different ( p > 0.05 ) between rabbits fed f0 ( 1788.5 g ) , f5 ( 1805.0 g ) , f10 ( 1718.5 g ) and f15 ( 1801.3 g ) . the lowest feed conversion ratio and feeding cost were recorded in rabbits fed f15 diet ( table 3 ) . the economic feed efficiency that reports the revenue from the live body weight gain comparatively to the feeding cost , was not significantly affected by the dietary treatment ( p > 0.05 ) . thus , included , up to 15% in balanced diet , palm - press fibres had no significant effect on the survivability of growing rabbits . the carcass yields of rabbits were similar ( p > 0.05 ) between dietary treatments ( table 4 ) . additionally , the relative weight of digestive tract and abdominal fat evaluated comparatively to the carcass weight were not significantly affected by the level of palm - press fibres in diets ( p > 0.05 ) . however , compared to the control diet ( f0 ) , the proportion of liver was significantly lower in rabbit fed f5 and f15 dietary treatments ( p < 0.05 ) . the feed intakes recorded in all dietary treatments were close to 78.7 g / day ; but higher than 53.360.4 g / day and lower than 136.3 and 149.9 g / j . the light increase of feed intake of rabbits fed with palm press fibres - based diets ( f5 , f10 and f15 ) confirms the statements of [ 4 , 12 ] according to which , the feed intake is positively correlated with the level of fibre in diet . in hot and humid climate , the keeping of an optimal level of feed intake is a challenge in livestock . the use of palm press fibres - based diets can therefore , reduce the requirement of forages to feed rabbits and allow them to develop their intestinal microflora that is necessary for efficient digestion . the similar growth between rabbits fed different level of palm press fibres - based diets indicates the efficiency of that feedstuff in rabbit feeding . the daily weight gains of the experimental rabbits ( 19.65 to 23.07 g ) were higher than the 7.48 to 10.91 g reported in nigeria and 16.7 g found in benin with similar rabbit breed . compared to the control diet f0 , f5 and f15 diets improved lightly the growth performance of rabbits without any adverse effect on their survivability . the final live body weights of rabbit ( 1718 to 1805 g ) are close to 1746 g found at the same age in local population of rabbit in tunisia . the body weights of rabbits are also in the range of 1638.9 to 1862.5 g . the low performance of rabbits fed f10 diet might be due to a health or digestive problem . the decrease of feed conversion ratio and feeding cost in f5 and f15 diets confirms the efficiency of these diets and the profitability of palm press fibres inclusion in growing rabbits ' diets . feed conversion ratios ( 3.78 to 4.64 g feed / g body weight gain ) were lower than 5.81 to 8.11 feed / g weight gain , found in nigeria . however , feeding costs ( 760 to 816 fcfa feed / kg body weight gain ) were higher than about 596.4 to 685.1 fcfa feed / kg body weight gain . this economic result can be explained by the feed price ( 189 to 192 fcfa / kg feed ) that was higher than about 85.03 to 128.8 fcfa / kg feed reported by these authors . the result indicates in certain instance , the difference in feeds market between benin and nigeria . in monogastric livestock , compared to broiler , growing rabbits fed palm fibres - based diets produce therefore , about equally profitable white meat in benin . the carcass yields ( 60.8 to 62.9% ) are higher than 57.1% ; but lower than the 64.8 to 66.6% reported in rabbit fed pellet diets and fodder . the palm press fibres - based diets did not affect significantly the relative weight of digestive tract of rabbits . the abdominal fat in rabbits carcass increase lightly in f5 and f15 diets compared to the control diet ( f0 ) . these results show a similar effect of the experimental diets on rabbit meat productivity and carcass quality . moreover , the diets kept rabbits in apparently good health conditions as demonstrated the significantly low liver relative weight of rabbits fed f5 and f15 . this experiment suggests that growing rabbits can be fed exclusively with balanced palm press fibres - based diets . in such feeding strategy , up to 15% of palm press fibres can be included efficiently in the diets without any significant adverse effect on rabbits ' survivability and their abdominal carcass fat . to reduce grass and forage need in peri - urban rabbitry

an experiment was carried out to define the optimal rate of palm - press fibres in growing rabbits ' diet . in total , 64 weaned rabbits ( 35 days old ) of beninese breed were divided in 16 groups of 4 rabbits ( 2 males and 2 females ) each . during six weeks , rabbits were fed with 4 complete diets containing 0% ( f0 , control ) , 5% ( f5 ) , 10% ( f10 ) , and 15% ( f15 ) of fibres from a palm oil industry . results demonstrated that up to 15 of palm - press fibres can be included efficiently in growing rabbits ' diet . the daily feed intake was not significantly affected by the diet ( p > 0.05 ) . at 13 weeks old , the average live weights of rabbits were 1788.5 g , 1805.0 g , 1718.5 g , and 1801.3 g in respectively , f0 , f5 , f10 and f15 groups . no mortality of rabbits was recorded . compared to f0 , the feed conversion ratio and feeding cost decreased in the group of rabbits fed f15 diet . the carcass yield was similar between diets .

1. Introduction 2. Materials and Method 3. Results 4. Discussion 5. Conclusion

the promise of diverse applications including optical data processing and biological imaging has stimulated much interest in organic nonlinear optical ( nlo ) materials.1 within this field , organotransition metal complexes offer intriguing possibilities for creating new multifunctional materials in which potentially useful optical behaviour is combined with the redox , magnetic and other properties characteristic of such compounds.2 as a means to enhance the prospects for molecular materials , approaches to modulating reversibly molecular nlo properties have attracted considerable attention recently.3 the first report of a very pronounced and reversible redox - switching of the first hyperpolarisability ( the origin of quadratic molecular nlo effects ) clearly demonstrated the potential significance of metal complexes in this area.4 this work has been extended to second harmonic generation ( shg ) in langmuir blodgett ( lb ) thin films,5 and various related solution and molecular - level theoretical studies involving both quadratic and cubic nlo effects have been described.6 although the switching of nlo responses via redox chemistry has attracted much attention , using other stimuli is also of great interest . light - induced ( photochromic ) molecular rearrangements have been explored relatively widely.3 , 7 however , the speed of switching accompanying such structural changes is often quite limited , and their effects on macroscopic structures may be substantial . populating transient electronic excited states should allow much faster modulation effects without significant structural changes . early cndo / s calculations on some simple dipolar molecules , such as 4-nitroaniline , indicated that responses can be increased in excited states,8 and these predictions were verified subsequently.9 various experimental studies with purely organic chromophores reveal similar behaviour , mostly focusing on second hyperpolarisabilities ,10 and attempts to determine excited - state values by hyper - rayleigh scattering ( hrs ) have been reported.11 however , such measurements are fraught with complications and hence there is currently no reliable experimental method by which such molecular - level excited - state responses can be determined . therefore , the establishment of accurate theoretical approaches is of significant interest , as a guide to empirical studies that will most likely focus on the switching of bulk effects like shg . some time ago , sakaguchi et al . noted a small photoinduced switching of shg at 295 nm from alternating and highly diluted lb films containing the amide - substituted [ ru(2,2-bpy)3 ] ( bpy = bipyridyl ) derivative 1 ( figure 1).12 this observation was attributed to changes in on mlct excitation . however , the ground - state ( gs ) complex shows an intense 2,2-bpy - based absorption near the shg wavelength , so excitation - induced changes in absorption may affect the shg signal . notably , very few other related experimental or theoretical studies with metal complexes have been reported to our knowledge ( and these concern only responses).13 a ruthenium complex ( 1 ) studied previously for ps timescale photoswitching of shg in lb films,12 and the complexes 24 considered in the present work . the [ ru(nh3)5 ] complexes that we have studied as redox - switchable nlo chromophores4 , 5 show intense mlct bands in the visible region . consequently , they show very large responses that compare favourably with those of purely organic chromophores with moderate -conjugation lengths.2i , 14 these systems are therefore highly attractive subjects for photoswitching studies , and we describe here theoretical investigations , which indicate that mlct excitations lead to large changes in molecular nlo responses . the use of time - dependent density functional theory ( td - dft ) and ab initio methods to predict hyperpolarisabilities of gs chromophores is now well developed,15 but relevant considerations of electronic excited states are restricted to polarisabilities and/or small molecules.16 complex 2 is well studied,17 and stark spectroscopy in a 1:1 glycerol / water glass has been used to derive a modest static first hyperpolarisability 0 ( < 10 esu ) for the salt [ bf4]3.18 we have used hrs in acetonitrile ( mecn ) solutions and stark measurements in butyronitrile ( prcn ) glasses to afford substantially larger 0 values ( hrs / stark , 10 esu ) of 246/240 for [ pf6]319 , 20 and 744/1092 for [ pf6]3.21 note that we consistently use the so - called t - convention in this work,22 whereas previous reports1921 use the b - convention ; to convert to the t - convention , we use t=2 b . in addition , all of our values refer to the dominant component along the long molecular axis , approximately parallel to the dipole moment . the pronounced increases in nlo response on moving along the series 24 are consistent with their steadily extending -conjugated structures . in order to determine the most appropriate theoretical method for treating ru ammine complexes , we have tried various approaches to model the mlct excited states . previous gas - phase dft calculations using the b3p86 functional with the lanl2dz basis set proved qualitatively useful , but lack quantitative accuracy.21 a similar basis set combination lanl2dz(ru)/6 - 31 g * or 6 - 31+g*(h , c , n , o ) has been used by inerbaev et al.,23 and in a recent investigation by zhang and champagne.24 here , we use a larger basis set ( lanl2tz(f ) ) for ru in dft calculations , as well as different larger basis sets for various high - level ab initio methods . we provide a more detailed account of the methodology in the computational methods . comparing the new computational results with the experimental data shows that td - dft with the hybrid functionals b3lyp , b3p86 or m06 yields very good values for the first dipole - allowed excited state ( fdaes ) of 3 , when mecn solvent is included via the polarisable continuum model ( pcm ; table 1 ) . selected simulated spectra are shown in figure 2 , together with the experimental spectra of complexes 3 and 4 as their pf6 salts . comparisons with data published previously23 , 24 show that although using a larger basis set for ru does not affect the qualitative picture of the excitation properties , some significant quantitative differences are observed . selected data calculated for complexes 24 by using dft and ab initio methods , together with previously reported measured data [ a ] molecules 2 and 3 were optimised with b3lyp/6 - 31g**/lanl2tz(f ) ( ru ) , whereas 6 - 31 g * was used for 4 . all optimisations were performed in the gas phase , except for 2 , which was optimised in the gas phase and in h2o . [ b ] mecn used as solvent for 3 and 4 , h2o used for 2 . [ h ] for [ clo4]3 in h2o ( a very weak nir band at max = 855 nm is observed also),17e [ pf6]3,19 and [ pf6]3;21 max values in mecn at room temperature ; directly corresponding fos values are unavailable , so those quoted are in prcn at 77 k ( only slight variations due to changing the solvent and temperature are expected).20 a ) normalised electronic absorption spectra of 2 ( simulated ) and 3 ( simulated and experimental ) in solution ; all the simulated spectra are convolutions of the computed b3lyp values with a gaussian function with =2000 cm . b ) experimental and simulated electronic absorption spectra of 4 ; both cam - b3lyp and b3lyp simulated spectra are shown . the experimental data were obtained with the complex salts [ pf6]3 or [ pf6]3 in mecn.19 , 21 the excitation into the fdaes consists for 3 and 4 nearly exclusively of the homolumo transition , whereas for 2 it is a homo1lumo transition . the orbitals , shown in figure 3 for b3lyp as an example , demonstrate clearly that in each case a charge transfer from ru to the organic ligand is involved , confirming the expected mlct character . to better quantify these transitions , recently for the semiquantitative analysis of photoinduced ct processes , which is based on the differences in electron density between the ground and excited states.25 figure 4 shows the spatially - resolved density differences upon excitation for the three complexes . this model also affords estimates of the transferred charge qct and the ct distance rct , which are 0.288 e/1.571 for 2 , 0.953 e/4.218 for 3 , and 0.978 e/5.799 for 4 , evaluated for b3lyp . to put these data into perspective , we note that the corresponding values for the prototypical ct molecule 4-nitroaniline in mecn are 0.62 e/2.72 .25c the calculated rct values agree relatively well with the effective ( localised ) electron - transfer distances rab calculated from 01ab / e , where 01ab is the dipole - moment change between the diabatic states involved in the mlct transition . based on stark spectroscopic measurements , respective rab values of 3.6 and 5.7 are determined for [ pf6]3 and [ pf6]3 in prcn glasses at 77 k.20 , 21 orbitals ( b3lyp ) involved in the main transition from the gs to the fdaes for 2 ( top ) , 3 ( middle ) and 4 ( bottom ) . plots showing difference electron density between the gs and the fdaes of 2 ( top ) , 3 ( middle ) and 4 ( bottom ) ; green denotes positive differences , whereas negative differences are in red ; isocontour values 0.001 . the predicted max values agree less well with those measured for 4 , and the observed blue shift in the mlct band on moving from 3 to 4 is not reproduced in solution . however , this blue shift is predicted by the gas - phase results , albeit with a decrease in the overall accuracy of the max values , reminiscent of previous gas - phase b3p86/lanl2dz calculations.21 our new calculations using b3lyp , b3p86 or m06 give rather large discrepancies between theory and experiment for 2 . nonetheless , it is gratifying that the results obtained for 3 by using these functionals are very similar to those from high - level restricted active - space scf second - order perturbation theory ( raspt2 ) with a very large basis set and large active space ( see the computational methods for details ) , both in solution and the gas - phase . the long - range corrected functionals ( lrcfs ) cam - b3lyp,26 lc-pbe27 and wb97xb28 give max predictions less accurate than those obtained when using b3lyp , b3p86 or m06 for all three complexes ( see also figure 2 b ) . these results are quite surprising because one of the reasons lrcfs were introduced was specifically to improve descriptions of charge - transfer excitations by standard dft functionals.2628 however , our results concur with other recent studies on organotransition metal compounds.29 for example , escudero and gonzlez29c found poor performance by cam - b3lyp and lc-pbe for mlct excitations in trans-[rucl2(2,2-bpy)(co)2 ] , when compared to experimental and raspt2 results , with more accurate predictions from hybrid functionals . the reasons for such unsatisfactory performance of lrcfs are unclear at present . although only gas - phase results are available for the fully ab initio and reasonably high - level resolution of identity approximate coupled - cluster ( ri - cc2 ) method , they differ substantially from those derived from dft and raspt2 , and notably overestimate max when compared with experiment for 2 . for 4 , ri - cc2 predicts two very close - lying transitions ( max=389 nm ) of comparable intensity , which is also not predicted by any other method . the relative failure of ri - cc2 may derive from the rather large values of the d1 diagnostic for the cc2 gs wavefunction ( 0.317 , 0.124 and 0.115 for 2 , 3 and 4 , respectively ) . values of d1 above 0.050 may indicate a large multi - configurational character of the gs , for which the single - reference method cc2 is not suitable.30 however , without taking into account the apparently large solvent effect , it is difficult to judge the performance of ri - cc2 with confidence . as a general point , we note that dft takes into account the non - dynamical correlation , although only partially and in a non - systematic way.31 this aspect may explain why the method performs better for complex 3 than for 2 , which according to the d1 diagnostic from cc2 may have stronger multi - configurational character . further tests using different optimised geometries show that the geometry does not have a large influence on max or fos . this observation validates the comparisons between the results of the raspt2 calculations for 3 , which for computational efficiency reasons used a geometry of cs symmetry , and the data obtained from the other methods that used a c1 symmetry . the relative geometry independence holds also for the nlo properties of 3 and 4 , but not for those of 2 . therefore , all of the properties of 2 were computed with the geometry optimised in the corresponding environment ( gas - phase or water solvent ) . considering that the nlo properties are very dependent on a good description of the excited - state manifold , it seems that , apart from highly accurate ( and computationally expensive ) multi - configurational methods , only the properties calculated with b3lyp , b3p86 or m06 may be at least approximately reliable . therefore , parameters for the gs and fdaes derived by using these functionals for the complexes embedded in a solvent continuum are collected in table 2 , together with cam - b3lyp results . all of the ( hyper)polarisabilities were computed by finite - field derivatives of the td - dft excited - state dipole - moments , and are thus static ( zero - frequency ) values . further data calculated for complexes 24 by using dft and raspt2 methods , together with previously reported measured data [ a ] all data calculated in h2o ( 2 ) or mecn ( 3 and 4 ) ; 3 and 4 optimised in vacuum , 2 optimised in h2o . [ b ] 2sa = two - state approximation ; 3sa = three - state approximation . calculated from 6 0iz(0i)/(e0i ) where 0i is the transition dipole - moment and e0i is the transition energy from the gs to the fdaes ( i=1 ) or sdaes ( i=2 ) ; n=1 ( 2 ) for 2sa ( 3sa ) ; an additional term for 3sa containing 12 was neglected because this property computed in the gas - phase is almost zero . the value for 4 is the total obtained by applying the 2sa to the two low - energy absorption bands separately ( the lowest energy band with mlct character involves the fdaes , whereas the other band has intraligand charge - transfer character and involves the sdaes).20 [ c ] data for [ bf4]3 taken from ref . 18 ; numbers in brackets indicate properties measured in ( or derived from data measured in ) prcn glasses . most of the fdaes properties were computed for the optimised gs geometries.32 nevertheless , in order to assess the possible effects of excited - state structural relaxation on the properties , an excited - state optimisation of 3 in the gas - phase was carried out , and properties were calculated also for the resulting geometry ( see the computational methods for details ) . the cam - b3lyp results are again clearly very different from those obtained with the other functionals . previously measured 01z and 01zz values were obtained by stark spectroscopy at 77 k in glassy prcn solution , and are thus not directly comparable to computed values in liquid mecn . nevertheless , the latter are of the right order of magnitude when using b3lyp , b3p86 or m06 . interestingly , zz is predicted to be smaller for the fdaes than for the gs for 2 and 3 , but the reverse is apparent for 4 when using b3lyp or m06.33 the calculations with b3lyp , b3p86 or m06 all predict the observed increases in 01z on moving along the series 24 , and the stark - based value of 8.8 au for 421 is closest to that obtained when using m06 . the gs first hyperpolarisability of complex 3 in the two - state approximation ( 2sa ) from raspt2(18,18 ) is very close to the value deduced from experimental hrs data ( 28 472 au).19 the corresponding values from the dft methods are considerably larger ; the reason for this can be traced back primarily to a substantially larger transition dipole - moment predicted by the dft methods , which is squared in the equation for 2sa , and is approximately 1.21.3-times larger than the raspt2 result . also , the dft calculations give slightly larger dipole - moment changes than does raspt2 . we find that the presence of diffuse functions in the basis set used to describe the first and second row atoms , which is generally of great importance for the nlo properties of the gs , has little influence on the nlo properties of the fdaes . the same can be said , to a lesser degree , of polarised functions , which generally are considered to be important for reliable descriptions of excited states . the basis set lan2tz(f ) for ru is about the minimum necessary for a reliable description of both the gs and fdaes properties . this last factor explains the main differences between our data and those obtained by inerbaev et al . and by zhang and champagne , who used the smaller basis set lan2dz.23 , 24 when considering the responses calculated by using b3lyp , b3p86 or m06 , these increase substantially ( as expected ) on increasing the -conjugation path - length along the series 24 , for both the gs and fdaes species ( table 2 ) . also , substantial enhancements are found for the fdaes with respect to the gs in each complex , with changes of similar magnitude predicted when using the three different functionals . however , the values calculated by using cam - b3lyp show less consistent trends . hence , although the gs ru - containing chromophores possess large nlo responses , the activity is even larger for the mlct excited states that formally contain ru coordinated to a reduced pyridyl ligand radical . the predicted excited - state enhancement of becomes more significant as the -conjugated system extends , being about threefold for 2 , approximately fivefold for 3 and about sevenfold for 4 . for 3 , geometry relaxation within the fdaes ( the s1 state ) leads to further considerable enhancement of , whereas increases slightly . the cubic nlo properties , denoted by the second hyperpolarisability , are generally more difficult to compute reliably with our method , and thus should be considered as more approximate . even so , they are also generally increased in the fdaes ( table 2 ) . however , unlike for , the results vary between the functionals b3lyp , b3p86 and m06 . using b3lyp or b3p86 yields enhancements of in each case , but these are much larger for 3 ( ca . in contrast , the calculations with m06 predict an excitation - induced increase in for 4 only ( ca . fourfold ) , whereas no change is evident for 3 and a decrease is found for 2 . unfortunately , no experimentally measured values are available for 24 to allow comparisons with theory , because these complexes are of interest primarily for their quadratic nlo properties . the general result that both and are larger in the fdaes is consistent with previous studies involving other types of chromophore.811 compared with previous computational studies on the electronic excitation and gs quadratic nlo properties of ru ammine complexes , we have used a larger basis set ( lanl2tz(f ) for ru ) in dft calculations . also , we have used different larger basis sets for various high - level ab initio methods . td - dft calculations with the hybrid functionals b3lyp , b3p86 or m06 and a mecn pcm yield very good agreement with the experimental spectrum for excitations to the fdaes of 3 . the same methods give a lower degree of matching with the experimental data for the shorter or longer complexes , underestimating max for 2 , but overestimating it for 4 . in each case , the calculations confirm the expected mlct character of the fdaes . a model developed by bahers et al . affords electron - transfer distances that agree well with those determined via stark spectroscopic measurements on [ pf6]3 and [ pf6]3 previously . notably , the results obtained for 3 by using b3lyp , b3p86 or m06 are very similar to those from raspt2 with a very large basis set and large active space , both in solution and the gas - phase . surprisingly , max values predicted by the long - range corrected functionals cam - b3lyp , lc-pbe and wb97xb are less accurate than those obtained with b3lyp , b3p86 or m06 for all three complexes . gas - phase results from the fully ab initio ri - cc2 method differ substantially from those derived from dft and raspt2 , possibly due to the relatively high multi - configurational character of the gs . considering both the gs and fdaes , polarisabilities and hyperpolarisabilities were computed by finite - field derivatives of the td - dft excited - state dipole - moments , by using the functionals b3lyp , b3p86 or m06 . the 01z and 01zz values are of magnitude similar to those measured previously by stark spectroscopy in the frozen solution state at 77 k. the gs 2sa value for 3 from raspt2(18,18 ) is very close to that derived experimentally by hrs , whereas the corresponding dft - based values are considerably larger , primarily due to substantially larger predicted 01 values . somewhat surprisingly , the presence of diffuse and polarised functions in the basis set used to describe the first and second row atoms has little influence on the nlo properties of the fdaes . as expected , the responses calculated by using b3lyp , b3p86 or m06 increase markedly as the -conjugation extends along the series 24 , for both the gs and fdaes species . also , substantial enhancements are found for the fdaes with respect to the gs in each complex , with the three different functionals predicting changes of similar magnitude . the excited - state enhancement of increases as the -conjugation extends , from approximately threefold for 2 to about sevenfold for 4 . although more approximate and of less interest for the complexes studied , the computed values also generally increase in the fdaes , but the results vary between the functionals b3lyp , b3p86 and m06 . in summary , state - of - the - art theoretical methods show that mlct excitation of ru ammine chromophores leads to large increases in molecular nlo responses . therefore , such complexes hold promise not only as redox - switchable species , but also for ultrafast photoswitching of bulk nlo effects in appropriate organised media , such as lb thin films . the molecules 2 and 3 were optimised with the 6 - 31 g * * basis set for chn and the lanl2tz(f ) ecp / basis set for ru at the dft level with the b3lyp functional . for 4 , the 6 - 31 g basis was used for h. molecule 2 was optimised in the gas - phase and in aqueous solution , by using the pcm , and the respective structures used for corresponding phase computations ; for 3 and 4 , gas - phase optimised structures were used for all calculations except for the raspt2 computations ( see below ) . excited - state optimisation of 3 in the gas - phase was carried out with three different basis sets for the atoms h , c , n , o : 6 - 31 g * * , 6 - 31+g * * and 6 - 31++g * * , while lanl2tz(f ) was applied to ru throughout . in order to be comparable with the other calculations , the properties were computed with the 6 - 31 g * * basis set and the pcm / mecn model . the results can be grouped into two different sets according to the basis sets underlying the excited - state optimisation . with the 6 - 31+g**-optimised structure , a small stokes shift , st , of 0.28 ev was obtained , with a large oscillator strength for the transition to s0 ( fos=0.43 ) . this is approximately in line with the results reported by zhang and champagne,24 ( st=0.25 ev , fos=0.31 ) , who apparently also used this basis set for the excited - state optimisation , although with lanl2dz for ru , the b3p86 functional and the pcm / mecn model already applied during the optimisation . however , contrary to their result of the relaxed state being s1 , we find it to be s3 , which is also the franck usually , such a highly excited state would relax into s1 by internal conversion before geometry relaxation is completed . for the 6 - 31 g * * and 6 - 31++g**-optimised structures , on the other hand , the relaxed state becomes s1 , showing large st values ( 1.2 and 1.1 ev for the 6 - 31 g * * and 6 - 31++g * * optimised structure , respectively ) and small fos values for dipolar transitions into s0 ( 0.05 for both structures ) , which is in reasonable agreement with the absence of luminescence observed experimentally . consequently , we used the 6 - 31g**-optimised structure to compute the excited - state properties . however , it should be noted that the optimisations of the second group were not fully successful in terms of the required criteria applied in gaussian 09 , even after about one hundred cycles . the best structures were finally used , where three of the four criteria were fulfilled . td - dft with several functionals was employed to compute transition moments and excited - state dipole moments , which in turn were used for finite - field numerical differentiations to obtain the hyperpolarisabilities in the fdaes . the dipole moments of the charged species are reported with respect to the centre of nuclear charge . the gs properties were calculated analytically or by finite - field differences from gs dipole moments . only the dominant long - axis component ( oriented in z - direction ) most of the pcm excited - state calculations were performed by using the state - specific description for the non - equilibrium solvation during a vertical excitation,34 although the differences when compared with the linear response non - equilibrium approximation35 were generally negligible . the transition energies were measured from the electronic gs minimum , and no vibrational averages were taken into account . it should be noted that the comparison of computed vertical excitation energies with the experimental absorption maxima is only an approximation condon factors ( overlap between the vibrational wavefunctions of ground and excited electronic states ) into account also . however , such an approach is computationally much more expensive,36 and has thus not been used here . the useable field strengths for the finite - field numerical differentiations had to be adapted for each molecule and functional individually : the lowest useful field strengths depended on the magnitude of the properties , while the high - field limit was set by field - induced state mixing and switching . the ri - cc2 calculations were carried out with turbomole.38 for the raspt2 calculations on complex 3 , its structure was first optimised at the pbe0/tzvp / mwb-28(ru ) level in cs symmetry with turbomole . although this structure is not a minimum , the symmetry was required to make the multi - configurational calculations manageable . tests with this structure at the dft level showed that the influence of the non - minimum structure on the properties of interest is minimal . state - averaged raspt2 calculations with extended ano - rcc basis sets , ( [ 8s 7p 6d 3f 2 g 1h ] ( ru ) , [ 4s 3p 2d 1f ] ( c , n ) , [ 3s 2p 1d ] ( h ) ) were then performed on this structure with molcas.39 extensive tests were performed to find the optimal active space . these led finally to the following partition : the ras2 space contains eight orbitals , five of ru 4d parentage , two of their bonding counterparts and the -orbital involved in the fdaes . single and double excitations were allowed out of ras1 and into ras3 , while all kinds of excitations were allowed in the ras2 space . for the three - state approximation of the first hyperpolarisability of 4 shown in table 2 , the excited - state dipole - moment between the fdaes and the second dipole - allowed excited state was computed with the dalton2011 package,40 in the gas phase . as the resulting value was very low , the corresponding term in the sum - over - states expression was neglected .

static excited - state polarisabilities and hyperpolarisabilities of three ruii ammine complexes are computed at the density functional theory ( dft ) and several correlated ab initio levels . most accurate modelling of the low energy electronic absorption spectrum is obtained with the hybrid functionals b3lyp , b3p86 or m06 for the complex [ ruii(nh3)5(meq+)]3 + ( meq+=n - methyl-4,4-bipyridinium , 3 ) in acetonitrile . the match with experimental data is less good for [ ruii(nh3)5l]3 + ( l = n - methylpyrazinium , 2 ; n - methyl-4-{e , e-4-(4-pyridyl)buta-1,3-dienyl}pyridinium , 4 ) . these calculations confirm that the first dipole- allowed excited state ( fdaes ) has metal - to - ligand charge - transfer ( mlct ) character . both the solution and gas - phase results obtained for 3 by using b3lyp , b3p86 or m06 are very similar to those from restricted active - space scf second - order perturbation theory ( raspt2 ) with a very large basis set and large active space . however , the time - dependent dft max predictions from the long - range corrected functionals cam - b3lyp , lc-pbe and wb97xb and also the fully ab initio resolution of identity approximate coupled - cluster method ( gas - phase only ) are less accurate for all three complexes . the ground state ( gs ) two - state approximation first hyperpolarisability 2sa for 3 from raspt2 is very close to that derived experimentally via hyper - rayleigh scattering , whereas the corresponding dft - based values are considerably larger . the responses calculated by using b3lyp , b3p86 or m06 increase markedly as the -conjugation extends on moving along the series 24 , for both the gs and fdaes species . all three functionals predict substantial fdaes enhancements for each complex , increasing with the -conjugation , up to about sevenfold for 4 . also , the computed second hyperpolarisabilities generally increase in the fdaes , but the results vary between the different functionals .

Introduction Results and Discussion Conclusion Computational Methods

for this study , we selected 20 patients at seoul national university hospital in south korea who had undergone hepatic resection due to hcc from july to september , 2010 . these patients have clinical evidence of chronic hepatitis b , such as serologic evidence of virus , more than 6 months of abnormal liver function , or radiologic evidence of hepatic fibrosis . there were 2 female and 18 male patients with ages ranging from 48 - 73 years ( with a median age of 58 ) . all patients had curative surgical resection ; 3 cases required liver transplantation and 17 needed partial resection . none of them underwent preoperative local treatment such as transarterial embolization , radiofrequency ablation and percutaneous ethanol injection therapy , nor preoperative systemic chemotherapy . there was one hepatitis c virus coinfection and one concomitant alcohol - related steatohepatitis with chronic hepatitis b. peritumoral tissues from each fresh liver specimen were sampled from the tumor border to a distance of 40 mm from the tumor . routine hematoxylin and eosin ( h&e ) and masson 's trichrome ( m - t ) stained slides were made as previously described.12,13 the adjacent pnlp was divided into eight 5 mm - sized columns , starting from the tumor border to a 40 mm distance from the tumor ( fig . the 5-mm column represents adjacent pnlp located between the tumor border and 5 mm distance from the tumor . the 10- , 15- , 20- , 25- , 30- , 35- , and 40-mm columns represent adjacent pnlp between 5 and 10 mm , 10 and 15 mm , 15 and 20 mm , 20 and 25 mm , 25 and 30 mm , 30 and 35 mm , and 35 and 40 mm from the tumor , respectively . the mean magnitude of each column was 15 mm ( width)5 mm ( length ) , and median number of portal tracts per column was 14 ( range , 3 to 17 ) . for comparison , background liver or remote pnlp was also taken farthermost from the tumor ( or at least > 40 mm from the tumor ) and treated similarly as the adjacent pnlp . parameters such as necroinflammatory activity of the hepatic parenchyma , fibrosis , bile ductular reaction , peliosis , perivenular inflammation , and steatosis were assessed by two pathologists ( k.b . lee and h.y . was applied as a grading system for necroinflammatory activity.14,15 spotty necrosis , periportal / periseptal interface hepatitis ( piecemeal necrosis ) , and portal inflammation were scored from 0 to 4 and confluent necrosis from 0 to 6 . the total modified hai score is the sum of all of these scores ( expected maximum score , 18 ) . in addition , the number of foci of spotty necrosis per 10 objective was counted at the most severely affected area . the first was scoring both h&e- and m - t - stained sections ( by light microscopy ) from 0 to 6 according to the ishak fibrosis staging system.15 in addition , collagen deposition shown by m - t staining was converted into a pixel count for an objective evaluation of fibrosis / cirrhosis . images of each column were taken using an olympus optical microscope ( bx50 , olympus , tokyo , japan ) with 4 objective and converted into jpeg format for analysis . 1f to include the majority of the samples so that we could exclude any selection bias . all images ( having mean image size of 15.98 mm ) were analyzed by image j software ( positive color : r , 0.8748878 ; g , 0.457825 65 ; b , 0.15829495 ; threshold : 0 to 290 ) . the ratio of collagen - positive pixel count to total pixel count was expressed in percentage terms . we defined peliosis - like lesions as blood - filled spaces , with or without sinusoidal lining , recognized with the 4 objective . the inflammatory activity around the central vein or the so - called hepatic venulitis was scored from 0 to 4 ( 0 , absent ; 1 , inflammatory cells accumulation in the lumen of hepatic venule ; 2 , focal inflammatory cells infiltration through the vascular wall ; 3 , continuous infiltration of infilammatory cells around the vascular wall ; and 4 , fibrinoid necrosis of the vascular wall ) . bile ductular proliferation was scored from 0 to 3 ( 0 , absent ; 1 , mild ; 2 , moderate ; 3 , severe ; or graded as <33 , 33 - 66% , and > 66% of the hepatic lobule by bile steatosis was graded 0 to 3 based on the percentage of hepatocytes in the biopsy ( 0 , none ; 1 , up to 33% ; 2 , 33 - 66% ; and 3 , > 66% ) , which is adopted from the nonalcoholic steatohepatitis clinical research network scoring system.16,17 the wilcoxon signed - rank test was used to compare pathologic characteristics of each column with those of adjacent columns , as well as remote parenchyma . tests having p - value less than 0.05 was considered as results with significant difference . for this study , we selected 20 patients at seoul national university hospital in south korea who had undergone hepatic resection due to hcc from july to september , 2010 . these patients have clinical evidence of chronic hepatitis b , such as serologic evidence of virus , more than 6 months of abnormal liver function , or radiologic evidence of hepatic fibrosis . there were 2 female and 18 male patients with ages ranging from 48 - 73 years ( with a median age of 58 ) . all patients had curative surgical resection ; 3 cases required liver transplantation and 17 needed partial resection . none of them underwent preoperative local treatment such as transarterial embolization , radiofrequency ablation and percutaneous ethanol injection therapy , nor preoperative systemic chemotherapy . there was one hepatitis c virus coinfection and one concomitant alcohol - related steatohepatitis with chronic hepatitis b. peritumoral tissues from each fresh liver specimen were sampled from the tumor border to a distance of 40 mm from the tumor . routine hematoxylin and eosin ( h&e ) and masson 's trichrome ( m - t ) stained slides were made as previously described.12,13 the adjacent pnlp was divided into eight 5 mm - sized columns , starting from the tumor border to a 40 mm distance from the tumor ( fig . the 5-mm column represents adjacent pnlp located between the tumor border and 5 mm distance from the tumor . the 10- , 15- , 20- , 25- , 30- , 35- , and 40-mm columns represent adjacent pnlp between 5 and 10 mm , 10 and 15 mm , 15 and 20 mm , 20 and 25 mm , 25 and 30 mm , 30 and 35 mm , and 35 and 40 mm from the tumor , respectively . the mean magnitude of each column was 15 mm ( width)5 mm ( length ) , and median number of portal tracts per column was 14 ( range , 3 to 17 ) . for comparison , background liver or remote pnlp was also taken farthermost from the tumor ( or at least > 40 mm from the tumor ) and treated similarly as the adjacent pnlp . parameters such as necroinflammatory activity of the hepatic parenchyma , fibrosis , bile ductular reaction , peliosis , perivenular inflammation , and steatosis were assessed by two pathologists ( k.b . lee and h.y . was applied as a grading system for necroinflammatory activity.14,15 spotty necrosis , periportal / periseptal interface hepatitis ( piecemeal necrosis ) , and portal inflammation were scored from 0 to 4 and confluent necrosis from 0 to 6 . the total modified hai score is the sum of all of these scores ( expected maximum score , 18 ) . in addition , the number of foci of spotty necrosis per 10 objective was counted at the most severely affected area . the first was scoring both h&e- and m - t - stained sections ( by light microscopy ) from 0 to 6 according to the ishak fibrosis staging system.15 in addition , collagen deposition shown by m - t staining was converted into a pixel count for an objective evaluation of fibrosis / cirrhosis . images of each column were taken using an olympus optical microscope ( bx50 , olympus , tokyo , japan ) with 4 objective and converted into jpeg format for analysis . 1f to include the majority of the samples so that we could exclude any selection bias . all images ( having mean image size of 15.98 mm ) were analyzed by image j software ( positive color : r , 0.8748878 ; g , 0.457825 65 ; b , 0.15829495 ; threshold : 0 to 290 ) . the ratio of collagen - positive pixel count to total pixel count was expressed in percentage terms . we defined peliosis - like lesions as blood - filled spaces , with or without sinusoidal lining , recognized with the 4 objective . the inflammatory activity around the central vein or the so - called hepatic venulitis was scored from 0 to 4 ( 0 , absent ; 1 , inflammatory cells accumulation in the lumen of hepatic venule ; 2 , focal inflammatory cells infiltration through the vascular wall ; 3 , continuous infiltration of infilammatory cells around the vascular wall ; and 4 , fibrinoid necrosis of the vascular wall ) . bile ductular proliferation was scored from 0 to 3 ( 0 , absent ; 1 , mild ; 2 , moderate ; 3 , severe ; or graded as <33 , 33 - 66% , and > 66% of the hepatic lobule by bile ductular proliferation , respectively ) . steatosis was graded 0 to 3 based on the percentage of hepatocytes in the biopsy ( 0 , none ; 1 , up to 33% ; 2 , 33 - 66% ; and 3 , > 66% ) , which is adopted from the nonalcoholic steatohepatitis clinical research network scoring system.16,17 the wilcoxon signed - rank test was used to compare pathologic characteristics of each column with those of adjacent columns , as well as remote parenchyma . tests having p - value dense inflammatory cell infiltration in the portal tracts adjacent to the tumor , which also lessened with distance , were observed as shown in fig . 1e ) columns . the severity of portal , periportal , and lobular activity scores in adjacent pnlp were illustrated for all cases in concentric graphs by color gradation and in bar graphs by mean of scores ( fig . the dark - colored centers of circular graphs indicate severe necroinflammatory activity near the tumor . the plotted mean value of the necroinflammatory activity as bar graph demonstrates a pattern of decreasing inflammatory cell infiltration in adjacent pnlp ( fig . however , at certain distances , the inflammation became stable and no longer differed from that of remote pnlp . moreover , the necroinflammatory activity in each column was compared using wilcoxon signed - rank test ( table 1 ) . portal inflammation was markedly severe in the 5-mm column ( mean score , 2.79 ) , and decreased with distance until the 25-mm column ( mean score , 1.84 ) ( p=0.011 between 5-mm and 10-mm column ; p=0.034 between 10-mm and 15-mm column ; p=0.046 between 20-mm and 25-mm column ) . therefore , in comparison to adjacent pnlp , the considerable cut - off point for portal inflammation could be 20 mm distance from the tumor . likewise , the foci of spotty necrosis were observed most frequently in the 5-mm column ( mean score , 2.65 ; mean count , 6.0 ) and decreased with distance until 25-mm column ( mean score , 1.45 ; mean count , 2.05 ) . both the score and the frequency of spotty necrosis did not change significantly beyond the 20 mm distance from the tumor . on the other hand , periportal inflammation were markedly severe in the 5-mm column ( mean score , 3.30 ) and significantly decreased in the 10-mm ( mean score , 2.55 ; p=0.001 ) and 15-mm column ( mean score , 2.20 ; p=0.008 ) . the modified hai , which is the sum of scores for portal , periportal inflammation and spotty necrosis , was markedly severe in the 5-mm column ( mean score , 8.75 ) and decreased until 15-mm column ( mean score , 6.10 ) , while it did not significantly change beyond 10 mm distance from the tumor . the lesions were irregularly dilated sinusoidal spaces filled with blood and fibrinoid material accompanied by damaged hepatocytes ( fig . 4a , b ) , especially starting from the tumor border towards the 10-mm column , while nearly no peliosis was found beyond the 10-mm column , denoted by a p - value of 0.018 between 10-mm and 15-mm column ( table 1 ) . apart from the usual occurrence of chronic viral hepatitis and neutrophic infiltration around the central veins , 10 cases of perivenular inflammation was observed in adjacent pnlp . perivenular inflammation was markedly severe from the tumor border until 10 mm distance from the tumor ( table 1 , fig . although all cases in this study resulted from cirrhosis or chronic hepatitis b backgrounds , the degree of fibrosis in pnlp varies with distance from the tumor ( fig . the ishak grade of fibrosis for all cases is illustrated in concentric circles ( fig . the mean value of the pixel fraction of collagen deposition for each column is presented as a bar graph ( fig . as shown in table 1 , the ishak grade of fibrosis was markedly higher in the 5-mm and 10-mm column ( p=0.007 between 5-mm and 10-mm column ; p=0.020 between 10-mm and 15-mm column ) . to quantify the amount of fibrosis , pixel fraction of collagen deposition this evaluation revealed that collagen deposition was much more severe in the 5-mm column than in more distant areas . thus , 10 mm could be the considerable cut - off point for the ishak grade of fibrosis , and 5 mm for pixel fraction of collagen deposition . bile ductular proliferation around the tumor was so severe that it was difficult to find remaining hepatocytes immediately adjacent to the tumor ( fig . 5c and d , its pattern was decreasing with distance but become stable beyond the 10 mm distance from the tumor border ( p=0.001 between 5-mm and 10-mm column ; p=0.008 between 10-mm and 15-mm column ) . however , there were no differences in steatosis between the columns ( data not shown ) . to confirm the gradation of histopathologic features in adjacent pnlp , we evaluated the same factors beyond 40 mm in remote pnlp , and then compared with each column of adjacent pnlp within 40 mm ( table 1 ) . parameters compared included portal inflammation , periportal inflammation , spotty necrosis score , spotty necrosis count , the modified hai score , peliosis , bile ductular proliferation and the ishak grade of fibrosis ( table 1 ) . the comparison demonstrated that most of the pathologic changes were markedly severe in 5-mm and 10-mm columns than those of those in remote parenchyma . these results were consistent with comparisons between adjacent columns for such parameters as periportal inflammation , the modifieid hai score , peliosis , bile ductular proliferation and the ishak grade of fibrosis , verifying that 10 mm distance from the tumor border could be the considerable cut - off point for those parameters . dense collagen deposition was observed within 5 mm pnlp , as opposed to remote pnlp . this was consistent with the result from the comparison between adjacent columns , suggesting this distance to be the considerable cut - off point for the collagen deposition . portal inflammation within 15 mm pnlp was markedly severe than that in remote pnlp , but the comparison between adjacent columns demonstrated changes fading from 20 mm . dense inflammatory cell infiltration in the portal tracts adjacent to the tumor , which also lessened with distance , were observed as shown in fig . 1e ) columns . the severity of portal , periportal , and lobular activity scores in adjacent pnlp were illustrated for all cases in concentric graphs by color gradation and in bar graphs by mean of scores ( fig . the dark - colored centers of circular graphs indicate severe necroinflammatory activity near the tumor . the plotted mean value of the necroinflammatory activity as bar graph demonstrates a pattern of decreasing inflammatory cell infiltration in adjacent pnlp ( fig . however , at certain distances , the inflammation became stable and no longer differed from that of remote pnlp . moreover , the necroinflammatory activity in each column was compared using wilcoxon signed - rank test ( table 1 ) . portal inflammation was markedly severe in the 5-mm column ( mean score , 2.79 ) , and decreased with distance until the 25-mm column ( mean score , 1.84 ) ( p=0.011 between 5-mm and 10-mm column ; p=0.034 between 10-mm and 15-mm column ; p=0.046 between 20-mm and 25-mm column ) . therefore , in comparison to adjacent pnlp , the considerable cut - off point for portal inflammation could be 20 mm distance from the tumor . likewise , the foci of spotty necrosis were observed most frequently in the 5-mm column ( mean score , 2.65 ; mean count , 6.0 ) and decreased with distance until 25-mm column ( mean score , 1.45 ; mean count , 2.05 ) . both the score and the frequency of spotty necrosis did not change significantly beyond the 20 mm distance from the tumor . on the other hand , periportal inflammation were markedly severe in the 5-mm column ( mean score , 3.30 ) and significantly decreased in the 10-mm ( mean score , 2.55 ; p=0.001 ) and 15-mm column ( mean score , 2.20 ; p=0.008 ) . the modified hai , which is the sum of scores for portal , periportal inflammation and spotty necrosis , was markedly severe in the 5-mm column ( mean score , 8.75 ) and decreased until 15-mm column ( mean score , 6.10 ) , while it did not significantly change beyond 10 mm distance from the tumor . the lesions were irregularly dilated sinusoidal spaces filled with blood and fibrinoid material accompanied by damaged hepatocytes ( fig . 4a , b ) , especially starting from the tumor border towards the 10-mm column , while nearly no peliosis was found beyond the 10-mm column , denoted by a p - value of 0.018 between 10-mm and 15-mm column ( table 1 ) . apart from the usual occurrence of chronic viral hepatitis and neutrophic infiltration around the central veins , 10 cases of perivenular inflammation was observed in adjacent pnlp . perivenular inflammation was markedly severe from the tumor border until 10 mm distance from the tumor ( table 1 , fig . although all cases in this study resulted from cirrhosis or chronic hepatitis b backgrounds , the degree of fibrosis in pnlp varies with distance from the tumor ( fig . the ishak grade of fibrosis for all cases is illustrated in concentric circles ( fig . the mean value of the pixel fraction of collagen deposition for each column is presented as a bar graph ( fig . as shown in table 1 , the ishak grade of fibrosis was markedly higher in the 5-mm and 10-mm column ( p=0.007 between 5-mm and 10-mm column ; p=0.020 between 10-mm and 15-mm column ) . to quantify the amount of fibrosis , pixel fraction of collagen deposition was evaluated . this evaluation revealed that collagen deposition was much more severe in the 5-mm column than in more distant areas . thus , 10 mm could be the considerable cut - off point for the ishak grade of fibrosis , and 5 mm for pixel fraction of collagen deposition . bile ductular proliferation around the tumor was so severe that it was difficult to find remaining hepatocytes immediately adjacent to the tumor ( fig . 5c and d , its pattern was decreasing with distance but become stable beyond the 10 mm distance from the tumor border ( p=0.001 between 5-mm and 10-mm column ; p=0.008 between 10-mm and 15-mm column ) . however , there were no differences in steatosis between the columns ( data not shown ) . to confirm the gradation of histopathologic features in adjacent pnlp , we evaluated the same factors beyond 40 mm in remote pnlp , and then compared with each column of adjacent pnlp within 40 mm ( table 1 ) . parameters compared included portal inflammation , periportal inflammation , spotty necrosis score , spotty necrosis count , the modified hai score , peliosis , bile ductular proliferation and the ishak grade of fibrosis ( table 1 ) . the comparison demonstrated that most of the pathologic changes were markedly severe in 5-mm and 10-mm columns than those of those in remote parenchyma . these results were consistent with comparisons between adjacent columns for such parameters as periportal inflammation , the modifieid hai score , peliosis , bile ductular proliferation and the ishak grade of fibrosis , verifying that 10 mm distance from the tumor border could be the considerable cut - off point for those parameters . dense collagen deposition was observed within 5 mm pnlp , as opposed to remote pnlp . this was consistent with the result from the comparison between adjacent columns , suggesting this distance to be the considerable cut - off point for the collagen deposition . portal inflammation within 15 mm pnlp was markedly severe than that in remote pnlp , but the comparison between adjacent columns demonstrated changes fading from 20 mm . in this study , we investigated that the gradual histologic changes from the tumor edges and tried to find reasonable cut - off points for adjacent and remote peritumoral parenchyma based on various morphologic characteristics that are believed to indicate microenvironmental changes . although the individual histologic parameters revealed several distances from the tumor edges , we found the area within 10 mm and beyond 20 mm distance from the tumor to be relatively constant . pnlp within 10 mm had significantly higher inflammatory cells infiltration around portal tract and hepatic parenchyma , bile ductular reaction , collagen deposition and peliosis than 10 mm distance from the tumor . moreover , pnlp beyond 20 mm had no distinct pathologic features compared with background liver parenchyma . hence , the parenchyma within 10 mm from the tumor would be considered the adjacent pnlp in which morphologic changes are believed to be directly affected by the tumor , and the parenchyma beyond 20 mm as the remote pnlp without tumor effect . the recurrence of hcc is one of the leading causes of death after curative liver resection , and the prognoses on cases of early and late recurrence are quite different.18 late recurrence , which is defined as that occurring more than 2 years after primary resection , has better prognosis , while early recurrence that develops within 2 year after resection carries a poor prognosis . early recurrence is strongly negatively correlated with patient 's survival.19 hence , many predictive or potential risk factors for early recurrence have been investigated , including vascular invasion , biliary tumor thrombi , intrahepatic metastasis , and positive surgical margin.18,20,21 these results imply that early recurrence is associated with local tumor factors rather than the background liver parenchyma . on the contrary , late recurrence of hccs represents the tumorigenic trait of the remaining liver parenchyma . currently , immunologic or inflammatory milieu of the adjacent peritumoral tissue , which is directly affected by the tumor , have been postulated to be important in tumor progression22 and early recurrence of hcc.7,23,24 jia et al.22 demonstrated that the colony - stimulating factor-1 receptor level of adjacent pnlp was associated with intrahepatic metastasis and early recurrence when the adjacent pnlp was defined as within 10 mm , there - by supporting our definition of adjacent pnlp as within 10 mm distance from the tumor . the remote pnlp , which is not affected by hcc , is the remaining hepatic parenchyma in patients after resection so it is related with multiple occurrence and late recurrence of hcc . it is reported in several studies that molecular signature of non - cancerous liver tissue can predict the risk for late recurrence of hccs and influence the clinical outcome of hcc patients . in this study , we defined the remote pnlp as beyond 20 mm distance from the tumor , which is consistent with the results of previous studies . okamoto et al.9 showed that specific gene - expression profiles of pnlp could predict the risk for multiple occurrence of hcc by using peritumoral liver tissue farthest from the tumor.9 hoshida et al.11 demonstrated that specific gene - expression profiles of pnlp predicted late recurrence of hcc using the peritumoral liver tissue that was available at the time of study . the morphological changes described here were based on the criteria for viral hepatitis , and might not be sufficient to detect all types of tumor effect on adjacent pnlp . for example , peliosis , hepatic venulitis and bile ductular proliferation could be caused by the elevation of sinusoidal and bile ductal pressure , and end up with hepatocyte damage.25 we revealed positive correlation between tumor size and the farthest distance from the tumor where the peliosis could be observed ( data not shown ; spearman correlation coefficient=0.556 ; p=0.009 ) . furthermore , this study was limited to a small sample size , so statistical analysis for parametric validation can not be conducted . however , this study is the first report on comparison between adjacent pnlp and remote pnlp based on several histologic parameters via semiquantitative and quantitative scoring systems . results of this study can be used as an objective histologic evidence that may help many hepatologists and reseachers select proper tissue specimen for research about primary hepatic tumors of patients with chronic liver disease . in conclusion , adjacent pnlp , especially that within 10 mm of the tumor border , showed severe inflammation , architectural changes , peliosis , and hepatic venulitis . however

backgroundthe molecular profile of peritumoral non - neoplastic liver parenchyma ( pnlp ) has recently been suggested as predictive factor of early and late recurrence of hepatocellular carcinoma ( hcc ) . however , there is no definite cut - off point for tumor - free pnlp in terms of either histological or molecular changes . therefore , our aim is to determine the numerical cut - off point for separating adjacent pnlp and remote pnlp in histopathologic perspective.methodsperitumoral tissues from 20 resected hcc patients were sampled from 0 to 40 mm distance from the tumor border ( divided into 5-mm columns ) . histopathologic parameters such as necroinflammatory activity , fibrosis , bile ductular reaction , hepatic venulitis , peliosis , and steatosis were compared between each column.resultsthe morphologic changes just adjacent to the tumor were notably severe and faded with distance . the parenchyma within 10 mm of the tumor showed significantly severe inflammation , fibrosis , peliosis and hepatic venulitis compared with those from farther areas . the histopathologic changes of the parenchyma became stable beyond 20 mm.conclusionsresults of this study revealed that the parenchyma within 10 mm distance from the tumor , or adjacent pnlp , has histopathologic changes that are directly affected by the tumor , and the parenchyma beyond 20 mm as the remote pnlp without tumor effect .

MATERIALS AND METHODS Patient characteristics Sampling of nonneoplastic liver tissue Grading and staging for histopathologic parameters Statistical analysis RESULTS Necroinflammatory activity in adjacent peritumoral hepatic parenchyma Peliosis and perivenular inflammation in adjacent peritumoral hepatic parenchyma Fibrosis, bile ductular reaction and steatosis in adjacent peritumoral hepatic parenchyma Comparison with adjacent and remote non-neoplastic hepatic parenchyma DISCUSSION

it has numerous adverse health effects and is considered as one of the main predisposing factors for the emerging epidemic of noncommunicable diseases . nowadays , overweight and obesity are growing in populations with different levels of economic situation . it is estimated that by continuing the actual trend , the global prevalence rate of 33.0% for overweight and obesity among adult population ( 1.3 billion people ) in 2005 would reach up to 57.8% ( 3.3 billion people ) by 2030 . the world health organization included excess weight , with a prevalence higher than undernutrition , as one of the top 10 health risks worldwide . the rise in the incidence in obesity matches the rise in the use and distribution of industrial chemicals that may have a role in development of obesity . in her interesting review in 2002 , baillie - hamilton postulated a role for chemical toxins in the etiology of obesity by presenting the coincidence of the obesity epidemic with the noticeable increase of industrial chemicals in the environment over the past four decades . an accumulating body of evidence suggests that substances as endocrine - disrupting chemicals ( edcs ) may be linked to the obesity epidemic . edcs are chemicals that alter the normal functioning of hormones and other signaling molecules in the body . obesogens , molecules with adverse effects on lipid metabolism and adipogenesis , and in turn resulting in obesity [ 6 , 7 ] . the environmental obesogen hypothesis suggests that prenatal or early - life exposure to certain substances as edcs may predispose exposed individuals to increased fat mass and excess weight . it is suggested that exposure to obesogens can modify the epigenome of multipotent stromal stem cells , biasing them to the adipocyte lineage at the expense of bone . hence , humans exposed to obesogens during early life might have an altered stem cell compartment , already preprogrammed for an adipogenic outcome . the list of chemicals studied as possible obesogens continues to grow and includes diethylstilbestrol ( des ) , bisphenol a ( bpa ) , phthalates , organotins , polybrominated diphenyl ethers ( pbdes ) , polyfluoroalkyl chemicals ( pfcs ) , organochlorine ( oc ) pesticides , and polychlorinated biphenyls ( pcbs ) and some solvents caused weight gain , and it is proposed that these chemicals were interfering with weight homeostasis by changing weight - controlling hormones , modifying sensitivity to neurotransmitters , or altering the sympathetic nervous system activity . the purpose of this paper is to systematically review the experimental and human studies on obesogenic chemicals and their mechanisms of action to provide a comprehensive view on underlying mechanisms and the multifactorial aspects of obesity for clinicians and public health stakeholders . relevant literature reporting the environmental obesogens was identified through electronic search of medline , pubmed , isi web of science , and scopus / embase with no time or language restrictions . we searched the databases using the following strategy : for scopus / embase we used the emtree thesaurus terms ; for pubmed search , we considered medical subheading ( mesh ) words , and for other databases we used keywords ( text words ) . for pubmed search , we used ( endocrine disruptors [ mesh ] or endocrine disrupting chemicals or obesogen [ mh ] or polychlorinated biphenyls [ mesh ] or hydrocarbons , chlorinated [ mesh ] or dioxins [ mesh ] or polybrominated biphenyls [ mesh ] or carbon tetrachloride [ mesh ] or organothiophosphorus compounds [ mesh ] or phthalic acid [ substance name ] or phthalic acids [ mesh ] or organotin compounds [ mesh ] or bisphenol a [ substance name ] and ( ( obesity [ mh ] or fat deposition [ mh ] ) and ( publisher[sb ] or in process [ sb ] ) . duplicates were removed ; the relevant papers were selected in three phases . in the first and second phases , titles and abstracts of papers were screened and irrelevant papers were excluded . in the last phase , the full text of recruited papers was explored intensely to select only relevant papers . for any additional pertinent studies , all these three screening phases were done by two independent reviewers ( fj and pp ) . in the next step , the eligibility of relevant papers was checked . identification of main findings of studies was conducted on a case - by - case basis and included consideration of any statistical analyses that might have been conducted , consistency of the general pattern across exposure groups . the required information that was extracted from all eligible papers was as follows : ( i ) general characteristics of the study ( first author 's name , publication year , study year , study design ) ( ii ) characteristics of the chemical , ( iii ) reason for using the chemical , ( iv ) suggested obesogen mechanism , and ( v ) adverse effects on humans or animals . two reviewers ( fj and pp ) extracted the data while another ( rk ) checked their extracted data . we found that actually many environmental obesogens are identified ; they are mainly classified as chemical simulators of metabolic hormones or brain neurotransmitters [ 10 , 11 ] . bisphenol a [ 1215 ] , tributyltin ( tbt ) [ 16 , 17 ] , nonylphenol [ 18 , 19 ] and genistein [ 20 , 21 ] , phatalate , perfluoroalkyl compounds ( pfcs ) , and perfluorooctanoic acid ( pfoa ) are some of the obesogen chemicals described by experimental studies . diverse mechanisms are explained for obesogen chemicals ; mainly they have disruptive effects on homeostasis of energy balance , glucose and lipid metabolism , and control of adipogenesis . the concentrations of many industrial obesogen chemicals are found to be high in general population . for instance , some studies examined the obesogenic effects of phthalates , which are esters mainly added to plastics to increase their flexibility , transparency , durability , and longevity . cross - sectional data from the national health and nutrition examination survey ( nhanes ) in the usa found significant associations between several phthalates metabolites ( monobenzyl phthalate ( mbzp ) , mono-(2-ethyl-5-hydroxyhexyl ) phthalate ( mehhp ) , and mono-(2-ethyl-5-oxohexyl ) phthalate ( meohp ) ) and measures of abdominal obesity and insulin resistance in men but not in women . a cross - sectional study on 90 girls aged 68 years found slightly higher concentrations of some phthalate metabolites as monoethyl phthalate ( mep ) , mono-(2-ethyl-5-hydroxyhexyl ) phthalate ( mehhp ) , and mono - n - butyl phthalate ( mbp ) among overweight girls than in their other counterparts some epidemiologic studies documented the obesogenic effects of some environmental chemicals , as pcb and bpa , whereas such effects are conflicting for some other chemicals as organochlorine pesticides [ 3032 ] . phytoestrogens , notably soy products , have beneficial health effects and are added to several food and food supplements . genistein is one the mostly used phytoestrogens in the human diet , and by its estrogenic activity , it has favorable effects for regulating the homeostasis of lipids and carbohydrates . though its beneficial effects in inhibiting fat deposition in the adipose tissue are considered to be obtained at high pharmacological doses , its low doses in foods are found to increase adiposity and mild peripheral insulin resistance particularly in males . in this review , we summarized information regarding environmental chemicals that can be associated with obesity . most evidence comes from experimental and laboratory studies ; however a growing number of human studies also support the role of obesogen chemicals . chemicals as heavy metals , some solvents , pesticides , bpa , organophosphates , phthalates , pcb , pbbs , and many other substances are documented to cause weight gain . these chemicals interfere with weight and lipid homeostasis by various mechanisms related to weight - controlling hormones , activity of the sympathetic nervous system , and sensitivity to neurotransmitters . exposure to these chemicals varies in different age groups ; their effects during fetal and infancy periods may be irreversible and long - lasting for adulthood . even exposure to low doses of edcs during critical times of differentiation can change the developmental programming and may result in obesity . barker 's hypothesis on the effects of intrauterine growth on fetal programming and fetal origins of adult diseases is well documented [ 36 , 37 ] ; however , other characteristics as later growth spurt and environmental factors are considered to influence this programming . exposure to environmental chemicals with endocrine - disrupting activities in early life may result in everlasting adverse health effects . such health consequences may become apparent not only in childhood , but also in adulthood , and even in succeeding generations . transgenerational effects may be because of mutations as well as because of factors regulating gene expression . our findings support the role of obesogens , as chemicals with disruptive effects on fat homeostasis and various weight controlling mechanisms , in programming the development of excess weight from early life . although all obesogen chemicals are not yet identified , and their detailed mechanisms of action remain to be explored , generally it is assumed that exposure to different doses of these environmental chemicals in various periods of life from fetal to adult period interacts with some endocrine signaling mechanisms and in turn leads to obesity . edcs act by diverse mechanisms ; accumulating body of evidence supports that these chemicals disrupt some epigenetic , structural , and functional mechanisms , which control energy homeostasis , lipid metabolism , appetite regulation , and adipogenesis [ 4044 ] . chemical obesogens are considered to function through various factors as leptin , ghrelin , melanocyte - stimulating hormones , neuropeptide y , amphetamine - regulated transcript , agouti - related protein , and cocaine , as well as through inhibiting aromatases as the p450 family members ( cyp19 and cyp3a1 ) [ 4244 ] or through modifying the expression of various receptors for steroid hormones , retinoic x , peroxisome proliferator - activated , and glucocorticoids . the exposure to obesogen chemicals may influence the steroid hormone receptors or may change serum levels of metabolic hormones or may influence nuclear receptor signaling pathways in preadipocytes , which would result in adipocyte differentiation and a tendency to excess weight [ 44 , 45 ] . the systemic reactions to exposure to environmental chemical factors can potentially increase the risk for obesity - related health effects , as metabolic syndrome , insulin resistance , prediabetes , diabetes , oxidative stress , prehypertension , hypertension , and nonalcoholic fatty liver diseases even in the pediatric age group . even in the pediatric age group , environmental chemicals can influence oxidative stress and proinflammatory cytokines [ 46 , 47 , 50 ] , which in turn would initiate the second hit suggested in the two - hit hypothesis [ 51 , 52 ] for the progression of fatty liver to metabolic syndrome and diabetes . the other aspect of the influences of environmental factors on obesity and its health consequences can be the impact of these chemicals on intrauterine growth retardation , low birth weight , and prematurity [ 5355 ] , which are documented as predisposing factors for obesity and adult chronic diseases . whether the results of laboratory models can be generalized to health hazards in humans remain to be determined , but a growing number of epidemiologic studies also suggest a link between exposure to environmental chemicals with obesity . however , it should be considered that in many human studies , weight gain has not been an endpoint in the original proposal , and excess weight has been reported as an adverse effect . environmental factors have diverse health effects [ 4750 , 5658 ] . although rapid changes in lifestyle habits , along with increased energy intake and decreased energy expenditure , are considered as the main causes of excess weight , but by considering the rapid escalating trend of obesity in various age groups and in populations with different lifestyle habits and diverse socioeconomic levels , it is obvious that it is simple - minded to consider only these two factors responsible for this expanding global problem ; the role of other environmental determinants as obesogen chemicals is being proposed in this regard . large - scale longitudinal studies with long - term followup are necessary to document the clinical importance of exposure to environmental chemicals . the current evidence proposes that the systemic responses to exposure to environmental factors , notably during developmental phases of life , could potentially increase the risk of excess weight . by taking into account the current knowledge on the adverse transgenerational effects of obesogen chemicals on human health , the global obesity epidemic should be considered as a multifactorial complex disorder necessitating the emphasis of public health interventions for environmental protection .

the purpose of this paper is to systematically review the experimental and human studies on obesogenic chemicals and their mechanisms of action to provide a comprehensive view on the multifactorial aspects of obesity . the literatures were searched in available databases . the relevant papers were selected in three phases . after quality assessment , two reviewers extracted the data while another checked their extracted data . in this review , we summarized information regarding environmental chemicals that can be associated with obesity . most evidence comes from experimental and laboratory studies ; however a growing number of human studies also support the role of obesogenic chemicals . the current evidence proposes that the systemic responses to exposure to environmental factors could potentially increase the risk of excess weight . the effects of exposure to these chemicals are of crucial importance during developmental phases of life , when preprogramming for an adipogenic outcome may occur . by considering the adverse transgenerational effects of obesogen chemicals on human health , the global obesity epidemic should be considered as a multifactorial complex disorder necessitating the emphasis of public health interventions for environmental protection .

1. Introduction 2. Methods 3. Results 4. Discussion 5. Conclusion

nanochemistry is predominating in major fields of science and technology , specifically in biotechnology and information technology . in the near future , nanochemistry will direct and guide towards nanomedicine and nanodiagnostics . however , obtaining suitable nanoparticles that can be used for diagnostic and medicinal purposes remains a significant challenge . moreover , the effect of these nanoparticles on biological entities such as proteins is considerably significant when it comes to ad . oligomeric aggregates a and tau protein or the protofibrils are considered as precursors for amyloid fibrillation in alzheimer 's disease . recently , the effect of fluorinated magnetic core - shell nanoparticles with the size range of 15.0 2.1 nm has been observed on amyloid model protein insulin ; these fluorinated nanoparticles show inhibition of insulin fibrils [ 3 , 4 ] . furthermore , the effect of various nanoparticles within the dimensions of 6200 nm on another model protein , 2 microglobulin , has been investigated . previously published studies have demonstrated that nanoparticles can act as catalysts for protein fibrillation [ 1 , 5 ] . very recently , li and coworkers have showed an inhibition effect of n - acetyl cysteine - capped cdte qds of size of 35 nm on a ( 140 ) fibrillation . in another case , dual effect of commercial polystyrene nanoparticles with amino modification having various sizes ( 57 , 120 , and 180 nm ) was observed on a ( 140 ) and recombinant a ( 140 ) and a ( 142 ) proteins . furthermore , there is only one recent publication on the effect of nanoparticles on a ( 142 ) fibrils . in this case , it was observed an increase in rate of amyloid fibrillation in presence of tio2 nanoparticles with size of approximately 20 nm . the interaction of nanoparticles with different proteins depends upon various factors such as surface coating of nanoparticles with ligands , surface properties , size , and composition of nanoparticles [ 1 , 5 ] . from the previous studies , [ 1 , 38 ] we can not generalize the concept that different nanoparticles can promote or inhibit the fibril formation for various amyloid model proteins . specifically , the only investigation that explains the effect of tio2 on a ( 142 ) shows that nanoparticles promote the fibrillation process by becoming nucleation centers . we report for the first time in our knowledge that cdse / zns qds of size of 2.5 1.3 nm can inhibit fibrillation of a ( 142 ) . in the present study , we have investigated the effect of the presence of dhla - capped cdse / zns qds either mixed with or conjugated to a ( 142 ) on fibrillation process of a ( 142 ) in aqueous phase . tem and afm studies show that the qds behave uniquely when they are conjugated to a ( 142 ) in comparison to a mixed sample of a ( 142 ) and qds . our study illustrates a considerable difference in morphology of the fibrils and the inhibition of fibrillation process when a ( 142 ) is conjugated to qds versus the mixed system a ( 142 ) and qds . these results are further supported by thioflavin t ( tht ) assay using fluorescence spectroscopy . all chemicals were commercially purchased and used without further purification . cadmium oxide ( cdo ) , selenium ( se ) , trioctylphosphine oxide ( topo ) , trioctylphosphine ( top ) , and hexamethyldisilathiane [ ( tms)2s ] were purchased from sigma - aldrich ( milwaukee , wi ) . the tetradecylphosphonic acid ( tdpa ) was obtained from alfa aesar ( ward hill , ma ) . the diethylzinc ( znet2 , 15 wt% solution in hexane ) was obtained from acros organics ( morrisplains , new jersey ) . dl--lipoic acid , a ( 142 ) , and tht were purchased from mp biomedicals ( solon , oh ) . briefly , cadmium oxide was reacted with a selenium reagent in the presence of a phosphine oxide surfactant at high temperature under argon flow . after the formation of the cdse core , the diethyl zinc and hexamethyldisilathiane in top was added dropwise at 130c . after the synthesis of topo - capped hydrophobic qds , modification to hydrophilic dhla - capped qds was carried out . briefly , first dl--lipoic acid ( 1 g ) was reduced using sodium borohydride ( 2 g ) in methanol / water ( v / v , 1:1 ) solution . after workup product was isolated in chloroform and characterized using h nmr ( 400 mhz , cdcl3 ) : ( ppm ) 1.3 ( d , 1h ) , 1.35 ( t , 1h ) , 1.41.8 ( m , 6h ) , 1.9 ( m , 2h ) , 2.4 ( t , 2h ) , 2.62.8 ( m , 2h ) , 2.9 ( m , 1h ) , and 11 ( s , 1h ) . dhla was used for ligand exchange with topo ; excess of dhla ( 0.5 g ) was added in 5 ml of topo - capped qds in methanol and heated at 60c70c for 4 h. once a homogeneous qds solution was obtained , solution was basified using potassium tert - butoxide and centrifuged to get the precipitates . the water - soluble qds were filtered through 0.2 m filter to get a clear solution . a(142 ) was chemically conjugated to qds by the formation of an amide bond between asp - nh2 end of the polypeptide chain and the cooh end of the dhla ligand using the protocol to conjugate proteins . freshly prepared dhla - capped qds ( 1.51 10 m , 100 l ) were taken in a clean borosilicate glass vial , and 500 l pbs buffer ( ph 7.4 ) was added to the qds . to lyophilize the peptide , 0.5 mg a ( 142 ) was dissolved in hexafluoroisopropanol ( hfip ) to bring the peptide in monomer form and evaporated under gentle flow of n2 . the dried protein was then dissolved in 500 l pbs buffer ( ph 7.4 ) to get the final concentration of 1 mg / ml . freshly prepared a(142 ) solution was then mixed in qds solution . 57 l of freshly prepared 10 mg / ml edc ( 1-ethyl-3-(3-dimethylaminopropyl ) carbodiimide hydrochloride ) solution in deionized water was then added to the mixture of peptide and qds , total volume of solution prepared was 1157 l . the solution was stirred for 4 h at the speed of 200 rpm . a ( 142 ) mixed with dhla - capped qds was prepared according to the above - mentioned protocol except for the addition of edc . total volume of the solution was kept at 1157 l . for the induction of fibrillation pure a ( 142 ) solution was prepared similarly , first by lyophilizing the peptide in hfip and evaporating the solvent under gentle nitrogen flow and then redissolving the dried peptide in 1157 l of pbs buffer ( ph 7.4 ) . electrophoresis of qds was performed using a minicuve 8.10 electrophoresis unit ( mp biomedicals , solon , oh ) . hand cast gels were composed of 1% agarose in 1 tbe ( 0.089 m tris base , 0.089 m boric acid , and 0.002 m ethylenediaminetetraaceticacid , ph 8.3 ) . 10 l of each sample was loaded into wells on the agarose gel using a micropipet . the samples were run in 1 tbe buffer on the 1% agarose gel at 84 v for 75 min . for visualization , the gel was placed on a uv transilluminator , and an image was captured with a gel doc xr system ( bio - rad , hercules , ca ) . tem measurements were performed at the center of advanced microscopy , scripps research institute ( la jolla , ca ) and at the center of advanced microscopy , ( cma ) , trinity college dublin ( ireland ) . for the images containing amyloid , briefly , copper grids ( carbon and formvar coated 400 mesh : electron microscopy sciences , hatfield , pa ) were glow discharged and inverted on an 5 l aliquot of sample for 3 min . excess sample was removed and the grids immediately placed briefly on a droplet of double - distilled water . grids requiring the negative stain were then placed on droplets of 2% uranyl acetate solution for 2 min . excess stain was removed and the grid was allowed to dry thoroughly . for unstained grids , the excess water was removed , and the dried grids were examined on a philips cm100 electron microscope ( fei , hillsbrough , or ) at 80 kv and images collected using a megaview iii ccd camera ( olympus soft imaging solutions , lakewood , co ) . grids at ireland were examined on a jeol 2100 electron microscope ( zeiss ) operating at 200 kv and images collected using a ccd camera . analysis of tem images was performed using image j software from nih ( http://rsbweb.nih.gov/ij/ ) . briefly , 4 l aliquots of a solutions were deposited on freshly cleaned and dried silicon wafers ( approximately 1 mm thick ) . after waiting for 10 min , nonadsorbed portions of the samples were washed with deionized water ( 400 l ) . the wet surface of the silicon wafer was then dried using gentle flow of air . the samples were analyzed by atomic force microscopy ( afm , a multimode spm , model no . tapping mode approach was used to acquire the images , which allows intermittent contact of the tip with the sample and minimizes the chances of deformation of the peptide samples . the cantilever force constant was approximately 20100 n / m with the resonance frequency between 200 and 400 khz . the software used for the analysis of fibrils was the nanoscope control , version 5.30 and the histogram analysis was performed using the postanalysis pico image software ( pico view version 1.6.2 ) . uv - vis spectra of solutions were recorded on a perkin - elmer lambda 900 uv / vis / nir spectrometer ( norwalk , ct ) . fluorescence spectra were obtained using spex fluorolog fluorospectrometer ( horiba jobin yvon , edison , nj ) . both uv - vis and fluorescence measurements were obtained using quartz cuvette with1 cm optical path length . 30 l of a ( 142 ) aliquots were extracted at different time periods , and 300 l of tht ( 10 m ) was added to the samples . the tht fluorescence was measured at 482 nm at an excitation wavelength of 440 nm in a semimicro quartz cuvette of an optical pathlength of 1 cm . characterization of dhla - capped qds was carried out using uv - vis and fluorescence spectroscopy ( figure 1(a ) ) . the fluorescein ( qy is 0.94 in 0.1 m naoh ) was employed as reference . the qy was calculated by using the following equation : ( 1)qyq = qyf[afnq2iq()d][aqnf2if()d ] . a is the absorbance at the excitation wavelength , n is the refractive index of the solvent used , i is the emission wavelength - dependent emission intensity , and is the emission wavelength . qy was calculated from the intensity of luminescence and the absorbance in figures 1(b ) and 1(c ) for fluorescein ( 0.1 m naoh as solvent ) and qds ( water as solvent ) , respectively . the qy of the dhla - capped cdse / zns qds was around 25% . to characterize the qds conjugated to a ( 142 ) , it is important to estimate the number of a monomers bound to qds after conjugation . firstly , characterization of samples of pure a ( 142 ) , a ( 142 ) mixed and conjugated to qds was performed using uv - vis and fluorescence spectroscopy ( figure 2 ) . the emission band for the tyrosine moiety in a ( 142 ) was observed at 309 nm at the excitation wavelength of 280 nm , slit width at emission and excitation was set at 5 nm . the absorption band for a ( 142 ) was observed at 275 nm ( figure 2(a ) ) , whereas the emission band for the a ( 142 ) mixed and conjugated to qds was observed at 560 nm at the excitation wavelength of 467 nm . the absorption band for the qds was observed at 547 nm and for the a ( 142 ) a little hump was observed at 275 nm as shown in figure 2(b ) . molar concentration of the qds and a ( 142 ) was calculated from uv - vis spectrum of the solution [ 12 , 13 ] , the optical path length used was 1 cm . the ratio of these concentration values gave the average number of a per quantum dot nanoparticles . the molar extinction coefficient of qds at 547 nm is 105.8 10 m cm and at 275 nm is 2.6 10 m cm . extinction coefficient for a ( 142 ) at 275 nm is 1.4 10 m cm . the calculations to determine the ratio of a ( 142 ) and qds are shown below . qds concentration ( conjugated sample ) is ( 2)abs547547l=0.1561.05 105 m1 cm11 cm=1.5106 m. absorption at 275 nm from qds is ( 3)abs547275547=0.1562637.21.05105=3.9103 . absorption at 275 nm from a ( 142 ) is ( 4)abs275[abs547275547]=2.23.9 103=2.2 . a ( 142 ) concentration in the sample conjugated to qds is ( 5)abs for a at 275 for a at 275l=2.21390 m1cm11 cm=1.6103 m , loading = a concentrationqds concentration=1.6103 m1.5106 m=1.1103 . theoretically , the total number of molecules / particle of a ( 142 ) ( molecular weight 4514.1 g ) present in 0.5 mg of the 1157 l of sample can be calculated by multiplying the number of moles with na ( avogadro 's number ) number of molecules . hence , the total number of molecules of a ( 142 ) present in the sample is 5.8 10 . similarly , the total number of qds particles present in the solution is 9.0 10 . therefore , the ratio of a ( 142 ) molecules per qd particle is 6400 . subtracting the experimental value ( 1100 ) from the theoretical value ( 6400 ) , it can be inferred that there are 5300 molecules of a ( 142 ) that are free in the solution per qd particle that is conjugated to a ( 142 ) . to confirm that the qds were indeed conjugated to a ( 142 ) , we have used the agarose gel electrophoresis for the control dhla - capped cdse / zns qds along with a ( 142 ) mixed and conjugated to the qds ( figure 3 ) . the gel was run in tae buffer ( ph 7.4 ) at 84 v for 75 min , and the volume of the samples in each well was 10 l . figure 3 shows the distance moved by three different samples : dhla - capped qds ( 1 ) , a ( 142 ) mixed with dhla - capped qds ( 3 ) , and a ( 142 ) conjugated with dhla - capped qds ( 5 ) . from the gel electrophoresis , we can clearly distinguish that the distance moved by the qds mixed with a ( 142 ) is the same as for the pure dhla - capped qds . whereas when the qds are conjugated to a ( 142 ) , the distance moved is lower . this shows that when the qds are chemically conjugated to a ( 142 ) , the distance moved is reduced due to the higher molecular weight . moreover , comparison of polyethylene glycol ( peg)-capped qds ( 2 ) , a ( 142 ) mixed peg - capped qds ( 4 ) , and a ( 142 ) conjugated peg - capped qds ( 6 ) shows that peg - capped qds when conjugated travel the least distance . purified fractions of dhla- ( 7 ) and peg - capped ( 8) qds conjugated to peptide show that free a ( 142 ) can be separated from the a ( 142 ) conjugated qds . different fractions of 1 ml each obtained from gel chromatography were checked for the presence of free a ( 142 ) using uv - vis absorption and fluorescence spectroscopy . first evidence on the inhibition in fibrillation comes from tem images ( figure 4 ) taken on the 7th day of incubation at 37c . tem images containing a ( 142 ) are negatively stained using 2% uranyl acetate solution . three different samples , namely , pure a ( 142 ) , a ( 142 ) mixed with dhla - capped cdse / zns qds , and a ( 142 ) conjugated to dhla - capped cdse / zns qds , are shown in figures 4(a ) , 4(c ) , and 4(d ) , respectively . in all the three samples , the concentration of a ( 142 ) is 0.96 10 m and the concentration of qds is 1.4 m . analysis of this image indicates that the length of the fibrils varies from 30 to 1730 nm . the width of the shorter fibrils is 4.0 0.7 nm whereas for the longer fibrils it is 7.5 0.5 nm . figure 4(b ) presents the pure dhla - capped cdse / zns qds , the average particle size is 2.5 1.3 nm ( figure 5(a ) ) . the size of qds is an important parameter for the biodiagnostic studies , since smaller size qds are capable of passing through the blood - brain barrier [ 15 , 16 ] . figure 4(c ) shows the incubated sample of a ( 142 ) in the presence of qds whereas figure 4(d ) shows a ( 142 ) conjugated qds . comparison of the results in the three images containing a ( 142 ) illustrates very interesting pattern . sample containing pure a ( 142 ) , figure 4(a ) , has a large number of fibrils ranging from short fibrils around 30 nm to long fibrils around 2 micron whereas images of samples in presence of qds are very different . figure 4(c ) is the image of a ( 142 ) mixed with qds ; it shows long - length fibrils of around 1 micron . the width of the fibrils for the sample having mixed qds is 7.7 0.7 nm . figure 4(d ) for a ( 142 ) conjugated to qds shows short - length fibrils ranging from 30 to 80 nm . for this sample , the variation in the thickness of fibrils is significant in this case as compared to the other two . one can see a distinguishable inhibition of the fibrillation when a ( 142 ) is conjugated to qds . histogram showing the size of dhla - capped qds is shown in figure 5(a ) . the average size analyzed from the histogram obtained from tem images is 2.5 1.3 nm . furthermore , to consolidate the results , we have performed the statistical analysis on the tem images ( 1318 images per sample ) . the number of short - length fibrils ( 80150 nm ) observed in the sample containing pure a ( 142 ) was extremely high as compared to samples containing qds . statistical analysis showed ( figure 5(b ) ) that the number of fibrils having length 50100 nm dropped to 90% in the case of a ( 142 ) mixed to qds . there were only 26% of short - length fibrils observed for a ( 142 ) conjugated to qds . the total number of fibrils in the samples containing qds mixed or conjugated to a ( 142 ) was similar ( 35 fibrils approximately ) . . figures 6(a ) and 6(b ) show the tem images of unstained samples of a ( 142 ) mixed with qds . contrary to the tem images of stained samples where we can observe only fibrils and no qds , in this case , we were able to observe the qds , as well as fibrils . it could be discerned from the results that qds are enveloping the fibrils and more number of qds are observed at the ends of the fibrils . for the samples containing a ( 142 ) conjugated to qds ( figures 6(c ) and 6(d ) ) , we could observe less number of qds and short - length fibrils . the qds observed in this case are segregated at one end of the fibrils as seen in figure 6(d ) . it could be infered from the results obtained using unstained samples ( figure 6 ) that qds envelop the fibrils and could block the ends to elongate . importance of the c terminus of the a ( 142 ) in controlling the self - assembly of fibrillation was revealed before . the reason for the inhibition of fibrillation in presence of qds could be that the small size of particles could block the c - terminal end of the fibrils ( ~10 nm ) or the protofibrils ( ~5 nm in diameter ) , which is considered as the terminus with lower degree of freedom and accessibility for elongation mechanism . furthermore , binding between the qds and the a ( 142 ) could block the active sites leading to low local protein concentration , hence increasing the lag time for nucleation or disrupting the nucleation process leading to inhibition of the fibrillation process . besides , presence of a ( 142 ) conjugated to qds in the sample containing free a ( 142 ) may perturb the nucleation mechanism with decrease in localised concentration of the a ( 142 ) as thereby inhibiting fibrillation process [ 19 , 20 ] . however , mixed sample of a ( 142 ) and the qds might increase the localised concentration of the polypeptide , thereby increasing the length of fibrils but the number of fibrils still remains low suggesting that there is a perturbation in the mechanism of the fibrillation process . the tem results are supported by the afm images as shown in figure 7 for the 7th day of incubation at 37c . analysis of afm image for a ( 142 ) in absence of qds ( figure 7(a ) ) shows that the length of the longest fibril is 523 nm and the shortest fibril is 30 nm . a bigger number of short length fibrils ( 3080 nm ) are observed as witnessed by the tem images whereas in the sample containing a ( 142 ) mixed to qds ( figure 7(c ) ) the length of the longest fibrils is 849 nm , comparable to the length of fibrils ( 1 m ) found in the tem images . however , when we compare the length of fibrils ( figure 7(d ) ) in the sample containing a ( 142 ) conjugated to qds , very few long fibrils were observed , which correspond to the tem images of the same sample . the length of the longest fibrils found is 468 nm and the shortest fibril is 58 nm , while in the case of the tem images the length of fibrils is between 30 and 80 nm . the height analysis of qds ( figure 7(b ) ) shows that the root mean square height of qds is 2.3 nm , which is comparable to the average height of qds found in tem images ( 2.5 1.3 nm ) . the measurement of z - height of the a aggregates shows that when a ( 142 ) is conjugated to qds the height distribution histogram changes significantly . it is known for the a oligomers that the average height is between 3 and 5 nm , and for the fibrils it varies from 3 to 9 nm [ 21 , 22 ] . from the height distribution curves ( figure 8) one can see that in the case of amyloid fibrils in absence of qds 40% of aggregates have height greater than 8 nm whereas 60% of aggregates have height between 6 and 8 nm . for the sample of a ( 142 ) mixed with qds , 30% of the aggregates have height greater than 7 nm , and 70% of the aggregates have height between 1 and 3 nm . interestingly , when we analyze the height distribution for a ( 142 ) conjugated to qds only 14% of the aggregates have height greater than 7 nm . almost 90% of the aggregates have height between 2 and 4 nm . to further examine the fibrillation process and to support the image analysis , it is known that the fluorescence intensity of the tht dye grows with increasing concentration of fibrils . it has to be pointed out that previous studies confirmed that the fluorescence enhancement of tht depends upon the structure of the aggregated state of the amyloid peptides [ 23 , 24 ] . figure 9(a ) shows the tht assay on the 7th day for the samples incubated at 37c . when the pure solution of 10 m tht in pbs buffer ( ph 7.4 ) is excited at 440 nm , the emission band at 482 nm is observed with a very low intensity . in the presence of amyloid fibrils , the tht emission band at 482 nm is enhanced significantly . for the sample containing qds mixed to the fibrils , the intensity of the emission band at 482 nm is decreased by 66% as compared to the band for pure amyloid fibrils . whereas the amyloid fibrils , conjugated to qds show a decrease in intensity for the emission band by 40% as compared to the qds mixed to the fibrils . the variation of tht intensity yields information regarding the extent of fibrillation . for the sample containing pure a ( 142 ) , a sigmoidal curve is observed , lag phase is between 0 and 24 h , and rapid progress in fibrillation is observed after 50 h of incubation . however , for the sample containing dhla - capped qds mixed to a ( 142 ) , lag time is increased to 48 h and it can be observed with decrease in intensity of fluorescence that the qds are inhibiting the fibril formation . similarly , in the case of sample containing a ( 142 ) conjugated to the dhla - capped qds , a decrease in intensity of fluorescence and completion of saturation in fibrillation are observed at 72 h. these results show , in the presence of qds , that the self - assembly of a ( 142 ) is perturbed . a remarkable diminution in fibrillation process in the presence of qds and a significant change in morphology contrary to the results that have been published previously on the nanoparticles such as tio2 , copolymer particles , cerium oxide , qds , and carbon nanotubes behaving as catalyst for fibrillation [ 5 , 8 ] , we did not observe the same behavior for the dhla - capped cdse / zns qds . moreover , our results are in line with a very recent publication showing the inhibition of a ( 140 ) by cdte nanoparticles which have similar diameter size ( 35 nm ) . major difference from other set of nanoparticles being used could be the composition and the size of the particles . the size range for the particles that have been used for the previous studies varies from 16 to 200 nm whereas the qds used in our work have an average size of 2.5 1.3 nm . to investigate the effect on the tyrosine residue , which is an intrinsic probe of a ( 142 ) , we have examined the tyrosine fluorescence spectra for the three samples on the 7th day of incubation at 37c . there is a notable quenching of the tyrosine fluorescence intensity at 309 nm ( figure 9(c ) ) in the presence of mixed or conjugated qds . this effect could be due to the fact that the tyrosine moiety ( tyr ) interacts with the qds . for example , the three histidine residues ( his , his , and his ) in the vicinity of the tyrosine may interact or form coordination bond with the surface of qds . this phenomenon happens due to the presence of overcoated zns shell offering zn ions , hence rendering tyrosine to interact with qds and consequently decreasing significantly the fluorescence intensity of tyrosine band . another explanation could be the fret mechanism between the donor ( tyrosine moiety ) and the acceptor ( qds ) , since there is an overlap between the absorption spectrum of the acceptor ( qds ) and the emission spectrum of the donor ( tyrosine ) . fret efficiency in case of a ( 142 ) conjugated to qds was 0.84 whereas for a ( 142 ) mixed with qds was 0.94 . it could be interpreted that the forster distance ( ro ) between the a ( 142 ) and qds in aqueous solution was less than 60 which is the critical distance for energy transfer . it means that in both the samples , a ( 142 ) mixed with or conjugated to qds , a ( 142 ) is present very near to the qds . this is an indirect evidence that qds are present very near to fibrils ; that is also observed in the tem images of the unstained samples ( figure 6 ) . furthermore , to examine the inhibition effect of cdse / zns qds , we performed the same set of experiments using polyethylene glycol ( peg ) ( mw 400)-capped cdse / zns qds . no inhibition on fibrillation process is observed when peg - capped qds are mixed or conjugated to a ( 142 ) . figures 10(a ) and 10(b ) show the afm images of peg - capped qds conjugated and mixed to a ( 142 ) , respectively , after 2 days . the length of the fibrils is between 700 nm and 3 m and the height of oligomers is observed between 2.5 and 5.9 nm . increase in intensity of fluorescence at 482 nm for the peg - capped qds mixed or conjugated with a ( 142 ) shows that there is increase in fibrillation in presence of peg - capped qds . experiments were also designed where dhla- or peg - capped qds were purified using gel chromatography to check the inhibition effect . similar results are obtained over a period of 72 h with the purified fractions of dhla - or peg - capped qds , that is , inhibition and absence of inhibition on fibrillation process , respectively . it shows that if we change the ligand of the qds , it changes its behavior towards the fibrillation process . the emission band for the peg - capped qds was observed at 472 nm , when the excitation wavelength was set at 467 nm . the average size for the peg - capped qds obtained using tem analysis was 19.4 4.7 nm ( figure 10 ) . this change in behavior might be due to the fact that peg - capped qds tend to aggregate in buffer solutions , and peg polymer increases the size of the qds . these two factors make the qds nanoparticles less dynamic in solution and less accessible for the a ( 142 ) monomers , where the nanoparticles can block the active sites for extended fibrillation . figures 11(a ) and 11(b ) show the tem images of peg - capped qds . the average size for the peg - capped qds obtained using tem analysis was 19.4 4.7 nm as illustrated in the histogram ( figure 11(c ) ) . qds mixed or conjugated to a ( 142 ) show a decrease in the fibrillation as compared to pure a ( 142 ) , when incubated at 37c for 7 days . longer fibrils ( 2 micron ) are observed in the sample containing a ( 142 ) mixed with qds . pure a ( 142 ) sample contained large number of short- and long - length fibrils ( 301730 nm ) . thicker and shortest length fibrils ( 3080 nm ) are observed in the case of a ( 142 ) conjugated to qds . the height analysis of afm images shows significant decrease in height of aggregates greater than 7 nm ( only 14% ) when qds are conjugated to a ( 142 ) and 30% when qds are mixed to a ( 142 ) as compared to pure a ( 142 ) solution . tht assay for the samples confirmed the inhibition of the fibrillation process when a ( 142 ) is mixed or conjugated to qds . moreover , quenching of tyrosine signal is observed in the presence of qds , which indicates an interaction of the qds with the tyr residue in a ( 142 ) . however , in presence of peg - capped qds mixed or conjugated to a ( 142 ) , an absence of inhibition on fibrillation is observed as revealed by afm images and tht fluorescence . the conclusion of this work is presented in figure 12 that shows diminution in fibrillation in presence of dhla - capped qds , either mixed with or conjugated to a ( 142 ) . to investigate the use of qds in vivo studies is very important part of biomedical applications , there is a recent investigation showing the use of qds for imaging and delivery purposes , where qds carrying snare - tagged rbd were delivered at the synaptic contacts in the cultures from hippocampal neurons obtained from mice . moreover , qds doped with sio2 nanoparticles showed imaging and gene carrier capabilities , it was demonstrated that these qds were internalized by primary cortical neural cells without inducing cell death in vitro and in vivo . point to be noted is cdse quantum dots are toxic and might not be used for medicinal purposes . however , some toxicology studies have shown that the toxicity of qds is size and concentration dependent . for example , cytotoxicity studies of cdse qds on b16 f10 melanoma cells , and c57/bl6 mice showed no detectable toxicity . early studies have shown high toxicity of cdse qds due to the release of toxic cd ions ; however , coating of zns has shown to reduce the toxicity in cell culture to a great extent . nevertheless , extensive studies are required in the field of toxicology . in the light of these studies , it would be important to test a ( 142 ) mixed with or conjugated to qds in the cultures from neurons of mice to investigate the effect of qds in in vivo systems .

nanoparticles have enormous potential in diagnostic and therapeutic studies . we have demonstrated that the amyloid beta mixed with and conjugated to dihydrolipoic acid- ( dhla ) capped cdse / zns quantum dots ( qds ) of size approximately 2.5 nm can be used to reduce the fibrillation process . transmission electron microscopy ( tem ) and atomic force microscopy ( afm ) were used as tools for analysis of fibrillation . there is a significant change in morphology of fibrils when amyloid ( 142 ) ( a ( 142 ) ) is mixed or conjugated to the qds . the length and the width of the fibrils vary under modified conditions . thioflavin t ( tht ) fluorescence supports the decrease in fibril formation in presence of dhla - capped qds .

1. Introduction 2. Experimental Section 3. Results and Discussion 4. Imaging and Analysis 5. Conclusion

the influence of ovarian hormone activity on migraine with ( ma ) and without aura ( mo ) throughout the female lifecycle is well known [ 1 , 2 ] . estrogenic production induces dichotomy in the incidence of migraine between the two genders at the time of puberty , which becomes wider during the childbearing age and diminishes after menopause . in women , the attacks often begin at menarche and then occur maximally in correlation with menses as pure menstrual migraine or menstrual - related migraine in a large amount of patients [ 3 , 4 ] . indeed , a change in migraine pattern is frequently observed during pregnancy [ 5 , 6 ] , puerperium and after menopause [ 8 , 9 ] , and is related to hormonal therapies . we present the case of a woman with a 36-year history of migraine with aura and describe the effect on the attacks of the hormonal physiological modifications and of the various hormonal therapeutic treatments that rarely could be found in a single individual . a 48-year old woman presented at our headache centre for a long - standing history of migraine with aura ( ichd - ii ) . she experienced her first episode by the age of 12 years , a few months after menarche . the attacks were characterized by gradual onset of flickering lights localized over the temporal aspect of both visual fields with an average duration of 3040 min , followed within a half - hour by bilateral , throbbing and moderate to severe headache , accompanied by nausea , photophobia and phonophobia with a duration of about 6 h. at the beginning , the attacks usually occurred during the menstrual period with a frequency of one episode every other month . other trigger factors were reported , including emotional stresses and difficulties with study and , later on , with her work as a clerk . the frequency of attacks remained quite unchanged until the age of 26 when she became pregnant . during the second and third trimester , the patient experienced an increased frequency with at least two episodes a month , or more , in the last month prior to delivery . the attacks remained unchanged during puerperium and the 4 months of breast - feeding , after which the episodes persisted with a frequency of once a month . at the age of 31 , the patient was diagnosed with ovarian endometriosis for which she was started on oral contraceptives ( oc ) . during the 6-month period of oc therapy for this reason , a prophylactic therapy with lisuride at the dosage of 0.025 mg tid was added , without relevant improvement . afterwards , the oc therapy was stopped and the patient underwent a partial ovariectomy . in the subsequent 6 months , she was treated with the gonadotropin - releasing hormone agonist ( gnrh - a ) triptoreline at the dosage of 3.75 mg i m once monthly , during which period the patient did not present with any attack . nevertheless , at the end of treatment at the age of 33 , the ma attacks recurred with high frequency . at that time , the patient experienced important emotional distress due to a severe disease suffered by her mother . at the age of 40 , she was diagnosed with a breast cancer . a radical mastectomy was performed and pathology showed a ductal adenocarcinoma with metastatic invasion of the axillary lymphonodes ; estrogen and progesterone receptors were positive . the surgery was followed by six cycles of chemotherapy with cyclophosphamide , methotrexate and 5-fluorouracil . during chemotherapy , the patient reported about three crises monthly , of which one was regularly , at the end of every cycle . after the end of chemotherapy , tamoxifen 20 mg daily was started and the therapy lasted for 5 years . in the 5 years of tamoxifen therapy , the patient experienced only three attacks , but soon after the stop of therapy ma built up again with two or three episodes a month of severe headache preceded by visual disturbance and paresthesia , the latter being very unusual until then . migraine prophylactic treatment was prescribed with flunarizine 5 mg daily for 6 months and then amitriptyline 50 mg at bedtime for 8 months with poor efficacy . this case considers the milestones of the physiological hormonal life of a woman and their effects on the course of ma . moreover , the pathologies presented by the patient ( endometriosis and breast cancer ) allow to evidence the importance of the treatments performed , in particular those with influence on hormonal activity , on ma attacks . the data , regarding the frequency of the crises are precise because , for many years before presenting to our headache centre , the patient entered in her detailed personal diary the events of her life , including the occurrence of the attacks and of menses . clearly , the trigger factors for ma are not only hormonal , but also emotional , causes ( the disease of her mother , the neoplasia , problems in the job ) . however , the relationships with the physiological hormonal modifications are very evident : first of all , we notice the beginning of the attacks a few months after menarche and the occurrence of the attacks often in relation to menses . then , she developed a worsening of the attacks at the beginning of the third month of pregnancy , an unusual but not extraordinary circumstance in ma , that respect to migraine without aura ( mo ) may show a less favourable course or that sometimes develops during pregnancy . finally , we noted a persistence of the attacks during puerperium and breast - feeding . regarding pharmacological treatments , we evidenced drugs that caused worsening or improvement of the attacks . in the first instance , there was a remarkable worsening of the crisis with the use of oc , in spite of the concomitant prophylactic treatment . moreover , although it is difficult to establish the exact mechanism of action by which antiblastic drugs might provoke the attacks at the end of every treatment , a cause effect relationship appears clear . in the second instance , the treatment with gnrh - a for therapy of endometriosis and then with tamoxifen for adjuvant treatment of the neoplasia proved to be very effective in the prevention of the attacks , particularly tamoxifen that was prescribed for 5 years . the patient reported not more than three attacks during the entire period of anti - oestrogenic treatment . about tamoxifen , there are two studies in the literature [ 13 , 14 ] . in an open - label non - randomized study on eight women suffering from not further specified catamenial migraine , five patients reported marked improvement or disappearance of headache , two mild moderate improvement and one was unchanged . tamoxifen was given at a dosage of 1020 mg / days for 714 days before menstruation and continued at 510 mg days for 3 days after the start of menstruation for four cycles . the second report was on a series of six women with migraine - type headaches and benign mammary dysplasia treated with tamoxifen 20 mg / day . improvement was seen in all patients who no longer required migraine drug therapy , but the attacks returned a few weeks after tamoxifen discontinuation of the drug . in contrast with these data , one case report of catamenial migraine showed a worsening of the attacks with tamoxifen . we found two studies on the use of gnrh - a with partially divergent conclusions [ 16 , 17 ] . the first was a non - randomized prospective study , in which five patients with menstrual migraine were treated with 3.75 mg i m gnrh - a monthly for 10 months . for the last 6 months of treatment , patients also received transdermal estrogen and medroxyprogesterone 2.5 mg . all the patients reported a marked reduction of the attacks with leuprolide and with leuprolide and hormonal add - back therapy . conversely , martin et al . in a randomized , placebo - controlled study on 21 patients , treated with gnrh - a and with gnrh - a associated with estrogens , demonstrated a modest preventive benefit only in the group treated with gnrh - a ( goserelin 3.6 mg implant ) associated with a transdermal patch containing 100 g of oestradiol-17. the above reported studies , the only ones present in literature on this topic to the best of our knowledge , consider the use of tamoxifen and gnrha only in the treatment of mo . we highlight the possible use of these treatments also in ma , but this needs further studies . a possible caveat is that often the course of ma is irregular with long periods of spontaneous remission and this pattern could make testing the efficacy of a therapy difficult . but this statement is not applicable to our patient who presented a rather regular course of the crisis . ma is commonly thought to worsen in periods of high plasma estrogen concentration , such as the last two trimesters of pregnancy , but not with estrogen withdrawal . in this case , ma worsened with both low and high estrogen levels ( i.e. , menstrual period , post - partum , pregnancy ) . it seems that both hormonal fluctuations and stable high estrogen levels could trigger ma attacks , whereas stable low estrogen levels , obtained pharmacologically by anti - estrogen and gnrh - a drugs , could be beneficial . in our case , these therapies were given , incidentally , to treat other diseases ( endometriosis and breast cancer ) as in the powles report for benign mammary dysplasia . we believe , considering these results , that in particular and selected situations , when the crises are particularly related to hormonal changes and difficult to treat , or when associated with concomitant gynecologic diseases , these drugs could be considered for use , although not as a first - line treatment , but with caution and in cooperation with a gynecologist .

we present the case of 48-year - old woman suffering from migraine with aura ( ma ) since menarche . during her life the patient frequently presented catamenial ma attacks with an increasing frequency during pregnancy in particular in the second and third trimesters , and then during breast - feeding . treatment with oral contraceptive ( oc ) for endometriosis and later with cyclophosphamide , methotrexate , fluorouracil ( cmf ) for breast cancer produced a higher number of attacks . instead , she referred an improvement with gonadotropin releasing hormone agonist ( gnrh - a ) for the treatment of endometriosis and then with tamoxifen as hormonal therapy after mastectomy and chemotherapy for breast cancer . we highlight the importance of physiological hormonal modification and hormonal therapies on the course of ma .

Introduction Case report Discussion

amp - activated protein kinase birt - hogg - dub syndrome folliculin interacting protein hypoxia - inducible factor mouse embryonic fibroblast peroxisome proliferator - activated receptor coactivator 1 reactive oxygen species sustaining rapid and persistent proliferation represents a bioenergetic and biosynthetic challenge for cancer cells , which must efficiently manage their energetic resources to survive and grow in unfavorable environments . this is achieved through metabolic reprogramming to stimulate aerobic glycolysis , a process known as the warburg effect , which is now a well - appreciated hallmark of cancer . however , the signaling pathways and key regulators of this metabolic transformation are still poorly defined . amp - activated protein kinase ( ampk ) , a major physiological regulator of cellular energy homeostasis , is located at the center of a metabolic network . indeed , ampk functions as a sensor of cellular energy fluctuation and a driver of pathways that minimize energy consumption and maximize energy production upon energetic stress . despite its critical function in cell metabolism , the role of ampk in cancer is controversial as both pro- and anti - tumorigenic effects have been described . in fact , while ampk activation might prevent tumor initiation through its ability to restrict cell proliferation , several reports have shown that ampk gain of function acts as a driver of tumorigenesis by enhancing glycolytic energy production and cell survival under metabolic stress conditions . our recent work sheds light on how ampk activation could drive metabolic transformation and tumorigenesis . germline inactivating mutations in the folliculin ( flcn ) tumor suppressor gene predispose to birt - hogg - dub ( bhd ) syndrome , an inherited cancer disorder associated with lung cysts , pneumothorax susceptibility , renal cell carcinoma , and skin tumors . although flcn and its uncharacterized binding partners folliculin interacting protein 1 ( fnip1 ) and 2 ( fnip2 ) were identified as ampk binding partners and phosphorylation tar binding partner and phosphorylation target , its physiological role and tumor suppressor mechanism and its impact on ampk - dependent functions are still poorly characterized . we previously reported that loss of flcn enhances transcriptional activity of hypoxia - inducible factor ( hif ) and increases the glycolytic rate in human kidney cancer cells . moreover , a recent publication demonstrated that conditional deletion of flcn in mouse kidney and muscle results in increased mitochondrial oxidative phosphorylation , suggesting that loss of flcn enhances cellular metabolism . to maintain cellular homeostasis under hypoxic conditions , hif drives the transcription of genes that stimulate glycolysis , angiogenesis , and energy supply , which in turn promotes solid tumor growth , invasion , and metastasis . however , how flcn and ampk regulate hif activity and metabolic adaptation in normoxic conditions , and whether this effect is linked to tumorigenesis , is not defined . using untransformed flcn mouse embryonic fibroblasts ( mefs ) and cancer cell lines naturally deficient for flcn expression , we demonstrated that flcn depletion constitutively activates ampk independent of the cellular energy state . using a non - phosphorylatable form of flcn that is mutated at a previously identified ampk phosphorylation and binding site we established that loss of flcn binding to ampk chronic ampk activation leads to upregulation of the peroxisome proliferator - activated receptor coactivator 1 ( pgc-1 ) , a known target of ampk , which in turn increases mitochondrial content and the oxidative phosphorylation rate , leading to enhanced production of reactive oxygen species ( ros ) . surprisingly , elevated mitochondrial ros production is not associated with increased oxidative protein and dna damage , but rather acts as a signaling molecule to activate hif transcriptional activity without affecting hif-1 protein stability . upon flcn depletion , the active hif complex mediates transcription of glycolytic effectors , thus enhancing glucose uptake and the glycolytic rate . strikingly , knockout of ampk , knockdown of pgc-1 , or reduction of ros levels by antioxidants abolish the hif - dependent glycolytic increase ( fig . 1 ) . by concomitantly upregulating mitochondrial oxidative phosphorylation and glycolysis , the chronic ampk activation induced by flcn deficiency increases cellular atp levels and biosynthetic precursors , mimicking the metabolic signature of highly proliferative cells . interestingly , this metabolic transformation is not associated with a direct effect on cell proliferation or spontaneous transformation of primary cells per se . however , loss of flcn significantly enhances the hif-1-dependent anchorage - independent and in vivo tumor growth of human cancer cell lines . finally , hif-1 nuclear translocation and upregulation of glycolytic effectors controlled by hif were observed in a chromophobe tumor from a bhd patient , further suggesting that flcn deficiency induces ampk- and hif - dependent metabolic reprogramming that confers a tumorigenic advantage in vivo . taken together , our recently reported data suggest a tumor suppressor mechanism for flcn . we identify flcn as a new physiological negative regulator of ampk - dependent metabolic reprogramming , which might have wider implications for other cancers . although ampk was previously reported to increase the transcriptional activity of hif without affecting its stability , the mechanism involved was not identified . strikingly , our findings confirm a link between ampk and hif transcriptional activation in normoxic conditions and identify pgc-1 as an intermediate effector . in addition , our data highlight a non - canonical role for ros in hif activation that differs from the classical ros - dependent inhibition of prolyl - hydroxylases . moreover , our work demonstrated that an increase in glycolysis is not necessarily associated with reduced mitochondrial oxidative phosphorylation and that both atp generation processes could work simultaneously to provide metabolic flexibility , thus conferring bioenergetic and biosynthetic advantages on cancer cells . our data are compatible with recent reports showing that ampk and pgc-1 gain of function mutations are drivers of tumorigenesis by promoting the metabolic plasticity required to support malignant growth and survival under energetic stress conditions , such as hypoxia and nutrient limitation . this ampk - dependent metabolic adaptation process might be particularly crucial during cancer progression and the development of metastasis . folliculin ( flcn ) binds and inhibits phosphorylation ( p ) of amp - activated protein kinase ( ampk ) via serine 62 ( s62 ) , a previously described ampk phospho - site . upon loss of flcn , ampk is activated by phosphorylation by an unidentified kinase ( kinase x ) and stimulates transcription and expression of peroxisome proliferator - activated receptor coactivator 1 ( pgc-1 ) , leading to enhanced mitochondrial biogenesis and reactive oxygen species ( ros ) production . this drives hypoxia - inducible factor ( hif ) transcriptional activation and enhances warburg metabolic reprogramming . folliculin ( flcn ) binds and inhibits phosphorylation ( p ) of amp - activated protein kinase ( ampk ) via serine 62 ( s62 ) , a previously described ampk phospho - site . upon loss of flcn , ampk is activated by phosphorylation by an unidentified kinase ( kinase x ) and stimulates transcription and expression of peroxisome proliferator - activated receptor coactivator 1 ( pgc-1 ) , leading to enhanced mitochondrial biogenesis and reactive oxygen species ( ros ) production . this drives hypoxia - inducible factor ( hif ) transcriptional activation and enhances warburg metabolic reprogramming .

tumor cells manage their energy to support aberrant proliferation by reprogramming their cellular metabolism , for example through the warburg effect . although ampk is a major regulator of energy homeostasis , its role in cancer metabolic adaptation is unclear . we recently identified the tumor suppressor folliculin as a new regulator of ampk - dependent metabolic transformation .

Abbreviations None Disclosure of Potential Conflicts of Interest Acknowledgments

the steroid hormone estrogen and the estrogen receptor alpha ( er ) are necessary for the physiology of the female reproductive system ( musgrove and sutherland 2009 ) . these factors play an essential role in the breast , ovaries , and uterus , where they control cell division and differentiation , and the deregulation of er transcriptional activity may result in an increased proliferation and eventually in cancer onset . breast cancer is a heterogeneous disease with a different subgroup of patients showing distinct molecular profiles ( perou et al . 2000 ; sorlie et al . 2001 ; curtis et al . 2012 ; gray and druker 2012 ) . however , the most widespread type is the luminal group of tumors , and they share the common feature of being positive for the expression of er ( dowsett 2001 ; prat and baselga 2008 ) . er is a transcription factor that mediates the response to estrogens and to anticancer therapies , including the selective estrogen receptor modulator ( serm ) tamoxifen ( katzenellenbogen and frasor 2004 ; hurtado et al . the incorporation of new technologies such as high - throughput sequencing has been crucial for a deep understanding of er function . chromatin immunoprecipitation ( chip ) combined with sequencing studies in breast cancer cell lines and human tissue shows a dispersed occupancy pattern of er binding sites bearing heterogeneous recognition motifs ( carroll et al . 2006 ; lin et al . 2007 ; ross - innes et al . 2012 ) . estrogen and tamoxifen can affect the gene expression profile by inducing thousands of er binding events ( frasor et al . . moreover , er binds to chromatin with a multitude of transcription factors ( er - cooperating factors ) that influence transcriptional activity of er and ultimately affect the outcome of anti - estrogen therapies ( carroll et al . 2005a , b ; cheng et al . 2006 ; hurtado et al . 2011 ; kong et al . 2011 ) . a second group of breast cancer patients is characterized by an amplification of chromosome region 17q12 - 21 , leading to the overexpression of the epidermal growth factor receptor 2 , erbb2/her2/neu ( wolff et al . 2007 ) . moreover , about half of her2-positive patients are also positive for er ( dowsett 2001 ) , and the activation of other signaling pathways such as the pi3k pathway is critical for er / her-2-positive tumor development ( berns et al . yet , the molecular mechanism by which these signaling pathways modulate er and er - cooperating factors is not completely understood . in this review , we describe how cooperating factors influence the transcriptional activity of er , and we speculate how these signaling pathways may modulate the function of er and er - cooperating factors . er is a ligand - regulated transcription factor that recognizes a consensus sequence of nucleotides , establishing the binding to dna , and thereby triggering the recruitment of the transcription machinery . however , most of the genomic regions where er interacts are in a heterochromatic state ( hurtado et al . pioneer transcription factors interact with chromatin and expose dna for subsequent transcription factor binding and initiation of transcription ( liu et al . 1991 ; monaghan et al . 1993 ) . genomic analyses of er binding maps have shown that its union is accompanied with the binding of various transcription factors , which includes forkhead box a ( foxa ) ( carroll et al . 2005a , b ; eeckhoute et al . 2006 , 2007 ) , gata ( krum et al . 2011 ) , ap2 ( tan et al . 2011 ) , and pbx1 ( magnani et al . 2011 ) . in this section of the manuscript 1role of pioneering factors in regulation of er chromatin interactions . in the absence of pioneering factors , chromatin regions foxa1 , in cooperation with other transcription factors , opens chromatin regions and facilitates ligand er binding . pbx1 seems to have a foxa1-independent effect role of pioneering factors in regulation of er chromatin interactions . in the absence of pioneering factors , chromatin regions foxa1 , in cooperation with other transcription factors , opens chromatin regions and facilitates ligand er binding . pbx1 seems to have a foxa1-independent effect foxa proteins are the most studied pioneer transcription factors that bind to chromatin and enable gene activity . foxa1 ( also known as hnf3 ) recruitment to chromatin is mediated by the epigenetic signature consisting of mono- and dimethylated histone h3 on lysine 4 ( h3k4me1/me2 ) ( lupien et al . the pioneering properties of foxa1 reside on its protein structure , which contains a winged helix domain that can structurally mimic histone h1 and h5 , and thus permits its stable interaction with histone h3 and h4 with high affinity ( cirillo et al . the high chromatin affinity of foxa1 is a unique feature that allows its binding to the specific dna sequences on the nucleosome core and displaces the linker histones , leading to de - compaction of chromatin and facilitation of the binding of other transcription factors . in breast hormone - sensitive and resistant cancer cell lines , almost all er chromatin interactions and gene expression changes are dependent on the expression of foxa1 ( hurtado et al . moreover , foxa1 influences genome - wide chromatin accessibility of er ( hurtado et al . 2011 ) . recently , ross - innes et al . have established that hormone - resistant breast cancers still recruit er to the chromatin , and this binding is associated with foxa1 ( ross - innes et al . interestingly , er shows a distinct binding profile in patients with poor clinical outcome to anti - estrogen therapies . these newly identified regions are enriched toward the genes that previously were described to predict clinical outcome ( ross - innes et al . have shown that snps associated with breast cancer risk are located in a subset of the foxa1 binding regions , which influences the binding affinity for the pioneer factor foxa1 ( cowper - sal lari et al . therefore , data published to date suggest that foxa1 is a major determinant of estrogen er activity in breast cancer . six gata transcription factors have been identified in vertebrates ( gata-1 to gata-6 ) ( kouros - mehr et al . 2008 ) . in breast , gata-3 is expressed in luminal tumors ( sorlie et al . however , the mechanism of gata-3 action or its potential role as a pioneer factor of er has not been described yet . by contrast , gata-4 has been shown to have pioneering properties during early development ( bossard and zaret 1998 ) and for er binding in u2os osteosarcoma cell line ( krum et al . 2011 ) , which stably expresses exogenous er and very low levels of foxa1 ( hurtado et al . 2011 ) . dna interaction in mda - mb-231 breast cancer cell line ( stender et al . 2010 ) , which stably expresses exogenous er and is negative for the expression of foxa1 and her2 . these results support the idea that distinct pioneer proteins influence er binding in foxa1-negative tissues . the pre - b cell leukemia homeobox 1 factor ( pbx1 ) is a cofactor for homeobox ( hox ) transcription factors as it increases their affinity and specificity to chromatin ( moens and selleri 2006 ) . pbx1 has been described as a pioneer factor whose function is essential for the er - mediated transcriptional response ( magnani et al . magnani et al . demonstrated that estrogen - induced transcriptional response is preferentially associated with regulatory regions where er co - bounds with pbx1 or pbx1-foxa1 . indeed , the authors point out pbx1 , and not foxa1 , as a novel prognostic marker for recurrence in er - positive breast cancers ( magnani et al . genomic analyses of er binding sites from chip - sequencing experiments also identified enrichment for ap-2 motifs ( tan et al . the authors demonstrated that perturbations of the expression of the transcription factor ap-2 prevent er binding to dna and gene transcription . interestingly , the lack of this factor is even affecting er long - range chromatin interactions , which have been shown to be essential for er - mediated transcription ( fullwood et al . 2009 ) . further molecular studies indicate that both factors collaborate in er - mediated transcription ( tan et al . the groucho homologue transducin - like enhancer of split 1 ( tle1 ) is a multitasking transcriptional co - repressor . tle proteins can associate with condensed chromatin by binding to the histone tails of nucleosomes ( sekiya and zaret 2007 ) . the groucho / tle / grg family of co - repressors operates in many signaling pathways and distinct biological processes ( jennings et al . 1992 ) has critical transcription factor partners such as tcf / lef-1 ( daniels and weis 2005 ) , hairy / enhancer of split 1 ( dasen et al . 2010 ) , and the aml / cbfa runt domain transcription factor ( levanon et al . biologically , the loss of tle coincides with increased global protein synthesis and enhanced cell proliferation ( ali et al . moreover , recently , holmes et al . have published that tle1 positively assists some er chromatin interactions , a role that is distinct from its general role as a transcriptional repressor . the specific silencing of tle1 inhibits the ability of er to bind a subset of er binding sites within the genome , and this is accompanied by perturbations in phospho - rna pol ii recruitment ( holmes et al . interestingly , tle1 action occurs at regions where foxa1 binds more weakly ( holmes et al . foxa1 and gata3 proteins are expressed in er - positive luminal breast cancers ( sorlie et al . 2003 ) . in fact , foxa1 expression is associated with the expression of steroid hormone receptors ( er , progesterone receptor , and androgen receptor ) and other variables of good prognosis such as smaller tumor size , lower histological grade , and expression of luminal cytokeratins ( ck18 and ck7/8 ) , brca1 , and e - cadherin ( habashy et al . 2008 ) . these evidences imply that high foxa1 expression is linked with survival and a better outcome in breast cancer patients . accordingly , a recent publication suggests that foxa1 directly represses a subset of basal signature genes ( bernardo et al . the silencing of foxa1 causes a partial shift from luminal to basal gene expression signatures , which results in an increased migration and invasion of luminal cancer cells . this phenotype is representative of the basal subtype of tumors , which are negative for er and her2 expression . in breast , gata-3 plays an important role in mammary gland development and differentiation ( bossard and zaret 1998 ; ho and pai 2007 ) . moreover , the inactivation of gata-3 in mice results in contracted mammary epithelial structure , severely impaired lactogenesis , and disrupted differentiation of luminal progenitor cells into ductal and alveolar cells ( asselin - labat et al . , gata-3 has been positively implicated in mediating the estrogen er signaling ( eeckhoute et al . all in all , foxa1 and gata3 that are subsequently used by er to bind chromatin and regulate gene transcription , respectively ( carroll et al . 2005 ; eeckhoute et al . 2007 ; hurtado et al . 2011 ) , might be considered as biomarkers of luminal tumors . in fact , 83.1 % of foxa1-positive tumors are comprised in the luminal a subtype . similarly , 87.7 % of gata-3-positive tumors fall within this molecular subtype ( wilson and giguere 2008 ; albergaria et al . the pioneer factor foxa1 also plays an important role in androgen receptor ( ar ) signaling of molecular apocrine tumors , which have been recently identified as an additional subgroup of er - negative and ar - positive breast tumors ( ni et al . 2011 ) . on the one hand , ni et al . identified ar as a mediator of the ligand - dependent activation of wnt and her2 signaling pathways through direct transcriptional induction of wnt7b and her3 ( ni et al . 2011 ) . on the other hand , robinson et al . demonstrated that the specific silencing of foxa1 inhibits ar binding , expression of the majority of the molecular apocrine gene signature , and cell growth ( robinson et al . moreover , ni et al . proved that specific targeting of ar , wnt , or her2 signaling impairs androgen - stimulated tumor cell growth , suggesting potential therapeutic approaches for er/her2 + breast cancers ( ni et al . altogether , it seems that , in breast tumors , er and ar binding and their functionality is fully dependent on foxa1 . by contrast , in prostate cancer , the effect of foxa1 on ar binding is more complex . recently , two studies have reported a new paradigm for the forkhead protein foxa1 action in androgen signaling . besides the pioneering function on the ar pathway , foxa1 depletion elicited extensive redistribution of ar - binding sites ( sahu et al . interestingly , both groups identified three distinct classes of ar binding sites and androgen - responsive genes : some independent of foxa1 , others pioneered by foxa1 , and some others masked by foxa1 and functional upon foxa1 depletion . importantly , foxa1 protein level in primary prostate tumors has a significant association with the disease outcome ; high foxa1 level is associated with poor prognosis , whereas low foxa1 level , even in the presence of high ar expression , predicts good prognosis . the role of foxa1 in androgen signaling and prostate cancer ( gerhardt et al . 2012 ) is different from that in estrogen signaling and breast cancer ( sahu et al . by contrast , in breast cancer , there is a clear association between high foxa1 expression and a better survival ( habashy et al . 2008 ) . in fact , the oncotype dx test for breast cancer prognosis shows a negative and significant correlation between foxa1 expression and recurrence ( ademuyiwa et al . , studies focused on these tissue - specific properties of foxa1 will be instrumental for our understanding of hormone - regulated cancers . in endometrial cancer tumors , foxa1 is expressed in 37 % of the cases , and its expression is significantly and negatively associated with lymph node status ( abe et al . 2012 ) . interestingly , in er - positive endometrial cancer cells , foxa1 has been suggested to function as a tumor suppressor through modulation of proliferation and migration of endometrial cancer cells ( abe et al . 2012 ) . however , it is not clear whether foxa1 action occurs through er or progesterone receptor ( pr ) . very recently , clarke et al . have reported that foxa1 alters pr transcriptional response in normal breast ab32 cells , a pr - positive clone of the mcf-10a cell line ( clarke and graham 2012 ) . the conclusions of this study suggest that foxa1 is not absolutely required for progesterone response . however , when foxa1 is overexpressed in ab32 cells , it induces the expression of genes involved in negative regulation of apoptosis . yet , we do not know the role of foxa1 in progesterone- and estrogen - induced transcription in endometrial tissue . in summary , all the published data suggest that the idea of using foxa1 as a therapeutic target in breast and endometrial cancers could be an alternative for those patients with recurrence to current treatments . we need to know in what other functions , apart from that of pioneering , foxa1 is involved . furthermore , it is important to know how the function of foxa1 is regulated . finally , to decipher the specific weight of other pioneering functions that might compensate functionally the inactivation of foxa1 is critical for future therapies . estrogen may activate or repress transcription of er target genes potentially by recruiting distinct classes of co - regulators that have chromatin remodeling properties . structural and functional studies revealed that er co - activators are recruited to hormone - responsive genes through their interaction with activated receptors . in turn , the co - activator complex remodels the chromatin at this region through histone acetylation , facilitating rna polymerase ii - mediated transcription ( onate et al . 1995 ; anzick et al . 1997 ; torchia et al . 1997 ; chen et al . it has also been established that , in estrogen - repressed genes , estrogen er stimulates the selective association of co - repressors ( carroll et al . the interaction of these co - repressors prompts the binding of chromatin deacetylatases and therefore leads to transcriptional inhibition . some transcription factors have been shown to be responsible for er cofactor binding ( gata-3 , foxa1 , and rara ) , to function as cofactors by themselves ( xbp1 ) or to be mediators of er - repressive action ( pitx-1 ) . in the next paragraphs , we discuss the function of these transcription factors ( fig . cell lines , the complex created by foxa1 , gata3 , and er regulates estrogen ( red bold dot ) transcription . these three factors are necessary for the recruitment of the co - activator p300 and rna polymerase ii . rara , after binding its ligand atra ( blue bold dot ) , interacts and cooperates with er at er binding sites , where it stabilizes both er co - activator and co - repressor binding . pitx-1 represses transcription of a subset of er - regulated genes er - cooperating factors influence estrogen - mediated transcription . in breast carcinoma cell lines , the complex created by foxa1 , gata3 , and er regulates estrogen ( red bold dot ) transcription . these three factors are necessary for the recruitment of the co - activator p300 and rna polymerase ii . rara , after binding its ligand atra ( blue bold dot ) , interacts and cooperates with er at er binding sites , where it stabilizes both er co - activator and co - repressor binding . pitx-1 represses transcription of a subset of er - regulated genes recently , kong et al . reported in mcf-7 breast carcinoma cells that foxa1 , gata-3 , and er form a protein complex , which regulates er - mediated transcription ( kong et al . the chromatin regions occupied by all these three transcription factors were associated with the highest p300 co - activator recruitment ( histone acetylase enzyme ) , rna pol ii occupancy , and chromatin opening . interestingly , co - transfection of these three transcription factors was sufficient to restore the estrogen - responsive growth of er - negative mda - mb-231 and bt-549 cells . these findings are very significant and suggest that all three transcription factors are needed for co - activator recruitment and , ultimately , for er - mediated transcription in breast tissue . however , it is not clear yet whether the complex of er , foxa1 , and gata-3 is necessary for all er - regulated transcripts in breast tissue . retinoic acid receptor alpha ( rara ) is a nuclear receptor , which regulates gene expression by retinoic acid ( ra ) ( giguere et al . 2012 ) and antagonists of rara ( dawson et al . 1995 ; toma et al . moreover , rara is known to be an estrogen - induced target gene in breast cancer cells ( laganiere et al . yet , the mechanisms of action by which the rara agonists or antagonists carry out a repressive effect in breast cancer are not entirely clear . the white and carroll groups have tried to solve this conundrum . although both teams agree that rara binding throughout the genome is highly coincident with er binding ( hua et al . 2010 ) , they propose contradictory mechanisms of action . whereas white 's group supports a genomic antagonism between ra and estrogen signaling ( hua et al . 2009 ) , carroll 's group supports a cooperative interaction between rara and er ( ross - innes et al . altogether , it seems that rara might have two distinct roles in breast cancer cells : first , repressing estrogen transcription via the classic function of rara with its interacting partner retinoid x receptor and , second , interacting with er and maintaining er both rara agonist and antagonist actions show benefit on breast cancer , both mechanisms of action might be taking place . xbp1 is a transcription factor that belongs to the basic region / leucine zipper ( bzip ) family of proteins ( clauss et al . 1996 ) . regulation of transcription by xbp1 is a consequence of its binding to and activation of specific camp - responsive element . the xbp1 spliced form , xbp1(s ) , has the ability to bind to and activate er in a ligand - independent manner ( ding et al . furthermore , xbp1 is also rapidly induced in response to estrogen stimulation ( wang et al . 2009 ) , which suggests that transcription of er - regulated genes might be also modulated by the complex er xbp1 . recently , the pituitary homeobox 1 ( pitx-1 ) transcription factor has been related as a repressor for a subset of er target genes ( stender et al . all together , these evidences suggest that er - cooperating factors might be needed for estrogen er - mediated transcription . interestingly , the transcription of some of these cooperating factors is induced both by estrogen at early time points ( hurtado et al . 2011 ) as directly by foxa1 ( nakshatri and badve 2009 ) . this supports the established hypothesis and also suggests that these factors are needed for a sustained transcriptional activity of er . perhaps , foxa1 induces the transcription of these cooperating factors to allow the expression of early er - regulated genes . subsequent activation of the transcription of these cooperating factors by er would then allow the sustained expression of er targets . however , the mechanism of action of these factors for er - mediated transcription is not completely understood . it has been suggested that they might be important for recruitment of chromatin remodeling factors ( ross - innes et al . breast tumors positive for er expression represent around 70 % of these cancers ( dowsett 2001 ; prat and baselga 2008 ) . targeting estrogen action has been a therapeutic choice of breast cancer treatment so far ( harvey et al . , various endocrine treatments have been developed in order to block estrogen action in breast cancer cells . one of the most successful treatments is represented by the serm tamoxifen ( jensen and jordan 2003 ) . it antagonizes estrogen action by competing for the binding of er in breast cancer cells and is thought to repress er - mediated transcriptional activation by actively recruiting co - repressors ( katzenellenbogen and frasor 2004 ; malik et al . 2010 more recently , another class of anti - estrogen drug has been incorporated into clinical treatment , namely aromatase inhibitors ( ai ) . these inhibitors antagonize estrogen metabolism , and therefore , their use is restricted to postmenopausal women . unfortunately , one third of women treated with any of these treatments will relapse ( musgrove and sutherland 2009 ) . the molecular mechanisms by which tamoxifen induces repression on breast cancer cells are not completely understood ( harvey et al . 1999 ) , and diverse models of endocrine resistance have been hypothesized ( higgins and stearns 2009 ) . in this section of the review , we discuss which transcriptional cooperating factors can affect er genomic activity in response to endocrine treatment and how this process can affect cell proliferation and survival . the effectiveness of tamoxifen requires both the binding with er and the consequent interaction with dna . importantly , genomic maps of er binding induced with estrogen or tamoxifen are almost identical ( hurtado et al . 2011 ) , which evidences that tamoxifen er for its repressive action . from these evidences , one might assume that tamoxifen er and estrogen er use the same mechanisms to interact with dna ( hurtado et al . interestingly , ross - innes et al . observed that , in tumors resistant to endocrine therapy , er interactions were enriched with foxa1 motifs ( ross - innes et al . crosstalk between the er and her2 pathways has long been implicated in cancer onset and response to tamoxifen , but no direct connection at transcriptional level has been shown . tamoxifen - resistant breast tumors are characterized by elevated erbb2 levels ( osborne et al . 2003 ) , and er - positive cell line models overexpressing erbb2 acquire resistance to tamoxifen ( benz et al . 1992 ) . in 2008 , a new mechanism of resistance to tamoxifen treatment was suggested ( hurtado et al . 2008 ) , which revealed a novel interplay between er and erbb2 on a genomic level . this study proposes that the anti - proliferative effects of tamoxifen require repression of erbb2 and that breast cancer cells acquire resistance by deregulating the mechanisms that normally repress erbb2 transcription . this repression is mediated by the transcription factor pax2 , which cooperates with er at this locus . pax2 belongs to the pair box gene ( pax ) family , a group of transcription factors characterized by the presence of two dna - binding domains and are known for their role in terminal differentiation during organogenesis ( mansouri et al . pax2 is expressed in around 60 % of breast tumors ( muratovska et al . 2003 ) , and its nuclear localization is more frequent in luminal tumors than in nonluminal tumors ( silberstein et al . moreover , in luminal breast cancer cell lines , pax2 has been shown to be activated and confers a low invasive phenotype ( beauchemin et al . interestingly , pax2 silencing is able to abrogate the inhibition of erbb2 transcription and increases erbb2-dependent cell proliferation ( hurtado et al . moreover , the expression of pax2 is reduced in tamoxifen - resistant cells , and the overexpression of pax2 is able to restore the sensitivity to tamoxifen in these cells ( hurtado et al . nonetheless , another study showed that changes in erbb2 expression are not dependent on differences in pax2 expression among various populations of tamoxifen - resistant and estrogen - deprived mcf-7 cells ( leung et al . tamoxifen - resistant cells are also characterized by increased levels of the er co - activator aib-1 ( osborne et al . indeed , there is a competition between aib-1 and pax2 for the binding to the er binding region of the erbb2 gene , which might explain the differences between the two studies . this event has also been shown in tamoxifen - treated breast cancer samples , where the pax2-positive aib-1-negative tumors have the best prognosis and the lowest percentage of erbb2-positive cells ( hurtado et al . these results suggest that the critical event for erbb2 repression and tamoxifen resistance is not just explained by the loss of pax2 expression , but it supports the idea that the balance between pax2 and aib-1 recruitment at chromatin level is crucial for the determination of tamoxifen response and resistance . yet , the molecular mechanism underlying the competition between pax2 and aib-1 in er - mediated regulation of transcription is not completely understood . we have observed that tamoxifen mainly enhances the binding of pax2 at genome - wide level ( gilfillan et al . 2012 ) , which suggests that pax2 might be functioning as a general repressor for er tamoxifen action ( fig . 3 ) . however , all the genomic regions where pax2 interacts with dna after estrogen or tamoxifen treatment have not been identified yet , and therefore , it can not be established whether pax2 is required for all estrogen - repressed genes . furthermore , it is not clear yet if the competition between pax2 and aib-1 might be affecting the transcriptional regulation of many different er target genes . in summary , all these studies denote that the repressive action of tamoxifen is regulated by cooperating factors at least at two different levels : foxa1 , which orchestrates er binding on the chromatin , and pax2 , which dictates the transcriptional activity of er induced by tamoxifen . furthermore , all these findings highlight the complexity of er tamoxifen transcriptional regulation in human breast cancer.fig . 3the balance between aib-1 and pax2 governs er tamoxifen action . in breast cancer cells , after tamoxifen treatment ( in blue , bound to er ) , pax2 and aib-1 compete for the binding of er , and this competition determines tamoxifen response . high levels of pax2 may recruit co - repressors and other factors that promote chromatin compaction , er - mediated repression , and tamoxifen sensitivity ( on the left ) . on the contrary , high levels of aib-1 promote chromatin opening , transcription activation , and tamoxifen resistance ( on the right ) the balance between aib-1 and pax2 governs er tamoxifen action . in breast cancer cells , after tamoxifen treatment ( in blue , bound to er ) , pax2 and aib-1 compete for the binding of er , and this competition determines tamoxifen response . high levels of pax2 may recruit co - repressors and other factors that promote chromatin compaction , er - mediated repression , and tamoxifen sensitivity ( on the left ) . on the contrary , high levels of aib-1 promote chromatin opening , transcription activation , and tamoxifen resistance ( on the right ) although tamoxifen is a successful er antagonist in breast cancer therapy , it shows partial agonistic effects in other target tissues ( fisher et al . in particular , tamoxifen treatment has been associated with an increased incidence of endometrial carcinoma ( persson 2000 ; zeleniuch - jacquotte et al . gene expression analysis has shown that the genes targeted by tamoxifen are different from those targeted by estrogen , in endometrial epithelial cancer cells ( wu et al . 2005 ) . pax2 is a common target of estrogen- and tamoxifen - bound er and is a crucial effector for the proliferation of endometrial cancer cells . furthermore , pax2 is silenced in normal endometrium , and its expression is reactivated in endometrial cancer upon hypomethylation of its promoter . altogether , these evidences suggest that pax2 plays a crucial role in the determination of tamoxifen response both in breast and endometrial cancer cells , by repressing and promoting cell proliferation , respectively . for these reasons , further studies on the role of pax2 in cooperation with er may shed light on tamoxifen molecular mechanisms of action and resistance . in previous sections , we have discussed the role of xbp-1(s ) in ligand - independent activation of er . moreover , xbp-1(s ) is also a key mediator of er - independent growth ( gomez et al . 2007 ; davies et al . 2008 ) . gomez et al . showed that just the overexpression of xbp-1(s ) explained both phenotypes ( gomez et al . importantly , the study confirms xbp-1(s ) as an essential regulator of bcl2 transcription , which is a prosurvival / antiapoptotic factor and confers resistance to aromatase therapy in breast cancer patients ( ding et al . xbp-1(s ) may be considered an important diagnostic and prognostic biomarker of breast cancer samples and may be also a useful tool in the identification of er - positive breast tumors with a relatively poor response.fig . 4xbp-1(s ) has a role in ligand - independent er activation and anti - estrogen drug resistance . xbp-1(s ) overexpression plays a dual role in estrogen independence and anti - estrogen resistance . xbp-1(s ) can bind and activate er in a ligand - independent manner ( upper panel ) and induces transcription of bcl-2 gene ( lower panel ) , which might have implications in anti - estrogen drug resistance xbp-1(s ) has a role in ligand - independent er activation and anti - estrogen drug resistance . xbp-1(s ) overexpression plays a dual role in estrogen independence and anti - estrogen resistance . xbp-1(s ) can bind and activate er in a ligand - independent manner ( upper panel ) and induces transcription of bcl-2 gene ( lower panel ) , which might have implications in anti - estrogen drug resistance in addition to ligand binding , posttranslational modifications ( acetylation and phosphorylation ) of er and its associated co - activators ( e.g. , src1 , src2 , aib1 , p300 ) and co - repressors ( e.g. , mta1 , ncor , and smrt ) play a role in er action . histone - modifying enzymes interact with er and influence its activity and that of its cooperating factors . moreover , in response to estrogen treatment , er can activate a variety of kinases ( e.g. , map kinases , erk , and akt ) and phosphatases ( e.g. , pp1 , pp2a , and pdxp ) , which can regulate histone proteins ( e.g. , msk1 , msk2 , and histone h1 ) and er co - regulators . in this section , we review and discuss the importance of these enzymes in modulating er , er cooperating partners , and their relevance in hormone - resistant tumors ( fig . receptor tyrosine kinases egfr , her2 , and igfr1 activate downstream signaling pathways including pi3k / akt , map kinases , and erk . these kinases may phosphorylate er , which can be activated in a ligand - independent manner . igfr-1 represses pax2 transcription factor by inducing specific phosphorylation the crosstalk between growth factor signaling pathways and er - cooperating factors . receptor tyrosine kinases egfr , her2 , and igfr1 activate downstream signaling pathways including pi3k / akt , map kinases , and erk . these kinases may phosphorylate er , which can be activated in a ligand - independent manner . igfr-1 represses pax2 transcription factor by inducing specific phosphorylation er is modulated by membrane receptor tyrosine kinases / growth factor signaling , including epidermal growth factor receptor ( egfr ) , her2 , and insulin - like growth factor receptor ( nicholson et al . 2003 ) , which contributes to endocrine resistance ( drury et al . 2011 ; fagan et al . the overexpression of these receptor kinases can activate the downstream mapk / erk and pi3k / akt pathways ( kato et al . 2011 ) , which results in phosphorylation of er at multiple serine residues ( e.g. , 104 , 106 , 118 , 167 , and 305 ) , and can influence er signaling ( arnold et al . importantly , phosphorylation of er at serine 305 is associated with endocrine resistance and poor prognosis ( kok et al . the phosphorylation of er by cytoplasmic kinases also regulates its function via interaction with other transcription factors such as ap-1 , sp1 , and creb , which mediate er interaction with chromatin ( porter et al . her2 signaling has also connection with the er - cooperating factors foxa1 , pax2 , and aib-1 . in molecular apocrine however , the precise mechanism behind the crosstalk between her2 and foxa1 signaling is not completely understood yet . her2 signaling also induces aib-1 phosphorylation ( osborne and schiff 2003 ) , which contributes to tamoxifen resistance . moreover , igf-1 negatively regulates pax2 activity in breast by inducing its phosphorylation ( beauchemin et al . perhaps , regulation of protein phosphorylation might be a mechanism of control of the activity of pax2 and aib-1 and may ultimately dictate the outcome to anti - estrogen therapies . in summary , er signaling and its crosstalk with various signaling pathways have been clinically associated with poor clinical outcome and resistance to anti - estrogen therapies . therefore , affecting either kinases or phosphatases regulating er might help in treating patients with resistance to these therapies . importantly , pp1 phosphatase is known to dephosphorylate aib-1 , and this results in suppression of its degradation ( li et al . the other phosphatases pdxp and pp2a inhibit src3 interaction with er in the absence of ligand ( li et al . future studies identifying how these phosphatases and kinases regulate er and its cooperating factors might improve the anti - estrogen therapies .

estrogen receptor ( er ) is a hormone - regulated transcription factor that controls cell division and differentiation in the ovary , breast , and uterus . the expression of er is a common feature of the majority of breast cancers , which is used as a therapeutic target . recent genetic studies have shown that er binding occurs in regions distant to the promoters of estrogen target genes . these studies have also demonstrated that er binding is accompanied with the binding of other transcription factors , which regulate the function of er and response to anti - estrogen therapies . in this review , we explain how these factors influence the interaction of er to chromatin and their cooperation for er transcriptional activity . moreover , we describe how the expression of these factors dictates the response to anti - estrogen therapies . finally , we discuss how cytoplasmatic signaling pathways may modulate the function of er and its cooperating transcription factors .

Introduction Pioneer transcription factors mediate ER binding Function of ER-cooperating factors in hormone-regulated cancers ER-cooperating factors influence estrogen-mediated transcription ER-cooperating transcription factors and anti-estrogen drug response Cell signaling pathways modulating ER and ER-cooperating factors

although the term myiasis was coined by f.w . hope in 1840 , it was first described by laurance in 1909 . myasis has been defined as a pathological condition in which there is an infestation of living mammals with dipterous larvae , which , for at least a certain period , feed on living or dead tissue in the host and develop as parasites . in humans , the most commonly affected sites are the nose , eyes , skin wounds , sinuses , lungs , ears , gut , gall bladder , vagina , nasal cavities and rarely the mouth . the occurrence of myiasis in the oral cavity is unusual as oral tissues are rarely exposed to the external environment . globally , a higher incidence of oral myiasis ( om ) is observed in tropical and subtropical regions of africa , america and south east asia due to favorable climatic conditions . it is classified as primary myiasis ( caused by biophagous larvae also called obligatory myiasis ) or secondary myiasis ( caused by necrobiophagous larvae also called facultative myiasis ) . oral factors like incompetent lips , poor oral hygiene , halitosis , anterior open bite , nocturnal mouth breathing , extraction wounds , facial trauma , ulcer - like lesions and oral carcinoma are predisposing factors for the occurrence of om . oral myiasis caused by the chrysomya bezziana ( cb ) species is very rare in humans , which makes this case more unique . a 12-year old boy was reported with a chief complaint of swelling in the maxillary anterior region especially in the gingiva . presence of worms was reported in his mouth , noticed by his parents for two days . he reported a maxillofacial trauma a week ago , leading to avulsion of teeth # 11 and # 21 . the patient s medical history revealed that he was epileptic ( not under any antiepileptic drug ) and mentally retarded since birth ; consequently , he was unable to do his daily routine and required the help of his parents for daily activities . intraoral examination revealed live larvae in the socket of tooth # 11 and lingual sulcus of teeth # 12 and # 13 along with a swelling in the right premaxillary region and larvae showing a wriggling movement . there was an empty socket in place of teeth # 11 and # 21 and ellis class i fracture in teeth # 12 , # 13 and # 22 . gingiva was red in color , soft and edematous in consistency and generalized bleeding on probing was observed . in addition , laceration of upper labial mucosa , incompetent lips , poor oral hygiene , halitosis and mouth breathing habit were also noticed ( fig 1 ) . a cotton swab impregnated with turpentine was then placed at the opening of the socket for 5 minutes . dozens of larvae rushed out from the infected area , measuring one inch in length , which were then manually removed one by one with the help of clinical forceps ( fig . larvae wriggling in right pre - maxillary region and avulsed tooth socket the patient was then placed on oral ivermectin 6 mg once daily for three days and oral amoxicillin 250 mg three times daily for seven days . the procedure of manual removal of larvae was repeated once daily for three consecutive days . a total of 33 live larvae were removed from the wound . on the fourth day the patient s parents were advised to maintain proper oral hygiene for their child and advised to rinse his mouth twice daily with 0.2% chlorhexidine gluconate for 15 days under supervision . was followed by topical application of 1.23% acidulated phosphate fluoride gel , restoration for teeth # 12 , # 13 , # 22 and replacement of the missing teeth . literature review revealed that there are a number of species , which can cause om . male predominance has been noted ( because of their outdoor activities and negligence of oral hygiene ) . it may be proposed that this leads to halitosis leading to attraction of flies as seen in almost all cases . however , in some cases it may be due to serious medical conditions , which are debilitating . the anterior part of the oral cavity including both jaws and the palate is commonly affected by om suggesting direct inoculation of tissues as described in the majority of cases but involvement of the posterior areas of both jaws is rare . clinically , om may present as oral mucosal swelling , gingival inflammation [ 3,5 , 12 ] , laceration [ 2,3 , 11 ] ( as in our case ) , ulceration , periodontal disease , non - healing extraction wound , jaw bone fracture and secondary infestation to cancrum oris . myiasis in human beings is caused by many species of larvae belonging to the order diptera . the cb , ( screw - worm fly ) , belongs to the genera calliphoridae , whose larvae develop only in living tissues , and human cases of cb infestations are rare [ 5,6 , 9 ] . the female adult cb fly lays around 150200 eggs on exposed wounds of mucous membranes of the nose , mouth and ear . the eggs hatch after 24 hours and the larvae thrive on living tissues for 57 days . the peculiarity of this maggot infestation is its ability to cause tissue invasion even without pre - existing necrosis . if there are multiple larvae in advanced stages of development and tissue destruction , local application of several substances will help remove all the larvae . if mechanical removal is impossible , placement of a variety of substances like petroleum , nail polish , animal fat , bees wax , paraffin , hair gel and mineral oil will deprive the oxygen and help in resolution of infested wounds either by killing the larvae or by forcing them superficially where they can be removed . systemic prescription of oral ivermectin 6 mg once daily for three days [ 13,16 , 17 ] ( which is a semi - synthetic macrolide antibiotic derived from streptomyces avermitilis ) often results in recovery of patients suffering from om . it acts by blocking the nerve impulses on nerve endings through the release of gamma amino butyric acid , which leads to paralysis and subsequent death of the parasite . flushing of gingival wounds with topical application of nitrofurazone has shown promising results with no further intervention . oral myiasis can be prevented by controlling fly population and maintaining personal and oral hygiene .

myiasis is a rare disease caused by infestation of tissue by larvae of flies . oral myiasis is still rare and unique owing to the fact that oral cavity rarely provides the necessary habitat for a larval lifecycle . herein , we present a case of extensive gingival myiasis in a 12-year - old mentally retarded , epileptic child as well as a literature review .

INTRODUCTION CASE REPORT DISCUSSION CONCLUSION

with a life expectancy of about 80 years , most women are expected to spend one third to one half of their lives as postmenopausal women.1 middle age is frequently seen as a marker of decline in women s health , and the most remarkable phase for most women is that of hormonal changes and their associated effects.2 in women , decreasing ovarian steroid hormone production around menopause affects several metabolic systems , such as the turnover of bone tissues , lipoprotein metabolism , and vessel walls . health promotion , therefore , in midlife women has become more important due to increased life expectancy of women and consequent postmenopausal complications , such as osteoporosis , atherosclerosis , genital prolapse , and urinary incontinence.3 physical activity has essential physical and psychological benefits for older people , particularly for women . it has been reported in various populations to prevent or reduce the incidence of cardiovascular disease , obesity , osteoporosis , colon cancer , breast cancer , anxiety and depression , and to reduce the frequency of vasomotor symptoms in midlife women.47 physical activity might be the best prescription for women in midlife to protect their health status.8 the preventive steps taken during midlife will help build a basic foundation to ensure good health and vitality that extends well into the postmenopausal years.9 in this study , we address the efficiency of multimodal program in increasing level of activity and if those women using the intervention would able to attain significant improvement in their physical activity . the sample was recruited from a subset of women who were referred to shahrood health service in iran . women were considered eligible for inclusion in the study if they were aged between 50 and 65 years and physically inactive . physically inactive women are those who do not get the recommended level of regular physical activity including 30 minutes of moderate 5 days per week ; or 20 minutes of vigorous exercise 3 days per week . randomization was achieved by allocating the surveys as they were received to group 1 ( intervention ) or group 2 ( control ) sequentially . of the 115 women , 55 were invited to take part in the intervention program , and 60 were allocated to control . of the 115 women who began the study , 20 women from group 2 and 15 women from group 1 failed to complete the second questionnaire , leaving 40 women in the control and 40 women in the intervention group eligible for analysis . primary reasons for drop - outs were family health priorities , planned recreational travel , and a perceived lack of time to complete the program . women who were allocated to the intervention group received a combination of physical activity and health education ; the women in the control group continued their normal physical activities . these assessments were undertaken at t1 ( prior to intervention ) and t2 ( 12 weeks from commencement of the intervention ) . the women s wellness program was included in the specific strategies that were used in the intervention group . women in the intervention group undertook a 12-week program , which was a multimodal intervention consisting of a physical activity and health education program consultation by a registered nurse . topics covered included health information for women , such as recommended nutrition and physical activity information specific to women s health . a consultation by a registered nurse and individual health education and goal setting session were provided to each woman . this intervention included cognitive behavioral strategies aimed at increasing positive lifestyle changes in midlife women . women received a second consultation at the end of the 12 weeks , and exercise records were collected . all participants recorded their frequency of performing aerobic exercise , with the goal being 57 exercise sessions per week to adhere to the physical activity component of the intervention . the women in the control group completed surveys at t1 and t2 and continued their normal daily activities . these assessments were undertaken at t1 ( prior to intervention ) and t2 ( 12 weeks from commencement of the intervention ) . the women completed a questionnaire , which included measures for items of interest for this analysis , such as menopausal status , sociodemographic , and exercise and activity levels . exercise and activity levels were measured using the monica optional study of physical activity questionnaire ( mospa ) . the questionnaire was developed by world health organization ( who ) and was used to assess physical activity in 13 who - mospa centers in nine countries.10 the strength of the mospa questionnaire is that it assesses all dimensions of physical activity including household , occupational , leisure time , and transportation activity . the sample was recruited from a subset of women who were referred to shahrood health service in iran . women were considered eligible for inclusion in the study if they were aged between 50 and 65 years and physically inactive . physically inactive women are those who do not get the recommended level of regular physical activity including 30 minutes of moderate 5 days per week ; or 20 minutes of vigorous exercise 3 days per week . randomization was achieved by allocating the surveys as they were received to group 1 ( intervention ) or group 2 ( control ) sequentially . of the 115 women , 55 were invited to take part in the intervention program , and 60 were allocated to control . of the 115 women who began the study , 20 women from group 2 and 15 women from group 1 failed to complete the second questionnaire , leaving 40 women in the control and 40 women in the intervention group eligible for analysis . primary reasons for drop - outs were family health priorities , planned recreational travel , and a perceived lack of time to complete the program . women who were allocated to the intervention group received a combination of physical activity and health education ; the women in the control group continued their normal physical activities . these assessments were undertaken at t1 ( prior to intervention ) and t2 ( 12 weeks from commencement of the intervention ) . the women s wellness program was included in the specific strategies that were used in the intervention group . women in the intervention group undertook a 12-week program , which was a multimodal intervention consisting of a physical activity and health education program consultation by a registered nurse . topics covered included health information for women , such as recommended nutrition and physical activity information specific to women s health . a consultation by a registered nurse and individual health education and goal setting session were provided to each woman . this intervention included cognitive behavioral strategies aimed at increasing positive lifestyle changes in midlife women . women received a second consultation at the end of the 12 weeks , and exercise records were collected . all participants recorded their frequency of performing aerobic exercise , with the goal being 57 exercise sessions per week to adhere to the physical activity component of the intervention . the women in the control group completed surveys at t1 and t2 and continued their normal daily activities . these assessments were undertaken at t1 ( prior to intervention ) and t2 ( 12 weeks from commencement of the intervention ) . the women completed a questionnaire , which included measures for items of interest for this analysis , such as menopausal status , sociodemographic , and exercise and activity levels . exercise and activity levels were measured using the monica optional study of physical activity questionnaire ( mospa ) . the questionnaire was developed by world health organization ( who ) and was used to assess physical activity in 13 who - mospa centers in nine countries.10 the strength of the mospa questionnaire is that it assesses all dimensions of physical activity including household , occupational , leisure time , and transportation activity . women who agreed to participate in this study were aged between 50 and 65 years ( mean age , 58.3 years ) . data for this variable were normally distributed , and the independent t - test comparison of the control and intervention groups showed that there was no significant difference between them for the age variable . an independent t - test was conducted to determine the differences between intervention and control groups leisure - time activity at the baseline of the study . general daily activity included activity such as housework , caring for children , shopping , or activity at work . the test revealed no significant differences between the intervention and control groups in leisure time activity . during the past year , there had been no significant differences between intervention and control groups in the months they did exercise . with regards to long - term exercise , there were no significant differences between the intervention and control groups in the years they did exercise . in the weekly exercise levels , there was no significant relationship between the intervention and control groups determined at the baseline of the study ( table 1 ) . with reference to vigorous activity , women were categorized into four activity levels : 1 ) no physical activity weekly , 2 ) only light physical activity , 3 ) vigorous physical activity at least 20 minutes once or twice a week ( vigorous activity causes shortness of breath , a rapid heart rate , and sweating ) , 4 ) vigorous physical activity for at least 20 minutes three or more times per week . an analysis of covariance test was conducted to determine differences between intervention and control in vigorous activity . the test showed that there was a significant difference between intervention and control in current vigorous activity . to interpret the significant interaction of time and group , independent bonferroni pairwise comparisons were conducted between the intervention and control groups over the two time points . this test showed that , even after controlling for baseline differences , the intervention group had significantly higher physical activity levels than the control group ( p = 0.00 ) ( table 2 ) . an independent t - test was conducted to determine the differences between intervention and control groups leisure - time activity at the baseline of the study . general daily activity included activity such as housework , caring for children , shopping , or activity at work . the test revealed no significant differences between the intervention and control groups in leisure time activity . during the past year , there had been no significant differences between intervention and control groups in the months they did exercise . with regards to long - term exercise , there were no significant differences between the intervention and control groups in the years they did exercise . in the weekly exercise levels , there was no significant relationship between the intervention and control groups determined at the baseline of the study ( table 1 ) . with reference to vigorous activity , women were categorized into four activity levels : 1 ) no physical activity weekly , 2 ) only light physical activity , 3 ) vigorous physical activity at least 20 minutes once or twice a week ( vigorous activity causes shortness of breath , a rapid heart rate , and sweating ) , 4 ) vigorous physical activity for at least 20 minutes three or more times per week . an analysis of covariance test was conducted to determine differences between intervention and control in vigorous activity . the test showed that there was a significant difference between intervention and control in current vigorous activity . to interpret the significant interaction of time and group , independent bonferroni pairwise comparisons were conducted between the intervention and control groups over the two time points . this test showed that , even after controlling for baseline differences , the intervention group had significantly higher physical activity levels than the control group ( p = 0.00 ) ( table 2 ) . exercise and fitness are vital because women are dramatically at risk for osteoporosis and fracture , heart disease , and chronic diseases such as diabetes and breast cancer . the results of the study showed a significant relationship between taking a multimodal intervention and increasing the level of activity . these interventions include patient goal setting , written exercise prescriptions , individual physical activity regimens , and mailed or telephone follow - up support provided by specially trained staff . the belief in one s ability to accomplish behaviors successfully is seen as a major reason for choosing the amount , time , and type of activity that women undertake . similarly a randomized controlled trial was conducted by elley et al11 to assess the effectiveness of the green prescription program in general practice which included verbal and written advice about physical activity to patients during normal consultations . the results of the study showed significant changes in physical activity , quality of life , cardiovascular risk , and blood pressure over the 12-month period of the study . also , due to the significance of exercise in the prevention of disease such as osteoporosis and cardiovascular disease , it may be essential for health and exercise specialists to intervene to increase levels of activity.12 observational research suggests that the success of an intervention is affected by individual factors , such as motivation , social support , health , beliefs , and education , and by organizational factors , such as resources , convenience , and type of physical activity.13,14 previous studies have shown that success in making lifestyle changes can be improved by appropriate social support.14 for example , a recent trial of health system - sponsored telephone support by trained health educators revealed increased physical activity in the patients.15,16 behavioral support provided by health educators increases activity and fitness levels compared with modest counseling efforts.16 also , studies suggest that specific counseling advice such as a detailed exercise prescription may result in higher maintenance rates . moreover , short physical activity counseling may help the patient s improvement through the stages of behavior change , which makes it more possible for them to increase their physical activity when advised to perform exercise in the future . understanding the individual factors that might affect physical activity is necessary to design an intervention with the highest chance of participation and adherence to recommended physical activity behaviors.17 for example , cohen - mansfield et al18 found barriers to exercise to be highly related to motivators . poor health could reduce an older adult s ability to exercise and is also frequently mentioned as a motivator for increasing physical activity . other motivators for being more active include having more time , having more information on exercise benefits , or living nearer to an exercise facility.19 physical activity is a complex process , which may be affected by other variables . considering the barriers that might affect physical activity is necessary to design an intervention with the highest chance of participation and adherence to recommended physical activity behaviors . behavioral and biological changes that occur during the menopausal transition highlight the importance of behavioral change interventions to prevent or reduce the changes associated with menopause.13,16,1921 physical activity should be encouraged for prevention and reduction of risks for chronic disease and for improvement of health in midlife women.13,2228 the study revealed that a multimodal intervention could increase the level of activity in midlife women . women stated that they felt physically and mentally better , and the program motivated them into being more active . they mentioned that the program was easy to understand and follow , and the concept of the program was well organized and useful for them . this is an important finding as attitudes to exercise is a difficult health behavior to change . alternatives to traditional group - based interventions , such as helping midlife women to exercise at home during leisure time , are necessary to improve health promotion for this population . the results of this study may have implications for designing and implementing exercise interventions in further studies . women who intend to be healthy need to choose a regular approach to maintain their health . to achieve this goal , health professionals who are aware of the effect of regular exercise on the physical and psychological problems of women in midlife and beyond can help them to increase their physical activity .

objectives : the purpose of this study is to determine the effect of a multimodal intervention ( including the women s wellness program ) on increasing levels of physical activity in iranian midlife women.study design : this 12-week study was conducted in women aged 5065 years living in the general population . women who were allocated to the intervention group ( n = 40 ) received an intervention , which combined a multimodal program of physical activity and health education . women in the control group continued their normal physical activities ( n = 45).mean outcome measure : the women completed a questionnaire that included measures for items of interest for this analysis , such as menopausal status , sociodemographic , and exercise and activity levels.results:analysis of covariance indicated that the intervention was effective in improving women s physical activity . the test showed that there was a significant difference between intervention and control in current vigorous activity.conclusion:physical activity should be encouraged for prevention and reduction of risks for chronic disease and for improvement of health in midlife women . the multimodal intervention program may offer implications for designing and implementing exercise interventions in further studies .

Introduction Methods Sample recruitment Drop outs Procedures Intervention group Control group Instruments Results Physical activity in intervention and control groups at baseline of the study Current vigorous physical activity Discussion Conclusion

the columnar organization of neocortex at the minicolumnar ( 2050 m ) and macrocolumnar ( 300600 m ) scales has long been known ( see mountcastle , 1997 ; horton and adams , 2005 for reviews ) . minicolumn - scale organization has been demonstrated on several anatomical bases ( lorente de no , 1938 ; defelipe et al . , 1990 ; peters and sethares , 1996 ) . there has been substantial debate as to whether this highly regular minicolumn - scale structure has some accompanying generic dynamics or functionality . i.e. , one that would apply equally well to all cortical areas and species has been determined . one basis upon which a functionality for the minicolumn has been suggested is possession of highly similar receptive field characteristics , or tuning , by the cells comprising the minicolumn , e.g. , v1 orientation columns ( hubel and wiesel , 1962 , 1968 ) and minicolumn - sized regions innervating cutaneous zones ( favorov and diamond , 1990 ) . the reasoning here appears to be that because a group of cells all have very similar tuning to a particular feature , , e.g. , an edge at a particular orientation , they form a unit whose function is to recognize . however , in searching for a possible generic minicolumn function , we need not limit ourselves to considering only recognition functions . furthermore , possession of highly similar tuning can not be a basis for a generic minicolumn functionality since in many cortical areas , the cells encountered along vertical penetrations can have quite variable tuning ( cf . on closer analysis , this is true in orientation column data as well ( hetherington and swindale , 1999 ; ringach et al . , 2002 ) . if there is a generic minicolumn functionality , then it must be compatible with varying degrees of tuning correlation amongst the minicolumn 's cells . i propose that the minicolumn does have a generic functionality ( given shortly ) , but one that only becomes clear when seen in the context of the function of the higher - level , subsuming unit , namely , the macrocolumn , which has been demonstrated anatomically ( goldman and nauta , 1977 ; lbke et al . , 2003 ; egger et al . , 2008 ) and functionally ( mountcastle , 1957 ; woolsey and van der loos , 1970 ; hubel and wiesel , 1974 ; albright et al . , 1984 ) . i propose that the function of a macrocolumn ( e.g. , hypercolumn , segregate , barrel ) is to store sparse distributed representations of its overall input patterns , and to act as a recognizer of those patterns . by overall input pattern , i mean the macrocolumn 's overall input at a given moment , including not only its bottom - up ( bu ) inputs from thalamus or lower cortical areas , but also its top - down ( td ) inputs from higher cortical areas and its horizontal ( h ) inputs , which i propose carry temporal ( sequential ) context information ( recurrently ) from the representations previously active in the same and nearby macrocolumns . thus , an overall input pattern can equally well be termed , a context - dependent input . thus , it is in fact the macrocolumn whose generic functionality is appropriately characterized as recognition ; i.e. , recognition of a class determined by the history of context - dependent inputs to which it has been exposed . a distributed representation of an item of information is one in which multiple units collectively represent that item , and crucially , such that each of those units generally participates in the representations of other items as well . distributed representations are also referred to as cell assemblies , population codes , or ensembles . in this paper , representation and a sparse distributed code ( sdc ) is one in which only a small fraction of the pool of available representing units is part of any particular code ( palm , 1982 ; lynch et al . , 1986 ; kanerva , 1988 ) . if the macrocolumn stores sdcs , then there must be some mechanism that enforces sparseness and this , i propose , is the generic function of the minicolumn . specifically , i propose that small , physically localized pools of l2/3 pyramidals , e.g. , 20 such cells , act as winner - take - all ( wta ) competitive modules ( cms ) . this implies that macrocolumnar codes should consist of about 6080 active l2/3 cells , one per minicolumn : for simplicity , assume 70 minicolumns per macrocolumn hereafter . defined in this way , the minicolumn has a more flexible relation to the ontogenetic column , the apical dendrite bundle , the dbc horsetail , etc . for example , a given minicolumn might include l2/3 pyramidals from more than one apical dendrite bundle , consistent with the findings of yoshimura and callaway ( 2005 ) of fine - scale networks of preferentially interconnected l2/3 pyramidals . there is increasing evidence for the use of sdc in the cortex and other brain structures ; e.g. , auditory cortex ( hromdka et al . , 2008 ) , visual areas ( young and yamane , 1992 ; vinje and gallant , 2000 ; waydo et al . , 2006 ; quian quiroga et al . , 2008 ) , zebra finch neopallium ( hahnloser et al . , 2002 ) , olfactory structures ( jortner et al . , 2007 ; linster and cleland , 2009 ; poo and isaacson , 2009 ) , and hippocampus ( leutgeb et al . , 2007 ) . particularly supportive of the proposed hypothesis is the reid lab 's calcium imaging data of rat v1 during stimulation by drifting square - wave gratings ( ohki et al . , their movie ( http://reid.med.harvard.edu/movies.html ) shows sparse collections of l2/3 cells extending over an approximately macrocolumn - sized region synchronously turning on and off in response to particular grating orientations . ( two frames from the movie ) show distinct sets of cells , i.e. , codes , responding to bars moving left and right , respectively , and emphasize that individual units may participate in multiple codes ( red - circled cells ) . in terms of the proposed model , the active neurons would be the winners in their respective minicolumns , as suggested in figures 1c , d . figure s1 in supplementary material provides another view of how the proposed model maps onto cortex . calcium ( tangential ) images of l2/3 of rat visual cortex showing sparse sets of cells activating in unison ( see movie link in text ) in response to leftward ( a ) and rightward ( b ) drifting gratings . from ohki ( c , d ) sketch of proposed sparse distributed coding concept , which could plausibly give rise to data like ( a ) and ( b ) . : to make the sketches look more like the calcium images , black is used for inactive units and white for active : this is reversed in subsequent figures . if the macrocolumn does indeed function as a sdc field in the way suggested here , then we must answer two key questions regarding its dynamics . how is any particular set of winners , one in each of the 70 minicolumns , initially chosen in response to an input pattern and bound into a holistic code ? that is , how are macrocolumnar codes learned ? how is a previously learned code reactivated in response to future presentations of the input pattern that it was initially chosen to represent ? that is , how are stored macrocolumnar codes retrieved ( reactivated ) ? in the next section , i describe an algorithm , referred to as the code selection algorithm ( csa ) , which answers both questions . a key property of the csa is that it causes similar inputs to be assigned to similar , i.e. , more highly intersecting , codes . this property , which will be referred to as sisc ( similar inputs map to similar codes ) , is very important in terms of computational efficiency ( see discussion ) and is possessed by most distributed coding schemes . however , the csa achieves it in a novel , probabilistic fashion , which can be summarized as follows : determine the familiarity of a macrocolumn 's input . to a first approximation , an input 's familiarity is its maximum similarity to any input previously stored in the macrocolumn . set the amount of randomness ( noise ) in the process of selecting winners in the wta modules in inverse proportion to the input 's familiarity . the algorithm 's rationale is described in detail in the next section , but broadly , the idea is as follows . when an input , 1 , is familiar , we want to reactivate the code , 1 , to which 1 was previously assigned . the cells comprising 1 will have had their synapses ( from the cells comprising 1 ) increased during learning . thus , if 1 is presented again , the cells of 1 will have the highest synaptic input summations in their respective wta modules . in this case , winners should be chosen on the deterministic basis of these summations : no noise should be present in the winner selection process . on the other hand , increasingly novel inputs should be assigned to increasingly distinct codes , i.e. , codes having progressively smaller intersection with existing codes . this can be achieved by increasing the noisiness of the winner selection process in each wta module , which can be achieved by suppressing the influence of the deterministic synaptic inputs ( which reflect prior learning ) relative to baseline random ( spontaneous ) activity . by adjusting parameters that control the global ( i.e. , across the whole macrocolumn ) noise level , we can modulate the expected intersection between the set of cells which have the maximal input summations in their respective wta modules and the set of winners that are actually chosen , thus implementing sisc . many experimental and theoretical studies implicate neuromodulators , notably norepinephrine ( ne ) and acetylcholine ( ach ) , in functionality similar to the above , which can be described generally as modulating signal - to - noise ratio ( snr ) . doya ( 2002 ) proposed that ne levels control the amount of noise in a process of choosing output actions . however , doya 's model assumes a localist representation of the choices , which precludes possession of the sisc property ( see discussion ) . in addition , increased ach has been shown to selectively increase the strength of afferent relative to intrinsic inputs in piriform cortex ( hasselmo and bower , 1992 ) and other brain structures ( see hasselmo , 2006 for review ) . these ach findings have been summarized as showing that increased ach adjusts network dynamics to favor encoding new memories compared to retrieving old memories , which fits well with the proposed csa functionality . following the model description , i offer a speculative mapping of my proposed model onto neural circuitry and discuss evidence for novelty - contingent noise modulation by both ne and ach . however , the specifics of this mechanism are a subject of ongoing research and likely will involve interactions between neuromodulatory systems ( cf . any discussion of columnar function of course centrally concerns cortical circuitry , and more specifically , the putative canonical cortical microcircuit ( rockland and pandya , 1979 ; douglas et al . , 1989 ; douglas and martin , 1991 ) . we have made huge progress in understanding many of the components of cortical microcircuitry a tiny sample of which includes ( defelipe et al . , 1990 ; , 2004 ; feldmeyer et al . , 2006 ; fukuda et al . , 2006 ; , 2008 ; hirata and castro - alamancos , 2008 ; berger et al . , 2009 ; murayama et al . , 2009 ; symes and wennekers , 2009 ; briggs , 2010 ; and see thomson et al . , 2002 ; bannister , 2005 ; silberberg et al . , 2005 for reviews ) nevertheless , we remain far from any sort of comprehensive and consensual understanding of how cortical columnar circuitry manipulates , i.e. , stores and retrieves , specific items of information . in the main , only very broad conclusions regarding information processing are asserted in the experimental literature , e.g. , horizontal connections between fast - spiking l4 interneurons and pyramidals are involved in formation of l4 assemblies and sharpening of tuning ( sun et al . , 2006 ) ; that both the populations of l4 pyramidals and of l5a pyramidals have transcolumnar connectivity patterns allowing them to act as integrators of information coming in from multiple vibrissae in parallel , or in close sequence ( schubert et al . , 2007 ) ; that the receptive fields of barrel - related l2/3 pyramids are dynamic and thus may reflect learning to recognize spatiotemporal patterns of vibrissae deflections ( brecht et al . , 2003 ) ; that wta competition occurs in the supra- and infragranular layers ( douglas and martin , 2004 ) ; and that local ( 100 m ) l2/3-to - l2/3 connections might serve to synchronize firing of l2/3 cell assemblies ( lbke and feldmeyer , 2007 ) ; etc . i believe the hypothetical model described herein to be a significant contribution because it goes beyond broad conclusions and offers a mechanistic explanation of how specific informational items are learned and retrieved and in so doing , proposes a generic function for the minicolumn , i.e. , that it functions as a wta module in support of manipulating sdcs at the next higher , i.e. , macrocolumnar , scale . in particular , it was stated in the introduction that sparse macrocolumnar codes are chosen in response to a macrocolumn 's overall input , which includes its bu , h , and td inputs . however , illustrations of the model in operation in that general case become rather complex , particularly since the h ( and td ) weights carry temporal information , which necessitates showing the model at multiple successive time steps while processing spatiotemporal patterns . more importantly , the core elements of the hypothesis which are : ( a ) that the macrocolumn stores sdcs consisting of one winning l2/3 cell per minicolumn ; and ( b ) that the sisc property is achieved by modulating the amount of randomness ( noise ) present in the winner selection process in inverse proportion to input familiarity can be clearly and more simply described for the bu - only case ( i.e. , where inputs are purely spatial patterns ) . therefore , the model description in this paper will be limited to the bu - only case . however , the generalized model ( with bu , h , and td inputs ) and the accompanying generalized version of the csa are given in figures s2 and table s1 in supplementary material . functional architecture . the input field ( f1 ) consists of binary feature detectors : a particular input consisting of five active features is shown . it consists of winner - take - all competitive modules ( cms ) proposed as analogous to minicolumns . bottom - up connectivity is all - to - all : gray lines signify initially 0 weights . the familiarity ( g ) of the input is proposed to be computed via a subcortical , neuromodulator - based mechanism , which then modulates the f2 unit activation function parameters ( e.g. , sigmoid height ) contingent on g ( purple arrows ) . the input field , f1 , is comprised of 12 binary units and can be considered analogous to a specific thalamic nucleus , though topographical organization is not assumed . the coding field , f2 , consists of q = 4 wta cms , each containing k = 3 binary units . complete ( all - to - all ) bu connectivity from f1 to f2 is assumed for simplicity . these bu weights ( synapses ) are binary , initially 0 , and are permanently set to a weight of 1 the first time the pre- and postsynaptic units are co - active ( i.e. , hebbian learning ) . the model 's core algorithm , the csa , determines which cells are chosen to represent an input , during both learning and retrieval . a single iteration of the algorithm involves two rounds of competition in the cms of f2 . the first round is a hard wta competition ( represented by boxes labeled max in figure 2 ) . the purpose of the first round is to compute a global familiarity measure , g , of the input pattern . g then drives a global modulation of the f2 unit activation function ( figure 2 : purple arrows ) in preparation for the second competitive round , which is a soft wta competition , the intent of which is that : as g goes to 1 ( indicating a completely familiar input ) , the probability that the unit with the highest input summation in a cm wins approaches 1 , and as g goes to 0 ( indicating a completely novel input ) , all units in a cm become equally likely to win ( regardless of their input summations ) . ( 1)u(i)=j nw(j , i ) where n is the current input ( f1 ) pattern . because unit activations are binary , we can simply sum the weights , w(j , i ) , which are also binary . normalize u(i ) to [ 0 .. 1 ] , yielding v(i ) . v(i ) is a local measure of support , or likelihood , that f2 unit i should be activated . it reflects how well unit i 's receptive field ( rf ) , specified by its afferent weight vector , matches the current input vector . ( round 1 competition ) the maximum v(i ) , v^x , is found in each of the q cms . ( 3)v^x = maxi cx{v(i ) } where x indexes the cms and i indexes the units in a cm , cx . average the q v^xvalues , yielding g , a global measure of the familiarity of the current input . ( 4)gx=1qv^x / q the expansivity , , of the probabilistic activation function ( which is implemented via steps 68 ) is set as an increasing nonlinear function of g ( eq . 5 , expressed as a table ) . the idea is to increase the range of relative win likelihoods , (i ) ( defined in step 6 ) over any given cm 's units as g goes to 1 . this in turn , serves to nonlinearly exaggerate the difference in the final win probabilities ( eq . the specific parameters of any instance of the g - to- mapping will determine the specifics of the relation between input similarity and code similarity , i.e. , the expected code intersection as a function of input similarity . 5 were chosen to yield the -distributions in the examples of figures 3 and 4 . circled numbers refer to algorithm steps in text . here , i show the case of the first input , 1 , presented to the model . the algorithm detects that 1 is completely unfamiliar , i.e. , g is computed to be 0 , and sets the f2 activation function to a constant function ( red line ) , which makes the choice of winner in each cm completely random , and thus , the overall f2 code , 1 , also completely random . green f1 ( f2 ) units denote units not in common with 1 ( 1 ) . circled numbers refer to algorithm steps in text . here , i show the case of the first input , 1 , presented to the model . the algorithm detects that 1 is completely unfamiliar , i.e. , g is computed to be 0 , and sets the f2 activation function to a constant function ( red line ) , which makes the choice of winner in each cm completely random , and thus , the overall f2 code , 1 , also completely random . the csa and the sisc property . green f1 ( f2 ) units denote units not in common with 1 ( 1 ) . the v values of all units in all cms are then passed through the sigmoidal activation function ( eq . 6 ) whose shape / scale reflects g. again , particular parameter values affect the relation of input similarity to code similarity ( and therefore , storage capacity ) : values of = 28 and = 5 produce the v - to- mappings in figure 4 . as noted above , within each cm , the output variable , (i ) , can be viewed as a relative likelihood that unit i should be chosen winner . ( 6)(i)=1+e ( v(i ) + )+1 when g = 1 ( perfectly familiar ) , is maximized ( in eq . 7 ) probabilities of winning for units with the maximum v value in their respective cms . in contrast , when g = 0 ( completely novel ) , = 0 , which collapses the sigmoid to the constant function , = 1 , thus making all units in a cm equally likely to win . this causes the expected intersection of the code being chosen in the current instance with any previously assigned code to be at chance level . in general , this modulation of the sigmoid activation function tends toward code completion in proportion to the familiarity of the input and code separation in proportion to its novelty . transform relative likelihood distribution ( ) in each cm to true probability distribution ( ) . ( 7)(i)=(i)k cm(k ) ( round 2 competition ) choose an f2 code by drawing a winner from the -distribution ( soft max ) in each cm . thus , choosing an f2 code is actually performed as q separate draws . when g = 0 , these draws are statistically independent , as in figures 3 and 4d . as we consider increasingly familiar inputs , i.e. , for g approaching 1 ( and , assuming the model is still operating in a regime where crosstalk is sufficiently low ) , the draws become increasingly correlated ( dependent ) , as can be seen in going from figure 4c to 4b to 4a . figure 3 graphically illustrates the operation of the csa in the case of the model being presented with its first input , 1 . the gray arrows indicate that the bu signals propagating from the active f1 units will be traversing connections with zero synaptic strength . this leads to unnormalized ( u ) and normalized ( v ) input summations of 0 for all 12 f2 units ( steps 1,2 ) . in step 3 , the max v , v^ , in each cm is found ( ties broken at random ) . in step 4 , g is computed as the average of the v^ values : in this case all the v^ are 0 , so g = 0 . in step 5 , the value , g = 0 , maps to = 0 , which causes the activation function of the f2 units to collapse to the constant function , = 1 . in step 6 , each f2 unit applies this activation function to its v value , yielding the uniform relative likelihood distribution in each cm . in step 7 , the relative likelihood function in each cm is normalized to a true probability ( ) distribution , which in this case , is again uniform . finally , in step 8 , a winner is drawn in each cm , resulting in a random f2 code , e.g. , 1 . figure 4 demonstrates that the csa realizes the sisc property by considering four possibilities ( a d ) for the second input presented to the model of figure 3 . these four inputs , 25 , range from being identical to 1 ( completely familiar ) to having zero overlap with 1 ( completely unfamiliar ) . to save space , the panels of figure 4 use an abbreviated version of the format of figure 3 . most noticeably , the intermediate variable , ( relative likelihood ) , is not shown . black bu connections are ones that were increased to one when 1 was learned ( figure 3 ) . working from figure 4a to 4d , the inputs have progressively lower similarity ( intersection ) with 1 : f1 units not in common with 1 are shown in green . as g drops , the sigmoid expansivity drops ( note the changing scale ) . thus , the -distributions become progressively flatter , which in turn results in f2 codes , 25 , having progressively smaller intersection with 1 . figure 4a shows the case of presenting a completely familiar input again , and is thus a recognition test trial , demonstrating retrieval . this leads , via csa steps 3 and 4 , to g = 1 , which yields , via steps 5 and 6 , the expansive nonlinear v - to- mapping shown ( red sigmoid ) . this nonlinearity is applied to every f2 unit , yielding the highly peaked -distributions shown . finally , one unit is drawn in each cm . the probability of drawing the correct unit in any single cm is approximately 98% . of course , what 's crucial in this case , i.e. , when the input is completely familiar ( g = 1 ) , is that the entire correct f2 code is reactivated . in this case , that probability is ( 0.98 ) 92% . thus , the familiarity , g , which depends on the entire f2 layer and is thus global information , influences the local activation functions so as to produce the desired overall result , in this case , reactivation of the code ( memory trace ) , 1 , of the familiar input pattern , 1 . the explanations of the remaining panels follow that of figures 3 and 4a . in going from figure 4b to 4d , one can readily see decreasing intersection with 1 , decreasing u and v values , decreasing g , decreasing sigmoid expansivity , progressively flatter -distributions , and ultimately , decreasing intersection with 1 . given a desired probability , r , of correctly reactivating an entire code ( i.e. , of choosing the correct unit in each cm ) , when g = 1 , given values for q and k , we could compute the needed value of . however , the macrocolumn model is a content - addressable associative memory and in actual usage , multiple sparse codes will be stored in superposition . any thorough analysis of the model 's expected retrieval error must include the effect of overlap between the stored codes ( i.e. , cross - talk ) : this influences the shapes of the -distributions and thus , the expected retrieval accuracy for any given number of stored codes . such an analysis will be conducted empirically and reported in a separate paper . before leaving figure 4 first , while the -distributions become flatter as g decreases , the units comprising the code of the most similar previously learned input ( here , 1 ) remain most likely to win in their respective cms . if we simply deterministically chose the unit with maximum v(i ) in each cm , we would have chosen the same f2 code , 1 , in response to all four inputs , 25 . thus , the computation of a quantity , g , which depends on all the cms is essential to achieving the sisc property . it constitutes a channel through which information transfers between all f2 units throughout the whole macrocolumn . as noted earlier , the full model also assumes direct h connections between f2 units , analogous to the horizontal matrix of l2/3 ( see figure s2 in supplementary material ) . these also mediate communication , but of the prior code active in the macrocolumn , not of the simultaneous state of all f2 units throughout the macrocolumn . second , learning is single - trial and involves only one iteration of the csa . this is largely facilitated by the fact that when a given input - code association , jj , is learned , each of j 's f2 units simultaneously has its afferent weight from all of j 's f1 units increased . the effect of these simultaneous correlated potentiations allows a rapid , even single - trial , formation of an association , even if the individual synaptic potentiations are small , consistent with the recent characterization of thalamocortical learning described in bruno and sakmann ( 2006 ) . third , figure 4a shows that recognizing an exact instance of a previous input also requires only one iteration of the csa . although this example does not directly show it , this holds for recognition of non - exact matches as well . evidence for this will be presented in a separate work . that both learning and recognition require only a single csa iteration is especially significant since , as can readily be seen , none of the csa steps involves iterations over stored codes : thus , the time it takes for the csa to either store a new input or retrieve the closest matching stored input remains constant as the number of stored codes increases . this does not imply that an infinite number of codes can be stored : of course , the model has finite storage capacity . this capacity will be characterized in future research , but should be similar to other sparse associative memories ( willshaw et al . , 1969 ; palm , 1982 ; moll and miikkulainen , 1995 ; knoblauch et al . , 2010 ) . there remain huge gaps in our knowledge of the intrinsic physiological , synaptic , morphological , and connectional properties of all classes of cortical cell and of functional relationships between cortical and sub - cortical structures . nevertheless , figure 5 shows a possible neural realization of the model 's wta cm , i.e. , minicolumn , and dynamics ( csa ) . i have attempted to respect known constraints but the realization is admittedly speculative and ongoing modifications will undoubtedly be required . figures 5a e show the critical events transpiring in a single minicolumn at five points in time during the csa 's computational cycle . note that due to space limitations figure 5 can not depict the true extents of the various axonal and dendritic systems of the cells involved . ( a e ) depict critical events transpiring in a single minicolumn at five points in time during the csa 's computational cycle , which i propose corresponds to one gamma cycle : approximate timings relative to start of csa cycle are shown across top . the units labeled c ( b ) represent the local chandelier ( basket cell ) populations , respectively ; see text for detailed explanation . figure 5a shows the initial csa steps 1 and 2 when the l2/3 pyramidals ( here only two cells , but in reality , 20 ) integrate their inputs . while the csa explanation in the prior section included only the bu inputs , all three input classes are included here : bu inputs ( labeled 2 ) are mediated via l4 ( rockland and pandya , 1979 ) td inputs ( 1 ) are mediated via l2/3 apical tufts ( rockland and drash , 1996 ) h inputs ( 3 ) are mediated via the horizontal matrix of l2/3 ( gilbert and wiesel , 1989 ; feldmeyer et al . , 2006 ) all three input vectors arrive in parallel and collectively give rise to postsynaptic potentials ( psps ) in the l2/3 pyramidals . the three ( normalized ) inputs are combined multiplicatively ; see the generalized version of the csa ( table s1 in supplementary material ) . c ) are firing at this time , preventing the l2/3 pyramids from firing . in figure 5b , the chandeliers shut off ( grayed out ) and the l2/3 pyramid with the highest psp ( cell 2 ) is assumed to be the first to spike ( csa step 3 ) . this winning cell , and more specifically , its psp value ( v in eq . 2 ) , represents this minicolumn 's local judgment of how similar the macrocolumn 's closest - matching stored input is to the current overall ( i.e. , bu , h , and td ) input . the output of cell 2 is then communicated to some locus where it is averaged with the round 1 winners from the other 70 minicolumns of the macrocolumn , yielding g ( csa step 4 ) . as noted in the introduction , the functionality related to g seems most consistent with the phenomenology of neuromodulatory systems , especially ach and ne . note that the communication of cell 2 s psp value is hypothesized to be mediated via l5 , one of whose pyramidal cells is seen integrating here ( light green ) ; this is based loosely on evidence that l5 cells , specifically l5b pyramidals , almost exclusively target pontine areas ( with collaterals to thalamus ) ( deschnes et al . , 1994 ; krieger et al . , 2007 ) . l2/3 pyramidals are the primary source of bu signals to higher cortical areas ( rockland and pandya , 1979 ; and see thomson et al . , 2002 ; brecht et al . , 2003 ; schubert et al . , 2003 ; bannister , 2005 ; helmstaedter et al . , 2007 ; lbke and feldmeyer , 2007 ; petersen , 2007 ; egger et al . , 2008 ; , 2009 for wider background on cortical columnar circuitry relevant to the current proposal ) . in addition , as stated earlier , the horizontal l2/3-to - l2/3 connections are proposed to communicate this macrocolumn 's final hypothesis regarding its total input pattern in the current csa cycle recurrently back to the same ( and surrounding ) macrocolumns on the next csa cycle . hence , it is crucial that since that final hypothesis is not present until the second round of competition completes ( figure 5e ) , the output pathways carrying those signals must be closed ( red xs on paths 4 and 5 ) . though not depicted here , one possible mechanism for selectively preventing horizontal signaling in l2/3 is activation of the double bouquet cells ( defelipe et al . , 1990 , 2006 ; peters and sethares , 1997 ) . axons , being interdigitated , nearly one - to - one with minicolumns would allow them to make contact with a substantial portion of the horizontally ( and obliquely ) oriented dendritic and axonal processes , in l2/3 , and thus prevent passage of horizontal signals . in figure 5c , the l5 pyramidal mediating the winning l2/3 cell 's psp value has reached threshold and sends that output to the sub - cortical averaging locus ( path 6 ) . in addition , the winning cell itself has activated the local basket cell network ( electrically coupled , cf . b , which rapidly deactivates and re - polarizes ( resets ) the l2/3 pyramidals ( grayed out ) . this reset need not be back to a completely even baseline : some remnant of the relative psp distribution prior to basket cell activation might remain , biasing the second round of competition . in figure 5d , the result of the subcortical computation of g is returned to the macrocolumn ( path 7 ) in the form of neuromodulator release ( purple cloud surrounding the l2/3 pyramidals ) . cloud actually extends across a broad , i.e. , macrocolumnar ( or wider ) , expanse of l2/3 , not just within a single minicolumn as this figure may suggest . the chandeliers are again firing to prevent any l2/3 from firing as the second round of integration occurs . the basket cells are inactive , allowing this integration to take place . in figure 5e , in general , the pyramidal cell winning on this second round of competition may differ from the first round winner . in particular , the probability that the second round winner is the same as the first round winner increases with g. the set of l2/3 winners , one per minicolumn , across the whole macrocolumn represents that macrocolumn 's final decision ( hypothesis ) as to identity of its current overall ( td , h , and bu ) input . thus , the output of the winning l2/3 cell in each minicolumn is now communicated to : lower cortical regions via l5 and its backprojections to the lower regions l1 ( labeled 8 ) ( rockland and drash , 1996 ) . l2/3 pyramids in the same and neighboring macrocolumns via the local horizontal l2/3 matrix ( 5 ) ( gilbert and wiesel , 1989 ; feldmeyer et al . , 2006 ) , thus delivering temporal context information ( recurrently ) to the local region to be integrated on the next csa cycle . the l4 layer of higher cortical regions ( 4 ) ( rockland and pandya , 1979 ) . note that the output of the winning l2/3 cell should be prevented from recurring to the local basket network at this time so as to allow the integration period to occur at the beginning of the next computational cycle ; hence , the red x on the link to basket cell . i reiterate that the above possible cortical realization of the proposed sdc model is highly speculative . it clearly lacks numerous details , especially regarding processing in the intermediate processing stages , e.g. , l4 , and output processing involving l5 ( and l6 ) . nevertheless , it is a starting point and can be falsified , especially as experimental methods mature . we still have decidedly little in the way of hard constraints on the time courses of activation of the many cell types involved in cortical ( and hippocampal ) circuits , though progress is being made ( klausberger et al . , 2003 , 2004 ; silberberg et al . , 2005 ; silberberg and markram , 2007 ; klausberger and somogyi , 2008 ; otsuka and kawaguchi , 2009 ; woodruff et al . , 2009 ) . moreover , the proposed theory 's key assumption that the l2/3 pyramidals are the core repository of information in cortex and that the codes laid down in l2/3 are the context - dependent memories of our experiences , is subject to challenge . specifically , the anatomy of the l5 thick tufted cells suggests that they too have access to bu ( via l4 ) , td ( via their apical tufts in l1 ) , and h ( via an extensive intra - l5 horizontal network , schubert et al . , 2007 ) inputs , and therefore that l5 might store the most detailed and context - dependent codes in cortex , a view supported by findings such as ( de kock et al . , 2007 ) . in the end , for the purpose of this hypothesis and theory paper , i believe the architecture and algorithm ( csa ) to be more important than the specifics of any particular neural realization . in this section , i consider evidence relating to six model predictions : a}signals generated in the macrocolumn [ i.e. , the v^x ( eq . strictly interpreted , figure 2 suggests that the model can only be true of cortical areas that have direct projections to the activation function modulator ( afm ) , hypothesized to be instantiated in midbrain neuromodulator source areas , e.g. , basal forebrain ( bf , source of ach ) and locus coeruleus ( lc , source of ne ) . direct cortical afferents to bf arise mainly from prepyriform , anterior insula , orbitofrontal , entorhinal and medial temporal areas ( mesulam and mufson , 1984 ) . direct cortical afferents to lc arise from dorsal prefrontal cortex ( arnsten and goldman - rakic , 1984 ) , medial prefrontal cortex ( jodo et al . , 1998 ) . while direct projections are limited , a much larger fraction of cortex may be able to influence the hypothesized afm via multi - synaptic pathways involving thalamus and other subcortical structures , especially via pathways interconnecting bf , lc , and other neuromodulator source areas . for example , bf cholinergic neurons are excited by lc ( jones et al . , 2004 ) , which allows dorsal and medial prefrontal areas indirect influence on bf . similarly , lc receives input from the raphe nuclei ( reviewed in samuels and szabadi , 2008 ) which would allow further extension of the sphere of cortical influence upon the afm . however , it is clearly possible that my macrocolumnar model applies only to the smaller set of cortical areas suggested above . after all , there would be some advantage to deferring the decision as to the overall familiarity / novelty of the current input ( moment ) to the very highest cortical levels , which are in position to make the most informed decisions . in this case , once g is computed , it is then broadcast pan - cortically , i.e. , to all levels of the hierarchy , allowing the local choice of code to proceed accordingly , i.e. , with a level of randomness appropriate to g. figure s2 in supplementary material illustrates this view . 5 ) , which correlates with the detection of familiarity , and/or inversely with the detection of novelty . such correlations have been shown for both ach ( miranda et al . , 2000 , 2003 ) and ne ( sara et al . , 1994 ; vankov et al . , lc projects to all of cortex ( foote and morrison , 1987 ; berridge and waterhouse , 2003 ; samuels and szabadi , 2008 ) . bf projects to almost all cortical areas ( reviewed in briand et al . , 2007 ) . the amount of randomness to be added to the winner selection process is a global parameter , which applies non - specifically to all the minicolumns . this is consistent with volume transmission believed to be used by neuromodulatory systems ( descarries et al . , 1997 ; see sarter et al . d}the signal determines ( eqs 68 ) the amount of noise ( randomness ) in the selection ( activation ) of cortical ( i.e. , macrocolumnar ) codes . controlling the noisiness of a process of choosing a winner from a competing group of neurons can be achieved by some combination of two actions : ( i ) increasing the spike probability of cells with high input summations relative to those with low summations and ( ii ) lowering the spike probability of low - input cells relative to high - input cells . both of these actions can be achieved by uniformly ( i.e. , to all competing cells in a wta module ) modulating intrinsic cell properties such as excitability . numerous studies have demonstrated both excitatory and suppressive effects on target cell responses ( both principal neurons and interneurons ) for both ach ( kawasaki and avoli , 1996 ; shalinsky et al . , 2002 ; cobb and davies , 2005 ; tateno et al . , 2005 ; isakova and mednikova , 2007 ; lawrence , 2008 ; eggermann and feldmeyer , 2009 ) and ne ( foote et al . , 1975 ; kawaguchi and shindou , 1998 ; harley and helen , 2007 ; moxon et al . , 2007 ) . it is not my intention here to argue for a precise realization of this mechanism . as suggested in many reviews ( berridge and waterhouse , 2003 ; lucas - meunier et al . , 2003 ; sara , 2009 ) , the landscape of this research is very complex and we are far from a comprehensive understanding of the how the various neuromodulatory systems affect high - level cognitive processing either alone or in concert ( briand et al . , 2007 ) . nevertheless , the large and varied body of evidence at least admits the possibility that one or more of these neuromodulators could implement the familiarity - contingent afm mechanism ( csa steps 58 ; see doya , 2002 , p. 502 e}decreased , i.e. , increased noise , leads to greater code separation ( decreased intersection ) . recently , goard and dan ( 2009 ) showed that increased bf stimulation decreased the correlation amongst a population of rat v1 cells . this decreased correlation essentially shows increased separation between population codes , which in the model proposed here , would manifest as decreased intersection between sparse codes . f}disabling of the brain 's ability to produce high noise , i.e. , causing to be permanently high , should reduce the ability to learn new inputs , while sparing or having much less effect on recognition of known items . looking at figure 4 , if the afm was stuck in the highly expansive sigmoid condition ( low noise ) , all four inputs , 25 , would have high probability of mapping to the same code , 1 . however , in general , inputs that were mapped to unique codes prior to such a disabling event will reliably activate those codes on future presentations . in accord with this , browning et al . ( 2010 ) found that severely diminishing cholinergic inputs to inferotemporal cortex severely reduced macaques performance on a visual episodic memory task , while having little effect on a dnms task . ( 2005 ) found a similar effect : cholinergic deafferentation of entorhinal cortex reduced performance on dnms tasks involving novel odors but not familiar odors . the model 's core algorithm , the csa , determines which cells are chosen to represent an input , during both learning and retrieval . a single iteration of the algorithm involves two rounds of competition in the cms of f2 . the first round is a hard wta competition ( represented by boxes labeled max in figure 2 ) . the purpose of the first round is to compute a global familiarity measure , g , of the input pattern . g then drives a global modulation of the f2 unit activation function ( figure 2 : purple arrows ) in preparation for the second competitive round , which is a soft wta competition , the intent of which is that : as g goes to 1 ( indicating a completely familiar input ) , the probability that the unit with the highest input summation in a cm wins approaches 1 , and as g goes to 0 ( indicating a completely novel input ) , all units in a cm become equally likely to win ( regardless of their input summations ) . ( 1)u(i)=j nw(j , i ) where n is the current input ( f1 ) pattern . because unit activations are binary , we can simply sum the weights , w(j , i ) , which are also binary . normalize u(i ) to [ 0 .. 1 ] , yielding v(i ) . v(i ) is a local measure of support , or likelihood , that f2 unit i should be activated . it reflects how well unit i 's receptive field ( rf ) , specified by its afferent weight vector , matches the current input vector . ( round 1 competition ) the maximum v(i ) , v^x , is found in each of the q cms . ( 3)v^x = maxi cx{v(i ) } where x indexes the cms and i indexes the units in a cm , cx . average the q v^xvalues , yielding g , a global measure of the familiarity of the current input . ( 4)gx=1qv^x / q the expansivity , , of the probabilistic activation function ( which is implemented via steps 68 ) is set as an increasing nonlinear function of g ( eq . the idea is to increase the range of relative win likelihoods , (i ) ( defined in step 6 ) over any given cm 's units as g goes to 1 . this in turn , serves to nonlinearly exaggerate the difference in the final win probabilities ( eq . the specific parameters of any instance of the g - to- mapping will determine the specifics of the relation between input similarity and code similarity , i.e. , the expected code intersection as a function of input similarity . 5 were chosen to yield the -distributions in the examples of figures 3 and 4 . circled numbers refer to algorithm steps in text . here , i show the case of the first input , 1 , presented to the model . the algorithm detects that 1 is completely unfamiliar , i.e. , g is computed to be 0 , and sets the f2 activation function to a constant function ( red line ) , which makes the choice of winner in each cm completely random , and thus , the overall f2 code , 1 , also completely random . green f1 ( f2 ) units denote units not in common with 1 ( 1 ) . , i show the case of the first input , 1 , presented to the model . the algorithm detects that 1 is completely unfamiliar , i.e. , g is computed to be 0 , and sets the f2 activation function to a constant function ( red line ) , which makes the choice of winner in each cm completely random , and thus , the overall f2 code , 1 , also completely random . the csa and the sisc property . green f1 ( f2 ) units denote units not in common with 1 ( 1 ) . the v values of all units in all cms are then passed through the sigmoidal activation function ( eq . 6 ) whose shape / scale reflects g. again , particular parameter values affect the relation of input similarity to code similarity ( and therefore , storage capacity ) : values of = 28 and = 5 produce the v - to- mappings in figure 4 . as noted above , within each cm , the output variable , (i ) , can be viewed as a relative likelihood that unit i should be chosen winner . ( 6)(i)=1+e ( v(i ) + )+1 when g = 1 ( perfectly familiar ) , is maximized ( in eq . 7 ) probabilities of winning for units with the maximum v value in their respective cms . in contrast , when g = 0 ( completely novel ) , = 0 , which collapses the sigmoid to the constant function , = 1 , thus making all units in a cm equally likely to win . this causes the expected intersection of the code being chosen in the current instance with any previously assigned code to be at chance level . in general , this modulation of the sigmoid activation function tends toward code completion in proportion to the familiarity of the input and code separation in proportion to its novelty . transform relative likelihood distribution ( ) in each cm to true probability distribution ( ) . ( 7)(i)=(i)k cm(k ) ( round 2 competition ) choose an f2 code by drawing a winner from the -distribution ( soft max ) in each cm . thus , choosing an f2 code is actually performed as q separate draws . when g = 0 , these draws are statistically independent , as in figures 3 and 4d . as we consider increasingly familiar inputs , i.e. , for g approaching 1 ( and , assuming the model is still operating in a regime where crosstalk is sufficiently low ) , the draws become increasingly correlated ( dependent ) , as can be seen in going from figure 4c to 4b to 4a . figure 3 graphically illustrates the operation of the csa in the case of the model being presented with its first input , 1 . the gray arrows indicate that the bu signals propagating from the active f1 units will be traversing connections with zero synaptic strength . this leads to unnormalized ( u ) and normalized ( v ) input summations of 0 for all 12 f2 units ( steps 1,2 ) . in step 3 , the max v , v^ , in each cm is found ( ties broken at random ) . in step 4 , g is computed as the average of the v^ values : in this case all the v^ are 0 , so g = 0 . in step 5 , the value , g = 0 , maps to = 0 , which causes the activation function of the f2 units to collapse to the constant function , = 1 . in step 6 , each f2 unit applies this activation function to its v value , yielding the uniform relative likelihood distribution in each cm . in step 7 , the relative likelihood function in each cm is normalized to a true probability ( ) distribution , which in this case , is again uniform . finally , in step 8 , a winner is drawn in each cm , resulting in a random f2 code , e.g. , 1 . figure 4 demonstrates that the csa realizes the sisc property by considering four possibilities ( a d ) for the second input presented to the model of figure 3 . these four inputs , 25 , range from being identical to 1 ( completely familiar ) to having zero overlap with 1 ( completely unfamiliar ) . to save space , the panels of figure 4 use an abbreviated version of the format of figure 3 . most noticeably , the intermediate variable , ( relative likelihood ) , is not shown . black bu connections are ones that were increased to one when 1 was learned ( figure 3 ) . working from figure 4a to 4d , the inputs have progressively lower similarity ( intersection ) with 1 : f1 units not in common with 1 are shown in green . as g drops , the sigmoid expansivity drops ( note the changing scale ) . thus , the -distributions become progressively flatter , which in turn results in f2 codes , 25 , having progressively smaller intersection with 1 . f2 units not in common with 1 also shown in green . figure 4a shows the case of presenting a completely familiar input again , and is thus a recognition test trial , demonstrating retrieval . this leads , via csa steps 3 and 4 , to g = 1 , which yields , via steps 5 and 6 , the expansive nonlinear v - to- mapping shown ( red sigmoid ) . this nonlinearity is applied to every f2 unit , yielding the highly peaked -distributions shown . the probability of drawing the correct unit in any single cm is approximately 98% . of course , what 's crucial in this case , i.e. , when the input is completely familiar ( g = 1 ) , is that the entire correct f2 code is reactivated . in this case , thus , the familiarity , g , which depends on the entire f2 layer and is thus global information , influences the local activation functions so as to produce the desired overall result , in this case , reactivation of the code ( memory trace ) , 1 , of the familiar input pattern , 1 . the explanations of the remaining panels follow that of figures 3 and 4a . in going from figure 4b to 4d , one can readily see decreasing intersection with 1 , decreasing u and v values , decreasing g , decreasing sigmoid expansivity , progressively flatter -distributions , and ultimately , decreasing intersection with 1 . given a desired probability , r , of correctly reactivating an entire code ( i.e. , of choosing the correct unit in each cm ) , when g = 1 , given values for q and k , we could compute the needed value of . however , the macrocolumn model is a content - addressable associative memory and in actual usage , multiple sparse codes will be stored in superposition . any thorough analysis of the model 's expected retrieval error must include the effect of overlap between the stored codes ( i.e. , cross - talk ) : this influences the shapes of the -distributions and thus , the expected retrieval accuracy for any given number of stored codes . such an analysis will be conducted empirically and reported in a separate paper . before leaving figure 4 first , while the -distributions become flatter as g decreases , the units comprising the code of the most similar previously learned input ( here , 1 ) remain most likely to win in their respective cms . if we simply deterministically chose the unit with maximum v(i ) in each cm , we would have chosen the same f2 code , 1 , in response to all four inputs , 25 . thus , the computation of a quantity , g , which depends on all the cms is essential to achieving the sisc property . it constitutes a channel through which information transfers between all f2 units throughout the whole macrocolumn . as noted earlier , the full model also assumes direct h connections between f2 units , analogous to the horizontal matrix of l2/3 ( see figure s2 in supplementary material ) . these also mediate communication , but of the prior code active in the macrocolumn , not of the simultaneous state of all f2 units throughout the macrocolumn . second , learning is single - trial and involves only one iteration of the csa . this is largely facilitated by the fact that when a given input - code association , jj , is learned , each of j 's f2 units simultaneously has its afferent weight from all of j 's f1 units increased . the effect of these simultaneous correlated potentiations allows a rapid , even single - trial , formation of an association , even if the individual synaptic potentiations are small , consistent with the recent characterization of thalamocortical learning described in bruno and sakmann ( 2006 ) . third , figure 4a shows that recognizing an exact instance of a previous input also requires only one iteration of the csa . although this example does not directly show it , this holds for recognition of non - exact matches as well . evidence for this will be presented in a separate work . that both learning and recognition require only a single csa iteration is especially significant since , as can readily be seen , none of the csa steps involves iterations over stored codes : thus , the time it takes for the csa to either store a new input or retrieve the closest matching stored input remains constant as the number of stored codes increases . this does not imply that an infinite number of codes can be stored : of course , the model has finite storage capacity . this capacity will be characterized in future research , but should be similar to other sparse associative memories ( willshaw et al . , 1969 ; palm , 1982 ; moll and miikkulainen , 1995 ; knoblauch et al . , 2010 ) . there remain huge gaps in our knowledge of the intrinsic physiological , synaptic , morphological , and connectional properties of all classes of cortical cell and of functional relationships between cortical and sub - cortical structures . nevertheless , figure 5 shows a possible neural realization of the model 's wta cm , i.e. , minicolumn , and dynamics ( csa ) . i have attempted to respect known constraints but the realization is admittedly speculative and ongoing modifications will undoubtedly be required . figures 5a e show the critical events transpiring in a single minicolumn at five points in time during the csa 's computational cycle . note that due to space limitations figure 5 can not depict the true extents of the various axonal and dendritic systems of the cells involved . ( a e ) depict critical events transpiring in a single minicolumn at five points in time during the csa 's computational cycle , which i propose corresponds to one gamma cycle : approximate timings relative to start of csa cycle are shown across top . the units labeled c ( b ) represent the local chandelier ( basket cell ) populations , respectively ; see text for detailed explanation . figure 5a shows the initial csa steps 1 and 2 when the l2/3 pyramidals ( here only two cells , but in reality , 20 ) integrate their inputs . while the csa explanation in the prior section included only the bu inputs , all three input classes are included here : bu inputs ( labeled 2 ) are mediated via l4 ( rockland and pandya , 1979 ) td inputs ( 1 ) are mediated via l2/3 apical tufts ( rockland and drash , 1996 ) h inputs ( 3 ) are mediated via the horizontal matrix of l2/3 ( gilbert and wiesel , 1989 ; feldmeyer et al . , 2006 ) all three input vectors arrive in parallel and collectively give rise to postsynaptic potentials ( psps ) in the l2/3 pyramidals . the three ( normalized ) inputs are combined multiplicatively ; see the generalized version of the csa ( table s1 in supplementary material ) . c ) are firing at this time , preventing the l2/3 pyramids from firing . in figure 5b , the chandeliers shut off ( grayed out ) and the l2/3 pyramid with the highest psp ( cell 2 ) is assumed to be the first to spike ( csa step 3 ) . this winning cell , and more specifically , its psp value ( v in eq . 2 ) , represents this minicolumn 's local judgment of how similar the macrocolumn 's closest - matching stored input is to the current overall ( i.e. , bu , h , and td ) input . the output of cell 2 is then communicated to some locus where it is averaged with the round 1 winners from the other 70 minicolumns of the macrocolumn , yielding g ( csa step 4 ) . as noted in the introduction , the functionality related to g seems most consistent with the phenomenology of neuromodulatory systems , especially ach and ne . note that the communication of cell 2 s psp value is hypothesized to be mediated via l5 , one of whose pyramidal cells is seen integrating here ( light green ) ; this is based loosely on evidence that l5 cells , specifically l5b pyramidals , almost exclusively target pontine areas ( with collaterals to thalamus ) ( deschnes et al . l2/3 pyramidals are the primary source of bu signals to higher cortical areas ( rockland and pandya , 1979 ; and see thomson et al . , 2002 ; brecht et al . , 2003 ; schubert et al . , 2003 ; bannister , 2005 ; helmstaedter et al . , 2007 ; lbke and feldmeyer , 2007 ; petersen , 2007 ; egger et al . , 2008 ; , 2009 for wider background on cortical columnar circuitry relevant to the current proposal ) . in addition , as stated earlier , the horizontal l2/3-to - l2/3 connections are proposed to communicate this macrocolumn 's final hypothesis regarding its total input pattern in the current csa cycle recurrently back to the same ( and surrounding ) macrocolumns on the next csa cycle . hence , it is crucial that since that final hypothesis is not present until the second round of competition completes ( figure 5e ) , the output pathways carrying those signals must be closed ( red xs on paths 4 and 5 ) . though not depicted here , one possible mechanism for selectively preventing horizontal signaling in l2/3 is activation of the double bouquet cells ( defelipe et al . , 1990 , 2006 ; peters and sethares , 1997 ) . axons , being interdigitated , nearly one - to - one with minicolumns would allow them to make contact with a substantial portion of the horizontally ( and obliquely ) oriented dendritic and axonal processes , in l2/3 , and thus prevent passage of horizontal signals . in figure 5c , the l5 pyramidal mediating the winning l2/3 cell 's psp value has reached threshold and sends that output to the sub - cortical averaging locus ( path 6 ) . in addition , the winning cell itself has activated the local basket cell network ( electrically coupled , cf . b , which rapidly deactivates and re - polarizes ( resets ) the l2/3 pyramidals ( grayed out ) . this reset need not be back to a completely even baseline : some remnant of the relative psp distribution prior to basket cell activation might remain , biasing the second round of competition . in figure 5d , the result of the subcortical computation of g is returned to the macrocolumn ( path 7 ) in the form of neuromodulator release ( purple cloud surrounding the l2/3 pyramidals ) . cloud actually extends across a broad , i.e. , macrocolumnar ( or wider ) , expanse of l2/3 , not just within a single minicolumn as this figure may suggest . the chandeliers are again firing to prevent any l2/3 from firing as the second round of integration occurs . the basket cells are inactive , allowing this integration to take place . in figure 5e , the chandeliers again deactivate . , the pyramidal cell winning on this second round of competition may differ from the first round winner . in particular , the probability that the second round winner is the same as the first round winner increases with g. the set of l2/3 winners , one per minicolumn , across the whole macrocolumn represents that macrocolumn 's final decision ( hypothesis ) as to identity of its current overall ( td , h , and bu ) input . thus , the output of the winning l2/3 cell in each minicolumn is now communicated to : lower cortical regions via l5 and its backprojections to the lower regions l1 ( labeled 8 ) ( rockland and drash , 1996 ) . l2/3 pyramids in the same and neighboring macrocolumns via the local horizontal l2/3 matrix ( 5 ) ( gilbert and wiesel , 1989 ; feldmeyer et al . , 2006 ) , thus delivering temporal context information ( recurrently ) to the local region to be integrated on the next csa cycle . the l4 layer of higher cortical regions ( 4 ) ( rockland and pandya , 1979 ) . note that the output of the winning l2/3 cell should be prevented from recurring to the local basket network at this time so as to allow the integration period to occur at the beginning of the next computational cycle ; hence , the red x on the link to basket cell . i reiterate that the above possible cortical realization of the proposed sdc model is highly speculative . it clearly lacks numerous details , especially regarding processing in the intermediate processing stages , e.g. , l4 , and output processing involving l5 ( and l6 ) . nevertheless , it is a starting point and can be falsified , especially as experimental methods mature . for example , the many timing relationships in the circuit can be tested . we still have decidedly little in the way of hard constraints on the time courses of activation of the many cell types involved in cortical ( and hippocampal ) circuits , though progress is being made ( klausberger et al . silberberg and markram , 2007 ; klausberger and somogyi , 2008 ; otsuka and kawaguchi , 2009 ; woodruff et al . , 2009 ) . moreover , the proposed theory 's key assumption that the l2/3 pyramidals are the core repository of information in cortex and that the codes laid down in l2/3 are the context - dependent memories of our experiences , is subject to challenge . specifically , the anatomy of the l5 thick tufted cells suggests that they too have access to bu ( via l4 ) , td ( via their apical tufts in l1 ) , and h ( via an extensive intra - l5 horizontal network , schubert et al . , 2007 ) inputs , and therefore that l5 might store the most detailed and context - dependent codes in cortex , a view supported by findings such as ( de kock et al . , 2007 ) . in the end , for the purpose of this hypothesis and theory paper , i believe the architecture and algorithm ( csa ) to be more important than the specifics of any particular neural realization . in this section , i consider evidence relating to six model predictions : a}signals generated in the macrocolumn [ i.e. , the v^x ( eq . strictly interpreted , figure 2 suggests that the model can only be true of cortical areas that have direct projections to the activation function modulator ( afm ) , hypothesized to be instantiated in midbrain neuromodulator source areas , e.g. , basal forebrain ( bf , source of ach ) and locus coeruleus ( lc , source of ne ) . direct cortical afferents to bf arise mainly from prepyriform , anterior insula , orbitofrontal , entorhinal and medial temporal areas ( mesulam and mufson , 1984 ) . direct cortical afferents to lc arise from dorsal prefrontal cortex ( arnsten and goldman - rakic , 1984 ) , medial prefrontal cortex ( jodo et al . , 1998 ) . while direct projections are limited , a much larger fraction of cortex may be able to influence the hypothesized afm via multi - synaptic pathways involving thalamus and other subcortical structures , especially via pathways interconnecting bf , lc , and other neuromodulator source areas . , 2004 ) , which allows dorsal and medial prefrontal areas indirect influence on bf . similarly , lc receives input from the raphe nuclei ( reviewed in samuels and szabadi , 2008 ) which would allow further extension of the sphere of cortical influence upon the afm . however , it is clearly possible that my macrocolumnar model applies only to the smaller set of cortical areas suggested above . after all , there would be some advantage to deferring the decision as to the overall familiarity / novelty of the current input ( moment ) to the very highest cortical levels , which are in position to make the most informed decisions . in this case , once g is computed , it is then broadcast pan - cortically , i.e. , to all levels of the hierarchy , allowing the local choice of code to proceed accordingly , i.e. , with a level of randomness appropriate to g. figure s2 in supplementary material illustrates this view . 5 ) , which correlates with the detection of familiarity , and/or inversely with the detection of novelty . such correlations have been shown for both ach ( miranda et al . , 2000 , 2003 ) and ne ( sara et al . , 1994 ; vankov et al . , lc projects to all of cortex ( foote and morrison , 1987 ; berridge and waterhouse , 2003 ; samuels and szabadi , 2008 ) . bf projects to almost all cortical areas ( reviewed in briand et al . , 2007 ) . the amount of randomness to be added to the winner selection process is a global parameter , which applies non - specifically to all the minicolumns . this is consistent with volume transmission believed to be used by neuromodulatory systems ( descarries et al . , 1997 ; see sarter et al . , 2009 for discussion of the complexities of the evidence regarding volume transmission ) . d}the signal determines ( eqs 68 ) the amount of noise ( randomness ) in the selection ( activation ) of cortical ( i.e. , macrocolumnar ) codes . controlling the noisiness of a process of choosing a winner from a competing group of neurons can be achieved by some combination of two actions : ( i ) increasing the spike probability of cells with high input summations relative to those with low summations and ( ii ) lowering the spike probability of low - input cells relative to high - input cells . both of these actions can be achieved by uniformly ( i.e. , to all competing cells in a wta module ) modulating intrinsic cell properties such as excitability . numerous studies have demonstrated both excitatory and suppressive effects on target cell responses ( both principal neurons and interneurons ) for both ach ( kawasaki and avoli , 1996 ; shalinsky et al . , 2002 ; cobb and davies , 2005 ; tateno et al . , 2005 ; isakova and mednikova , 2007 ; lawrence , 2008 ; eggermann and feldmeyer , 2009 ) and ne ( foote et al . , 1975 ; kawaguchi and shindou , 1998 ; harley and helen , 2007 ; moxon et al . it is not my intention here to argue for a precise realization of this mechanism . as suggested in many reviews ( berridge and waterhouse , 2003 ; lucas - meunier et al . , 2003 ; sara , 2009 ) , the landscape of this research is very complex and we are far from a comprehensive understanding of the how the various neuromodulatory systems affect high - level cognitive processing either alone or in concert ( briand et al . , 2007 ) . nevertheless , the large and varied body of evidence at least admits the possibility that one or more of these neuromodulators could implement the familiarity - contingent afm mechanism ( csa steps 58 ; see doya , 2002 , p. 502 e}decreased , i.e. , increased noise , leads to greater code separation ( decreased intersection ) . recently , goard and dan ( 2009 ) showed that increased bf stimulation decreased the correlation amongst a population of rat v1 cells . this decreased correlation essentially shows increased separation between population codes , which in the model proposed here , would manifest as decreased intersection between sparse codes . f}disabling of the brain 's ability to produce high noise , i.e. , causing to be permanently high , should reduce the ability to learn new inputs , while sparing or having much less effect on recognition of known items . looking at figure 4 , if the afm was stuck in the highly expansive sigmoid condition ( low noise ) , all four inputs , 25 , would have high probability of mapping to the same code , 1 . this would prevent the model from being able to distinguish them in future presentations . however , in general , inputs that were mapped to unique codes prior to such a disabling event will reliably activate those codes on future presentations . in accord with this , browning et al . ( 2010 ) found that severely diminishing cholinergic inputs to inferotemporal cortex severely reduced macaques performance on a visual episodic memory task , while having little effect on a dnms task . ( 2005 ) found a similar effect : cholinergic deafferentation of entorhinal cortex reduced performance on dnms tasks involving novel odors but not familiar odors . in this section , i consider evidence relating to six model predictions : a}signals generated in the macrocolumn [ i.e. , the v^x ( eq . strictly interpreted , figure 2 suggests that the model can only be true of cortical areas that have direct projections to the activation function modulator ( afm ) , hypothesized to be instantiated in midbrain neuromodulator source areas , e.g. , basal forebrain ( bf , source of ach ) and locus coeruleus ( lc , source of ne ) . relatively few cortical areas project directly to bf or lc . direct cortical afferents to bf arise mainly from prepyriform , anterior insula , orbitofrontal , entorhinal and medial temporal areas ( mesulam and mufson , 1984 ) . direct cortical afferents to lc arise from dorsal prefrontal cortex ( arnsten and goldman - rakic , 1984 ) , medial prefrontal cortex ( jodo et al . , 1998 ) . while direct projections are limited , a much larger fraction of cortex may be able to influence the hypothesized afm via multi - synaptic pathways involving thalamus and other subcortical structures , especially via pathways interconnecting bf , lc , and other neuromodulator source areas . for example , bf cholinergic neurons are excited by lc ( jones et al . , 2004 ) , which allows dorsal and medial prefrontal areas indirect influence on bf . similarly , lc receives input from the raphe nuclei ( reviewed in samuels and szabadi , 2008 ) which would allow further extension of the sphere of cortical influence upon the afm . however , it is clearly possible that my macrocolumnar model applies only to the smaller set of cortical areas suggested above . after all , there would be some advantage to deferring the decision as to the overall familiarity / novelty of the current input ( moment ) to the very highest cortical levels , which are in position to make the most informed decisions . in this case , once g is computed , it is then broadcast pan - cortically , i.e. , to all levels of the hierarchy , allowing the local choice of code to proceed accordingly , i.e. , with a level of randomness appropriate to g. figure s2 in supplementary material illustrates this view . 5 ) , which correlates with the detection of familiarity , and/or inversely with the detection of novelty . such correlations have been shown for both ach ( miranda et al . , 2000 , 2003 ) and ne ( sara et al . , 1994 ; vankov et al . , lc projects to all of cortex ( foote and morrison , 1987 ; berridge and waterhouse , 2003 ; samuels and szabadi , 2008 ) . bf projects to almost all cortical areas ( reviewed in briand et al . , 2007 ) . the amount of randomness to be added to the winner selection process is a global parameter , which applies non - specifically to all the minicolumns . this is consistent with volume transmission believed to be used by neuromodulatory systems ( descarries et al . , 1997 ; see sarter et al . , 2009 for discussion of the complexities of the evidence regarding volume transmission ) . d}the signal determines ( eqs 68 ) the amount of noise ( randomness ) in the selection ( activation ) of cortical ( i.e. , macrocolumnar ) codes . controlling the noisiness of a process of choosing a winner from a competing group of neurons can be achieved by some combination of two actions : ( i ) increasing the spike probability of cells with high input summations relative to those with low summations and ( ii ) lowering the spike probability of low - input cells relative to high - input cells . both of these actions can be achieved by uniformly ( i.e. , to all competing cells in a wta module ) modulating intrinsic cell properties such as excitability . numerous studies have demonstrated both excitatory and suppressive effects on target cell responses ( both principal neurons and interneurons ) for both ach ( kawasaki and avoli , 1996 ; shalinsky et al . , 2002 ; cobb and davies , 2005 ; tateno et al . , 2005 ; isakova and mednikova , 2007 ; lawrence , 2008 ; eggermann and feldmeyer , 2009 ) and ne ( foote et al . , 1975 ; kawaguchi and shindou , 1998 ; harley and helen , 2007 ; moxon et al . , 2007 ) . it is not my intention here to argue for a precise realization of this mechanism . as suggested in many reviews ( berridge and waterhouse , 2003 ; lucas - meunier et al . , 2003 ; sara , 2009 ) , the landscape of this research is very complex and we are far from a comprehensive understanding of the how the various neuromodulatory systems affect high - level cognitive processing either alone or in concert ( briand et al . , 2007 ) . nevertheless , the large and varied body of evidence at least admits the possibility that one or more of these neuromodulators could implement the familiarity - contingent afm mechanism ( csa steps 58 ; see doya , 2002 , p. 502 e}decreased , i.e. , increased noise , leads to greater code separation ( decreased intersection ) . recently , goard and dan ( 2009 ) showed that increased bf stimulation decreased the correlation amongst a population of rat v1 cells . this decreased correlation essentially shows increased separation between population codes , which in the model proposed here , would manifest as decreased intersection between sparse codes . f}disabling of the brain 's ability to produce high noise , i.e. , causing to be permanently high , should reduce the ability to learn new inputs , while sparing or having much less effect on recognition of known items . looking at figure 4 , if the afm was stuck in the highly expansive sigmoid condition ( low noise ) , all four inputs , 25 , would have high probability of mapping to the same code , 1 . this would prevent the model from being able to distinguish them in future presentations . however , in general , inputs that were mapped to unique codes prior to such a disabling event will reliably activate those codes on future presentations . ( 2010 ) found that severely diminishing cholinergic inputs to inferotemporal cortex severely reduced macaques performance on a visual episodic memory task , while having little effect on a dnms task . ( 2005 ) found a similar effect : cholinergic deafferentation of entorhinal cortex reduced performance on dnms tasks involving novel odors but not familiar odors . i have described a theoretical model of cortical function that explains the functional relationship between the minicolumn and macrocolumn . specifically : a}the macrocolumn ( in any of its forms ) is proposed to store information in the form of sdcs , and b}the minicolumn ( specifically , its l2/3 pool of pyramidals ) is proposed to operate as a wta cm , the purpose of which is to enforce the sparseness of the macrocolumnar code . two key motivations for this model are the computational advantages of sdc and the increasingly strong evidence for sdc in the brain , cited in the section introduction . one important advantage of sdc over a localist code is that the number of unique items that can be stored can be far larger than the number of representing units . for example , the 12 f2 units of the model in figure 2 allow 3 = 81 unique codes , though in realistic systems , e.g. , with less than complete connectivity leading to and from a coding field like f2 , the number of those codes that can safely ( i.e. , while maintaining retrieval error rates below some acceptable criterion ) be assigned will be substantially lower than 81 . nevertheless , if the number of input items that will need to be distinguished is not known a priori , sdc is more flexible . a second computational advantage of sdc is that , if used in conjunction with an appropriate storage / retrieval algorithm it possesses the sisc property . i demonstrated , with the small but statistically reasonable example of figures 3 and 4 , that the csa yields the sisc property . the sisc property strongly differentiates sdc from localist models : it is not even defined for a localist model since every code is formally disjoint with every other code . hence , there is no structural way to represent degrees of similarity in a localist code . if there is no way to represent a measure , e.g. , similarity , structurally , then whenever that measure is required e.g. , when the closest matching stored item in a database ( i.e. , macrocolumn ) to an input must be returned it must be computed , which takes time and energy . in contrast , when items codes are stored in physically overlapped fashion such that the degree of code overlap represents item similarity , as is the case for the proposed model , the most closely matching stored item will be returned immediately , i.e. , without requiring any serial search through the stored items . figure s4 in supplementary material shows test retrievals of the four unique codes stored in the model of figures 3 and 4 , demonstrating possession of this immediate access property for this small example . i consider the representation and the csa to be the most important contributions of this paper because of the computational advantages just described . however , i believe the suggestion that the minicolumn 's generic function is to act as a wta cm is also important . saying only that a group of l2/3 units forms a wta cm places no a priori constraints on what their tuning functions or receptive fields should look like . this is what gives that functionality a chance of being truly generic , i.e. , of applying across all areas and species , regardless of the observed tuning profiles of closely neighboring units . indeed , a recent calcium imaging study of mouse auditory cortex by rothschild et al . ( 2010 ) shows highly heterogeneous small - scale ( even immediately adjacent cells ) tuning even though the large - scale tuning is tonotopic . experimental methods are only now just reaching the point where this hypothesis might be directly testable , e.g. , modifying calcium imaging methods to have millisecond temporal granularity ; see ohki and reid ( 2007 ) . in a sense , the main point of this paper is that a generic minicolumnar function becomes apparent as soon as we postulate that what the cortex , i.e. , a macrocolumn , generally does is store and retrieve ( access ) sdcs of specific context - dependent inputs . as noted in the section introduction , the experimental literature contains little in the way of proposals linking the formation and retrieval of specific sdcs ( i.e. , of specific input items , especially of temporal context - dependent items ) to the cortical microcircuitry . my proposed model goes beyond broad conclusions and offers a mechanistic explanation of how specific informational items are learned and retrieved and in so doing , proposes a generic function for the minicolumn , i.e. , that it functions as a wta module in support of manipulating sdcs at the next higher , i.e. , macrocolumnar , scale . there have been several recent models linking formation / retrieval of specific items to cortical circuitry and which describe specific roles for the minicolumn ( kupper et al . , 2007 ; george and hawkins , 2009 ; litvak and ullman , 2009 ; schrader et al . , however , all of these models use localist representations and therefore would not possess the advantages of sdc described above . the cortext model ( kupper et al . , 2007 ; schrader et al . , 2009 ) assumes that each minicolumn in a hypercolumn represents one particular input feature . on each computational cycle , a wta process runs within each hypercolumn , such that exactly one minicolumn wins , which would be strongly at odds with the calcium image data ( ohki et al . , 2005 ) . a second problem is that the assumption that whole minicolumns compete with each other implies that any given hypercolumn ( at any level of the cortical hierarchy ) can represent only 70 unique features ( equivalence classes ) , which seems severely restrictive , especially for hypercolumns at higher cortical levels , e.g. , it . the litvak and ullman ( 2009 ) model also postulates that the l2/3 pool of neurons in a minicolumn implements a max function . however , their model proposes that each single minicolumn ( specifically , its l2/3 pool ) is partitioned into several disjoint groups ( cliques ) of cells , each representing a different item . since any particular cell can participate in only one clique , this constitutes a localist code . george and hawkins ( 2009 ) also assume that minicolumns represent informational items in a localist fashion . note however that both george and hawkins ( 2009 ) and litvak and ullman ( 2009 ) explicitly mention moving to a more general combinatorial code , a.k.a . a core principle of the proposed model is this notion of controlling the amount of noise in the process of choosing ( activating ) a macrocolumnar code as an inverse function of input similarity . doya ( 2002 ) uses the same principle , referred to as boltzmann selection , to modulate the amount of noise in the process of choosing amongst output action actions . doya specifically hypothesizes that ne controls the noise whereas i can assert only that it is some neuromodulator - based mechanism . in doya 's model , as ne levels increase , the action with the greatest expected reward is chosen with probability approaching 1 . this is suggested as corresponding to the exploitation end of the exploitation exploration continuum . as ne levels drop to 0 , all actions become equally probable , i.e. , exploration , which is appropriate if no single action has a particular high expected reward , which generally correlates with the condition of novelty , i.e. , of being in a novel environment wherein it is harder to anticipate the outcome of known actions . the analogy to high expected reward in my model is a highly familiar input ( g 1 ) in which case we want the stored code for that familiar input to be reactivated with probability approaching 1 ; the condition where no action has a high expected reward is analogous to low familiarity , i.e. , where no stored input is very similar to the current input , in which case we want to lay down a new memory trace for the novel input . despite the similarities , doya 's model also assumes a localist representation of the choices and , like the other models just mentioned , can not realize the advantages of sdc . i have identified several avenues of active and future research at various points in the text and as noted in the previous section , the prospective neural realization is highly speculative and very incomplete . several additional questions / issues for future research are : is the current proposal that the l2/3 cells engage in two rounds of competition in each computational ( putatively , gamma ) cycle plausible ? for simplicity , i have described the model in the simplest case of having only one internal coding field ( f2 ) and processing only purely spatial input patterns . however the core model was originally developed for the spatiotemporal pattern ( sequence ) case ( rinkus , 1996 ) and was generalized some time ago to have an arbitrarily deep hierarchy of coding fields ( rinkus and lisman , 2005 ) . see figure s2 in supplementary material . how do these generalized versions of the model map to neural structures ? is there evidence that chandeliers become active twice as frequently as baskets , as the proposed realization predicts ? is there evidence for the converse ? although not elaborated herein , the proposed mini-/macrocolumn model is easily generalized to allow substantial overlap between minicolumns ( see figure s5 in supplementary material ) and multiple winners in a minicolumn on each computational cycle . we know of the fast , phasic , time scales of operation for ne ( rajkowski et al . , 2004 ) and da ( schultz , 1998 ) and of slightly slower but still phasic mode for ach ( gulledge and kawaguchi , 2007 ) , but these have been proposed as signaling other measures besides pure novelty ( redgrave et al . , 1999 ; bouret and sara , 2005 ; dayan and yu , 2006 ) . how might all these signals conspire to implement a pure novelty signal ? the author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest .

no generic function for the minicolumn i.e. , one that would apply equally well to all cortical areas and species has yet been proposed . i propose that the minicolumn does have a generic functionality , which only becomes clear when seen in the context of the function of the higher - level , subsuming unit , the macrocolumn . i propose that : ( a ) a macrocolumn 's function is to store sparse distributed representations of its inputs and to be a recognizer of those inputs ; and ( b ) the generic function of the minicolumn is to enforce macrocolumnar code sparseness . the minicolumn , defined here as a physically localized pool of 20 l2/3 pyramidals , does this by acting as a winner - take - all ( wta ) competitive module , implying that macrocolumnar codes consist of 70 active l2/3 cells , assuming 70 minicolumns per macrocolumn . i describe an algorithm for activating these codes during both learning and retrievals , which causes more similar inputs to map to more highly intersecting codes , a property which yields ultra - fast ( immediate , first - shot ) storage and retrieval . the algorithm achieves this by adding an amount of randomness ( noise ) into the code selection process , which is inversely proportional to an input 's familiarity . i propose a possible mapping of the algorithm onto cortical circuitry , and adduce evidence for a neuromodulatory implementation of this familiarity - contingent noise mechanism . the model is distinguished from other recent columnar cortical circuit models in proposing a generic minicolumnar function in which a group of cells within the minicolumn , the l2/3 pyramidals , compete ( wta ) to be part of the sparse distributed macrocolumnar code .

Introduction Results: Model Description Model dynamics: the code selection algorithm Prospective mapping to cortical circuitry Support for neuromodulator-based implementation of familiarity-contingent noise Discussion Supplementary Material Conflict of Interest Statement

obesity has been declared a global epidemic by world health organization ( who ) which has not only crossed geographical boundaries but has spread across all ages . rising prevalence of obesity among children and adolescents and the fact that two - third of childhood obesity persists into adulthood , is increasingly contributing to the escalating pool of this noncommunicable disease . both developed and developing countries have witnessed a steep rise in the prevalence of overweight and obesity among children and adolescents . the prevalence of overweight and obesity has shown increasing trends in india also . more so , the prevalence reported among children and adolescents of some metro cities in india are comparable to that in some developed countries westernization of culture , rapid mushrooming of fast food joints , lack of open spaces for physical activity , and increasing sedentary pursuits in the metro cities are some of the reasons implicated for increased overweight and obesity . are the nutritional changes in small town school children following the same pattern of larger cities ? keeping these research questions in mind , a study was undertaken among the school - going adolescents of aligarh , a small town located in the central india , about 132 km from new delhi , with the following objectives : ( 1 ) to study the prevalence of overweight and obesity among school - going adolescents of aligarh and ( 2 ) to study the sociodemographic and behavioral correlates of the same . part of this development includes opening up of fast food chains , increasing social norm of eating out , more access to internet , video games and television ( tv ) viewing and school children of affluent families having more spending money . although in large sections of the population the age - old customs of eating home food still persists , multinational companies are luring the young to new eating habits . a cross - sectional study was conducted from august 2009 to july 2010 , in two affluent ( having tuition fees more than rs . 10,000/annum ) and two nonaffluent schools ( having tuition fees < rs . 10,000/annum ) in aligarh . taking estimated prevalence of overweight as 3.23% , alpha error of 5% , 2% absolute allowable error and 10% nonresponse rate , sample size calculated was 321 and rounded off to 330 . thus , 330 adolescents were covered in both types of schools ( affluent and nonaffluent group ) , making the total sample size 660 . purposive selection of two affluent and two nonaffluent schools was done to allow for practical feasibility . probability proportionate to size of the population technique was used and systematic random sampling done . apparently healthy school children of v x standard , who had completed 10 years of age on the date of interview and were not more than 16 years of age ( as per school records ) were interviewed after taking informed consent from the school authorities and the parents . children having any chronic illness , severe malnutrition , endocrinal problems , physical , and mental defects , those with apparent obesity - induced or associated with any syndrome and those found to be smokers ( defined as any amount of smoking or tobacco chewing at any time during past 6 months ) and those not cooperating for anthropometric measurements were excluded . a predesigned and pretested questionnaire was used to collect data for sociodemographic and behavioral factors . information regarding parent 's education and occupation and family history of obesity were collected from the child 's parents . deficient , adequate , and excess calorie intakes per day were defined as per the total calorie requirements of adolescents , age and sex wise , as recommended by indian council of medical research . a pretested food frequency questionnaire was used to assess the frequency of fruit and fast food intake during the past 1 month . fast foods were defined as the foods sold in a restaurant or store which are rapidly prepared and quickly served in a packaged form for take away and included burgers , pizzas , fries , patties , nuggets , and indian foods such as pakora , samosa , and namkeen . students were interviewed about duration of watching tv and time spent in other sedentary activities per day during the past 1 month , which were then converted into categorized variables . total physical activity level ( pal ) of the adolescents and the total sedentary time per day was assessed using global physical activity questionnaire . anthropometric measurements of weight ( to the nearest 0.1 kg ) and standing height ( to the nearest 0.1 cm ) were taken according to standard methodology . body mass index ( bmi ) was calculated as the ratio of body weight to body height squared expressed as kg / m . nutritional status was defined using bmi for age and sex percentiles given by who growth reference 2007 . for the purpose of studying determinants of overweight and obesity , all the students were grouped into ( a ) overweight ( including obese ) and ( b ) nonoverweight / nonobese . the strength of association of determinants of overweight ( including obesity ) variables having significant association were subjected to stepwise multiple logistic regression model to determine the significant independent risk factors of overweight and obesity . data analysis was done using ibm spss version 20 and p < 0.05 was considered as statistically significant . the age group of 1013 years included 49.1% of adolescents and 50.9% were in the > 1316 years age group . the nutritional status of the study population according to bmi has been shown in table 1 . nutritional status of the study population with respect to sex and type of school the overall prevalence of overweight and obesity among school - going adolescents was found to be 9.8% and 4.8% , respectively [ table 1 ] . although a higher prevalence of overweight and obesity was found among boys ( 11.3% overweight and 5.5% obesity ) as compared to girls ( 7.9% overweight and 3.9% obesity ) , the difference was not statistically significant . the nutritional status was found to differ significantly ( = 99.593 , df = 3 , p < 0.05 ) between the affluent and nonaffluent group as shown in table 1 . in the nonaffluent schools , the proportion of underweight adolescents was significantly higher than in affluent schools . furthermore , in the affluent schools , the proportion of overweight ( 14.8% ) and obese ( 8.2% ) adolescents were significantly higher compared to nonaffluent schools . looking at the two ends of the spectrum , proportion of over - nutrition in affluent schools ( 14.8% overweight and 8.2% obesity ) was much higher than under - nutrition ( 13.6% ) . the sociodemographic profile of the study population and various behavioral factors were studied according to type of school , by applying chi - square , and found to differ significantly between the affluent and nonaffluent group [ tables 2 and 3 , respectively ] . ninety percent of the adolescents of nonaffluent group were having a large family size as compared to about three - fourth adolescents in affluent group . significantly higher proportions of adolescents from affluent group had higher paternal and maternal education . more than 55% of the affluent adolescents had fathers with business as their occupation as compared to 40% in case of adolescents of nonaffluent group . parental history of obesity was also found to be significantly higher among the adolescents of affluent group . vegetarian diet , use of ghee and vanaspati , excess total calories intake , eating out at least once a week and fast food intake 5 times or more per week was found to be significantly higher among the adolescents of affluent group than the nonaffluent group . pal was found to be high among only 15.8% of affluent group as compared to 23% among the nonaffluent group adolescents ( p < 0.05 ) . significantly higher proportions of affluent adolescents were found to have more total sedentary time per day and tv viewing as compared to nonaffluent adolescents . on multiple logistic regression analysis , belonging to affluent group , mother 's education more than or equal to graduate , parental history of obesity , frequent fast food intake , and tv viewing more than 2 h / day were found to be the independent risk factors for overweight and obesity [ table 4 ] . sociodemographic profile of the study subjects association between behavioral factors and type of school risk factors for overweight ( including obesity ) using stepwise logistic regression analysis the prevalence of overweight and obesity among the school - going adolescents of aligarh was found to be almost as high as reported in larger cities of the country . the double burden of nutritional disease faced by the asian countries is also the result of this transition . this double burden of nutritional disorders is also evident in this study , with the prevalence of overweight ( including obesity ) being 14.7% ( 97 out of 660 ) while about 30% of the adolescents were underweight . rapid urbanization has created an obesogenic environment by promoting motorized transport , unsafe roads and traffic , eating up open spaces and playgrounds on one hand ; and on another by providing more opportunities for sedentary leisure pursuits and fast food consumption outlets . this has been reported to be the cause of rising trend of obesity in the larger cities of india , especially the affluent section of society . interestingly , even smaller but fast developing cities are also witnessing the problem of overweight and obesity , as shown by this study . the obesogenic environment of large metro cities is being duplicated in these cities , and unless timely action is taken to address these changes , the problem of overweight and obesity may escalate uncontrollably . in this study , it was found that adolescents of affluent schools were 2.4 times more at risk of having overweight and obesity . this trend of increased overweight and obesity among affluent section has been reported by many other researchers too . this may be explained by the fact that affluent group goes hand - in - hand with more spending money and more accessibility to fast foods , motorized transport , and sedentary pursuits such as computer and video games . the affluent group in this study had significantly higher use of ghee , eating out , fast food intake , tv viewing , and time spent in sedentary activities as compared to the nonaffluent group . a higher maternal education level was found to increase 3.1 times the odds of having overweight and obesity among school - going adolescents . it is expected that mothers who are educated should be planning better meals for their children but apparently they are not . this emphasizes the need for enriching and reinforcing individual awareness at family and community level . educating parents of obese children interestingly , working status of mothers was not found to be a risk factor for overweight . parental obesity has been implicated as a risk factor for overweight and obesity among children and adolescents by many authors and was found to be an independent risk factor in this study too . family history of obesity in both the parents increased the odds of overweight and obesity by 6.7 times . parental obesity may increase the risk of obesity through genetic mechanisms or by shared familial characteristics in the environment such as food preferences . the study has found fast - food intake to be a significant risk factor of overweight and obesity , and the risk increased with increased frequency of intake . fast food typically incorporates all of the potentially adverse dietary factors , including saturated and trans fat , high glycemic index , high energy density , and increasingly , large portion size . another indian study has also reported the prevalence of overweight to be higher among those adolescents who were fond of junk foods . the authors have found in their study that the children from private schools consumed more of fast food items and carbonated drinks due to easy availability in the school canteen . fast food intake was found to be higher in affluent adolescents in this study also . the association between fast food consumption and obesity clearly indicates the need for improvements in family and school food environments . tv viewing > 2 h daily was found to increase the odds of overweight and obesity among adolescents by 2.8 times . furthermore , tv advertising could adversely affect dietary patterns at other times throughout the day . a randomized controlled trial has shown that reducing tv , videotape , and video game use may be a promising , population - based approach to help prevent childhood obesity . on univariate analysis , low pal was found to increase the risk of overweight and obesity by 2.6 times ( ci 1.25.4 , p < 0.05 ) , but no independent risk was found on multivariate analysis . in spite of proven benefits , levels of physical activity have been decreasing among urban children and adolescents . in this study , high pal was found to be significantly ( p < 0.5 ) lower among affluent adolescents ( 15.8% ) than among the nonaffluent adolescents ( 23.0% ) . it can be concluded from this study that overweight and obesity among school - going adolescents is a crisis facing even smaller cities in india , and action to control it must begin now . given the current trends in pediatric overweight and obesity , it is very crucial that preventive strategies should be implemented through schools and community - based programs involving both education and intervention . prevention starting in early childhood ( life course approach ) is a critical area of work to prevent obesity . limitations of the study include a purposive selection of schools and use of 24 h recall for assessment of dietary intake per day . because most individuals diets vary greatly from day to day , data from a single 24 h recall might fail to characterize an individual 's usual diet . as the findings of a school - based study like this can not be generalized to the whole population , a larger study conducted in schools as well as the general adolescent population can provide more conclusive results about overweight and obesity and their risk factors .

introduction : there has been an increasing secular trend in the prevalence of overweight and obesity in developing countries . the prevalence reported among children and adolescents of some metro cities in india are comparable to that in some developed countries . westernization of culture , rapid mushrooming of fast food joints , lack of physical activity , and increasing sedentary pursuits in the metro cities are some of the reasons implicated for this . the nutritional changes in small town school children might be following the same pattern of larger cities.aims and objectives : to study the prevalence of overweight and obesity among school - going adolescents of aligarh and to study the sociodemographic and behavioral correlates of the same.materials and methods : a cross - sectional study done in two affluent and two nonaffluent schools in aligarh , taking 330 adolescents from each group ( total-660 ) . study tools included a predesigned and pretested questionnaire , global physical activity questionnaire , and anthropometric measurement . overweight and obesity were defined based on world health organization 2007 growth reference . chi - square test and multiple logistic regression analysis were done.results:prevalence of overweight and obesity was 9.8% and 4.8% among school - going adolescents . the difference in prevalence of overweight and obesity among affluent schools ( 14.8% and 8.2% ) and nonaffluent schools ( 4.8% and 1.5% ) was significant . risk factors for overweight and obesity were affluence , higher maternal education , parental history of obesity , frequent fast food intake , and television ( tv ) viewing more than 2 h / day.conclusion : overweight and obesity among school - going adolescents is a crisis facing even smaller cities in india . behavior change communication should be focused to adolescents , especially of the affluent section , toward restricting fast food intake , and tv viewing .

Introduction Materials and Methods Results Discussions and Conclusion Financial support and sponsorship Conflicts of interest

cytomegalovirus ( cmv ) , part of herpesviridae genus , is a common virus , with positive serology found in more than two - thirds of the population . however , the virus remains latent in immunocompetent individuals , while reactivation may occur in the setting of immunosuppression . cmv is known to be opportunistic in immunocompromised individuals with hiv infection , organ transplantation , immunosuppressive chemotherapy , and corticosteroid therapy . in immunocompromised patient , cmv infections can have an effect on the retina , respiratory system , central nervous system and gastrointestinal ( gi ) tract . however , over the past decade , there have been emerging cases of severe cmv infections in immunocompetent individuals , with the gi tract found to be the most frequently affected site . in both immunocompromised and immunocompetent individuals , the majority of cmv enteritis cases have been reported in the ileum , including severe complications leading to perforation and ischemia , , . presented is a case report of cmv duodenitis that manifested with life - threatening hemorrhage in an immunocompetent patient . past medical history included alcohol abuse and hypertension , treated with hydrochlorothiazide . upon admission , the patient was found to have methicillin - sensitive staphylococcus aureus ( mssa ) bacteremia with aortic valvular endocarditis and disseminated septic emboli . investigations revealed wide spread infection , including mssa meningitis , c6 - 7 osteomyelitis , and spinal and sternoclavicular joint abscesses . multiple septic emboli infarcts were identified in the brain , liver , spleen and kidneys . the patient ultimately required an aortic valve replacement . while in hospital , the patient developed significant upper gi bleeding , requiring aggressive blood transfusions . general surgery was initially consulted , but less - invasive therapies were favored at the time due to the patient s severe comorbidities . the duodenal ulcers were found to be actively bleeding on five subsequent endoscopies , with attempts to halt the bleeding through epinephrine injection , bicap cauterization , endoclipping of vessels , hemospray with procoagulant , and argon plasma coagulation . ir embolization of the gastroduodenal artery and multiple branches of the superior and inferior pancreaticoduodenal arteries also failed to control bleeding ( fig . 1 , fig 3 ) . the patient continued to hemorrhage , requiring daily transfusions to maintain hemodynamic stability , totaling more than 95 units of packed red cells during the admission in the intensive care unit . the last endoscopy revealed a generalized mucosal bleed throughout the duodenum . with no further options available within gi or ir s scopes of practice , duodenal resection , which included a whipple procedure , was recommended as treatment for the unrelenting duodenal hemorrhage . however , given the patient 's critical condition and ongoing hemorrhage , it was felt that the patient would be at high risk ( > 30% ) for pancreaticojejunostomy anastomotic leak and significant mortality . therefore , duodenal resection with total pancreatectomy and splenectomy was performed to control the hemorrhage and remove the risk of pancreaticojejunostomy leak . multiple aberrant blood vessels extending into the duodenum were successfully controlled at the time of surgery . the patient was critically ill throughout the procedure , and was transferred to the icu after the resection of the duodenum and pancreas . the patient returned to the operating room in stages to complete the gastrojejunostomy and hepaticojejunostomy . gross examination of the resected specimen revealed a flattened , congested , and focally ulcerated duodenal mucosa . histologic sections from an ulcer revealed viral cytopathic changes in keeping with cmv ( fig . the surrounding surface duodenal mucosa had extensive autolysis ; no vasculitis or intravascular thrombi were identified . notably , ductal epithelial cells had viral cytopathic changes , which were also in keeping with cmv ( fig . immunohistochemical stains for cmv were positive in both the duodenum and pancreas ( see insets of figs . post - duodenal resection , the patient remained hemodynamically stable , requiring no additional blood transfusions . infectious disease initiated intravenous ganciclovir , 5 mg / kg twice daily then transitioned to oral valganciclovir 900 mg bid once tolerating an oral diet for a total course of three weeks . while on antiviral medications , the completed blood count and creatinine were closely monitored for evidence of pancytopenia and renal dysfunction . cmv infections commonly occur in the gi tract , while localized duodenal infection is very rare . a 2011 study of cmv infection in the upper gi tract , found the stomach to be the most common site of involvement and only one out of thirty cases involved the duodenum . literature review identified four case reports of cmv duodenitis , , , , where all four cases involved immunocompromised patients . presented here is an atypical case of cmv duodenitis causing life - threatening hemorrhage in an immunocompetent individual , with no history of immunosuppressive treatments or infections . however , this patient did present with critical illness from his disseminated mssa bacteremia and infective endocarditis , which could have caused a transient depression in immunity . icu admission , use of antibiotics , and use of antacids including h2 blockers and ppis , are found to be risk factors for cmv reactivation in immunocompetent patients . a recent review of reactivation of cmv infection in immunocompetent critically - ill patients found that cmv colitis was the most prevalent manifestation , carrying a 71% in - hospital mortality rate despite specific treatment with ganciclovir . although severe gi cmv is uncommon in immunocompetent hosts , there can be a significant mortality rate associated and thus cmv reactivation should be considered in the differential diagnosis of uncontrolled gi bleeding , especially in the setting of a critically - ill patient . the diagnostic gold standard for cmv infection is histopathological examination of endoscopic biopsy or surgical specimen . hematoxylin - eosin stains typically show intranuclear owl - eye or cowdry type a inclusion bodies in stromal and endothelial cells , which are hypertrophic cells containing eosinophilic intranuclear viral inclusions . serologic detection of cmv igm and igg are often not helpful in identifying active disease but may determine recent or past exposure . virologic testing options include cmv dna pcr and cmv blood antigenemia assays . however , it s not uncommon to have isolated gastrointestinal cmv disease without detectable viremia , as in the case of this patient . therefore , the roles of serologic and virologic testing appears to be limited in the diagnosis of gi - restricted cmv disease . first - line treatment for gastrointestinal cmv disease is intravenous ganciclovir 5 mg / kg bid or oral valganciclovir 900 mg bid . there is significant toxicity with ganciclovir , including headaches , transaminitis , fever , rash , and myelosuppression in the form of pancytopenia . an alternative is foscarnet , which can be used as initial treatment or in ganciclovir failure . the role of treatment is unclear in immunocompetent hosts as some will resolve disease without any treatment . there are limited data on duration of therapy for immunocompetent hosts , but studies have documented response in two to three weeks , . unfortunately , gastrointestinal cmv disease is not always readily diagnosed , especially in an immunocompetent patient as suspicion may be low . in the case of cmv duodenitis , there does appear to be a significant potential for mortality . here we presented an immunocompetent patient with cmv duodenitis that manifested with ongoing hemorrhage , failing multiple attempts at non - surgical treatments , and ultimately requiring surgical intervention . this is the first known case report of life - threatening hemorrhage from cmv duodenitis managed successfully with surgery . among the four cmv duodenitis case reports found during literature review , three manifested with life - threatening bleeding , only one patient survived , , , . in the surviving case , cmv was identified emergently on histopathologic examination of endoscopic biopsy . the patient was started on ganciclovir immediately and stabilized after 4 days of therapy . interestingly , acute necrotizing pancreatitis secondary to arterial embolizations , was found in our patient . this likely exacerbated the duodenal bleed and would have lead to further complications if surgical intervention was delayed . gi cmv infections should be on the differential diagnosis of immunocompetent patients presenting with recurrent gi bleeding , especially in critically ill patients due to transiently suppressed immunity . cmv duodenitis has significant potential to be life - threatening . if failing noninvasive treatments , surgical intervention may be indicated . written informed consent was obtained from the patient for publication of this case report and the accompanying images . a copy of the written consent is available for review by the editor - in - chief of this journal on request . ( 1 ) lucy shen : drafting of the article , critical revision of the article for important intellectual and clinical content ; ( 2 ) david youssef : drafting of the article , critical revision of the article for important intellectual and clinical content ; ( 3 ) suzan abu - abed : image creation , critical revision of the article for important intellectual and clinical content ; ( 4 ) sangita k. malhotra : critical revision of the article for important intellectual and clinical content ; ( 5 ) kenneth atkinson : critical revision of the article for important intellectual and clinical content ; ( 6 ) elena vikis : critical revision of the article for important intellectual and clinical content ; ( 7 ) george melich : critical revision of the article for important intellectual and clinical content , final approval of the version to be submitted ; ( 8) shawn mackenzie : drafting of the article , critical revision of the article for important intellectual and clinical content , final approval of the version to be submitted .

highlightsgastrointestinal cytomegalovirus infections can occur in immunocompetent patients.diagnosis relies on histopathologic examination of endoscopic biopsy specimen.early recognition and antiviral treatment are important to patient outcome.cytomegalovirus duodenitis has significant potential to be life - threatening .

Introduction Presentation of case Outcome and follow-up Discussion Conclusion Conflicts of interest Funding sources Ethical approval Consent Author contributions Registration of research studies Guarantor

enteropathy - associated t - cell lymphoma ( eatl ) is a rare intestinal tumor , accounting for less than 5% of gastrointestinal lymphoma . it is known to arise from t lymphocytes that reside in the intraepithelial space of the intestines and is classified into two types.1 the classic eatl , also known as eatl type i , is predominantly found in western countries and is strongly associated with refractory celiac disease . in this type , tumor cells are large and pleomorphic and positive for cd3 and cd7 in immunohistochemistry staining , but negative for cd4 , cd8 , or cd56 . the other type , namely eatl type ii , comprises 10% to 20% of all eatl cases . eatl type ii is mainly composed of small to medium - sized cells , which show positivity for cd3 , cd7 , cd8 , and cd56 . it develops sporadically and is independent of celiac disease.2 eatl is most frequently found in the small intestine , especially the proximal jejunum , followed by stomach , colon , and rectum . it is clinically associated with symptoms of mal - absorption and is typically diagnosed upon laparotomy , as the first presenting signs are usually spontaneous intestinal perforation and/or obstruction.3 currently , only few published reports are available regarding the endoscopic findings of eatl type ii distinct from classic eatl . here five cases of eatl type ii were diagnosed from january 2009 to september 2012 at samsung medical center . of the five cases , four were diagnosed endoscopically and the other one surgically . the patients ( three men and one woman ) ranged in age from 48 to 67 years ( median , 52.5 years ) . two patients presented with chronic diarrhea and the other two with abdominal pain . both the small and large intestines were involved in two patients while the disease was limited to the small intestine in the other two patients ( table 1 ) . a 67-year - old man was admitted for evaluation of abdominal mass , night sweating and weight loss over the period of 6 months . computed tomography ( ct ) scanning and positron emission tomography ( pet ) showed a 6-cm - sized homogeneous mass on the terminal ileum and ascending colon . 1a ) and a 1.5-cm - sized pinkish flesh - like , flat thickened lesion on the proximal descending colon ( fig . biopsy specimens from each lesion showed diffuse infiltration of small- to medium - sized atypical lymphoid cells with cd4 , cd8 + and cd56 + immunophenotypes . despite conventional chemotherapy , leptomeningeal seeding was confirmed after the fourth cycle of cyclophosphamide , doxorubicin , vincristine , and prednisone ( chop ) . a 50-year - old man was admitted with complaints of abdominal pain and low grade fever for 20 days . colonoscopy revealed about 3-cm - sized discrete ulcerative lesion with hyperemic edematous mucosa on the proximal ascending colon ( fig . biopsy specimens from the lesion showed diffuse infiltration of small- to medium - sized atypical lymphoid cells with cd4 , cd8 + , cd56 + , and t - cell intracellular antigen 1 ( tia-1)+ immunophenotypes ( fig . bowel wall thickening on the distal ileum extended 15 cm in length , its severe adhesion to surrounding structures forming a mass . successful complete remission was achieved after six cycles of rituximab , cyclophosphamide , doxorubicin , vincristine , and prednisone ( r - chop ) . double - balloon - enteroscopy ( dbe ) revealed diffuse fine granularity with circumferential shallow ulceration in the mid - ileum ( fig . he underwent autologous peripheral blood stem cell transplantation ( apbsct ) and has been free of disease for 11 months . a 48-year - old male was admitted with complaints of chronic diarrhea and weight loss of 14 kg over the course of 1 year . although the initial esophagogastroduodenoscopy ( egd ) and colonoscopy were unremarkable , ct scan revealed the focal enhancing lesion in small bowel . dbe via antegrade approaches revealed diffuse mucosal thickening and nodularity with multiple shallow semicircular ulcerations from mid to distal jejunum ( fig . pathologic specimens from the lesions demonstrated diffuse infiltration of small- to medium - sized atypical lymphoid cells . after the diagnosis , the patient refused further treatment and died at 14 months after diagnosis . a 55-year - old woman was referred to gastroenterology department because of chronic diarrhea , abdominal pain , and weight loss , which persisted for 1 year . although the initial egd was unremarkable , abdomen and pelvic ct revealed luminal narrowing in the 3rd portion of duodenum . she was admitted for evaluation and during admission , obstructive symptoms , such as vomiting , developed . re - evaluation with egd showed luminal obstruction due to an encircling mass at the proximal jejunum . moreover , without definite 2-deoxy-2-[fluorine-18]fluoro - d - glucose uptake , pet suggested inflammatory condition of the lesion rather than malignancy . during the surgery , there was diffuse swelling and luminal narrowing from the ligament of treitz to proximal jejunem and the involved segment was 15 cm in length . because surgeon judged to have no resectability , gastrojejunostomy without duodenectomy was performed to relieve obstructive symptoms after the biopsy of enlarged lymph node . biopsy specimens from enlarged lymph node revealed only reactive change with no evidence of malignancy . only 2 weeks after discharge , she was re - admitted for abdominal pain , nausea , and poor oral intake . a subsequent egd through the gastrojejunostomy site revealed shallow ulcerations which encircled the diffusely swollen lumen of the afferent loop of the jejunum ( fig . edematous mucosa with innumerable fine granular elevations , described as velvety or sand - like mucosa , caused obstruction of the , mid to distal jejunum ( fig . biopsy specimens from these lesions revealed diffuse infiltration of small- to medium - sized atypical lymphoid cells with cd4 , cd8 + , cd56 + , and tia-1 positivity ( fig . tissue dna analysis demonstrated monoclonal t - cell receptor rearrangement . based on these findings after ten months of therapy , she underwent apbsct because of disease progression but during the course , she died of sepsis . a 67-year - old man was admitted for evaluation of abdominal mass , night sweating and weight loss over the period of 6 months . computed tomography ( ct ) scanning and positron emission tomography ( pet ) showed a 6-cm - sized homogeneous mass on the terminal ileum and ascending colon . 1a ) and a 1.5-cm - sized pinkish flesh - like , flat thickened lesion on the proximal descending colon ( fig . biopsy specimens from each lesion showed diffuse infiltration of small- to medium - sized atypical lymphoid cells with cd4 , cd8 + and cd56 + immunophenotypes . despite conventional chemotherapy , leptomeningeal seeding was confirmed after the fourth cycle of cyclophosphamide , doxorubicin , vincristine , and prednisone ( chop ) . a 50-year - old man was admitted with complaints of abdominal pain and low grade fever for 20 days . colonoscopy revealed about 3-cm - sized discrete ulcerative lesion with hyperemic edematous mucosa on the proximal ascending colon ( fig . biopsy specimens from the lesion showed diffuse infiltration of small- to medium - sized atypical lymphoid cells with cd4 , cd8 + , cd56 + , and t - cell intracellular antigen 1 ( tia-1)+ immunophenotypes ( fig . bowel wall thickening on the distal ileum extended 15 cm in length , its severe adhesion to surrounding structures forming a mass . successful complete remission was achieved after six cycles of rituximab , cyclophosphamide , doxorubicin , vincristine , and prednisone ( r - chop ) . double - balloon - enteroscopy ( dbe ) revealed diffuse fine granularity with circumferential shallow ulceration in the mid - ileum ( fig . he underwent autologous peripheral blood stem cell transplantation ( apbsct ) and has been free of disease for 11 months . a 48-year - old male was admitted with complaints of chronic diarrhea and weight loss of 14 kg over the course of 1 year . although the initial esophagogastroduodenoscopy ( egd ) and colonoscopy were unremarkable , ct scan revealed the focal enhancing lesion in small bowel . dbe via antegrade approaches revealed diffuse mucosal thickening and nodularity with multiple shallow semicircular ulcerations from mid to distal jejunum ( fig . pathologic specimens from the lesions demonstrated diffuse infiltration of small- to medium - sized atypical lymphoid cells . after the diagnosis , the patient refused further treatment and died at 14 months after diagnosis . a 55-year - old woman was referred to gastroenterology department because of chronic diarrhea , abdominal pain , and weight loss , which persisted for 1 year . although the initial egd was unremarkable , abdomen and pelvic ct revealed luminal narrowing in the 3rd portion of duodenum . she was admitted for evaluation and during admission , obstructive symptoms , such as vomiting , developed . re - evaluation with egd showed luminal obstruction due to an encircling mass at the proximal jejunum . moreover , without definite 2-deoxy-2-[fluorine-18]fluoro - d - glucose uptake , pet suggested inflammatory condition of the lesion rather than malignancy . during the surgery , there was diffuse swelling and luminal narrowing from the ligament of treitz to proximal jejunem and the involved segment was 15 cm in length . because surgeon judged to have no resectability , gastrojejunostomy without duodenectomy was performed to relieve obstructive symptoms after the biopsy of enlarged lymph node . biopsy specimens from enlarged lymph node revealed only reactive change with no evidence of malignancy . only 2 weeks after discharge , she was re - admitted for abdominal pain , nausea , and poor oral intake . a subsequent egd through the gastrojejunostomy site revealed shallow ulcerations which encircled the diffusely swollen lumen of the afferent loop of the jejunum ( fig . edematous mucosa with innumerable fine granular elevations , described as velvety or sand - like mucosa , caused obstruction of the , mid to distal jejunum ( fig . biopsy specimens from these lesions revealed diffuse infiltration of small- to medium - sized atypical lymphoid cells with cd4 , cd8 + , cd56 + , and tia-1 positivity ( fig . after ten months of therapy , she underwent apbsct because of disease progression but during the course , she died of sepsis . eatl is a rare disease in asia and only a few case series have been reported.2,4,5 the classic eatl is known to be strongly associated with celiac disease . tumor cells are large and pleomorphic , which are positive for cd3 and cd7 , but negative for cd4 , cd8 , or cd56 . eatl type ii is mainly composed of small- to medium - sized monomorphic cells , showing immunophenotypic positivity for cd3 , cd7 , cd8 , and cd56 . it develops sporadically and is independent of celiac disease.6 in our cases , cd3 , cd8 , and cd56 were positive in all patients , while none of them had a history of celiac disease . these results are consistent with another study conducted in taiwan.7 the typical endoscopic features of eatl have scarcely been reported . recently , there have been a few literatures of eatl type ii findings based on double - balloon endoscopy and capsule endoscopy . they reported that diffuse mucosal thickening and edema with multiple shallow ulcerations , and a nodular or mosaic mucosal pattern were characteristics of the disease.810 in our cases , small bowel was almost always involved and colonic involvement was found in half the patients . endoscopy of the small intestine revealed multiple circular or semicircular shallow ulcerations covered with whitish mucus - like exudate . when the ulcers were encircling the lumen of the small bowel , it was often associated with obstruction . the surrounding mucosa was edematous and thickened by countless fine granularities , showing so - called mosaic mucosal pattern or velvety mucosa these endoscopic features of small bowel may be specific to the disease and thus could be useful for the detection of eatl type ii . on the contrary , endoscopy of the colon revealed discrete ulcer with edematous margin or mucosal thickening , sometimes combined with central ulcer . these endoscopic findings of colon are nonspecific to distinguish eatl type ii from other disease . therefore , it may be difficult to diagnose eatl type ii only by endoscopic findings of the colon without clinical suspicion . patients treated with anthracycline - based chemotherapy regimens had better survival rates than those treated with other forms of therapy ( including surgery ) or no therapy at all . however , long - term survival is known to be poor even with treatment . according to a retrospective study of 31 patients , the 1- and 5-year survival rates were 38.7% and 19.7% , respectively.3 another recent study showed that patients treated with high - dose chemotherapy followed by apbsct had a significantly improved survival . it has been estimated that approximately 70% of all eatl patients may benefit from this therapy.11 in summary , we report four cases of eatl type ii diagnosed by endoscopy . the endoscopic findings are the mosaic mucosal pattern and diffuse thickening of the mucosa with circumferential shallow ulcerations causing luminal narrowing or obstruction in the small bowel and a discrete ulcer with diffuse mucosal thickening in the colon . eatl mainly involves the small bowel causing diagnostic delay due to the difficulty of access , especially if the symptoms were mild . however , modalities for evaluating the small bowel , such as enteroscopy and capsule endoscopy , have become more developed . hence , certain typical endoscopic features may give a clue to both clinicians and pathologists in diagnosing eatl in patients with unknown causes for abdominal pain , diarrhea , or bowel obstruction . high - dose chemotherapy followed by autologous stem cell transplantation may be a better treatment option for eatl compared to conventional chemotherapy .

enteropathy - associated t - cell lymphoma ( eatl ) is a rare extranodal t - cell lymphoma arising from the intestine . two types of eatl have been reported . in contrast to the classic eatl type i , eatl type ii occurs sporadically , is unrelated to celiac disease , and comprises 10% to 20 % of all eatl cases . a total of five cases of eatl type ii were diagnosed at our clinic from january 2009 to september 2012 . four of the five patients were diagnosed with the help of endoscopy . among the four patients , two of the cases involved both the small and large intestines , whereas in the other two patients , eatl was limited to the small intestine . common endoscopic findings included innumerable fine granularities ( also called mosaic mucosal patterns ) and diffuse thickening of the mucosa with a semicircular shallow ulceration in the lesions of the small bowel . in contrast , the endoscopic findings of the colon were nonspecific and could not distinguish eatl type ii from other diseases . there are only few published reports regarding the representative endoscopic findings of eatl . here , we present the clinical and endoscopic findings of four cases of eatl type ii diagnosed by endoscopy .

INTRODUCTION CASE REPORTS 1. Case 1 2. Case 2 3. Case 3 4. Case 4 DISCUSSION

the international diabetes federation stated that 382 million people worldwide suffered from diabetes in 2013 , and this number is expected to rise to 592 million by 2035 . diabetes resulted in 1.3 million mortalities in 2010 , which was twice as high as that in 1990 . furthermore , diabetes - related complications , such as retinopathy , neuropathy , nephropathy , and cardiovascular and cerebrovascular diseases , are increasing the burden on individuals and healthcare systems . the american diabetes association ( ada ) and european association for the study of diabetes recommend that the management of patients with type 2 diabetes should include glucose control to achieve a hemoglobin a1c ( a1c ) level of 7% , as well as lifestyle changes , including smoking cessation and control of blood pressure ( bp ) and lipid levels . the prevalence of diabetes increased from 8.6% to 11.0% from 2001 to 2013 in a nationally representative sample of koreans aged 30 years , and the prevalence of diabetes is expected to rise to 5.5 million by 2030 , which is 10.9% of the adult population aged 20 years . the prevalence of diabetes has increased particularly in individuals aged 70 years ; the rate of diabetes in this age group was 27.6% in 2013 , which was approximately twice as high as that in 2001 . in addition , the prevalence of diabetes has also increased slightly in younger and middle - aged subjects . the median age of new patients with diabetes decreased by approximately 6 years from 2004 to 2012 . several studies have shown that the onset of type 2 diabetes at a younger age may lead to poorer glycemic control , greater risk of complications , and higher morality compared with an older age of onset [ 9 - 11 ] . according to the diabetes fact sheet of the korean diabetes association ( kda ) , the prevalence of prediabetes , defined as a fasting glucose level of 100 to 125 mg / dl , also increased from 21.5% to 25.0% from 2006 to 2013 . annually , 5% to 10% of those with prediabetes progress to diabetes , and prediabetes also causes concomitant damage to end organs such as the eyes , kidneys , blood vessels , and the heart . considering this situation , effective and diverse strategies to prevent diabetes and prediabetes are needed . the ada recommended obesity control to prevent progression from prediabetes to diabetes and to improve glycemic control in type 2 diabetes . in korea , the prevalence of obesity has increased from 29.2% in 2001 to 31.8% in 2013 . in particular , the number of obese patients with diabetes has increased . according to a primary care clinic - based survey , 77% of patients with newly diagnosed diabetes have a body mass index ( bmi ) > 23.0 kg / m . in 2013 , the prevalence of obesity / overweight with diabetes was 71.6% in men and 74.2% in women . the mean bmi of patients with diabetes increased from 21.9 to 24.8 kg / m over nearly two decades . furthermore , an inverse linear relationship was detected between bmi and age at diabetes diagnosis among newly diagnosed patients . the mean bmi decreased from 30.4 kg / m in the youngest age group to 24.4 kg / m in the oldest age group . the diabetes control and complications trial ( dcct ) and the united kingdom prospective diabetes study showed that improving glycemic control , lowering bp and lipid levels , and avoiding smoking help reduce microvascular and macrovascular diseases [ 22 - 27 ] . therefore , guidelines for diabetes care recommend management of lifestyle ( diet , weight control , smoking cessation , and physical activity ) and risk factors ( a1c < 7.0% , bp < 140/90 mmhg , and low density lipoprotein cholesterol [ ldl - c ] < 100 mg / dl ) and regular screening to treat conditions related to diabetes during the early stages . the 2015 kda 's guideline recommended a bp target of < 140/85 mmhg in patients with diabetes . because reduced adherence to regimens results in poor health outcomes , comprehensive management of type 2 diabetes should consider adherence to relevant medications . according to the kda , the medication adherence rate , which is estimated using the medication possession ratio , increased from 12.8% to 44.9% from 2002 to 2013 . the proportion of patients with diabetes treated with antihypertensive medications increased from 56.0% to 62.5% during 2006 to 2013 . approximately 50% of patients with diabetes were being treated with lipid - lowering medications in 2013 , a 1.8-fold increase since 2006 . according to the 2014 korea national health and nutrition examination survey ( knhanes ) study , < 7.0% , 72.8% achieved bp < 140/85 mmhg , and 58.0% achieved ldl - c < 100 mg / dl . only 19.7% of patients with diabetes had good control of all three parameters ( fig . 1 , unpublished data ) . control rates in 2014 improved compared with those from the 2005 health insurance data , in which 40.3% of patients achieved a1c < 7.0% , 58.6% achieved bp < 140/90 mmhg , and 38.3% achieved ldl - c < 100 mg / dl . in particular , the glycemic control rate ( defined as a1c 8.0% ) decreased steadily from 33.6% in 2005 to 25.9% in 2012 to 22.5% in 2014 ( fig . almost half of the male patients with diabetes are still smoking ( fig . 1 , unpublished data ) . the a1c level is considered a clinical marker of diabetes as well as a precise indicator of long - term glycemic control . thus , many studies have translated a1c values into blood glucose levels to increase understanding of the clinical implications of a1c . in korea , kim et al . also suggested an association between the mean blood glucose level measured by the oral glucose tolerance test and a1c , expressed as a linear regression : mean glucose ( mg / dl ) = 49.4 a1c ( % ) 149.6 ( r = 0.54 , p < 0.001 ) . the linear regression equation was fairly dissimilar from that in the a1c derived average glucose study and dcct cohort . diabetes is associated with chronic complications , such as microvascular and macrovascular diseases , and other diseases including dementia and depression . the dcct / edic demonstrated that achieving glycemic control reduces the rate of microvascular complications . previous studies have shown that the duration of diabetes is associated with an increased risk of micro- and macrovascular complications . the prevalence rates of neuropathy , retinopathy , and nephropathy in korea are 33.5% , 20.0% , and 5.5% , respectively , in patients with diabetes . according to the diabetes fact sheet , 1.2% of patients with type 2 diabetes have end - stage renal disease ( esrd ) , and 15.9% have diabetic retinopathy . in particular , the incidence of diabetic nephropathy is increasing rapidly , and it is the most common cause of esrd . the prevalence rates of cardiovascular , cerebrovascular , and peripheral vascular diseases in patients with type 2 diabetes were 5.5% , 5.0% , and 1.1% , respectively , during 2006 to 2009 according to the korean national diabetes program . the 2009 to 2011 health insurance review and assessment database indicated that the prevalence rates of coronary artery , cerebrovascular , and peripheral artery diseases were 14.1% , 8.8% , and 0.3% , respectively , in patients newly diagnosed with type 2 diabetes . the presence of macrovascular complications was higher in patients with type 2 diabetes than in those without ( 295 cases of ischemic stroke , 248 cases of ischemic heart disease , and 41 cases of cerebral hemorrhage/10,000 persons with diabetes ; 62 cases of ischemic stroke , 59 cases of ischemic heart disease , and 17 cases of cerebral hemorrhage/10,000 non - diabetic persons ) . however , only 36.3% and 40.5% of patients received screening for diabetic retinopathy and nephropathy , respectively , in korea . convincing evidence indicates that diabetes is associated with an increased risk of several types of cancers . the presence of cancer - related hospitalization in korea was higher in patients with type 2 diabetes than in those without . specifically , in subjects with type 2 diabetes , the risks of hospitalization events due to stomach , colorectal , liver , pancreatic , and lung cancers were 37.9 , 43 , 48 , 17.6 , and 36/10,000 persons , respectively . the knhanes reported that diabetes is associated with a marked increase in suicidal ideation and suicide attempts . . showed that patients with diabetes had a higher risk of mild cognitive impairment that did those without . according to the diabetes fact sheet , the prevalence of dementia in patients with type 2 diabetes increased from 1.2% to 5.2% during 2006 to 2013 and was higher than in those without diabetes . as the korean population ages and the prevalence of diabetes increases , it will become increasingly crucial to find ways to overcome associated complications through good diabetes management . diabetes self - management education is an important element of care for all those with diabetes and those at risk of developing the disease . however , only 39.4% of patients with diabetes have received comprehensive diabetes self - management education in korea . therefore , a systematic approach to manage diabetes , including self - management education , is needed to prevent or delay complications . more concentrated efforts should be focused on early detection and management of diabetic complications and psychiatric disorders . the government needs to establish a long - term policy to address the growing burden posed by diabetes .

diabetes mellitus is an increasing global health problem . guidelines for diabetic care recommend management of lifestyle and risk factors ( glucose , blood pressure , and cholesterol ) , as well as regular screening for complications associated with treatment of the conditions related to diabetes . the prevalence of diabetes increased from 8.6% to 11.0% from 2001 to 2013 . according to the diabetes fact sheet 2015 , the proportion of patients with diabetes treated with antihypertensive medications increased from 56.0% to 62.5% from 2006 to 2013 , and 49.5% of those with diabetes were being treated with lipid - lowering medications in 2013 , a 1.8-fold increase since 2006 . according to the 2014 korea national health and nutrition examination survey data , 45.6% of patients with diabetes achieved a hemoglobin a1c level of < 7.0% , 72.8% achieved a blood pressure of < 140/85 mmhg , and 58.0% achieved a low density lipoprotein cholesterol level of < 100 mg / dl . only 19.7% of patients with diabetes had good control of all three of these parameters . despite improvements in health promotion efforts , the rates of adherence to medication and risk - factor control are low . therefore , a systematic approach to managing diabetes , including self - management education , is needed to prevent or delay complications . the government needs to establish a long - term policy to address the growing burden of diabetes .

INTRODUCTION PREVALENCE OF DIABETES OBESITY AND DIABETES MANAGING DIABETES DIABETES-RELATED COMPLICATIONS CONCLUSIONS

bladder cancer is the seventh most common malignancy in men and 8 most common malignancy in women . in india , bladder cancer is the fifth most common cancer in men according to delhi based registry with age adjusted incidence rate of 5.8/100,000 person years . it is predominantly a disease of the male population with male to female ratio of 8.6:1 with the median age at presentation of 60 years ( ranges from 18 to 90 years ) . for non - muscle invasive bladder carcinoma ( nmibc ) , transurethral resection of bladder tumor ( turbt ) is the cornerstone of treatment . reasons for such a high recurrence rate for nmibc have been cited as incomplete resection in initial turbt , aggressive tumor biology , implantation of the tumor cells and possibly a field change to start with . the conventional turbt ( ct ) technique involves piecemeal resection of the tumor , which is contrary to the established oncological principles of removing tumor in other parts of the body . unfortunately , there has never been a certain way to provide a complete resection of the visible tumor in the bladder . similarly , it has been observed in one study that almost 81% of the tumors recurred at the site of previous resection , which indirectly suggests that the technique of resecting tumor is not adequate . in view of the high rate of recurrence , perhaps turbt should be modified to provide en - bloc resection of the specimen , based on the established oncological principle of dissecting through normal tissue . these studies on en - bloc tumor removal were attractive in their simplicity , use of existing equipment , clinical safety profile and adequacy of pathology , but they have not commented on the essential outcome , i.e. , recurrence and progression rate . this study was aimed at conceptualizing the technique of sculpting and resecting in form of et and comparing its outcomes in terms of recurrence and progression with the conventional technique of incising and scattering . after seeking an institutional ethics committee approval , a prospective non - randomized interventional study was conducted between september 2007 to june 2011 . end points of the study , i.e. , recurrence and progression rates were compared in two groups . et was carried out by a single surgeon . to minimize the bias toward deliberate attempt by a surgeon who did et to resect tumor completely , all three urologists were senior consultants with more than 10 years of experience in endourology . clinical data on the size ( measured by ultrasonography in 37 patients and contrast enhanced computerized tomogram scan on 33 patients ) and the location of the tumor were recorded . two sided z - test with pooled variance was used to calculate the sample size . with existing recurrence rate of 60% with ct , an estimate of reduction of recurrence rate by 40% gave a sample of 23 patients in each group to achieve 82% power at the significance level of 0.05 . patients presenting for the first time with single tumor on imaging and the tumor size from 2 to 4 cm were included in the study . patients with prior turbt and recurrences , pedunculated tumors , multiple tumors , biopsy specimen with absent detrusor muscles and those with tumor size of more than 4 cm were excluded . tumors less than 2 cm were excluded as the technique would not make a real difference in them . patients were followed - up after an initial turbt with check cystoscopy at 3 months interval for initial 2 years , 6 monthly for next 2 years and then yearly a total of 70 patients were included , 30 had et and 40 had ct . as patients with stage t2 and those with absence of detrusor muscle on the first turbt were excluded , for the final analyses there were 21 and 24 patients in et and ct groups respectively [ graph 1 ] . the usual tungsten loop electrode and 26 fr resectoscope ( storz , germany ) with 30 the angle of the loop electrode was changed manually from 90 to 45 for et as published before [ figure 1 ] . feasibility of en - bloc resection was initially established in tumors of less than 2 cm in six cases before initiating this study . angle of the loop electrode was changed manually from 90 to 45 for en - bloc transurethral resection of bladder tumor normal mucosa around the tumor base was scored by using coagulation current at setting of 60 - 80 w ( valley lab , usa ) . retrograde resection was started in the deep layer of detrusor muscle elevating the tumor off the base with the help of angle of the loop and beak of the resectoscope . free lying tumor which was too large to be taken out through urethra was cut into 2 - 3 pieces in a way that all the layers are there in the piece of the tumor tissue . in a partially filled bladder with minimal inflow , the tumors were divided using a cutting current with the tumor sited over the trigone for the current to pass . once the groove was created , the loop was entangled in the groove and tumor was lifted away from the trigone and then cut against the beak of the resectoscope . use of a nephroscope and grasping forceps was helpful in retrieving the tumor , the largest single piece being a 3 cm tumor in a female . six , weekly doses of intravesical bacillus calmette - guerin ( bcg ) ( oncovac , danish 1331 strain ) was instilled in patients with ta high grade and t1 disease . the compliance rate for bcg at our center is as high as 85% and was similar in both ct and et . histopathological examination was carried out using the 2004 world health organization - international society of urological pathological grading system . blood loss was calculated in terms of fall in hemoglobin levels measured before and a day after turbt . recurrences free survival ( rfs ) and progression - free survival ( pfs ) were calculated using kaplan - meier method and long rank test . two sided z - test with pooled variance was used to calculate the sample size . with existing recurrence rate of 60% with ct , an estimate of reduction of recurrence rate by 40% gave a sample of 23 patients in each group to achieve 82% power at the significance level of 0.05 . patients presenting for the first time with single tumor on imaging and the tumor size from 2 to 4 cm were included in the study . patients with prior turbt and recurrences , pedunculated tumors , multiple tumors , biopsy specimen with absent detrusor muscles and those with tumor size of more than 4 cm were excluded . tumors less than 2 cm were excluded as the technique would not make a real difference in them . patients were followed - up after an initial turbt with check cystoscopy at 3 months interval for initial 2 years , 6 monthly for next 2 years and then yearly . progression was defined as any upgradation of stage or grade . a total of 70 patients were included , 30 had et and 40 had ct . as patients with stage t2 and those with absence of detrusor muscle on the first turbt were excluded , for the final analyses there were 21 and 24 patients in et and ct groups respectively [ graph 1 ] . the usual tungsten loop electrode and 26 fr resectoscope ( storz , germany ) with 30 the angle of the loop electrode was changed manually from 90 to 45 for et as published before [ figure 1 ] . feasibility of en - bloc resection was initially established in tumors of less than 2 cm in six cases before initiating this study . angle of the loop electrode was changed manually from 90 to 45 for en - bloc transurethral resection of bladder tumor normal mucosa around the tumor base was scored by using coagulation current at setting of 60 - 80 w ( valley lab , usa ) . retrograde resection was started in the deep layer of detrusor muscle elevating the tumor off the base with the help of angle of the loop and beak of the resectoscope . free lying tumor which was too large to be taken out through urethra was cut into 2 - 3 pieces in a way that all the layers are there in the piece of the tumor tissue . in a partially filled bladder with minimal inflow , the tumors were divided using a cutting current with the tumor sited over the trigone for the current to pass . once the groove was created , the loop was entangled in the groove and tumor was lifted away from the trigone and then cut against the beak of the resectoscope . use of a nephroscope and grasping forceps was helpful in retrieving the tumor , the largest single piece being a 3 cm tumor in a female . six , weekly doses of intravesical bacillus calmette - guerin ( bcg ) ( oncovac , danish 1331 strain ) was instilled in patients with ta high grade and t1 disease . the compliance rate for bcg at our center is as high as 85% and was similar in both ct and et . histopathological examination was carried out using the 2004 world health organization - international society of urological pathological grading system . blood loss was calculated in terms of fall in hemoglobin levels measured before and a day after turbt . recurrences free survival ( rfs ) and progression - free survival ( pfs ) were calculated using kaplan - meier method and long rank test . two sided z - test with pooled variance was used to calculate the sample size . with existing recurrence rate of 60% with ct , an estimate of reduction of recurrence rate by 40% gave a sample of 23 patients in each group to achieve 82% power at the significance level of 0.05 . patients presenting for the first time with single tumor on imaging and the tumor size from 2 to 4 cm were included in the study . patients with prior turbt and recurrences , pedunculated tumors , multiple tumors , biopsy specimen with absent detrusor muscles and those with tumor size of more than 4 cm were excluded . tumors less than 2 cm were excluded as the technique would not make a real difference in them . patients were followed - up after an initial turbt with check cystoscopy at 3 months interval for initial 2 years , 6 monthly for next 2 years and then yearly . progression was defined as any upgradation of stage or grade . a total of 70 patients were included , 30 had et and 40 had ct . as patients with stage t2 and those with absence of detrusor muscle on the first turbt were excluded , for the final analyses there were 21 and 24 patients in et and ct groups respectively [ graph 1 ] . the usual tungsten loop electrode and 26 fr resectoscope ( storz , germany ) with 30 lens and monopolar cautery was used . the angle of the loop electrode was changed manually from 90 to 45 for et as published before [ figure 1 ] . feasibility of en - bloc resection was initially established in tumors of less than 2 cm in six cases before initiating this study . angle of the loop electrode was changed manually from 90 to 45 for en - bloc transurethral resection of bladder tumor normal mucosa around the tumor base was scored by using coagulation current at setting of 60 - 80 w ( valley lab , usa ) . retrograde resection was started in the deep layer of detrusor muscle elevating the tumor off the base with the help of angle of the loop and beak of the resectoscope . free lying tumor which was too large to be taken out through urethra was cut into 2 - 3 pieces in a way that all the layers are there in the piece of the tumor tissue . in a partially filled bladder with minimal inflow , the tumors were divided using a cutting current with the tumor sited over the trigone for the current to pass . once the groove was created , the loop was entangled in the groove and tumor was lifted away from the trigone and then cut against the beak of the resectoscope . use of a nephroscope and grasping forceps was helpful in retrieving the tumor , the largest single piece being a 3 cm tumor in a female . six , weekly doses of intravesical bacillus calmette - guerin ( bcg ) ( oncovac , danish 1331 strain ) was instilled in patients with ta high grade and t1 disease . the compliance rate for bcg at our center is as high as 85% and was similar in both ct and et . histopathological examination was carried out using the 2004 world health organization - international society of urological pathological grading system . blood loss was calculated in terms of fall in hemoglobin levels measured before and a day after turbt . recurrences free survival ( rfs ) and progression - free survival ( pfs ) were calculated using kaplan - meier method and long rank test . patients who had detrusor muscle invasion or had no detrusor muscle in the first turbt were excluded from the analyses . patients in whom follow - up was not present were also excluded [ graph 1 ] . at the final analysis 21 patients of et the mean age was 52.6 12.2 and 55 13.6 years in et and ct group . median follow - up period was 40 months and 30 months in et and ct groups respectively [ tables 1 and 2 ] . stage , grade and locations of tumor in two groups on initial turbt tumor characteristics and the outcome in two groups of turbt recurrence rate was 28.6% versus 62.5% ( p = 0.03 ) and progression rate was 19% versus 33.3% ( p = 0.32 ) in et versus ct group respectively [ table 2 ] . in the et group , the recurrence in non - lamina invasive nmibc tumors was 16% , where as it was 53% in ct . similarly in lamina invasive tumor , the recurrence rate was 44% and 72% in et and ct group . mean rfs was 45.1 months ( 95% ci : 19.0 - 38 months ) with et and 28.5 months ( 95% ci : 35.4 - 54.7 months ) in ct with p value of 0.018 [ figure 2 and table 2 ] . regarding the site of tumor recurrence , only 1 ( 16% ) patient had recurrence at the same site in et group while 6 ( 40% ) patients had recurrence at the same site with ct [ table 3 ] . recurrence free survival site of recurrences in two groups four patients in en - bloc and eight patients in conventional group had disease progression ( 19% vs. 33.3% , p = 0.32 ) . mean pfs in et and ct group was 48.32 months ( 95% ci : 35.5 - 53.0 months ) and 44.26 months ( 95% ci : 39.0 - 57.5 months ) with p value of 0.46 [ figure 3 and table 2 ] . in et group , three patients had progressed without prior recurrence ; one had progressed after one recurrence . in ct group , six patients had progressed on first recurrence ; one had progressed after one recurrence and one patient had progressed after two recurrences . progression free survival turbt is a procedure with a varied outcome in terms of adequacy of resection , recurrence and progression . there are a few surrogate markers to assess adequate resection such as presence of detrusor muscle in the specimen and the rate of subsequent recurrence . successful management of bladder tumors ( particularly non - muscle - invasive tumors ) , relies on adequate initial resection and accurate histological diagnosis . an ideal turbt would mean complete resection of the visible tumor , resection of the surrounding healthy looking mucosa for up to 1 cm and then the removal of detrusor muscle . herr and donat described three ways to measure the quality of a good turbt , i.e. , complete resection , presence of deep muscle in the specimen and the rate of recurrence at the site of previous turbt . they also suggested classifying tumor resection as r0 ; microscopic negative margin , r1 with microscopic positive margin and r2 that is macroscopic positive margin . this kind of assessment is not practical in ct , but could be possible in en - bloc resection , where we can have a piece of tumor tissue , which has all three layers , i.e. , urothelium , lamina propria and detrusor muscle in contiguity . the outer - most surface of the detrusor muscle in the resected specimen could then be inked to assess margin status and thereby discerning a true perspective of level of resection , i.e. , r0-r1 [ figure 4 ] . en - bloc resection provides a tissue piece of the bladder with all the layers in contiguity to assess the t stage and margin status . in inset , a 3 cm tumor removed en - bloc inadequacy of ct is not only judged by absence of detrusor muscle in an initial specimen , but also by the rate of recurrence . recurrence is seen in 50 - 70% of non - muscle invasive bladder cancer , mostly during the 1 year . these may be due to incomplete resection , cell implantation or the tumor biology itself . incomplete resection seems to be the most important reason for the recurrence . in a review of seven randomized controlled trials , after controlling established factors for recurrence such as tumor size , multiplicity , stage and grade , it was concluded that a wide range of recurrence rate , i.e. , 0 - 46% , was due to the difference in quality of resection . inadequate resection leading to higher rate of recurrence at the same site is supported by another study where 81% of recurred tumor occurred at the site of previous resection . various techniques using different kinds of loops and laser have been described to improve the quality of turbt . en - bloc resection technique is one of the ways to provide better pathological evaluation for ta and t1 tumors . in a study on et , although the authors did not describe presence or absence of detrusor muscle in the resected specimen , they concluded that invasion of lamina was better delineated with en - bloc resection . a limitation of this technique was the inability to use a flat loop for tumors located at the anterior and upper posterior wall . it may not matter much whether we do et or ct for a small size papillary tumor , but for tumors of 2 - 4 cm size , et would give better tissue configuration for assessing the exact t stage and commenting on margin status . there is paucity of literature on et for tumors of 2 - 4 cm size . we used a 45 angle loop electrode , which helped in scooping out the tumor in retrograde fashion . once the tumor was resected en - bloc , removal of 4 cm size tumor from the urethra is a challenge particularly in a male patient . we could remove 3 cm size tumor in a female , but in males we had to cut the free lying tumor into two or three pieces . the most common technique was to place a nephroscope and hold the tumor with forceps to remove the whole assembly along with the tumor . results of this prospective non - randomized study have shown that recurrence rate in et was significantly lower than ct . best results of et were seen in non - lamina invasive bladder cancer , where recurrence rate was reduced to 16% as compared with 53% with ct . therefore , en - bloc resection not only provided a tissue piece with all the layers of bladder in contiguity for better histopathological characterization , but also resulted in reduction in the recurrence rate . looking at the pattern of recurrence in our patients , it seems that et is a better way to reduce the risk of recurrence as it provides a complete resection as only 1 ( 16% ) patient had recurrence at the same site as compared to 6 ( 40% ) patients in ct group 6 ( 40% ) patients in ct group regarding the learning curve , et is rather more controlled technique of resection than ct as it gives better hemostasis and thereby a good vision , which is crucial to avoid complications . depth of the resection could also be modified with et and it does not take more than three cases to get a knack of this technique if it is started with a relatively small tumor . first , tumor retrieval from the bladder was technically difficult and it had to be cut into 2 - 3 pieces once it was lying free in the bladder . second , there could be surgeon related factors as ct was done by two different surgeons . turbt is a procedure with a varied outcome in terms of adequacy of resection , recurrence and progression . there are a few surrogate markers to assess adequate resection such as presence of detrusor muscle in the specimen and the rate of subsequent recurrence . successful management of bladder tumors ( particularly non - muscle - invasive tumors ) , relies on adequate initial resection and accurate histological diagnosis . an ideal turbt would mean complete resection of the visible tumor , resection of the surrounding healthy looking mucosa for up to 1 cm and then the removal of detrusor muscle . herr and donat described three ways to measure the quality of a good turbt , i.e. , complete resection , presence of deep muscle in the specimen and the rate of recurrence at the site of previous turbt . they also suggested classifying tumor resection as r0 ; microscopic negative margin , r1 with microscopic positive margin and r2 that is macroscopic positive margin . this kind of assessment is not practical in ct , but could be possible in en - bloc resection , where we can have a piece of tumor tissue , which has all three layers , i.e. , urothelium , lamina propria and detrusor muscle in contiguity . the outer - most surface of the detrusor muscle in the resected specimen could then be inked to assess margin status and thereby discerning a true perspective of level of resection , i.e. , r0-r1 [ figure 4 ] . en - bloc resection provides a tissue piece of the bladder with all the layers in contiguity to assess the t stage and margin status . in inset , a 3 cm tumor removed en - bloc inadequacy of ct is not only judged by absence of detrusor muscle in an initial specimen , but also by the rate of recurrence . recurrence is seen in 50 - 70% of non - muscle invasive bladder cancer , mostly during the 1 year . these may be due to incomplete resection , cell implantation or the tumor biology itself . incomplete resection seems to be the most important reason for the recurrence . in a review of seven randomized controlled trials , after controlling established factors for recurrence such as tumor size , multiplicity , stage and grade , it was concluded that a wide range of recurrence rate , i.e. , 0 - 46% , was due to the difference in quality of resection . inadequate resection leading to higher rate of recurrence at the same site is supported by another study where 81% of recurred tumor occurred at the site of previous resection . various techniques using different kinds of loops and laser have been described to improve the quality of turbt . en - bloc resection technique is one of the ways to provide better pathological evaluation for ta and t1 tumors . in a study on et , although the authors did not describe presence or absence of detrusor muscle in the resected specimen , they concluded that invasion of lamina was better delineated with en - bloc resection . a limitation of this technique was the inability to use a flat loop for tumors located at the anterior and upper posterior wall . it may not matter much whether we do et or ct for a small size papillary tumor , but for tumors of 2 - 4 cm size , et would give better tissue configuration for assessing the exact t stage and commenting on margin status . there is paucity of literature on et for tumors of 2 - 4 cm size . we used a 45 angle loop electrode , which helped in scooping out the tumor in retrograde fashion . once the tumor was resected en - bloc , removal of 4 cm size tumor from the urethra is a challenge particularly in a male patient . we could remove 3 cm size tumor in a female , but in males we had to cut the free lying tumor into two or three pieces . the most common technique was to place a nephroscope and hold the tumor with forceps to remove the whole assembly along with the tumor . results of this prospective non - randomized study have shown that recurrence rate in et was significantly lower than ct . the progression rate , though not significant , was lower with et . best results of et were seen in non - lamina invasive bladder cancer , where recurrence rate was reduced to 16% as compared with 53% with ct . therefore , en - bloc resection not only provided a tissue piece with all the layers of bladder in contiguity for better histopathological characterization , but also resulted in reduction in the recurrence rate . looking at the pattern of recurrence in our patients , it seems that et is a better way to reduce the risk of recurrence as it provides a complete resection as only 1 ( 16% ) patient had recurrence at the same site as compared to 6 ( 40% ) patients in ct group 6 ( 40% ) patients in ct group regarding the learning curve , et is rather more controlled technique of resection than ct as it gives better hemostasis and thereby a good vision , which is crucial to avoid complications . depth of the resection could also be modified with et and it does not take more than three cases to get a knack of this technique if it is started with a relatively small tumor . first , tumor retrieval from the bladder was technically difficult and it had to be cut into 2 - 3 pieces once it was lying free in the bladder . second , there could be surgeon related factors as ct was done by two different surgeons . turbt is a procedure with a varied outcome in terms of adequacy of resection , recurrence and progression . there are a few surrogate markers to assess adequate resection such as presence of detrusor muscle in the specimen and the rate of subsequent recurrence . successful management of bladder tumors ( particularly non - muscle - invasive tumors ) , relies on adequate initial resection and accurate histological diagnosis . an ideal turbt would mean complete resection of the visible tumor , resection of the surrounding healthy looking mucosa for up to 1 cm and then the removal of detrusor muscle . herr and donat described three ways to measure the quality of a good turbt , i.e. , complete resection , presence of deep muscle in the specimen and the rate of recurrence at the site of previous turbt . they also suggested classifying tumor resection as r0 ; microscopic negative margin , r1 with microscopic positive margin and r2 that is macroscopic positive margin . this kind of assessment is not practical in ct , but could be possible in en - bloc resection , where we can have a piece of tumor tissue , which has all three layers , i.e. , urothelium , lamina propria and detrusor muscle in contiguity . the outer - most surface of the detrusor muscle in the resected specimen could then be inked to assess margin status and thereby discerning a true perspective of level of resection , i.e. , r0-r1 [ figure 4 ] . en - bloc resection provides a tissue piece of the bladder with all the layers in contiguity to assess the t stage and margin status . in inset , a 3 cm tumor removed en - bloc inadequacy of ct is not only judged by absence of detrusor muscle in an initial specimen , but also by the rate of recurrence . recurrence is seen in 50 - 70% of non - muscle invasive bladder cancer , mostly during the 1 year . these may be due to incomplete resection , cell implantation or the tumor biology itself . incomplete resection seems to be the most important reason for the recurrence . in a review of seven randomized controlled trials , after controlling established factors for recurrence such as tumor size , multiplicity , stage and grade , it was concluded that a wide range of recurrence rate , i.e. , 0 - 46% , was due to the difference in quality of resection . inadequate resection leading to higher rate of recurrence at the same site is supported by another study where 81% of recurred tumor occurred at the site of previous resection . various techniques using different kinds of loops and laser have been described to improve the quality of turbt . en - bloc resection technique is one of the ways to provide better pathological evaluation for ta and t1 tumors . in a study on et , although the authors did not describe presence or absence of detrusor muscle in the resected specimen , they concluded that invasion of lamina was better delineated with en - bloc resection . a limitation of this technique was the inability to use a flat loop for tumors located at the anterior and upper posterior wall . it may not matter much whether we do et or ct for a small size papillary tumor , but for tumors of 2 - 4 cm size , et would give better tissue configuration for assessing the exact t stage and commenting on margin status . there is paucity of literature on et for tumors of 2 - 4 cm size . we used a 45 angle loop electrode , which helped in scooping out the tumor in retrograde fashion . once the tumor was resected en - bloc , removal of 4 cm size tumor from the urethra is a challenge particularly in a male patient . we could remove 3 cm size tumor in a female , but in males we had to cut the free lying tumor into two or three pieces . the most common technique was to place a nephroscope and hold the tumor with forceps to remove the whole assembly along with the tumor . results of this prospective non - randomized study have shown that recurrence rate in et was significantly lower than ct . the progression rate , though not significant , was lower with et . best results of et were seen in non - lamina invasive bladder cancer , where recurrence rate was reduced to 16% as compared with 53% with ct . therefore , en - bloc resection not only provided a tissue piece with all the layers of bladder in contiguity for better histopathological characterization , but also resulted in reduction in the recurrence rate . looking at the pattern of recurrence in our patients , it seems that et is a better way to reduce the risk of recurrence as it provides a complete resection as only 1 ( 16% ) patient had recurrence at the same site as compared to 6 ( 40% ) patients in ct group 6 ( 40% ) patients in ct group regarding the learning curve , et is rather more controlled technique of resection than ct as it gives better hemostasis and thereby a good vision , which is crucial to avoid complications . depth of the resection could also be modified with et and it does not take more than three cases to get a knack of this technique if it is started with a relatively small tumor . first , tumor retrieval from the bladder was technically difficult and it had to be cut into 2 - 3 pieces once it was lying free in the bladder . second , there could be surgeon related factors as ct was done by two different surgeons . it demands meticulous care and attention to achieve adequate cancer control and improve recurrence rates . in our study , though et did not significantly affect the progression rate , it showed a significant reduction in the recurrence rate for nmibc in comparison with ct . the concept of removing a bladder tumor by ct should be changed to a technique of en - bloc resection to provide better cancer control and long term outcome in non - muscle invasive bladder cancer .

purpose : conventional , transurethral resection of bladder tumor ( turbt ) involves piecemeal resection of the tumor and has a very high recurrence rate . we evaluated the outcome of en - bloc turbt ( et ) in comparison with conventional turbt ( ct ) in non - muscle invasive bladder carcinoma in terms of recurrencew and progression.materials and methods : from september 2007 to june 2011 , in a prospective non - randomized interventional setting , et was compared with ct in patients with solitary tumor of 2 - 4 cm size in terms of recurrence and progression . pedunculated tumors , size > 4 cm , tumors with associated hydroureteronephrosis and biopsy specimen with absent detrusor muscles were excluded . fisher 's exact test and survival analyses were used to compare the demography and the outcome.results:a total of 21 patients of et were compared with 24 patients of ct . mean tumor size was 2.8 cm in et and 3.3 cm in ct group . location of tumor , stage and grade were comparable in both groups . recurrence rate was 28.6% versus 62.5% ( p = 0.03 ) and progression rate was 19% versus 33.3% ( p = 0.32 ) in et versus ct group respectively . recurrence free survival was 45.1 ( 95% ci : 19.0 - 38 months ) and 28.5 ( 95% ci : 35.4 - 54.7 months ) in et and ct group ( p = 0.018 ) . progression free survival in et and ct was 48.32 ( 95% ci : 35.5 - 53.0 months ) and 44.26 ( 95% ci : 39.0 - 57.5 months ) , p = 0.46.conclusion:there was a significant reduction in the recurrence rate and time to recurrence with et . rate of progression was also relatively less with et , though not statistically significant .

INTRODUCTION MATERIALS AND METHODS None Sample size Inclusion criteria Exclusion criteria Treatment and follow-up Final analysis Technique of ET, sculpting and resection technique Statistical analysis RESULTS None Discussion CONCLUSION

blood samples : peripheral blood samples were obtained from several farmers and veterinarians for diagnosis of blv infection at the hokkaido university veterinary teaching hospital . informed consent was obtained from each owner , and approval for all procedures was obtained from the institutional animal care and use committee of hokkaido university . dna was purified from 500 l blood samples using the wizard genomic dna purification kit ( promega , madison , wi , u.s.a . ) according to the manufacturer s protocol and finally suspended in 50 l buffer . cells : ku-1 cells infected with blv were maintained at 37c in roswell park memorial institute ( rpmi)-1640 medium ( sigma - aldrich , st . louis , mo , u.s.a . ) supplemented with 10% fetal bovine serum ( cell culture technologies , gravesano , switzerland ) and penicillin / streptomycin / l - glutamine ( life technologies , carlsbad , ca , u.s.a . ) . blood samples not infected with blv that contained various numbers of ku-1 cells ( 1010 cells/1,000 l of blood ; 1010 cells/l ) were used as pcr - db templates , and dna purified from those blood samples was used as nested pcr templates . pcr - db : amplification of blv provirus from whole blood used kod fx neo ( toyobo , osaka , japan ) , which is superior for amplification from crude samples , and a specific primer pair ( pv2-f 5-act ttc aga ccc cct tga ctg aca-3 and pv2-r 5-aaa cct ctg ccc tgg tga tta agg-3 ) . this primer pair was designed by primer3 to amplify blv provirus ( genebank accession number : both k02120 and af033818 ) , and the intron region of the provirus ( 33083580 in k02120 ) was amplified by the primer pair . briefly , each 30 l reaction mixture contained 0.4 mm dntps , 0.5 m of primers , 1 u of kod fx neo and 1 l of whole blood ( 10- , 50- or 100-fold dilutions in double distilled water ; fig . 2.comparison of nested pcr and pcr - db sensitivity . to assess pcr method sensitivity , dna samples purified from blv - uninfected blood containing ku-1 cells ( 1010 cells/l ) were used as nested pcr templates , and the blood samples were used as pcr - db templates ( 1- , 10- , 50- or 100-fold diluted in double distilled water ) . ( a ) representative images of electrophoresis of amplicons generated using each pcr condition . ( b , c ) the results from detectable samples using each pcr condition are presented . white bars indicate ku-1 cell counts which were undetectable by electrophoresis , while the gray ( dna ) and black ( blood ) bars indicate the templates used for each pcr condition . amplifications were performed under the following conditions : one lysis cycle at 94c for 2 min and then 45 cycles of template denaturation at 94c for 15 sec followed by annealing and extension at 68c for 50 sec . the -globin gene was amplified as an internal control using the following primer pairs : 5-tgc tga ctg ctg agg aga agg ctg-3 and 5-gtc ctc aca cgc cca ggt gca ttt c-3. comparison of nested pcr and pcr - db sensitivity . to assess pcr method sensitivity , dna samples purified from blv - uninfected blood containing ku-1 cells ( 1010 cells/l ) were used as nested pcr templates , and the blood samples were used as pcr - db templates ( 1- , 10- , 50- or 100-fold diluted in double distilled water ) . ( a ) representative images of electrophoresis of amplicons generated using each pcr condition . ( b , c ) the results from detectable samples using each pcr condition are presented . white bars indicate ku-1 cell counts which were undetectable by electrophoresis , while the gray ( dna ) and black ( blood ) bars indicate the templates used for each pcr condition . nested pcr : to amplify the long terminal repeat ( ltr ) in the blv provirus , nested pcr was performed using rtaq ( takara - bio , otsu , japan ) as previously described . briefly , the blv ltr was amplified using primer pairs , blv - ltr1 and blv - ltr533 , for the first pcr reaction , and 1.5 l of dna from whole blood or blv - uninfected blood with ku-1 cells were used as templates . and then , 1.5 l of the first pcr products were reamplified using blv - ltr256 and blv - ltr453 for the second pcr reaction . real - time pcr : to confirm the provirus loads of blv - infected cattle diagnosed by nested pcr , we used a real - time pcr system ( lightcycler 480 system ii ; roche diagnostics , mannheim , germany ) , sybr premix dimer - eraser ( takara - bio ) , and the primers pv2-f and pv2-r for blv and 5-aca caa ctg tgt tca cta gc-3 and 5-caa ctt cat cca cgt tca cc-3 for -globin . amplification of dna samples from whole blood was performed as follows : one cycle at 95c for 30 sec , followed by a 3-step pcr procedure consisting of 5 sec at 95c , 30 sec at 60c and 30 sec at 72c for 45 cycles . to obtain a standard curve , serial dilutions of the standard plasmid containing from 10 to 10 copies tumor samples : to diagnose bovine leukemia by using pcr - db , tumor cells from three cattle with clinically diagnosed lymphoma were collected : case no . 1 ( holstein - friesian , 4 months old , enzootic bovine leukosis ) , case no . 2 ( japanese black , 5 years old , enzootic bovine leukosis ) and case no . the tumor cells were stained with an antibody specific to b cell markers and analyzed by flow cytometry as described previously . in brief , double staining was performed using anti - bovine igm ( il - a30 ; abd serotec , oxford , u.k . ) pre - labeled with zenon alexa fluor 488 ( life technologies ) and the following antibodies : anti - wc4 ( cc55 ; cd19-like ; abd serotec ) ; anti - b - b7 ( gb25a ; cd21-like ; vmrd , pullman , wa , u.s.a . ) ; and anti - bovine cd5 ( cact105a ; vmrd ) . alexa fluor 647-conjugated anti - mouse igg ( life technologies ) was used for bound antibody detection ( anti - wc4 , anti - b - b7 and anti - cd5 ) . tumor cells were incubated with anti - wc4 , anti - b - b7 and anti - cd5 as the first antibody , anti - mouse igg as the second antibody and anti - igm as the third antibody . blv infection was diagnosed from blood and tumor cells by nested pcr as described above . approximately 12 mm of tumor tissue suspended in 1 ml of phosphate buffered saline was used as a template for pcr - db . pcr - db amplification of blv provirus from whole blood : first of all , we tried to use blv - ltr 256 and blv - ltr 453 for pcr - db amplification of blv provirus . but , the tm value of this primer pair was not suitable for the polymerase we used for pcr - db , resulted in appearance of many extra bands ( data not shown ) . because of that , we designed an optimal primer pair for the polymerase of pcr - db following the manufacturer s protocol . the pv2 primer pair was determined from seven ones based on their ability to show the most sensitive and reproducible results ( data not shown ) . to confirm the amplification of blv provirus from whole blood , pcr - db was performed using blood samples for which blv infection had been previously diagnosed by nested pcr . we found single bands approximately 272 bp using the pv2 primer pair , with the results from pcr - db amplification completely consistent with those from nested pcr reactions ( fig . blv provirus amplification was performed by ( a ) nested pcr and ( b ) pcr - db . blood samples were collected from cattle with ( n=4 ) and without ( n=4 ) diagnosed blv infections . nested pcr and pcr - db , dna samples purified from blv - positive cattle were used as a positive control ( pc ) , and double distilled water was used as a negative control ( nc ) . ) . the amplification of -globin was observed as bands of approximately 100 bp in all samples , although a second band of approximately 400 bp was also produced in pcr - db using the -globin primer pair ( data not shown ) . blv provirus amplification was performed by ( a ) nested pcr and ( b ) pcr - db . blood samples were collected from cattle with ( n=4 ) and without ( n=4 ) diagnosed blv infections . the -globin gene was amplified as an internal control . for both of nested pcr and pcr - db , dna samples purified from blv - positive cattle were used as a positive control ( pc ) , and double distilled water was used as a negative control ( nc ) . pcr - db results are reproducible with sample dilution : to compare the sensitivity of nested pcr and pcr - db methods , blv provirus was amplified from ku-1 cells mixed in blood from healthy cattle ( fig . the provirus was detected by nested pcr even from samples containing 0.1 cells or 1 cell per 1 l of blood ( average level of undetectable cell numbers : 0.083 cells/l ; fig . pcr - db amplification using dna samples as templates was also performed to confirm the effects of its primer pair and polymerase on assay sensitivity . results showed a similar sensitivity to that of nested pcr ( 0.067 cells/l ; fig . however , the results of pcr - db used undiluted blood samples indicated less sensitivity and reproducibility . on the other hand , pcr - db performed under variable conditions , with blood samples diluted 10- , 50- and 100-fold with double distilled water , showed improved reproducibility , even though the sensitivity was lower than for undiluted samples ( 0.55 , 5.5 and 25 cells/l , respectively ; fig . pcr - db diagnosis of most of blv - infected cattle that showed detectable provirus loads : in total , 225 bovine blood samples were tested by nested pcr and pcr - db . whole blood was diluted 50-fold with double distilled water for pcr - db , representing the middle condition tested in fig . 2c . using both methods , 37 samples were positive , and 176 samples were negative , with no samples that were positive by pcr - db and negative by nested pcr , thus indicating a pcr - db specificity of 100% ( table 1table 1.amplification of blv provirus in clinical blood samplespcr resultnested pcr positivenested pcr negativetotalpcr - db positive37037pcr - db negative12176188total49176225 ) . the provirus in 12 samples was detected only using nested pcr and not with pcr - db , indicating a pcr - db sensitivity of 75.51% . because we considered that those false - negative results are responsible for poor infection levels , provirus loads of clinical samples that were positive by nested pcr were measured by real - time pcr . the results showed that the provirus loads of these 12 samples were quite low , suggesting that the animals were asymptomatic carriers at the aleukemic stage ( fig . dna samples from blv - infected cattle diagnosed by nested pcr were evaluated to determine provirus loads using real - time pcr ( n=49 ) . the y - axis indicates the rates of blv genome copies in 100 cells as determined by -globin amplicon copy numbers . the dot colors depict the pcr - db results ( white : negative ; black : positive ) . dna samples from blv - infected cattle diagnosed by nested pcr were evaluated to determine provirus loads using real - time pcr ( n=49 ) . the y - axis indicates the rates of blv genome copies in 100 cells as determined by -globin amplicon copy numbers . the dot colors depict the pcr - db results ( white : negative ; black : positive ) . pcr - db directly detected blv provirus in tumor samples : to investigate whether pcr - db can be used to diagnose blv infection from tumor tissues , the provirus in tumor samples was amplified using pcr - db . in the three sample cases , two out of three cases were blv - positive tumor tissues , and all pcr - db results were entirely consistent with those of nested pcr ( fig . amplification of the blv provirus in blood and tumor samples isolated from three cattle with bovine leukemia was performed using pcr - db , with 50-fold diluted blood and tumor suspensions used as templates . ln : lymph node . ( a ) case no . 1 ( holstein - friesian , 4 months old ) : 1 , blood ; 2 , thymus ; 3 , spleen ; 4 , gastric ln ; 5 , mesenteric ln ; and 6 , inguinal ln . ( b ) 2 ( japanese black , 5 years old ) : 1 , blood ; 2 , spleen ; 3 , heart ; 4 , superficial cervical ln ; 5 , mesenteric ln ; 6 , mediastinal ln ; and 7 , renal ln . ( c ) 3 ( holstein - friesian , 2 years old ) : 1 , blood ; 2 , cervical thymus ; 3 , thoracic thymus ; 4 , superficial cervical ln ; and 5 , bronchial ln . ) . 1 , a blv - positive tumor , expressed several b - cell markers , such as igm , wc4 ( cd19-like ) and b - b7 ( cd21-like ) on the tumor cell membrane , and on the other hand , case no . 3 , which was blv - negative , did not show b - cell phenotypes ( table 2table 2.phenotyping and diagnosis of tumor samples from cattlecase no.blv infectionlymphocytes ( 10/l)cell surface markerstumor cell typesdiagnosislymphocytesb cellscd5wc4b - b7igm1 + 3,881++/++b cellsenzootic bovine leukosis2+n.t.n.t.unknownenzootic bovine leukosis3 - 23 + ---t cellsthymic lymphosarcoma ) . these results strongly supported the clinical diagnosis , cases no.1 and no.2 as enzootic bovine leukosis and case no.3 as thymic lymphosarcoma of sporadic bovine leukosis . amplification of the blv provirus in blood and tumor samples isolated from three cattle with bovine leukemia was performed using pcr - db , with 50-fold diluted blood and tumor suspensions used as templates . 1 ( holstein - friesian , 4 months old ) : 1 , blood ; 2 , thymus ; 3 , spleen ; 4 , gastric ln ; 5 , mesenteric ln ; and 6 , inguinal ln . 2 ( japanese black , 5 years old ) : 1 , blood ; 2 , spleen ; 3 , heart ; 4 , superficial cervical ln ; 5 , mesenteric ln ; 6 , mediastinal ln ; and 7 , renal ln . 3 ( holstein - friesian , 2 years old ) : 1 , blood ; 2 , cervical thymus ; 3 , thoracic thymus ; 4 , superficial cervical ln ; and 5 , bronchial ln . in this study , we developed novel diagnosis method named pcr - db for amplifying the blv provirus directly from whole blood . our method showed high specificity and reproducibility with diluted blood samples , while undiluted ones resulted in less reproducibly probably because of endogenous pcr inhibitors contained in the blood samples and blood viscosity , which made it difficult to measure the sample volume accurately . although the sensitivity of pcr - db was lower than that of nested pcr , all clinical samples detected only using nested pcr and not with pcr - db showed slight provirus loads , suggesting that those were from carriers at early stage . so , we believe that our study demonstrates the utility of pcr - db for rapid diagnosis of blv infection . in previous studies , some researchers have reported the amplification of dna directly from whole blood using pcr methods for diagnosing bacterial or viral infections , including mycoplasma haemofelis , bartonella quintana and hepatitis b virus . moreover , in another report , pcr - db was used for mutation screening of gm1 gangliosidosis in dogs , demonstrating that this technique can also be a good method for hereditary disease screening and not only for detecting infectious diseases . these reports suggest that pcr - db has the potential to be applied in multiple clinical situations as a novel , rapid and viable method of diagnosis . one of the primary methods used to identify blv - infected cattle is a serological test ( agid , elisa , etc . ) those tests are appropriate for screening thousands of cattle , because of easy sample preparation compared with pcr tests which require dna extraction and availability of a rapid and cost - effective diagnosis kit . however , in some cases , these serological tests show several problems , including poor sensitivity compared with pcr testing , false positive samples , detection of maternal antibodies and inability to perform a diagnosis using tissue or semen samples [ 3 , 5 , 11 , 15 ] . although sweden achieved eradication of blv - infected cattle and elimination of blv using only an elisa test , pcr testing would enable a more definitive surveillance program to eradicate blv infection . there are many advantages of using pcr - db to detect the blv provirus : i ) pcr - db specificity as calculated by diagnosing clinical samples was 100% ; ii ) the technique does not require a special and expensive thermal cycler like real - time pcr ; iii ) it is not labor intensive or time - consuming and is cost - effective ; iv ) because it is a rapid and straightforward procedure , there is less possibility of contamination ; and v ) less than 10 l of blood is enough to run the pcr - db assay , even in duplicate . the biggest challenge with pcr - db is the existence of pcr inhibitors in whole blood , which contains igg , hemoglobin and lactoferrin [ 1 , 2 ] . our results demonstrate that endogenous pcr inhibitors do not impact the reproducibility of the pcr reaction by sample dilution . thus , pcr - db is a suitable method for use by clinical veterinarians to perform blv diagnosis in a typical veterinarian s office . nested pcr using purified genomic dna is likely the best method for detecting blv infection , because provirus in the blood from several cattle showing slight provirus loads was not detected by pcr - db . although the amplification of low - copy provirus may be difficult using pcr - db , the sensitivity of pcr - db can be improved by simply increasing the template blood volume . as demonstrated in fig . 2c , pcr - db using 10-fold diluted blood samples showed higher sensitivity than other dilutions and adequate reproducibility . therefore , we consider pcr - db to be appropriate in first screening diagnosis in an individual farm or region to systematically eradicate blv - infected cattle . this technique is preferred , because the use of nested pcr for diagnosis in a large number of cattle is both labor intensive and time - consuming . pcr - db represents the best practical way for eliminating blv infection through periodic screening and isolation or culling of all infected animals at intervals of several months or a few years . our preliminary data showed that the cell number in the pcr reaction buffer influenced the stability of the results and that excessive cell numbers inhibited the pcr reaction ( data not shown ) . thus , suspending tumor cells in phosphate buffered saline or other suitable solutions are important in order to adjust the templates to the appropriate pcr conditions . in tumors , pcr - db may be a better method for diagnosing blv infection than nested pcr or other methods , because the most rapid and definitive method for diagnosing blv infection in cattle with lymphoma is required by clinical veterinarians and because serological tests are not suitable for tissue diagnosis . incidentally , calf lymphoma ( case no.1 ) was diagnosed with enzootic bovine leukosis which is caused by blv infection , because the lymphoma was constructed with clonal cd5 igm b cells highly expressing viral protein gp51 ( data not shown ) . however , denmark did so by peripheral blood cell counts without serological tests . in our opinion , other countries can eliminate the infection more definitively than denmark using pcr - db . countries with a much higher prevalence can work to eradicate all infected cattle through pcr - db screening and other strategies , such as isolating blv - positive cattle and reducing the incidence of bovine leukemia . we conclude that this pcr - db assay is a highly simplified , cost - effective and rapid method ( results obtained in less than 3 hr ) that serves as a new alternative way to diagnosis blv infection without dna purification .

bovine leukemia virus ( blv ) infection induces bovine leukemia in cattle and causes significant financial harm to farmers and farm management . there is no effective therapy or vaccine ; thus , the diagnosis and elimination of blv - infected cattle are the most effective method to eradicate the infection . clinical veterinarians need a simpler and more rapid method of diagnosing infection , because both nested polymerase chain reaction ( pcr ) and real - time pcr are labor intensive , time - consuming , and require specialized molecular biology techniques and expensive equipment . in this study , we describe a novel pcr method for amplifying the blv provirus from whole blood , thus eliminating the need for dna extraction . although the sensitivity of pcr directly from whole blood ( pcr - db ) samples as measured in bovine blood containing blv - infected cell lines was lower than that of nested pcr , the pcr - db technique showed high specificity and reproducibility . among 225 clinical samples , 49 samples were positive by nested pcr , and 37 samples were positive by pcr - db . there were no false positive samples ; thus , pcr - db sensitivity and specificity were 75.51% and 100% , respectively . however , the provirus loads of the samples detected by nested pcr and not pcr - db were quite low . moreover , pcr - db also stably amplified the blv provirus from tumor tissue samples . pcr - db method exhibited good reproducibility and excellent specificity and is suitable for screening of thousands of cattle , thus serving as a viable alternative to nested pcr and real - time pcr .

MATERIALS AND METHODS RESULTS DISCUSSION

several techniques can be performed to improve the defination of the nasal tip such as cartilaginous resection , tip grafts , or suture placement . resection techniques have gradually been replaced by maneuvers that are more effective in preserving the nasal tip support mechanisms1 2 3 4 5 6 7 8 9 10 . the aim of study is evaluate the outcome of lateral intercrural suture at the lower lateral cartilage ( llc ) of the caucasian nose through endonasal rhinoplasty using a basic technique without delivery to decrease the angle of domal divergence and improve the definition of the nasal tip . the present study was carried out between the years of 2008 and 2009 at the parana institute for otorhinolaryngology ( ipo ) hospital in the city of curitiba . from a 100-patient sample , we excluded those who had a history of nasal surgery , previous nasal trauma , and a non - caucasian nose . sixty - four patients participated of the study , including 43 males and 21 females that were between 16 and 59 years old ( m = 37.5 ) . all of the patients had knowledge of the study and signed a free informed term of consent ( fitc ) form in compliance with the brazilian federal ruling of national concill of health ( cns ) 196/96 . we used the converse - diamond 1 , which is a classic rhinoseptoplasty surgical technique . the nasal tip was accessed through septocolumelar and intercartilaginous incisions . in all cases , la garde 's maneuver was performed without resection of the cephalic border of the llc ( the mcindoe technique ) . the lateral intercrural suture must be performed on the cephalic border of llc through the intecartilaginous incision , on the junction between the dome and lateral crus ( figure 1 ) , and its grip must be gradual and progressive , thus allowing for adjustments to achieve the most appropriate tip ( figure 2 ) . surgical anatomy of the nasal tip . the lateral intercrural suture must be done after the septocolumelar suture and before the intercartilaginous suture , using colorless polydioxanone 4'0 ' ( pds ) with a sharp , curved needle . performing the intercrural stitch at the end of the surgery avoids excessive manipulation of the tip and possible enlargement of the interdomal distance ( the angle of domal divergence ) . it is considered normal to have an angle of domal divergence that is less than 30 ( figure 3)4 10 . a normal angle of domal divergence . lateral intercrural suture steps : subsequent to the displacement of the skin of the llc using la garde 's maneuver and the dislocation of the cartilage from the skin of the vestibule , introduce the pds to the junction between the dome and the lateral crus ( about 3 mm from the llc - cephalic border ) . the thread must be introduced through the cephalic to the caudal margin ( figure 4 ; step 1 ) . move the thread to the contralateral nostril through the transfixant incision ( figure 5 ; step 2 ) . perform step 1 on the contralateral nostril through the caudal to the cephalic margin , and avoid crossing the threads ( figure 6 ; step 3 ) . return the needle to the nostril in which the stitch was initiated and gradually grip the suture . the lateral intercural suture was performed on 64 patients with caucasian noses through endonasal rhinoseptoplasty using a basic technique without delivery . pre- and postoperative pictures were evaluated after a 6-month evolution period . in all of the cases , an improved nasal tip definition was achieved with results that were satisfactory to both the patients and the surgeon ( qualitative , observational , and subjective assessment ) . the present work was approved by the institution 's ethics committee ( protocol number 004/2008 ) . the replacement of cartilaginous resection techniques with suture techniques to improve nasal tip definition is a global trend5 . the report regarding sutures that were applied to the nasal tip was originally published by bahman guyuron and ramin a. behmand in 20036 . our results were evaluated 6 months postoperatively and had success that was similar to that of the work that was published by nassif et al11 . the final result of the suture technique is primarily influenced by factors such as the intrisic force of the cartilage , the degree of tightening of the suture , and the limitation imposed by the soft tissues ( ligaments , subcutaneous tissue , and skin ) . skin thickness is another determining factor in the effectiveness of the lateral intercrural suture . in patients with thin skin and sparse subcutaneous tissue however , in patients with thicker skin and excessive subcutaneous tissue , the lateral intercrural suture may be ineffective , thus requiring a reduction of the angle of domal divergence and of the domal definition by using other techniques , such as the goldman technique , transdomal suture , interdomal or medial crus suture , or a lateral spanning - type surgery ( which compromises more of the lateral crus)6 . there are some details concerning the lateral intercrural suture technique that must be observed : slight nasal tip projection , diverging from the results described in the literature2 . the more laterally that the suture is placed on the lateral crus , the better the resulting nasal tip projections and definition . discrete pinching of the supra - alar region , especially in patients with very thin skin and weak supra - alar cartilage , when performed at a distance superior to 2 - 3 mm from de nasal dome . asymmetry of the tip can be observed if the stitches are not placed at corresponding levels . the suture can be held in place using long - term absorbable threads ( monocryl or pds ) or with non - absorbable threads , with consideration given to the tensile strength and level of absorption of each material . in all of the cases that were described in this work , non - absorbable threads were used , and there were no cases of extrusion or other complications that are described in the literature ( abscess , extrusion , asymmetry , or pinching of the tip)2 . lateral intercrural suture is an effective method to improve nasal tip definition in the caucasian nose and can be performed through endonasal rhinoplasty without delivery . this technique had already being reported in the literature through opened and closed access with delivery , but not through closed access with intercartilaginous and septocolumelar incisions . this suture is easy to perform , predictable , controlled , and extremely useful to the surgeon dedicated to tip surgery . this stitch allows for better management of the tip through basic rhinoseptoplasty , therby minimizing the requirement of surgery procedures through delivery or the open procedure . the present study evaluated the improvement of nasal tip definition on the angle of domal divergence using simple suture of the cephalic board and lateral crus of the llc . we emphasize that each suture has its own precise indication , and the individual surgeon is responsible for assessing and choosing the suture that best fits the needs of the patient .

summary introduction : several techniques can be performed to improve nasal tip definition such as cartilage resection , tip grafts , or sutures . objctive : to evaluate the outcome of lateral intercrural suture at the lower lateral cartilage by endonasal rhinoplasty with a basic technique without delivery in decreasing the angle of domal divergence and improving the nasal tip definition . method : this prospective study was performed in 64 patients in which a suture was made on the board head of the lower lateral cartilage in the joint between the dome and lateral crus , using polydioxanone ( pds ) with sharp , curved needle . results : in all of the cases , better definition of the nasal tip was achieved by intercrural suturing for at least 6 months postoperatively . conclusion : lateral intercrural suture of the lower lateral cartilage provides improved nasal tip definition and can be performed by endonasal rhinoplasty without delivery in the caucasian nose .

Introduction Method Results Discussion Conclusion

fractures of the proximal femur and hip are relatively common injuries in adults and common source of morbidity and mortality among the elderly . incidence of fractures is increasing , which is not unexpected because the general life expectancy of the population has increased significantly during the past few decades . fractures of the upper part of the thigh bone ( femur ) are termed hip or proximal femoral fractures . roughly half of all hip fractures are extracapsular in that they lie outside the hip joint capsule . extracapsular hip fractures are defined as those fractures that occur within the area of bone bounded by the attachment of the hip joint capsule and extending down to a level which is five centimeters below the distal ( lower ) border of the lesser trochanter ( 1 ) . many of the patients have significant comorbidities , which lead to delays in surgery and functional recovery . these patients should be mobilized as soon as possible to prevent complications associated with immobilization . therefore , a surgical technique allowing anatomic alignment and a stable fixation with early mobilization is accepted as the standard approach for intertrochanteric fractures . surgeon can control of fracture reduction , implant selection and implant placement , all of which must be optimized to ensure the success of the surgical intervention . examples include the gamma nail ( stryker - howmedica ) , the intramedullary hip screw ( smith and nephew richards ) , the proximal femoral nail ( synthes ) and the ace trochanteric nail ( depuy orthopaedics ) . pfna , designed by ao in 2004 , is an intramedullary device with a helical blade rather than a screw for better purchase in the femoral head ( 2 , 3 ) . in this study , we aimed to assess the results of osteosynthesis using the pfna system , ( synthes , switzerland ) , in the treatment fractures of the proximal femur included operative and postoperative complications , general complications and final outcome measurements . after approval by the ethics committee of the hospital we retrospective analyzed all the patients with fractures of the hip treated with pfna at the clinic of orthopedic and traumatology , university clinical centre tuzla from the first of january 2012 to 31 december 2012 years . the supine position were used in all of the patients . all surgical operations except one the desired position of the implant was a central position in the femoral neck on both ap and lateral views , and the tip within 510 mm from the subchondral bone . the nail was inserted proximally to the tip of the greater trochanter without canal reaming except from proximal 17 mm reaming . closed nails were placed in all of the patients with the exception of two patients . radiographs were examined to assess the fracture type , post - reduction deformity and union . fracture type was classified as intertrochanteric ( 31.a.1 , a.2 and a.3 ; arbeitsgemeinschaft fr osteosynthesefragen classification ) and subtrochanteric fractures ( seinsheimer classification ) ( 4 , 5 ) . nonunion was defined by routine clinical and radiological criteria , and the need for a further surgical procedure . the absence of the radiologic features of fracture healing after four months represents delayed union . quality of fracture reduction was assessed on postoperative radiographs . for the reduction to be considered unsatisfactory there was misalignment on the antero - posterior radiograph of more than 10 mm of any fragment , angulation of 10 degrees and more in any plane , and shortening of the leg bigger than 1 cm . duration of operation was measured as the interval between the start of the act reposition to the surgical wound closure . duration of the fluoroscopy was determined as the number of issues exposure , read on the fluoroscopy device at the end of the operation . the blood transfusions performed during or after the operation were recorded in terms of units . traffic accident and fall from height as fracture cause was defined as high - energy trauma . in three cases the pfna was used in reosteosynthesis : one angular plate broken , one targon pf ( aesculap ) broken and one condylar plate cut out . all patients received prophylactic antibiotic therapy as follows : 2grams of cefazolin or ceftriaxon were given before and 72h after treatments . after treatment , the muscles active contraction exercises were carried out , such as ankle active dorsiflexion and plantar flexion and isometric contraction activity of quadriceps . one day after , joint of lower extremity passive activities were carried out by the assistance of rehabilitation therapists . after 2 - 3 days , the initiative straight leg and raising , and joint of lower extremity activity were carried out . after 4 - 6 days , ( depending on the general condition ) these patients were allowed to out - of - bed activity . the medical condition was assessed and classified according to the american society of anaesthesiologists ( asa ) grade ( 6 ) . health status was classified as poor ( asa 34 ) or good ( asa 12 ) ( 7 ) . prefracture and postoperativ functional level evaluated by the new mobility score ( nms ) with a scale of 0 ( immobile ) to 9 ( independently mobile ) ( 8) . during the work on the study , we contacted 56 patients ( excluding two died in the hospital and no contact with five ) or their family members by phone , which gave us information about the functional level evaluated by the nms . the mean length of follow up was 22 months ( range 14 to 25 ) . the study included 39 female patients and 24 male , averaged 73.611.9 years ( range , 29 to 88 years ) . there was statistically significant difference prevalence of female compared to male patients ( p=0.012 ) . low energy trauma was the cause of fractures in 57(90.5% ) patients , fall from height three , traffic accidents two and one suicide attempt . averaged waiting time for hospitalization was 3.2 7.5 days ( range , 0 to 32 days ) . the longest hospitalization was 43 days ( patients with deep infection and subsequent nonunion ) and another 41 days ( with refixation , deep infection with escherichia coli and acinetobacter species and lethal outcome ) . because of urinary infection , suffered icv a month ago , heart disease , and hypertension he did not receive consent for the operation . he was discharged to outpatient treatment and admitted to hospital again 25 days after injury . one 81-years - old female patient with a fracture was admitted 29 days after injury . suspecting the hypostatic pneumonia she was treated with antibiotics ( ciprofloxacine eight days ) . as the ct of the lungs did not verify the pneumonia the patient got approval for surgery . in the postoperative the ratio between with or without co - existent disease was 4.7:1 ( table 1 ) . it was a significant difference between patients with two or more comorbidities compared to one or no comorbidity ( p = 0.048 ) . of the 14 deaths two patients had no comorbidities . 28 ( 44.4% ) patients had previous surgery ( p=0.0001 ) . eight patients had eye surgery , two other hip fracture , and one knee prosthesis . number of co - existent disease there were no statistically significant differences between the patients of good and poor health status ( p=0.164 ) ( table 2 ) . during the three months there were no significant differences in deaths compared to asa score of 1 and 2 ( p=0.52 ) . subtrochanteric type was classified as : 2 as ii a ; 2 as iib ; 1 as iic ; 3 as iiia ; 1 as iiib ; 1 as iv ; 5 as v. there were no statistically significant differences between types a1 , a2 , a3 fractures ( p=0.56 ) . there were no statistically significant difference between stable and unstable fractures ( p = 0.06 ) . asa score health status 18 ( 38.6% ) patients did not receive blood . on average , most blood , 3300 ml , received a patient with attempted suicide ( fracture of the pelvis ) , and patients with infection , revision surgery and nonunion 2530 ml . it was found significantly more patients who received blood or blood products ( p=0.0001 ) . the number of intraoperative radiation exposure was 65 ( range , 13 to 148 exposures ) . the average duration of surgery was 73.138 min ( range , 30 to 210 min ) . in 13(20.6% ) patients were not strictly followed the technical steps ( p=0.009 ) ( table 3 ) . of the two poor positioning the blade in one we performed reoperation 12 days after the first surgery ( infection and died ) . another poor positioned blade is brought to cut out , nonunion and removal of the same ( table 4 ) . intraoperative complications the most common postoperative complication in the treatment was mental disturbances ( p=0.017 ) . five out of six subjects , the asa was 3 and 4 but there was no statistical significance ( p=0.09 ) . one patient developed deep vein thrombosis and was diagnosed by color doppler sonography after a week postoperatively and treated by the high dose of low - molecular - weight heparin ( figure 1 ) . post - operative complications and hospital stay reoperation for the treatment of implant or fracture - related complications was required in three patients ( infection , reimplantation and extraction ) . there were three nonunion : one is infected nonunion ( staphylococcus aureus ) , one after the cut outs ( the blade was poor placed ) . the three patients underwent reoperation : after the broken targon pf , occurred cut out blade ( nonunion , dropped from the new operative treatment , patient alive , walk with a walker indoors ) , and when we removed the broken angular plates of 130 , there was a healing and a full functional recovery ( nms=9 ) , after removal of the condylar blade plate and complications with urinary infection , the patient did not walk and died the eighty - eighth postoperative day . fracture - related postoperative complications and gender of the patient fracture - related postoperative complications and outcome there was no mechanical failure of the implants despite the early patient mobilization . the incidence of deaths in the first three months was more frequent ( 10/16 ) of which seven women ( p=0.20 ) . two patients died in the early postoperative period in the hospital and one for complications nine months after surgery ( figure 4 ) . two patients have been moved to the physiotherapy and the others were discharged home , regardless of functional recovery . one patient who returned to pre - fracture mobility status died after 15 and the other after 19 months . wilcoxon test was used to establish whether differences of parameters measuring preinjury and postoperative mobility score . the incidence of hip fractures has been growing as a result of longer life expectancy owing to better quality of life but also better health care . these patients usually have additional systemic diseases and require prolonged hospital stay after fracture occurrence , making them susceptible to many complications that adversely affect prognosis and increase mortality , such as deep vein thrombosis , pulmonary embolism , pneumonia , urinary tract infections , and pressure ulcers . for this reason , there is general consensus in the literature that the primary goal of treatment should be to obtain a stable fixation of the fracture that will allow early mobilization ( 1 ) . study on 3628 patients shows a significant increase in length of stay that was found in patients operated on after 48 hours when compared with those in the earlier group ( 21.6 vs 32.5 days ) . their study did not find any difference in mortality rates for patients who underwent surgery within 48 hours of admission . any delay of more than 48 hours , other than to improve an acute and treatable condition , must be avoided ( 2 ) . in our study there were 33(52.3% ) patients operated on within 72 h of their injury , the average length of hospital stay was 12.96.2 days . in 26(41.2% ) patients the asa class is strongly associated with medical problems in the perioperative period following hip fracture surgery in the elderly . patients in asa class 3 had a 3.78 times greater chance of having a medical complication than did those in class 2 ( p < 0.001 ) . patients in asa class 4 had a 7.39 times greater chance of having medical complications than did those in class 2 ( p = 0.001 ) . no significant relationship was identified between the asa class and surgical complications ( 9 ) . in our study there were no statistically significant differences in the patients of good and poor health status ( p=0.164 ) . during the three months postoperatively with asa score 3 and 4 six patients died . there were no significant differences in deaths compared to asa score of 1 and 2 ( p=0.52 ) . five out of six subjects , the asa was 3 and 4 but there was no statistical significance ( p=0.09 ) . concluded that a delay of more than 24 hours resulted in a mortality rate of 34% vs 11% for patients treated between the second and fifth day . they included patients with serious medical comorbidities in their study , and recommended a delay of 24 hours to treat and improve acute medical conditions ( 10 ) . believe that early operation was crucial for the good functional outcome and for the absence of serious postoperative complications . all 112 patients were operated on within 36 h of their injury , and 59% of the patients were operated on within the first 6 h. at the latest follow - up , 65% of the patients of the gamma nail group and 63% of the patients of the ace tn group had reached the preoperative mobility status . additionally , there was no significant difference between the two groups as far as the final mobility scores were concerned . of the patients five were lost to follow - up and 19 died within the study period ( 3 ) . considering the injuries , the length of hospitalization and surgeries in our study , we expected to have poorer results . statistically significant difference was found in the deaths in the first three months compared to the next three months ( p=0.02 ) . theoretically and experimentally due to de - central implant positioning the load torque can outrun resistance of the cancellous bone around the implant in normal daily activities . the center - center position in the head of femur of any kind of lag screw or blade is to be achieved to minimize rotation of the femoral head and to prevent further mechanical complications ( 11 ) . in our study in one , 12 days after the first surgery was performed reoperation ( infection and died ) . another poor positioned blade is brought to cut out , nonunion and removal of the same . study shows that osteosynthesis with the pfna does not improve the position of the implant in the femoral head compared with the pfn . however , the risk of a secondary complication and the necessity of a late reoperation are significantly higher in patients treated with a pfn compared with patients treated with a pfna because of implant - related complications , three patients in the pfn group and four patients in the pfna group needed an early reoperation ( p=0.136 ) ( 12 ) . in our study , long or short blade was no indication of a new surgical treatment . after the broken targon pf , occurred cut out blade ( nonunion , dropped from the new operative treatment , patient alive , walk with a walker indoors ) . reoperation for the treatment of implant or fracture - related complications was required in three ( 4.7% ) patients ( infection , reimplantation and extraction ) . emphasizes that regardless of the implant choice and its specific technical characteristics , in the end , it is the technique of inserting it properly that is the key to succeed with stable fixation and prevent major complications ( 13 ) . in our study there were 13(20.6% ) patients where not strictly followed the technical steps with one cut out ( p = 0.009 ) . there were two deep and one superficial infection ( 4.8% ) . in a large study from strasbourg in 3066 patients was 1.5% infection and 1.85% cut out ( 14 ) . the american college of surgeons national surgical quality improvement program database was used to identify 4331 patients undergoing surgery for hip fracture . patient age , especially age greater than 80 years and male gender were associated with both increased mortality and morbidity . additionally , complete functional dependence , active malignancy , patient race , cardiopulmonary disease , laboratory derangements , prolonged operating time , and open versus percutaneous surgery independently influenced outcomes ( 15 ) . in our study of the 16 deaths , eight were females . the incidence of deaths in the first three months was more frequent ( 10/16 ) of which seven women ( p = 0.20 ) . two patients died in the early postoperative period in the hospital and one for complications nine months after surgery . surgical technique is an important factor in the outcome of treatment for intertrochanteric hip fracture , and that it can be influenced by education and improved methods of assessment ( 16 ) . despite the poor results in the treatment of intertrochanteric fractures in comparison with other studies which occur as a result : a longer time the past from injury to admission , time from admission to surgery , comorbidity , lack of proper implants and deviations from strict surgical techniques , we have concluded that pfna is an excellent device for osteosynthesis as it can be easily inserted and provides stable fixation , which allows early full weight bearing mobilization of the patient .

introduction : fractures of the proximal femur and hip are relatively common injuries in adults and common source of morbidity and mortality among the elderly . many methods have been recommended for the treatment of intertrochanteric fractures.material and methods : we retrospective analyzed all the patients with fractures of the hip treated with proximal femoral nail antirotation ( pfna ) at the clinic of orthopedic and traumatology , university clinical centre tuzla from the first of january 2012 to 31 december 2012 years . the study included 63 patients averaged 73.611.9 years ( range , 29 to 88 years ) . fracture type was classified as intertrochanteric ( arbeitsgemeinschaft fr osteosynthesefragen classification 31.a.1 , a.2 and a.3 ) and subtrochanteric fractures ( seinsheimer classification).results and discussion : the ratio between the genders female - male was 1.6:1 . there was statistically significant difference prevalence of female compared to male patients ( p=0.012 ) . there were 31 left and 32 right hip fractured . low energy trauma was the cause of fractures in 57(90.5% ) patients . averaged waiting time for hospitalization was 3.27.5 days ( range , 0 to 32 days ) . 44 patients were admitted the same day upon injuring . the average waiting time for the treatment was 3.65.7 days . the ratio between with or without co - existent disease was 4.7:1 . during the three months postoperatively with asa score 3 and 4 six patients died . there were no significant differences in deaths from asa score 1 and 2 ( p=0.52 ) . reoperation for the treatment of implant or fracture - related complications was required in three ( 4.7% ) patients ( infection , reimplantation and extraction ) . three patient developed deep vein thrombosis . statistically significant difference was found in the deaths in the first three months compared to the next three months ( p=0.02 ) . we found statistically significant difference between pre - injury and postoperative mobility score ( p=0.0001).conclusion : pfna is an excellent device for osteosynthesis as it can be easily inserted . moreover , it provides stable fixation , which allows early full weightbearing mobilization of the patient .

1. INTRODUCTION 2. STATISTICAL ANALYSIS 3. PATIENTS AND METHODS 4. RESULTS 5. DISCUSSION 6. CONCLUSION

cell nuclei in two - dimensional ( 2d ) pathology images can yield quantitative information about the presence or absence of disease processes and also help evaluate disease progress . detecting and segmenting nuclei correctly with minimum human effort is important for cell nuclei analysis . jung and kim showed that improved segmentation accuracy led to better classification performance using the unique classifier for thyroid follicular lesions . however , automatic nuclei segmentation in pathology images still remains a difficult problem due to the high variability in images caused by differences in slide preparation , image acquisition , and nuclei heterogeneity . cell nuclei detection plays a critical role in the overall segmentation procedure , which requires a point per nucleus and close to nucleus center , referred to as seed . many approaches have been described in the literature to locate cell nuclei in 2d microscopy images . the combination of finding peaks in the euclidean distance map and watershed , though often resulting in overseeding , can be applied to locate seeds . the circular - shaped nuclei can be effectively located using hough transformation methods at the cost of expensive computation . h - maxima / minima transform is a powerful approach to detect nuclei by finding the local maximums in images . the multiscale laplacian - of - gaussian ( log ) filtering constrained by the distance map - based adaptive scale selection can be used to detect cell nuclei . this method improves seed accuracy but is sensitive to minor peaks in the distance map and thus leads to overseeding . qi et al . proposed a method based on single - path voting followed by mean - shift clustering to find seeds for touching and overlapping nuclei . speaking of segmentation methods more broadly , a wide range of methods has been described in the literature . thresholding , morphological operation , watershed , region growing , active contour model , clustering , and graph cut are the cornerstones of the segmentation methods proposed in the literature . the simplest thresholding method followed by morphological operation works well for objects with little intensity variations and high foreground / background contrast . watershed is a nonparametric method widely applied in nuclei segmentation , with the disadvantage of over - segmentation . active contour models can be used to obtain a smooth contour by minimizing an energy function and can be utilized in pathology images where nuclei appear unclear . the well - known chan and vese model was used to obtain the outer contours of nuclei , followed by a watershed - like algorithm to separate the clustered nuclei . al - kofahi et al . utilized a graph - cut - based binarization to extract the foreground and then a second graph - cut - based algorithm to refine the initial contours obtained by constrained multiscale log filter , which was shown to perform well in pathology images with dense nuclei . proposed a method called ovuscule which was a modified snake model taking the shape of an ellipse . its evolution is driven by the combination of the integral of data over the inner ellipse and outer elliptical shell . more nuclei segmentation methods including active contour model , watershed - based method , and markov random field are described in irshad paper . here , we show a comparison between the method we propose and a few such modern methods . in this paper , we describe an unsupervised nuclei segmentation method , which we call multiscale edge selection in polar space ( mesps ) . specifically , a filter bank consisting of rings with various sizes is first constructed to locate nuclei by finding the local maximums in the response map . in the segmentation step , the nuclei contours are iteratively refined by selecting the correct edges in polar space at different smoothing levels . we believe the accurate nature of the segmentation procedure , simplicity of use , and computational efficiency are key advantages of our method as will be demonstrated . an edge pyramid is then constructed , where edge maps are generated using a set of smooth parameters . edge selection is performed at each level and the nuclei contour evolves across the edge pyramid to delineate the spatial content of cell nuclei tissue blocks and cytology slides were obtained from the archives of a local hospital ( approved as an exempt protocol by the institutional review board ) . cases for analysis included liver resection specimens and cytology slides prepared from fine - needle aspiration biopsies of thyroid nodules . all tissues were fixed in 10% neutral - buffered formalin and processed on a conventional tissue processor using a series of graded alcohols and xylenes before paraffin embedding . tissue sections were cut at 5 thickness from the paraffin - embedded block and placed on conventional 25 mm 75 mm 1.0 mm superfrost plus microscope slides using fisherbrand superslip coverslips ( 50 mm 24 mm 0.17 mm ; fisher scientific , thermo fisher scientific , inc . , all tissue sections for imaging were stained using conventional hematoxylin and eosin ( h and e ) protocol used in the histology laboratory . for the thyroid cytology preparations , aspirate smears were fixed in 95% ethanol and then stained with the papanicolaou ( pap ) staining technique . briefly , the pap stain uses hematoxylin , og-6 , and eosin azure ( combination of eosin y , light - green sf , and green fcf dyes ) to stain cytological preparations . nuclei stained with this technique have blue - green color and excellent chromatin detail that can be visualized by light microscopy . whole slide digital images of the liver slides were acquired using an omnyx vl4 digital whole slide scanner ( omnyx , llc , waterfront pi , pittsburg , pa , usa ) equipped with a 60 dry objective . images obtained had a resolution of 0.1375 /pixel and were saved in the proprietary format and then converted to lossless jpeg format . all thyroid cytology slide images were acquired using an olympus bx51 microscope equipped with a 100 uis2 uplanfl oil immersion objective ( numerical aperture 1.30 ; olympus america , central valley , pa , usa ) and 2 megapixel spot insight camera ( diagnostic instruments , sterling heights , mi , usa ) . image specifications were 24-bit rgb channels and 0.074 /pixel , 118 89 m field of view . the basic idea of nuclei detection is to find local evidence for the presence or absence of a nucleus in the image . to that end , we construct a filter bank composed of rings of different sizes modeled by the function : r x + y ( r + ) , where r is the radius and is the thickness . given a certain dataset , prior information such as , the size of the smallest and largest nuclei can be reasonably estimated ; thus , the size range of the filters can be defined according to image resolution . we note that the shape of filters can be changed and modeled by different functions to adapt the nuclei appearance in different datasets . in our experiment , the sampled locations = [ xi , yi ] can be obtained from a set of centered coordinates [ x1 , , x2r + 1 ] , r xi r + the filter image patch with size r denoted as fr ( ) is convolved with a gaussian function , which is meant to be an approximation of point spread function . given an image i ( ) , the likelihood of the pixel at being the center of an underlying nucleus is defined as follows : where denotes the normalized cross correlation ( ncc ) between the filter fr ( ) and the image i. and with being the neighborhood of pixel of the same size as the filter fr ( ) . the maximization procedure above is performed pixel by pixel searching for the filter fr within the filter bank which best matches the appearance of the potential nucleus at location . pixels having ring - shaped surrounding pixels with similar radius as that of a filter will have strong responses and are likely to be nuclei centers . on the contrary , irrelevant tissue structures or noisy background thus , the method is able to yield size estimation for each nucleus by searching for the best - matched filters . here , we note that most nuclei take the shape of an ellipse and thus , theoretically , elliptical filters would generate stronger responses compared with ring - shaped filters . however , since more parameters ( e.g. , length of major and minor axis , rotation angle ) would be required to control an ellipse , leading to a larger searching space when performing ncc operation , we use the ring - shaped filters instead . as we can see from the simulation experiment [ figure 2 ] , ring - shaped filters are able to generate the strong responses when applied to detect both circular and elliptical nuclei in noisy background . ( a ) constructed filter bank with filters of different sizes ( magnified for viewing purpose ) . ( e ) response map for ( d ) to locate the cell nuclei , the standard k - means clustering method is applied to classify the responses into three classes based on the response intensity : ( 1 ) background ; ( 2 ) weak responses from nonnuclei structures ; ( 3 ) strong responses from potential nuclei . using connected component analysis , nuclei seeds can be obtained by computing the mass center of each isolated pixel cluster classified as strong responses . ( d ) detected nuclei seeds ( green dots ) in practice , the false positive nuclei seeds can be filtered out by postprocessing operations , such as thresholding the area of isolated pixels clusters . with detected nuclei seeds , it is required that the subsequent segmentation algorithm delineate the nuclei contours efficiently and accurately with minimal manual intervention . our goal is to segment nuclei correctly in the complex background ( existence of a large variety of nuclei morphology , chromatin texture , staining procedure as well as tissue heterogeneity ) . as well known , edge detection produces outlines at locations where large gradient exists , for example , nuclei borders and noisy background structures [ figure 4a ] . to obtain the initial segmentation , a blurred version of the nuclei image is required , which describes the nuclei outlines and excludes noisy details hindering the delineation of nuclei contours . the multiscale strategy enables the nucleus contour to refine iteratively from the initial segmentation by changing the blur parameter smoothly . the proposed method is designed to discriminate the nuclei borders pixels from remaining garbage pixels . ( a ) original image with a subwindow showing the edge map for one nucleus ( detected by canny edge detector , i = 3 ) with the seed in the center ( red dot ) . ( b ) edge pixels are transformed into polar space with the nucleus seed being the origin . red points are the locations with locally maximal number of pixels ; green points show the edge pixels along the optimal path searched by dijkstra 's algorithm . ( c ) constructed undirected graph with nodes being the red points in ( b ) and edge weights being the cost defined by the combination of distance and intensity metrics . ( d ) final contour ( red ) , and optimal path ( green ) are shown in the image patch specifically , the input image is first convolved with the 2d gaussian function with zero mean at multiple scales = [ 0, ,n1 ] , with 0 and n1 being the minimum and the maximum of , respectively . next , an edge pyramid is constructed consisting of a set of edge maps generated by the edge detector ( e.g. , canny detector ) , where the top level and the bottom level correspond to 0 and n1 , respectively . we aim to select the correct edges in polar space starting from the bottom level and then take it as guidance for edge selection in the next higher level . the algorithm refines the contour iteratively and produces the final contour when edge selection is performed at the top level of the edge pyramid . the first step is to select correct edges from the edge map obtained at the largest scale n1 , where artifacts are the least prevalent . the size of the image patch for each nucleus can be determined adaptively according to the size estimation from nuclei detection step . in the nucleus edge map , edges can be classified into three categories : correct edges ( forming the nucleus contour ) , edges inside the nucleus , and edges outside the nucleus . one prominent feature to discriminate these three kinds of edges is that , intuitively , correct edge pixels on the nucleus counter often have smoother distance changes away from the seed in comparison to the drastic distance fluctuations of pixels on noisy edges inside or outside the nucleus . in addition , considering the intensity , edge pixels along the nucleus border have relatively consistent intensity compared with that of incorrect edge pixels . with these simple observations in mind , the solution of delineating nucleus contour becomes finding the path with the minimal transportation cost ( nonzero ) starting and ending at any chosen point on the nucleus border based on both distance and intensity metrics . the polar coordinate system provides a natural space to search for the optimal path connecting the start point and the end point for each nucleus . given the edge map ei detected at the i level , edge pixel = [ x , y ] in cartesian coordinate can be transformed into polar space by , where = [ x , y ] is the coordinate of nucleus seed in the image patch . figure 4b shows that the edge map in the subwindow of figure 4a is transformed in polar space . in the polar coordinate system , the transportation cost between any two neighbor edge pixels pm = [ rm , ] and pn = [ rn , + ] is defined as follows : where vm and vn denote pixel intensities for pm and pn ; is infinitesimal ; a , b are the weights for the distance term and intensity term , respectively ; rmax and vmax are the maximal distance difference and the maximal intensity difference , respectively , between pm and pn in the edge map , enabling both two metrics to have the same scale . the optimal path * can be found by minimizing the function defined as follows : where l denotes the length for the path . in the discrete setting , the function above can be rewritten as follows : where n is the number of edge pixels along the path . dijkstra 's algorithm is an algorithm widely applied to find the shortest path between the source node and the terminal node in a graph , such as road networks and telephone network . we represent the edge pixels in polar space in the form of undirected graph g = [ v , e ] [ figure 4c ] , denote the edge pixels and the graph edges with weights c( , pm , pn ) in e are only feasible for any two adjacent angle nodes pm , pn . to make the algorithm robust against noisy edge pixels , the edge pixels are further represented / discretized by finding the locations with locally a maximal number of edge pixels for each angle in the polar space . a sliding window with width w and height h , moving along the distance direction for each , the number of edge pixels in the sliding window centered at [ rj , i ] is denoted as n ( rj , i ) and locations with locally maximal number of pixels at angle i are denoted as ( i ) . these detected locations are the approximate representation of the original edge pixels in polar space [ red dots in figure 4b ] . the benefit of discretizing edge pixels is that it helps reduce the number of possible paths between the source node and the terminal node . thus , the computational cost is reduced dramatically when searching for the optimal path using dijkstra 's algorithm . in practice , it is not easy to select the source node and terminal node along the nucleus border . in this paper , we propose that the source node and the terminal node can be chosen as edge pixels with the same distances away from the seed at angle 0 and 2. however , there might be multiple source - terminal pairs in the graph , and thus multiple optimal paths are found by dijkstra 's algorithm . this is so especially when a small is applied , where many noisy edge pixels exist at the angle 0 and 2. when noisy edge pixels are selected as the source or terminal node , the optimal path would be searched by dijkstra 's algorithm at the cost of passing through edges with large weights in the constructed graph . thus , the real nucleus contour can be found by choosing the path with the minimal cost connecting source - terminal pairs . one potential issue is that some detected edges may not be complete due to the weak gradient at the nucleus border and thus some pixels along the optimal path are not necessarily on the real nucleus contour . here , we apply the ransac algorithm and the spline curve fitting method to estimate the nucleus contour . given the edge pixels on the optimal path , a subset of pixels is selected to generate a fitted curve model describing the rough shape of the optimal path . the points fit the estimated model well are called inliers and points with large errors are called outliers . the step repeats for a fixed number of times , and the model with the maximal number of inliers is kept . the curve fitting step takes as input the pixels along the optimal path and outputs the final smooth contour c connecting the isolated and incomplete detected edges when performed at the k level of the edge pyramid . the smooth contour generated from the k level is taken as the initial nucleus border and helps guide the edge selection for the k + 1 level . specifically , at the k + 1 level , edge pixels within the distance range [ c d , c + d ] are chosen as edge candidates and edge pixels outside the range are discarded in the sense that a more refined contour at the k + 1 level should be close to the contour obtained from the k level with a distance tolerance d. when the blur parameter is changed slightly , the edge locations change smoothly and would not shift too much . therefore , for the k + 1 level , the edge pixel locations at angle should be within the range [ c()d , c( ) + d ] . with the set of edge candidates , the edge selection is performed as described above to generate a more accurate nucleus contour c. as the contour is refined iteratively from the bottom level of the edge pyramid up to the top level , it gradually attaches to the real border of nucleus . given the small blurring 0 at the top level , our algorithm can delineate the nucleus spatial extent precisely . tissue blocks and cytology slides were obtained from the archives of a local hospital ( approved as an exempt protocol by the institutional review board ) . cases for analysis included liver resection specimens and cytology slides prepared from fine - needle aspiration biopsies of thyroid nodules . all tissues were fixed in 10% neutral - buffered formalin and processed on a conventional tissue processor using a series of graded alcohols and xylenes before paraffin embedding . tissue sections were cut at 5 thickness from the paraffin - embedded block and placed on conventional 25 mm 75 mm 1.0 mm superfrost plus microscope slides using fisherbrand superslip coverslips ( 50 mm 24 mm 0.17 mm ; fisher scientific , thermo fisher scientific , inc . , all tissue sections for imaging were stained using conventional hematoxylin and eosin ( h and e ) protocol used in the histology laboratory . for the thyroid cytology preparations , aspirate smears were fixed in 95% ethanol and then stained with the papanicolaou ( pap ) staining technique . briefly , the pap stain uses hematoxylin , og-6 , and eosin azure ( combination of eosin y , light - green sf , and green fcf dyes ) to stain cytological preparations . nuclei stained with this technique have blue - green color and excellent chromatin detail that can be visualized by light microscopy . whole slide digital images of the liver slides were acquired using an omnyx vl4 digital whole slide scanner ( omnyx , llc , waterfront pi , pittsburg , pa , usa ) equipped with a 60 dry objective . images obtained had a resolution of 0.1375 /pixel and were saved in the proprietary format and then converted to lossless jpeg format . all thyroid cytology slide images were acquired using an olympus bx51 microscope equipped with a 100 uis2 uplanfl oil immersion objective ( numerical aperture 1.30 ; olympus america , central valley , pa , usa ) and 2 megapixel spot insight camera ( diagnostic instruments , sterling heights , mi , usa ) . image specifications were 24-bit rgb channels and 0.074 /pixel , 118 89 m field of view . the basic idea of nuclei detection is to find local evidence for the presence or absence of a nucleus in the image . to that end , we construct a filter bank composed of rings of different sizes modeled by the function : r x + y ( r + ) , where r is the radius and is the thickness . given a certain dataset , prior information such as , the size of the smallest and largest nuclei can be reasonably estimated ; thus , the size range of the filters can be defined according to image resolution . we note that the shape of filters can be changed and modeled by different functions to adapt the nuclei appearance in different datasets . in our experiment , the sampled locations = [ xi , yi ] can be obtained from a set of centered coordinates [ x1 , , x2r + 1 ] , r xi r + the filter image patch with size r denoted as fr ( ) is convolved with a gaussian function , which is meant to be an approximation of point spread function . given an image i ( ) , the likelihood of the pixel at being the center of an underlying nucleus is defined as follows : where denotes the normalized cross correlation ( ncc ) between the filter fr ( ) and the image i. and with being the neighborhood of pixel of the same size as the filter fr ( ) . the maximization procedure above is performed pixel by pixel searching for the filter fr within the filter bank which best matches the appearance of the potential nucleus at location . pixels having ring - shaped surrounding pixels with similar radius as that of a filter will have strong responses and are likely to be nuclei centers . on the contrary , irrelevant tissue structures or noisy background thus , the method is able to yield size estimation for each nucleus by searching for the best - matched filters . here , we note that most nuclei take the shape of an ellipse and thus , theoretically , elliptical filters would generate stronger responses compared with ring - shaped filters . however , since more parameters ( e.g. , length of major and minor axis , rotation angle ) would be required to control an ellipse , leading to a larger searching space when performing ncc operation , we use the ring - shaped filters instead . as we can see from the simulation experiment [ figure 2 ] , ring - shaped filters are able to generate the strong responses when applied to detect both circular and elliptical nuclei in noisy background . ( a ) constructed filter bank with filters of different sizes ( magnified for viewing purpose ) . ( b ) ( e ) response map for ( d ) to locate the cell nuclei , the standard k - means clustering method is applied to classify the responses into three classes based on the response intensity : ( 1 ) background ; ( 2 ) weak responses from nonnuclei structures ; ( 3 ) strong responses from potential nuclei . using connected component analysis , nuclei seeds can be obtained by computing the mass center of each isolated pixel cluster classified as strong responses . ( d ) detected nuclei seeds ( green dots ) in practice , the false positive nuclei seeds can be filtered out by postprocessing operations , such as thresholding the area of isolated pixels clusters . with detected nuclei seeds , it is required that the subsequent segmentation algorithm delineate the nuclei contours efficiently and accurately with minimal manual intervention . our goal is to segment nuclei correctly in the complex background ( existence of a large variety of nuclei morphology , chromatin texture , staining procedure as well as tissue heterogeneity ) . as well known , edge detection produces outlines at locations where large gradient exists , for example , nuclei borders and noisy background structures [ figure 4a ] . to obtain the initial segmentation , a blurred version of the nuclei image is required , which describes the nuclei outlines and excludes noisy details hindering the delineation of nuclei contours . the multiscale strategy enables the nucleus contour to refine iteratively from the initial segmentation by changing the blur parameter smoothly . the proposed method is designed to discriminate the nuclei borders pixels from remaining garbage pixels . ( a ) original image with a subwindow showing the edge map for one nucleus ( detected by canny edge detector , i = 3 ) with the seed in the center ( red dot ) . ( b ) edge pixels are transformed into polar space with the nucleus seed being the origin . red points are the locations with locally maximal number of pixels ; green points show the edge pixels along the optimal path searched by dijkstra 's algorithm . ( c ) constructed undirected graph with nodes being the red points in ( b ) and edge weights being the cost defined by the combination of distance and intensity metrics . ( d ) final contour ( red ) , and optimal path ( green ) are shown in the image patch specifically , the input image is first convolved with the 2d gaussian function with zero mean at multiple scales = [ 0, ,n1 ] , with 0 and n1 being the minimum and the maximum of , respectively . next , an edge pyramid is constructed consisting of a set of edge maps generated by the edge detector ( e.g. , canny detector ) , where the top level and the bottom level correspond to 0 and n1 , respectively . we aim to select the correct edges in polar space starting from the bottom level and then take it as guidance for edge selection in the next higher level . the algorithm refines the contour iteratively and produces the final contour when edge selection is performed at the top level of the edge pyramid . the first step is to select correct edges from the edge map obtained at the largest scale n1 , where artifacts are the least prevalent . the size of the image patch for each nucleus can be determined adaptively according to the size estimation from nuclei detection step . in the nucleus edge map , edges can be classified into three categories : correct edges ( forming the nucleus contour ) , edges inside the nucleus , and edges outside the nucleus . one prominent feature to discriminate these three kinds of edges is that , intuitively , correct edge pixels on the nucleus counter often have smoother distance changes away from the seed in comparison to the drastic distance fluctuations of pixels on noisy edges inside or outside the nucleus . in addition , considering the intensity , edge pixels along the nucleus border have relatively consistent intensity compared with that of incorrect edge pixels . with these simple observations in mind , the solution of delineating nucleus contour becomes finding the path with the minimal transportation cost ( nonzero ) starting and ending at any chosen point on the nucleus border based on both distance and intensity metrics . the polar coordinate system provides a natural space to search for the optimal path connecting the start point and the end point for each nucleus . given the edge map ei detected at the i level , edge pixel = [ x , y ] in cartesian coordinate can be transformed into polar space by , where = [ x , y ] is the coordinate of nucleus seed in the image patch . figure 4b shows that the edge map in the subwindow of figure 4a is transformed in polar space . in the polar coordinate system , the transportation cost between any two neighbor edge pixels pm = [ rm , ] and pn = [ rn , + ] is defined as follows : where vm and vn denote pixel intensities for pm and pn ; is infinitesimal ; a , b are the weights for the distance term and intensity term , respectively ; rmax and vmax are the maximal distance difference and the maximal intensity difference , respectively , between pm and pn in the edge map , enabling both two metrics to have the same scale . the optimal path * can be found by minimizing the function defined as follows : where l denotes the length for the path . in the discrete setting , the function above can be rewritten as follows : where n is the number of edge pixels along the path . dijkstra 's algorithm is an algorithm widely applied to find the shortest path between the source node and the terminal node in a graph , such as road networks and telephone network . we represent the edge pixels in polar space in the form of undirected graph g = [ v , e ] [ figure 4c ] , denote the edge pixels and the graph edges with weights c( , pm , pn ) in e are only feasible for any two adjacent angle nodes pm , pn . to make the algorithm robust against noisy edge pixels , the edge pixels are further represented / discretized by finding the locations with locally a maximal number of edge pixels for each angle in the polar space . a sliding window with width w and height h , moving along the distance direction for each , the number of edge pixels in the sliding window centered at [ rj , i ] is denoted as n ( rj , i ) and locations with locally maximal number of pixels at angle i are denoted as ( i ) . these detected locations are the approximate representation of the original edge pixels in polar space [ red dots in figure 4b ] . the benefit of discretizing edge pixels is that it helps reduce the number of possible paths between the source node and the terminal node . thus , the computational cost is reduced dramatically when searching for the optimal path using dijkstra 's algorithm . in practice , it is not easy to select the source node and terminal node along the nucleus border . in this paper , we propose that the source node and the terminal node can be chosen as edge pixels with the same distances away from the seed at angle 0 and 2. however , there might be multiple source - terminal pairs in the graph , and thus multiple optimal paths are found by dijkstra 's algorithm . this is so especially when a small is applied , where many noisy edge pixels exist at the angle 0 and 2. when noisy edge pixels are selected as the source or terminal node , the optimal path would be searched by dijkstra 's algorithm at the cost of passing through edges with large weights in the constructed graph . thus , the real nucleus contour can be found by choosing the path with the minimal cost connecting source - terminal pairs . one potential issue is that some detected edges may not be complete due to the weak gradient at the nucleus border and thus some pixels along the optimal path are not necessarily on the real nucleus contour . here , we apply the ransac algorithm and the spline curve fitting method to estimate the nucleus contour . given the edge pixels on the optimal path , a subset of pixels is selected to generate a fitted curve model describing the rough shape of the optimal path . the points fit the estimated model well are called inliers and points with large errors are called outliers . the step repeats for a fixed number of times , and the model with the maximal number of inliers is kept . the curve fitting step takes as input the pixels along the optimal path and outputs the final smooth contour c connecting the isolated and incomplete detected edges when performed at the k level of the edge pyramid . the smooth contour generated from the k level is taken as the initial nucleus border and helps guide the edge selection for the k + 1 level . specifically , at the k + 1 level , edge pixels within the distance range [ c d , c + d ] are chosen as edge candidates and edge pixels outside the range are discarded in the sense that a more refined contour at the k + 1 level should be close to the contour obtained from the k level with a distance tolerance d. when the blur parameter is changed slightly , the edge locations change smoothly and would not shift too much . therefore , for the k + 1 level , the edge pixel locations at angle should be within the range [ c()d , c( ) + d ] . with the set of edge candidates , the edge selection is performed as described above to generate a more accurate nucleus contour c. as the contour is refined iteratively from the bottom level of the edge pyramid up to the top level , it gradually attaches to the real border of nucleus . given the small blurring 0 at the top level , our algorithm can delineate the nucleus spatial extent precisely . the first step is to select correct edges from the edge map obtained at the largest scale n1 , where artifacts are the least prevalent . the size of the image patch for each nucleus can be determined adaptively according to the size estimation from nuclei detection step . in the nucleus edge map , edges can be classified into three categories : correct edges ( forming the nucleus contour ) , edges inside the nucleus , and edges outside the nucleus . one prominent feature to discriminate these three kinds of edges is that , intuitively , correct edge pixels on the nucleus counter often have smoother distance changes away from the seed in comparison to the drastic distance fluctuations of pixels on noisy edges inside or outside the nucleus . in addition , considering the intensity , edge pixels along the nucleus border have relatively consistent intensity compared with that of incorrect edge pixels . with these simple observations in mind , the solution of delineating nucleus contour becomes finding the path with the minimal transportation cost ( nonzero ) starting and ending at any chosen point on the nucleus border based on both distance and intensity metrics . the polar coordinate system provides a natural space to search for the optimal path connecting the start point and the end point for each nucleus . given the edge map ei detected at the i level , edge pixel = [ x , y ] in cartesian coordinate can be transformed into polar space by , where = [ x , y ] is the coordinate of nucleus seed in the image patch . figure 4b shows that the edge map in the subwindow of figure 4a is transformed in polar space . in the polar coordinate system , the transportation cost between any two neighbor edge pixels pm = [ rm , ] and pn = [ rn , + ] is defined as follows : where vm and vn denote pixel intensities for pm and pn ; is infinitesimal ; a , b are the weights for the distance term and intensity term , respectively ; rmax and vmax are the maximal distance difference and the maximal intensity difference , respectively , between pm and pn in the edge map , enabling both two metrics to have the same scale . the optimal path * can be found by minimizing the function defined as follows : where l denotes the length for the path . in the discrete setting , the function above can be rewritten as follows : where n is the number of edge pixels along the path . dijkstra 's algorithm is an algorithm widely applied to find the shortest path between the source node and the terminal node in a graph , such as road networks and telephone network . we represent the edge pixels in polar space in the form of undirected graph g = [ v , e ] [ figure 4c ] , denote the edge pixels and the graph edges with weights c( , pm , pn ) in e are only feasible for any two adjacent angle nodes pm , pn . to make the algorithm robust against noisy edge pixels , the edge pixels are further represented / discretized by finding the locations with locally a maximal number of edge pixels for each angle in the polar space . a sliding window with width w and height h , moving along the distance direction for each , the number of edge pixels in the sliding window centered at [ rj , i ] is denoted as n ( rj , i ) and locations with locally maximal number of pixels at angle i are denoted as ( i ) . these detected locations are the approximate representation of the original edge pixels in polar space [ red dots in figure 4b ] . the benefit of discretizing edge pixels is that it helps reduce the number of possible paths between the source node and the terminal node . thus , the computational cost is reduced dramatically when searching for the optimal path using dijkstra 's algorithm . in practice , it is not easy to select the source node and terminal node along the nucleus border . in this paper , we propose that the source node and the terminal node can be chosen as edge pixels with the same distances away from the seed at angle 0 and 2. however , there might be multiple source - terminal pairs in the graph , and thus multiple optimal paths are found by dijkstra 's algorithm . this is so especially when a small is applied , where many noisy edge pixels exist at the angle 0 and 2. when noisy edge pixels are selected as the source or terminal node , the optimal path would be searched by dijkstra 's algorithm at the cost of passing through edges with large weights in the constructed graph . thus , the real nucleus contour can be found by choosing the path with the minimal cost connecting source - terminal pairs . one potential issue is that some detected edges may not be complete due to the weak gradient at the nucleus border and thus some pixels along the optimal path are not necessarily on the real nucleus contour . here , we apply the ransac algorithm and the spline curve fitting method to estimate the nucleus contour . given the edge pixels on the optimal path , a subset of pixels is selected to generate a fitted curve model describing the rough shape of the optimal path . the points fit the estimated model well are called inliers and points with large errors are called outliers . the step repeats for a fixed number of times , and the model with the maximal number of inliers is kept . the curve fitting step takes as input the pixels along the optimal path and outputs the final smooth contour c connecting the isolated and incomplete detected edges when performed at the k level of the edge pyramid . the smooth contour generated from the k level is taken as the initial nucleus border and helps guide the edge selection for the k + 1 level . specifically , at the k + 1 level , edge pixels within the distance range [ c d , c + d ] are chosen as edge candidates and edge pixels outside the range are discarded in the sense that a more refined contour at the k + 1 level should be close to the contour obtained from the k level with a distance tolerance d. when the blur parameter is changed slightly , the edge locations change smoothly and would not shift too much . therefore , for the k + 1 level , the edge pixel locations at angle should be within the range [ c()d , c( ) + d ] . with the set of edge candidates , the edge selection is performed as described above to generate a more accurate nucleus contour c. as the contour is refined iteratively from the bottom level of the edge pyramid up to the top level , it gradually attaches to the real border of nucleus . given the small blurring 0 at the top level , our algorithm can delineate the nucleus spatial extent precisely . before our algorithm is applied to pathology images , the nuclei channel should be extracted from rgb color space by color deconvolution ( e.g. , extracting hematoxylin channel from h and e - stained images ) . after that , all image data are normalized to fit the intensity range [ 0 , 1 ] . we demonstrate the proposed method on two real datasets including thyroid dataset ( 35 representative images , pap - stained , 903 cell nuclei ) and liver datasets ( 25 images , h and e - stained , 2145 cell nuclei ) . in our experiment , the sliding window width w and height h were set as 15 degrees and 2 pixels , respectively , and were fixed for both two datasets . the only parameter to be changed differently for the two datasets is the maximal smooth level max which was set to be 3 and 5 for the thyroid dataset and the liver dataset , respectively . the minimal smooth level min is usually set to be 1 to capture the precise nucleus border . for comparison , we choose the following state - of - the - art algorithms used for nuclei segmentation including the ovuscule , level set and template matching . template matching has the ability of detecting nuclei in the image while level set and the ovuscule need detected nuclei seeds for segmentation . in our experiment , level set and the ovuscule adopted the seeds detected by mesps for comparing the segmentation performance . for qualitative comparison , sample segmentation results by approaches listed above are shown in figure 5 , where the rows from the top to the bottom correspond to the results from level set , the ovuscule , template matching , and our method , respectively , and the columns from left to right correspond to sample images from liver dataset and thyroid dataset , respectively . first column : liver dataset ; second column : thyroid dataset . from the top row to the last row are the results by level set , the ovuscule , template matching , and multiscale edge selection in polar space , respectively . note that segmentation flaws are pointed out by black arrows in addition , we evaluated the nuclei detection efficiency of template matching and mesps using the miss rate ( mr ) defined as follows : where sa are the seeds detected by the algorithms and sm are the seeds selected manually ; sasm and sasm are the number of seeds in the union set and the intersection set of sa and sm , respectively . the segmentation accuracy was measured by the area error rate ( aer ) focusing on the number of incorrectly segmented pixels and the spatially - aware evaluation metric normalized sum of distances ( nsd ) with the ground truth labeled manually . quantitative analysis of nuclei detection and segmentation efficiency of different approaches is shown in table 1 . quantitative evaluation of different approaches on nuclei detection and segmentation efficiency from the quantitative evaluation of different approaches , we note that the proposed method showed similar or superior performance compared with existing segmentation methods validated on two datasets . for the thyroid dataset , level set segmented nuclei with the highest accuracy with aer and nsd being 8.31% and 0.29 , respectively . our method generated similar results as that of level set , showing that mesps has the nuclei segmentation ability comparable to the state - of - art method . moreover , for the liver dataset in the complex setting ( nonuniform illumination , noisy background , and nuclei heterogeneity ) , mesps could still be able to find the nuclei borders accurately and perform the best compared with the listed approaches . considering the comprehensive performance over the two validation datasets , mesps archived the best segmentation accuracy with 10.34% aer and 0.33 nsd on average . for the overall nuclei detection efficiency , both template matching and mesps could detect most nuclei labeled manually with the similar mrs . however , we should be aware of the supervised fashion of template matching method that needs users to select a set of nuclei for training and then finds the templates that best match the testing nuclei from the constructed statistical model . this paper proposed an unsupervised method to detect and segment cell nuclei automatically from the 2d pathology images based on ncc and mesps . the validation experiment showed that the method could segment the cell nuclei accurately when applied to real pathology images with different stainings ( e.g. , h and e , pap staining ) and image qualities ( e.g. , blurring , noise , texture heterogeneity ) . the multiscale strategy ensures that the ill effects caused by noise , nonuniform intensity , etc . the small smooth level at the top of the edge pyramid helps the generated contour gradually cling to the real nucleus border at the pixel level . with the small step size of , the contour changes smoothly as it iterates from the bottom level up to the top level of the edge pyramid . second , it is designed in an unsupervised way that does not need users to train a model used for segmentation . once the parameters are set , the algorithm could detect and segment the cell nuclei in the dataset automatically . the performance of mesps depends on the image gradient ; thus , it is not sensitive to staining techniques or imaging modalities , which makes it useful and applicable to various datasets in clinic settings . finally , the proposed algorithm is light weight , consisting of several basic but effective algorithms including ncc , edge detection , and dijkstra 's algorithm . the proposed framework is mathematically simpler than the mentioned state - of - the - art methods . in addition , we proposed some ways to reduce the computational cost by reducing the number of both nodes and edges when dijkstra 's algorithm is applied . first , the edge pixels in polar space are represented by the points which have locally maximal number of pixels within a sliding window for each angle . this operation reduces the number of nodes greatly in the constructed undirected graph with the additional benefit of denoising . moreover , edges between two nodes in the graph would be deleted if the distance difference is over a certain threshold , in the sense that pixels at adjacent angles on the nucleus contour should be near each other and the distance away from the nucleus center changes little . each node only connects a few nodes at adjacent angles , which prominently cut down the number of possible paths between the source and the terminal nodes . we should note that there are parameters introduced in our proposed method , including filter size , min , max , smooth step size , cost weights ( a , b ) , and the threshold for edge deletion used to reduce computational cost . here , the parameters to be set to adapt to various datasets are filter size and max . as described in the previous section , the filter size depends on the image resolution as well as the cell nuclei type in study , whose size could be usually found in the literature . it is desired to keep the correct nuclei edge pixels in the edge map , at the same time , be able to filter out the noisy edges . in practice , the optimal max can be set experimentally by randomly selecting a few sample images in the dataset and observing the edge maps so that the edge detector could describe the outlines of most nuclei . our algorithm is not sensitive to other parameters and they were fixed when validated on two datasets . in our experiment , the values of min , smooth step size , a , b , and the threshold were set to be 1 , 0.5 , 0.4 , 0.6 , and 20 pixels , respectively . besides the advantages mentioned above , the method also has some limitations that are noteworthy of discussion . first , the method is designed for segmenting convex - shaped cell nuclei . in the polar space , parts of the contour for nonconvex shape nucleus are mapped to multiple locations at the same angle , which violates our assumption that there is only one optimal location along the nucleus contour per angle . even though most cell nuclei have the shape of sphere or ellipsoid , highly concave cell nuclei can be sometimes observed under microscopy due to the sectioning of nuclei at odd angles or tissue distortion in slides preparation procedure , or both . second , the method could not handle overlapping cell nuclei even if the nuclei seeds are detected correctly . because of the blurring of border in the overlapping area , the edge detector usually does not generate the edge pixels delineating the two nuclei . the method would treat the two nuclei as one and produce the outer border of them . however , we should note that ( 1 ) the ultimate goal of nuclei segmentation is for exploring the correlation between nuclei morphology and cellular / disease progress , ( 2 ) overlapping cell nuclei provides limited information for analysis due to the difficulty of recovering inherent information within the overlapping area . therefore , with plenty of isolated cell nuclei available in the dataset , nuclei overlapping problem is negligible in nuclei based analysis . the proposed method locates cell nuclei by measuring the matching degree between local image patches and the predefined nucleus - shaped filters . afterward , the method transforms the object segmentation problem into a classic shortest path problem . the accurate delineation of cell nuclei is based on the detected edge pixels on the border which can be correctly selected by the well - known dijkstra 's algorithm . the multiscale strategy enables the contour generated at each level evolves smoothly to the actual nuclei border . in the future , the method could be further automated by enabling the algorithm to select the optimal maximal smooth parameter based on image gradient statistics . nih awards ca188938 , gm090033 , and pa state health department award 4100059192 supported the study . nih awards ca188938 , gm090033 , and pa state health department award 4100059192 supported the study .

introduction : cell nuclei are important indicators of cellular processes and diseases . segmentation is an essential stage in systems for quantitative analysis of nuclei extracted from microscopy images . given the wide variety of nuclei appearance in different organs and staining procedures , a plethora of methods have been described in the literature to improve the segmentation accuracy and robustness.materials and methods : in this paper , we propose an unsupervised method for cell nuclei detection and segmentation in two - dimensional microscopy images . the nuclei in the image are detected automatically using a matching - based method . next , edge maps are generated at multiple image blurring levels followed by edge selection performed in polar space . the nuclei contours are refined iteratively in the constructed edge pyramid . the validation study was conducted over two cell nuclei datasets with manual labeling , including 25 hematoxylin and eosin - stained liver histopathology images and 35 papanicolaou - stained thyroid images.results:the nuclei detection accuracy was measured by miss rate , and the segmentation accuracy was evaluated by two types of error metrics . overall , the nuclei detection efficiency of the proposed method is similar to the supervised template matching method . in comparison to four existing state - of - the - art segmentation methods , the proposed method performed the best with average segmentation error 10.34% and 0.33 measured by area error rate and normalized sum of distances ( 10).conclusion : quantitative analysis showed that the method is automatic and accurate when segmenting cell nuclei from microscopy images with noisy background and has the potential to be used in clinic settings .

INTRODUCTION MATERIALS AND METHODS Case Selection Tissue Procurement and Processing Digital Image Acquisition Nuclei Detection Nuclei Segmentation Edge selection Edge iteration RESULTS DISCUSSION AND CONCLUSION Financial Support and Sponsorship Conflicts of Interest

stroke is a common neurological disease and a leading cause of chronic disability worldwide1 . it often causes hemiplegia , which is accompanied by several complications including motor , perceptive and cognitive , and sensory abnormalities , as well as language disorders , and visual impairments2 . the deterioration of motor skills due to hemiplegia is a major factor in the reduction of the activities of daily living and socialization3 . eighty - five percent of stroke patients show upper limb disorders in the acute stage4 . after 36 months between 5575% of post - stroke patients reported persistent upper limb5 . upper limb dysfunction is the biggest reasons for limitations in the daily activities of post- stroke patients6 . the movement limitations from the permanently affected upper limb make difficult for the post - stroke patients to lead normal lives7 . hemiplegia makes functional use of the affected upper limb for performing activities of daily living difficult8 . for this reason , improvements in the upper limb motor ability of post - stroke patients that enable the performance of the independent activities of daily living are discussed in the rehabilitation process . the importance of the upper limb functions should be emphasized in the function improvement programs of the rehabilitation treatment9 . upper limb functional recovery of stroke patients appears slower than that of the lower limb10 . studies on the upper limb function of stroke patients are limited to the affected side and rehabilitation programs focus on improving the function of the affected side11 . in reality , there are no studies on the post - stroke function of the affected hands . thus , this study was conducted to determine the grip power and strength of the unaffected area of patients with hemiplegia . this study was conducted between june 1 , 2012 and august 31 , 2012 , and involved 83 post- stroke korean patients with hemiplegia as subjects . the purpose and methods of the study were explained to the participants before their inclusion in the study . the grip strength was measured by using the jamar hydraulic hand dynamometer ( preston , usa ) . the appropriate posture when measuring grip strength was presented by the american society of hand therapists ( asht ) and the grip strength of the unaffected hand of the subject was measured by adducting the shoulder joint , bending the elbow joint by 90 and placing the lower arm and wrist joint in the middle , and the average value after 3 measurements was recorded . date on the normal grip power of korean adults were collected and analyzed according to age using the paired t - test spss software version 18.0 and the significance level was set to 0.01 . there were 51 ( 61.40% ) male and , 32 ( 38.60% ) female patients in this study with an average age of 57.59 and 69.16 year , respectively ( table 1table 1.general characteristics of the study subjects ( n=83)subjects gendermale51 ( 61.4%)female32 ( 38.6%)age ( sd)male 57.6 ( 12.7)female 69.2 ( 14.2)affected sideleft 33 ( 39.8%)right 50 ( 60.2%)sd : standard deviation ) . the grip strength of the unaffected side of patients with hemiplegia was significantly lower compared to that of the patients in the normal control group ( p<0.01 ) ( table 2table 2.comparison of grip strengths between the study groupaffected side ( n)grip strength of the non - affected sidehemiplegia meansdnormal person meansdmalelt . during dominant hand dysfunction due to stroke , the ability to participate in a variety of tasks is damaged and , stroke patients face difficulties in performing many tasks12 , 13 . thus , this study was performed in order to determine the grip strength of the unaffected side of patients with hemiplegia . according to previous research findings , the grip strength of the unaffected side of patients with hemiplegia was found to be significantly lower than that of people without hemiplegia . when performing activities of daily living , stroke patients mainly use the unaffected side and are only interested in the paralyzed side during rehabilitation assessment or treatment , and relatively neglect the evaluation and treatment of the unaffected side14 . despite problems with the function of the unaffected hand of patients with hemiplegia , clinical treatment only focuses on the affected side . based on the results of this study , interventions that focus on the unaffected hand

[ purpose ] this study was performed in order to investigate the grip strength of the unaffected hand of hemiplegic post - stroke patients . [ subjects ] this study conducted on 83 hemiplegic post - stroke patients from may to august 2012 . [ methods ] this study was measured the mean grip strength of the unaffected hand of patients with hemiplegia and comparatively analyzed this with the mean normal grip strength . [ results ] the grip strength of the unaffected hand of patients with hemiplegia was weaker compared to the of normal . [ conclusion ] patients with hemiplegia demonstrated problems in both their unaffected and affected sides . based on the results of this study , it is necessary to expand treatment from the affected to unaffected areas of patients with hemiplegia .

INTRODUCTION SUBJECTS AND METHODS RESULTS DISCUSSION

most decisions to withhold or withdraw life - sustaining treatment from ( newborn ) infants are made with mutual consent of both physicians and parents [ 10 , 15 ] . in the context of the multiculturalism of most western european countries it is unlikely , however , that physicians and parents will always hold the same values . they may have conflicting perceptions about which course of action is in the best interest of the critically and incurably ill child . the discussion and solution of these and similar disagreements call for a bioethical approach that helps identifying and evaluating the different arguments concerned . childress in 1979 and promoted in europe by r. gillon , seems the most promising candidate [ 2 , 13 ] . it claims that whatever our personal philosophy , politics , religion , moral theory , or life stance , we will find no difficulty in committing ourselves to four prima facie moral principles . these four allegedly trans - cultural principles ( respect for autonomy , nonmaleficence , beneficence and justice ) would offer a common set of moral commitments , a common moral language and a common set of moral issues . this then would fulfil the need of a culturally neutral approach to thinking about ethical issues in health care . the four principles approach has often been criticised , e.g. because conflicts between the four principles seem unsolvable , since there is no unified moral theory from which they are all derived . nevertheless , the approach has been popularly accepted as a set of universal guidelines for bioethics , especially in medical circles . on the basis of a case - history ( described in the case report ) , this paper challenges the appropriateness of communicating in terms of these four principles with parents with a different background . the case describes the situation when muslim parents bring forward that their religion keeps them from consenting to end - of - life decisions of non - religious paediatricians . in western europe , muslims form a large religious minority . the term non - religious ethics is used to indicate forms of ethics not explicitly based on religious texts or beliefs . first we shall give a brief outline of the four principles approach , often referred to as principlism . this same paragraph will mirror the non - religious meanings and roles of the principles . subsequently , we will describe the different meanings and roles of the principles in islamic ethics . this will reveal that the parties involved in the described disagreement may feel committed to seemingly similar , but actually quite different principles . this is , as beauchamp and childress put it , the unphilosophical common sense and tradition shared generally by the members of a society . the common morality comprises all and only those norms that all morally serious persons accept as authoritative . by contrast , morality in the community - specific sense includes the moral norms that spring from particular cultural , religious , and institutional sources . beauchamp and childress accept the fact that morality in the community - specific sense reflects significant cultural differences , but also believe that a set of four general principles , shared by everyone regardless of their background , could form the basis of a culturally neutral approach to bioethical issues . one of these principles , justice , has little relevance for the disagreement we focus on in this paper and we shall therefore refrain from discussing it . beauchamp and childress describe the three other principles as follows [ 46 ] . throughout the history of health care , it has become understood , however , that acts of beneficence can conflict with the requirement to respect a patient s autonomy . this principle refers to the individual s self - determination , free from control and influence by others . in the patient physician relationship , the patient s autonomy is firstly based on informed consent and refusal . if minors are involved , the child s autonomy and accessory rights are assigned to the parents . . the principle of nonmaleficence is closely related to beneficence ; it asserts an obligation not to inflict harm intentionally . beauchamp and childress emphasise that when medical treatment is futile or when its burdens outweigh the benefits , the principle of nonmaleficence might justify or sometimes even require withholding or withdrawing life - sustaining procedures . arguing that treatment occasionally violates a patient s interests , the principlists give considerable weight to quality - of - life judgements . rules , which means that they are non - absolute : each of them is binding unless it conflicts with another . conflicting principles call for careful balancing and overriding : the balancing of the respective weights of the competing principles to determine one s actual obligations . specification must be used to reduce the abstractness of the principles ; to provide them with action - guiding content . this process of specification is context - related and may also be influenced by one s particular cultural or religious background , i.e. by one s morality in the community - specific sense . this means that the same principle can be translated into various forms of actual guidance . moral justification proceeds from a coherence model that provides principles for specific cases and illuminates case analysis from general principles . the islamic tradition ( the quran , the sayings of prophet muhammed and the interpretative literature derived from them ) offers muslims a guide for all aspects of life . the main islamic guiding principles are respect for human dignity and the maintenance and protection of life , property and honour . several authors claim that the roots of the four principles of beauchamp and childress are clearly identifiable in islamic tradition as well [ 1 , 17 ] . van bommel suggests that these four principles even summarise the islamic norms of care and concern in medicine . the way beauchamp and childress present the four principles ( as summarised above ) mirrors certain aspects of their own morality . having a similar background as the principlists , many non - religious western european paediatricians will attach the same meaning to these principles . aksoy and elmai , for example , demonstrate that islamic tradition offers many statements relating to the principle of nonmaleficence , in the sense of refraining from doing harm to others . refraining from treatment that might cause or prolong harm , however , is generally not a topic in islamic medical ethics . because of the unconditional valuation of human life , every additional day lived is of value ; a treatment that prolongs life therefore can not be harmful . the trust in an omnipotent god is a second reason why decisions to forgo life - prolonging treatments can not be justified . van bommel : muslims feel very strong that it is allah who does the actual healing , the doctor being only the agent for the will of allah . this consciousness is based on the quranic verse : if allah touch you with affliction , none can remove it but he . a muslim scholar or a group of paediatricians will assert that this does not necessarily rule out the possibility to refrain from treatment [ 11 , 16 ] . aksoy and elmai also give many instances in which islamic tradition shows respect for a patient s autonomy . likewise , many muslims defend the point of view that a religious morality is not incompatible with human freedom and responsibility [ 8 , 12 , 17 ] . the quran puts its trust in the rational power of human beings to distinguish between truth and falsehood , says van bommel . ebrahim explains : reason was given to man so that he may be in a position to freely accept the law and obey allah , or not to do so at all. ; and if he would not be free , the burden of responsibility and morality would not have been placed upon him . but does this islamic autonomy authorise muslims to make their own decisions about life and death ? this view is endorsed by van bommel : for a muslim patient , absolute autonomy is very rare , there will be a feeling of responsibility towards god , and he or she lives in a social coherence , in which influences of the imam and relatives play their roles . questionable decisions that would be acceptable according to the non - religious variant of respect for autonomy , can not be permitted according to the islamic variant . in such cases the islamic notion of respect for the patient requires to oppose the patient s self - determination . the emphasis is on beneficence over autonomy . for in protecting patients from making questionable choices , the doctor shows respect for the patient as a person . many non - religious doctors would call this paternalism . one could say that non - religious ethics applies the principle of nonmaleficence to justify withholding or withdrawing futile or damaging medical treatment , whereas in islamic ethics it is used to forbid all kind of actions or omissions that may harm life . and while the non - religious version of the principle of respect for autonomy emphasises the need for informed consent , the islamic version focuses on the first part of the principle : respect . clearly , the muslim parents and non - religious paediatricians who disagree on which course of action would be in the best interest of their critically and incurably ill child may feel committed to seemingly similar , but actually quite different principles . the paediatricians may apply the principle of nonmaleficence to justify withdrawing life - sustaining treatment and may be convinced they need an explicit consent for this from the parents in order to respect their autonomy . the parents , however , do not consider the extra days harm and trust their omnipotent god , which keeps them from making decisions about life and death . in such situations , communication in terms of these principles may create a conflict ( as described in the case - history ) within an apparently common conceptual framework . when paediatricians do not hold the same values as ( the parents of ) their patients , an approach based on a search for shared beliefs is in itself not impossible , as certain beliefs can be justified from different outlooks on life . however , when the difference in background between physicians and patients is substantial , an alternative approach may be needed that pays genuine attention to the different backgrounds instead of putting them between brackets . the non - religious paediatricians could for instance emphasise the natural character of the suggested path , rather than explaining that they would like to give the child the chance to die . this would leave some room for hope , within the limits of what we as physicians can humanly do for the child . in addition , it may often be necessary to clarify expressions used , for some meanings , such as those of unnecessary suffering and quality of life . sometimes it may be enough to realise that differences do exist ; being aware that some terms may be interpreted differently is an important step in achieving effective terminology when addressing parents . secondly , caution is required regarding the explicitness and time process of the desired consent . many western physicians tend to involve patients and their families as much as possible in the decision process , while muslim parents believe that life and death are decided by allah only . without challenging the decision it must be clear what the options are in such situations . regarding the time process , it may be helpful to slow down the pace : if it seems difficult to come to a consensus on a certain day , it may be possible after one or two more days of reflection . in our experience , the approach we put forward can even result in consent to the proposed end - of - life decision . it demands from paediatricians a sincere interest in the differences between normative standpoints related to cultural or religious beliefs and dedicated efforts to grasp these . undoubtedly this will not always lead to unanimity , but a transparent disagreement would seem preferable to a conflict situation . a turkish woman , mother of three healthy children , gave birth to twins at 29 weeks gestational age . the second - born twin was a girl with birth weight 945 g. apgar scores were 8 and 9 after 1 and 5 min , respectively . the girl was admitted on a level iii neonatal intensive care unit . after a mild respiratory distress syndrome ( rds ) , for which treatment with continuous positive airway pressure was initiated , she developed necrotising enterocolitis only 10 days after birth . laparotomy was performed with major bowel resection and creation of a double - sided stoma . despite high caloric intake , partially parenterally , a small - intestine anastomosis was made , but shortly after , a relaparotomy was needed because of a severely painful bloated belly and abdominal wound leakage . the wound was sealed but burst open again . after a repetition of this event conservative treatment was given . mechanical ventilation had been reinitiated because of an acute rds and the high settings could not be decreased . infections were difficult to treat and enteral feeding was no option anymore . at age 4 months the girl weighed 400 g more than at birth , but this gain was mainly the result of oedema . gradually , the medical team came to realise that further treatment offered no chance of survival : the open belly and other complications would not recover and would cause her death in the near future . the medical team felt that life - sustaining treatment should be withdrawn , because prolonging would harm the girl . when the doctors discussed their opinion with the parents and asked for their explicit consent , the parents explained that because of their islamic religious beliefs , they would not consent to this strategy . explanation of the team s motives in terms of nonmaleficence and respect for autonomy , two of the four principles of biomedical ethics , evoked resistance from the parents . the conversation resulted in a conflict , which could only be solved through the agency of an external paediatrician : the parents agreed to respect his second opinion and did not raise objections at the time this opinion turned out to be similar to the one made by their own medical team .

the four principles approach has been popularly accepted as a set of universal guidelines for biomedical ethics . based on four allegedly trans - cultural principles ( respect for autonomy , nonmaleficence , beneficence and justice ) , it is supposed to fulfil the need of a culturally neutral approach to thinking about ethical issues in health care. on the basis of a case - history , this paper challenges the appropriateness of communicating in terms of these four principles with patients with a different background . the case describes the situation in which muslim parents bring forward that their religion keeps them from consenting to end - of - life decisions by non - religious paediatricians . in a literature analysis , the different meanings and roles of the relevant principles in non - religious and islamic ethics are compared . in non - religious ethics , the principle of nonmaleficence may be used to justify withholding or withdrawing futile or damaging treatments , whereas islamic ethics applies this principle to forbid all actions that may harm life . and while the non - religious version of the principle of respect for autonomy emphasises the need for informed consent , the islamic version focuses on respect for the patient . we conclude that the parties involved in the described disagreement may feel committed to seemingly similar , but actually quite different principles . in such cases , communication in terms of these principles may create a conflict within an apparently common conceptual framework . the four principles approach may be very helpful in analysing ethical dilemmas , but when communicating with patients with different backgrounds , an alternative approach is needed that pays genuine attention to the different backgrounds .

Introduction The four principles approach to biomedical ethics The four principles rooted in Islamic ethics Discussion Case report

animal use was approved by the institutional animal care and use committees at the university of oklahoma health sciences center , oklahoma city , oklahoma , and the university of houston and conformed to the arvo statement for the use of animals in ophthalmic and vision research . the cngb1 line , the rds line ( originally obtained from neeraj agarwal currently at the national eye institute , bethesda , md , usa ) , and the rho line ( originally obtained from janice lem , tufts university , boston , ma , usa ) have been described previously . cngb1 mice on the rds , rds , rho , and rho backgrounds were generated in our facility . wild - type ( i.e. , cngb1/ rds / rho ) , rds , rds , rho , and rho littermates were used from our colony as controls . all animals were maintained in cyclic light ( 12 hours light , 12 hours dark , 30 lux ) and fed standard lab chow . experiments were repeated three to seven times , and densitometry was done using the image lab software ( bio - rad , temecula , ca , usa ) . eyes for immunofluorescence were harvested , fixed , sectioned , and immunolabeled as previously described . primary antibodies are described in the table , and anti - mouse , anti - rabbit , or anti - goat alexafluor conjugated secondary antibodies ( life technologies , grand island , ny , usa ) were used . images were captured on an olympus bx-62 microscope ( center valley , pa , usa ) equipped with a spinning disc confocal unit and analyzed as described previously . antibodies used for immunofluorescence and western blotting tissue collection , processing , and plastic embedding and transmission electron microscopy ( tem ) have been described previously . light microscopy images were captured at 40 using a zeiss ( peabody , ma , usa ) universal microscope . to evaluate outer nuclear layer ( onl ) and os layer thickness , images were captured from central superior and inferior regions containing the optic nerve head , and at least three retinal sections from two to four eyes / genotype were used . assessment of rod photoreceptor function ( scotopic erg ) was performed on dark - adapted animals with a strobe flash stimulus of 157 cd - s / m intensity while photopic responses were recorded using a similar stimulus from light - adapted animals . differences between genotypes were assessed by 1-way or 2-way anova with bonferroni 's post hoc pairwise comparisons . p < 0.05 was considered significant ( p < 0.05 , p < 0.01 , and p < 0.001 ) . animal use was approved by the institutional animal care and use committees at the university of oklahoma health sciences center , oklahoma city , oklahoma , and the university of houston and conformed to the arvo statement for the use of animals in ophthalmic and vision research . the cngb1 line , the rds line ( originally obtained from neeraj agarwal currently at the national eye institute , bethesda , md , usa ) , and the rho line ( originally obtained from janice lem , tufts university , boston , ma , usa ) have been described previously . cngb1 mice on the rds , rds , rho , and rho backgrounds were generated in our facility . wild - type ( i.e. , cngb1/ rds / rho ) , rds , rds , rho , and rho littermates were used from our colony as controls . all animals were maintained in cyclic light ( 12 hours light , 12 hours dark , 30 lux ) and fed standard lab chow . experiments were repeated three to seven times , and densitometry was done using the image lab software ( bio - rad , temecula , ca , usa ) . eyes for immunofluorescence were harvested , fixed , sectioned , and immunolabeled as previously described . primary antibodies are described in the table , and anti - mouse , anti - rabbit , or anti - goat alexafluor conjugated secondary antibodies ( life technologies , grand island , ny , usa ) were used . images were captured on an olympus bx-62 microscope ( center valley , pa , usa ) equipped with a spinning disc confocal unit and analyzed as described previously . tissue collection , processing , and plastic embedding and transmission electron microscopy ( tem ) have been described previously . light microscopy images were captured at 40 using a zeiss ( peabody , ma , usa ) universal microscope . to evaluate outer nuclear layer ( onl ) and os layer thickness , images were captured from central superior and inferior regions containing the optic nerve head , and at least three retinal sections from two to four eyes / genotype were used . layer thickness was measured using adobe photoshop cs5 ( adobe systems , inc . , san jose , ca , usa ) . assessment of rod photoreceptor function ( scotopic erg ) was performed on dark - adapted animals with a strobe flash stimulus of 157 cd - s / m intensity while photopic responses were recorded using a similar stimulus from light - adapted animals . differences between genotypes were assessed by 1-way or 2-way anova with bonferroni 's post hoc pairwise comparisons . p < 0.05 was considered significant ( p < 0.05 , p < 0.01 , and p < 0.001 ) . previously we evaluated the interplay between rds and rhodopsin in os morphogenesis , and here we wanted to understand the effects of eliminating cngb1 at the same time as either rhodopsin or rds . we crossed the cngb1 line , which lacks all cngb1 gene products including cngb1a and garp1/2 , onto the rds , rds , rho , and rho backgrounds ( which were all used as control lines for the purpose of comparison throughout the study ) . at postnatal day ( p ) 30 we assessed levels of rhodopsin , rds , and rom-1 by reducing sds - page / western blot . data are presented as percentage of wt after normalization to actin ( a loading control ) ( figs . c ) and are plotted as means sem ( p < 0.05 , p < 0.01 , and p < 0.001 by 1-way anova with bonferroni 's post hoc comparison ) . though rhodopsin levels were virtually normal in the cngb1 and the rds ( fig . 1a ) , they were reduced in cngb1/rds to 56% of levels in the rds . levels of rhodopsin in the rds were reduced by 84% and were not further reduced by ablating cngb1 . retinal extracts were isolated from p30 eyes of the indicated genotypes and were analyzed by reducing sds - page / western blot . the blots were probed with ( a ) mab 1d4 against rhodopsin , ( b ) anti - rds - ct , and ( c ) anti - rom-1-ct . protein was quantified densitometrically , normalized to actin , and plotted as a percentage of wt ( shown are means sem , * p < 0.05 , * * p < 0.01 , and * * * p < 0.001 by 1-way anova with bonferroni 's post hoc comparison ) . nonreducing sucrose gradient velocity sedimentation ( d , e ) was performed on p30 retinal extracts from wt and cngb1 . fractions from gradients ( 112 ) were further separated by sds - page / reducing western blot . resulting blots were probed with anti - rds - ct ( d ) and anti - rom-1-ct ( e ) . the relative percent of total rds or rom-1 in each fraction was assessed densitometrically and plotted as mean sem from 3 or 4 independent experiments . this more pronounced effect of cngb1 ablation in the rds compared to the rho continued when we examined rds levels ( fig . in cngb1/rds retinas , rds levels were reduced to 54% of those in the rds while rds levels in cngb1/rho remained at 87% of those in the rho . rod outer segment membrane protein-1 levels were not altered in either the cngb1/rds versus the rds or the cngb1/rho versus the rho ( fig . we also observed that rds and rom-1 are severely reduced by the coablation of cngb1 and rhodopsin ( cngb1/rho had rds / rom-1 levels that were 8.8% and 7.9% those of rho , respectively ) . cyclic nucleotide gated channel b1a is known to bind to rds in the os , and proper binding and complex assembly of rds / rom-1 are necessary for os formation , so we asked whether eliminating cngb1 altered rds / rom-1 oligomerization . retinal extracts from wt and cngb1 animals were fractionated on 5% to 20% nonreducing sucrose gradients and then separated on reducing sds - page . in the wt retina , rds is present as tetramers ( fractions 68 ) , octamers ( fractions 45 ) , and higher - order oligomers ( fractions 13 ) while rom-1 is detected only in tetrameric and octameric fractions . 1e ) complex formation in cngb1 retinas , suggesting that rds / rom-1 oligomerization is not tied to cngb1 . previously we observed that cngb1a and garp2 protein levels are reduced by 50% in the rds and are undetectable in the rds . when combined with our data here showing that rds levels are decreased in the cngb1/rds compared to the rds cyclic nucleotide gated channel b1a and rds binding occurs during the os targeting process prior to arrival in the os , so we next used immunofluorescence labeling to ask whether the targeting of rds , rom-1 , rhodopsin , or cngb1a / garp1/2 is affected by co - elimination of cngb1 , rhodopsin , or rds . retinal degeneration slow and rom-1 labeling was properly restricted to the os layer in the wt , cngb1 , rds , cngb1/rho , rho , and cngb1/rho retinas ( fig . 2a , green ) . similarly , rhodopsin localization is not affected in most of these genotypes ; however , some accumulation of rhodopsin in the onl is observed in the cngb1/rho ( fig . large amounts of rhodopsin accumulate in the inner segment and onl , and this is recapitulated in the cngb1/rds ( fig . in contrast , in the rho and cngb1/rho retinas , the majority of rds is not found in the inner segment , but is properly restricted to the distal tips of the photoreceptors , consistent with our previous observation showing that rds and rom-1 are found in the small nascent oss of the rho . however , in the rho and cngb1/rho retinas , some mild mislocalization of rds ( but not rom-1 ) to the inner segment , onl , and outer plexiform layer is seen ( arrows , fig . combined , these data suggest that while rhodopsin is more susceptible to mislocalization than rds , cngb1 ablation has little to no effect on the os targeting of rds , rom-1 , or rhodopsin . eliminating cngb1 does not affect targeting of rds or rhodopsin . paraffin - embedded retinal sections from p30 animals of the indicated genotypes were labeled ( a ) with antibodies against rds ( rds - ct , green ) , rhodopsin ( mab-1d4 , red ) , or rom-1 ( rom1-ct , green ) ; ( b ) mab 1d4 ( red ) or rom1-ct ( green ) ; ( c ) rds - ct or rom1-ct ( green ) , or ( d ) cngb1 gene products ( garp-4b1 , red ) . in all cases nuclei os , outer segment ; onl , outer nuclear layer ; is , inner segment ; opl , outer plexiform layer . conversely , to see whether reduction / elimination of rds or rhodopsin affected cngb1a / garp1/2 targeting , we labeled with garp-4b1 , which recognizes all cngb1 gene products ( fig . 2d , red ) . in wt , rds , and rho retinas , cngb1a / garp1/2 properly localized to the os layer . this observation was replicated in the rho retina ; cngb1a / garp1/2 properly localized to the os layer , even though the rho does not form fully elaborated oss . in striking contrast , and consistent with our western blot data , in the absence of rds ( rds ) , cngb1a and garp1/2 are virtually undetectable in the retina . this decrease in cngb1 gene products in the absence of rds is clearly not due to a requirement for proper os formation , since the oss in the rho retina , while more formed than in the rds , are still just tiny sacs of vesicle - containing membrane at the tip of the os , yet the rho model still expresses cngb1a / garp1/2 . rather it suggests that the stability or transport of cngb1a and/or garp 1/2 are dependent directly on rds or on the initiation / formation of oss by rds ( which can be seen in nascent form even in the rho ) . however , though the differences do not attain statistical significance , mean onl thickness in the cngb1 , cngb1/rds , and cngb1/rho was decreased by 10% to 15% compared to their respective controls ( wt , rds , and rho ) , suggesting that degeneration in the cngb1 starts earlier than that in the rds and rho . there is no difference in onl thickness in rho versus cngb1/rho or rds versus cngb1/rds , suggesting that the photoreceptor degeneration in the rds and rho is not additive with that in cngb1 . representative light micrographs ( lm ) were captured from plastic - embedded retinal sections harvested at p30 from the indicated genotypes . rpe , retinal pigment epithelium ; os , outer segment ; is , inner segment ; onl , outer nuclear layer . ( b , c ) outer nuclear layer and os layer thicknesses were measured in sections captured from the central superior and central inferior retina from 2 to 4 eyes per genotype . plotted are means sem , * p < 0.05 , * * p < 0.01 , and * * * p < 0.001 by 2-way anova with bonferroni 's post hoc comparison . it was previously shown that oss are shorter and more disorganized in the cngb1 and rds retinas compared to wt , and our data confirm this ( fig . 3c ) . interestingly , this effect was additive : in the cngb1/rds , mean os length was 41% of wt , compared to 52% and 73% of wt for rds and cngb1 , respectively ( fig . as expected , at p30 , oss in the rho are similar to those in wt , but we do see os shortening in the cngb1/rho due to the absence of cngb1a ; oss in the rho are 89% of wt , while those in the cngb1/rho are 59% of wt . again , the effects of eliminating cngb1a from the rds retina are more severe than in the rho retina ; for example , oss in the cngb1/rds are decreased to 56% of those in cngb1 ( p < 0.05 ) , while the oss of the cngb1/rho are 81% of cngb1 ( not significant ) . figure 4a shows representative waveforms , and maximum saturating a- and b - wave amplitudes are plotted in figure 4b ( mean sem , p < 0.001 by 1-way anova with bonferroni 's post hoc comparison ) . our results for control animals ( cngb1 , rds , and rho ) are consistent with previous publications ( fig . 4b ) . again , elimination of cngb1 had a much more severe effect in the rds background than it did in the rho background . scotopic a - wave values in the cngb1/rho were not significantly reduced compared to the cngb1 , suggesting that all of the functional decrease in the cngb1/rho is due to the absence of cngb1 . in contrast , in the cngb1/rds , scotopic erg responses were severely reduced compared to both cngb1 and rds ( fig . this effect was seen in both the scotopic a- and b - waves , and scotopic a - waves in the cngb1/rds were virtually undetectable . scotopic erg function is undetectable in the rds and rho retina at p30 , so we did not perform ergs on animals in those backgrounds . the additive erg defect in the cngb1/rds could be due to reductions in cnga1 ; however , levels of cnga1 in cngb1 are virtually undetectable , and this finding is recapitulated in cngb1/rds ( supplementary fig . thus while it is possible that further reduction in cnga1 levels contributes to the additive defects seen in the cngb1/rds , we can not conclusively assess the possibility given that the levels of cnga1 are below the limit of detection . ( a ) representative waveforms ; ( b ) plots of mean amplitude sem from 4 to 7 mice per genotype ( * p < 0.05 , * * p < 0.01 , and * * * p < 0.001 by 1-way anova with bonferroni 's post hoc comparison ) . ( c ) scale bars : 10 m for low - magnification em images and 500 nm for higher - magnification em images . rpe , retinal pigment epithelium ; os , outer segment ; cc , connecting cilium . we conducted tem to determine whether the severe effects of simultaneously eliminating cngb1 and reducing rhodopsin / rds led to defects in os ultrastructure ( fig . the os shortening we quantified on the light microscopy level in the cngb1 is also evident by low - magnification em ( 3000 , top , fig . 4c ) , we find that the disc diameter and often the disc alignment are abnormal in the cngb1 retina . in some cases , new discs grew abnormally parallel to the plasma membrane ( arrow , fig . outer segments in the rds were characterized by abnormal disc size and the formation of highly dysmorphic whorl structures , but interestingly , this phenotype was not worsened in the cngb1/rds retina . outer segment structure in the cngb1/rho was worse than in the rho ( which is largely normal ) . the phenotype in the cngb1/rho was of the same type seen in the cngb1 , namely , abnormalities in disc size and alignment but not whorl formation ; however , the defects appeared to be more severe in the cngb1/rho compared to the cngb1 . the rds retina forms no os at the tip of the connecting cilia ( fig . 5 , cc marks connecting cilia ) , and the cngb1/rds is not different from the rds . in contrast , the rho forms well - characterized tiny nascent oss ( arrows , fig . similar structures at the distal tip of the connecting cilium were seen in the cngb1/rho ( arrows , fig . outer segment ultrastructure in the rds and rho is not affected by the ablation of cngb1 . scale bars : 10 m for low - magnification em images ( top ) and 500 nm for higher - magnification em images ( bottom ) . though cngb1 is expressed only in rods , secondary cone loss can occur after rod defects . figure 6a shows representative photopic erg waveforms while figure 6b plots mean photopic b - wave amplitudes ( mean sem , p < 0.01 by 1-way anova with bonferroni 's post hoc comparison ) . consistent with previous reports , at this time point significant decreases in cone function are not detected in the rds or cngb1 . likewise , no significant reductions in cone function were noticed in cngb1/rho versus rho or wt . however , a striking 75% reduction in cone function was observed in cngb1/rds compared to wt , rds , and cngb1 . to identify whether this defect was associated with loss of cone cells , m - opsin - positive cones were counted in a region in the superior central retina while s - opsin - positive cones were counted in the inferior central portion of the retina ( representative images in fig . 6c ; fig . consistent with the dramatic decrease in photopic erg response in the cngb1/rds compared to the cngb1 or the rds , we observed a 50% reduction in s - cones in the cngb1/rds compared to cngb1 , rds , or wt controls ( p < 0.001 by 1-way anova ) . photopic ergs were recorded from wt , cngb1 , rds , cngb1/rds , rho , and cngb1/rho at p30 . ( a ) representative waveforms ; ( b ) plots of the mean maximum photopic b - wave amplitude . n = 4 to 7 mice per genotype ( * p < 0.05 , * * p < 0.01 , and * * * p < 0.001 by 1-way anova with bonferroni 's post hoc comparison ) . ( c ) paraffin - embedded retinal sections from p30 animals were labeled with anti s - opsin ( green , top ) and anti - m - opsin ( green , bottom ) and were all counterstained with dapi ( blue ) . os , outer segment ; onl , outer nuclear layer ; opl , outer plexiform layer . ( d ) cells positive for cone opsins were counted in a 300-m region of the central retina either inferior ( s - opsin - positive cells ) or superior ( m - opsin - positive cells ) of the optic nerve . plotted previously we evaluated the interplay between rds and rhodopsin in os morphogenesis , and here we wanted to understand the effects of eliminating cngb1 at the same time as either rhodopsin or rds . we crossed the cngb1 line , which lacks all cngb1 gene products including cngb1a and garp1/2 , onto the rds , rds , rho , and rho backgrounds ( which were all used as control lines for the purpose of comparison throughout the study ) . at postnatal day ( p ) 30 we assessed levels of rhodopsin , rds , and rom-1 by reducing sds - page / western blot . data are presented as percentage of wt after normalization to actin ( a loading control ) ( figs . c ) and are plotted as means sem ( p < 0.05 , p < 0.01 , and p < 0.001 by 1-way anova with bonferroni 's post hoc comparison ) . though rhodopsin levels were virtually normal in the cngb1 and the rds ( fig . 1a ) , they were reduced in cngb1/rds to 56% of levels in the rds . levels of rhodopsin in the rds were reduced by 84% and were not further reduced by ablating cngb1 . retinal extracts were isolated from p30 eyes of the indicated genotypes and were analyzed by reducing sds - page / western blot . the blots were probed with ( a ) mab 1d4 against rhodopsin , ( b ) anti - rds - ct , and ( c ) anti - rom-1-ct . protein was quantified densitometrically , normalized to actin , and plotted as a percentage of wt ( shown are means sem , * p < 0.05 , * * p < 0.01 , and * * * p < 0.001 by 1-way anova with bonferroni 's post hoc comparison ) . nonreducing sucrose gradient velocity sedimentation ( d , e ) was performed on p30 retinal extracts from wt and cngb1 . fractions from gradients ( 112 ) were further separated by sds - page / reducing western blot . resulting blots were probed with anti - rds - ct ( d ) and anti - rom-1-ct ( e ) . the relative percent of total rds or rom-1 in each fraction was assessed densitometrically and plotted as mean sem from 3 or 4 independent experiments . this more pronounced effect of cngb1 ablation in the rds compared to the rho continued when we examined rds levels ( fig . in cngb1/rds retinas , rds levels were reduced to 54% of those in the rds while rds levels in cngb1/rho remained at 87% of those in the rho . rod outer segment membrane protein-1 levels were not altered in either the cngb1/rds versus the rds or the cngb1/rho versus the rho ( fig . we also observed that rds and rom-1 are severely reduced by the coablation of cngb1 and rhodopsin ( cngb1/rho had rds / rom-1 levels that were 8.8% and 7.9% those of rho , respectively ) . cyclic nucleotide gated channel b1a is known to bind to rds in the os , and proper binding and complex assembly of rds / rom-1 are necessary for os formation , so we asked whether eliminating cngb1 altered rds / rom-1 oligomerization . retinal extracts from wt and cngb1 animals were fractionated on 5% to 20% nonreducing sucrose gradients and then separated on reducing sds - page . in the wt retina , rds is present as tetramers ( fractions 68 ) , octamers ( fractions 45 ) , and higher - order oligomers ( fractions 13 ) while rom-1 is detected only in tetrameric and octameric fractions . 1e ) complex formation in cngb1 retinas , suggesting that rds / rom-1 oligomerization is not tied to cngb1 . previously we observed that cngb1a and garp2 protein levels are reduced by 50% in the rds and are undetectable in the rds . when combined with our data here showing that rds levels are decreased in the cngb1/rds compared to the rds cyclic nucleotide gated channel b1a and rds binding occurs during the os targeting process prior to arrival in the os , so we next used immunofluorescence labeling to ask whether the targeting of rds , rom-1 , rhodopsin , or cngb1a / garp1/2 is affected by co - elimination of cngb1 , rhodopsin , or rds . retinal degeneration slow and rom-1 labeling was properly restricted to the os layer in the wt , cngb1 , rds , cngb1/rho , rho , and cngb1/rho retinas ( fig . similarly , rhodopsin localization is not affected in most of these genotypes ; however , some accumulation of rhodopsin in the onl is observed in the cngb1/rho ( fig . large amounts of rhodopsin accumulate in the inner segment and onl , and this is recapitulated in the cngb1/rds ( fig . in contrast , in the rho and cngb1/rho retinas , the majority of rds is not found in the inner segment , but is properly restricted to the distal tips of the photoreceptors , consistent with our previous observation showing that rds and rom-1 are found in the small nascent oss of the rho . however , in the rho and cngb1/rho retinas , some mild mislocalization of rds ( but not rom-1 ) to the inner segment , onl , and outer plexiform layer is seen ( arrows , fig . combined , these data suggest that while rhodopsin is more susceptible to mislocalization than rds , cngb1 ablation has little to no effect on the os targeting of rds , rom-1 , or rhodopsin . eliminating cngb1 does not affect targeting of rds or rhodopsin . paraffin - embedded retinal sections from p30 animals of the indicated genotypes were labeled ( a ) with antibodies against rds ( rds - ct , green ) , rhodopsin ( mab-1d4 , red ) , or rom-1 ( rom1-ct , green ) ; ( b ) mab 1d4 ( red ) or rom1-ct ( green ) ; ( c ) rds - ct or rom1-ct ( green ) , or ( d ) cngb1 gene products ( garp-4b1 , red ) . in all cases nuclei os , outer segment ; onl , outer nuclear layer ; is , inner segment ; opl , outer plexiform layer . conversely , to see whether reduction / elimination of rds or rhodopsin affected cngb1a / garp1/2 targeting , we labeled with garp-4b1 , which recognizes all cngb1 gene products ( fig . 2d , red ) . in wt , rds , and rho retinas , this observation was replicated in the rho retina ; cngb1a / garp1/2 properly localized to the os layer , even though the rho does not form fully elaborated oss . in striking contrast , and consistent with our western blot data , in the absence of rds ( rds ) , cngb1a and garp1/2 are virtually undetectable in the retina . this decrease in cngb1 gene products in the absence of rds is clearly not due to a requirement for proper os formation , since the oss in the rho retina , while more formed than in the rds , are still just tiny sacs of vesicle - containing membrane at the tip of the os , yet the rho model still expresses cngb1a / garp1/2 . rather it suggests that the stability or transport of cngb1a and/or garp 1/2 are dependent directly on rds or on the initiation / formation of oss by rds ( which can be seen in nascent form even in the rho ) . 3a ) . as expected at early time points , onl thickness is not changed in rds or rho versus wt ( figs . however , though the differences do not attain statistical significance , mean onl thickness in the cngb1 , cngb1/rds , and cngb1/rho was decreased by 10% to 15% compared to their respective controls ( wt , rds , and rho ) , suggesting that degeneration in the cngb1 starts earlier than that in the rds and rho . there is no difference in onl thickness in rho versus cngb1/rho or rds versus cngb1/rds , suggesting that the photoreceptor degeneration in the rds and rho is not additive with that in cngb1 . representative light micrographs ( lm ) were captured from plastic - embedded retinal sections harvested at p30 from the indicated genotypes . rpe , retinal pigment epithelium ; os , outer segment ; is , inner segment ; onl , outer nuclear layer . ( b , c ) outer nuclear layer and os layer thicknesses were measured in sections captured from the central superior and central inferior retina from 2 to 4 eyes per genotype . plotted are means sem , * p < 0.05 , * * p < 0.01 , and * * * p < 0.001 by 2-way anova with bonferroni 's post hoc comparison . it was previously shown that oss are shorter and more disorganized in the cngb1 and rds retinas compared to wt , and our data confirm this ( fig . 3c ) . interestingly , this effect was additive : in the cngb1/rds , mean os length was 41% of wt , compared to 52% and 73% of wt for rds and cngb1 , respectively ( fig . as expected , at p30 , oss in the rho are similar to those in wt , but we do see os shortening in the cngb1/rho due to the absence of cngb1a ; oss in the rho are 89% of wt , while those in the cngb1/rho are 59% of wt . again , the effects of eliminating cngb1a from the rds retina are more severe than in the rho retina ; for example , oss in the cngb1/rds are decreased to 56% of those in cngb1 ( p < 0.05 ) , while the oss of the cngb1/rho are 81% of cngb1 ( not significant ) . figure 4a shows representative waveforms , and maximum saturating a- and b - wave amplitudes are plotted in figure 4b ( mean sem , p < 0.001 by 1-way anova with bonferroni 's post hoc comparison ) . our results for control animals ( cngb1 , rds , and rho ) are consistent with previous publications ( fig . , elimination of cngb1 had a much more severe effect in the rds background than it did in the rho background . scotopic a - wave values in the cngb1/rho were not significantly reduced compared to the cngb1 , suggesting that all of the functional decrease in the cngb1/rho is due to the absence of cngb1 . in contrast , in the cngb1/rds , scotopic erg responses were severely reduced compared to both cngb1 and rds ( fig . this effect was seen in both the scotopic a- and b - waves , and scotopic a - waves in the cngb1/rds were virtually undetectable . scotopic erg function is undetectable in the rds and rho retina at p30 , so we did not perform ergs on animals in those backgrounds . the additive erg defect in the cngb1/rds could be due to reductions in cnga1 ; however , levels of cnga1 in cngb1 are virtually undetectable , and this finding is recapitulated in cngb1/rds ( supplementary fig . thus while it is possible that further reduction in cnga1 levels contributes to the additive defects seen in the cngb1/rds , we can not conclusively assess the possibility given that the levels of cnga1 are below the limit of detection . ( a ) representative waveforms ; ( b ) plots of mean amplitude sem from 4 to 7 mice per genotype ( * p < 0.05 , * * p < 0.01 , and * * * p < 0.001 by 1-way anova with bonferroni 's post hoc comparison ) . scale bars : 10 m for low - magnification em images and 500 nm for higher - magnification em images . rpe , retinal pigment epithelium ; os , outer segment ; cc , connecting cilium . we conducted tem to determine whether the severe effects of simultaneously eliminating cngb1 and reducing rhodopsin / rds led to defects in os ultrastructure ( fig . the os shortening we quantified on the light microscopy level in the cngb1 is also evident by low - magnification em ( 3000 , top , fig . 4c ) , we find that the disc diameter and often the disc alignment are abnormal in the cngb1 retina . in some cases , outer segments in the rds were characterized by abnormal disc size and the formation of highly dysmorphic whorl structures , but interestingly , this phenotype was not worsened in the cngb1/rds retina . outer segment structure in the cngb1/rho was worse than in the rho ( which is largely normal ) . the phenotype in the cngb1/rho was of the same type seen in the cngb1 , namely , abnormalities in disc size and alignment but not whorl formation ; however , the defects appeared to be more severe in the cngb1/rho compared to the cngb1 . the rds retina forms no os at the tip of the connecting cilia ( fig . 5 , cc marks connecting cilia ) , and the cngb1/rds is not different from the rds . in contrast , the rho forms well - characterized tiny nascent oss ( arrows , fig . similar structures at the distal tip of the connecting cilium were seen in the cngb1/rho ( arrows , fig . outer segment ultrastructure in the rds and rho is not affected by the ablation of cngb1 . scale bars : 10 m for low - magnification em images ( top ) and 500 nm for higher - magnification em images ( bottom ) . though cngb1 is expressed only in rods , secondary cone loss can occur after rod defects . figure 6a shows representative photopic erg waveforms while figure 6b plots mean photopic b - wave amplitudes ( mean sem , p < 0.01 by 1-way anova with bonferroni 's post hoc comparison ) . consistent with previous reports , at this time point significant decreases in cone function are not detected in the rds or cngb1 . likewise , no significant reductions in cone function were noticed in cngb1/rho versus rho or wt . however , a striking 75% reduction in cone function was observed in cngb1/rds compared to wt , rds , and cngb1 . to identify whether this defect was associated with loss of cone cells , m - opsin - positive cones were counted in a region in the superior central retina while s - opsin - positive cones were counted in the inferior central portion of the retina ( representative images in fig . consistent with the dramatic decrease in photopic erg response in the cngb1/rds compared to the cngb1 or the rds , we observed a 50% reduction in s - cones in the cngb1/rds compared to cngb1 , rds , or wt controls ( p < 0.001 by 1-way anova ) . cone function is significantly reduced in the cngb1/rds retina . photopic ergs were recorded from wt , cngb1 , rds , cngb1/rds , rho , and cngb1/rho at p30 . ( a ) representative waveforms ; ( b ) plots of the mean maximum photopic b - wave amplitude . n = 4 to 7 mice per genotype ( * p < 0.05 , * * p < 0.01 , and * * * p < 0.001 by 1-way anova with bonferroni 's post hoc comparison ) . ( c ) paraffin - embedded retinal sections from p30 animals were labeled with anti s - opsin ( green , top ) and anti - m - opsin ( green , bottom ) and were all counterstained with dapi ( blue ) . os , outer segment ; onl , outer nuclear layer ; opl , outer plexiform layer . ( d ) cells positive for cone opsins were counted in a 300-m region of the central retina either inferior ( s - opsin - positive cells ) or superior ( m - opsin - positive cells ) of the optic nerve . plotted in this study , our goal was to understand how rds ( a rim protein ) , rhodopsin ( primarily a disc protein ) , and cngb1a ( a plasma membrane protein ) are interrelated in their ability to support os structure and function . recent work showed that rds can bind rhodopsin and suggested that a complex composed of cngb1a , rds , and rhodopsin may play a structural role in anchoring the rim to the plasma membrane ( via rds - cngb1a interactions ) , and a functional role ensuring that proteins are properly localized for optimal phototransduction . when combined with other work showing that cngb1a / garp interactions with phosphodiesterase 6 may provide a role for garp in cgmp turnover , these observations suggest that rds may organize the rim region into a hotspot area or environment for highly regulated phototransduction . this hypothesis is consistent with our results here showing that cngb1a and rds can act additively , exacerbating rds haploinsufficiency , and resulting in ( 1 ) severely decreased rod function in cngb1/rds versus cngb1 or rds and ( 2 ) modest additional reductions in the thickness of the os layer and the onl in the cngb1/rds versus the rds and cngb1 . critically , however , these additive effects occur without any difference in rod ultrastructure in cngb1/rds versus rds . this suggests that defects in rod function and overall retinal structure can not be completely attributed to a role for cngb1/rds interactions in maintaining rim structure , but rather that these interactions also organize a functional environment critical for proper signal transduction . this role for rds as an interactor / organizer of many proteins ( i.e. , not just rom-1 ) is consistent with the observation that rds also interacts with rhodopsin as well as the known broader role of tetraspanins , which often act as organizers of membrane domains containing a wide variety of different proteins . an interesting outcome from our work cngb1 is expressed only in rods , and cone function in cngb1 animals is normal at p30 and starts decreasing only later , likely a secondary phenomenon due to rod loss . similarly , while rds is expressed in rods and cones , cones can better tolerate reduced rds levels than rods , so cone function in the rds is also preserved until approximately 4 months of age . yet here we see cone degeneration and a dramatic reduction in cone function in cngb1/rds as early as p30 . this likely represents a rapid acceleration of rds haploinsufficiency in cones ; however , why elimination of cngb1 in rods should accelerate rds - associated cone degeneration is not clear . this cone phenotype is not completely due to overt rod loss since onl thickness is only mildly affected in the cngb1/rds versus the rds . there may be several underlying causes , including overall alterations in retinal homeostasis , altered secretion of signaling factors from rods needed for cone health , or alterations in other cell types such as horizontal cells and retinal glia that interact with both rods and cones . further exploration of the mechanisms underlying this cone defect are of great interest given the proliferation of retinal disease wherein secondary cone loss following rod - specific defects leads to worsened patient visual outcomes . the trafficking pathways for rhodopsin have been extensively studied , and rds and rhodopsin are thought to traffic separately . recent work has shown that in contrast to rhodopsin , the majority of rds does not traffic through the trans - golgi , but uses an unconventional secretory pathway during os targeting . little is known about the regulation of cngb1a / garp1/2 trafficking ; however , recent work from goldberg 's group shows that rds / cngb1a interactions first occur in the inner segment , raising the intriguing possibility that cngb1a may traffic with rds . however , whether the cngb1a would traffic with conventionally or unconventionally processed rds remains to be further explored . here we find that in general , trafficking of rds , rom-1 , and rhodopsin was not affected by cngb1 ablation . the presence of a clear region of cngb1a / garp1/2 immunoreactivity in the distal inner segment region , likely inside the small abnormally formed os nubs , suggests that overall , cngb1a / garp1/2 targeting is not affected by elimination of rhodopsin ; however , we can not assess the role of rds in cngb1a / garp1/2 trafficking because cngb1a / garp1/2 are not detectable in rds mice . thus , it is not possible to differentiate whether cngb1a / garp1/2 trafficking to the os requires rds , whether cngb1a protein stability requires rds , or whether cngb1a trafficking / stability require the rds - mediated assembly of oss . interestingly , in some cases eliminating the cngb1 channel can be beneficial in preventing or retarding retinal degeneration . for example , the removal of cngb1 significantly rescued the rapid degenerative phenotypes in the rd1 mouse . degeneration in the rd1 was hypothesized to be tied to observed elevated cgmp levels . however , the removal of cng channels led to rescue of rod photoreceptors without ameliorating cgmp levels , suggesting that removing cgmp - mediated signaling was beneficial rather than removing cgmp per se . as a parallel , eliminating rds in the rd1 retina ( rds / pde6b ) also delayed retinal degeneration regardless of the massive accumulation of cgmp . our observation that cngb1a levels are drastically reduced in the rds suggests that attenuation of rd1-associated retinal degeneration in the rd1 rds double knockout is likely due to an elimination of the cng channel / cngb1a rather than to the loss of rds per se . in conclusion , we here present data showing that elimination of cngb1 exacerbates rds - associated functional but not structural haploinsufficiency . these observations suggest that rds / cngb1 interactions have a role in os function in addition to structure and are consistent with the hypothesis that rds functions as a component of a multiprotein plasma membrane - rim - disc complex critical for oss .

purposerod photoreceptor outer segment ( os ) morphogenesis , structural integrity , and proper signal transduction rely on critical proteins found in the different os membrane domains ( e.g. , plasma , disc , and disc rim membrane ) . among these key elements are retinal degeneration slow ( rds , also known as peripherin-2 ) , rhodopsin , and the beta subunit of the cyclic nucleotide gated channel ( cngb1a ) , which have been found to interact in a complex . the purpose of this study was to evaluate the potential interplay between these three proteins by examining retinal disease phenotypes in animal models expressing varying amounts of cngb1a , rhodopsin , and rds.methodsouter segment trafficking , retinal function , and photoreceptor structure were evaluated using knockout mouse lines.resultseliminating cngb1 and reducing rds leads to additive defects in rds expression levels and rod electroretinogram ( erg ) function , ( e.g. , cngb1//rds+/ versus rds+/ or cngb1/ ) but not to additive defects in rod ultrastructure . these additive effects also manifested in cone function : photopic erg responses were significantly lower in the cngb1//rds+/ versus rds+/ or cngb1/ , suggesting that eliminating cngb1 can accelerate the cone degeneration that usually presents later in the rds+/. this was not the case with rhodopsin ; reducing rhodopsin levels in concert with eliminating cngb1a did not lead to phenotypes more severe than those observed in the cngb1 knockout alone.conclusionsthese data support a role for rds as the core component of a multiprotein plasma membrane - rim - disc complex that has both a structural role in photoreceptor os formation and maintenance and a functional role in orienting proteins for optimal signal transduction .

Materials and Methods Ethics Statement and Animal Care and Use Immunofluorescence Labeling and Protein Chemistry Light and Transmission Electron Microscopy Electroretinography Statistical Analysis Results Levels of Rhodopsin, RDS, and ROM-1 Are Altered by Co-elimination of CNGB1 and RDS/Rhodopsin Trafficking of OS Protein Is Largely Unaffected by Removing Elimination of CNGB1 Exacerbates OS Shortening When RDS Is Also Reduced Eliminating Elimination of Discussion Supplementary Material

pseudoaneurysm of the mitral - aortic fibrosa ( pmaf ) or intervalvular fibrosa is an uncommon condition , consisting of a pulsatile cavity in the mitral - aortic junction communicating with the left ventricular outflow tract ( lvot ) . when intervalvular fibrosa pseudoaneurysm communicates to both the left ventricle ( lv ) and left atrium ( la ) , eccentric jet flow from the anterior to posterior mitral annulus may occur during systole and mimic mitral regurgitation due to perforation in the anterior leaflet . a 24-year - old male was referred to our emergency room with a history of acute dyspnea of 2 days duration associated with orthopnea . at admission , he had nyha class iv dyspnea . he had no history of prolonged fever , cough , or chest pain . on physical examination , examination of the lungs and heart revealed extensive crackles , grade 4/6 pan systolic murmur at the apex and gallops . no skin lesions were noted and the extremities did not show any peripheral edema . there was no clinical evidence of acute rheumatic activity or infective endocarditis . the chest x - ray showed mild cardiomegaly with a cardiothoracic ratio of 0.55 with evidence of pulmonary edema . the erythrocyte sedimentation rate ( esr ) was 35 mm at 1 h. the c - reactive protein ( crp ) level was 2.2 mg / dl and antistreptolysin o ( aslo ) titer was normal . two - dimensional transthoracic echocardiogram ( tte ) demonstrated a false aneurysm - like structure in the maif at the lvot [ figure 1 , video 1 ] . it also demonstrated the neck of pseudoaneurysm communicating with the lvot and also a defect in the aneurysmal wall communicating with the la . color doppler examination showed a communication between the echo - free space and lvot and a turbulent flow through the defect in the aneurysmal wall into the la [ figure 2 , video 2 ] suggestive of supra - annular mitral regurgitation . the mitral , aortic valve , and tricuspid valves were normal and there were no vegetations over mitral or aortic valves and no annular abscess . the diagnosis of a pseudoaneurysm of the maif was confirmed using transesophageal echocardiography ( tee ) . it demonstrated a large pseudoaneurysm of maif measuring 3.0 4.2 cm communicating with the lvot through a narrow neck [ figure 3 , video 3 ] and also rupture in its wall [ figure 4 , video 4 ] resulting in communication between the lvot and la causing a large shunt . transthoracic echocardiography in a parasternal long - axis view showing an aneurismal sac posterior to aorta ( arrow ) transthoracic echocardiography in an apical four - chamber view showing an aneurismal sac in la with rupture ( arrow ) into la with color doppler showing a turbulent jet resulting in supra annular mr and valvular mr transesophageal echocardiography in a four - chamber view showing aneurismal sac with neck ( arrow ) communicating with the lvot transesophageal echocardiography in four chamber view showing aneurismal sac in maif with rupture ( arrow ) into la with color doppler showing a turbulent jet resulting in supra - annular mr maif is the junction between the left half of the non - coronary cusp and the adjacent third of the left coronary cusp of the aortic valve and the anterior mitral leaflet . pseudoaneurysm of the maf is a rare but potentially life - threatening complication of aortic valve endocarditis , aortic valve surgery , or chest trauma . aortic valve endocarditis is usually the main reason that predisposes the maif to perforate and form a pseudoaneurysm . both direct extension of the infection from the aortic wall and the aortic jet striking the subaortic structures and anterior mitral leaflet may damage and infect the maif . the relatively avascular tissue of this region contributes to the extension of infection and subsequent distortion . rupture of an maif pseudoaneurysm may give rise either to a pericardial tamponade , an eccentric jet of mitral regurgitation , or a direct communication between the lvot and the la . in some instances , the pseudoaneurysm remains intact and progressive enlargement may compress the coronary arteries causing symptomatic coronary obstruction.[68 ] these false aneurysms are prone to rupture , embolize , or even cause further destruction of the aortic or mitral valve apparatus . when the pseudoaneurysm communicates with the ascending aorta or lv or la ; it may present as heart failure with a clinical picture similar to that of aortic or mitral regurgitation , respectively . karalis and colleagues described 24 ( 44% ) complications involving 55 consecutive cases of aortic endocarditis , including 8 abscesses and aneurysms in interfibrosa , 7 interfibrosa perforations into the adjacent la , and 9 anterior mitral aneurysms and perforations . however , in the present case , there was no evidence of the above - mentioned risk factors . tee is known to be superior to tte in the visualization of valvular vegetations , abscesses , and other complications in patients with infective endocarditis . tte may show the aneurysm located behind the aortic root by the occurrence of systolic expansion and diastolic collapse seen by echocardiography . this should be differentiated from a typical aortic ring abscess which does not show this phenomenon . both tte and tee can detect a pseudoaneurysm of the maif with sensitivity rates of 43% and 90% , respectively . 3d echocardiography may provide excellent three - dimensional anatomical information and also help in guiding the appropriate surgical therapy . the recommended treatment for pmaf is surgery even in asymptomatic patients in order to prevent the development of complications . resection and repair of the defect can be done with or without aortic valve replacement or homograft replacement of the aortic root . surgery for this condition is technically complex since patients often have a background of prior surgery ; hence the associated morbidity and mortality are not negligible . if the anatomy of the maif aneurysm is suitable even percutaneous device closure of the aneurysm can be an option . to the best of our knowledge , it is rare for maif aneurysm to develop in the absence of aortic valve disease , infective endocarditis , prosthetic aortic valve , or trauma . maif aneurysm can rupture into la and can result in large lv to left atrial shunt . both tte and tee are quite sensitive in identifying the relationship as well as complication resulting from rupture into surrounding structures , and also help in guiding the appropriate surgical therapy .

aneurysm of the mitral - aortic intervalvular fibrosa ( maif ) is an exceptionally rare but a potentially catastrophic complication , commonly following aortic valve endocarditis . we present a 24-year - old male presenting with acute onset dyspnea secondary to maif aneurysm rupturing into a left atrium causing large shunt which was diagnosed on echocardiography . the maif aneurysm in the absence of infective endocarditis rupturing into left atrium is extremely rare .

INTRODUCTION CASE PRESENTATION DISCUSSION CONCLUSION Videos available on

the most common congenital heart disease in childhood is ventricular septal defect ( vsd ) , occurring in 50% of all children with congenital heart diseases and in 20% as an isolated lesion . double - outlet right ventricle ( dorv ) is a conotruncal malformation found in a group of complex heart lesions , which are unified by the characteristic that both great arteries arise predominantly from the right ventricle . the physiology of dorv after birth is determined mainly by the location of the ventricular septal defect ( vsd ) in relation to the great arteries , as well as the presence or absence of outflow tract obstruction . patients with dorv with a simple subaortic vsd ( vsd - type ) present with clinical signs of over - circulation from an unrestrictive vsd and usually require a one - stage biventricular repair within the first 6 months of life , some units in developing countries continue to practice a staged approach using pulmonary artery banding.the vsd can be closed through the right atrium or through a right ventriculotomy . the frequent requirement for a vsd enlargement and a right ventricular approach distinguishes this lesion from other vsds . . in closing a vsd , temporary detachment of the tricuspid valve leaflets may provide better exposure of the defect in the usual trans - atrial approach . however , this technique carries the risk of tricuspid valve dysfunction , which is discussed below . the girl had been previously diagnosed at the first month of age as dorv , subaortic vsd with normally related great vessels for which she had pulmonary artery banding at 2 months of age , then complete repair ( vsd closure through a trans - atrial approach with detachment of the tricuspid valve ) at the age of one year . on examination , the patient had mild central cyanosis , congested neck veins , pan - systolic murmur over the precordium and marked hepatosplenomegaly . echocardiography revealed hugely dilated right side of the heart with compressed left side , borderline function of the right ventricle , free tricuspid regurgitation , mainly via a defect between the base of anterior leaflet and the free wall ( figures 1 , 2 ) , normal pulmonary artery pressure and right to left shunting across a small residual atrial septal defect . in surgery , the anterior leaflet of tricuspid valve was found to be dehiscent from the annulus at site of detachment that was done in the previous operation leaving a large gap ( about 2.5 cm ) . the gap between the anterior leaflet and the annulus was closed by a fresh autologous pericardial patch . post - operative echocardiography showed trivial tricuspid regurgitation with mean diastolic gradient of 1 mmhg ( figures 5 , 6 ) . the postoperative course was uneventful and the patient was discharged from hospital after 5 days . the trans - atrial approach for vsd closure is a safe and effective method for most of the cases . although temporary tricuspid valve detachment may improve the visualization of the ventricular septal defect , liberal use of this adjunct is not widely supported , mainly because of concerns about iatrogenic complications such as tricuspid valve dysfunction and heart block . we believe that in most of the cases , the vsd can be effectively closed using the less damaging technique , through the tricuspid valve orifice , even in the presence of chordal attachments that cross the vsd . the patch can be placed to cover the vsd with the sutures carefully positioned to avoid entangling the chords , always respecting the structural and functional integrity of the valve . the technique of tricuspid valve detachment is usually reserved to the relatively rare cases when the vsd is almost totally covered by aneurysmal tissue from the tricuspid valve with many residual defects that can not be reliably closed separately . in the reported case , the long - standing gap in tricuspid valve caused severe regurgitation with secondary changes around the edges of the gap and dilatation of the tricuspid valve annulus . we elected to close the gap between the anterior leaflet and the annulus using a patch of autologous pericardium instead of directly suturing the leaflet to the annulus it to avoid undue tension at the site of the gap . the routine use of tricuspid valve detachment for closure of ventricular septal defects should be avoided because of the increased risk of unnecessarily affecting the tricuspid valve function . trans - atrial approach through the tricuspid valve orifice offers a safe and effective method in most cases .

we report on the case of 5-year - old girl with severe tricuspid regurgitation following previous repair of double outlet right ventricle with subaortic ventricular septal defect , performed through trans - atrial approach using detachment of tricuspid valve leaflet . the severe tricuspid regurgitation was found to be due to dehiscence at the site of the previous detachment and was repaired using a pericardial patch . in this report , we discuss the relative merits and risks of using this technique .

Background Case report Discussion Conclusion

claudius amyand first performed a successful appendectomy on an 11-year - old boy with a perforated appendix within an inguinal hernia sac in 1735 . in a recent report of 1950 patients with groin ( inguinal and femoral ) hernias , an appendix was found in 0.51% of cases , and acute appendicitis was found in 0.10% of all groin hernia sacs . a normal appendix within an inguinal hernia the finding of appendicitis in the inguinal hernia is 0.08% in a series of 1341 inguinal hernia operations . the appendix has even been found in left - sided inguinal hernias as well as in laparoscopic port - site hernias . it has been shown that endoscopic total extraperitoneal treatment of amyand 's hernia can be accomplished . in this case report , we describe a young adult who presented with an appendix mass 10 months after and as a direct result of a laparoscopic extraperitoneal bilateral inguinal hernia repair . in august 2004 , a 22-year - old man had a laparoscopic extraperitoneal bilateral inguinal hernia repair . before this operation , he had been complaining of a lump in the groin diagnosed as a left - sided , inguinoscrotal hernia . during the operation , he had a 30-hour history of periumbilical pain that had settled in his right iliac fossa . this pain was associated with one episode of vomiting . on clinical examination , the patient was comfortable with mild pyrexia . blood investigations showed a raised white blood cell count and a mildly elevated c - reactive protein . three days after admission , a vague lump could be felt in the right iliac fossa , and an abdominal ultrasound scan was carried out . this showed thick - walled matted bowel loops ; the proximal small bowel was dilated , suggestive of bowel obstruction . at this time , the surgical team made a diagnosis of appendix mass , which was to be treated conservatively . the patient 's inflammatory markers continued to remain elevated despite antibiotics , and a further ultrasound scan showed that fluid collection was present behind the bladder . two weeks after discharge , he was well and his inflammatory markers had improved , but he continued to have a mass in his right iliac fossa and mild diarrhea . it was decided that inflammatory bowel disease or malignancy must be excluded , and a computed tomographic ( ct ) scan and barium meal were arranged . the ct scan showed inflammation around the appendix and small bowel , and a collection of fluid persisted behind the bladder . two weeks later , a barium meal and follow through showed free flow of barium from the small bowel to the colon . the patient was readmitted to the hospital on an emergency basis before this could be performed electively . on admission , he had right iliac fossa pain , a firm lump , and small bowel dilatation ( figure 1 ) . the ct scan showed an inflammatory mass in the right iliac fossa ( figure 2 ) . random biopsies were taken that showed no evidence of crohn 's disease . at this point , a decision was made to perform a diagnostic laparotomy because the patient 's symptoms and condition were not improving . at laparotomy , an appendix mass was found . the omentum and the appendix were fixed to the mesh from the previous repair , within the residual hernia sac . the relationship between incarceration and inflammation of the appendix is not clear in amyand 's hernia . the inflammatory swelling may lead to incarceration and subsequent impaired blood supply and bacterial over - growth . as soon as the appendix enters the hernia sac , it becomes vulnerable to trauma and is ultimately retained there by adhesions . its blood supply may subsequently be cut off or significantly reduced , resulting in inflammation and bacterial overgrowth . preoperative ct scans have revealed the previously un - suspected diagnosis of amyand 's hernia in some reports . the second ct scan visualized the inflammatory mass , and the involvement of the right hernia sac could not be seen . this was complicated further by the fact that the omentum was also in the hernia sac . laparoscopic extraperitoneal repair of inguinal hernia does not visualize the contents of the hernia sac , ie , appendix or omentum , so the contents can not be visually reduced . if the contents can not be reduced completely , it would be advisable to change to a technique that can . in an open or laparoscopic transabdominal approach to inguinal hernia repair it is not appropriate , after the appendix is easily reduced by these techniques , to perform an appendectomy , as the possibility of bacteremia must be kept to a minimum . however , if significant trauma occurs to the appendix while it is being reduced , an appendectomy is indicated because the trauma induced to the appendix while being reduced would increase the risk of appendicitis developing postoperatively . laparotomy for peritonitis or problems of releasing the appendix incarcerated into the deep inguinal ring has been performed and reported . however , in our case , this was not an option because this was not technically possible as there was an appendiceal mass , and we needed to confirm a diagnosis and rule out crohn 's disease or malignancy . appendicitis within an amyand 's hernia is rare , and when it occurs it is usually misdiagnosed as strangulated inguinal hernia . in this present case , amyand 's hernia and appendicitis presented as a right iliac fossa mass that did not respond to conservative treatment . this was because the appendix and omentum were still in the hernia sac and chronically inflamed . although laparoscopic extraperitoneal inguinal hernia is still acceptable in appropriate cases , this possible presentation and complication must always be remembered in this type of inguinal hernia repair and a limitation compared with the open or laparoscopic transabdominal approach to this type of hernia repair .

amyand 's hernia ( appendix in the sac of an inguinal hernia ) although rare is a fairly well - recognized clinical entity . it is associated with an increased risk of developing appendicitis . amyand 's hernia can be repaired by open or laparoscopic methods . we present the case of a laparoscopic extraperitoneal repair with a potential hazard when repairing this type of hernia in this manner , and we review the literature on this condition .

INTRODUCTION CASE REPORT DISCUSSION CONCLUSION

we report the case of a 25-year - old caucasian male who developed an acute right scrotum secondary to bile within peritoneal fluid that entered the scrotum through a previously undiagnosed communicating hydrocele . to the best of our knowledge , approximately 10 ml to 15 ml of bile was spilled during the procedure after inadvertent entry into the gallbladder during its dissection from the gallbladder fossa . after the gallbladder was removed , the abdomen was irrigated until aspirated fluid was clear . the right cremaster muscles were noted to be in spasm . a urologic consultation was obtained . the patient 's complaints and examination were concerning for testicular torsion , and right scrotal exploration was performed 3 hours after completion of the laparoscopic cholecystectomy . opening of the tunica vaginalis revealed 10ml of bile - stained fluid and a normal right testicle . the tunica vaginalis and right testicle were irrigated with saline , and a communicating hydrocele was identified and ligated . postoperatively , the patient noted immediate relief of pain , and examination revealed minimal tenderness in the right scrotum . the total bilirubin value of the fluid drained from the scrotum was 10 mg / dl . the patients ranged in age from 7 to 20 years of age and presented with symptoms between postoperative day 1 and 10 . acute postoperative scrotum due to early hernia recurrence has also been described in an infant after an open inguinal herniorrhaphy . yasumoto et al reported a case of a 10-year - old male who underwent open appendectomy for perforated appendicitis on postoperative day 1 following incision and drainage of a left scrotal abscess . infarction of the upper pole of the right testicle causing acute scrotal pain has been reported after a laparoscopic total extraperitoneal inguinal herniorrhapy . bile causes peritoneal signs on examination in some patients with cystic duct stump leaks after cholecystectomy . although the mechanism of irritation is not fully understood , bile salt concentration and bacteria are thought to be possible causes of bile - induced abdominal pain . the cause of acute scrotal pain in this case was due to bile within peritoneal fluid that entered the right scrotum through a communicating hydrocele . the fluid entered the right scrotum after spillage occurred while the patient was in a reverse trendelenberg position with increased intraperitoneal pressure due to carbon dioxide insufflation . the possibility of bile causing the patient 's pain was included in our differential diagnosis ; however , with no prior cases reported in the literature and our concern for testicular torsion , we felt urgent exploration was indicated . future management of a similar patient may include the option of percutaneous aspiration of the hydrocele with laboratory examination to determine bile concentration . if symptoms persist following aspiration , urgent scrotal exploration would be indicated to rule out testicular torsion . the surgical literature is scattered with only a handful of reported cases of an acute scrotum developing after laparoscopic procedures . an acute suppurative process associated with laparoscopic appendectomy is the most common cause described to date . the patient 's symptoms completely resolved after urgent scrotal exploration with drainage of bilious fluid that entered via a communicating hydrocele . to the best of our knowledge , this is the first case of an acute scrotum due to bile after laparoscopic cholecystectomy . as the volume of minimally invasive procedures performed increases , so does the number of unusual complications that develop . reporting of such uncommon disorders developing after minimally invasive procedures provides a reference that may potentially allow earlier recognition and treatment of similar complications by fellow surgeons in the community .

we report our experience with a patient that developed an acute right hemiscrotum immediately after undergoing an uncomplicated laparoscopic cholecystectomy for gallbladder dyskinesia . the etiology of the acute scrotal pain was due to bile which was spilled into the peritoneum after entry into the gallbladder during dissection . the bile obtained access to the right hemiscrotum via a communicating hydrocele . to the best of our knowledge this is the first report of bile causing an acute scrotum following laparoscopic surgery . a review of the current literature on the topic of the postoperative acute scrotum follows our case presentation .

INTRODUCTION CASE REPORT DISCUSSION CONCLUSION

our prospectively collected data came from 23,134 children 2 months to 13 years of age during 20032012 . all had attended angola s largest pediatric center , the 300-bed david bernardino children s hospital in luanda , which has been the core of our treatment trials ( 2 ) , all approved by the local ethics committee . from these children , 6,030 pleural fluid samples and 17,104 csf samples were examined by microscopy , gram - stained , and cultured . any child with symptoms and signs of pleural effusion and a large , not blade - like , opacity on chest radiographs underwent thoracentesis , with or without chest tube insertion , under local anesthesia . some 200 children a year fall into this category ( 3 ) , and the procedure has become routine among attending pediatricians or surgeons . in 2002 , in collaboration with the national health institute of lisbon , portugal , the hospital established a basic bacteriology laboratory and provided staff training ( 4,5 ) . microscopy and gram - staining of each pleural or csf sample were performed 24 hours a day ( ziehl - neelsen staining on demand ) , whereas bacterial culture on blood and chocolate agar plates was conducted only during working hours ( specimens maintained at room temperature ) . routine serotyping of h. influenzae and s. pneumoniae isolates was also beyond the reach of this institution . however , as routine hospital procedure , several hundred pleural fluid and csf samples were sent to bacteriologists in lisbon for further investigation ( serotyping , pcr , some culture and susceptibility confirmation ) . neither antigen - detection methods in luanda nor pcr in lisbon were used routinely , nor was hiv testing routinely performed in luanda ; however , in an earlier meningitis trial ( 2 ) , we found that 8% of children in the study were hiv positive , in accordance with findings of a local epidemiologic survey ( 6 ) . for patients with mixed bacterial infections , all agents were taken into account for analysis . likely skin contaminants ( 5% ) were excluded by a microbiologist ( l.m . ) . after thoracentesis , pneumothorax or subcutaneous emphysema developed in a few patients but resolved spontaneously for all . the use of pretreatment antimicrobial drugs could not be determined , but because 271 ( 40% ) of 679 children in our prospective meningitis study ( 2 ) were receiving antimicrobial drugs when they arrived at the hospital , pretreatment was likely . in all , 2,634 ( 44% ) of 6,030 pleural fluid samples yielded bacteria . as is characteristic of empyema patients ( 3 ) , most were 723 months of age . h. influenzae was the third most common isolate ( 486 [ 18% ] ) , exceeded only by s. pneumoniae ( 1,044 [ 40% ] ) and staphylococcus aureus ( 690 [ 26% ] ) . thereafter came escherichia coli ( 95 [ 4% ] ) , streptococci other than pneumococcus ( 88 [ 3% ] ) , proteus spp . ( 48 [ 2% ] ) , and other gram - negative bacteria ( 96 [ 4% ] ) . no mycobacterium tuberculosis was detected . after vaccination launch in 2006 , the number of h. influenzae isolations from patients with empyema clearly decreased ( figure 1 ) . although h. influenzae , sometimes concomitantly with pneumococci , was isolated 415 times during 20032007 , it was isolated only 71 times during 20082012 , an 83% decline . serotyping was performed for 29 isolates , and all except 1 were hib . only 8 isolates of s. pneumoniae from patients with empyema were serotyped ; distribution was 6a / b / c ( n = 3 ) , 1 ( n = 2 ) , 14 ( n = 2 ) , and 23f / a / b ( n = 1 ) . distribution of 2,634 pleural fluid ( empyema ) ( a ) and 2,996 cerebrospinal fluid ( csf ) isolates ( b ) from children who received treatment at david bernardino children s hospital , luanda , angola , during 20032012 . numbers above the light green bars in the upper panel comprise the total haemophilus influenzae isolates found alone or with streptococcus spp . the numbers of mixed infections were as follows : 24 , 24 , 9 , 15 , 6 , 2 , 4 , 6 , 0 , and 0 , respectively . hib , h. influenzae type b. after vaccination launch in 2006 , the number of h. influenzae isolates from patients with meningitis also decreased ( figure 1 ) . of 17,104 csf specimens , 2,996 yielded bacteria , of which 1,109 ( 37% ) were s. pneumoniae ; of 45 serotyped strains , the following serotypes were found : 6 ( n = 14 ) , 23 ( n = 11 ) , 1 ( n = 6 ) , 19f / a / b / c ( n = 5 ) , 14 ( n = 3 ) , 4 ( n = 2 ) , 18f / a / bc ( n = 2 ) , 3 ( n = 1 ) , and 5 ( n = 1 ) . h. influenzae ( 776 [ 26% ] ) was the second most common bacterial agent isolated . from the first 5-year period ( 683 cases ) to the second period ( 93 cases ) , h. influenzae isolations decreased by 86% . all 55 serotyped h. influenzae strains were type b. no similar decreasing trend was found for streptococcus agalactiae , 196 ( 7% ) ; neisseria meningitidis , 175 ( 6% ) ; or gram - negative rods such as e. coli , 164 ( 5% ) , klebsiella spp . , 152 ( 5% ) , or salmonella spp . , 51 ( 2% ) . all major changes occurred only for the empyema and meningitis caused by hib , not for diseases caused by s. pneumoniae or other bacteria . proportional decrease in haemophilus influenzae isolates starting in 2007 shows the effect of hib vaccination launched in june 2006 . positive samples / no . cultured cultured samples ( % ) for all empyema and meningitis cases combined . although empyema represents only a fraction of all cases of pneumonia among children in angola , and only a few h. influenzae or s. pneumoniae isolates from pleural fluid and csf were serotyped , the potential for decreasing pneumonia and bacterial meningitis by use of conjugate vaccines was demonstrated . the institution s policy of performing thoracentesis for patients with empyema enabled us to examine the effects of hib vaccination because the etiologic agent was determined for specimens obtained directly from the infection focus . a method much simpler and safer than chest tube insertion would have been transthoracic needle aspiration , for which risks are much exaggerated ( 7,8 ) ; regrettably , this reliable method is rarely used ( 9 ) . when performed in the right place by the right clinicians on the right patients , it is a great tool for clinicians , patients , and epidemiologists . that the bacterium most commonly isolated from pleural fluid was s. pneumoniae was not unexpected , nor was the large role of s. aureus , as documented in africa , unexpected ( 10,11 ) . the lesson learned was the high prevalence of hib among patients with empyema . because 79% ( 11/14 ) of cases of h. influenzae pneumonia in the gambia were caused by hib ( 12 ) , and because a vaccination study in the same country provided strong evidence that hib causes 21% of radiologically proven cases of pneumonia ( 13 ) , the dramatic decline in hib pneumonia and meningitis in luanda fits the general picture well . because by 2012 , already 91% of vaccinees had received 3 doses , the vaccine effect was undeniable . a serologic study from china also showed hib to be a major cause of childhood pneumonia ( 14 ) . obviously , not only empyema but also many other forms of pneumonia are preventable by hib vaccination ( 15 ) . because of economic constraints , only a fraction of the strains could be typed , and no m. tuberculosis , parasites , or viruses were sought . still , our data showed that , besides meningitis , hib is a major cause of severe pneumonia in luanda . this vaccine - preventable disease is almost certainly not a problem specific to angola ; therefore , efforts should be made to implement hib vaccination throughout angola and elsewhere in sub - saharan africa .

in angola during 20032012 , we detected haemophilus influenzae in 18% of 2,634 and 26% of 2,996 bacteriologically positive pleural or cerebrospinal fluid samples , respectively , from children . after vaccination launch in 2006 , h. influenzae empyema declined by 83% and meningitis by 86% . severe h. influenzae pneumonia and meningitis are preventable by vaccination .

The Study Conclusions

to investigate the relation between diet and chronic disease , several dietary assessment methods have been developed and evaluated . the food frequency questionnaire ( ffq ) has been used most frequently in large - scale epidemiologic studies , because ffq is less expensive to administer than are other dietary assessment methods , and the ffq evaluates long - term diet rather than 24-h dietary recall or food records . in addition , dietary intakes estimated by ffqs have shown clear associations with coronary heart disease , type 2 diabetes , and blood lipids [ 1 - 3 ] . however , several studies [ 4 - 7 ] suggested that other types of dietary assessment need to be used in epidemiologic studies of diet and diseases to overcome the limitations of ffqs . these limitations include weak associations with dietary biomarkers and a lack of consistency across studies examining diet and cancer risk . food records ask participants to record all foods and beverages consumed over a specific period of time , usually 3 to 7 days or during multiple periods within a year . because food records do not rely on memory , food records have been used as a reference method to validate other dietary assessment methods . however , due to day - to - day variations and seasonal variations in food records , multiple - day food records over four seasons have been used as a reference standard to evaluate other dietary assessment methods . food records have revealed relationships not observed in the ffq [ 8 - 9 ] . a significant relationship between dietary fat and the risk of breast cancer was found based on multiple - day food records , but was not seen in the ffq [ 8 - 9 ] . however , multiple - day food records require highly motivated participants , and they are expensive to administer in large samples , thus 3-day food records have been commonly used in practical settings . given these aspects , it has been debated which dietary assessment method would be appropriate in large - scale epidemiologic studies . in the present study , we investigated the relative validities of 3-day food records and the ffq , respectively , by comparing them with 9-day food records . subjects were recruited from december 2002 to may 2004 in the health examination center at hallym university sacred heart hospital located in anyang , korea . full details of the methods used in the study are given elsewhere and are summarized below . a total of 199 subjects between the ages of 40 to 70 years consented to join the study and completed the first food record ( fr ) . among them , 130 subjects completed the 3-day frs over four seasons , as well as the ffq . six people who changed their diet for weight - loss purposes during the study period were excluded . this food - based ffq was developed with 24-h data from the korea national health and nutrition examination survey in 1998 . the procedures of development and evaluation of the ffq are described in detail elsewhere [ 10 - 11 ] . briefly , food items were selected based on the cumulative percent contribution of each food and the cumulative r of multiple regression of each nutrient . the consumption frequency was classified into nine categories : never or seldom , one a month , two to three times a month , one to two times a week , three to four times a week , five to six times a week , once a day , twice a day , or three or more times a day . for the food items with different seasonal availability , like fruits , participants were additionally asked to mark one of four categories with respect to how many months they ate each particular item : three , six , nine and 12 months . several photos of serving sizes of certain foods were presented to help in the understanding of portion sizes . each participant was asked to keep 12-day frs for one year . to capture seasonal variations and weekly variations , participants were asked to keep non - consecutive 3-day frs including one weekend day or holiday during each of the four seasons . the participants were asked to record the amounts of foods consumed with multiples of household tableware in order to increase the accuracy of portion size . a standardized protocol was developed by a research dietitian supervisor , which included the manual providing information for fr procedure in detail . dietitians trained participants with the manual and reviewed unclear descriptions , errors , omissions , or doubtful entries in frs and asked the participants to clarify them . twelve - day frs were collected to validate the ffq . in the previous validation study between 12-day frs and the ffq , the pearson 's correlation coefficients between 12-day frs and the second ffq were between 0.10 and 0.46 ( median for all nutrients 0.33 ) . pearson 's correlation coefficients between the first ffq and the second ffq ranged between 0.24 ( carbohydrate ) and 0.58 ( cholesterol ) . in the current study , 3-day frs and the remaining 9-day frs nutrient intake in the ffq was calculated using a weighted frequency per day and a portion size per unit of each food item . the daily nutrient intakes of each participant were the sum of the nutrient intakes of each food item . the seventh edition of the food composition table of korea was used as the nutrient database . three - day frs from each season and a randomly selected season were compared with the remaining 9-day frs , respectively . the mean difference of each nutrient between the 12-day frs and the ffq was tested by paired t - test . correlations of nutrient intake were assessed by pearson 's correlation coefficient after adjustment for sex . most nutrient distributions were skewed , thus , all nutrients were natural log transformed prior to analysis . de - attenuated correlation coefficients were applied to correct the within - person error in the measurements of the frs . the observed correlations were multiplied by the de - attenuation factor ( 1+/n ) , where is the ratio of the withinand between - person variances and n is the number of repeats . using the sas varcomp procedure , within- and between - person variances the agreement of 3-day frs with 9-day frs and the agreement of 9-day frs with the ffq were compared by cross - classification analysis . subjects were classified into quartiles based on nutrient intake , and the percentages of agreement and disagreement were calculated . all statistical analyses were performed using the sas software ( version 9.1 sas institute inc . , cary , nc ) , and p values < 0.05 were considered to be significant . subjects were recruited from december 2002 to may 2004 in the health examination center at hallym university sacred heart hospital located in anyang , korea . full details of the methods used in the study are given elsewhere and are summarized below . a total of 199 subjects between the ages of 40 to 70 years consented to join the study and completed the first food record ( fr ) . among them , 130 subjects completed the 3-day frs over four seasons , as well as the ffq . six people who changed their diet for weight - loss purposes during the study period were excluded . this food - based ffq was developed with 24-h data from the korea national health and nutrition examination survey in 1998 . the procedures of development and evaluation of the ffq are described in detail elsewhere [ 10 - 11 ] . briefly , food items were selected based on the cumulative percent contribution of each food and the cumulative r of multiple regression of each nutrient . the consumption frequency was classified into nine categories : never or seldom , one a month , two to three times a month , one to two times a week , three to four times a week , five to six times a week , once a day , twice a day , or three or more times a day . for the food items with different seasonal availability , like fruits , participants were additionally asked to mark one of four categories with respect to how many months they ate each particular item : three , six , nine and 12 months . several photos of serving sizes of certain foods were presented to help in the understanding of portion sizes . each participant was asked to keep 12-day frs for one year . to capture seasonal variations and weekly variations , participants were asked to keep non - consecutive 3-day frs including one weekend day or holiday during each of the four seasons . the participants were asked to record the amounts of foods consumed with multiples of household tableware in order to increase the accuracy of portion size . a standardized protocol was developed by a research dietitian supervisor , which included the manual providing information for fr procedure in detail . dietitians trained participants with the manual and reviewed unclear descriptions , errors , omissions , or doubtful entries in frs and asked the participants to clarify them . the research dietitian supervisor checked all completed records for accuracy . twelve - day frs were collected to validate the ffq . in the previous validation study between 12-day frs and the ffq , the pearson 's correlation coefficients between 12-day frs and the second ffq were between 0.10 and 0.46 ( median for all nutrients 0.33 ) . pearson 's correlation coefficients between the first ffq and the second ffq ranged between 0.24 ( carbohydrate ) and 0.58 ( cholesterol ) . in the current study , 3-day frs and the remaining 9-day frs nutrient intake in the ffq was calculated using a weighted frequency per day and a portion size per unit of each food item . the daily nutrient intakes of each participant were the sum of the nutrient intakes of each food item . the seventh edition of the food composition table of korea was used as the nutrient database . three - day frs from each season and a randomly selected season were compared with the remaining 9-day frs , respectively . the mean difference of each nutrient between the 12-day frs and the ffq was tested by paired t - test . correlations of nutrient intake were assessed by pearson 's correlation coefficient after adjustment for sex . most nutrient distributions were skewed , thus , all nutrients were natural log transformed prior to analysis . de - attenuated correlation coefficients were applied to correct the within - person error in the measurements of the frs . the observed correlations were multiplied by the de - attenuation factor ( 1+/n ) , where is the ratio of the withinand between - person variances and n is the number of repeats . using the sas varcomp procedure , within- and between - person variances were calculated . the agreement of 3-day frs with 9-day frs and the agreement of 9-day frs with the ffq were compared by cross - classification analysis . subjects were classified into quartiles based on nutrient intake , and the percentages of agreement and disagreement were calculated . all statistical analyses were performed using the sas software ( version 9.1 sas institute inc . , cary , nc ) , and p values < 0.05 were considered to be significant . men made up 26.6% of the total number of subjects , and the mean age of the subjects was 47.4 years . the mean body mass index ( bmi ) of the subjects was 23.4 kg / m . the proportions of current alcohol drinkers and current smokers were 41.1% and 12.9% , respectively . mean daily intakes of nutrients estimated by four 3-day frs and the ffq are given in table 2 . when four 3-day frs were used to estimate energy and nutrient intakes , mean intakes of energy , protein , fat , carbohydrate , vitamin b1 and b2 , niacin , phosphorus , na , fe , zinc , and cholesterol in men were higher than those of women . whereas , mean intakes of vitamin c , folate , and calcium in women were higher than those of men . when the ffq was applied to estimate energy and nutrient intakes , there were no differences in nutrient intakes between men and women . the intakes of fat , fiber , vitamins a , e , and b6 , -carotene , and na in four 3-day frs were higher than those of the ffq . the intake of carbohydrate in the ffq was higher than that of the four 3-day frs . the crude pearson 's correlation coefficients after adjustment for sex between 3-day frs and 9-day frs for spring , summer , fall , and winter were 0.18 - 0.54 , 0.20 - 0.50 , 0.16 - 0.56 , and 0.14 - 0.49 , respectively . the pearson 's correlation coefficients after adjustment for sex between the ffq and the 9-day frs with exclusions of spring , summer , fall , and winter were 0.07 - 0.39 , 0.12 - 0.41 , 0.11 - 0.41 , and 0.09 - 0.38 , respectively . the crude pearson 's correlation coefficients between the 3-day frs and the 9-day frs were higher than the crude pearson 's correlation coefficients between the ffq and the 9-day frs in most nutrients ( table 3 ) . among the crude correlation coefficients between the 3-day frs and the 9-day frs , energy , carbohydrate , fiber , folate , phosphorus , sodium , and iron showed higher correlations ( 0.4 ) than did the other nutrients . vitamin a , retinol , and -carotene showed seasonal differences in the correlations . among the crude correlation coefficients between the ffq and the 9-day frs , vitamin a , vitamin e , vitamin b2 , and sodium showed lower correlations ( 0.2 ) than did the other nutrients . de - attenuated correlation coefficients in most nutrients were improved in the comparisons ( 3-day frs vs. 9-day frs and ffq vs. 9-day frs ) . de - attenuated correlation coefficients of vitamin a , retinol , and -carotene between 3-day frs and 9-day frs constantly showed seasonal differences . after adjusting for sex and energy intake , the correlation coefficients of most nutrients in the comparison were decreased . the crude , de - attenuated , and energy - adjusted correlation coefficients between the 3-day frs and the 9-day frs were constantly higher than those between the ffq and the 9-day frs . the average proportions of classification into the same quartiles , adjacent quartiles , and distant quartiles between the 3-day frs and the 9-day frs were 35.8% , 40.5% , and 5.2% , respectively . the nutrients which showed 10% seasonal differences in the classification into the same quartiles or adjacent quartiles between the 3-day frs and 9-day frs were energy , fiber , vitamin a , retinol , vitamin b2 , phosphorus , iron , and zinc . on average , the proportions of classification into the same quartiles , adjacent quartiles , and distant quartiles between the ffq and 9-day frs were 31.1% , 39.4% , and 6.9% , respectively . in this validation study , we evaluated the relative validities of 3-day food records ( frs ) and the food frequency questionnaire ( ffq ) by comparing them with that of the 9-day frs . correlation coefficients between the 3-day frs and the 9-day frs were higher than those between the ffq and the 9-day frs . average proportions of classification into the same quartiles and adjacent quartiles between the 3-day frs and the 9-day frs were higher than those between the ffq and the 9-day frs , but cross - classifications of two methods ( 3-day frs and ffq ) with 9-day frs showed that both the 3-day frs and the ffq were able to reasonably categorize individuals by nutrient intake . three - day frs showed higher correlations and higher agreement proportions of quartile classification with the 9-day frs than did the ffq , but both of the relative validities of 3-day frs and ffq were acceptable for use as dietary assessment tools . in the present study , correlations between 3-day frs and 9-day frs were higher than correlations between 9-day frs and the ffq . the ffq used in our study was a food - based ffq and , thus , seasonings and cooking oils were omitted , which might affect the estimations of some nutrients and correlations with frs . in the study by yun et al . , excluding oils and seasonings from a ffq underestimated vegetable fat , vitamin e , and sodium intake , and shim et al . reported that seasonings contributed 8.4% of energy intake , 34.4% of fat intake , 20.5% of iron intake , and 17.9% of -carotene intake . thus , intakes of seasonings and oils should be considered in the selection of the items of the ffq . a dish - based ffq can be a solution for including seasonings and oils in the estimation of nutrients , but due to a lack of standard korean recipes , the development of standard recipes for korean dishes is required first . the correlations of the ffq with the 9-day frs in this study appear to be lower than western countries [ 16 - 17 ] , but comparable to other korean studies [ 18 - 20 ] . a typical korean meal consists of cooked rice , soup , and multiple side dishes and a meal is often served family style and side dishes are shared with multiple persons . thus , koreans may have difficulties in answering the consumption frequency and portion size for a specific food item . since the consumption of carbohydrate in koreans is higher than that of western countries , more food items containing high carbohydrate were listed in the ffq , which may result in higher mean of carbohydrate intake in the ffq than frs . lower correlations of the ffq with the 9-day frs than those of the 3-day frs with the 9-day frs in the present study may be partially attributed to a concept of ffqs . the basic assumption of ffqs is that the average long - term diet is the conceptually important factor rather than dietary intake over a few specific days . in ffqs participants might have trouble remembering a consumption frequency or the amount of food consumed in a year . in a qualitative study using cognitive interviews for the ffq used in the present study , participants had difficulties in remembering events over the course of a full year . elements contributing to those difficulties included the consumption of diverse foods , calculating the averages for seasonal foods , estimating consumption amounts from photos , adjusting frequency when the amount consumed is higher or lower than the quantities presented , and combining the frequency and quantity of each food item when several food items are clustered into one category , etc . lee et al . to overcome the limitations of ffq , several approaches including detailed questions regarding preparation , questions on seasonal intakes for several foods , inclusion of portion size ranges , additional response categories for frequency of intake , and addition of the food glossary and written cues were suggested [ 23 - 24 ] . however , despite these limitations of the ffq , cross - classification showed that the ffq classified approximately 71% of the subjects within the same or adjacent quartiles and only 7% of the subjects were classified into distant quartiles . with respect to expediency of administration and day - to - day variation , the ffq can be a useful tool for estimating usual intake in a large epidemiologic study . three - day frs showed a relatively higher validity than did the ffq , but 3-day frs have a weakness when it comes to characterizing an individual 's usual diet due to within - person variations of day - to - day dietary intake . reported components of variance in nutrient intake with the same data used in the current study . the major components of variance were within - individual variations ( 57.2 - 87.1% ) and between - individual variations ( 12.2 - 37.4% ) for all nutrients . weekly and seasonal variations contributed small components for most nutrients , but vitamin a , retinol , and -carotene showed seasonal differences in the correlations between the 3-day frs and 9-day frs in the current study . suggested that to estimate usual individual intakes within 20% of the true mean with 90% confidence level , energy , protein , carbohydrate , phosphorus , and iron required 3 - 9 days of dietary survey , fat and calcium required 13 - 19 days , and vitamins a and c required 25 - 29 days . depending on the nutrients of interest and the purpose of a study , the number of days for frs should be taken into account . despite the relatively higher validity of 3-day frs , to overcome the limitations of 3-day frs including day - to - day variation of intake and cost of administration , the ffq needs to be combined in a large epidemiologic study . subjects were recruited in the health examination center , thus , there is a restriction in generalizing the results of the study . the reference measurement should be independent from the evaluated method , but since 9-day frs share common limitations with 3-day frs , the correlation between 9-day frs and 3-day frs may be affected . reliable biomarkers should be introduced to validate food intake measurements for further studies . in conclusion , 3-day frs showed a relatively higher validity and agreement than ffq , but the ffq still has strength in large epidemiologic studies in terms of convenience of administration and estimation of usual intake . therefore , many factors such as research objective and study design should be considered when selecting a dietary assessment method .

the food frequency questionnaire ( ffq ) has been used as an important dietary assessment tool in epidemiologic studies , but the usefulness of the ffq has been debated in recent years . this study was performed to evaluate the relative validities of 3-day food records and the semi - quantitative ffq . a total of 124 subjects finished 3-day food records ( frs ) during each of the four seasons , as well as the ffq from december 2002 to may 2004 . the ffq was a food based semi - quantitative ffq including 103 items . three - day frs from each season and a randomly selected season were compared with the remaining 9-day frs . the remaining 9-day frs , as a reference measurement , were also compared with the ffq . pearson 's correlation coefficients between the 3-day frs and the 9-day frs were between 0.14 and 0.56 . pearson 's correlation coefficients between the ffq and the 9-day frs ranged between 0.07 and 0.41 . average proportions of classification into the same quartiles , adjacent quartiles , and distant quartiles between the 3-day frs and the 9-day frs were 35.8% , 40.5% , and 5.2% , respectively . on average , the proportions of classification into the same quartiles , adjacent quartiles , and distant quartiles between the ffq and the 9-day frs were 31.1% , 39.4% , and 6.9% , respectively . three - day frs showed higher correlations and higher agreement proportions of quartile classification with the 9-day frs than did the ffq , but both relative validities of 3-day frs and the ffq appear to be acceptable as dietary assessment tools . further studies for validating food intake by reliable biomarkers are necessary .

Introduction Subjects and Methods Subjects Food-frequency questionnaire Food record Statistical analysis Results Discussion

the infection is most commonly caused by aspergillus fumigatus , with aspergillus flavus , aspergillus niger , and aspergillus terreus less often implicated.1 profound and prolonged neutropenia is the most common risk factor associated with development of disease . as such , hematopoietic stem cell transplant ( hsct ) recipients and patients receiving aggressive chemotherapy for hematologic cancers are at particular risk.2,3 invasive aspergillosis most frequently begins in the lungs after inhalation of aspergillus conidia . initial , nonspecific manifestations include fever , cough , and dyspnea.4 without treatment , invasive pulmonary aspergillosis is almost always fatal.1,4,5 definitive diagnosis of invasive aspergillosis requires culture confirmation of aspergillus species after biopsy of a sterile specimen . however , culture results lack sensitivity , may take as long as 4 weeks , and be confounded by contamination.1,4 prompt treatment is essential to improve survival . in the high - risk host , these may include fever despite the use of broad - spectrum antimicrobial agents , pulmonary infiltrates on ct scan ( particularly with the presence of the halo or air - crescent sign ) , and/or detection of galactomannan antigen in the serum.1 several antifungal agents are indicated for the treatment of invasive aspergillosis , including amphotericin b and its lipid formulations , itraconazole , voriconazole and caspofungin . voriconazole , however , is the drug of choice for the primary treatment of invasive aspergillosis.1 voriconazole is initiated with a loading dose of 6 mg / kg intravenously ( iv ) every 12 hours for two doses and followed by 4 mg / kg every 12 hours . parenteral administration is recommended in seriously ill patients , but clinically stable patients may be converted to oral tablets ( with weight - based dosing rounded up to convenient pill sizes ) . a minimum of 6 to 12 weeks of therapy is required to adequately treat invasive pulmonary aspergillosis . longer durations are necessary when prolonged periods of immune suppression are present and in cases where infected lesions are slow to resolve.1 voriconazole levels have been correlated with antifungal efficacy and toxicity in several small studies.6,7 though not yet routinely advocated , therapeutic drug monitoring is reasonable when drug toxicity or refractory fungal disease is suspected.4 the incidence of inpatient - treated aspergillosis cases in the us in the late 1990s was between 3.02 and 3.80 per 10,000 hospital patients , representing over 10,000 aspergillosis - related discharges from community hospitals.8,9 the total us community hospital - related cost of aspergillosis in 1996 was estimated to be us$633.1 million.8 the estimated difference in hospital costs of patients with aspergillosis in the late 1990s were us$36,867 to us$59,356 higher than those of patients without the infection.8,9 using the us bureau of labor statistics cpi inflation calculator , the equivalent 2009 amounts are us$48,110 to us$80,468.10 compared to patients with other invasive fungal infections such as candidiasis , histoplasmosis , and cryptococcosis , those with aspergillosis had the highest per - patient treatment costs ( us$37,921/patient for inpatient care and us$34,871/patient for outpatient follow - up care).9 when adjusted to 2009 dollars the total cost to treat a patient with aspergillosis is us$94,991 which is consistent with 2003 estimates provided by tong and colleagues.11 although voriconazole is considered first - line therapy for the primary treatment of invasive aspergillosis , it does not have the lowest acquisition cost of the fda - approved treatments of invasive aspergillosis . therefore the purpose of this article is to review the pharmacoeconomic studies that included voriconazole for the treatment of invasive aspergillosis . voriconazole is a synthetic , broad spectrum triazole antifungal agent that inhibits fungal cytochrome p450-dependent enzyme lanosterol 14--demethylase , ultimately decreasing the biosynthesis of ergosterol , an essential component of the fungal cell membrane . voriconazole is fda - approved for the treatment of invasive aspergillosis , esophageal candidiasis , candidemia in nonneutropenic patients , invasive candidiasis and infections due to scedosporium apiospermum and fusarium species in patients refractory to or intolerant of other therapy.12 voriconazole is available as both oral and parenteral formulations . the oral tablet has a bioavailability exceeding 90% , which permits switching between formulations when clinically appropriate . the kinetics of voriconazole are nonlinear , dose - dependent , and exhibit a high degree of inter - patient variability . it is metabolized by the p450 ( cyp ) enzymes cyp2c19 , cyp2c9 , and cyp3a4 to inactive metabolites . its metabolism is saturable ; increasing doses of voriconazole result in disproportional increases in drug exposure.13 voriconazole is generally well tolerated . the most commonly reported adverse reactions , occurring in at least 5% of patients , include visual disturbances , elevated hepatic enzymes , fever , rash , nausea and vomiting.12,14,15 visual and auditory hallucinations have also been occasionally reported in patients receiving voriconazole.12,15 plasma voriconazole levels exceeding 5.5 g / ml have been linked to higher incidences of neurologic events , visual disturbance and hepatotoxicity.6,7 voriconazole has numerous drug - drug interactions , which may limit its usefulness in certain populations . voriconazole is both a substrate and inhibitor of p450 ( cyp ) enzymes cyp2c19 , cyp2c9 , and cyp3a4.12,14,15 voriconazole is available for iv use as a 200 mg powder for reconstitution and for oral use as 200 mg and 50 mg tablets and a 200 mg/5 ml powder for suspension.12 average wholesale prices are us$121.63 per 200 mg iv vial , us$10.33 per 50 mg tablet , and us$41.33 per 200 mg tablet.16 historically , invasive aspergillosis - associated mortality rates have ranged from 60% to 90% , with central nervous system or disseminated infection or disease in hsct patients conferring graver prognoses.1720 changes in transplantation practices , diagnostic procedures , and the extensive use of voriconazole have been credited with significant reductions in mortality rates.17,21 in 2002 , herbrecht and colleagues published the pivotal global comparative aspergillosis ( gca ) study sponsored by pfizer.22 the investigators compared the efficacy and safety of voriconazole and conventional amphotericin b desoxycholate ( cab ) for the primary treatment of invasive aspergillosis in immunocompromised patients . this prospective , randomized trial involved 277 patients ( n = 144 , voriconazole ; n = 133 , cab ) aged 12 years or greater with definite or probable aspergillosis . most had an underlying diagnosis of allogeneic hsct or hematologic cancer and nearly half were neutropenic . the most common site of infection was the lungs.22 voriconazole was dosed at 6 mg / kg iv every 12 hours 2 doses , then 4 mg / kg iv twice daily for at least 7 days , at which time it could be switched to oral administration of 200 mg twice daily . other licensed therapy was permitted in the case of therapeutic failure or drug intolerance , which occurred in 52 patients in the voriconazole and 107 patients in the cab groups . the planned duration of therapy was 12 weeks.22 at week 12 , voriconazole was associated with significantly improved response rates and survival and fewer adverse reactions than cab . successful response , defined as clinical improvement or resolution and at least 50% improvement of radiologic findings , was achieved by 52.8% of patients receiving voriconazole and 31.6% of patients receiving cab ( absolute difference 21.2% ; 95% ci 10.4% to 32.9% ) . the survival rate was 70.8% in the voriconazole group versus 57.9% in the cab group ( hr 0.59 ; 95% ci 0.40 to 0.88 ) . renal impairment and infusion - related fevers and chills were more common in patients receiving cab while voriconazole - treated patients were more likely to experience visual disturbances and dermatologic reactions.22 based on the results of this trial , voriconazole replaced amphotericin b as first - line therapy for the treatment of invasive aspergillosis . a recent observational study using data compiled by the multicenter prospective antifungal therapy ( path ) alliance registry demonstrated mortality rates consistent with those reported by the herbrecht trial.21 in this study , the epidemiology and outcomes of 144 hsct patients with invasive aspergillosis were examined . eighty - five percent of these patients received treatment with voriconazole , 47% in combination with at least one other antifungal agent . a medline search using the terms cost analysis or pharmacoeconomic analysis plus aspergillosis plus voriconazole was serially repeated , substituting voriconazole with caspofungin , amphotericin b , and itraconazole . studies were limited to those published in the english language that compared both the costs and outcomes of invasive aspergillosis therapy and included a voriconazole arm . these ten studies are compared globally by the type of analysis , methods used to estimate the cost and outcomes , results , transparency , and other methodological issues . the 10 pharmacoeconomic analyses were conducted in six different countries as indicated in table 1 . voriconazole was compared to cab,2330 liposomal amphotericin b ( l - amb),31 itraconazole,24 and caspofungin.32 generally speaking all of the studies used the appropriate procedures for conducting pharmacoeconomic analyses with regard to their research question , modeling procedures , data sources , resource valuation , transparency , discounting , use of sensitivity analyses , and use of incremental analyses.33 any exceptions to these standards are noted in this section . overall , the 10 studies had well - defined research questions , and they were transparent indicating that the data sources and methods for calculating expected costs and outcomes were obvious . eight of the studies were cost - effectiveness analyses ( cea),2329,31 one was a cost - minimization analysis ( cma),32 and one was a cost analysis ( ca).30 no cost - utility analyses of voriconazole were identified , which is not surprising given the limited treatment period and the overall poor health condition of people with invasive aspergillosis . eight of the voriconazole pharmacoeconomic studies used a decision analytic model such as a decision tree or markov model to estimate the expected costs and outcomes of therapy.2329,31 one of the studies calculated the costs and outcomes from actual clinical observations and used a decision tree to calculate the weighted average cost and outcomes.23 the three outcomes reported in the studies were successful response at 12 weeks , survival at 12 weeks , and mean survival time . tables 2 , 3 , and 4 present the results according to each of these outcomes , respectively . since the studies were conducted in different countries with different healthcare systems and different currencies , no attempt was made to combine the results . all cost - effectiveness analyses or cost - minimization analyses identified voriconazole treatment arms as the most cost - effective . this is not unexpected given the number of studies that used the results from gca study as the primary source for outcomes data . however , the analyses that used multiple studies as the primary source for outcomes data reported similar results.31,32 none of the studies discounted costs or outcomes . this is appropriate for all of the studies that used the first two outcome measures since the study periods were less than 12 months . three studies reported mean survival times . given that some of the costs and outcomes in these studies occurred outside the 12-month window , they should have been discounted . most likely this is not a major issue given that the average life expectancy of the people included in these analyses ranged from less than 12 months to 3 years.24,28,31 these three studies are described in greater detail below . jansen and colleagues used the results of the gca study22 as the basis of their decision tree which estimated 12 week cost and outcomes in a dutch population.24 in the model , patients were treated initially with voriconazole , cab , or itraconazole and were switched to other licensed antifungal agents in the case of severe toxicity or treatment failure . since itraconazole was not included in the gca study , they used other literature and expert opinion to identify resource use and probabilities of response and toxicities in the itraconazole arm . a markov model was then used to simulate the lifetime costs and outcomes of voriconazole , itraconazole , and amphotericin b as first - line treatments for invasive aspergillosis . patients treated successfully at the end of 12 weeks remained in the success state until they died ( an assumption of no relapses ) . patients not successfully treated at the end of 12 weeks entered the markov process in the failure state and remained there until they transitioned to the success or death states . patients were transitioned from state to state on a weekly cycle based on probabilities derived from the gca study . the mean survival times in this model were 174 weeks , 150.4 weeks , and 116.1 weeks for the voriconazole , itraconazole , and cab groups respectively ( see table 4).24 jansen and colleagues conducted a similar study for a german population . they used a decision tree and markov model to simulate the 12 week and lifetime costs and outcomes of voriconazole and amphotericin b as first - line treatments for invasive aspergillosis.28 the mean survival times in this model were 174 weeks and 116.1 weeks for the voriconazole and cab groups respectively ( see table 4).28 ament and colleagues created a model to compare voriconazole and l - amb as first - line therapy . after severe toxicity or treatment failure , a patient in the model could be switched to any combination of other antifungal agents.31 seven different treatment combinations were compared in the final analysis : 1 ) voriconazole as first - line and l - amb plus caspofungin as second - line therapy , 2 ) voriconazole as first - line and caspofungin as second - line therapy , 3 ) voriconazole as first - line and cab as second - line therapy , 4 ) voriconazole as first - line and l - amb as second - line therapy , 5 ) l - amb as first - line and voriconazole plus caspofungin as second - line therapy , 6 ) l - amb as first - line and voriconazole as second - line therapy , 7 ) l - amb as first - line and caspofungin as second - line therapy . the mean survival times ranged from 1.109 to 1.307 years as summarized in table 4.31 four additional studies are described in greater detail to highlight their unique designs or contributions to the literature . dominguez - gil and colleagues conducted a cost minimization analysis comparing voriconazole and caspofungin from a hospital perspective . based on probabilities obtained from multiple published studies , the authors determined or assumed that both agents would have equal efficacy . the average cost of the voriconazole - treated group was 1,132 lower than the caspofungin - treated group ( see table 5).32 green and colleagues used a subset of patients from the gca study that had thoracic computed tomographic ( ct ) scans at baseline to look at the cost - effectiveness of voriconazole compared to cab.29 they divided the patients into two groups , those with and without a halo sign on the ct scan at baseline . the probabilities of toxicity and success in these patients were used to model the expected cost and outcomes in each group . both groups had similar costs , but the group with the halo sign had better survival rates than the group without the sign . voriconazole was the most cost - effective agent in both groups ( see table 3).29 wingard and colleagues conducted a cost analysis using data from the gca study as the primary source of outcomes data.30 consideration was not given to any outcome measure , but the patients were subdivided into survivors and nonsurvivors . the group treated with voriconazole had lower treatment costs compared to the group treated with cab resulting in us$16,758 savings in the survivor group . conversely , the non - survivor group treated with cab had savings of us$10,176 compared to the voriconazole group . when all patients were considered together , patients treated with voriconazole had a us$4,997 savings compared to patients treated with cab ( see table 5).30 overall the results of all of the analyses were robust to the assumptions made during the modeling process . this means that the results of the analysis did not change when the key assumptions of the models were tested in sensitivity analyses ( ie , varied from high to low values ) . however the results of four studies were sensitive to drastic changes in either costs , the weight of the patient used to estimate the medication dose , or the renal toxicity of cab.23,27,31,32 in the model used by roststein and colleagues , patients were switched to l - amb due to toxicity or treatment failure of voriconazole or cab . if the cost of l - amb was cut in half , then the cab arm became more cost - effective.23 in the model used by garbino and colleagues , when the renal toxicity of amphotericin b was assumed to be less than 7% , then the cab arm became more cost - effective.27 the results published by dominguez - gil and colleagues were robust as long as the patients weight was less than 102 kg.32 testing the conclusions of the pharmacoeconomic analyses with sensitivity analyses described above is one way to validate study results . in an attempt to further validate the results of a similar pharmacoeconomic analysis that has not been published , van campenhout and colleagues compared the results of the model to actual data collected from 116 patients in 13 different hematology oncology intensive care settings in belgium.34 the clinical response rate at 12 weeks was similar ( 53% from the model , 50% from the observational study ) . however the model underestimated the mortality rates at 84 days ( 29% vs 42% ) and slightly overestimated the per - patient cost of hospitalizations ( 21,298 vs 19,674).34 two of the studies included in this review accounted for the cost of the galactomannan assays,24,28 but none included the costs of voriconazole levels . the galactomannan assay is a diagnostic test , therefore the cost of this test would be incurred regardless of the therapy selected . in other words , including the cost of this diagnostic test in any of the pharmacoeconomic analyses would not change the results . an observational study by pascual and colleagues evaluated the impact of measuring voriconazole blood levels.6 patient with troughs less than 1 mg / l had worse outcomes compared to those with troughs between 1 and 5.5 mg / l , while patients with troughs higher than 5.5 mg / l had more toxicity.6 the median number of troughs drawn per patient was 4.5 with the first drawn a median of 5 days after therapy and every 7 days thereafter . the cost of this test is difficult to identify ; however , the centers for medicare and medicaid services ( cms ) 2009 clinical diagnostic laboratory fee schedule limits for other drug assays ranges from us$17.40 to us$27.00.35 thus if one assumes the cost to a payer would be the upper end of this limit ( us$27 per trough ) with five troughs per patient , then an additional us$135 would be added to the cost of therapy . when the cost of the assay is added to the expected costs calculated in each of the us - based pharmacoeconomic studies in this review , the results do not change . amphotericin b and its lipid formulations , itraconazole , voriconazole and caspofungin , are all indicated for the primary treatment of invasive aspergillosis ; however , voriconazole is preferred.1 the gca study by herbrecht and colleagues provided the clinical evidence to support voriconazole s clinical role.22 this publication also served as the basis for multiple pharmacoeconomic analyses which demonstrated that voriconazole is cost - effective in the primary treatment of invasive aspergillosis . of the agents indicated for the primary treatment of invasive aspergillosis , the us average wholesale price of l - amb is the highest followed by caspofungin , voriconazole , itraconazole , and cab.16 while the acquisition costs of voriconazole are higher than those of conventional amphotericin b , the toxicity profile and treatment success rate associated with voriconazole result in lower total treatment costs per successfully treated patient.2330

invasive aspergillosis is a life - threatening fungal infection predominately affecting immunocompromised individuals . the incidence of inpatient - treated aspergillosis cases in the us is estimated to be between 3.02 and 3.80 per 10,000 hospitalized patients . the estimated difference in hospital costs of patients with an aspergillosis infection is us$36,867 to us$59,356 higher than those of patients without the infection . voriconazole is a synthetic , broad spectrum triazole antifungal agent , with fda - approved indications for the treatment of invasive aspergillosis , esophageal candidiasis , candidemia in nonneutropenic patients , invasive candidiasis , and infections due to scedosporium apiospermum and fusarium species in patients refractory to or intolerant of other therapy . eight cost - effectiveness analyses , one cost - minimization analysis , and one cost analysis were identified from a medline search . the 10 pharmacoeconomic analyses were conducted in six different countries comparing voriconazole to conventional amphotericin b , liposomal amphotericin b , itraconazole , and caspofungin . all the cost - effectiveness and cost - minimization analyses identified voriconazole as the most cost - effective therapy . the cost analysis demonstrated voriconazole cost - savings . while the acquisition costs of voriconazole are higher than those of conventional amphotericin b , the toxicity profile and rate of treatment success associated with voriconazole result in lower total treatment costs per successfully treated patient .

Overview and management of invasive aspergillosis Overview of voriconazole Clinical outcomes Economic outcomes Conclusions

infantile hemangiomas are the most common benign tumors , occurring in up to 10% of infants . although the majority of hemangiomas occur in otherwise healthy infants , there are increasing reports of associated systemic anomalies . the association of large facial hemangiomas with underlying cerebrovascular anomalies was first reported by pascual - castroviejo1 ) . in 1996 , frieden et al.2 ) proposed the definition of phace association to describe these findings associated with large facial hemangiomas . the acronym refers to the association of posterior fossa malformations , facial hemangiomas , arterial cerebrovascular anomalies , cardiovascular anomalies , and eye anomalies . more recently , the acronym has been enlarged to include ventral developmental defects ( sternal defects or supraumbilical raphe)3 ) , thus phaces association . most previous studies have stressed the heterogeneity of the association , and strict criteria of inclusion or exclusion have not been universally developed . to our knowledge in addition , intracranial hemangiomas are rare as a finding of phace association , and concomitant oropharyngeal hemangioma has not been previously reported in the literature of phace association . we report a premature infant case of phace association with facial , intracranial , and oropharyngeal hemangiomas with evidence of the dandy - walker variant and complicated cardiovascular anomalies , including a right - sided aortic arch and an atypical patent ductus arteriosus ( pda ) arising from the tortuous left subclavian artery . a female infant was born by caesarean section at a gestational age of 30 weeks and 5 days to a healthy 29-year - old mother . the birth weight was 1,545 g , and the apgar scores were 7 and 9 at 1 and 5 minutes , respectively . at 3 days of age , doppler echocardiography done at 4 days of age revealed normal intra - cardiac structure and a suspected pda measuring 4 mm in diameter between the left subclavian artery and the main pulmonary artery ( fig . 1 ) . two cycles of oral ibuprofen treatment ( 10 mg / kg for the first dose , followed at 24-hour intervals by 2 additional doses , 5 mg / kg / dose ) were given , but failed to close the pda . at 1 week of age , small hemangiomas involving the left periauricular , temporal , and infraocular area were detected . the hemangiomas subsequently developed into large facial hemangiomas that threatened the left eye ( fig . 2 ) . surgery at 2 weeks of age was performed because of the failure of oral ibuprofen treatment and persistent cardiomegaly . surgery showed an atypical pda arising from the left subclavian artery and entering the main pulmonary artery , which was closed by surgical clipping . a subsequent three - dimensional cardiac computed tomography ( ct ) scan and angiography not only confirmed this diagnosis , but also revealed complicated cardiovascular anomalies , including a right - sided aortic arch and the tortuous left subclavian artery . in detail , a three - dimensional cardiac ct scan and angiography showed a mirror image right - sided aortic arch . the first branch of the right - sided aortic arch was a left innominate artery which was divided into a left common carotid and subclavian artery . the second was the right common carotid artery , and the third a right subclavian artery . the pda arising from the base of the left subclavian artery was closed by surgical clipping , and did not form a vascular ring . a small collateral artery between the thoracic aorta and the left subclavian artery because of the large size of the facial hemangioma , oral prednisolone ( 1 mg / kg / day ) and topical clobetasol-17-propionate were initiated at 1 month of age . at 6 weeks of age , brain magnetic resonance imaging ( mri ) and angiography ( mra ) were obtained because phace association was suspected . these showed the presence of the dandy - walker variant with hypoplastic cerebellar vermis and multiple intracranial hemangiomas in left cerebellopontine angle ( fig . no definite abnormalities in the intracranial large vessels were noted on the brain mra . at 7 weeks of age , laryngoscopic examination revealed a hyperemic lesion on the uvula , and oropharyngeal hemangioma was suspected ( fig . in addition , no specific findings were detected in the chromosomal analysis , including array comparative genomic hybridization ( cgh ) to identify gene copy number variations . the prednisolone therapy was gradually tapered and oral propranolol was added at 10 weeks of age . thereafter , she was treated with intralesional triamcinolone and pulsed dye laser in addition to oral propranolol . no significant changes were noted on a subsequent laryngoscopic examination done at 3 and 8 months of age . at the follow - up examination at 12 months of age , the hemangioma in the infraocular area was significantly decreased . neurological examinations at 6 and 12 months of age demonstrated no developmental delay for her corrected age . in addition , physical measurement at 12 months showed a significant growth retardation in weight , height , and head circumference ( < 5th percentile for her age ) . the phace association can be diagnosed in children presenting with a characteristic hemangioma and at least one associated extracutaneous anomaly4 ) . approximately 30% of affected children exhibit two or more extracutaneous manifestations of the disease , but this is most certainly an underestimate since only a minority of patients has been completely evaluated5 ) . although the true incidence of phace is unknown , the syndrome appears to be uncommon . metry et al.6 ) reported that they have collected a database of 201 published cases and 25 new cases , and their phace patients represented 2.3% of children with facial hemangiomas in their overall study , and 19.7% of those with segmental hemangiomas of the face . it has been hypothesized that phace might be caused by microdeletion(s ) , a hypothesis which is based partly on the observation that several developmental syndromes with many features in common with phace have been found to be caused by microdeletions . a large , multicenter study is under way to investigate the genetic basis of phace using array cgh analysis7 ) . in our patient , as in previous reports , our patient did not present the full spectrum of abnormalities associated with phace association , but nonetheless presented a wide range : facial , intracranial , and oropharyngeal hemangiomas , posterior fossa malformations of dandy - walker variants , and complicated cardiovascular anomalies . large facial hemangiomas are the hallmark of phace . most of the hemangiomas associated with phace have a unique appearance , described as " segmental " . a segmental hemangioma is defined as a large , plaque - like , and geographic patterning over a territory of skin . many patients present with an isolated facial segmental hemangioma , although extracutaneous hemangiomas have also been found in approximately one third of patients , the subglottic airway being the most common location , one which can give rise to stridor2,5 ) . on laryngoscopic examnination , our patient had a small hyperemic lesion on the uvula , and we suspected an oroharyngeal hemangioma , instead of a subglottic hemangioma . to our knowledge , an oropharyngeal hemagioma has not been previously described in other reports of phace association . because the patient may be at an increased risk of respiratory or digestive problems with gradual proliferation of the hemangioma , careful monitoring by serial laryngoscopic examinations and proper management will be required . our patient also had ipsilateral intracranial hemangiomas in the left cerebellopontine angle with large segmental facial hemangiomas . intracranial hemangiomas are rare as a finding of phace although they are being increasingly reported in phace patients , likely as a result of more frequent and improved screening with contrast - enhanced neuroimaging3,6,8 - 12 ) . the intracranial hemangiomas were mainly located in the internal auditory canal and cerebellopontine angle , and involuted in parallel with the facial hemangiomas8,11,13 ) . cardiovascular abnormalities are also quite common with phace association , and at least one third of infants with this syndrome have cardiovascular anomalies5,6 ) . aortic arch anomalies , specifically coarctation of the aorta , are the most frequently described cardiovascular anomalies14 ) . other cardiac anomalies described in phace syndrome include right - sided aortic arch , aberrant origin of the subclavian artery , pda , atrial and ventricular septal defects , persistent left superior vena cava , and rarely , complex congenital heart disease7 ) . our patient showed complicated malformations , including a right - sided aortic arch and an atypical pda arising from the tortuous left subclavian artery entering the left pulmonary artery , instead of common malformations such as aortic coarctation or aneurysm . aberrant origin of pda and the tortuosity of the left subclavian artery shown in our patient are rare as a finding of phace association and quite distinct from other related cardiovascular anomalies reported in phace patients . these complicated anomalies also make it difficult to understand the anatomy of the supra - cardiac arteries . between 43% and 90% of patients with phace have a central nervous system ( cns ) structural malformation2,5,6,9,15 ) . the posterior fossa malformations constitute the most commonly observed developmental brain abnormalities associated with phace , and range from focal cerebellar hypoplasia to dandy - walker complex . cerebrovascular anomalies , particularly stenosis and tortuosity may lead to progressive neurologic sequelae , including phace - related ischemic stroke . our patient was not found to have any cerebrovascular anomalies on mri and mra . however , because most of the strokes reported occurred at the average age of 8.8 months ( range , 3 to 18 months ) with progressive obstructive arterial changes and proliferation of the hemangiomas , serial neuroimaging may also be justified in patients without cerebrovascular anomalies on initial examination , as with our patient16,17 ) . our patient showed no developmental delays , but significant growth retardation . despite the multidisciplinary nature of this association , no large , collaborative , cross - specialty studies have been taken . accordingly , very little is known about the natural history of phace , or outcomes of affected infants including premature infants like our patient7 ) . this case is significant in that intracranial , oropharyngeal hemangiomas and an atypical pda arising from the tortuous left subclavian artery are specific and rare findings in phace patients . in infants presenting with large , plaque - like facial hemangiomas , especially , special attention should be given to the laryngoscopic examination to search for hemangiomas in airway .

phace association is a rare neurocutaneous condition in which facial hemangiomas associate with a spectrum of posterior fossa malformations , arterial cerebrovascular anomalies , cardiovascular anomalies , and eye anomalies . we reported a case of phace association in a premature infant showing facial , intracranial , and oropharyngeal hemangiomas with evidence of the dandy - walker variant and complicated cardiovascular anomalies , including a right - sided aortic arch and an atypical patent ductus arteriosus arising from a tortuous left subclavian artery . to our knowledge , intracranial hemangiomas are rare in phace association , and a concomitant oropharyngeal hemangioma has not been previously reported in the phace association literature . in infants presenting with large , plaque - like facial hemangiomas , it is important to conduct active cardiovascular and neurological evaluations . special attention should be given to the laryngoscopic examination to search for additional hemangiomas in the airway .

Introduction Case report Discussion

kandang kerbau women s and children s hospital is one of the major centers in singapore for the admission of sick children , including those showing respiratory illness . after obtaining prior approval from the hospital s ethics committee ( approval number ec/043/2004 ) , we collected nasopharyngeal swabs from 400 pediatric patients between october 2005 and january 2007 . when admitted to the hospital , these patients exhibited symptoms of acute lower respiratory tract infections ( lrti ) ( bronchiolitis , bronchitis , pneumonia , asthma , and wheezing ) and urti ( pharnygitis ) . specimens were sent to the hospital s microbiologic laboratory for routine testing for influenza a and b viruses , rsv , adenovirus , and parainfluenza virus ( serotypes 13 ) by immunofluorescence assay ( lightdiagnostics , chemicon , tamacula , ca , usa ) . the clinical specimens were stored at 80c until further analysis for hmpv was performed ( not longer than a week after collection ) . viral rna ( vrna ) was extracted from each of the thawed nasopharyngeal swabs with the qiaamp viral rna minikit ( qiagen inc . , of the total rna extracted from the clinical specimens , 5 l was subjected to real - time reverse transcription pcr ( rt - pcr ) testing by using the n gene specific primer set nl this was performed with the onestep rt pcr kit ( qiagen ) on a corbett research rotorgene 3000 ( corbett life science , sydney , nsw , australia ) . the pcr cycling conditions were 50c for 30 min , 95c for 15 min , and 45 cycles ( 95c for 20 s and 60c for 60 s ) . specimens that tested positive by real - time rt - pcr analysis were confirmed by conventional rt pcr by using the nl n primer set . the amplified products ( 163 bp ) were detected by using agarose gel electrophoresis , and their identity was confirmed by dna sequencing . of the 400 samples collected , 21 tested positive for hmpv infection , which suggests an incidence rate of 5.3% , compared with an 11.5% incidence rate for rsv ( table 1 ) . previous reports have suggested that in some cases severe symptoms exhibited by rsv - infected patients are associated with dual infections involving hmpv ( 7 ) . although we detected the presence of hmpv and rsv in the patients screened , no evidence for co - infections was observed , which suggests a low occurrence for these viruses in singapore . in a recent study in australia , only 8 of 10,000 screened hospitalized patients showed evidence of co - infection with hmpv and rsv ( 8) . in contrast , several recent studies suggest that co - infections may account for a substantial number of instances in which hmpv has been detected . for example , a recent study in brazil , which used a lower sample size than in our study , reported an 8% incidence rate for pediatric patients who had rsv and hmpv co - infections ( 9 ) . therefore , environmental factors may be a key feature in the development of co - infections . the entire p gene sequences were amplified directly from the specimens by rt pcr using the primers hmptpf 5-atgtcgttccctgaaggaaaagatattc-3 and hmptpr 5-ttaaactacataattaagtggtaaat-3. amplicons 884 bp in size were generated and corresponded to 1209 nt2093 nt of the hmpv genome ( strain jps03 - 240 , ay530095 ) . touch - down procedure ; conditions were 94c for 5 min followed by 30 cycles of 94c for 15 s , 62c ( reducing by 0.5c / cycle ) for 30 s , 72c for 1 min , and a final extension step of 72c for 7 min . the sizes of the respective pcr - amplified products were examined by using agarose gel electrophoresis , gel - purified , and confirmed by dna sequencing . the genetic relationship between the singapore hmpv isolates and those hmpv isolates described previously was analyzed by comparing the p gene sequences ( 10 ) . alignments of nucleic acid sequences were created by using clustalx version 1.83 ( bips.u-strasbg.fr/fr/documentation/clustalx ) . phylogenetic trees were constructed by using the neighbor - joining method ( 1,000 bootstrap replicates ) and edited with mega 3.1 ( 11 ) . this analysis shows that although isolates representing both a and b genotypes were detected , the singapore isolates clustered more predominantly with representative hmpv strains in lineage a , in particular the sublineage a2 . in this study hmpv was detected throughout the year , which suggests that in singapore , hpmv is present in the pediatric community throughout the year . we also noted a slight increase in the incidence of b genotypes ( b1 and b2 ) during the last quarter of 2006 , but the implications of this finding are unclear . phylogenetic analyses of nucleotide sequences of hmpv phosphoprotein showing comparisons with singapore - nanyang technological university ( sin06-ntu * ) sequences . * the specimen number acquired during the course of the investigation ( e.g. , sin06-ntu14 ) was made with known strains ( highlighted ) from canada [ can99 - 81 ( ay145294 , ay145249 ) , can97 - 83 ( ay297749 ) , can97 - 82 ( ay145295 , ay145250 ) , can98 - 75 ( ay297748 ) , can98 - 79 ( ay145293 , ay145248 ) ] , japan [ jps03 - 180 ( ay530092 ) , jps03 - 240 ( ay530095 ) , jps03 - 187 ( ay530093 ) , jps02 - 76 ( ay530089 ) ] , and the netherlands [ nl-1 - 00 ( af371337 ) , nl-17 - 00 ( ay304360 ) , nl-1 - 99 ( ay525843 ) , nl-1 - 94 ( ay304362 ) ] . the age and clinical characteristics of the hmpv patients were next compared with the different hmpv lineages ( table 2 ) . children with hmpv infection were 1 month to 12 years in age ; 67% were < 1 year of age compared with 63% of rsv - infected children . of the hmpv - infected patients , 52% exhibited lrti ; of these , 82% were infected with the hmpv sublineage a2 . in contrast , 43% of the patients exhibited urti caused by the sublineages a2 and b2 . in comparison , 61% and 20% of the rsv patients had a clinical diagnosis of lrti or urti , respectively . our data suggested an increased association of sublineage a2 with lrti in the hmpv - infected patients . the implications of this are unclear , but several reports note a correlation between severity of infection and the presence of the a genotype ( 12,13 ) . unfortunately , we were not able to make a strict comparison of our data with data from recent studies in southeast asia ( 14,15 ) ; these studies used significantly smaller sample sizes and a different selection criterion for the patients screened ( i.e. , lrti and wheezing and asthma ) . * l , lower respiratory infections including bronchiolitis , bronchitis , pneumonia , asthma , wheezing or chest infection ; u , upper respiratory infections including infantile pyrexia and pharyngitis ; o , febrile fit . our study is the first , to our knowledge , that has attempted to assess the importance of hmpv among the pediatric population in singapore . we analyzed 400 samples that were collected from pediatric patients who were admitted to a hospital over a 16-month period . an infection rate of 5.3% was observed , which is consistent with the reported infection rates of several other industrialized countries . we also noted that of the viruses detected , 67% were of the a subtype and 33% were of the b subtype , which suggests that the former was the predominant hmpv subtype causing illness in these patients our findings suggest that hmpv is a substantial cause of illness among the pediatric population of singapore .

four hundred specimens were collected from pediatric patients hospitalized in singapore ; 21 of these specimens tested positive for human metapneumovirus ( hmpv ) , with the a2 genotype predominating . a 5% infection rate was estimated , suggesting that hmpv is a significant cause of morbidity among the pediatric population of singapore .

The Study Conclusions

historically , htt was initially identified as a caspase substrate and it was the first example of a protein associated with a neurodegenerative disorder cleaved during apoptosis . caspases are highly conserved cysteine - aspartic proteases associated primarily with apoptotic cell death and essential for the processing of a large number of substrates . proteolytic fragments processed by caspases are detectable in brains of hd patients and hd mice before the loss of neurons in the striatum , with the cleavage efficiency dependent on the polyq tract length . blocking htt cleavage by site - directed mutagenesis or by pharmacological approaches reduces cytotoxicity in cultured cells . in line with these findings , mice overexpressing a caspase-6 non - cleavable mutant htt have milder neuropathological defects and are protected against excitotoxic stimulation compared with mice carrying the cleavable mutant htt . this strongly suggests that caspase - dependent proteolytic cleavage of the aberrant protein might be a key step in the toxic events during hd , and that htt functions as prosurvival factor . htt is also a substrate of calcium - activated proteases , that is , calpains . calpains belong to the family of cysteine proteases typically activated by the elevation of intracellular ca levels , either in response to plasma membrane depolarization or in response to ca release from the intracellular stores . in mice overexpressing mutant htt , increased glutamate release from afferent neurons enhances nmda - r activity . this leads to an intracellular ca increase and therefore activation of calpains , which in turn cleave the htt protein into a series of proteolytic products that promote nmda - r - mediated excitotoxicity . moreover , calpains can modulate htt homeostasis via the catabolic process of autophagy . as shown by recent rnai and chemical compound screenings in cultured cells , inhibition of calpains another rnai screening study has also shown that small htt fragments can be generated by the proteolytic activity of some matrix metalloproteinases ( mmps ) . the activation of the mmps and the resulting cleavage of htt were confirmed in samples from hd mouse models . reduced mmp activity , especially mmp-10 and mmp-14 , correlates with lower amount of proteolytic fragments and , as a result , suppression of neuronal degeneration induced by mutant htt in cellular model systems as well as in drosophila . collectively , these findings suggest that protease inhibition might be a beneficial therapeutic approach for hd as it delays the formation of htt - containing intracellular aggregates . autophagy is a cellular catabolic process that seems to have an important role in the pathogenesis of cancer as well as in neurodegenerative disorders . the process of autophagy involves the formation of a double - membrane structure ( autophagosome ) that then encloses a portion of cytosol and delivers its cargo content to the lysosomes for digestion . autophagy occurs at constant low levels in all cells as part of ongoing cellular protein quality control and organelle turnover . however , it also has a primary role in the response to nutrient deprivation as it sustains metabolic functions by providing energy and metabolites to the cells . in different experimental settings , autophagy activation blocks detrimental processes and therefore facilitates cell stress resilience and survival . furthermore , autophagy is one of the primary degradation pathways for various aggregate - prone proteins associated with neurodegenerative diseases . as the tight regulation of autophagy is essential for cellular homeostasis , it is not surprising that autophagic dysfunction can cause metabolic stress and cell death mainly through apoptosis resulting from mitochondrial deficiency or via cleavage of atg proteins . among several key regulators of autophagy , the target of rapamycin ' ( tor ) senses energy status and the availability of the nutrients within the cell through the upstream class i phosphoinositol 3-kinase ( pi3k ) , the serine / threonine kinase akt and the 5-amp - activated protein kinase ( ampk ) . inhibition of the tor complex promotes the recruitment of beclin-1 and atg proteins involved in the formation of the mature autophagosome . the modulation of autophagy is therapeutically promising in hd : the inhibition of tor by rapamycin enhances the clearance of mutant htt - containing aggregates via the autophagy - lysosome pathway ( figure 1 ) . similarly , drugs that block a rise in intracellular ca , such as -type ca channel antagonists , decrease the activity of calpains and result in the indirect activation of autophagy , likely by preventing the degradation of beclin-1- and atg - related proteins . although calpain inhibition promotes autophagy in - vitro and in zebrafish , it still remains to be determined whether it can be effective against hd in in - vivo mammalian models or in clinical settings . autophagy induction clearly represents an appealing approach for hd treatment ; however , the therapeutic window remains to be determined as mutant htt has a negative effect on the sequestration of the autophagic cargo . although the autophagosomes seem to form and fuse to the lysosomes efficiently , there is a failure in the recognition of targeting signals , such as p62 or polyubiquitin , that results in delayed engulfment of cytosolic macromolecules and damaged organelles . several strategies have been suggested to improve the clearance of htt - containing aggregates by autophagy . one of them is based on the observation that histone deacetylase inhibitors block the polyq protein - dependent neuronal degeneration in drosophila . in this case , the acetylation of mutant htt facilitates the recruitment of the protein to the autophagosome and therefore increases the removal of toxic species within the cells . more recent evidence demonstrates that htt - mediated neuronal loss in drosophila can be suppressed by genetic or pharmacological inhibition of nad - dependent class iii deacetylases sirtuins . as pharmacological manipulation of sirtuins by resveratrol has been proposed to activate several pathways , including autophagy , these studies are of particular interest from a potential therapeutic standpoint . loss of proteostasis is a hallmark of several neurodegenerative disorders such as pd , ad and hd . in all of these disorders , aggregate - prone proteins trigger the formation of insoluble intracellular or extracellular aggregates as a result of environmental stress or metabolic changes . whether the fibrillar protein aggregates are pathogenic or have protective roles , remains controversial . in nematodes and in mice , loss - of - function or decreased insulin / insulin - like growth factor 1 ( igf-1 ) signaling prevent the proteotoxicity caused by aggregate - prone peptides . the insulin / igf-1 signaling pathway is an evolutionarily conserved process that stimulates cellular growth according to nutrient availability . the activation of the receptor leads to the potent activation of the downstream target pi3k and akt , which coordinates multiple cellular processes such as proliferation , energy metabolism and survival . together with tor , akt integrates the extracellular inputs with the intracellular status and tunes the cellular responses accordingly . in caenorhabditis elegans , loss - of - function mutations of the sole insulin / igf-1 receptor daf-2 extend the lifespan to more than twofold . genetic studies in c. elegans have revealed that the shift of polyq - containing proteins from the soluble to the aggregate form is time - dependent . loss - of - function of the pi3k age-1 not only extends the lifespan of nematodes but also significantly delays polyq aggregation and toxicity . these protective effects are determined by increased expression of stress - response genes , such as heat shock proteins under the control of the transcription factors daf-16 and hsf-1 . interestingly , overexpression of full - length , but not of truncated , htt lowers the expression of plasma igf-1 levels and , as result , affects body weight in mice . a decrease in igf-1 expression has also been observed in different tissues of hd patients , which indicates that htt loss - of - function can modulate igf-1 signaling over time . in primary dissociated neurons expressing mutant htt , treatment with igf-1 induces specific activation of akt and the direct phosphorylation of htt , which results in a reduced number of htt - containing intracellular inclusions and therefore neuroprotection . thus , these findings suggest that igf-1 signaling and htt can apparently influence each other , although it still remains elusive whether this cross - talk potentiates or prevents detrimental cascades , including apoptosis . modification of proteostasis by the insulin / igf-1 signaling pathway is not the only process , which affects htt homeostasis . recent screenings in c. elegans identified the evolutionarily conserved protein moag-4/serf1 - 2 as a modifier of protein aggregation during ageing . loss - of - function or silencing of moag-4 suppress the formation of aggregates in animals carrying mutant huntingtin , -synuclein or -amyloid . whether moag-4/serf1 - 2 and the interplay with other prosurvival pathways are relevant in hd remains to be explored , nevertheless the modulation of proteostasis remains a promising approach for the treatment of neurodegenerative disorders . energetic disturbances in hd is well described by post mortem , in - vitro and in - vivo evidences . the high metabolic rate of excitable cells such as neurons makes them strongly reliant upon mitochondrial functions . mitochondria are highly motile organelles that control dendritic spine formation and synaptic activity by buffering intracellular ca rise underneath the plasma membrane . mutant htt has been shown to affect mitochondrial morphology and the bioenergetic status by altering the balance between mitochondrial fusion and fission under the control of the dynamin - related protein 1 or the interaction with other mitochondria - associated proteins . alterations in mitochondria dynamics are reflected in deficits of the electron transport chain and of cellular respiration . the use of energy - related supplements , such as creatine , has been attempted in some clinical trials in order to correct mitochondrial defects in hd patients . as a result of extensive mitochondrial depolarization , neurons exposed to prolonged ca mutant htt affects glutamatergic signals as a result of altered neurotransmitter release and activity of the glutamate - ionotropic receptors at the plasma membrane ( figure 1 ) . in addition , aberrant htt with the expanded polyq tract inhibits the expression of the transcriptional co - activator pgc-1 , therefore compromising mitochondrial biogenesis and respiration . thus , the combination of the two effects alteration of ca influx and diminished capability of ca clearance by mitochondria seriously increases the susceptibility of striatal cells expressing mutant htt to excitotoxic insults . for this reason , agents that can affect glutamatergic signaling ( i.e. nmda receptor antagonists - like memantine ) have been undergoing clinical trials . similarly , other downstream targets that affect nmda signaling and the excitotoxic neuronal demise might have some potential applications for the treatment of hd . mitochondrial dysfunction resulting from ca overload , prolonged membrane depolarization or impairment of the electron transfer chain is the main source of intracellular reactive oxidative species . under certain circumstances , enhanced production of oxidative stress triggers neuroinflammatory responses by activation of the inflammasome in a cell - autonomous or non - autonomous manner . neuroinflammatory processes are key determinants of neurodegenerative disorders characterized by aggregate - prone proteins , as in the case of pd and ad . although the activation of inflammatory responses can be triggered by a variety of toxic species , the evidence indicates that most of the common neurodegenerative disorders have converging mechanisms that amplify the detrimental cascades . remarkably , in the majority of the brain pathologies , neuroinflammation is a presymptomatic event and similar patterns have been shown in unrelated pathologies . in case of hd , the expression of mutant htt in glial cells affects the buffering capacity by altering the expression of the glutamate transporters , thus precluding the uptake of glutamate and enhancing neuronal excitotoxicity . it has been shown that mutant htt can lower the expression and release of glial chemokine , which can be neuroprotective under different circumstances . whether targeting excessive activation of immune responses can be beneficial to hd remains to be determined , although it is tempting to consider it as a feasible possibility . the identification of the htt gene has contributed enormously to our understanding of the multiple pathogenic mechanisms involved in the onset of hd and in the selectively enhanced vulnerability of a subset of neurons to the mutant htt . as discussed in this review , hd is a monogenic disease that results in a gain - of - function of the mutant form and in the loss - of - functions of the wild - type protein , which together severely compromise cellular homeostasis in a complex manner . to date , there is no cure for hd and most of the treatments available only help to alleviate some of the movement and psychiatric symptoms associated with the pathology . as mutant htt is not considered to be an ideal pharmacological target due to its myriad biological functions , other biochemical pathways , such as those that prevent the abnormal accumulation of unfolded proteins , represent an encouraging alternative for the treatment of this neurodegenerative disorder . the identification and characterization of additional detrimental processes underlying cellular deficits in hd patients might provide new efficient and beneficial targets for neuroprotective intervention .

huntington 's disease ( hd ) is a complex and severe disorder characterized by the gradual and the progressive loss of neurons , predominantly in the striatum , which leads to the typical motor and cognitive impairments associated with this pathology . hd is caused by a highly polymorphic cag trinucleotide repeat expansion in the exon-1 of the gene encoding for huntingtin protein . since the first discovery of the huntingtin gene , investigations with a consistent number of in - vitro and in - vivo models have provided insights into the toxic events related to the expression of the mutant protein . in this review , we will summarize the progress made in characterizing the signaling pathways that contribute to neuronal degeneration in hd . we will highlight the age - dependent loss of proteostasis that is primarily responsible for the formation of aggregates observed in hd patients . the most promising molecular targets for the development of pharmacological interventions will also be discussed .

Proteolytic Cleavage of HTT Autophagy Ageing Modifiers as Regulators of Proteostasis Mitochondrial Deficiency, Excitotoxicity and Inflammation Concluding Remarks

ewing sarcoma ( es ) is the second most common malignant bone tumor in adolescents and young adults , leading to more than 200 cases of cancer in the united states per year ( seer ) . evidence of metastatic disease at diagnosis is the most clinically relevant prognostic factor , affecting 25% of patients ( bernstein et al . , 2006 ) . despite recent advances in biological understanding , intensification of chemotherapeutic treatments , and progress in local control with surgery and/or radiation therapy , patients with metastatic or recurrent es continue to have a dismal prognosis with less than 20% overall survival . nearly every case of es harbors a translocation of the ewsr1 gene , found on chromosome 22 , with a member of the ets family on chromosomes 11 , 21 , or others . other fusion partners have also been described and account for the remaining 15% ( turc - carel et al . oncogene influences the gene expression profile of tumor cells , directly or indirectly , driving aberrant expression of over 1000 genes ( smith et al . , 2006 ) . fli1 expression is associated with activation of some genes and repression of others , illustrating the complexity of cellular response to this oncogenic transcription factor ( may et al . , 1993 ) . the es translocation is thought to be the primary mechanism for tumorigenesis , but the heterogeneous biology found in the tumors of patients with es suggests that additional molecular mechanisms are also involved ( toomey et al . , 2010 ) . ( 2005 ) using murine primary bone derived cells ( mpbdc ) , have shown that serial passage of retrovirally transduced ews fli1 mpbdcs produced tumors efficiently only in later - passage cells ( > passage 15 ) . fli1 fusion protein that underwent p53 mediated growth arrest showing that for tumor formation to proceed , there is likely a multistep process including the acquisition of other genetic changes ( lessnick et al . , 2002 ) . fli1 translocation is an initiating event in sarcomagenesis , but that other biological processes are required for full tumorigenesis to occur ( lessnick et al . , 2002 ; castillero - trejo et al . , 2005 ) ewing sarcoma cells spread hematogenously to distant sites . despite negative imaging studies and bone marrow biopsies , why then are clinically detectable metastases such an important prognostic factor ? perhaps tumor cells have differing potentials to grow and develop at distant sites determined by therapy selective pressures , micro - environmental signals , and changes that are intrinsic to the tumor cell s genes . these metastatic clones may undergo genetic changes that allow them to react differently to chemotherapeutic agents as well as signals in the microenvironment ( of lung or bone ) leading to a more aggressive , resistant phenotype . many questions remain regarding the presence of es clones that may lead to occult metastatic deposits and subsequently to recurrence of disease after completion of therapy . are all es metastatic clones similar or are they a heterogeneous population of rogues of varying clinical threat ? this paper serves to review the current clinical knowledge about metastatic es , to highlight current areas of research regarding the molecular pathways that influence es metastasis , and to underscore questions that persist at this time . to survey the recently published literature in a comprehensive fashion , searches for es metastasis and metastatic es original supporting data ( some dated prior to 2000 ) were also used for the current review , based on the bibliography of the papers found . currently , metastatic disease is clinically defined by the presence of a es specific translocation in the tissue biopsy of at least one tumor site ( primary site ) plus the presence of characteristic lesions ( by imaging ) in bones , lungs , or malignant cells identified in a staging bone marrow aspirate or biopsy . if diagnostic imaging is inconclusive for bone or lung sites , tissue biopsy may be undertaken to prove metastasis . bone marrow is typically considered negative for metastatic disease if the cells present are morphologically hematopoietic in origin ; peripheral blood is never clinically tested for es cells . while these parameters clinically define metastatic disease and identify a high - risk sub - population of es patients , they likely do not completely quantify a patient s burden of disease . nor do such tests give us information about the genetic changes in a particular patient s es tumor cells . approximately 25% of patients will present with metastatic disease , primarily with metastasis in the lungs , bony sites , and/or bone marrow . as with most cancers , patients with metastatic es have a 5-year relapse free survival of 30% ( versus localized disease = 61.3% , p < 0.001 ; cotterill et al . , 2000 ) . patients with metastatic disease have a statistically significant proportion of larger primary tumors ( > 8 cm ) than patients without metastatic disease ( 76.8 versus 54.3% , p < 0.00001 ) suggesting that primary tumor size may correlate with metastasis ( rodriguez - galindo et al . , 2008 ; lee et al . , , some patients who present with small primary tumors do relapse with distant metastasis , indicating the propensity of es for dissemination . in terms of outcomes , patients with primary pulmonary metastasis fare better than their counterparts with bone or bone marrow disease ( 5 year efs 2952% ) signifying that not all metastasis are equal ( paulussen et al . , 1998 ) . the approach to treating those with metastatic disease involves systemic chemotherapy and local control of the primary site of disease . with regard to systemic therapy , there have been a variety of trials attempting to optimize a chemotherapeutic regimen specifically for patients with metastatic disease . these studies have investigated more intensive , time - compressed , and high - dose chemotherapy regimens , yet there has been minimal improvement in survival of patients with metastasis at presentation ( grier et al . , 2003 ; granowetter et al . , 2009 ; huang and lucas , 2011 ) first - line agents are the same as for clinically localized disease ( vincristine , doxorubicin , cyclophosphamide , ifosfamide , and etoposide ) , but there has been interest over the last decade in the use of camptothecin agents ( such as topotecan and irinotecan ) for metastatic disease ( wagner , 2011 ) . the current front line children s oncology group ( cog ) trial randomizes patients with localized es to receive topotecan in combination with cyclophosphamide to attempt to improve survival rates , as this combination has shown promise in patients with relapsed or refractory disease . despite systemic chemotherapy and good local control modalities , even patients with clinically localized es have a high - risk of relapse at distant sites , giving rise to the hypothesis that micrometastasis is almost universally present but undetected at initial diagnosis . reports have shown that 2530% of patients with clinically localized es have detectable tumor cells in the peripheral blood or bone marrow by polymerase chain reaction ( pcr ; west et al . , 1997 ) . the question then arises as to whether these metastatic cells are clinically nefarious clones or rogues presenting a limited clinical threat . no data has been reported regarding detectable tumor cells at diagnosis for patients with metastatic disease , but one can hypothesize that it would be at least equivalent to if not higher than levels seen in localized es . further studies using peripheral blood pcr and/or flow cytometry in the metastatic population would be of interest as the nature of the clones in patients with clinically metastatic disease may differ from those that are detected peripherally in cases of clinically isolated disease . perhaps comparative assessment of both primary and metastatic sites at diagnosis may also add to this body of knowledge . other , smaller studies have suggested that detection of such ews fusion oncogene transcripts in the blood or marrow after completion of therapy may portend relapse ( avigad et al . , ewing sarcoma relapse usually presents within 5 years following intensive multi - agent chemotherapy and aggressive local control measures ( stahl et al . , 2011 ) . the predominant type of relapse in patients with initial metastatic disease is systemic ( defined as distant recurrence only ) with 73% of patients presenting almost evenly with pulmonary , bone , or multisystem recurrent sites ( stahl et al . , 2011 ) . the median survival time after a first recurrence is 9 months , and the 5-year overall survival is 12% for recurrent es overall ( leavey et al . , 2008 ) . in recent data from the cog , the median time to recurrence in patients with metastatic disease at diagnosis is slightly earlier ( 1 year ; leavey et al . , 2008 ) . late recurrence , defined as greater than 2 years after initial diagnosis , is associated with a better prognosis ( currently greater than 25% overall survival ) whereas early recurrence portends a grave prognosis ( os = 710% ; huang and lucas , 2011 ) . 2011 ) have corroborated that patients with initially clinically localized disease relapsed significantly later than those with metastatic disease at diagnosis ( 434 versus 563 days , p < 0.001 ) . in addition , the patients that relapsed earlier had a significantly worse outcome ( os 02 years = 0.07 , 23 years = 0.27 , > 3 years = 0.30 , p < 0.001 ; stahl et al . , 2011 ) . overall , the data suggests that metastatic patients are more likely to relapse early with systemic disease and have a worse prognosis . this leads to the hypothesis that either tumor - related or patient - related factors may lead to these es clone s ability to evade destruction or removal during treatment . disease that is cytoreduced into an initial state of subclinical tumor burden , but not fully eradicated , necessarily harbors resistant clones of es . chemotherapy provides both selective pressure favoring such clones as well as additional dna damage able to induce genetic alterations that may generate new resistant clones . early clinical recurrence implies that either the clones were resistant enough to grow during therapy or aggressive enough to rebound rapidly after therapy - suppression is lifted . the continued poor prognosis for patients with metastatic es questions the possible need for distinctive treatment strategies designed specifically to prevent metastasis from the primary tumor site and to target and eradicate known or latent metastatic disease ( riggi and stamenkovic , 2007 ) . research has focused both on understanding what triggers dissemination as well as what factors support tumor cell survival and proliferation in ectopic sites . es cells have a propensity to metastasize to the lung , bone , and bone marrow ( arndt and crist , 1999 ) suggesting an important role of tumor cell microenvironment that may direct this tissue - specific metastasis ( kerbel , 1995 ; mundy , 2002 ) . in recent years , several labs have focused their efforts on understanding the contribution of metastatic sites in attracting es cells and supporting their growth . to prevent es metastasis , an understanding of these unique tumor microenvironment and host tumor interactions may offer new therapeutic targets . the bone is a rich repository of growth factors including stem cell factor ( scf , the ligand for c - kit receptor ) , basic fibroblast growth factor ( b - fgf ) , platelet derived growth factor ( pdgf ) , and transforming growth factor- ( tgf- ) , therefore providing chemo - attractants for metastatic disease and a favorable environment for metastatic growth of many types of tumors ( mundy , 2002 ; bussard et al . , 2008 ) . for example , metastatic sites highly express scf in the bone marrow stromal cells ( bmscs ) , osteoblasts , and endothelial cells . ( 2000 ) noted the presence of substantial surface c - kit receptors in six es cell lines ; transmembrane scf was also found on five of the six cell lines . exposure of these es cell lines to exogenous scf caused down - regulation of its receptor , decreased chemoattraction of es cell lines to scf , and significantly reduced metastasis to lungs and other extra - pulmonary organs in a metastatic xenograft model . these data suggest that scf expressed in potential metastatic sites may serve a chemoattractant role and that the c - kit receptor / scf interaction is a potential target for decreasing es metastasis ( landuzzi et al . , 2000 ) . fibroblast growth factor produced by bmscs may promote a metastatic phenotype in es tumors by increasing cell motility . conditioned medium from bmscs was shown to increase motility in human es cell lines , specifically through activation of fgf receptor-1 ( fgfr-1 ) by b - fgf and its downstream signaling cascade , phosphatidyl inositol 3 kinase ( pi3k)rac-1 ( kamura et al . , 2010 ) . receptors for fgf and pdgf are well - characterized and small molecule inhibitors against these catalytic receptors may provide a therapeutic option in es . lyn , a member of the src family of kinases , is a known regulator of tumor cell proliferation , adhesion , motility , and invasion . targeting lyn using a small interfering rna ( sirna ) or the small molecule inhibitor ap23994 resulted in suppression of tumor growth , decreased bony lysis due to tumor cells , and significantly fewer lung metastases in vivo ( in athymic nude mice injected with tc71 human es tumor cell lines ; guan et al . , 2008 ) . here such lysis creates space for tumor growth , and provides easier access for tumor cells to the bone stroma where they may enter the circulation and metastasize to the lung . this data suggests that targeting lyn upregulation may decrease the propensity of es cells to metastasize . finally , ezrin , a membrane cytoskeleton linking protein , has an effect on the development of metastasis in osteosarcoma and rhabdomyosarcoma ( khanna et al . , 2004 ; yu et al . , 2004 ) krishnan et al . ( 2006 ) have shown that this is true for es as well . in normal cells , phosphorylation at threonine 567 ( t567 ) of ezrin is essential for ezrin - mediated transduction of growth signals ; mutation at this site , leading to absence of phosphorylation at t567 ( so called ezrint567a mutants ) , causes down - regulation of growth via the akt / mtor ( mammalian target of rapamycin ) pathway . krishnan et al . ( 2006 ) have shown that es cell lines ( both previously established cell lines and primary cell lines from patient tumor samples ) have high levels of ezrin expression , and ezrint567a mutants maintain a significantly slower growth rate than those with wild type ezrin expression due to increased apoptosis . injection of ezrint567a mutant cells into mice produced fewer experimental metastases ( 2/30 mice developed metastasis ) than mice injected with wild type ezrin ( 8/10 mice ) showing that ezrin may also have a role in development and growth of metastasis in es . manipulation of the ezrin pathway may be explored in the future as a means to decrease the development of metastatic disease in es ( krishnan et al . , 2006 ) . as a tumor grows and metastasizes , its genome can continue to adapt allowing for creation of resistant clones that evade conventional therapies . newer technologies , such as copy number analysis , rendering more detailed analysis of the genome than is possible with traditional cytogenetics , have been used to also look at genomic imbalances beyond translocation status in these tumors . as cancer genomes become more unstable , the number of copy number aberrations ( cna ) increases ( jahromi et al . , 2011 ) . copy number analysis of primary tumors may be a way to identify tumors that are at higher risk of metastasis or relapse than others . several other tumor types have copy number changes that are being used to risk stratify therapy for patients ( e.g. , neuroblastoma ; attiyeh et al . , 2005 ) , but this is currently not possible for es due to its rarity and challenge of obtaining a large enough cohort to study . researchers continue to analyze genomic changes in es samples ( armengol et al . , 1997 ; tarkkanen et al . , 1999 ; brisset et al . , 2001 ; ozaki et al . , 2001 ; savola et al . , 2009 ) , but the results have been discordant , possibly due to the small samples sizes used and/or the variable biology of the disease coupled with a lack of detailed clinical phenotyping . in the late 1990s to early 2000s , several researchers described chromosomal gain in es tumor samples most commonly trisomy 1q [ due to derivative chromosome ( 1:16 ) ] , trisomy 8 , and trisomy 12 in 25 , 35 , and 25% of samples respectively ( armengol et al . , 1997 ; tarkkanen et al . , 1999 ) . the literature supports that 6387% of es tumor samples have cnas detected by cgh ( armengol et al . , 1997 ; tarkkanen et al . , 1999 ; brisset et al . , 2001 ; ozaki et al . , 2001 ; savola et al . , the most common of these cnas have been analyzed for possible prognostic capacity , but the results have been varied . many groups found no statistically significant changes in event - free survival or overall survival in es based on cnas ( armengol et al . , 1997 ; tarkkanen et al . , 1999 ; ozaki et al . , 2001 ) however , two different groups found that the number of aberrations did significantly predict patient survival . ozaki et al . ( 2001 ) showed in 48 patients that tumors with lower cnas ( less than five ) were significantly associated with improved survival ( p = 0.009 ) . ( 2009 ) reported that tumors with higher numbers of cna ( 3 ) faired significantly worse in terms of os ( p = 0.030 ) and efs ( p = 0.049 ) than those with fewer cnas . the findings to date are correlative in nature and require experimental testing to demonstrate whether cna s reflect tumor age , behavioral attributes , and both . currently , there is not a particular aberration or combination of changes being used to stratify patients for therapy . the most recent data using agilent s 44k oligoarray platform included 026 aberrations per tumor with a mean of 7.2 ( savola et al . , 2009 ) . older reports , using various cgh techniques , reported on average two aberrations per tumor ( range 1.143.6 ; armengol et al . , 1997 ; tarkkanen et al . , 1999 ; brisset et al . , 2001 ; ozaki et al . , much of this variation may be due to the samples and techniques available for cgh at the time the data were collected . mean copy number changes per tumor in other sarcomas such as osteosarcoma , malignant fibrous histiocytoma , and chondrosarcoma have been reported around 11 , 6 , and 6 respectively ( tarkkanen et al . in es , copy number changes were low in any given tumor sample lending credence to the primary translocation in es being a single major genetic hit of great import in development and maintenance of tumors . this supports studies on cultured human es cells in which knockdown of ews fli expression was shown to be sufficient to reverse transformation and tumorigenic properties ( may et al . , 1993 ) . as stated earlier , however , fli1 expression is likely not the only genetic or epigenetic hit that is required for development and maintenance of es ( lessnick et al . , 2002 ; castillero - trejo et al . , 2005 ) . hopefully , as the resolution of snp microarrays increases and next - generation sequencing is introduced , more clinically relevant and cooperating cnas may be discovered in es . numbers of cna in metastatic versus localized es have been studied and have yielded inconclusive results . ( 2001 ) found no difference between the type or average number of cnas of primary tumor samples in patients who presented with metastasis . however , savola et al . ( 2009 ) reported that metastatic tumors showed more cna ( mean 11.8 ) than primary tumors ( mean 5.8 ) . finally , samples from relapsed tumors had greater than three times as many copy number changes as did the samples of primary tumors ( 1.9 versus 4.4 per tumor sample ; armengol et al . , it can be hypothesized that cna appear with increased frequency as a tumor metastasizes or recurs , and that resistant clones with unstable genomes continue to gain genetic changes as such tumors progress . however , none of these studies have compared paired primary and metastatic lesion samples , so the clonal relationship of primary to metastatic tumors remains unknown in es . other tumor types , such as pancreatic carcinoma , have features in their metastatic deposits consistent with the parent clones , yet with the addition of newly acquired lesions reflecting that metastatic clones branched from the parent clone ( yachida et al . , 2010 ) . in patients with es , the use of cna on samples from both local and metastatic tumors may support such a mechanism and ultimately be an effective way to measure fitness of a clone for metastasis . ewing sarcoma is an aggressive cancer of bone that targets the adolescent and young adult population . in its metastatic form , survival remains poor despite an influx of knowledge regarding tumor biology and intensification of therapy . even if the disease is localized at diagnosis ( and particularly if it is not ) , there are an unfortunate number of patients who will relapse ; relapsed es is very difficult to cure . progressive disease is believed to arise via a combination of selection of chemotherapy - resistant clones , signaling from bone or lung microenvironments that may attract tumor cells to distant locations , and/or genetic changes within the es cells themselves . intrinsic genetic changes within the es cells , due to a combination of therapy - related selection and dna - damaging chemotherapeutic agents , may allow the attraction and migration of resistant es clones to locations where they may thrive . as these clones compete to survive by evading chemotherapy and responding to signal from metastatic sites , enhanced genomic instability may favor their adaptation . while understanding the biology of the primary tumor is of utmost importance , it is also critical to understand genetic and epigenetic changes that are associated with the metastatic state in order to effectively treat sarcoma patients with systemic disease . current advances in genetics and genomics provide new approaches to identify novel molecular markers that are associated with metastatic es and define their clinical implications . the authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest .

ewing sarcoma ( es ) is the second most common bone tumor affecting primarily adolescents and young adults . despite recent advances in biological understanding , intensification of chemotherapeutic treatments , and progress in local control with surgery and/or radiation therapy , patients with metastatic or recurrent es continue to have a dismal prognosis with less than 20% overall survival . all es is likely metastatic at diagnosis although our methods of detection and classification may not account for this . progressive disease may arise via a combination of : ( 1 ) selection of chemotherapy - resistant clones in primary tumor , ( 2 ) signaling from bone or lung microenvironments that may attract tumor cells to distant locations , and/or ( 3 ) genetic changes within the es cells themselves due to dna - damaging chemotherapeutic agents or other hits . these possibilities and the evidence base to support them are explored .

Introduction Metastatic Ewing Sarcoma: The Clinical Perspective The Tumor Microenvironment Metastatic Disease, Instability of the Clone Closing Remarks Conflict of Interest Statement

broncholith is an uncommon medical problem . when considering broncholiths from a therapeutic standpoint , the role of bronchoscopy has been somewhat controversial . we report here on two cases of successful removal of broncholith that were done without any clinically significant complications by using flexible bronchoscopy . a 65-year - old male patient was admitted to the hospital for the evaluation of atelectasis , and he had a history of recurrent hemoptysis and pneumonia for a few years . the broncholith was impacted at rb9 , and there was inflammation of the surrounding mucosa on bronchoscopy . we removed the broncholith using a tripod forcep and the inflammation subsided afterwards ( figure 1 ) . a 37-year - old female patient was referred from a general hospital due to a calcified lymph node from an unknown cause that was discovered on computerized tomography during the treatment for her pneumonia and parapneumonic effusion . we removed the broncholith using a balloon catheter and tripod forcep after antifungal treatment ( figure 2 ) . a 65-year - old male patient was admitted to the hospital for the evaluation of atelectasis , and he had a history of recurrent hemoptysis and pneumonia for a few years . the broncholith was impacted at rb9 , and there was inflammation of the surrounding mucosa on bronchoscopy . we removed the broncholith using a tripod forcep and the inflammation subsided afterwards ( figure 1 ) . a 37-year - old female patient was referred from a general hospital due to a calcified lymph node from an unknown cause that was discovered on computerized tomography during the treatment for her pneumonia and parapneumonic effusion . we removed the broncholith using a balloon catheter and tripod forcep after antifungal treatment ( figure 2 ) . broncholiths are calcified peribronchial lymph nodes that encroach upon the adjacent airways and they cause clinical and roentgenographic abnormalities1 ) . mycobacterial and fungal granulomatous lymphadenitis are the most frequently cited infections that are responsible for tissue calcification , although silicosis is a less commonly associated noninfectious cause . the most common infectious complication resulting from broncholithiasis appears to be bacterial pneumonia that is generally due to airway obstruction by a broncholith and also to the associated airway inflammation and edema . lung abscesses along with bronchoesophageal and bronchomediastinal fistulas are potentially more serious complications arising from symptomatic broncholithiasis , and these complications are responsible for cases of prolonged or recurrent infection2 ) . in our case , both patients had recurrent and prolonged pneumonia . bronchoscopy is considered the most important diagnostic test for broncholithiasis . however , its role in the treatment of broncholithiasis is controverial . olson and his coworkers3 ) reported that 100% of their patients with loose ( free in the airway ) broncholiths underwent flexible and rigid bronchoscopic extraction attempts without severe complications . massive life - threatening hemoptysis secondary to fistula or rupture of aorta or pulmonary arteries is a possible complication , but generally , massive hemoptysis caused by broncholithiasis is a rare complication3 - 5 ) . as compared with the morbidity and mortality associated with surgical intervention , bronchoscopic management appears favorable for patients with loose or partly eroded broncholiths6 ) . loose , movable broncholiths are especially suitable for removal by bronchoscopic extraction in the clinical setting having capabilities for rigid and flexible bronchoscopy and immediate thoracic surgical support , and after the relation of the broncholith to adjacent vascular structures has been studied by computerized tomography3 ) .

most broncholiths are related to infection with fungus or tuberculosis and they involve the lymph nodes ; those cases that are caused by silicosis are rarely seen . broncholith might lead complication such as bronchial rupture into the mediastinum , which can result in hemoptysis , cough , repeated pneumonia and so on . flexible bronchoscopy plays an important part in the diagnosis of broncholithiasis , but its therapeutic application in the clinical setting is controversial . we report here on two cases of broncholith removal without complication with the use of a balloon catheter and tripod forceps using flexible bronchoscopy .

INTRODUCTION CASE REPORT Case 1 Case 2 DISCUSSION

the 1978 alma ata declaration codified the right to primary health care ( phc ) for all . nine years later , african ministers of health convened in bamako , mali , to emphasize the need to strengthen phc on the continent , with a particular focus on maternal and child health . decades later , however , phc remains a lofty goal for many african countries , despite the impact on profile and funding for phc of alma ata , the bamako initiative and their successor initiatives . the alma ata declaration acknowledged the impact of good governance , economic and social development , inequality , health system functioning , inter - sector cohesiveness , and education on health outcomes . recent work by rohde et al . illustrated how these factors continue to influence progress in achieving phc for all . countries that have shown weak gains in life expectancy over the last couple of decades include those affected by conflict , those having a high hiv / aids prevalence , those plagued by poor governance and social inequality , and those experiencing specific adult mortality challenges . the country continues to have low immunization rates and a low life expectancy , despite significant financial and political support for phc since the 1980s . health inequities , pervasive corruption , and the autonomy of nigeria s 36 states have prevented the country from establishing a national framework to support a phc system that works for all . the autonomy of the states and local government authorities ( lgas ) has complicated the building of a cohesive phc system in nigeria . in the nigerian constitution , health is a concomitant responsibility of the three tiers of government : the federal level , 37 states including the federal capital territory , and 774 lgas . according to the national health policy , the federal level is responsible for tertiary care , the state level for secondary care and the lga level for phc . however , details in the policy regarding the roles and responsibilities for each level are unclear . matters have become arguably even less clear since the end of military rule in 1999 . reality on the ground frequently demonstrates how actors within the health system are unable to distinguish the roles and responsibilities between each level of government . there exists a myriad of different departments , directorates and units at each level with overlapping responsibilities . crucially , the way in which the three levels of government should interact has not been elaborated in policy . thus , it can be a challenge for innovations , lessons from experience and planned activities to permeate from one level to the next . for example , how do practitioners who are operating on the ground within states or lgas influence federal level policy makers and other states ? or , how do federal level policy makers ensure that planned activities are implemented across the three tiers of government ? these are the sorts of questions that are crucial if sustained efforts towards coordination of health provision - and concomitant population health gains - are to be attained in the nigerian context . they are particularly salient in the context of northern nigeria , where the coverage of health services ( and thus health outcomes ) lags well behind even the modest achievements of other parts of the country . a systematic survey across three northern nigerian states found that less than one - quarter of women who gave birth in the five years preceding the survey had ever received antenatal care ( anc ) from a trained health professional , and only one in eight of those women had delivered in a health facility . child health status indicators were also poor . only one in twenty children had received the third dose of dpt by the age of one year . a range of initiatives has been established to address the strengthening of health systems in these northern states . these include a range of focused initiatives , addressing specific diseases or program areas . bringing together as a combined programme two such initiatives - the partnership for reviving routine immunization in northern nigeria ( prrinn ) and the maternal , newborn and child health ( mnch ) programme - provided the opportunity to specifically address some of the wider systems issues that constrain health programming in nigeria . prrinn - mnch - with cofunding from the department for international development of the united kingdom ( dfid ) and the government of norway - has since 2007 provided a platform to specifically address the systems linkages required between federal , states and local structures to implement policy and service changes . programs for achieving the laudable goals set forth by alma ata and the bamako initiative have ranged from offering selective phc services to more comprehensive packages . the prrinn - mnch initiative was developed as a programme that sought to build upon the strategies outlined in the bamako initiative by explicitly addressing the broken linkages between phc services at all levels of government . by facilitating better partnerships , the prrinnmnch program supported the government s effort to integrate phc services and strengthen its implementation at the district level , support child immunizations through improved funding mechanisms , and ensure maternal health is addressed at the community level . this paper focuses upon three prrinnmnch supported initiatives that sought to improve linkages between , and the functioning of , the federal , state , and lga levels of health system responsible for phc : bringing phc under one roof ; enhancing access to global alliance for vaccines and immunization ( gavi ) funds ; and strengthening the midwives service scheme ( mss ) . these three examples provide an opportunity to explore how concepts and experience developed at subnational levels were utilized to influence national policy and practice , and the way in which work at subnational levels can contribute to nationally conceived and driven plans for phc . programs for achieving the laudable goals set forth by alma ata and the bamako initiative have ranged from offering selective phc services to more comprehensive packages . the prrinn - mnch initiative was developed as a programme that sought to build upon the strategies outlined in the bamako initiative by explicitly addressing the broken linkages between phc services at all levels of government . by facilitating better partnerships , the prrinnmnch program supported the government s effort to integrate phc services and strengthen its implementation at the district level , support child immunizations through improved funding mechanisms , and ensure maternal health is addressed at the community level . this paper focuses upon three prrinnmnch supported initiatives that sought to improve linkages between , and the functioning of , the federal , state , and lga levels of health system responsible for phc : bringing phc under one roof ; enhancing access to global alliance for vaccines and immunization ( gavi ) funds ; and strengthening the midwives service scheme ( mss ) . these three examples provide an opportunity to explore how concepts and experience developed at subnational levels were utilized to influence national policy and practice , and the way in which work at subnational levels can contribute to nationally conceived and driven plans for phc . this paper analyses the development of policy and programme implementation in these three areas by drawing upon documents from the federal ministry of health in nigeria , prrinn - mnch reports , and discussions - both informal and formal - at a range of national workshops and programme planning meetings . complexity theory provides a way of understanding health systems as complex adaptive systems , and has been increasingly advocated as a tool for health policy development and health systems reform . with complexity theory , health systems are seen as open systems in which different components are interdependent and influence each other in a non - linear fashion . non - linearity and the notion of emergent behavior ( i.e. behavior of a system that is not a property of any of the components of that system but a result of the interactions of the components ) mean that a change in one part of the system can have unpredictable ripple effects in other parts of the system . for example , the world health organization s report systems thinking for health system strengthening , heavily influenced by the ideas of complexity theory , acknowledges non - linearity and interdependence in a proposed framework for health system strengthening . this requires policymakers and health system reformers to adopt a whole system approach in order to ensure changes at one level will not impede changes at another . the complex adaptive systems approach reinforces concepts such as feedback loops ( both positive and negative , that influence the pace and direction of change ) ; path dependence ( processes that have similar starting points can have very dissimilar outcomes resulting from different contexts and histories and different choices ) ; scale - free networks ( incorporating focal points - including key powerful people - that can dominate a structure ) ; and phase transitions ( when critical - tipping - points are reached and initiate change ) . the ideas of complexity theory are closely linked to the drivers of change ( doc ) approach adopted by dfid . the doc approach conceptualizes three interacting components operating within any system and influencing change within that system : structural features / structures - the history of the state ; natural and human resources ; economic and social structures ; demographic changes ; regional issues ; globalization , trade and investment ; and urbanization ; institutions - the informal and formal rules that determine the realm of possible behavior by agents , such as political and public administration processes ; and agents - individuals and organizations pursuing particular interests . examples of agents include the political elite ; civil servants ; political parties ; local government ; the judiciary ; the military ; faith groups ; trade unions ; civil society groups ; the media ; the private sector ; academics ; and donors . the doc analysis and approach is essentially focused on power and the mechanisms through which that power is transacted within society and the health system . the doc approach formed the basis of political economy assessments at federal and state level health systems in nigeria , which led to a deeper understanding of the structural features , the power relations , the institutions ( particularly the informal rules ) and the agents operating in the sector . both complexity theory and the doc approach to political economy any new policy development needs to be understood in the context within which the potential change will be located . this context requires a deep and ongoing understanding of the structures , institutions and agents operating within the whole system . however , complexity theory requires a further understanding or analysis of the changes that a new policy will bring ( especially an appreciation of non - linearity and likely emergent behavior ; and an understanding of likely feedback loops , path dependent bifurcation points , focal points and transition points ) . only then , and in an ongoing fashion as the context and the whole system is dynamic , can policy be developed and implemented . the bamako initiative of 1987 supported strengthening health systems at the district and community - levels in parallel with efforts to decentralize political systems throughout africa . however , roles and responsibilities over phc programs , facilities , human resources , and financing remained unclear - a mishmash of centralization and decentralization . although the federal level is principally responsible for tertiary health care , the national primary health care development agency ( nphcda ) and national programme on immunization were developed at the federal level to maintain some control over phc . for example , the nphcda is intended to ( and does ) carry out supplemental immunization campaigns against vaccine preventable diseases including polio . state ministries of health are also involved in the building and managing of phc centers although , according to the national health policy , ostensibly responsible for managing secondary health care hospitals . the states provide health care services ( including phc services ) through the state ministry of health ( smoh ) , the state hospital management board ( shmb ) , and the state phc development agency ( sphcda ) . several bodies are involved in human resource management at the lga level for phc services : the ministry of local government ( molg ) , the state phc agency , the local government service commission , the public service commission and the lga . the local government service commission is a state level organization that is responsible for all health professionals ( level 7 and above ) while the lgas managed admin , security , and lower level personnel . budget development and release is similarly fragmented . while finance was nominally devolved in block grants to both states and lgas , state governments established joint accounts in which state and lga financial resources were placed . adding to the confusion over financial control , external donors usually direct programmatic funding into federal - level accounts , although ultimately implementation should occur at the local level . for example , large sums of money provided by the millennium development goal ( mdg ) office are given to the federal ministry of health to implement the community - based national health insurance scheme ( nhis ) scheme . the diversification of responsible units at the federal and state levels exacerbates the confusion of responsibilities between tiers . although phc is the responsibility of local governments , the multitude of different agents actually involved in phc services makes coordinated management across the ministry of health technically difficult . thus , several states - starting with enugu and jigawa , and then yobe and zamfara - have been exploring strategies for bringing phc under one roof . this first occurred through the partnership to transform health systems ( paths ) programme from 2002 to 2008 , and then through the prrinn - mnch programme , which began in 2006 . the possibility of the funding that would flow from the federal health act drove policy and legislative changes regarding phc in several states in nigeria . although implementation varies across states , relevant policy and legislative changes generally address three key issues . firstly , health services - particularly phc services - are being integrated , where previously all three tiers of government were involved in implementation . secondly , health services are being decentralized - both through devolution and de - concentration . and thirdly , but not uniformly , through the de - concentration to sub - state bodies ( the names are different in the different states ) , the balance of power in the management of key resources ( especially financial and human resources ) is shifting from the politicians to administrators and managers . it is important to highlight the process adopted through these adjustments and how the outcome of integrated health services ( at least of phc ) was achieved . since both federal government and states can pass legislation , both the paths and the prrinn - mnch programmes worked closely with the states to develop appropriate legislation and accompanying regulations for phc ; to strengthen systems ( especially financial , human resource and information ) ; and to reposition the state level bodies for their new roles and functions . this process was not without challenges and extended over substantial periods of time . at the same time , the states ( with support from the programmes ) lobbied at federal level to gain acceptance and to provide access to materials and support for states willing to embark on this process . draft policy memos and an implementation guide were finalized during the second workshop , were approved by the nphcda board in 2010 and submitted to the highest health policy body in nigeria ( the national council for health ) . as summarized in the official record of the council : council noted the thrust of the national health bill in strengthening primary health care ( phc ) through the creation of phc boards / agencies and the phc development fund . council noted efforts in bringing phc under one roof in line with the provisions of the national health bill . council also noted the importance of enacting relevant state legislation and regulations that will facilitate the implementation of national health bill . council therefore approved the implementation guide on bringing phc under one roof ( phcuor ) as a working document to be used by the three tiers of government and approved that all states establish primary health care boards . the national council for health not only adopted the policy document and implementation guide on bringing phc under one roof but encouraged the 36 states to proceed in implementing this concept ( table 1 ) . at the time of the 2012 workshop , 22 of the 36 states in nigeria were in various stages of implementing bringing phc under one roof . gavi has supported nigeria s immunization system since 2001 to address extremely poor immunization coverage , particularly in the northern states ( http://www.gavialliance.org/country/nigeria/ ) . states were able to access the first tranche of the gavi funds , which were managed at the federal level , following initial engagement with gavi , but several states were unable to retire the monies appropriately . thus in 2007 , prrinn - mnch began at the state level supporting state ministries of health to effectively retire and access ongoing funding tranches from gavi . this work shifted to the federal level where prrinn - mnch assisted the gavi office in nphcda to review the processes and tools for accessing and retiring the funds and participated in developing a set of master trainers who would train others across all states in nigeria . in 2009 , prrinn - mnch supported nphcda to develop financial guidelines for gavi fund management and provided appropriate training on the use of these guidelines for relevant staff at agency headquarters and in its programme states . the nphcda also requested that prrinn - mnch train focal nphcda staff on the use of the financial guidelines and tools in the non - programme states . the subsequent workshop enabled the participants to understand the use of the financial guidelines and equipped them with the capacity to train other relevant staff at the lower levels . the twenty - two participants comparised six senior staff from nphcda headquarters , two representatives of the nphcda offices from each of the six geo - political zones of the federation , and gavi fund accountants from the four prrinn - mnch focal states . this example illustrates how state level experience of an international agency s funds was used to drive changes in how the funds were administered and accessed at federal level . initial work started within the states to ensure that the proposed system would work , and had significant impact on coverage ( figure 1 ) . later this was taken up to federal level where capacity was built to maintain and nationally roll out the new system . nigeria has a high maternal mortality ratio , low attendance for antenatal services , and few births are attended by a skilled birth attendant . thus , to improve access to care for pregnant women , the mss was a federally conceived and driven scheme to place retired and unemployed midwives in health facilities ; later this was extended to community health extension workers ( chews ) to ensure remote communities have access to perinatal services . the nphcda initiated the mss using funds from mdg fund . in each state , four midwives were deployed to each of the selected phc facilities to ensure provision of maternal and child health care services on a 24/7 basis . in each state , a selection of four phc facilities is clustered around the referral general hospital , with the creation of 156 clusters nationwide . six of these clusters are in three prrinn - mnch target states ( katsina , yobe and zamfara ) . this was followed by a second wave ( both midwives and chews ) in late 2010 . specific areas of collaboration between prrinn - mnch and nphcda under the banner of mss have included : i ) participation in the recruitment of midwives for the north - west zone in nigeria ; ii ) sharing of relevant tools for health facility baseline assessment , participatory appraisal and continuous transformation ( including impact , a systems strengthening and management capacity building initiative developed by health partners international : http://www.healthpartners-int.co.uk/ ; http://www.prrinn-mnch.org/index.html ) and assessment of training institutions ; iii ) sharing experience on planning and conducting baseline assessments , development of a monitoring and evaluation framework , and the comprehensive emergency obstetric care ( ceoc ) cluster model used ; iv ) participation in the planning of refresher training of midwives countrywide by nphcda - mss ; v ) developing national integrated supportive supervision ( iss ) tools ( the iss tools have been institutionalized and the iss teams oriented nationwide ) ; vi ) providing in - service training to mss midwives in the three states based on training needs earlier identified during an induction workshop . while there are multiple interventions in the clusters and the states , the increased presence of midwives ( and chews ) is considered a major contribution to increased utilization of mnh services in all the prrinn - mnch supported facilities where mss midwives are deployed ( as compared to baseline data collected between august and october 2008 ; figure 2 ) . overall , more significant increases were noted in anc attendance when compared with intrapartum care ( delivery ) . for example , in furfuri phc , zamfara , the number of anc visits increased from 0 to 455 , and deliveries from 0 to 28 between april and june , 2010 . mss midwives initiated community mobilization activities to increase utilization of mnh services , especially skilled care at delivery . mss has also shown improvement in documentation , including the keeping of registers and summary graphs and statistics in all facilities ( and bar charts in some facilities ) . additionally , all prrinn - mnch supported health facilities where there are mss midwives ( at least 3 - 4 mss midwives per facility ) now provide 24-h intra - partum care . for instance , a night shift was introduced by mss midwives on arrival at baimari maternity phc , yobe . problems experienced by the midwives continue to be largely administrative and systems related : e.g. payment issues , accommodation , poor working environment etc . although there has been progress in most of these areas , they remain critical issues to monitor in support of retention of these important health workers . this third example illustrates how state level practitioners can assist in supporting , and adding value to , nationally conceived and driven plans . in this case the nphcda had no formal jurisdiction but clearly needed support to implement a laudable scheme with promising results . the bamako initiative of 1987 supported strengthening health systems at the district and community - levels in parallel with efforts to decentralize political systems throughout africa . however , roles and responsibilities over phc programs , facilities , human resources , and financing remained unclear - a mishmash of centralization and decentralization . although the federal level is principally responsible for tertiary health care , the national primary health care development agency ( nphcda ) and national programme on immunization were developed at the federal level to maintain some control over phc . for example , the nphcda is intended to ( and does ) carry out supplemental immunization campaigns against vaccine preventable diseases including polio . state ministries of health are also involved in the building and managing of phc centers although , according to the national health policy , ostensibly responsible for managing secondary health care hospitals . the states provide health care services ( including phc services ) through the state ministry of health ( smoh ) , the state hospital management board ( shmb ) , and the state phc development agency ( sphcda ) . several bodies are involved in human resource management at the lga level for phc services : the ministry of local government ( molg ) , the state phc agency , the local government service commission , the public service commission and the lga . the local government service commission is a state level organization that is responsible for all health professionals ( level 7 and above ) while the lgas managed admin , security , and lower level personnel . budget development and release is similarly fragmented . while finance was nominally devolved in block grants to both states and lgas , state governments established joint accounts in which state and lga financial resources were placed . adding to the confusion over financial control , external donors usually direct programmatic funding into federal - level accounts , although ultimately implementation should occur at the local level . for example , large sums of money provided by the millennium development goal ( mdg ) office are given to the federal ministry of health to implement the community - based national health insurance scheme ( nhis ) scheme . the diversification of responsible units at the federal and state levels exacerbates the confusion of responsibilities between tiers . although phc is the responsibility of local governments , the multitude of different agents actually involved in phc services makes coordinated management across the ministry of health technically difficult . thus , several states - starting with enugu and jigawa , and then yobe and zamfara - have been exploring strategies for bringing phc under one roof . this first occurred through the partnership to transform health systems ( paths ) programme from 2002 to 2008 , and then through the prrinn - mnch programme , which began in 2006 . the possibility of the funding that would flow from the federal health act drove policy and legislative changes regarding phc in several states in nigeria . although implementation varies across states , relevant policy and legislative changes generally address three key issues . firstly , health services - particularly phc services - are being integrated , where previously all three tiers of government were involved in implementation . secondly , health services are being decentralized - both through devolution and de - concentration . and thirdly , but not uniformly , through the de - concentration to sub - state bodies ( the names are different in the different states ) , the balance of power in the management of key resources ( especially financial and human resources ) is shifting from the politicians to administrators and managers . it is important to highlight the process adopted through these adjustments and how the outcome of integrated health services ( at least of phc ) was achieved . since both federal government and states can pass legislation , both the paths and the prrinn - mnch programmes worked closely with the states to develop appropriate legislation and accompanying regulations for phc ; to strengthen systems ( especially financial , human resource and information ) ; and to reposition the state level bodies for their new roles and functions . this process was not without challenges and extended over substantial periods of time . at the same time , the states ( with support from the programmes ) lobbied at federal level to gain acceptance and to provide access to materials and support for states willing to embark on this process . draft policy memos and an implementation guide were finalized during the second workshop , were approved by the nphcda board in 2010 and submitted to the highest health policy body in nigeria ( the national council for health ) . as summarized in the official record of the council : council noted the thrust of the national health bill in strengthening primary health care ( phc ) through the creation of phc boards / agencies and the phc development fund . council noted efforts in bringing phc under one roof in line with the provisions of the national health bill . council also noted the importance of enacting relevant state legislation and regulations that will facilitate the implementation of national health bill . council therefore approved the implementation guide on bringing phc under one roof ( phcuor ) as a working document to be used by the three tiers of government and approved that all states establish primary health care boards . the national council for health not only adopted the policy document and implementation guide on bringing phc under one roof but encouraged the 36 states to proceed in implementing this concept ( table 1 ) . at the time of the 2012 workshop , 22 of the 36 states in nigeria were in various stages of implementing bringing phc under one roof . gavi has supported nigeria s immunization system since 2001 to address extremely poor immunization coverage , particularly in the northern states ( http://www.gavialliance.org/country/nigeria/ ) . states were able to access the first tranche of the gavi funds , which were managed at the federal level , following initial engagement with gavi , but several states were unable to retire the monies appropriately . thus in 2007 , prrinn - mnch began at the state level supporting state ministries of health to effectively retire and access ongoing funding tranches from gavi . this work shifted to the federal level where prrinn - mnch assisted the gavi office in nphcda to review the processes and tools for accessing and retiring the funds and participated in developing a set of prrinn - mnch supported nphcda to develop financial guidelines for gavi fund management and provided appropriate training on the use of these guidelines for relevant staff at agency headquarters and in its programme states . the nphcda also requested that prrinn - mnch train focal nphcda staff on the use of the financial guidelines and tools in the non - programme states . the subsequent workshop enabled the participants to understand the use of the financial guidelines and equipped them with the capacity to train other relevant staff at the lower levels . the twenty - two participants comparised six senior staff from nphcda headquarters , two representatives of the nphcda offices from each of the six geo - political zones of the federation , and gavi fund accountants from the four prrinn - mnch focal states . this example illustrates how state level experience of an international agency s funds was used to drive changes in how the funds were administered and accessed at federal level . initial work started within the states to ensure that the proposed system would work , and had significant impact on coverage ( figure 1 ) . later this was taken up to federal level where capacity was built to maintain and nationally roll out the new system . nigeria has a high maternal mortality ratio , low attendance for antenatal services , and few births are attended by a skilled birth attendant . thus , to improve access to care for pregnant women , the mss was a federally conceived and driven scheme to place retired and unemployed midwives in health facilities ; later this was extended to community health extension workers ( chews ) to ensure remote communities have access to perinatal services . the nphcda initiated the mss using funds from mdg fund . in each state , four midwives were deployed to each of the selected phc facilities to ensure provision of maternal and child health care services on a 24/7 basis . in each state , a selection of four phc facilities is clustered around the referral general hospital , with the creation of 156 clusters nationwide . six of these clusters are in three prrinn - mnch target states ( katsina , yobe and zamfara ) . this was followed by a second wave ( both midwives and chews ) in late 2010 . specific areas of collaboration between prrinn - mnch and nphcda under the banner of mss have included : i ) participation in the recruitment of midwives for the north - west zone in nigeria ; ii ) sharing of relevant tools for health facility baseline assessment , participatory appraisal and continuous transformation ( including impact , a systems strengthening and management capacity building initiative developed by health partners international : http://www.healthpartners-int.co.uk/ ; http://www.prrinn-mnch.org/index.html ) and assessment of training institutions ; iii ) sharing experience on planning and conducting baseline assessments , development of a monitoring and evaluation framework , and the comprehensive emergency obstetric care ( ceoc ) cluster model used ; iv ) participation in the planning of refresher training of midwives countrywide by nphcda - mss ; v ) developing national integrated supportive supervision ( iss ) tools ( the iss tools have been institutionalized and the iss teams oriented nationwide ) ; vi ) providing in - service training to mss midwives in the three states based on training needs earlier identified during an induction workshop . while there are multiple interventions in the clusters and the states , the increased presence of midwives ( and chews ) is considered a major contribution to increased utilization of mnh services in all the prrinn - mnch supported facilities where mss midwives are deployed ( as compared to baseline data collected between august and october 2008 ; figure 2 ) . overall , more significant increases were noted in anc attendance when compared with intrapartum care ( delivery ) . for example , in furfuri phc , zamfara , the number of anc visits increased from 0 to 455 , and deliveries from 0 to 28 between april and june , 2010 . mss midwives initiated community mobilization activities to increase utilization of mnh services , especially skilled care at delivery . mss has also shown improvement in documentation , including the keeping of registers and summary graphs and statistics in all facilities ( and bar charts in some facilities ) . additionally , all prrinn - mnch supported health facilities where there are mss midwives ( at least 3 - 4 mss midwives per facility ) now provide 24-h intra - partum care . for instance , a night shift was introduced by mss midwives on arrival at baimari maternity phc , yobe . problems experienced by the midwives continue to be largely administrative and systems related : e.g. payment issues , accommodation , poor working environment etc . although there has been progress in most of these areas , they remain critical issues to monitor in support of retention of these important health workers . this third example illustrates how state level practitioners can assist in supporting , and adding value to , nationally conceived and driven plans . in this case the nphcda had no formal jurisdiction but clearly needed support to implement a laudable scheme with promising results . the bamako initiative of 1987 supported strengthening health systems at the district and community - levels in parallel with efforts to decentralize political systems throughout africa . however , roles and responsibilities over phc programs , facilities , human resources , and financing remained unclear - a mishmash of centralization and decentralization . although the federal level is principally responsible for tertiary health care , the national primary health care development agency ( nphcda ) and national programme on immunization were developed at the federal level to maintain some control over phc . for example , the nphcda is intended to ( and does ) carry out supplemental immunization campaigns against vaccine preventable diseases including polio . state ministries of health are also involved in the building and managing of phc centers although , according to the national health policy , ostensibly responsible for managing secondary health care hospitals . the states provide health care services ( including phc services ) through the state ministry of health ( smoh ) , the state hospital management board ( shmb ) , and the state phc development agency ( sphcda ) . several bodies are involved in human resource management at the lga level for phc services : the ministry of local government ( molg ) , the state phc agency , the local government service commission , the public service commission and the lga . the local government service commission is a state level organization that is responsible for all health professionals ( level 7 and above ) while the lgas managed admin , security , and lower level personnel . budget development and release is similarly fragmented . while finance was nominally devolved in block grants to both states and lgas , state governments established joint accounts in which state and lga financial resources were placed . adding to the confusion over financial control , external donors usually direct programmatic funding into federal - level accounts , although ultimately implementation should occur at the local level . for example , large sums of money provided by the millennium development goal ( mdg ) office are given to the federal ministry of health to implement the community - based national health insurance scheme ( nhis ) scheme . the diversification of responsible units at the federal and state levels exacerbates the confusion of responsibilities between tiers . although phc is the responsibility of local governments , the multitude of different agents actually involved in phc services makes coordinated management across the ministry of health technically difficult . thus , several states - starting with enugu and jigawa , and then yobe and zamfara - have been exploring strategies for bringing phc under one roof . this first occurred through the partnership to transform health systems ( paths ) programme from 2002 to 2008 , and then through the prrinn - mnch programme , which began in 2006 . the possibility of the funding that would flow from the federal health act drove policy and legislative changes regarding phc in several states in nigeria . although implementation varies across states , relevant policy and legislative changes generally address three key issues . firstly , health services - particularly phc services - are being integrated , where previously all three tiers of government were involved in implementation . secondly , health services are being decentralized - both through devolution and de - concentration . and thirdly , but not uniformly , through the de - concentration to sub - state bodies ( the names are different in the different states ) , the balance of power in the management of key resources ( especially financial and human resources ) is shifting from the politicians to administrators and managers . it is important to highlight the process adopted through these adjustments and how the outcome of integrated health services ( at least of phc ) was achieved . since both federal government and states can pass legislation , both the paths and the prrinn - mnch programmes worked closely with the states to develop appropriate legislation and accompanying regulations for phc ; to strengthen systems ( especially financial , human resource and information ) ; and to reposition the state level bodies for their new roles and functions . this process was not without challenges and extended over substantial periods of time . at the same time , the states ( with support from the programmes ) lobbied at federal level to gain acceptance and to provide access to materials and support for states willing to embark on this process . draft policy memos and an implementation guide were finalized during the second workshop , were approved by the nphcda board in 2010 and submitted to the highest health policy body in nigeria ( the national council for health ) . as summarized in the official record of the council : council noted the thrust of the national health bill in strengthening primary health care ( phc ) through the creation of phc boards / agencies and the phc development fund . council noted efforts in bringing phc under one roof in line with the provisions of the national health bill . council also noted the importance of enacting relevant state legislation and regulations that will facilitate the implementation of national health bill . council therefore approved the implementation guide on bringing phc under one roof ( phcuor ) as a working document to be used by the three tiers of government and approved that all states establish primary health care boards . the national council for health not only adopted the policy document and implementation guide on bringing phc under one roof but encouraged the 36 states to proceed in implementing this concept ( table 1 ) . at the time of the 2012 workshop , 22 of the 36 states in nigeria were in various stages of implementing bringing phc under one roof . gavi has supported nigeria s immunization system since 2001 to address extremely poor immunization coverage , particularly in the northern states ( http://www.gavialliance.org/country/nigeria/ ) . states were able to access the first tranche of the gavi funds , which were managed at the federal level , following initial engagement with gavi , but several states were unable to retire the monies appropriately . thus in 2007 , prrinn - mnch began at the state level supporting state ministries of health to effectively retire and access ongoing funding tranches from gavi . this work shifted to the federal level where prrinn - mnch assisted the gavi office in nphcda to review the processes and tools for accessing and retiring the funds and participated in developing a set of master trainers who would train others across all states in nigeria . in 2009 , prrinn - mnch supported nphcda to develop financial guidelines for gavi fund management and provided appropriate training on the use of these guidelines for relevant staff at agency headquarters and in its programme states . the nphcda also requested that prrinn - mnch train focal nphcda staff on the use of the financial guidelines and tools in the non - programme states . the subsequent workshop enabled the participants to understand the use of the financial guidelines and equipped them with the capacity to train other relevant staff at the lower levels . the twenty - two participants comparised six senior staff from nphcda headquarters , two representatives of the nphcda offices from each of the six geo - political zones of the federation , and gavi fund accountants from the four prrinn - mnch focal states . this example illustrates how state level experience of an international agency s funds was used to drive changes in how the funds were administered and accessed at federal level . initial work started within the states to ensure that the proposed system would work , and had significant impact on coverage ( figure 1 ) . later this was taken up to federal level where capacity was built to maintain and nationally roll out the new system . nigeria has a high maternal mortality ratio , low attendance for antenatal services , and few births are attended by a skilled birth attendant . thus , to improve access to care for pregnant women , the mss was a federally conceived and driven scheme to place retired and unemployed midwives in health facilities ; later this was extended to community health extension workers ( chews ) to ensure remote communities have access to perinatal services . the nphcda initiated the mss using funds from mdg fund . in each state , four midwives were deployed to each of the selected phc facilities to ensure provision of maternal and child health care services on a 24/7 basis . in each state , a selection of four phc facilities is clustered around the referral general hospital , with the creation of 156 clusters nationwide . six of these clusters are in three prrinn - mnch target states ( katsina , yobe and zamfara ) . this was followed by a second wave ( both midwives and chews ) in late 2010 . specific areas of collaboration between prrinn - mnch and nphcda under the banner of mss have included : i ) participation in the recruitment of midwives for the north - west zone in nigeria ; ii ) sharing of relevant tools for health facility baseline assessment , participatory appraisal and continuous transformation ( including impact , a systems strengthening and management capacity building initiative developed by health partners international : http://www.healthpartners-int.co.uk/ ; http://www.prrinn-mnch.org/index.html ) and assessment of training institutions ; iii ) sharing experience on planning and conducting baseline assessments , development of a monitoring and evaluation framework , and the comprehensive emergency obstetric care ( ceoc ) cluster model used ; iv ) participation in the planning of refresher training of midwives countrywide by nphcda - mss ; v ) developing national integrated supportive supervision ( iss ) tools ( the iss tools have been institutionalized and the iss teams oriented nationwide ) ; vi ) providing in - service training to mss midwives in the three states based on training needs earlier identified during an induction workshop . while there are multiple interventions in the clusters and the states , the increased presence of midwives ( and chews ) is considered a major contribution to increased utilization of mnh services in all the prrinn - mnch supported facilities where mss midwives are deployed ( as compared to baseline data collected between august and october 2008 ; figure 2 ) . overall , more significant increases were noted in anc attendance when compared with intrapartum care ( delivery ) . for example , in furfuri phc , zamfara , the number of anc visits increased from 0 to 455 , and deliveries from 0 to 28 between april and june , 2010 . mss midwives initiated community mobilization activities to increase utilization of mnh services , especially skilled care at delivery . mss has also shown improvement in documentation , including the keeping of registers and summary graphs and statistics in all facilities ( and bar charts in some facilities ) . additionally , all prrinn - mnch supported health facilities where there are mss midwives ( at least 3 - 4 mss midwives per facility ) now provide 24-h intra - partum care . for instance , a night shift was introduced by mss midwives on arrival at baimari maternity phc , yobe . problems experienced by the midwives continue to be largely administrative and systems related : e.g. payment issues , accommodation , poor working environment etc . although there has been progress in most of these areas , they remain critical issues to monitor in support of retention of these important health workers . this third example illustrates how state level practitioners can assist in supporting , and adding value to , nationally conceived and driven plans . in this case the nphcda had no formal jurisdiction but clearly needed support to implement a laudable scheme with promising results . informed by the whole systems approach of complexity theory , both the paths and prrinn - mnch programmes were either conceived or morphed into broad health systems strengthening programmes , and engaged non - health ministries , departments , and agencies . a key component of complexity theory is allowing - and often encouraging - variation in the system . this is a result of the path dependence principle noted earlier where , from similar starting points , different outcomes can emerge based on different contexts and different decisions at key bifurcation points . thus , faced by similar challenges , some states adopted an integrated phc system ( e.g. yobe and zamfara ) while other adopted an integrated phc and secondary health care system ( e.g. enugu and jigawa ) . this was a combination of history and context ( e.g. jigawa had no state hospital management board ) and of different choices at key moments ( usually by the state governor ) . in one example , key legislative changes in the gunduma or district system in jigawa meant that the previously fragmented management of financial and human resources was transferred to the gunduma health services board from state and lgas . the outcome was that administrative management and procedures were strengthened at the expense of political power and control . improvements in jigawa , as demonstrated by the 2010 national immunization cluster survey data , led to other states exploring variations of the gunduma approach . this illustrates to further features of complex systems : the importance of positive feedback loops ( as initially there was widespread scepticism of the changes in jigawa ) and the influence of phase transitions where a critical tipping point is reached to initiate change . in the second strategy , states encouraged coordination with federal agencies in order to strengthen the system involved in accessing , spending and retiring gavi funds . the whole systems principle meant that all had to be addressed . improved state - level gavi systems led to increased funding in the northern states , which led to the nphcda requesting assistance to strengthen the federal level gavi systems . this illustrates the non - linearity principle . once the federal level nphcda was made aware of the challenges at state level in accessing gavi funds and the changes brought by strengthening state level processes , the nphcda was more amenable to changing processes for accessing the gavi funds . increased frequency of accessing , spending and retiring gavi funds from prrinn - mnch supported states led to nphcda requesting assistance in rolling out the methodology to other states in addition , in one state ( jigawa ) the positive experience with the gavi funds led to the state applying the same methodology to other funds . finally , the tipping point was the realization by the federal level gavi office that states that previously could not access the funds could now readily be assisted to comply with the guidelines . mss also involved both the federal and state levels of government , except here coordination was initiated from the top - down . the federal level nphcda realized that it needed to look creatively for options to redress the problem of poor maternal health indices , hence supporting retired and unemployed midwives to find jobs in underserved states . the interaction between the nphcda planners and the prrinn - mnch has identified tools and approaches that can be shared and experiences that can be built on to improve the mss . each of these examples thus illustrated the influences on services and provision of multiple drivers , some within the health system and some outside of it . in advance , it would have been hard to anticipate all the factors that would prove influential on specific outcomes . rather , a sensitivity to the potential for such influences in real time policy and implementation work served to highlight emerging opportunities - and barriers - and develop appropriate strategies with respect to them . we consider that understanding and utilizing complexity theory and the complex adaptive systems approach has had a profound impact on how to strategize regarding health systems development in northern nigeria . it has introduced flexibility in the implementation of key health systems strengthening initiatives that stands to significantly benefit health care services and improve longer - term health outcomes in this challenging environment . such application of systems thinking is emerging as an important approach to tackling recurrent challenges in health systems development , on issues ranging from disease control programme sustainability and integration and the management of user fees to the resilience of health systems in times of civic crisis .

the partnership for reviving routine immunization in northern nigeria - maternal , newborn and child health initiative supports efforts by the government of nigeria to bridge primary health care ( phc ) policies and services at three levels of government : federal , state and local . the paper suggests that understandings informed by complexity theory and complex adaptive systems have been helpful in shaping policy and programme design across these levels . to illustrate this , three initiatives are explored : bringing phc under one roof , enhancing access to funding provided by the global alliance for vaccines and immunization , and strengthening the midwives service scheme . these initiatives have demonstrated how concepts and experience developed at subnational level can influence national policy and practice , and how work at subnational levels can add value to nationally conceived and nationally driven plans for phc .

Introduction The Partnership for Reviving Routine Immunization in Northern Nigeria - Maternal, Newborn and Child Health Materials and Methods Analysis Bringing primary health care under one roof Enhngaccess to Global Alliance for Vaccines and Immunization funds Strngthening the midwives service scheme Results and Discussion

the benefits of regular physical activity for older adults , including reduced risk of chronic diseases and disabilities , are well known [ 16 ] . the centers for disease control and prevention ( cdc ) currently recommends 150 minutes per week of moderate - intensity ( e.g. , brisk walking ) or 75 minutes of vigorous - intensity aerobic activity per week for adults aged 65 and older . however , the most recent cdc data indicate that only 15.9% of american older adults met these guidelines in 2011 and are far from reaching physical activity goals set by healthy people 2020 . walking is the most common type of moderate - intensity physical activity among older adults [ 911 ] . walking may be done for two primary purposes : ( 1 ) for intentional exercise and recreation or ( 2 ) simply as a means of getting from place to place for utilitarian purposes ( e.g. , to accomplish errands or get to work ) . the biomechanics , optimal walking speed , and energy expenditure of these two types of walking may differ , as load or gradient differs [ 1214 ] . several previous studies have investigated how recreational walking and utilitarian walking are influenced by the walking environment [ 1517 ] . found that utilitarian walkers had significantly higher risks of falling and being injured in falls than recreational walkers . however , to our knowledge , no study has looked at the wider range of determinants specifically to see how they might differ between the two types of walking , such as walkers ' physical abilities , socioeconomic factors , environmental features , and neighborhood characteristics . we examined the recreational and utilitarian walking habits of older adults living in 16 neighborhoods in the greater boston , massachusetts area . we investigated the extent and determinants of community - level variations in walking frequencies , and possible implications to public health practices . briefly , it is a prospective cohort study to investigate risk factors and mechanisms of falls among community - dwelling persons , mainly aged 70 years and older . the cohort included 765 participants living in the boston , ma area , who are able to read and speak in english and walk 20 feet without the assistance of another person , intending to stay in the boston area for at least two years , and who are without moderate to severe cognitive impairment ( score 18 on the mini - mental state exam ( mmse ) ) . participants were recruited from september 2005 to december 2007 , using door - to - door recruitment in randomly sampled households within 5 miles of the study clinic at hebrew seniorlife in boston with at least one member aged 70 years or older as recorded in city and town lists . domestic companions aged 64 and older living with study participants ( aged 70 years ) were eligible to enroll in the study . this analysis excluded 20 participants who did not have data on walking habits or on covariates used in the analyses , for a final sample size of 745 participants . the two - part baseline assessment included a home interview , followed within 4 weeks by a study clinic visit . during the baseline home interview , trained interviewers administered questionnaires to assess self - rated general health , cognitive function , physical function , health behaviors , fall history in the 12 months prior to baseline , medication use , comorbid conditions [ 24 , 25 ] , and sociodemographic characteristics . during the home visit the frequency of outdoor walking was assessed with the question , over the past seven days , how often did you take a walk outside your home or yard for any reason ( never , seldom ( 1 - 2 days ) , sometimes ( 3 - 4 days ) , or often ( 57 days ) ) ? utilitarian walking was determined by the query , do you walk to the store , post office , bank or other businesses in your neighborhood ? never , less than once per month , 13 times per month , 1 - 2 times per week , and 3 or more times per week . for the purpose of the current analysis , three operational outcomes of walking habits were defined , namely , habitual walking ( walking outside the home for any purpose five or more days per week ) , recreational walking at least once per week , and utilitarian walking at least once per week . during the clinical examination at baseline , participant body height and weight an inability to stand from a chair without using arms was taken as an indicator of poor lower extremity muscle strength . lower extremity function was assessed by the short physical performance battery ( sppb ) [ 27 , 28 ] . gait speed ( m / sec ) was assessed by the shortest time taken to complete 2 trials of a 4-meter walk at self - selected walking speed . a participant 's community was defined as the town , city , or subdivision of a large city of residence . the city of boston includes 16 communities according to neighborhood planning districts defined by the boston redevelopment authority . in order to ensure the compatibility of community sizes and adequate sample sizes for each geographic unit of analysis , we combined several adjacent communities with similar sociodemographic profiles into a single community unit . larger cities with larger sample sizes were divided into smaller units based on established geographic concepts ( frequently used neighborhood names ) . as shown in figure 1 , each of the participants ' home addresses was geocoded using arcgis desktop 10 ( esri 2011 , redlands , ca ) and their census blocks were determined by linking the geographic coordinates to us census block maps . community - level demographic and ses data were derived by aggregating census track level data from 5 year rolling averages of 20052009 american community surveys of us census . participants ' community - level characteristics of interest included measures of income , educational attainment , housing characteristics , community stability , and racial composition . measures of geographic access to community resources were derived using geographic information system ( gis ) based road network distances to community amenities . from the massachusetts geographic information system ( massgis ) , we obtained gis data layers of libraries ( 2005 ) , town halls ( 2013 ) , public parks ( 2014 ) , transportation infrastructure ( 2012 ) , and land use and housing density data ( 2010 ) . gis layer of food stores was obtained from infousa ( 2012 ) and gis layer of post offices , from united states post office ( 2014 ) . using arcgis 10.1 ( esri , redlands , ca ) , we calculated the road network distance in miles from the participant 's residence to the closest amenity of each type and residential density as number of households per acre of residential land . participant characteristics found to be associated with at least one of the walking outcomes of interest in previous studies were summarized with descriptive statistics . multivariable logistic regression models adjusted for the personal composite score were used to estimate associations of selected community socioeconomic factors and amenity distances with the three walking outcomes . these measures were treated as linear continuous variables except for percentage of vacant housing units and percentage minority . because of their u - shaped associations with utilitarian walking , we constructed three categories of each of these variables . we modeled participants in the same community as a cluster for the socioeconomic measures , because they shared the same ses values , but each participant had his / her own unique amenity - distance scores . a seemingly - unrelated - estimation test [ 29 , 30 ] was used to assess the equality of the associations ( odds ratios ) of these community characteristics and distance - to - amenities measures with recreational versus utilitarian walking . community level differences in prevalence of walking habits were assessed using logistic regression models , where each of the three walking habit variables was the dependent variable , and community indicators were predictors . four models were estimated for each walking habit : ( 1 ) community differences without adjustment ; ( 2 ) with adjustment for personal characteristics ; ( 3 ) with adjustment for personal characteristics and distances to amenities ; and ( 4 ) with adjustment for personal characteristics , amenity distances , and community - level ses factors . in order to preserve degrees of freedom but still adjust for these factors , we derived a single composite adjustment score for each walking outcome for each individual using the entire set of characteristics as predictors in logistic models [ 22 , 31 ] . a person 's composite score was calculated as the summation of all the products of each specific regression coefficient multiplied by his / her value of the corresponding predictor . the area under the roc ( receiver operator characteristic ) curves of each model was used as a measure of model fit . a comparison between those participants aged 64 to 79 years and those 80 years and older revealed very similar community - level trends , so all ages were combined in the analysis . all statistical analyses were carried out using stata mp 12 ( stata corp lp , college station , tx ) . one in three participants reported walking at least five days per week outside the home ; 42% walked recreationally at least once a week ; and 28% walked for utilitarian purposes at least once a week . mean self - selected walking speed for this population was 0.92 m / sec for women and 0.99 m / sec for men . the associations of selected personal characteristics with the three walking outcomes under investigation were strong , especially so with habitual walking ( table 1 ) . associations with the specific behaviors of recreational and utilitarian walking were less robust but were similar to each other , especially for traits related to physical impairments such as slow walking speed ( < 0.68 m / sec ) , poor lower - body strength , and poor balance which may make walking difficult or more dangerous . despite the fact that fairly similar determinants at the personal level . recreational and utilitarian walking showed very different patterns of association with community - related factors , the communities differed greatly in the average walking distances to the nearest bus stop , subway , hospital , shopping center , post office , park , food store , town hall , and library , and each of these distances was negatively associated with utilitarian walking ( p < 0.01 , table 2 ) . the difference between utilitarian walking and recreational walking with respect to these destination distances was significant in every case . walking at least five days per week was associated with shorter distances to the nearest subway stop , hospital , post office , and food store ( table 2 ) . as with amenity distances , community ses characteristics were more likely to be associated with utilitarian walking than with recreational walking . utilitarian walking was significantly associated with a lower community median household income , a lower proportion of owner - occupied housing units , and intermediate percentages of vacant housing units ( 510% ) and minority population ( 2050% ) ( table 2 ) . with the exception of median income , each of the above factors associated with utilitarian walking was thereby also associated with the likelihood of walking five or more days per week , but none of the factors was significantly associated with recreational walking . a comparison of the prevalence of habitual walking across the 16 boston - area communities showed great variation , ranging from 16.7% in hyde park to 48.1% in boston downtown ( table 3 ) . this variation appeared to result mainly from community differences in utilitarian rather than recreational walking ( figure 1 ) . both before and after adjustment for personal characteristics ( table 3 , models 1 and 2 ) , there were significant differences among communities in utilitarian walking at least once per week ( p < 0.001 overall ) but not in recreational walking ( p > 0.85 ) . further adjustment for distance from home to amenities diminished the magnitudes of community associations with utilitarian walking somewhat , such that the community variable was no longer a significant predictor overall ( p = 0.10 , table 3 , model 3 ) , and the final adjustment for community ses greatly decreased the overall association ( p = 0.94 , table 3 , model 4 ) , indicating that access to amenities and socioeconomic factors had accounted for a great deal of the community variation in utilitarian walking . even after all adjustments , however , the odds ratios for community differences from the referent community remained higher in magnitude for utilitarian walking ( range : 1.906.96 ) than for recreational walking ( range : 0.721.14 ) . measures of community associations with walking at least five days per week ( habitual ) were diminished by adjustment for distance to amenities and community ses in a way similar to that of utilitarian walking , showing the importance of utilitarian walking in producing the patterns of total walking observed but community differences remained significant overall ( p = 0.01 , table 2 , model 4 ) . the three communities with the highest percentages of elders who walked five or more days per week for any purpose ( brookline north , jamaica plain , and boston downtown ) also had the highest percentages of persons who walked at least once per week for utilitarian purposes , and they were the only communities with more utilitarian than recreational walkers . areas under the roc curve , indicating the goodness - of - fit of models in table 3 , show that community alone ( model 1 ) was a stronger predictor of a person 's utilitarian walking habit ( area = 0.70 ) than of recreational walking habit ( area = 0.56 , p < 0.001 ) . adjustments for personal characteristics and distances improved each model significantly , but the fit of the recreational walking model never became as good as that for utilitarian walking ( p < 0.001 for each model ) . this study found variability among communities in the percentage of elders walking five or more times per week . much of this variability could be attributed to differences in utilitarian rather than recreational walking habits . prevalence of recreational walking at least once per week was low ( 40% ) among elders in the area , regardless of socioeconomic and built environmental conditions . prevalence of utilitarian walking was also generally low ( 28% overall ) but varied significantly among communities , accounting for much of the difference in the percentage of elders walking regularly . the data imply , on one hand , the importance of utilitarian walking , and on the other hand , the limited contribution of recreational walking , to total physical activity . while many personal characteristics , especially those concerning physical abilities and disabilities , were associated with recreational ( and utilitarian ) walking , we did not find any socioeconomic or environmental factors that were significant predictors of recreational walking . in contrast , utilitarian walking was strongly associated with many community characteristics including shorter walking distances from home to several amenities and neighborhood socioeconomic factors such as lower income and lower housing occupancy . this agrees with the findings for general adult populations [ 15 , 32 ] and for older adults . van holle and associates made objective measures of the walkability of neighborhoods and found that neighborhood characteristics were associated with walking for transport or walking for errands but not with walking for recreation . it is worth noting that we found the same patterns of association and nonassociation of community characteristics with walking of the three types among those participants aged 80 and older as well as among those aged 64 to 79 years . first , this study examined walking habits in a large cohort of community - dwelling elders aged 70 and above , with 37% aged 80 and older , a segment of the population that has been little studied with regard to walking . this older age of our cohort may account for the somewhat slower mean gait speed than that reported in the literature for healthy septuagenarians . the mobilize boston participants were strategically recruited to represent a broad range of socioeconomic and residential conditions ; the cohort resembled the underlying population well . we obtained detailed measurement of a wide range of personal and socioeconomic characteristics and distances to amenities that might attract walkers in a well - characterized urban area . the distinction between walking for recreational versus utilitarian purposes afforded the opportunity to identify two different sets of determinants specific to the two types of walking , filling a knowledge gap in the elder population . it is limited to one urban area in the northeastern region of the country where the older adult population tended to be english - speaking , of white race and have higher income . although the mobilize boston cohort matched the general older population according to sex , race , and ethnicity , the participants had somewhat higher education than the general community . still , relative frequencies across communities should be fairly accurate , especially after adjustment for a wide range of demographic characteristics . duration of walking activity was not collected except in very broad categories which did not allow for community - level or person - level comparisons . we also did not know whether or how often a load might have been carried by walkers . one might infer that this would be more common among utilitarian walkers ( while shopping , etc . ) , possibly adding a physiological benefit of extra energy expenditure but increasing risk of injury in a fall . the unmeasured potential neighborhood self - selection and the cross - sectional design do not allow examination of longitudinal changes in walking habits which might elucidate causality . to address these issues , our current studies have been collecting detailed information on time and location of walking and selection of walking paths among older adults , using accelerometer and global positioning system devices . clearly , an older person 's decision to walk regularly depends on a whole host of factors in addition to the built environment : necessary errands if they do not drive , access to public transportation , physical ability , time availability , feelings of fear , culture , and social influences being but a few . however , the benefits of physical activity , in preventing obesity , arthritis , and their associated health problems and especially in warding off disability as people age [ 15 ] , suggest that efforts to encourage walking to the extent possible by modifications of the environment may be worthwhile . our findings point toward further investigation of communities like brookline north , jamaica plain , and downtown boston to see which features distinguish them from other boston communities in promoting physical activity by elders . the primary finding of this study was that while the prevalence of recreational walking was relatively uniform across all communities , the prevalence of utilitarian walking varied widely and was more strongly associated with multiple factors at both the community and individual levels . in most communities examined in this study , the prevalence of regular walking behavior was low , which suggests a tremendous opportunity for health promotion . the challenge for public health is not only to find ways to promote utilitarian walking by elders using the knowledge gained to date but also to increase our understanding of factors that encourage recreational walking , so that both types of walking become more appealing , accessible , and safe .

background . regular walking is critical to maintaining health in older age . we examined influences of individual and community factors on walking habits in older adults . methods . we analyzed walking habits among participants of a prospective cohort study of 745 community - dwelling men and women , mainly aged 70 years or older . we estimated community variations in utilitarian and recreational walking , and examined whether the variations were attributable to community differences in individual and environmental factors . results . prevalence of recreational walking was relatively uniform while prevalence of utilitarian walking varied across the 16 communities in the study area . both types of walking were associated with individual health and physical abilities . however , utilitarian walking was also strongly associated with several measures of neighborhood socioeconomic status and access to amenities while recreational walking was not . conclusions . utilitarian walking is strongly influenced by neighborhood environment , but intrinsic factors may be more important for recreational walking . communities with the highest overall walking prevalence were those with the most utilitarian walkers . public health promotion of regular walking should take this into account .

1. Introduction 2. Materials and Methods 3. Results 4. Discussion 5. Conclusions

autoimmune diseases ( aids ) are the third most common category of disease after cancer and heart disease and affect approximately 5~8% of the general population . sex - linked differences are striking , with aids considered a top 10 leading cause of death in women under the age of 65 ( 1 ) . more than 100 different types have been recognized , and the majority of autoimmune problems are associated with eight disorders : rheumatoid arthritis ( ra ) , type i diabetes mellitus , multiple sclerosis , psoriasis , systemic lupus erythematosus ( sle ) , ulcerative colitis , crohn 's disease , and scleroderma ( 2 ) . aids arise from interactions between environmental , epigenetic , and genetic factors that result in persistent activation of immune responses and their biological networks ( 3 ) . the development of autoimmunity is strongly influenced by inherited polymorphisms ( or dna sequence variations ) . however , the enormous diversity of genetic variants contributes to the susceptibility for aids . hla haplotype linkages are shared between aids , and most hla associations seem to be disease - specific ( 4 ) . for example , the hla class ii molecule , hla - dr3 , shows a strong correlation with sle , sjgren 's syndrome ( 5 ) , and subtypes of autoimmune myositis and is associated with the production of antibodies against dna in lupus and anti - jo1 production in myositis ( 6 ) . in sjgren 's syndrome , the association between hla - drb103 and the production of auto - antibodies against ro is even stronger than the association of hla with the disease ( 7 ) . many of the strong loci that have been associated with one aid are also involved in other aids . typically , the allele of these shared variants that is a risk factor for one autoimmune disease is also a risk factor for other autoimmune diseases . for instance , variants in the ptpn22 gene have been associated , with varying degrees of risk , with type 1 diabetes , autoimmune thyroid diseases , and ra ( 8,9 ) . in genome - wide association studies , several inherited polymorphisms or dna sequence variations that cause the sequence variations ( single nucleotide polymorphisms , snps ) are highly " polygenic , " predominantly determined by non - hla genes , and have limited impact on disease onset ( 10 ) . however , most of the identified snps are not linked to disease - related genetic markers . a number of snps are estimated to share pathogenic pathways in the development of aids or link common genes with the risk of autoimmune and/or inflammatory diseases . about 100 disease - risk snps have been identified in celiac disease , crohn 's disease ( 11 ) , multiple sclerosis ( 12 ) , psoriasis ( 13 ) , rheumatoid arthritis ( 14,15 ) , sle ( 16 ) , and type 1 diabetes ( 17 ) . interestingly , hu et al . found that 47/107 ( 44% ) immune - mediated disease risk snps are associated with multiple autoimmune diseases , leading to the proposal that distinct groups of interacting molecules that share a disease risk are encoded close to snps that influence the same subsets of diseases ( 18 ) . to help identify the precise causal alleles in specific cell types , the genomes of diseased cell types that are studied need to contain disease - associated genetic variants . this challenge is highlighted in systemic aids , such as ra , where any of a broad range of immunological cell types are potentially impacted by genetic variation to cause disease . potentially pathogenic cell types in autoimmune diseases have been identified : transitional b cell genes in sle , epithelial - associated stimulated dendritic cell genes in crohn 's disease , and cd4 + effector and memory t cell genes within ra loci ( 18 ) . the most striking evidence of environmental effects on the development of aids is the high discordance rate observed in monozygotic twins ( 19 ) . discordance enables the study of epigenetic changes that lead to the development of autoimmunity . in an individual with a susceptible genotype , exposure to environmental factors , including sunlight , diet , chemicals , smoking , allergens , infectious agents , or environmental toxins , not only triggers downstream signaling of the susceptible genes but also initiates epigenetic changes before and after the development of autoimmune responses ( 20,21 ) . epigenetics is defined as the inheritable effects that influence gene activity without changes in dna sequence . epigenetic gene regulation has an essential role in determining individual gene function and activity in each specific cell type . the epigenetic changes include four predominant mechanisms ( 22 ) : dna methylation , histone modifications , nucleosome positioning , and micrornas ( mirnas ) . these four mechanisms control gene expression and assist in the regulation of cell differentiation , proliferation , dna repair , and replication . epigenetic modifications are far more sensitive to environmental stimuli than the sequence of dna . candidate gene studies of aids have identified a small set of genes that undergo epigenetic changes , such as aberrant dna demethylation , histone modification , and mirnas , in rheumatic diseases . t cells from patients with sle or ra , as well as synovial fibroblasts from individuals with ra ( 8,23 ) , contain hypomethylated dna sequences and/or histone modifications in particular cell types . the identification of target sequences for epigenetic deregulation will provide clinical markers for diagnosis , disease progression , and therapies for aids . high - throughput sequencing is necessary to screen for epigenetic alterations in specific tissue and cell types that are relevant to disease pathogenesis ( 24 ) . another area of study is mirnas , a class of small noncoding rnas that regulate gene expression by pairing with their target mrnas and are often deregulated in aids ( 25 ) . to further understand the role of epigenetic changes in aids , we have to keep in mind that most autoimmune disorders are not due simply to the possession of a specific gene but also to conditions that affect the gene . exposure to environmental triggers by a genetically susceptible host favors the activation of both the innate and adaptive immune systems . the innate immune system , consisting of physical mucosal barriers , proteins , and cells , serves as the front line against infectious agents or other environmental challenges . innate immune activation in autoimmunity leads to the production of type 1 interferon ( ifn ) , usually produced in response to viral infection , which in turn activates about 400 genes , denoted the interferon signatures ( 26 ) . type 1 ifn induces the activation of dendritic cells ( 27,28 ) , increasing the expression of mhc class i and ii molecules , costimulatory molecules , chemokines , and chemokine receptors ( 29 ) and inducing b - cell maturation and differentiation into plasma cells by secretion of il-6 , production of b cell activating factor ( tnfsf13b ) , and a proliferation - inducing ligand ( tnfsf13 ) . dendritic cells activated by ifn- support and contribute to the plasticity and differentiation of t - cell subsets , and promote the expansion of t cells . ifn- further stimulates cd4 + t cells to enhance antigen - specific b - cell responses . in the adaptive immune system , antigen presenting cells , including monocytes / macrophages and dendritic cells , can be activated by endogenous and/or exogenous antigens , resulting in the release of cytokines that promote differentiation of naive t cells into effector subsets . th1 cell differentiation is promoted by il-12 and ifn- , th2 cells depend on il-4 , and tgf- is crucial for the development of regulatory t cells . in addition , in the presence of il-6 , tgf- differentiates into a highly proinflammatory subset of th17 cells , initially characterized by il-17 production . increased amounts of il-17 and a high proportion of il-17-producing t cells have been reported in patients with sle ; a correlation with disease activity has also been noted . t cells that produce il-17 are detectable in the main target organs in sle ( i.e. , the skin , kidneys , and lungs ) , suggesting that il-17 has a role in local inflammation and tissue damage ( 30 ) . furthermore , patients with sjgren 's syndrome show high levels of expression and increased concentrations of il-17 and il-23 in the plasma . enhanced expression of il-17 , together with augmented production of ifn- and expression of mhc class i , has been identified in muscle specimens from autoimmune myositis patients . several genetic risk factors in sle and sjgren 's syndrome are related to the formation or maintenance of th17 cells . interferon regulatory factor 5 ( irf5 ) plays a role in type 1 ifn pathways and in the expression of genes important for th17 cell responses ( 31 ) by acting as a transcription factor for il-6 and the p40 subunit of il-23 . the potential functional effect of this genetic association is supported by increased amounts of both il-6 and p40 in patients with sle ( 32 ) and sjgren 's syndrome ( 5 ) . among pre - immune b cells , augmented proportions of transitional and naive b cells are detectable in patients with sjgren 's syndrome . these memory cells can be activated by a combination of toll - like receptor agonists and tnfsf13 or tnfsf13b and by cytokine combinations , such as il-21 and tnfsf13b . blood transcriptome studies to determine the expression levels of mrnas of a given cell population are essential for autoimmunity - related translational research ( 33,34,35,36 ) . such transcriptome studies measure the levels of rna transcripts in patient samples , which have been influenced by environmental factors or pathologic conditions . samples from cells , serum , fluid , and tissues are crucial for aids translational research and should be carefully stored , under standardized methods of patient sample aquisition , archiving , sequential high - throughput molecular analyses , and ongoing phenotypic data possession , allowing for the bioinformatics testing . using polychromatic flow cytometry , intracellular or extracellular markers in each cell phenotype can be identified . in vitro cellular assays can measure the innate or antigen - specific responsiveness of cells exposed to exogeneous or endogenous antigens . multiple proteomic assays can be used to determine the antibody specificity of serum levels of cytokines or chemokines ( 37 ) . during the past decade , new next generation sequencing technology has been used for dna - based microarrays and studies of cellular rna levels for different aids . whole transcriptome profiling studies have been used to identify biomarkers for diagnosis , assess disease activity , predict flare - ups , and determine the response to treatment . more quantitative and sensitive high - throughput rna sequencing methods have resulted in the precise evaluation of the blood transcriptome as a routine test in the clinical setting . well - known examples of successful blood transcriptome analyses have been reported in the case of sle . in 2003 , two independent teams identified a strong ifn signature in pediatric and adult sle patients ( 38 ) , with a central role for dendritic cells and ifn- in the disease ( 39 ) , and this was later confirmed by additional studies using microarrays and rt - pcr . subsequent genetic studies identified strong associations between sle and type i ifn - related gene polymorphisms ( i.e. , irf5 ( 31 ) , stat4 ( 40,41 ) , trex1 ( 42,43 ) ) and proteomics studies showed that the levels of some ifn - regulated chemokines could be used to predict sle flare - ups in patients with quiescent disease ( 44 ) . although dna microarray studies have led to important advances in the study of autoimmunity , their use is limited because changes in transcript abundance can occur by many parameters other than disease status . an additional problem lies in the fact that a large proportion of mrnas are not translated into proteins , despite being upregulated at the level of transcription . thus , more standardized proteomic work and well - designed public datasets need to be developed . transcriptomic research in patients with aids can be used to guide other biologic approaches , including proteomics or genomic studies , and can also provide the basis for early translational and clinical applications . biomarkers have been identified from the variety of human genes , genetic variation , measurements of rna , proteins , and metabolites . numerous biomarkers can be quantitatively measured in patient samples , including plasma , serum , cerebrospinal fluid , bronchoalveolar lavage , tissue biopsies , whole blood , urine , and saliva . biomarkers are dynamic and informative biological substances ( i.e. , cellular , biochemical , molecular , genetic , protein , metabolite , specific post - translational modification , or physiological or physical signs ) that can be evaluated as indicators of normal versus pathogenic biological processes , and disease progression or response to a therapeutic intervention . clinically , biomarkers can be classified based on their application , such as predictor , diagnostic , prognostic , mechanistic , pharmacodynamic , safety , and surrogate endpoint biomarkers ( 45 ) . advances in high - throughput and multiplexed processes , microarray , and global - scale genomic and proteomic approaches have made it possible to characterize different clinical spectra associated with disease and the therapeutic interventions . novel analytical technologies have led to various methods of immune cell profiling , such as multi - parameter flow cytometry , multiplex analysis of intra- and extra - cellular mediators , and genome - wide profiles of gene expression . the use of multi - omics platforms and multiplexed approaches in the analysis of systemic aids will not only help to identify numerous useful biomarkers but also will expose areas for further improvement in translational research ( 46,47,48,49 ) . there is growing agreement that more than one biomarker is needed for accurate efficacy or safety decisions . in this context , using multiplexed technology and a multi - omics approach could offer a significant contribution to biomarker discovery for translational research in early stages of aids . improved genomic approaches that use high - throughput molecular and cellular profiling of cells in different clinical subsets and consisting of measuring the abundance of cellular rna and micrornas expressed by t cells will help in biomarker discovery . the biomarker discovery used for the cd4 t cell differentiation process 2 . during the differentiation of th17 cells in the presence of chemical compounds or small interfering rna ( sirna ) libraries , cell - specific transcriptomics and proteomics were applied to discover biomarkers targeting th17 cells ( 50,51 ) . the function of identified candidate genes was further investigated using rna interference ( rnai ) and by defining regulatory protein - binding sites in the genome via chromatin immunoprecipitation ( chip ) ( fig . researchers have recently explored the genes expressed at different time points during th17 cell development . they detected almost 1,300 genes involved in over 10,000 interactions , with 71 regulators ( 53 ) . researchers validated potential immune regulatory biomarkers for th17 autoimmunity using silicon nanowires to deliver sirna into naive t cells ( 54 ) . the biomarkers they found during th17 cell differentiation , derived from improved , advanced approaches with multi - omics , could be particularly useful in the development of targeted therapies and identification of aids subgroups . most of the novel biomarkers and their correlations to disease were derived largely from two or more samples at one point in time . the methodologies employed show snapshot events of the disease state at a specific time , whereas signaling networks are dynamic in both structure and their use . because single measurements rarely capture all dimensions of clinical outcomes , a multidimensional and continuous model is needed ( 34 ) . the post - genomic era has provided a wealth of novel approaches for generating high - dimensional genetic and transcriptomic data sets from large cohorts of human diseases and normal individuals . over the last 10 years , there has been a strong focus on molecular characterization of biological systems in various disease states . in addition to the blood profiling approach , the study of specific cell subsets using multi - omics approaches will be useful for dissecting molecular heterogeneity , allowing for the discovery of new biomarkers and translation of those biomarkers into new therapeutic options for aids ( fig . 3 ) . systems biology in aids has included expression profiling and functional analysis of dna , rna , protein , and metabolites of specific cell subsets in each stage of disease ( 55 ) . current efforts for discovery and development of disease - related biomarkers will assist in optimal decision - making throughout the various stages of disease . furthermore , effective translation of biomarkers into the clinic will lead to effective implementation of personalized therapies that benefit patients with aids . in order to achieve this , well - designed , large - scale profiling studies should be designed for new biomarker discovery . because extensive cellular and molecular profiling of human subjects generates vast amounts of disparate data , effective data management and integration solutions are essential for preserving this information in an interpretable form . aside from ongoing technological improvements , data mining will play an essential role in generating large amounts of information and for providing the full potential of high throughput profiling approaches in patients with aids ( 34 ) . systems biology approaches have been broadly applied in treating a variety of aids and have been well - suited for investigating molecular heterogeneity . microarray technology for blood transcriptome analysis has provided new insight into the pathogenesis of complex diseases and the discovery of new biomarkers ( 56 ) . to identify the most predictive biomarkers across dna , rna , protein , phenotype , and metabolites , more standardized multi - omics approaches , along with network analysis for large - scale data mining , are required . along with ongoing technological improvement , carefully designed large - scale profiling studies should be adopted for better translation into clinical application .

because autoimmune diseases ( aids ) result from a complex combination of genetic and epigenetic factors , as well as an altered immune response to endogenous or exogenous antigens , systems biology approaches have been widely applied . the use of multi - omics approaches , including blood transcriptomics , genomics , epigenetics , proteomics , and metabolomics , not only allow for the discovery of a number of biomarkers but also will provide new directions for further translational aids applications . systems biology approaches rely on high - throughput techniques with data analysis platforms that leverage the assessment of genes , proteins , metabolites , and network analysis of complex biologic or pathways implicated in specific aid conditions . to facilitate the discovery of validated and qualified biomarkers , better - coordinated multi - omics approaches and standardized translational research , in combination with the skills of biologists , clinicians , engineers , and bioinformaticians , are required .

INTRODUCTION INHERITED GENES OF AIDs ENVIRONMENTAL FACTORS PRECIPITATE AIDs ACTIVATION OF IMMUNE RESPONSES PROMOTES THE AIDs PHENOTYPE BLOOD TRANSCRIPTOME ANALYSIS FOR TRANSLATIONAL RESEARCH SYSTEMS BIOLOGY APPROACHES FOR BIOMARKER DISCOVERY CHALLENGES AND FUTURE PERSPECTIVES OF SYSTEMS BIOLOGY APPROACHES CONCLUSION

considerable improvements in health care during the course of the last century have led to unprecedented increases in current life expectancies . however , longevity continues to favor women and as a consequence chinese and australian national health policies recognize the need to address male health in aging . while increased life expectancy is a broad consequence of quality health care , it also produces an aging population whose health care burden suggests wellbeing has not equally paralleled longevity . several areas of male health decline with age with increasing incidence of impaired spatial ability and depression being significant barriers to mental health . a sex difference in longevity intuitively points to a role of sex - hormones in maintaining health during aging . the sex - hormone testosterone is the primary androgen produced in men and circulating levels progressively decrease from 30 years onward so that by 60 years of age , up to 1 in 4 men have developed androgen deficiency . with increasing longevity the proportion of androgen deficient or hypogonadal men is likely to grow , along with predicted adverse consequences for male health . although clinically diagnosed hypogonadism is remediable with testosterone replacement therapy , understanding a causative relationship between age - related physiological decline and reduced androgen levels will enable better defined interventional strategies . the hippocampus is a key component of the temporal lobe and is notable for retaining ongoing adult neurogenesis within the dentate gyrus subregion . impaired hippocampal function resulting from neurogenesis deficits is hypothesised to contribute to the etiology of both depression and spatial memory impairment . in considering the collective clinical and rodent model data , a coincident age - related decline in circulating testosterone , hippocampal neurogenesis and hippocampal function becomes evident . however , a causal relationship between the age - related decline of these factors has yet to be established . this review raises a hypothesis that testosterone contributes to preserving hippocampal function in aging men by maintaining neurogenesis levels . herein , the intention is to briefly discuss the available evidence and highlight the necessity of further studies to establish , or refute , clinically relevant causal relationships . production of the primary male androgen testosterone is reduced as men age ( 1 ) . circulating testosterone targets the hippocampus , which has been functionally demarcated into dorsal ( 2 ) and ventral segments ( 3 ) . testosterone can support spatial memory ( 2 ) and provide anti - depressant efficacy ( 3 ) . intrinsic hippocampal circuitry comprises a well described tri - synaptic connection between ca1 , ca3 and dentate gyrus ( dg ) subregions ( 4 ) . ongoing adult neurogenesis proceeds in the sub - granular zone ( sgz ) of the dg through sequential proliferative and post - mitotic steps to produce functionally integrated neurons in the granule cell layer ( gcl ) of the dg ( 5 ) . androgen receptors are expressed in the dg but whether testosterone can directly or indirectly affect neurogenesis remains unresolved ( 6 ) . dosage and duration of testosterone and aromatasemediated metabolism into 17-estradiol may be important determinants of efficacy ( 7 ) . declines in circulating testosterone levels , hippocampal neurogenesis and hippocampal function are coincident in aging ( 8) . testosterone is the primary male androgen and is produced through the co - ordinated actions of the hypothalamic - pituitary - testes ( hpt ) axis . while there is normal variation among men , serum total testosterone in men aged under 35 years generally exceeds 20 nm . according to several endocrinology health bodies serum concentrations of total testosterone below 12 nm constitute a clinical diagnosis of hypogonadism , which can be further classified according to a taxonomy that directs remedial strategies . for example , testicular dysfunction , or primary hypogonadism , manifests in the presence of high luteinizing hormone / follicle stimulating hormone ( lh / fsh ) and is potentially indicated for testosterone replacement therapy . secondary hypogonadism occurs when hypothalamic / pituitary pathology fails to produce lh / fsh in sufficient levels to stimulate testicular androgen production . in this case , age - related low circulating testosterone can be the result of either primary or secondary hypogonadism . otherwise normal aging is associated with reduced total circulating testosterone levels ( below 20 nm ) concomitant with increased sex - hormone binding globulin ( shbg ) . testosterone bound to shbg is not bioactive and can affect the clearance rate of testosterone by the liver . however , the age - related increase in shbg levels has been shown to be independent of the age - related decline in bioactive testosterone levels . testosterone replacement therapy is advised based on symptomatic low circulating testosterone levels . however , applying this criterion to aging men presents potential limitations . firstly the age at which testosterone levels become low is an important determinant of resulting symptoms . age - related , or late - onset hypogonadism , may therefore elicit a unique spectrum of symptoms that are yet to be fully established . secondly , controversy surrounds the reliability of widely used measures of total and free serum testosterone to detect low circulating levels . as symptoms other than sexual dysfunction and frailty are not readily attributed to low circulating testosterone , symptomatic testosterone deficiency could be more common than generally recognised . testosterone therapy in aging men has hitherto been directed toward treating sexual and cardiovascular dysfunction , muscle mass loss and immobility . hence , the symptom profile of late - onset hypogonadism may well include declining mental health . although there are cross - sectional variations in measures of cognitive ability , a more robust decline is observed in longitudinal analyses . notwithstanding the view held by some that age - related cognitive decline is normal , maintaining cognition in longevity at young levels would have an undeniable impact on wellbeing . procedural memory remains largely unaffected , whereas declarative memory , particularly episodic memory shows demonstrable decline with increasing age . declarative memory as a whole is closely associated with temporal lobe function and abilities related to spatial memory are intimately coupled with the hippocampus . the decline in spatial ability of aging men is a domain of cognition particularly studied in relation to testosterone levels . this interest may be attributed to the fact that aspects of spatial ability are superior in men compared to women . a sex bias in spatial ability is also reflected in rodent studies that have been largely demonstrated using maze navigation tasks . men and women employ the same brain regions , including the hippocampus , when undertaking spatial navigation tasks . these observations suggest that testosterone may target the hippocampus in a manner that enhances spatial ability in men . notions of sex differences in brain anatomy and function have centred largely on the effects of sex hormones in development . evidence supports a possible organisational role of androgen signalling during brain development that imparts superior spatial cognitive ability in adulthood . longitudinal studies showing a correlation between age - related cognitive decline and reduced testosterone , raise the possibility that testosterone may perform a similar , but activational role in the mature brain . this idea led to studies demonstrating that testosterone therapy promotes spatial ability in aged men . additionally , the substantial evidence demonstrating pro - cognitive effects of oestrogen replacement therapy in postmenopausal women , including enhanced hippocampal plasticity and function , underscores the possibility of a similar mechanistic role of testosterone in aging men . oestrogen is a major metabolite of testosterone in the male brain further suggesting that low circulating testosterone may be a readily modifiable factor predisposing aging men to cognitive decline . androgens protect the adult brain from degenerative insults such as stroke and traumatic brain injury . although neurodegenerative diseases increase with advancing age , their consideration needs to be distinguished from normal age - related cognitive decline . along with the dentate gyrus the ca1 and ca3 subregions form anatomical demarcations of the hippocampus . androgen receptors are expressed in the hippocampus of humans , non - human primates , mice and rats with higher levels in ca1 compared to the ca3 or dentate gyrus subregions . evidence derived from young rodents shows that androgen withdrawal in development will reversibly reduce ca1 and ca3 synaptogenesis and subsequent adult spatial ability . synaptic loss during aging may underlie functional decline of the hippocampus , ( however also see ) . studies from rodents and non - human primates have provided evidence that serum androgens support ca1 synaptic density in young adulthood . these data provide a mechanism by which androgens could participate in the long - term preservation of hippocampal function . considered in reverse , the data suggests that age - related androgen deficiency may lead to ca1 synaptic loss and hippocampal dysfunction . as acknowledged above however , longitudinal studies indicate that the dentate gyrus subregion is more closely associated with age - related hippocampal impairment . evidence that sex - hormones increase dentate gyrus synaptogenesis has been extensively derived from examining the effects of oestrogen . in contrast , there is a relative paucity in studies reporting the effects of testosterone on dendritic structure and synaptic density of dentate gyrus granule neurons . it remains plausible that circulating androgens also target the aging dentate gyrus to preserve mechanisms of neuronal plasticity and hippocampal function . however , these theories were immersed in the basic tenet that the mature brain lacks ongoing neuronal production . this dogma was overturned with the widespread acceptance that adult neurogenesis occurs in mammalian brains . although spatially restricted , neurons generated in the adult dentate gyrus provide a functional form of neuronal plasticity . despite ongoing debate regarding the function of adult hippocampal neurogenesis , the weight of associative evidence points to a role of adult - generated granule neurons in spatial ability and perhaps emotional behaviour related to depression . in contrast to the ca1 subregion , androgens could preserve functional plasticity in the dentate gyrus through the addition of new granule neurons . levels of adult hippocampal neurogenesis decline with age , which has been hypothesised as a contributing factor to age - related decline in spatial ability . importantly , age - related declining adult hippocampal neurogenesis and spatial ability are reversible with factors such as physical exercise . if androgens play a critical role in maintaining adult hippocampal neurogenesis levels then late - onset hypogonadism may be a remediable cause of hippocampal dysfunction in aging men . adult hippocampal neurogenesis proceeds through a series of sequential steps : asymmetric division of neural stem cells , proliferative expansion of neural progenitors , neuronal differentiation and finally survival of mature neurons including both efferent and afferent synaptogenesis . intrinsic proliferation and differentiation markers together with exogenous markers such as 5-bromo-2deoxyuridine ( brdu ; which is incorporated into dividing cells and can assess proliferation and survival at short and longer time - points , respectively ) are widely used to measure adult hippocampal neurogenesis . mechanisms of age - induced reductions in adult hippocampal neurogenesis include decreased progenitor proliferation and neuronal survival , but factors mediating these mechanisms remain unknown . notions of sex - specific regulation of adult hippocampal neurogenesis were a significant impetus for exploring the effects of sex hormones on proliferation , differentiation and survival of adult - generated hippocampal neurons ( reviewed in ) . there is more hippocampal neurogenesis in neonatal male rats than females and several studies have demonstrated sex - specific rates of hippocampal neurogenesis in adult rodents . whether there is a sex - specific decline in adult hippocampal neurogenesis with advancing age remains hitherto unestablished . early studies withdrawing androgen through gonadectomy in young male rats showed no effect on proliferation but reduced neuronal survival as demonstrated by a reduction in the number of 30-day - old brdu - labelled cells in the dentate gyrus . repletion of testosterone at high but not low levels in these animals restored adult hippocampal neurogenesis in an androgen receptor - dependent manner . in contrast , another study showed that exogenous injections of nandrolone , a synthetic derivative of testosterone and androgen receptor agonist , reduced adult hippocampal neurogenesis by decreasing neuronal precursor proliferation in young adult male rats . our own recent work demonstrated that chronic testosterone therapy in young male adult mice had no effect on precursor proliferation as measured by the intrinsic marker ki67 , but did promote adult hippocampal neurogenesis through increased neuronal survival and differentiation 28-days after brdu administration . we measured hippocampal neurogenesis during the last 4 weeks of 3 months of supraphysiological doses of testosterone through sustained - release pellets , whereas a similar dosage limited to 3 days via repeated injections had no effect on neurogenesis . another study of young male mice demonstrated that precursor proliferation also measured by ki67 expression was unchanged , while the generation of maturing neurons measured by another intrinsic marker doublecortin , was decreased in the absence of androgen through gonadectomy . single administration of brdu to measure precursor proliferation in gonadectomised young adult male rats untreated or made replete with physiological levels of testosterone showed no effect of androgen withdrawal . however , the same study showed that testosterone exacerbated the up - regulated proliferation in response to the anti - depressant imipramine . in a contrasting finding , ki67 was used to demonstrate a decrease in precursor proliferation in gonadectomised young male rats compared to sham - surgery controls . this study also employed brdu to further examine survival and neuronal differentiation , showing that androgen withdrawal through gonadectomy decreased surviving 24-day - old brdu - labelled cells in the dentate gyrus without change in neuronal differentiation . furthermore , polysialic acid - neural cell adhesion molecule ( psa - ncam ) was used to demonstrate androgen withdrawal decreases maturing / migrating neurons . using a different approach , intact male rats given placebo or testosterone and brdu to measure proliferation , survival and differentiation showed no effect of exogenous androgen on any of these hippocampal neurogenesis parameters . manipulating testosterone levels in young male rats by gonadectomy or exogenous administration to intact the authors of this study make a pertinent argument that testosterone 's effects on hippocampal neurogenesis may be dose and duration - dependent and specific to the developmental stage of newly - generated neurons . in addition , the mode of hormone delivery , repeated injections versus constant release implants likely impacts on serum testosterone levels . hence differences in delivery mode could confound direct comparisons between studies in which serum testosterone levels are reported . this notion is reflected clinically , where testosterone therapy through long - term skin patches could provide better efficacy compared to repeated surges that accompany periodic injections . further potential confounds reside in the methodology used to measure hippocampal neurogenesis , for example intrinsic markers such as ki67 , psa - ncam and doublecortin versus the timing and dose of exogenous markers like brdu . more importantly , the manipulations of testosterone levels in young male rodents in these studies do not recapitulate the late - adult onset and gradual decrease in circulating androgen manifest in normal aging . hence , extrapolating these data to explain a possible causal relationship between low testosterone and declining adult hippocampal neurogenesis in age is limited and specific longitudinal studies examining models of normal aging are required . androgen receptor signal transduction incorporates both genomic mechanisms and non - genomic pathways including ; camp response element - binding protein ( creb ) , extracellular signal - regulated kinase ( erk ) and akt signalling . these non - genomic signalling pathways in particular could represent intrinsic cellular mechanisms by which testosterone directly effects hippocampal neurogenesis . however , despite androgen receptor expression in the dentate gyrus region , whether neural stem cells , transient precursor intermediates or maturing neurons exhibit differential expression is unclear . cultured neural stem cells have been found to express androgen receptor , though these in vitro studies used cells derived from the sub - ventricular zone of adult female rats . hence it remains to be determined if hippocampal neurogenesis can be directly affected by testosterone or whether effects are transmitted by cellular and/or molecular intermediates . the local microenvironment , or neurogenic niche , is considered to play a significant role in regulating neurogenesis levels in the adult hippocampus . astrocytes are an integral cellular component of the neurogenic niche that support hippocampal neurogenesis through mechanisms not fully understood but includes promoting neuronal differentiation and maturation . one mechanism by which astrocytes stimulate hippocampal neurogenesis is through the secretion of soluble neurotrophic factors such as fibroblast growth factor ( fgf)-2 . expression of fgf-2 by astrocytes residing in the hippocampal neurogenic microenvironment decreases during aging and may contribute to the age - related decline in hippocampal neurogenesis . hippocampal astrocytes in male rats express androgen receptor and hence testosterone could influence hippocampal neurogenesis indirectly . testosterone triggers fgf-2 production in germ - line stem cells of the adult male testis that may play a role in spermatogenesis . whether such signalling also occurs in neural stem cells to promote hippocampal neurogenesis and whether reductions in this signalling precipitate age - related decline in hippocampal neurogenesis remains untested . brain derived neurotrophic factor ( bdnf ) is another compound that both maintains and mediates up - regulation of hippocampal neurogenesis in rodents and is decreased in the aged hippocampus . the ability of testosterone to promote survival of adult - generated neurons in adult canaries is mediated by bdnf . however , fluctuations in circulating testosterone during the early development of male mice are independent of hippocampal bdnf levels . studies using aging rats have shown no sex - specific changes in declining hippocampal bdnf levels , nor any correlations between levels of serum oestrogen or testosterone with hippocampal bdnf in aging male rats . the collective evidence would suggest that age - related declining serum testosterone and hippocampal bdnf levels are independent and do not interact to cause falling hippocampal neurogenesis . this association could be important in aging men given the recent findings that circulating bdnf levels are ; higher in aging women compared to men , negatively correlated with age in men and positively correlated with bioavailable circulating testosterone levels in men . these observations raise a possibility that bdnf could be a systemic factor mediating the cognitive efficacy of testosterone therapy . moreover , age - related decline in cellular and molecular elements including signal transduction pathways necessary to mediate testosterone 's effects could significantly impact on the effectiveness of androgen therapy and underscores the importance of their elucidation . the physiological metabolism of testosterone is another important consideration in elucidating the mechanisms of cognitive efficacy . testosterone is metabolised by 5-reductase into the high - affinity androgen receptor ligand dihydrotestosterone and by aromatase into the oestrogen receptors and ligand 17-estradiol . thus , whether it be intrinsic production or the result of exogenous therapy , effects of circulating testosterone can be mediated through either androgen or oestrogen receptors . however , while both androgen and oestrogen mediated signalling contribute to preserving ca1 synaptic density in females , the same effect in males is androgen receptor dependent . although one study using rats showed that testosterone therapy tended to increase circulating levels of 17-estradiol ( albeit a non - statistically significant increase ) , oestrogen activity was not responsible for the increased adult hippocampal neurogenesis . the ability of testosterone therapy to restore declining spatial ability in aging rats was tested in advance of the general acceptance of adult hippocampal neurogenesis . more recent studies administering testosterone to aged rats however , have shown restorative effects on declining spatial ability . moreover , studies examining the effects of androgens on spatial abilities in rodents across life - span have yielded complex results that more generally reflect the collective clinical data examining aging men . the relationship between testosterone levels and different parameters of cognition in aging men has been recently reviewed in detail . decreased circulating testosterone in aging men is linked to poorer performances on tasks requiring spatial ability . several clinical studies show that spatial ability is improved in aging men receiving testosterone therapy . this effect of testosterone is also seen in men suffering mild cognitive impairment and even alzheimer 's disease . however , others have shown no effect of testosterone therapy on cognitive parameters in healthy and mildly cognitive impaired aged men . the magnitude of demonstrated spatial ability improvements have varied and may dependent on the dose of testosterone and the length of therapy . spatial ability varies with endogenous circulating testosterone levels in aging men and appears to respond better to intermediate doses of exogenous testosterone compared low and supraphysiological doses that show no efficacy . circulating 17-estradiol levels could change in elderly men receiving testosterone therapy as a consequence of peripheral aromatisation . however , the efficacy of testosterone therapy on spatial ability in aging men appears to be independent of oestrogen activity , though 17-estradiol may mediate concomitant improvements in verbal memory . prospective clinical studies of prostate health support the idea that both testosterone and 17-estradiol levels impact on male aging . both rodent and clinical studies suggest spatial ability in aged males is enhanced when high testosterone is coincident with low 17-estradiol levels . thus , in parallel with the notion of optimal testosterone levels , is the view that the balance of testosterone and 17-estradiol plays a significant role in spatial ability . debate over the function of adult hippocampal neurogenesis has evolved to include a specific role in pattern separation , which is to encode and retrieve similar events and is linked to dentate gyrus function . the strongest evidence from rodent studies also suggest an association between age - related decline in adult hippocampal neurogenesis and impaired pattern separation ability . given the relative infancy of interest in age - related pattern separation impairment , there is hitherto no definitive evidence for sex differences in the decline of this domain of spatial cognition . it therefore remains possible that testosterone therapy in aging men may preserve pattern separation ability , which could be mediated through maintaining neurogenesis levels in the aging dentate gyrus . the notion that androgens subserve specific domains of mental health includes effects on emotion - based behaviours . furthermore , along with spatial ability , adult hippocampal neurogenesis has also been linked with emotion - based behaviour . a hypothesis based on several associative links posits that impaired adult hippocampal neurogenesis elicits depression and that efficacy of antidepressant interventions is mediated through adult hippocampal neurogenesis . how does a link between depression and adult hippocampal neurogenesis relate to testosterone levels and advancing age ? as with memory loss , age is a risk factor for depression . gender difference in the incidence of depression disappears with advancing age and the occurrence of depression in elderly men is associated with low testosterone . to explore these observations in the context of declining adult hippocampal neurogenesis requires a consideration of a functional distinction in hippocampal structure . the discussion has hitherto observed the classic tri - synaptic circuitry intrinsic to the hippocampus mediated through the interconnectiveness of the dentate gyrus , ca1 and ca3 subregions . however , on a more global level the rodent hippocampus has been regionalised into dorsal ( septal pole or posterior in humans ) and ventral ( temporal pole or anterior in humans ) functional subregions . this regionalisation has partly been based on functional assessments , differential gene expression and connectivity , with spatial ability and emotion - based behaviour preferential to the dorsal and ventral hippocampal regions , respectively . neurogenesis rates may be higher in the dorsal compared to the ventral region of young adult hippocampus , but this regional difference attenuates with advancing age , indicating a relatively higher impact of age on dorsal hippocampal neurogenesis . clinical efficacy of antidepressant treatment is associated with specific increases in adult neurogenesis in the anterior hippocampus in depressed patients . whether androgen deficiency with advancing age differentially affects neurogenesis rates along the septal - temporal axis in the adult hippocampus in parallel with functional deficits such as depression and impaired spatial ability is not known . the question of whether antidepressant and spatial ability efficacy of testosterone therapy for aging men is mediated by region - specific hippocampal neurogenesis remains intriguing . intriguing in part , because addressing this cause - effect relationship will help refine the neurogenesis - depression and neurogenesis - cognition hypotheses and also elucidate links between impaired neural substrates , hypogonadism and symptoms of cognitive dysfunction . this latter point will in turn help define position statements that advocate testosterone therapy based on low testosterone in conjunction with manifest symptoms . clinical studies using testosterone therapy in elderly men showing either benefit or no effect rather than deterioration in cognition have employed inconsistent and even inadequate measures of mental health . a significant point to consider in evaluating this literature is the notion that androgens likely affect mental health in a domain - specific manner . moreover , conclusions drawn from clinical studies will depend significantly on the cognitive measures used . uncertainty as to what biochemically measured level of circulating free testosterone constitutes late - onset hypogonadism and associated symptoms in aging men is a significant impediment to standardised testosterone replacement therapy . the prevailing view that age - related mental health decline is not an indicator for testosterone therapy is because of inconclusive rather than negative evidence . ethical and technical limitations in clinical studies , including varied cognitive assessment methodologies , study inclusion criteria and population size and age range of participants have played a large part in generating this equivocal evidence . this review premises that reduced testosterone is a mediating factor of impaired spatial ability and depression incidence in aging males because of reduced dorsal and ventral hippocampal neurogenesis , respectively . in discussing the known effects of both androgen withdrawal and therapy on hippocampal function and plasticity , it is clear new understanding will be needed to establish a causal relationship between these factors in the context of normal male aging . there remain several key questions concerning the role androgens play in regulating adult hippocampal neurogenesis , including age - related decline and mediation of stimulatory factors such as exercise . an active lifestyle predicts higher circulating testosterone levels in aging men ; could testosterone mediate the ability of physical activity to promote neurogenesis and function in the aged hippocampus ? if so , given that intensity could determine the effects of exercise on testosterone and neurogenesis levels , is aerobic or anaerobic exercise best ? emerging studies showing the cognitive benefit of resistance training in the elderly could provide a paradigm shift in the way physical activity is prescribed to preserve mental health . testosterone promotes synaptogenesis in the ca1 subregion ; does testosterone support synaptogenesis in neurons generated in the aging dentate gyrus ? . menopause - mediated oestrogen withdrawal is posited play a role in cognitive decline and depressive symptoms in women that manifest early than in males . because menopause is a far more precipitous event compared to the gradual decline in male androgen production , what role in maintaining hippocampal neurogenesis and function in aging men does testosterone aromatisation into 17-estradiol play ? the hippocampus expresses receptors for lh and gonadotropin - releasing hormone ( gnrh ) and their role , directly or indirectly through promoting local steriodogenesis , in age - related decline is uncertain . studies examining these questions will address the paucity in knowledge regarding the areas of impaired mental health to which low testosterone predisposes and also elucidate ongoing debate surrounding the clinical relevance of adult hippocampal neurogenesis . new clinical and basic research endeavours that encompass measures of hippocampal - dependent spatial memory , pattern separation and depression in conjunction with serum measures of hpt axis hormones will shed further light on physiological roles of testosterone in maintaining mental health in aging men .

interest surrounds the role of sex - hormones in regulating brain function outside of reproductive behaviour . declining androgen production in aging males has been associated with cognitive impairment , depression and increased risk of developing alzheimer 's disease . indication for testosterone replacement therapy is based on biochemically determined low circulating testosterone combined with manifest symptoms . however , which aspects of age - related cognitive decline are attributable to low circulating testosterone remain ambiguous . studies examining cognition in aging men receiving testosterone replacement therapy have yielded equivocal results . the exact role of testosterone in maintaining cognitive function and the underlying neural mechanisms are largely unknown , though it would appear to be domain specific . clarity in this area will provide clinical direction toward addressing an increasing healthcare burden of mental health decline coincident with increasing longevity . the premise that androgens contribute to maintaining aspects of mental health in aging men by preserving hippocampal neurogenesis will be used as a forum in this review to discuss current knowledge and the need for further studies to better define testosterone replacement strategies for aging male health .

INTRODUCTION ANDROGEN PRODUCTION DURING MALE AGING COGNITIVE IMPAIRMENT WITH ADVANCING AGE ANDROGENS AND HIPPOCAMPAL PLASTICITY AND FUNCTION ANDROGENS AND THE REGULATION OF ADULT HIPPOCAMPAL NEUROGENESIS ANDROGEN RECEPTOR-MEDIATED EFFECTS ON ADULT HIPPOCAMPAL NEUROGENESIS EFFECTS OF TESTOSTERONE THERAPY ON COGNITION IN ELDERLY MEN CONCLUDING REMARKS

some mechanisms involved in cell morphogenesis , such as membrane vesicle transport , are conserved at least among crown eukaryotes ( metazoa , fungi and plants ) , whereas others , such as those involving extracellular structures or the precise roles of different rho - like gtpases , are not . yet other cellular processes , such as cytokinesis , often recruit conserved proteins to accomplish superficially dissimilar tasks ( for example , budding , cleavage or phragmoplast - based cell division of plant cells ) . for many morphogenetic mechanisms , the question of evolutionary conservation remains unresolved because available information is limited to one or a few model organisms . for example , this is the case for the molecular mechanisms that ensure the communication between the cytoskeleton and the surface of the cell . however , the recent increase in the data available from a number of genome projects allows wide - ranging searches for homologs of known components of signaling and morphogenetic pathways . the results of such searches can lead both to experimentally testable hypotheses and to general conclusions regarding the evolution of morphogenetic processes . formins , also known as formin homology ( fh ) proteins , are proteins implicated in cellular and organismal morphogenesis of both metazoa and fungi . on the cellular level , they are involved in the establishment and maintenance of cell and/or tissue polarity , in cytokinesis and in the positioning of the mitotic spindle . they interact directly or indirectly with actin , profilin , rho - like gtpases , the yeast spa2 protein and septins , proteins containing sh3 or ww domains , dynein and microtubules . the yeast formin homolog encoded by bni1 is localized to the cell periphery and participates in positioning cortical actin patches towards distinct regions of the plasma membrane . some kind of contact with the plasmalemma ( in addition to that mediated by a rho - like gtpase ) might therefore be expected , although there is no evidence as yet for such a contact . nothing is known about formin function in plants , although the existence of two arabidopsis thaliana proteins containing the conserved formin - homology 2 ( fh2 ) domain has been reported recently . given that all known formins represent a well - defined family , this class of proteins may be a good candidate for a systematic genome sequence search . here , i present the results of such an approach , which has led to the identification of putative plant formin genes , as well as to the finding that the evolutionarily old formin domain may be used in a number of different ways and contexts ( ' modules ' as defined by hartwell et al . ) by recent eukaryotes . formins are defined by the presence of two sequence domains - the low - complexity , proline - rich fh1 and the carboxy - terminal fh2 . a third domain - the amino - terminal fh3 motif - has been characterized biochemically but is rather poorly delimited in sequence terms . despite a conflicting consensus definition , this motif appears to be identical to the amino - terminal conserved block found in some formins by wasserman . i have used the l - x - x - g - n - x - m - n ( single - letter amino - acid notation ; x is any amino acid ) motif present in the fh2 domain of most fungal and metazoan formins to search for putative arabidopsis formin homologs and found eight such inter - related genes ( see materials and methods and table 1 ) . all of them correspond either to hypothetical open reading frames ( orfs ) or to unannotated genomic or cdna clones , indicating that at least some of them are expressed in vivo . these putative genes and their predicted protein products will be referred to henceforth as atformins 1 to 8 . putative formin - related genes of arabidopsis thaliana orf coordinates refer to the longest putative orf in the first sequence ( first primary accession ) listed . sequence comparison with known formins revealed the presence of genuine fh2 domain in all arabidopsis formins ( figure 1 ) . however , even the longest predicted proteins , encoded by the atformin 3 , -4 and -5 genes , lack parts of the fh2 region ubiquitously conserved among corresponding genes of fungi and metazoa ( figures 1 and 2 ) , although not necessarily among their protein products , because some formin mrnas undergo complex splicing . sequence motifs corresponding to the missing regions were found in all cases within the predicted introns by visual inspection of three - frame translation data . because the reliability of mrna structure prediction is limited , failure to identify exons correctly may explain the apparent deletion of this region of the fh2 domain . the possibly mispredicted intron encoding subdomain g of atformin4 is split by a frameshift mutation , however . although this could reflect a sequencing error , the possibility remains that plant formin homologs have a modular structure within the fh2 domain at the gene level , and that at least some of the fh2-related sequences within predicted introns are vestiges of exons lost by mutation . red dots denote the position of introns ( not shown in mformin , for which only mrna sequence is available ) . numbers indicate positions within the sequence and the size of unaligned insertions ; residues corresponding to unambiguous consensus and/or shared by all arabidopsis formins are highlighted . for gene terminology letters denote subdomain modules with in fh2 as defined in figure 1 . only the ' highly likely ' membrane - spanning segments are shown . surprisingly , there are two such regions in atformins 2 , 6 and 8-a feature not observed in the non - plant formins examined ( listed in materials and methods ) . neither motifs corresponding to fh3 nor coiled - coil regions flanking fh1 ( common but not ubiquitous in non - plant formins ) were found . the structure of fh2 , the overall protein size ( smaller than most non - plant formins ) and the domain layout of arabidopsis formins therefore show possible plant - specific features ( figure 2 ) . this idea is supported by the topology of an evolutionary tree that consistently places arabidopsis formins in a branch separate from other members of the formin family ( figure 3 ) . unrooted evolutionary tree of fh2 subdomains a , c and h constructed by the neighbor - joining method . branches in agreement with the tree previously reported by zeller et al . are highlighted in green , novel branches in yellow . as in the non - plant formins , the amino - terminal portions of all arabidopsis formins are divergent , although there is 63% identity between atformins 1 and 4 in the overlaping parts of their sequences . analysis of atformin sequences with smart revealed no previously characterized domains outside the fh2 region . however , putative amino - terminal membrane insertion signals ( signal peptides ) followed by a segment highly likely to be membrane - spanning and a variable number of possible transmembrane domains were found in atformins 1 , 2 , 4 , 6 and 8 . a possible membrane insertion signal was also identified in atformin5 by one of the two methods used ( see materials and methods , and figures 2,4 ) . the length of predicted signal peptides suggests that they may represent membrane anchors rather than secretion signals . a putative transmembrane segment was also found in the apparently amino - terminally truncated sequence of atformin3 . in contrast , no signal peptides were found in 12 fungal and animal formins listed in materials and methods , although transmembrane - like segments were observed in some . surprisingly , the putative transmembrane segment lies between the two pro - rich regions in atformins 2 , 6 and 8 . obviously , only the cytoplasmic one of these two motifs can act as a conventional fh1 domain . its size ranges from 106 to 423 amino acids , with proline content of 13 to 41% and multiple stretches to five to nine consecutive proline residues . interestingly , the fh1 domains of atformins 2 , 7 and 8 are extremely rich in serine ( up to 20% ) and contain stretches of up to seven consecutive serine residues . putative membrane anchors and transmembrane domains of arabidopsis formins . aliphatic ( i , l , v ) , aromatic ( f , h , w , y ) and other potentially hydrophobic ( a , c , g , k , m , r , t ) amino acids are highlighted the other proline - rich domain of atformins 2 , 6 and 8 is predicted to be exposed to a non - cytoplasmic compartment . given that polyproline stretches are characteristic for a class of structural cell - wall proteins known as extensins , it is tempting to speculate about a possible role for this domain in communication between formins and structures within the cell wall . apart from this , although formins are well conserved with respect to their molecular structure , we do not know the extent of their conservation within signaling or structural modules . as the relationships between protein structure , module structure and biological function are far from straightforward , we can at present neither prove nor exclude the possibility that plant formins contribute to similar functional modules to their animal and fungal counterparts . the question of whether these proteins have a direct role in cytokinesis , in mitotic spindle localization , or in some other cellular process , possibly involving cytoskeleton rearrangement or cell - surface growth , will have to be answered experimentally . a systematic search of the available arabidopsis genomic and cdna sequences revealed the presence of eight genes encoding proteins that define a novel subfamily of the formin family . this indicates a mechanism of membrane localization that may be specific to plants and functionally related to a possible role for formins in the communication between the plant cell and extracellular structures . the initial search for formin homologues in the non - redundant arabidopsis thaliana protein ( nrat ) database , performed using the patmatch program with the query pattern l - x - x - g - n - x - m - n , yielded three potential formin homologs - atformin1 to atformin3 . atformins 2 to 8 were found by a tblastn 2.0 search in genbank , using the predicted protein sequence of atformin 1 as query ( p(n ) values in the range of 5.810 to 1.310 ) . known members of the formin family ( a human diaphanous homolog and drosophila melanogaster cappucino ) were found in the same search ( p(n ) values 110 and 1.310 , respectively ) , verifying the statistical significance of the initial patmatch results . intron positions in the genomic sequences were determined ( or confirmed ) using the netgene2 server . all sequence comparisons were done on a set of 20 metazoan , yeast and plant formin sequences . these were fugu , fugu rubripes formin homolog gb|aac34395.1 ; lformin , mouse lymphocyte - specific formin gb|aado1273 ; bnr1 , yeast bnr1 protein sp|p40450 ; bni1 , yeast bni1 protein sp|p4183 ; fhos , human formin - like protein gb|aad39906.1 ; caeno , caenorhabditis elegans formin homolog gb|aab42354.1 ; cappu , d. melanogaster cappuccino gb|aac46925.1 ; p14omdia and p134mdia2 , mouse diaphanous homologs gb|aac53280 and gb|aac71771.1 ; dia - drome , d. melanogaster diaphanous sp|p48608 ; cyk1 , c. elegans cyk1 assembled from gb|aaa81161.1 and gb|aac17501.1 ; mformin , mouse formin sp|qo5860 ; and atformin 1 to 8 . protein sequences were aligned with the aid of macaw , using the gibbs sampler and segment pair algorithms , blosum45 matrix . only blocks with p<10 were considered . no homology to fh3 as defined by petersen et al . or to the amino - terminal conserved region was revealed by this tool , whereas the fh2 domain was readily identified . consensus of the resulting alignment of fh2 ( deposited in the embl alignment database , accession number ds39866 ) has been calculated for each subdomain separately ( see figure 1 ) by the method of brown and lai . the smart program was used to examine predicted protein sequences for the presence and location of known sequence domains , putative secretion signals , transmembrane segments , coiled - coil motifs and low sequence complexity regions ( usually representing proline - rich fh1 domains whose location was confirmed by visual inspection ) . prediction of signal peptides by the neural network ( nn ) method ) was independently verified by a hidden markov model - based ( hmm ) method on the signalp 2.0 server ) . results of both methods were in agreement , with the exception of atformin5 , which was predicted to be membrane - anchored by nn but cytoplasmic by hmm . the tree ( figure 3 ) was calculated from the three fh2 subdomains present in all formins studied , using programs from the phylip package version 3.573 . an input file was prepared by joining subdomains a , c and h and was used to produce a bootstrapped data set by seqboot with 500 sampling cycles . distances were calculated using protdist with the pam distance matrix , and the results were used for tree construction using the neighbor - joining method by neighbor . the initial search for formin homologues in the non - redundant arabidopsis thaliana protein ( nrat ) database , performed using the patmatch program with the query pattern l - x - x - g - n - x - m - n , yielded three potential formin homologs - atformin1 to atformin3 . atformins 2 to 8 were found by a tblastn 2.0 search in genbank , using the predicted protein sequence of atformin 1 as query ( p(n ) values in the range of 5.810 to 1.310 ) . known members of the formin family ( a human diaphanous homolog and drosophila melanogaster cappucino ) were found in the same search ( p(n ) values 110 and 1.310 , respectively ) , verifying the statistical significance of the initial patmatch results . intron positions in the genomic sequences were determined ( or confirmed ) using the netgene2 server . all sequence comparisons were done on a set of 20 metazoan , yeast and plant formin sequences . these were fugu , fugu rubripes formin homolog gb|aac34395.1 ; lformin , mouse lymphocyte - specific formin gb|aado1273 ; bnr1 , yeast bnr1 protein sp|p40450 ; bni1 , yeast bni1 protein sp|p4183 ; fhos , human formin - like protein gb|aad39906.1 ; caeno , caenorhabditis elegans formin homolog gb|aab42354.1 ; cappu , d. melanogaster cappuccino gb|aac46925.1 ; p14omdia and p134mdia2 , mouse diaphanous homologs gb|aac53280 and gb|aac71771.1 ; dia - drome , d. melanogaster diaphanous sp|p48608 ; cyk1 , c. elegans cyk1 assembled from gb|aaa81161.1 and gb|aac17501.1 ; mformin , mouse formin sp|qo5860 ; and atformin 1 to 8 . protein sequences were aligned with the aid of macaw , using the gibbs sampler and segment pair algorithms , blosum45 matrix . only blocks with p<10 were considered . no homology to fh3 as defined by petersen et al . or to the amino - terminal conserved region was revealed by this tool , whereas the fh2 domain was readily identified . consensus of the resulting alignment of fh2 ( deposited in the embl alignment database , accession number ds39866 ) has been calculated for each subdomain separately ( see figure 1 ) by the method of brown and lai . the smart program was used to examine predicted protein sequences for the presence and location of known sequence domains , putative secretion signals , transmembrane segments , coiled - coil motifs and low sequence complexity regions ( usually representing proline - rich fh1 domains whose location was confirmed by visual inspection ) . prediction of signal peptides by the neural network ( nn ) method ) was independently verified by a hidden markov model - based ( hmm ) method on the signalp 2.0 server ) . results of both methods were in agreement , with the exception of atformin5 , which was predicted to be membrane - anchored by nn but cytoplasmic by hmm . the tree ( figure 3 ) was calculated from the three fh2 subdomains present in all formins studied , using programs from the phylip package version 3.573 . an input file was prepared by joining subdomains a , c and h and was used to produce a bootstrapped data set by seqboot with 500 sampling cycles . distances were calculated using protdist with the pam distance matrix , and the results were used for tree construction using the neighbor - joining method by neighbor . this work has been supported by the grant agency of the czech republic grant 204/98/0482 and by the czech ministry of education program j13/98:113100003 .

background : the formin family of proteins has been implicated in signaling pathways of cellular morphogenesis in both animals and fungi ; in the latter case , at least , they participate in communication between the actin cytoskeleton and the cell surface . nevertheless , they appear to be cytoplasmic or nuclear proteins , and it is not clear whether they communicate with the plasma membrane , and if so , how . because nothing is known about formin function in plants , i performed a systematic search for putative arabidopsis thaliana formin homologs.results:i found eight putative formin - coding genes in the publicly available part of the arabidopsis genome sequence and analyzed their predicted protein sequences . surprisingly , some of them lack parts of the conserved formin - homology 2 ( fh2 ) domain and the majority of them seem to have signal sequences and putative transmembrane segments that are not found in yeast or animals formins.conclusions:plant formins define a distinct subfamily . the presence in most arabidopsis formins of sequence motifs typical or transmembrane proteins suggests a mechanism of membrane attachment that may be specific to plant formins , and indicates an unexpected evolutionary flexibility of the conserved formin domain .

Background Results and discussion Conclusions Materials and methods Identification of Sequence alignment and domain structure analysis Construction of the evolutionary tree Acknowledgements

intermaxillary fixation ( imf ) is a technique utilized in maxillofacial surgery to relate the maxilla and mandible in three dimensions of space . various techniques and methods have been described and utilized in the literature , which include arch bars , imf screws , hybrid imf , orthodontic brackets / buttons , islet wires , embrasure wires , and gunning splints . its applications typically include trauma , orthognathic surgery , and maxillofacial reconstruction , and it serves as an invaluable technique in correctly positioning the maxilla and mandible relative to each other and the facial skeleton . there are factors involved in all of the above - mentioned techniques which can limit its usage , such as in settings where there are insufficient dentition and comminuted dentoalveolar segments , precluding the use of teeth or alveolar bone as anchorage points for imf . this paper reports on a case where traditional methods of imf were unable to be applied due to the nature of the injury , and a novel method was utilized to ensure effective postoperative imf . a 33-year - old male was airlifted to fiona stanley hospital , western australia , with mandibular trauma after being struck in the face with a boating winch . he sustained bilateral condylar neck fractures , comminuted body , and symphyseal fractures with multiple dentoalveolar segment fractures [ figure 1 ] . furthermore , the nature of the fractured segments did not allow for the placement of imf screws as no solid segment was available superior to the depth of the mandibular vestibule . preoperative mandible the mandible was reconstructed through an external approach and placement of a 2.0 reconstruction plate ( depuy synthes , matrixmandible recon ) along the inferior border with bicortical locking screws to establish anatomical reduction . further bicortical screws were used to reduce and secure the sagittal fractures through the mandible and reestablish alveolar width . unsalvageable teeth were removed , and the fractured mandibular incisor dentoalveolar segment was splinted with 25-gauge circumdental wire . to achieve imf to treat the bilateral condylar fractures ( which were unable to be treated with open reduction internal fixation due to the size of the segments ) , two l- shaped bone plates ( depuy synthes , compact 2.0 combi ) were placed on the stabilized mandibular symphyseal segment with the vertical arm emerging through a transmucosal stab incision made in the sulcus [ figures 2 and 3 ] . the most superior hole of each plate was transected to allow for easy application of elastics . in the maxilla , four 8 mm imf screws ( depuy synthes , imf screw set ) were placed between the right and left first premolars . anterior elastic imf was sufficient to guide the mandible into centric occlusion and prevent the development of a class 2 anterior open bite . the patient was placed in imf utilizing heavy elastics for the first 2 weeks postoperatively and was then switched to guiding elastics for a further 4 weeks , which were removed by the patient during the day to facilitate mouth - opening exercises . he was prescribed chlorhexidine 0.2% mouthwash to use three times a day and simple analgesics . at 8-week postsurgery , the patient maintained a class i occlusion and reestablishment of his preexisting overbite and overjet . the bone plates were removed at 8-weeks postsurgery , and there were no complications associated with healing or fixation infection . imf remains an integral technique in maxillofacial surgery in both the intraoperative setting as well as postoperatively . while there is a wide range of commonly utilized techniques to aid in establishing fixation , each has their own contraindications and limitations . the use of bone plates extending through the mucosa appears to be both an effective and safe option without the need for additional equipment and should be considered in cases where traditional forms of imf are unable to be performed .

intermaxillary fixation ( imf ) is an integral technique utilized by maxillofacial surgeons to appropriately reduce and relate maxillary and mandibular fractures to both one another and the facial skeleton . this case report reviews the management of a comminuted mandibular fracture including inoperable bilateral condylar fractures that precluded the use of convention imf techniques necessitating an alternative technique . this was achieved in the form of modified bony plates extending intraorally . postoperative review showed favorable results with occlusion and range of motion comparable to the premorbid function and no unforeseen complications .

I C D Financial support and sponsorship Conflicts of interest

a 43-year - old woman positive for hepatitis b surface antigen was diagnosed as having hepatocellular carcinoma ( hcc ) with two intrahepatic tumor nodules , one nodule 2 cm in diameter in the left lateral segment of the liver and the other nodule 3.5 cm in diameter in the dome . the patient underwent one session of transarterial chemoembolization ( tace ) , followed by percutaneous ethanol injection targeting the area of the residual viable tumor in the liver dome . however , two months later , a viable portion was found to be present at the margin of the nodule in the hepatic dome and the patient was referred to our center . at that time , the laboratory test results included an aspartate transaminase ( ast ) level of 86 iu / l ) , total bilirubin level of 1.0 mg / dl ( reference , 0.2 - 1.2 mg / dl ) and alpha - fetoprotein level of 1,460 ng / ml ( reference , 0 - 20 ng / ml ) . rfa was performed percutaneously under ultrasonographic guidance , with the use of local anesthesia and conscious sedation . a single , 17-g , internally cooled electrode ( valleylab , burlington , ma ) was used and radiofrequency current was emitted for 12 minutes with a 200 w generator set to deliver maximum power with the automatic impedance control method . two ablations were performed with the use of the same method . a follow - up ct scan obtained immediately after rfa showed complete ablation of the hcc without direct evidence of diaphragmatic injury except for a small amount of reactive pleural effusion ( fig . the patient reported pain at the right upper quadrant of the abdomen and right shoulder after rfa and the pain gradually improved over five days with the administration of analgesics . the patient developed a 38.0 fever on the next day after rfa , which subsided after one day . two months after rfa , the patient revisited our hospital with a complaint of a productive cough with large amounts of green - yellow sputum ( up to 200 ml per day ) , accompanied with a 38.4 fever with chills and right upper quadrant abdominal pain . decreases in breath sounds on the right lower lung field and slight tenderness to percussion of the right upper quadrant of the abdomen were noted on a physical examination . plain chest radiograph demonstrated the presence of an ill - defined consolidation in the right lower lobe with right - sided pleural effusion . an abdominal ct scan showed the presence of a liver abscess at the rfa site and pneumonia , with a small abscess in the right lower lung , suggestive of a focal diaphragmatic defect with communication between the lung and liver abscesses ( fig . ultrasonography - guided percutaneous drainage of the liver abscess with a 10.2 fr pigtail catheter was performed and 10 ml of thick dark - yellowish pus mixed with necrotic debris was drained . contrast material injection via the needle demonstrated the presence of opacified cavities of the lung and the bronchial tree communicating with the biliary tree , which was consistent with a bbf ( fig . no organism other than bacillus spp , which is a common contaminant , was isolated from a culture of the drainage material . following catheter insertion and treatment with antibiotics , symptoms including fever and bilioptysis were markedly improved . bile mixed with pus ( 20 to 100 ml daily ) was drained initially , but the rate of drainage gradually decreased to less than 10 ml per day over a month . follow - up abdominal ct scans obtained five weeks after catheter insertion showed the presence of a small residual lesion with low attenuation in the hepatic dome around the catheter , and repeated cholangiography confirmed no leakage of contrast material through the fistula . however , fever and productive cough with sputum containing bile resumed the day after removal of the pigtail catheter . a new cavitary lesion with low attenuation and parenchymal consolidation in the right basal lung were observed on ct images , suggesting reopening of the bbf . a pigtail catheter was reinserted into the remnant abscess in the liver through the previous drainage tract . percutaneous tubography showed filling of the contrast material in the right lower lobe of the lung , with contrast material leakage into the right subphrenic space , indicating the presence of a bbf although there was no definite communication between the biliary and bronchial systems ( fig . thereafter , the amount of percutaneous drainage decreased gradually and the lesions in the liver and lung shrank significantly , as shown on follow - up ct scans three weeks after reinsertion of the pigtail catheter ( fig . as there was no drainage for a week and the patient did not complain of any fistula - related symptoms , the pigtail catheter was removed . four weeks after removal , there was no evidence of a bbf or other related lesions on ct images . two months later , the patient underwent a repeat session of rfa for a recurrent hcc in segment 7 without any treatment - related complications , including a bbf . radiofrequency ablation has been increasingly used for the treatment of primary and metastatic hepatic tumors as an alternative or adjunct to surgical resection . although rfa is a safe modality overall , rfa is associated with minor and major complication rates of 9% ( 9 ) . biliary complications , including stricture and leakage , are relatively uncommon , with a prevalence of 1% ( 9 ) . a bbf as a complication of rfa is extremely rare , with only seven cases reported worldwide ( table 1 ) ( 5 - 10 ) . to the best of our knowledge , no patient with a bbf that occurred after rfa has undergone successful percutaneous drainage leading to complete blockage of the fistula . thus , the present case is the first report of bbf due to rfa that was successfully managed by percutaneous drainage and safe removal of the catheter . a bbf due to rfa may be caused by rupture of a growing biloma into a diaphragmatic defect caused by thermal injury , a finding supported by our imaging results . the proximity of a tumor to the lung base could cause thermal injury to the diaphragm following rfa , and symptomatic biloma formation may develop in patients with large tumors owing to more severe bile duct damage ( 8) . the ablated tumor in our patient was located in the hepatic dome adjacent to the right diaphragm , although the tumor was not large . as described in the present case , clinical findings for a bbf include pneumonitis , fever , chest pain , right upper abdominal pain and cough productive of bile - stained sputum , known as bilioptysis ( 8) . plain chest radiographs often show abnormal findings and may demonstrate right pleural effusion , right basilar atelectasis or the presence of a lung abscess . a ct scan can be used to identify both hepatic abscesses and air within the biliary tree , but images will not delineate a fistulous tract . endoscopic retrograde cholangiography or percutaneous transhepatic cholangiography will adequately demonstrate the presence of a bbf ( 3 , 4 ) . in our patient , we were able to identify the fistula tract with tubography after percutaneous drainage . to date traditionally , the definitive treatment for a bbf has involved extensive surgery , with or without simple drainage of the subdiaphragmatic abscess and resection of the fistulous tract ( 2 ) . the conservative approach that has been reported most frequently has involved the use of endoscopic sphincterotomy with removal of any stones or sludge , followed by stent placement in the common bile duct ( 3 , 5 ) . reduction of the pressure gradient between the common bile duct and the duodenum may lead to preferential drainage of bile through the stent , which then has a lower pressure than the fistula . percutaneous drainage for a bbf not related to rfa has been previously described ( 4 ) . in patients with a bbf complicated with liver abscess , as in our patient , external drainage of an abscess or biloma can facilitate both alleviation of hepatic inflammation and the pressure gradient across the biliary tract and bronchial tree . in all of the previous cases , patients with a bbf following rfa complicated by a biloma or liver abscess underwent external drainage with or without endoscopic drainage ( 6 , 8 , 10 ) . we found that an initial five weeks of percutaneous drainage plus antibiotic therapy was insufficient to clear the fistula tract . hence , long - term drainage maintenance with antibiotics after symptomatic improvement is likely to be required for complete remission of a bbf . in summary , although rfa is a safe and effective modality for the treatment of hcc , the procedure should be performed with caution to prevent bbf formation in patients with liver dome tumors . we report the first case of a bbf as a complication of rfa in a patient with hcc in the liver dome adjacent to the right diaphragm , which was successfully eliminated by percutaneous drainage and antibiotic treatment .

radiofrequency ablation ( rfa ) is a minimally invasive , image - guided procedure for the treatment of hepatic tumors . while rfa is associated with relatively low morbidity , sporadic bronchobiliary fistulae due to thermal damage may occur after rfa , although the incidence is rare . we describe a patient with a bronchobiliary fistula complicated by a liver abscess that occurred after rfa . this fistula was obliterated after placement of an external drainage catheter into the liver abscess for eight weeks .

CASE REPORT DISCUSSION

in june 2007 , investigators visited the veterinary clinic and the household of the index cat and conducted a contact investigation and carrier study . interviews of 2 household members and 8 veterinary staff members indicated no recent respiratory illness , skin infection , or risk factors for diphtheria ( e.g. , travel to countries to which diphtheria is endemic or contact with known case - patients ) . cultures of oropharyngeal swab samples obtained from each person were negative , including cystine tellurite blood agar , which is selective for c. diphtheriae . household members also were interviewed about medical history of a convenience sample of household animals ( 4 cats , including the index cat ; 2 dogs ; and 1 horse ) . each animal was briefly examined , and oropharyngeal , otic , or ocular swab samples were collected . otitis was observed in all 4 cats and 1 dog . animal specimens yielded 3 additional isolates of c. diphtheriae : 1 from each ear of the index cat and 1 from the left ear of a 2-year - old domestic medium - hair cat . both cats had been born on the premises and had remained with the same household since birth . tinsdale agar plate growth ( remel , lenexa , ks , usa ) gave rise to black colonies with a brown halo , typical of cysteinase - producing c. diphtheriae , c. ulcerans , or c. pseudotuberculosis . after 24 hours on blood agar , 12-mm grey - white or opaque , rounded , convex colonies with no hemolysis were observed . microscopically , the bacteria were gram - positive , club - shaped rods , 1 m in diameter , arranged singly or at angles . biochemical profiles to determine species and biotype were done by using an api coryne strip ( biomrieux , durham , nc , usa , and st - laurent , quebec , canada ) . query of api coryne code 0010304 obtained for all isolates by apiweb ( https://apiweb.biomerieux.com ) indicated a decreased level of confidence of c. diphtheriae biotype mitis or belfanti ( 89.5% ) because of a maltose - negative result . isolates were further characterized morphologically and biochemically by using tube substrates ( 2 ) and were identified by using a standard taxonomic scheme ( 3 ) . feline isolates were biochemically identical with each other and phenotypically consistent with c. diphtheriae biotype belfanti , except for the lack of maltose fermentation , which was considered an unusual finding ( 3 ) . * cd , centers for disease control and prevention identifier number ; atcc , american type culture collection ; nd , not deposited in this study ; nctc , national collection of type cultures , london , uk . additional strains used as controls for specific assays : toxigenic c. diphtheriae biotype belfanti isolates used for real - time pcr of tox gene were 718 , g4182 , c59 , c60 , c75 , c76 , c77 ; toxigenic c. diphtheriae atcc 27012 used as positive control for elek ; c. diphtheriae nctc 10481 and c. ulcerans cd199 used as positive and negative controls for vero cell assay . nctc 10356 is described in the nctc catalogue as c. diphtheriae biotype mitis ; however , analyses in this study found this strain to be nitrate negative and therefore consistent with c. diphtheriae biotype belfanti . antimicrobial drug susceptibility testing was performed according to the clinical and laboratory standards institute s recommended methods and interpretative criteria ( 4 ) . all 4 feline isolates were sensitive to ampicillin , cefepime , cefotaxime , ceftriaxone , cefuroxime , chloramphenicol , ciprofloxacin , clindamycin , daptomycin , erythromycin , ertapenam , gatifloxacin , gentamicin , levofloxacin , linezolid , meropenem , moxifloxacin , penicillin , quinupristin / dalfopristin , rifampin , telithromycin , tetracycline , tigecycline , trimethoprim / sulfamethoxazole , and vancomycin . cellular fatty acid composition analysis was performed as described ( 5 ) by using the sherlock system ( midi , inc . , newark , de , usa ) , except that version 4.5 of the operating software was used . the cellular fatty acid composition profiles were consistent for c. diphtheriae , c. ulcerans , or c. pseudotuberculosis , including a substantial proportion ( 28%30% of total ) of c16:17c ( 5 ) . all feline isolates produced 715 meq / l of propionic acid among fermentation products , a feature associated with c. diphtheriae ( 2 ) . results from use of the modified elek test ( 6 ) indicated that all feline isolates were negative for production of diphtheria toxin ; however , an atypical precipitation was observed after 36 h of incubation . lack of toxin expression was corroborated by negative vero cell assay results ( 7 ) and confirmed by using western blot . real - time pcr selective for the c. diphtheriae and c. ulcerans toxin gene ( tox ) ( 8) was positive for all feline isolates . however , real - time pcr for a and b subunits of tox ( 9 ) amplified subunit a but not subunit b. sequence analysis of the tox gene was performed as previously outlined ( 10 ) and compared with a reference tox gene , genbank accession no . the 4 feline tox sequences were identical to each other but contained multiple nucleotide substitutions and deletions compared with the reference gene . by ncbi blast search ( http://blast.ncbi.nlm.nih.gov/blast.cgi ) , the feline tox had higher sequence identity ( 97%98% ) to the tox sequences of c. ulcerans , compared with those from c. diphtheriae ( 94%95% ) . a deletion at nt 55 , coupled with a cytosine - to - thymine substitution at nt 74 , prematurely terminated the peptide at aa 25 . species characterization was corroborated by using 16s rrna ( 11 ) and partial rpob ( 12 ) gene sequencing . by 16s rrna gene sequence analysis , the feline strains had 100% identity with each other and > 99.1% identity with various reference sequences for c. diphtheriae biotype gravis and belfanti sequences , including nctc 11397 . partial rpob sequence analyses indicated 100% identity among the feline isolates and 97.7% identity with c. diphtheriae nctc 11397 . neighbor - joining phylogenetic trees based on both 16s rrna ( figure 1 ) and partial rpob gene sequencing ( figure 2 ) positioned the feline isolate sequences within the c. diphtheriae clade but clearly distinguished them from the other c. diphtheriae isolates . comprehensive molecular analyses to characterize differences between biotype belfanti strains , including these feline isolates , with other c. diphtheriae biotypes , are the subject of a separate publication ( c.g . neighbor - joining phylogenetic tree based on 16s rrna gene sequence analysis of corynebacterium diphtheriae isolates , including 4 feline isolates from west virginia , 2008 ( atcc baa-1774 , cd 448 , cd 449 , cd 450 ) . the tree was constructed from a 1,437-bp alignment of 16s rrna gene sequences by using the neighbor - joining method and kimura 2-parameter substitution model . bootstrap values ( expressed as percentages of 1,000 replicates ) > 40% are illustrated at branch points . feline isolates had 100% identity with each other and > 99.1% identity with c. diphtheriae biotypes gravis and belfanti . atcc , american type culture collection ; cd , centers for disease control and prevention identifier number ; nctc , national collection of type cultures . jukes - cantor derived phylogenetic tree based on sequence analysis of a selected region of the rpob gene of corynebacterium isolates , including 2 feline isolates from west virginia , 2008 ( atcc baa-1774 , cd 450 ) . feline isolates had 100% identity with each other and 97.7% identity with c. diphtheriae biotypes gravis and belfanti . atcc , american type culture collection ; cd , centers for disease control and prevention identifier number ; nctc , national collection of type cultures . we identified a potentially novel biotype of c. diphtheriae recovered from domestic cats in west virginia but found no evidence of zoonotic transmission . although rare , isolation of c. diphtheriae from animals has been reported , including c. diphtheriae biotype belfanti from a skin lesion of a cow ( 13 ) and toxigenic c. diphtheriae biotype gravis from a wound of a horse ( 14 ) . c. ulcerans is a known animal pathogen , and zoonotic transmission of toxigenic c. ulcerans from companion animals has been reported , often associated with predisposing concurrent illnesses ( 15 ) . the feline strains isolated during this investigation differed phenotypically from previously described biotypes but were otherwise regarded as typical of c. diphtheriae . however , isolates were nontoxigenic and harbored a modified tox gene with sequence differences from corynebacterium spp . capable of expressing diphtheria toxin . on the basis of published criteria ( 11 ) , the feline strain might represent a novel subspecies of c. diphtheriae because it shares < 98% sequence homology to the type strain within the rpob gene . potential for zoonotic transmission of this novel , cat - associated c. diphtheriae and associated public health implications are unknown . large - scale screening of domestic cat populations is recommended to determine the prevalence of c. diphtheriae and its pathogenic potential and to identify additional isolates for more formal description and classification .

novel nontoxigenic corynebacterium diphtheriae was isolated from a domestic cat with severe otitis . contact investigation and carrier study of human and animal contacts yielded 3 additional , identical isolates from cats , although no evidence of zoonotic transmission was identified . molecular methods distinguished the feline isolates from known c. diphtheriae .

The Study Conclusions

the global epidemics of obesity and type 2 diabetes have heightened the need to understand the molecular mechanisms that contribute to their pathogenesis . patients with cushing 's syndrome develop central obesity , insulin resistance and in some cases type 2 diabetes ; this has focused attention on the potential pathogenic role of the hypothalamo pituitary adrenal axis , and endogenous glucocorticoid ( gc ) production and metabolism in simple obesity . furthermore , the widespread therapeutic use of gcs means that understanding the mechanisms that lead to their adverse event profile has a huge clinical relevance . gcs cause global insulin resistance . however , there is increasing evidence to suggest that gcs may have tissue - specific effects on insulin action . we have shown that short - term ( 24 h ) treatment with the synthetic gcs , dexamethasone ( dex ) and cortisol , causes insulin sensitization in human adipose tissue , in cells cultured in the absence of insulin . additionally , we have shown that this is functionally important and augments insulin - stimulated glucose uptake . although these observations have contradicted the widely held dogma that gcs cause global pan - tissue ' insulin resistance , it remains plausible that prolonged administration of gcs may have differing effects on insulin signalling . in addition , gc excess leads to hyperinsulinemia , which may further fuel insulin resistance , and high concentrations of insulin may modify the effect of gcs in adipose tissue . we have therefore determined the impact of short- and long - term gc treatment on insulin signalling in adipose tissue at differing insulin concentrations . proliferating chub - s7 cells were cultured in dulbecco 's mem / nutrient mixture f- , dmem - f12 ( sigma , poole , uk ) with 10% fcs and seeded into 12-well plates and grown until confluent . differentiated chub - s7 cells were cultured in media ( dmem - f12 ) without additives for 24 h. cells were then incubated with either 5 or 50 n insulin , with or without 0.5 dex for either 24 h or 7 days . we have previously cultured cells without insulin in the presence and absence of dex , and the purpose of this study was not only to examine the impact of long - term dex treatment , but also to replicate an environment that more closely resembles the physiological situation and includes high insulin concentrations . in all cell culture experiments investigating insulin signalling cascade protein phosphorylation , and in order to activate the insulin signalling cascade , media was spiked with human insulin ( 0.1 g ml , sigma ) for the final 15 min of the treatment period . total rna was extracted using the tri - reagent system and mrna levels or target genes were determined using an abi 7500 sequence real - time pcr detection system ( perkin - elmer applied biosystems , warrington , uk ) . assay on demand ' probes and primers ( perkin - elmer applied biosystems ) were used ( 18s ribosomal rna pre - optimized control probe ) . data were obtained as ct values ( ct = cycle number at which logarithmic pcr plots cross a calculated threshold line ) and used to determine ct values ( ct=(ct of the target gene)(ct of the housekeeping gene ) ) . data are expressed as arbitrary units using the following transformation : expression ( = 10 ( 2 ) arbitrary units ( au ) . fifteen micrograms of protein sample was resolved on a 12.5% sds - page gel and transferred onto a nitrocellulose membrane , hybond ecl ( ge healthcare , chalfont st giles , uk ) . primary ( anti - pkb / akt , irs 1 and irs 2 , upstate , dundee , uk ; anti - pser473akt / pkb , r&d systems , abingdon , uk ; anti - ptyr612irs1 , biosource , nivelle , belgium ) and secondary antibodies ( dako , glostrop , uk ) were used at a dilution of 1/1000 as described previously . membranes were re - probed for -actin ( antibody dilution 1/5000 , abcam plc , cambridge , uk ) . bands were quantified with genesnap ( syngene , cambridge , uk ) . where data were normally distributed , unpaired student 's t - test was used to compare single treatments with control . one - way analysis of variance on ranks was used to compare multiple treatments , doses or times ( sigmastat 3.1 , systat software inc . , point richmond , ca , usa ) . statistical analysis on real - time pcr data was performed on mean ct values and not on fold changes . proliferating chub - s7 cells were cultured in dulbecco 's mem / nutrient mixture f- , dmem - f12 ( sigma , poole , uk ) with 10% fcs and seeded into 12-well plates and grown until confluent . differentiated chub - s7 cells were cultured in media ( dmem - f12 ) without additives for 24 h. cells were then incubated with either 5 or 50 n insulin , with or without 0.5 dex for either 24 h or 7 days . we have previously cultured cells without insulin in the presence and absence of dex , and the purpose of this study was not only to examine the impact of long - term dex treatment , but also to replicate an environment that more closely resembles the physiological situation and includes high insulin concentrations . in all cell culture experiments investigating insulin signalling cascade protein phosphorylation , and in order to activate the insulin signalling cascade , media was spiked with human insulin ( 0.1 g ml , sigma ) for the final 15 min of the treatment period . total rna was extracted using the tri - reagent system and mrna levels or target genes were determined using an abi 7500 sequence real - time pcr detection system ( perkin - elmer applied biosystems , warrington , uk ) . assay on demand ' probes and primers ( perkin - elmer applied biosystems ) were used ( 18s ribosomal rna pre - optimized control probe ) . data were obtained as ct values ( ct = cycle number at which logarithmic pcr plots cross a calculated threshold line ) and used to determine ct values ( ct=(ct of the target gene)(ct of the housekeeping gene ) ) . data are expressed as arbitrary units using the following transformation : expression ( = 10 ( 2 ) arbitrary units ( au ) . fifteen micrograms of protein sample was resolved on a 12.5% sds - page gel and transferred onto a nitrocellulose membrane , hybond ecl ( ge healthcare , chalfont st giles , uk ) . primary ( anti - pkb / akt , irs 1 and irs 2 , upstate , dundee , uk ; anti - pser473akt / pkb , r&d systems , abingdon , uk ; anti - ptyr612irs1 , biosource , nivelle , belgium ) and secondary antibodies ( dako , glostrop , uk ) were used at a dilution of 1/1000 as described previously . membranes were re - probed for -actin ( antibody dilution 1/5000 , abcam plc , cambridge , uk ) . where data were normally distributed , unpaired student 's t - test was used to compare single treatments with control . one - way analysis of variance on ranks was used to compare multiple treatments , doses or times ( sigmastat 3.1 , systat software inc . , point richmond , ca , usa ) . statistical analysis on real - time pcr data was performed on mean ct values and not on fold changes . dex ( 24 h , 0.5 ) increased irs2 and pi3k mrna expression in the presence of both 5 and 50 n insulin ( table 1 ) . insulin - stimulated ptyr612irs1 increased following dex pre - treatment , but this was less marked in the presence of high - dose insulin . total irs1 protein levels were not altered ( figures 1a and b ) , but irs2 protein was increased ( figures 1c and d ) . further downstream , dex treatment for 24 h increased insulin - stimulated ps473akt / pkb , with no alteration in total akt / pkb levels in the presence of either 5 or 50 n insulin ( figures 1e and f ) . in cells that were not spiked with insulin to activate the insulin signalling , dex pre - treatment alone did not alter irs1 or akt / pkb phosphorylation . only in the presence of high - dose insulin ( 50 n ) did dex increase fabp4 mrna expression ( table 1 ) . seven - day dex treatment increased irs2 and pi3k mrna expression in the presence of both 5 and 50 n insulin ( table 1 ) . insulin - stimulated ptyr612irs1 levels increased following dex pre - treatment at both doses of insulin ( 5 and 50 n ) , but total irs1 protein levels did not change ( figures 1a and b ) . however , 7 days treatment with dex increased irs2 protein levels ( figures 1c and d ) . insulin - stimulated ps473akt / pkb in the presence of either 5 or 50 n insulin increased following chronic dex treatment , without changing the total akt / pkb protein levels ( figures 1e and f ) . although not the major purpose of the study , we were able to compare the effects of 5 and 50 n insulin pre - treatment and the duration of pre - treatment on the ability of insulin to activate the insulin signalling cascade . basal samples without any additives were not available for comparison , but have been reported previously . in comparison with 24 h treatment , 7-day exposure to 5 n insulin increased pi3k expression , but decreased akt1/pkb expression . there were no significant differences in gene expression between cells treated with 50 n insulin for either 24 h or 7 days ( table 1 ) . chronic exposure to high doses of insulin is known to cause insulin resistance . in agreement with this , 7 days ( as compared with 24 h ) treatment with high - dose insulin ( 50 n ) decreased insulin - stimulated ptyr612irs1 and akt / pkb protein levels without changing total irs2 protein expression ( figure 2 ) . dex ( 24 h , 0.5 ) increased irs2 and pi3k mrna expression in the presence of both 5 and 50 n insulin ( table 1 ) . insulin - stimulated ptyr612irs1 increased following dex pre - treatment , but this was less marked in the presence of high - dose insulin . total irs1 protein levels were not altered ( figures 1a and b ) , but irs2 protein was increased ( figures 1c and d ) . further downstream , dex treatment for 24 h increased insulin - stimulated ps473akt / pkb , with no alteration in total akt / pkb levels in the presence of either 5 or 50 n insulin ( figures 1e and f ) . in cells that were not spiked with insulin to activate the insulin signalling , dex pre - treatment alone did not alter irs1 or akt / pkb phosphorylation . only in the presence of high - dose insulin ( 50 n ) did dex increase fabp4 mrna expression ( table 1 ) . seven - day dex treatment increased irs2 and pi3k mrna expression in the presence of both 5 and 50 n insulin ( table 1 ) . insulin - stimulated ptyr612irs1 levels increased following dex pre - treatment at both doses of insulin ( 5 and 50 n ) , but total irs1 protein levels did not change ( figures 1a and b ) . however , 7 days treatment with dex increased irs2 protein levels ( figures 1c and d ) . insulin - stimulated ps473akt / pkb in the presence of either 5 or 50 n insulin increased following chronic dex treatment , without changing the total akt / pkb protein levels ( figures 1e and f ) . although not the major purpose of the study , we were able to compare the effects of 5 and 50 n insulin pre - treatment and the duration of pre - treatment on the ability of insulin to activate the insulin signalling cascade . basal samples without any additives were not available for comparison , but have been reported previously . in comparison with 24 h treatment , 7-day exposure to 5 n insulin increased pi3k expression , but decreased akt1/pkb expression . there were no significant differences in gene expression between cells treated with 50 n insulin for either 24 h or 7 days ( table 1 ) . chronic exposure to high doses of insulin is known to cause insulin resistance . in agreement with this , 7 days ( as compared with 24 h ) treatment with high - dose insulin ( 50 n ) decreased insulin - stimulated ptyr612irs1 and akt / pkb protein levels without changing total irs2 protein expression ( figure 2 ) . we have demonstrated that both short - term ( 24 h ) and prolonged ( 7 days ) treatment with gcs have similar effects on insulin action . in both situations , gcs cause insulin sensitization , as evidenced by enhanced insulin - stimulated ptyr612irs1 and ps473akt / pkb levels , without altering total irs1 or akt / pkb expression . also , irs2 mrna and protein expression increased . the impact of gcs on insulin signalling has only been studied in a small number of studies using human models . in omental cells , gcs decrease insulin - stimulated glucose uptake , but are without effect in subcutaneous ( s.c . ) however , detailed analysis of the insulin signalling cascade was not performed in this study . adipocytes , and that insulin - stimulated glucose uptake is enhanced by gc pre - treatment . more recently , studies endorsing our published data have shown that dex treatment ( 48 h only ) in human isolated pre - adipocytes causes insulin sensitization with increased irs1 and akt / pkb phosphorylation . our data extend these findings and suggest that chronic gc exposure ( 7 days ) is also able to insulin - sensitize human adipose tissue . however , there are limitations with the models that have been used . in our own studies adipocyte cell line . in previous papers differentiated cultured adipocytes have been used , and in others intact isolated adipocytes . all these different methodologies can make data difficult to interpret ; however , there still appears to be an emerging consensus that gcs , far from causing insulin resistance in adipose tissue , may actually cause insulin sensitization . a further important caveat is that these are systems examined in isolation and clinical studies are needed to determine the impact of gcs on insulin action in human adipose tissue in vivo . species specificity of response is likely to underpin the discrepancy in observations between rodent models and human studies . however , rodents do not develop the classic cushing 's phenotype that is observed in humans in response to gc administration , and indeed can suffer from weight loss . the results of our study add weight to the body of evidence supporting tissue - specific and species - specific regulation of insulin action by gcs . gcs regulate foxo1a and foxo3a in rodents and humans , and it has been suggested that the gc induction of these transcription factors may lead to increased irs1 expression . however , we observed no increases in irs1 mrna or protein expression even after 7 days of gc treatment this occurs in adipose tissue ( cell lines , primary cultures , and in both s.c.and omental depots ) and skeletal muscle , but is not a consistent finding in rodents . although in some tissues this may be a compensatory mechanism to try to augment insulin signalling in the face of insulin resistance , in human adipose tissue it represents an additional mechanism by which gcs enhance insulin signalling . cushing 's syndrome is a state of hyperinsulinemia , and high insulin concentrations are a cause of insulin resistance ; our data endorse this in human adipose tissue . chronic insulin treatment causes phosphorylation of irs1 at a number of serine residues ( including serine 302 , 307 , 612 and 623 ; rat numbering ) and inhibits function . the aim of our study was not to look specifically at the effect of insulin administration on specific phosphorylation patterns ; however , in our chub - s7 model , 7-day administration of high - dose insulin ( 50 n ) did induce insulin resistance . when we incubated gcs with both 50 and 5 n insulin ( concentrations that are probably in excess of those seen in patients with cushing 's syndrome ) , we still observed insulin sensitization , suggesting that , in human adipose tissue , the impact of gc treatment is able to overcome the insulin - induced insulin resistance . gc - induced adipose tissue insulin sensitization , even in the context of hyperinsulinaemia , will further enhance adipocyte differentiation and lipid accumulation . the depot specificity of action in human adipose tissue remains an important and unanswered question . further investigations to determine the precise molecular events underpinning the tissue specificity of response are now warranted . a better understanding of these mechanisms raises the prospect for the development of novel classes of gc that are therapeutically efficacious , but do not drive adiposity .

background : endogenous or exogenous glucocorticoid ( gc ) excess ( cushing 's syndrome ) is characterized by increased adiposity and insulin resistance . although gcs cause global insulin resistance in vivo , we have previously shown that gcs are able to augment insulin action in human adipose tissue , contrasting with their action in skeletal muscle . cushing 's syndrome develops following chronic gc exposure and , in addition , is a state of hyperinsulinemia.objectives:we have therefore compared the impact of short- ( 24 h ) and long - term ( 7 days ) gc administration on insulin signalling in differentiated human adipocytes in the presence of low or high concentrations of insulin.results:both short- ( 24 h ) and long - term ( 7 days ) treatment of chub - s7 cells with dexamethasone ( dex ) ( 0.5 ) increased insulin - stimulated ptyr612irs1 and pser473akt / pkb , consistent with insulin sensitization . chronic high - dose insulin treatment induced insulin resistance in chub - s7 cells . however , treatment with both high - dose insulin and dex in combination still caused insulin sensitization.conclusions:in this human subcutaneous adipocyte cell line , prolonged gc exposure , even in the presence of high insulin concentrations , is able to cause insulin sensitization . we suggest that this is an important mechanism driving adipogenesis and contributes to the obese phenotype of patients with cushing 's syndrome .

Introduction Materials and methods Chub-s7 cell line RNA extraction, reverse transcription and real-time PCR Protein extraction and immunoblotting Statistical analysis Results Short-term Dex treatment (24h) and insulin signalling in chub-s7 cells Long-term Dex treatment (7 days) and insulin signalling in chub-s7 cells Insulin treatment and insulin signalling in chub-s7 cells Discussion

urinary tract infections are , after respiratory , the most common infection in humans ( 1 ) . at least 80 - 90% of outpatient and 30 - 50% of inpatient urinary tract infections is caused by uropathogenic escherichia coli ( e. coli ) ( 2 ) . specific human populations are at increased risk of developing urinary tract infection ( uti ) . these groups include children , pregnant women , the elderly , postmenopausal women , patients with spinal cord injuries and/or with catheters , patients with diabetes , multiple sclerosis , patients with human immunodeficiency virus ( hiv ) and patients with previous urological abnormalities ( 3 ) . in children with a suspected urinary tract infection , the most common management strategy is to treat empirically with an antibiotic while waiting for results of culture and susceptibility testing . young children are more vulnerable to immediate and long term complications , such as renal scarring and renal failure , and therefore require prompt appropriate treatment . escherichia coli is the most common cause of bacteriaemia and also causes meningitis in neonates ( 4 ) . although urinary tract infections can occur in both men and women , it is more common in adult women than adult men . in addition to frequency , urinary tract infections are also recurrent , and due to the resistance of uropathogenic bacteria to antibiotics , the access to alternative therapeutic procedures is growing ( 5 ) . the high frequency of infections , not only leads to major economic costs , but also to a decrease in labor productivity and high morbidity of patients ( 1 ) . the aim of treatment for acute urinary tract infections is the eradication of pathogens , relief of symptoms , and reduction of the risk of permanent damage to the kidneys . the choice of medicaments for initial , empirical treatment ( pending the outcome of susceptibility testing ) is based on local sensitivities . the sensitivity of bacteria to antibiotics varies in relation to the geographical region , due to frequent use and misuse ( 6 ) . since the discovery of antibiotics and their widespread use , many bacteria have developed mechanisms that make them resistant to some , but in some cases to almost all antibiotics ( 7 ) . in europe , the antimicrobial resistance of gram - negative bacteria is increasing , especially e. coli , which accounts for the majority of invasive gram - negative strains in european countries ( 8) . the contribution of primary healthcare is particularly important as this is where about 80% of all antibiotics used within the health service are prescribed ( 4 ) . continuing education as well as the implementation of effective measures of activities to prevent and control infections may also reduce the occurrence of resistance ( 9 ) . the aim of this study was to determine the frequency of outpatient and inpatient urinary tract infections caused by e. coli and to examine the presence of antimicrobial resistance / susceptibility strains of escherichia coli in inpatients and outpatients . during the period from march 1 until march 31 , 2016 , 3863 urine samples were tested in the region of zenica - doboj canton , bosnia and herzegovina . midstream , clean - catch urine samples were sent to the laboratory for standard urinalysis and culture . the tested material was an urine sample of patients with symptoms of urinary tract infections processed in the microbiological laboratory of the cantonal hospital in zenica and the microbiological laboratory of the general hospital tesanj , bosnia and herzegovina . bacteriological analysis of urine samples included microscopic identification , cultivation , standard biochemical testing and antimicrobial susceptibility testing . urine samples were inoculated on blood agar and endo agar , with incubation of 37c for 24 hours . after the incubation period , we determined the number of bacteria in 1 ml of urine . significant number of bacteria in urine ( > 10 bacteria / ml ) were tested to the basic biochemical reactions characteristic for e. coli , including double sugar , peptone water , mannitol , urea , and citrate . after the detection and identification of bacteria , we approached analyzing antimicrobial susceptibility by disc - diffusion method according to eucast ( the european committee on antimicrobial susceptibility testing ) standards . for susceptibility testing of enterobacteriaceae it is used mueller - hinton ( mh ) agar by disc - diffusion method . in our study , the susceptibility of e. coli was tested on the following antimicrobials : amoxicillin / clavulanic acid ( amc ) 30 mg ( ratio 20:10 ) , cephalexin ( cn ) 30 mg , cefuroxime ( cxm ) 30 mg , ceftazidime ( caz ) 30 mg , amikacin ( ak ) 30 mg , gentamicin ( gen ) 10 mg , ciprofloxacin ( cip ) 5 mg , nitrofurantoin ( nit ) 100 mg , trimethoprim / sulfamethoxazole ( stx ) 5 mg . for the statistical analysis we used spss software program ( statistical package for social sciences ) results of descriptive statistical analysis were broken down according to frequency and presented in absolute numbers and percentages . the shapiro - wilk test was used for testing the significance of differences deviations from the normal distribution . results are presented in tabular form and graphically , and accepted statistical level of significance difference was p<0.05 . the research showed that out of 3863 urine culture examined , 452 ( 11.70% ) was positive and 3411 ( 88.30% ) of tested urine culture was negative . table 1 . shows the frequency of causes for positive urine culture and it can be seen that from a total of 452 samples of positive urine culture , 56.42% of samples were positive on e. coli . there were 13.27% of samples with positive urine culture on proteus mirabilis , followed by 5.31% of samples positive on klebsiella pneumoniae , enterococcus spp ( 4.65% ) , citrobacter spp ( 3.98% ) , enterococcus faecalis ( 3.10% ) and pseudomonas spp ( 2.88% ) . distribution of bacteria in positive urine culture urine cultures positive for e. coli ( 255 ) were isolated in 158 patients . out of 158 patients , 123 ( 77.85% ) based on gender distribution positive test for e. coli was recorded in 142 ( 89.87% ) female patients and 16 ( 10.13% ) male patients . based on the age distribution , patients with isolated e. coli were split in four age groups : age 0 to 6 , age 7 to 18 , age 19 to 60 and age group over 60 . it has seen that 54 patients ( 34.18% ) were in the age group 19 to 60 years , 53 patients ( 33.54% ) were in the age group over 60 years , 36 patients ( 22.78 ) were in the age group 0 to 6 years and 15 patients ( 9.49% ) were in the age group 7 to 18 . based on gender distribution in each age group ( figure 1 . ) significantly lowest incidence is in the age group from 7 to 18 years ( p<0.001 ) . within males , the ratio of gender and age groups of patients with isolated e. coli the susceptibility of e. coli strains to antibiotics of inpatients and outpatients the resistance of e. coli strains to antibiotics of inpatients and outpatients there was no significant difference in susceptibility between the groups any of the antibiotics . the greatest resistance of e. coli strains was observed to trimethoprim / sulfamethoxazole , in both , inpatients ( 48.60% ) and outpatients ( 35.80% ) . the lowest resistance of e. coli strains of inpatients was observed to nitrofurantoin ( 5.70% ) , while the lowest resistance of e. coli strains of outpatients was observed to amikacin ( 0.80% ) . amikacin resistance in inpatients amounted to 17.10% , while in outpatients was 0.80% , therefore there was a statistically significant difference ( p < 0.001 ) . urinary tract infections are one of the most common bacterial infection that can affect the bladder , urethra or kidneys . escherichia coli , as gram - negative bacteria , is the dominant cause and can be easily grown in the laboratory . first , there is fecal contamination of periurethral area , then the bacteria spreads on ascending through the bladder and causes cystitis . these infections of the lower urinary tract , in some cases , can affect the kidneys and cause acute pyelonephritis , which consequently may result in bacteremia and sepsis ( 10 ) . according to our study , of 158 patients with e. coli 142 ( 89.87% ) patients were female and 16 patients ( 10.13% ) were males . there was a statistically significant difference in favor of females ( p < 0.05 ) . malmartel ( 11 ) also in its research conducted in france proved the prevalence of female gender , where 86.4% of e. coli positive urine culture were women . the reason for this may be that , anatomically , women have a shorter urethra which facilitates the ascending spread of bacteria ( 5 ) . by examining the frequency of e. coli in hospital and outpatients , we came to the result that 77.85% were outpatients and 22.15% were hospital patients . ( 12 ) with his study in spain , which included 25 microbiological laboratories also proved that the isolates from the community are more common than the hospital ones . treatment of urinary tract infections is becoming more complicated with an increase of the number of resistant strains to antibiotics and prevalence of antibiotic resistance mechanisms . the majority of strains of e. coli were identified as resistant to the antibiotics such as ampicillin , amoxicillin / clavulanic acid , norfloxacin , cefuroxime , ceftriaxone , and trimethoprim / sulfamethoxazole ( 13 ) . the emergence of antibiotic resistance is a major threat to public health , which is driven by excessive use of antibiotics . antibiotics are among the most frequently prescribed medications in hospitalized patients , which are often prescribed inappropriately . the guidelines recommend avoiding antibiotic therapy in bacteriuria in the absence of symptoms , with a few exceptions , such as pregnancy . despite the recommendations , antibiotic treatment is prevalent and every day contributes to increasing antibiotic resistance , increased costs , and antibiotic side effects , such as clostridium difficile infection ( 14 ) . according to the results of our study , e. coli strains showed the highest antimicrobial susceptibility to amikacin ( 94.94% ) and ceftazidime ( 93.67% ) . the sensitivity of e. coli to cefuroxime was 89.87% , ciprofloxacin 89.24% , gentamicin 89.24% , cefalexin 87.97% , nitrofurantoin 87.97% , amoxicillin / clavulanic acid 74.68% , trimethoprim / sulfamethoxazole 61.39 % , indicating that the e. coli is significantly sensitive to all tested antibiotics ( p<0.01 ; p < 0.05 ) . the greatest resistance strains of e. coli to antibiotics in our study showed trimethoprim / sulfamethoxazole ( 38.61% ) and amoxicillin / clavulanic acid ( 19.62% ) . e. coli resistance to ciprofloxacin was 9.49% , gentamicin 8.86% , cephalexin 8.23% , nitrofurantoin 8.23% , cefuroxime 7.52% , ceftazidime 7.52% and amikacin 4.43% . in research conducted at the department of urology of the university clinical centre in sarajevo , the highest level of resistance of e. coli found on trimethoprim / sulfamethoxazole ( 55% ) and ampicillin ( 53% ) , followed by ciprofloxacin 17% , the in vitro activities of trimethoprim / sulfamethoxazole and amoxicillin / clavulanic acid found in our study suggest that they would provide adequate alternative therapy in locations where trimethoprim / sulfamethoxazole use is no longer prudent because of elevated ( > 10 to 20% ) rates of resistance . bacteria have developed mechanisms of genetic adaptation , and a result of the use of antibiotics is always faster or slower development of resistance . because of the increase in bacterial resistance to antibiotics it is necessary to consistently monitor and be aware of resistance rates for specific pathogens in their own environment . if the resistance to the antibiotic is higher than 20% , the antibiotic should not be prescribed in an empirical antimicrobial therapy ( 16 ) . the current global threat of antimicrobial resistance , an urgent need for it to be controlled , and the discovery of new antibacterial products has prompted many scientists to take measures such as rational use of antibiotics , infection control in health care , the formation of a strategy to reduce risk factors in the environment , the development of rapid diagnostic tests , promoting research on the prevention and control of antimicrobial resistance , the development of new antimicrobial and antibacterial agents strategies , improving awareness of population on the use of antibiotics and the risk of increasing their resistance in order to prevent the development and spread of resistance to antibiotics in the world ( 17 ) . it is not a new problem , but it is becoming increasingly dangerous and requires urgent investment of effort and resources into its resolution ( 18 ) . our research has shown that the largest number of e. coli isolates was found among outpatient population . considering the highest resistance percentages of trimethoprim / sulfamethoxazole and amoxicillin / clavulanic acid , in both , outpatients and inpatients , we can conclude that these agents are not suitable for the empirical treatment of urinary tract infections . from our study , it is evident that unbiased surveillance of pathogens is important for antimicrobial decision - making . unfortunately , such a database is non - existent in zenica - doboj canton , as in other cantons of bosnia and herzegovina . the results of our study indicate the existence of a great need for prevention of urinary tract infections rational use of antibiotics , as well as the multidisciplinary approach to further control the development of resistance .

objectives : the aim of this study was to examine the presence of antimicrobial resistance / susceptibility strains of escherichia coli in inpatients and outpatients.materials and methods : it is a retrospective study carried out at the department of microbiology , parasitology and virology faculty of medicine , university of sarajevo . in cooperation with the microbiological laboratory of the cantonal hospital zenica and the microbiological laboratory of the general hospital tesanj , 3863 urine samples were processed in the period from march 1st to march 31st 2016.results:our study showed that e. coli had the highest antimicrobial resistance to trimethoprim / sulfamethoxazole ( 38.61% ) , followed by amoxicillin / clavulanic acid ( 19.62% ) , ciprofloxacin ( 9.49% ) , gentamicin ( 8.86% ) , cephalexin ( 8.23% ) , nitrofurantoin ( 8.23% ) , cefuroxime ( 7.52% ) , ceftazidime ( 6.33% ) , cefuroxime ( 89.87% ) , amikacin ( 4.43%).conclusions : the isolated strains of e. coli showed the highest resistance to trimethoprim / sulfamethoxazole and amoxicillin / clavulanic acid . the isolated strains of e. coli showed the greatest susceptibility to amikacin and ceftazidime . gender distribution of positive e. coli isolates showed statistically significant differences in favor of females .

1. INTRODUCTION 2. MATERIAL AND METHODS 3. RESULTS 4. DISCUSSION 5. CONCLUSIONS

an aortoesophageal fistula ( aef ) is a rare condition that is frequently fatal and requires emergency treatment . the potential causes of aef include surgery , esophageal reflux , tuberculosis , trauma , corrosive esophagitis , aortic aneurysm , foreign body , or malignancy . irrespective of the cause , the resulting massive upper gastrointestinal hemorrhage requires urgent treatment , such as surgery or embolization . in cases of aef , we report a case of aef with mediastinitis treated using a planned two - stage approach : an initial thoracic endovascular aortic repair ( tevar ) as a bridge to stabilization , followed by esophageal reconstruction surgery . we believe that a two - stage approach is the optimal therapeutic option in certain aef cases . a 52-yr - old man who experienced syncope after severe hematemesis was admitted to the emergency department on september 9 , 2012 . chest computed tomography ( ct ) did not detect any aortic lesions , such as a thoracic aortic aneurysm , while an abscess - like lesion of the esophagus with blood leakage was detected ( fig . 1 ) . therefore , we performed endoscopy to obtain hemostasis of the upper gastrointestinal bleeding . at endoscopy , the blood loss was found to be too severe to manage , and the patient was prepared for emergency surgery . as the patient 's vital signs were unstable , aortography confirmed the presence of a circular mass beside the esophagus at the t9 level . a seal thoracic stent graft ( 30 100 mm , s&g biotech , seoul , korea ) was inserted at the t7 - 10 level , and subsequent aortography confirmed that no bleeding was present ( fig . the patient was monitored for hematemesis in the intensive care unit for 12 hr after surgery . as there was no hematemesis , the patient was transferred to a general ward and prepared for esophageal reconstruction . since concurrent inflammation of the mediastinum was very likely after the white blood cell count and other inflammatory signs normalized , esophageal reconstruction was performed . after preparing for a gastric pull - up through a midline laparotomy , necrosis of the diverticulum was observed directly above the esophagogastric junction , which was found to contain thrombotic masses . the esophagus was dissected until the point beneath the azygos vein ; after resection , an end - to - end anastomosis stapler ( 28 mm ) was used for the esophagogastrostomy . after confirming the location of the l - tube , a 28-fr chest tube was inserted , and the incision was closed . on pathological examination , the subserosal lymphoid tissue in the esophagus showed chronic granulomatous inflammation with caseous necrosis , and polymerase chain reaction analysis of tuberculosis was positive . , this aef was considered to be a complication of tuberculous esophagitis and esophageal diverticulitis . esophagography performed 7 days after the esophageal reconstruction showed a small esophageal anastomotic leak , and esophagogastroduodenoscopy ( egd ) was performed using dermabond to seal the anastomotic leak ( 1 ) . the egd and esophagography were repeated 7 days later and confirmed the absence of anastomotic leakage . subsequently , a soft diet was resumed and anti - tuberculosis treatment initiated ( fig . the patient was discharged 20 days after the esophageal reconstruction and underwent anti - tuberculosis treatment for 9 months after the surgery . based on the results of radiological examinations and a sputum acid - fast bacilli ( afb ) smear and culture , the patient was deemed to be cured of tuberculosis . aortic ct and egd performed 1 and 2 yr postoperatively confirmed that the patient had recovered without any complications . although aef is a rare disease , it requires urgent treatment and can be fatal . in most cases , it involves an aortic aneurysm , and the classical treatment is aortic aneurysm surgery under cardiopulmonary bypass , followed by esophageal reconstruction or closing of the esophagus . however , mediastinitis is also seen in many cases , and the mortality rates associated with aortic aneurysm surgery performed under cardiopulmonary bypass are very high due to contamination of the surgical field ( 2 ) . in recent years , aortic stents have been used to treat such cases ( 34 ) . however , one report stated that the treatment of a thoracic aortic aneurysm using a stent graft can result in aef ( 5 ) . moreover , in cases where mediastinitis is also seen , the infection can progress to recurrent aef . in our case , however , the aef was believed to have been caused by esophageal diverticulum inflammation rather than by an aortic aneurysm . in addition , due to the severe hematemesis , the risk of cardiopulmonary bypass was considered to be high . therefore , an emergency tevar was performed . after excluding the aef and before reconstructing the esophagus , the patient was administered preoperative antibiotic therapy to minimize the complications caused by mediastinal infection . as there have been no reports on the duration of antibiotic treatment , we performed the reconstructive surgery once the white blood cell count , erythrocyte sedimentation rate , and c - reactive protein values were normalized , although this might not be sufficient . the esophageal diverticulum was found to occupy half of the lower esophagus , as assessed by egd , and was accompanied by esophageal inflammation over a wide area ; consequently , primary repair was considered impossible . the upper one - third of the esophagus appeared normal , while the middle and lower thirds showed severe adhesions , edematous changes , and esophageal swelling , although there were no gross signs of infection , such as pus . to ensure that the anastomosis was performed on the normal portion of the esophagus , the anastomosis was performed above the azygos vein . the postoperative anastomotic leakage was believed to be due to the insertion of the aortic stent graft , which reduced the esophageal blood supply . as the anastomotic leakage was the size of a pin point , an endoscopic intervention was considered to be better than a revision thoracotomy . a large portion of aefs are located at the connection between a thoracic aortic aneurysm and the esophagus ; therefore , in such cases , using an aortic stent graft can reduce the risk of bleeding . however , the fistula between the false lumen and esophagus remains intact and can potentially result in complications , such as graft infection . one recent report described a patient with no prior aef who developed an aef after tevar ( 5 ) . in general , tevar involves the use of a stent graft that is slightly larger in diameter than that of the aorta ; the resulting structural friction and reduced blood supply were believed to have caused the aef ( 6 ) . after tevar , depending on the location of the aef , aortic replacement can be performed under cardiopulmonary bypass or under a temporary bypass connecting the left subclavian artery to the distal thoracic aorta . the aef that occurs after tevar is very likely to be accompanied by an aortic stent graft infection ; therefore , the stent graft is removed , and extra - anatomical bypass or aortic replacement surgery is conducted ( 67 ) . tuberculous esophageal disease does not arise primarily in the esophagus , but instead occurs by local extension from a nearby anatomical position ( 8) . compared with other locations in the gastrointestinal tract , if the esophagus and trachea are connected , liquid intake can lead to respiratory symptoms , such as coughing . the systemic symptoms are accompanied by weight loss in many cases . as the symptoms alone can not be used to distinguish such cases from those of esophageal cancer , such complications due to tuberculous esophagitis can lead to the development of fistulas into the mediastinum ( 9 ) . in our case , however , when considering the long - term benefits , the use of tevar remains controversial , and many reports have been published on this subject ( 5 ) . in cases such as ours , when a state of shock is suspected due to sudden , severe hematemesis , tevar can stop the bleeding quickly and accurately . we believe that this is an added value associated with the use of tevar as the primary treatment procedure , which is followed by planned secondary surgery . case reports on secondary surgery of the aorta performed after tevar have also been published ( 10 ) . when an aef is caused by an aneurysm , open surgery might be better than tevar . however , when an aef is caused by lesions in the esophagus , tevar is a good alternative .

an aortoesophageal fistula ( aef ) is an extremely rare , potentially fatal condition , and aortic surgery is usually performed together with extracorporeal circulation . however , this surgical method has a high rate of surgical complications and mortality . this report describes an aef caused by tuberculous esophagitis that was treated successfully using a two - stage operation . a 52-yr - old man was admitted to the hospital with severe hematemesis and syncope . based on the computed tomography and diagnostic endoscopic findings , he was diagnosed with an aef and initially underwent thoracic endovascular aortic repair . esophageal reconstruction was performed after controlling the mediastinal inflammation . the patient suffered postoperative anastomotic leakage , which was treated by an endoscopic procedure , and the patient was discharged without any further problems . the patient received 9 months of anti - tuberculosis treatment after he was diagnosed with histologically confirmed tuberculous esophagitis ; subsequently , he was followed as an outpatient and has had no recurrence of the tuberculosis or any further issues .

INTRODUCTION CASE DESCRIPTION DISCUSSION

most incidental cartilaginous tumours are small and lack suspicious features . small cartilaginous tumours without suspicious findings may be a normal concurrent finding . they are one of the most common osseous neoplasms and are often found incidentally on radiographs , computed tomography or magnetic resonance imaging ( mri ) , especially of the knee . it is important to distinguish them from atypical cartilaginous tumour / chondrosarcoma grade 1 ( act / cs1 ) , which requires surgical treatment . enchondromas are composed of lobules of hyaline cartilage , consisting of benign chondrocytes with or without surrounding reactive bone formation . mutations of isocitrate dehydrogenase 1 ( idh1 ) and idh2 have been identified in enchondromas and chondrosarcomas , in patients with both solitary and multiple neoplasms [ 4 , 5 ] . enchondromas are typically asymptomatic , except in the case of very large lesions which may be painful or may fracture . during routine screening of knee mris for incidental findings , performed in a cohort study to investigate osteoarthritis , cartilaginous tumours because enchondromas are clinically silent , reliable data concerning their incidence and prevalence is scarce [ 1 , 6 ] . the purpose of this study was to describe the prevalence , characteristics and location of incidental cartilaginous tumours on knee mri in a population - based cohort study the netherlands epidemiology of obesity ( neo ) study is a population - based prospective cohort study that includes 6673 individuals aged 45 to 65 years , with an oversampling of individuals deemed overweight or obese . this cohort was designed to prospectively study pathways that lead to disease in such individuals . detailed information about the study design and data collection has been described elsewhere . men and women aged between 45 and 65 years with a self - reported body mass index ( bmi ) of 27 kg / m or higher and living in the greater area of leiden ( in the west of the netherlands ) were eligible to participate in the neo study . in addition , all inhabitants aged between 45 and 65 years from one nearby municipality ( leiderdorp ) were invited , irrespective of their bmi . at baseline , participants completed a questionnaire about demographic and clinical data and underwent an extensive physical examination . in random subsamples of participants without contraindications , mri of abdominal fat , pulse wave velocity of the aorta , heart , brain or right knee was performed . incidental abnormal results with potential health consequences if left undiagnosed were disclosed to the participants and their general practitioners , accompanied by advice for further work - up . the present study is a cross - sectional analysis of the baseline measurements of the 1285 participants with an mri of the knee . the local medical ethics committee approved the study and all participants gave written informed consent . all participants were asked whether they had pain in the right knee during most days of the previous month . weight and height were measured without shoes and with precision of 0.1 cm / kg and 1 kg was subtracted from the weight for clothing . bmi was calculated by dividing the weight in kilograms by the height in metres squared . mri studies were performed on a 1.5-t mri system ( philips , best , the netherlands ) with a dedicated 8-channel knee coil . the following parameters were identical for the tse images : echo train length 6 , a 150160 mm field of view and a 304 512 matrix . sequences acquired were ( 1 ) coronal proton density ( pd ) ( repetition time ( tr)/echo time ( te ) 2335/35 ms ; 3 mm slice thickness ; 0.6 mm interslice gap ) ; ( 2 ) coronal fat suppressed pd tse images ( tr / te 2334/35 ms ; 3 mm slice thickness ; 0.6 mm interslice gap ) ; ( 3 ) sagittal pd tse images ( tr / te 2338/35 ; 3.5 mm slice thickness ; 0.7 mm interslice gap ) ; ( 4 ) sagittal frequency selective fat - suppressed t1-weighted 3d gradient echo ( ge ) sequence ( tr / te 11/5.5 ; 25 flip angle ; 150 mm field of view , 272 512 matrix , 2 mm slice thickness with a 1-mm overlap between images ; no gap ) ; ( 5 ) axial fat suppressed pd ( tse ) images ( tr / te 3225/15 ; 4 mm slice thickness ; 0.8 mm interslice gap ) . total acquisition time was 30 min . a research fellow trained in reading knee mris initially screened all mris for the presence of any abnormality . all lesions possibly fulfilling the criteria set for cartilaginous tumour were assessed by two musculoskeletal radiologists with more than 10 years experience in consensus to determine lesion characteristics . cartilaginous tumours were defined as a smooth or lobulated lesion of geographic bone destruction pattern within the bone marrow with low signal on pd - weighted images and high signal on pd fat - suppressed images . subchondral lesions were excluded , because they may represent subchondral cysts , intraosseous ganglia or subchondral oedema . we included and recorded characteristics of all other osseous lesions that could be bone tumours or tumour - like lesions of bone . for all included lesions we recorded size in three dimensions , shape ( lobulated , oval or round ) , bone destruction pattern i.e. geographic with well - defined or partially ill - defined margins , permeative or moth - eaten . the location was determined to be either central or eccentric and located in the epiphysis , epi - metaphysis , metaphysis and/or diaphysis . the distance of the tumour to the growth plate was classified as a lesion being in contact with the physis , within 2 cm , or further away from the physis . the relationship with the cortex in eccentric lesions was determined ( contact or no contact ) . the presence or absence of superficial ( one - third of depth ) or deep ( at least two - thirds of depth ) scalloping ( i.e. focal resorption of the inner margin of cortical bone ) , cortical bone destruction and periosteal reaction was recorded . signal intensity was scored as low , intermediate or high compared to muscle on both pd and fat - suppressed pd - weighted images . the presence of speckled low signal intensity on both the pd and gradient - echo sequence in the lesion was scored as calcifications . presence or absence of bone marrow oedema in direct contact or within 2 cm from the lesion was noted . participants with lesions that were larger than 20 mm or that had aggressive characteristics ( i.e. cortical bone destruction , periosteal reaction , deep endosteal scalloping , ( partial ) ill definition of margin ) were contacted and referred for dynamic contrast mri to differentiate enchondroma from act / cs1 . large lesion size is a known risk factor for chondrosarcoma but no specific limit is known which optimally differentiates between enchondroma and act / cs1 . we chose a conservative cut - off of 20 mm as a trade - off between increased sensitivity and avoiding unnecessary extra diagnostic procedures . data acquisition was performed during intravenous injection of gd - dtpa ( dose 2 mg / kg body weight , power injector with 2 ml / s ) with a temporal resolution of 3 s. we recorded on electronic subtraction images the time interval between arterial enhancement and the start of lesion enhancement . lesions enhancing within 10 s were classified as early enhancement consistent with act / cs1 , while lesions that did not enhance , or enhanced after more than 10 s were classified as enchondroma . in addition we retrieved follow - up radiographs , and mri studies when these had been performed . changes of described parameters between initial and follow - up mri studies and radiographs were recorded . when the aforementioned features on radiographs or mri suggesting the presence of act / cs1 were present , material was obtained ( curettage or resection ) to allow a histological diagnosis to be made . all involved pathologists had extensive experience with bone tumour pathology owing to the hospital s function as a tertiary referral centre for orthopaedic oncology . characteristics of the lesions were expressed as number of the total number of lesions . in order to correctly estimate the population prevalence of cartilaginous tumours and represent associations in the general population , all other results were based on weighted analyses adjusting for the oversampling of persons with a bmi of 27 this was done by weighing individuals towards the bmi distribution of participants from the leiderdorp municipality , whose bmi distribution was similar to the bmi distribution of the general dutch population . weighted baseline characteristics of the study population were expressed as mean ( sd ) or as percentage . participants were categorized into four groups based on their bmi ( bmi < 25 , 25 bmi < 30 , 30 bmi < 40 and bmi 40 kg / m ) . logistic regression analysis was used to examine the associations of bmi ( both as a continuous variable and as a categorical variable using bmi < 25 kg / m as the reference group ) , age ( continuous ) , sex , and knee pain with the presence of cartilaginous tumours . the netherlands epidemiology of obesity ( neo ) study is a population - based prospective cohort study that includes 6673 individuals aged 45 to 65 years , with an oversampling of individuals deemed overweight or obese . this cohort was designed to prospectively study pathways that lead to disease in such individuals . detailed information about the study design and data collection has been described elsewhere . men and women aged between 45 and 65 years with a self - reported body mass index ( bmi ) of 27 kg / m or higher and living in the greater area of leiden ( in the west of the netherlands ) were eligible to participate in the neo study . in addition , all inhabitants aged between 45 and 65 years from one nearby municipality ( leiderdorp ) were invited , irrespective of their bmi . at baseline , participants completed a questionnaire about demographic and clinical data and underwent an extensive physical examination . in random subsamples of participants without contraindications , mri of abdominal fat , pulse wave velocity of the aorta , heart , brain or right knee was performed . incidental abnormal results with potential health consequences if left undiagnosed were disclosed to the participants and their general practitioners , accompanied by advice for further work - up . the present study is a cross - sectional analysis of the baseline measurements of the 1285 participants with an mri of the knee . the local medical ethics committee approved the study and all participants gave written informed consent . all participants were asked whether they had pain in the right knee during most days of the previous month . weight and height were measured without shoes and with precision of 0.1 cm / kg and 1 kg was subtracted from the weight for clothing . bmi was calculated by dividing the weight in kilograms by the height in metres squared . mri studies were performed on a 1.5-t mri system ( philips , best , the netherlands ) with a dedicated 8-channel knee coil . the following parameters were identical for the tse images : echo train length 6 , a 150160 mm field of view and a 304 512 matrix . sequences acquired were ( 1 ) coronal proton density ( pd ) ( repetition time ( tr)/echo time ( te ) 2335/35 ms ; 3 mm slice thickness ; 0.6 mm interslice gap ) ; ( 2 ) coronal fat suppressed pd tse images ( tr / te 2334/35 ms ; 3 mm slice thickness ; 0.6 mm interslice gap ) ; ( 3 ) sagittal pd tse images ( tr / te 2338/35 ; 3.5 mm slice thickness ; 0.7 mm interslice gap ) ; ( 4 ) sagittal frequency selective fat - suppressed t1-weighted 3d gradient echo ( ge ) sequence ( tr / te 11/5.5 ; 25 flip angle ; 150 mm field of view , 272 512 matrix , 2 mm slice thickness with a 1-mm overlap between images ; no gap ) ; ( 5 ) axial fat suppressed pd ( tse ) images ( tr / te 3225/15 ; 4 mm slice thickness ; 0.8 mm interslice gap ) . a research fellow trained in reading knee mris initially screened all mris for the presence of any abnormality . all lesions possibly fulfilling the criteria set for cartilaginous tumour were assessed by two musculoskeletal radiologists with more than 10 years experience in consensus to determine lesion characteristics . cartilaginous tumours were defined as a smooth or lobulated lesion of geographic bone destruction pattern within the bone marrow with low signal on pd - weighted images and high signal on pd fat - suppressed images . subchondral lesions were excluded , because they may represent subchondral cysts , intraosseous ganglia or subchondral oedema . we included and recorded characteristics of all other osseous lesions that could be bone tumours or tumour - like lesions of bone . for all included lesions we recorded size in three dimensions , shape ( lobulated , oval or round ) , bone destruction pattern i.e. geographic with well - defined or partially ill - defined margins , permeative or moth - eaten . the location was determined to be either central or eccentric and located in the epiphysis , epi - metaphysis , metaphysis and/or diaphysis . the distance of the tumour to the growth plate was classified as a lesion being in contact with the physis , within 2 cm , or further away from the physis . the relationship with the cortex in eccentric lesions was determined ( contact or no contact ) . the presence or absence of superficial ( one - third of depth ) or deep ( at least two - thirds of depth ) scalloping ( i.e. focal resorption of the inner margin of cortical bone ) , cortical bone destruction and periosteal reaction was recorded . signal intensity was scored as low , intermediate or high compared to muscle on both pd and fat - suppressed pd - weighted images . the presence of speckled low signal intensity on both the pd and gradient - echo sequence in the lesion was scored as calcifications . presence or absence of bone marrow oedema in direct contact or within 2 cm from the lesion was noted . participants with lesions that were larger than 20 mm or that had aggressive characteristics ( i.e. cortical bone destruction , periosteal reaction , deep endosteal scalloping , ( partial ) ill definition of margin ) were contacted and referred for dynamic contrast mri to differentiate enchondroma from act / cs1 . large lesion size is a known risk factor for chondrosarcoma but no specific limit is known which optimally differentiates between enchondroma and act / cs1 . we chose a conservative cut - off of 20 mm as a trade - off between increased sensitivity and avoiding unnecessary extra diagnostic procedures . data acquisition was performed during intravenous injection of gd - dtpa ( dose 2 mg / kg body weight , power injector with 2 ml / s ) with a temporal resolution of 3 s. we recorded on electronic subtraction images the time interval between arterial enhancement and the start of lesion enhancement . lesions enhancing within 10 s were classified as early enhancement consistent with act / cs1 , while lesions that did not enhance , or enhanced after more than 10 s were classified as enchondroma . in addition we retrieved follow - up radiographs , and mri studies when these had been performed . changes of described parameters between initial and follow - up mri studies and radiographs were recorded . when the aforementioned features on radiographs or mri suggesting the presence of act / cs1 were present , material was obtained ( curettage or resection ) to allow a histological diagnosis to be made . all involved pathologists had extensive experience with bone tumour pathology owing to the hospital s function as a tertiary referral centre for orthopaedic oncology . characteristics of the lesions were expressed as number of the total number of lesions . in order to correctly estimate the population prevalence of cartilaginous tumours and represent associations in the general population , all other results were based on weighted analyses adjusting for the oversampling of persons with a bmi of 27 kg / m or higher in the neo study . this was done by weighing individuals towards the bmi distribution of participants from the leiderdorp municipality , whose bmi distribution was similar to the bmi distribution of the general dutch population . weighted baseline characteristics of the study population were expressed as mean ( sd ) or as percentage . participants were categorized into four groups based on their bmi ( bmi < 25 , 25 bmi < 30 , 30 bmi < 40 and bmi 40 kg / m ) . logistic regression analysis was used to examine the associations of bmi ( both as a continuous variable and as a categorical variable using bmi < 25 kg / m as the reference group ) , age ( continuous ) , sex , and knee pain with the presence of cartilaginous tumours . between september 2008 and october 2012 , 6673 persons aged 45 to 65 years were included in the neo study , of whom 1285 underwent mri of the right knee . weighted mean ( sd ) age was 56 ( 6 ) years , 45 % were men and mean bmi was 27.1 ( 4.7 ) kg / m . after screening of these 1285 mris , 49 lesions in 44 participants were observed and classified as cartilaginous tumours ( estimated population prevalence 2.8 % , 95 % ci 2.04.0 % ) . four participants had more than one lesion : three participants had two and one participant had three lesions . using logistic regression analysis , we did not find any association between bmi , age or sex and the presence of cartilaginous tumours ( data not shown ) . 1small enchondroma in the distal femur located centrally in the metaphysis and with a typical lobulated appearance : a pd - weighted coronal section , b pd - weighted coronal section with fat saturation . no further imaging was obtained small enchondroma in the distal femur located centrally in the metaphysis and with a typical lobulated appearance : a pd - weighted coronal section , b pd - weighted coronal section with fat saturation . no further imaging was obtained mean lesion size was 12 ( range 2 31 ) mm in the longest axis . thirty - six lesions were lobulated , 12 had a smooth round shape and one was oval - shaped . thirty - eight were located in the distal femur , eight in the proximal tibia , two in the proximal fibula and one in the patella . nineteen tumours were located centrally in the medullary canal and 30 eccentrically ( but still within the medullary canal ) . of all tumours , 27 were located in the metaphysis , 10 in the epi - metaphysis ( crossing the growth plate ) , ten in the diaphysis and one in the epiphysis ( not applicable for the lesion in the patella ) . twenty - nine were in contact with the growth plate , nine crossed the growth plate and ten were located more than 2 cm from the growth plate ( not applicable for the lesion in the patella ) . in 11 lesions there was contact with the cortex and in one lesion there was focal destruction of the cortex . in three cases signal intensity was intermediate on pd images and heterogeneously high on pd - spir images for all lesions . eight lesions in eight participants displayed at least one of the predefined aggressive criteria and were referred for follow - up . seven had a tumour larger than 20 mm ( range 2231 mm ) , including one with deep endosteal scalloping . one participant had a smaller tumour but with focal cortical destruction . in six of the seven participants referred because of tumour size , dynamic contrast mri was performed , while one patient was subsequently lost to follow - up . in four participants there was slow lesional enhancement ( i.e. the interval between arterial enhancement and lesion enhancement was greater than 10 s ) after intravenous gd - chelate administration consistent with benign enchondroma ( fig . 2 ) ; no subsequent follow - up was performed in these patients . in the fifth patient with a lesion of 22 mm , and in the sixth patient with a larger lesion with deep endosteal scalloping , dynamic contrast mri demonstrated a fast enhancement pattern consistent with act / cs1 . curettage and en bloc resection of the tumour were performed respectively , and pathology confirmed the diagnosis of act / cs1 ( fig . 3 ) . the patient with the smaller lesion but with focal cortical destruction had radiographic follow - up and underwent curettage 2 years later , showing an act / cs1 at histology . the three act / cs1s that were found correspond to an estimated population prevalence of 0.4 % ( 95 % ci 0.20.8 % ) .fig . 2large cartilaginous tumour centrally located in the distal femur , referred for follow - up : a axial and b sagittal t1-weighted images , c axial t2-weighted image , d axial and e sagittal t1-weighted images after gadolinium administration with fat suppression . the time signal intensity curve of the dynamic mri ( e ) showed slow enhancement consistent with enchondroma ( pink artery , orange tumour , and blue bone marrow as reference tissue ) . the vertical axis represents relative signal intensity and the horizontal axis represents time in secondsfig . 3large cartilaginous tumour centrally located in the distal femur , referred for follow - up : a axial and b sagittal t1-weighted images , c axial t2-weighted image , d axial and e sagittal t1-weighted images after gadolinium administration with fat suppression . the time signal intensity curve of the dynamic mri ( e ) showed fast enhancement ( < 10 s ) , interpreted as most likely act / cs1 , although chondrosarcoma grade 2 could not be excluded due to extensive presence of mucoid ( pink artery , orange tumour , and blue bone marrow as reference tissue ) . the vertical axis represents relative signal intensity and the horizontal axis represents time in seconds . curettage was performed and histology ( f ) confirmed the presence of cartilaginous tumour with increased cellularity and occasional binucleated cells as well as focal mucomyxoid matrix changes ( left lower area ) , diagnosed as atypical cartilaginous tumour / chondrosarcoma grade 1 large cartilaginous tumour centrally located in the distal femur , referred for follow - up : a axial and b sagittal t1-weighted images , c axial t2-weighted image , d axial and e sagittal t1-weighted images after gadolinium administration with fat suppression . the time signal intensity curve of the dynamic mri ( e ) showed slow enhancement consistent with enchondroma ( pink artery , orange tumour , and blue bone marrow as reference tissue ) . the vertical axis represents relative signal intensity and the horizontal axis represents time in seconds large cartilaginous tumour centrally located in the distal femur , referred for follow - up : a axial and b sagittal t1-weighted images , c axial t2-weighted image , d axial and e sagittal t1-weighted images after gadolinium administration with fat suppression . the time signal intensity curve of the dynamic mri ( e ) showed fast enhancement ( < 10 s ) , interpreted as most likely act / cs1 , although chondrosarcoma grade 2 could not be excluded due to extensive presence of mucoid ( pink artery , orange tumour , and blue bone marrow as reference tissue ) . the vertical axis represents relative signal intensity and the horizontal axis represents time in seconds . curettage was performed and histology ( f ) confirmed the presence of cartilaginous tumour with increased cellularity and occasional binucleated cells as well as focal mucomyxoid matrix changes ( left lower area ) , diagnosed as atypical cartilaginous tumour / chondrosarcoma grade 1 estimated population prevalence of cartilaginous tumours in bmi strata are shown in table 1 . univariate logistic regression analysis did not reveal associations between bmi , age , sex and the presence of cartilaginous tumour , but it was suggestive of an inverse association with knee pain ( table 2 ) . multivariate logistic regression using the same variables showed an inverse association between the presence of knee pain and the presence of cartilaginous tumour but no association with bmi ( as continuous variable ) , age or sex . compared with having a bmi < 25 kg / m , the odds ratio ( or , 95 % confidence interval ) of the presence of cartilaginous tumour associated with a bmi of 2530 kg / m was 1.79 ( 0.38 , 8.51 ) , with a bmi of 3040 kg / m it was 1.69 ( 0.38 , 7.47 ) , and with a bmi > 40 kg / m it was 3.74 ( 0.64 , 21.87).table 1participant characteristics and prevalence of cartilaginous tumours by bmi groupsbmi ( kg / m)<25(35 % ) 2530(44 % ) 3040(19 % ) 40(2 % ) age ( years)56 ( 6)56 ( 6)55 ( 6)53 ( 6)sex ( % women)63466084bmi ( kg / m)22.6 ( 1.5)27.4 ( 1.3)33.3 ( 2.7)42.9 ( 2.4)cartilaginous tumour prevalence ( % ) 1.93.23.17.1knee pain ( % yes)14172327results are based on weighted analysis of the study population ( n = 1285 ) . values are presented as mean ( sd ) or percentagestable 2univariate and multivariate analysis for risk factors of presence of cartilaginous tumoursvariablesunivariate analysismultivariate analysisor ( 95 % ci ) p or ( 95 % ci ) p bmi ( kg / m)1.05 ( 0.971.14)0.2021.06 ( 0.981.14)0.168age ( year)0.97 ( 0.911.04)0.4000.98 ( 0.911.05)0.482sex ( woman)1.20 ( 0.453.14)0.7171.23 ( 0.473.23)0.673knee pain ( yes)0.44 ( 0.181.10)0.0800.40 ( 0.180.93)0.034results are based on weighted analysis of the study population ( n = 1285 ) ci confidence interval , or odds ratio participant characteristics and prevalence of cartilaginous tumours by bmi groups results are based on weighted analysis of the study population ( n = 1285 ) . values are presented as mean ( sd ) or percentages univariate and multivariate analysis for risk factors of presence of cartilaginous tumours results are based on weighted analysis of the study population ( n = 1285 ) ci confidence interval , or odds ratio mean lesion size was 12 ( range 2 31 ) mm in the longest axis . thirty - six lesions were lobulated , 12 had a smooth round shape and one was oval - shaped . thirty - eight were located in the distal femur , eight in the proximal tibia , two in the proximal fibula and one in the patella . nineteen tumours were located centrally in the medullary canal and 30 eccentrically ( but still within the medullary canal ) . of all tumours , 27 were located in the metaphysis , 10 in the epi - metaphysis ( crossing the growth plate ) , ten in the diaphysis and one in the epiphysis ( not applicable for the lesion in the patella ) . twenty - nine were in contact with the growth plate , nine crossed the growth plate and ten were located more than 2 cm from the growth plate ( not applicable for the lesion in the patella ) . in 11 lesions there was contact with the cortex and in one lesion there was focal destruction of the cortex . in three cases signal intensity was intermediate on pd images and heterogeneously high on pd - spir images for all lesions . eight lesions in eight participants displayed at least one of the predefined aggressive criteria and were referred for follow - up . seven had a tumour larger than 20 mm ( range 2231 mm ) , including one with deep endosteal scalloping . one participant had a smaller tumour but with focal cortical destruction . in six of the seven participants referred because of tumour size , dynamic contrast mri was performed , while one patient was subsequently lost to follow - up . in four participants there was slow lesional enhancement ( i.e. the interval between arterial enhancement and lesion enhancement was greater than 10 s ) after intravenous gd - chelate administration consistent with benign enchondroma ( fig . 2 ) ; no subsequent follow - up was performed in these patients . in the fifth patient with a lesion of 22 mm , and in the sixth patient with a larger lesion with deep endosteal scalloping , curettage and en bloc resection of the tumour were performed respectively , and pathology confirmed the diagnosis of act / cs1 ( fig . 3 ) . the patient with the smaller lesion but with focal cortical destruction had radiographic follow - up and underwent curettage 2 years later , showing an act / cs1 at histology . the three act / cs1s that were found correspond to an estimated population prevalence of 0.4 % ( 95 % ci 0.20.8 % ) .fig . 2large cartilaginous tumour centrally located in the distal femur , referred for follow - up : a axial and b sagittal t1-weighted images , c axial t2-weighted image , d axial and e sagittal t1-weighted images after gadolinium administration with fat suppression . the time signal intensity curve of the dynamic mri ( e ) showed slow enhancement consistent with enchondroma ( pink artery , orange tumour , and blue bone marrow as reference tissue ) . the vertical axis represents relative signal intensity and the horizontal axis represents time in secondsfig . 3large cartilaginous tumour centrally located in the distal femur , referred for follow - up : a axial and b sagittal t1-weighted images , c axial t2-weighted image , d axial and e sagittal t1-weighted images after gadolinium administration with fat suppression . the time signal intensity curve of the dynamic mri ( e ) showed fast enhancement ( < 10 s ) , interpreted as most likely act / cs1 , although chondrosarcoma grade 2 could not be excluded due to extensive presence of mucoid ( pink artery , orange tumour , and blue bone marrow as reference tissue ) . the vertical axis represents relative signal intensity and the horizontal axis represents time in seconds . curettage was performed and histology ( f ) confirmed the presence of cartilaginous tumour with increased cellularity and occasional binucleated cells as well as focal mucomyxoid matrix changes ( left lower area ) , diagnosed as atypical cartilaginous tumour / chondrosarcoma grade 1 large cartilaginous tumour centrally located in the distal femur , referred for follow - up : a axial and b sagittal t1-weighted images , c axial t2-weighted image , d axial and e sagittal t1-weighted images after gadolinium administration with fat suppression . the time signal intensity curve of the dynamic mri ( e ) showed slow enhancement consistent with enchondroma ( pink artery , orange tumour , and blue bone marrow as reference tissue ) . the vertical axis represents relative signal intensity and the horizontal axis represents time in seconds large cartilaginous tumour centrally located in the distal femur , referred for follow - up : a axial and b sagittal t1-weighted images , c axial t2-weighted image , d axial and e sagittal t1-weighted images after gadolinium administration with fat suppression . the time signal intensity curve of the dynamic mri ( e ) showed fast enhancement ( < 10 s ) , interpreted as most likely act / cs1 , although chondrosarcoma grade 2 could not be excluded due to extensive presence of mucoid ( pink artery , orange tumour , and blue bone marrow as reference tissue ) . the vertical axis represents relative signal intensity and the horizontal axis represents time in seconds . curettage was performed and histology ( f ) confirmed the presence of cartilaginous tumour with increased cellularity and occasional binucleated cells as well as focal mucomyxoid matrix changes ( left lower area ) , diagnosed as atypical cartilaginous tumour / chondrosarcoma grade 1 estimated population prevalence of cartilaginous tumours in bmi strata are shown in table 1 . univariate logistic regression analysis did not reveal associations between bmi , age , sex and the presence of cartilaginous tumour , but it was suggestive of an inverse association with knee pain ( table 2 ) . multivariate logistic regression using the same variables showed an inverse association between the presence of knee pain and the presence of cartilaginous tumour but no association with bmi ( as continuous variable ) , age or sex . compared with having a bmi < 25 kg / m , the odds ratio ( or , 95 % confidence interval ) of the presence of cartilaginous tumour associated with a bmi of 2530 kg / m was 1.79 ( 0.38 , 8.51 ) , with a bmi of 3040 kg / m it was 1.69 ( 0.38 , 7.47 ) , and with a bmi > 40 kg / m it was 3.74 ( 0.64 , 21.87).table 1participant characteristics and prevalence of cartilaginous tumours by bmi groupsbmi ( kg / m)<25(35 % ) 2530(44 % ) 3040(19 % ) 40(2 % ) age ( years)56 ( 6)56 ( 6)55 ( 6)53 ( 6)sex ( % women)63466084bmi ( kg / m)22.6 ( 1.5)27.4 ( 1.3)33.3 ( 2.7)42.9 ( 2.4)cartilaginous tumour prevalence ( % ) 1.93.23.17.1knee pain ( % yes)14172327results are based on weighted analysis of the study population ( n = 1285 ) . values are presented as mean ( sd ) or percentagestable 2univariate and multivariate analysis for risk factors of presence of cartilaginous tumoursvariablesunivariate analysismultivariate analysisor ( 95 % ci ) p or ( 95 % ci ) p bmi ( kg / m)1.05 ( 0.971.14)0.2021.06 ( 0.981.14)0.168age ( year)0.97 ( 0.911.04)0.4000.98 ( 0.911.05)0.482sex ( woman)1.20 ( 0.453.14)0.7171.23 ( 0.473.23)0.673knee pain ( yes)0.44 ( 0.181.10)0.0800.40 ( 0.180.93)0.034results are based on weighted analysis of the study population ( n = 1285 ) ci confidence interval , or odds ratio participant characteristics and prevalence of cartilaginous tumours by bmi groups results are based on weighted analysis of the study population ( n = 1285 ) . values are presented as mean ( sd ) or percentages univariate and multivariate analysis for risk factors of presence of cartilaginous tumours results are based on weighted analysis of the study population ( n = 1285 ) ci confidence interval , or odds ratio in a cohort study including knee mri to investigate osteoarthritis , we observed incidental lesions that we classified as cartilaginous tumours on the basis of predefined imaging criteria in 2.8 % of individuals between 45 and 65 years of age . these cartilaginous tumours were all smaller than 32 mm , typically smaller than 20 mm and were located near the femoral or sometimes tibial metaphysis . the prevalence of act / cs1 in our population was low ( 0.4 % ) , but we found an act / cs1 in three out of seven participants whom we classified , on the basis of predefined criteria , as high risk of carrying an act / cs1 and had a complete data set . these act / cs1s were present in two participants with tumours exhibiting aggressive features ( deep endosteal scalloping or cortical bone destruction ) and one participant with a tumour of 22 mm and were either resected or removed by curettage . in four other lesions with a diameter of greater than 20 mm the criteria of dynamic mri were consistent with an indolent benign enchondroma . because cartilaginous tumours are typically clinically silent reliable data concerning their epidemiology are scarce . similar to our study , walden et al . reported an enchondroma prevalence of 2.9 % on clinical knee mri . in skeletally immature children undergoing knee mri for a variety of indications , enchondroma prevalence was also 2.9 % . in neither of these two studies was further follow - up performed . our study confirms these results with a similar prevalence of cartilaginous tumours of 2.8 % . however , we also showed that act / cs1s are relatively common among larger tumours and those with suspicious features . in an autopsy case series , a prevalence of enchondromas of only 0.2 % was observed , likely reflecting the higher sensitivity of mri for detecting small lesions . other asymptomatic osseous tumours were not encountered in our cohort , which means that the prevalence of these is , in our age group , less than that of cartilaginous tumours and below 0.1 % . our data did not reveal a clear association with age , sex or bmi as a continuous variable , and an inverse association with knee pain . the latter finding may merely reflect that participants with cartilaginous tumours do not suffer from knee pain . there was a clear trend towards a higher prevalence in higher bmi groups ; however , the number of detected cartilaginous tumours was probably too low to reach a significant association in the logistic regression analysis . the high sensitivity of mri in detecting small cartilaginous tumours on mri performed for other purposes can pose a dilemma to the clinician . the main differential diagnosis of enchondroma is act / cs1 . in high - grade chondrosarcoma , clinical , radiographic and pathological findings generally are apparent and treatment consists of surgical resection with a wide margin . however , differentiating act / cs1 from enchondroma is challenging , especially in the case of incidental asymptomatic lesions found on imaging . suggestions on how to address this dilemma have been made ( table 3 ) . radiographic signs are not useful in further classifying these small enchondromas . in a previous radiograph - based case series , location in the axial skeleton and size greater than 5 cm were the most reliable predictors for low - grade chondrosarcoma , while clinical symptoms and morphologic radiographic features did not have added value . only bone scintigraphy ( intense uptake on delayed images without presence of fracture ) and dynamic gd - chelate - enhanced mri ( start of enhancement within 10 s after arterial enhancement ) have been reported to add information on differentiating enchondroma from act / cs1 [ 1921 ] . we observed mri signs suggestive of chondrosarcoma such as deep endosteal scalloping , cortical destruction and soft - tissue extension in two out of three participants who indeed turned out to have act / cs1 . nevertheless , even with dynamic contrast - enhanced mri , differentiating cartilaginous tumours remains challenging with false - positive findings unavoidable .table 3imaging features reported in literature to be suggestive of chondrosarcomapain related to the tumourlocation in the axial skeletonlarge lesion size ( > 5 cm)lobulated contourill - defined marginenlargement of the medullary cavity and cortical thickeningendosteal scalloping > 2/3 of the cortical thickness or over > 2/3 of the lesion lengthneurovascular involvementliquefactionperitumoral oedema*moth - eaten or permeative osteolysis*spontaneous pathologic fracture*periosteal reaction*cortical destruction*soft - tissue extension*early ( < 10 s ) enhancement on dynamic contrast mriintense uptake on bone scintigraphyfdg - pet high uptake*imaging features reported in the literature making a diagnosis of chondrosarcoma more likely . [ 1721]*features suggestive of high - grade ( grade 1 and 2 ) chondrosarcoma imaging features reported in literature to be suggestive of chondrosarcoma imaging features reported in the literature making a diagnosis of chondrosarcoma more likely . list synthesized from refs . [ 1721 ] * features suggestive of high - grade ( grade 1 and 2 ) chondrosarcoma chondrosarcoma incidence has been estimated at 0.0005 % per year and prevalence at 0.0010.009 % , with only 7 % of those located around the knee [ 2325 ] . in our study we observed an unexpectedly high estimated population prevalence of act / cs1 of 0.4 % . as no further examinations or follow - up were performed when tumours were small and lacked suspicious features , the actual prevalence of act / cs1 may be even higher . thus knee mri performed in participants should be carefully reviewed for the presence of cartilaginous tumours . only small lesions lacking suspicious features may be regarded as a normal concurrent finding on mri . in patients with any of the described suspicious features , the chance of having an atc / cs1 is quite high ( three out of seven in our population ) . the present study was conducted in a cohort study of volunteers . compared to the general population , some may have had a healthier lifestyle , while others may have had more health complaints and participated because of the diagnostic examinations performed as part of the study . furthermore , a large proportion of participants were overweight or obese . to estimate the population prevalence we weighted the analyses towards the bmi distribution of a population comparable to the general dutch population . radiographs were not available for the study group , making it impossible to determine the discrepancy between prevalence on radiographs and mri . however , because the estimated population prevalence in our study was similar to that in earlier studies , we are confident that our results are robust . because of the benign nature of enchondromas , there are no histopathological studies confirming the origin of the otherwise unsuspicious lesions and they are classified as enchondromas solely on imaging findings . as we did not routinely do resections and do not yet have 10-year follow - up , the proof of excluding act / cs1 in the three unsuspicious larger lesions was incomplete . the estimated population prevalence of incidental asymptomatic cartilaginous tumours around the knee was 2.8 % . typically the lesions were less than 20 mm in size , were located within 2 cm of the growth plate and did not cause cortical abnormalities . the prevalence of act / cs1 may be higher than previously thought ( 0.4 % ) . given the high prevalence of enchondromas , as a practical rule we do not advocate further imaging examination or follow - up of accidentally found cartilaginous tumours in patients up to 65 years when the tumours are small ( at most 20 mm ) and suspicious features such as deep endosteal scalloping or cortical destruction are absent . however , when any of these suspicious features are present , or when the lesion is larger than 20 mm in diameter , further analysis is indicated .

objectivesthe purpose was to determine prevalence of enchondromas and atypical cartilaginous tumour / chondrosarcoma grade 1 ( act / cs1 ) of the knee on mri in a large cohort study , namely the netherlands epidemiology of obesity ( neo ) study.methodsparticipants aged 45 to 65 years were prospectively included , oversampling overweight and obese persons . within a subgroup of participants , mri of the right knee was performed and screened for incidental cartilaginous tumours , as defined by their characteristic location and appearance.resultsforty-nine cartilaginous tumours were observed in 44 out of 1285 participants ( estimated population prevalence 2.8 % , 95 % ci 2.04.0 % ) . mean largest tumour diameter was 12 mm ( range 231 mm ) . eight participants with a tumour larger than 20 mm or a tumour with aggressive features were referred to rule out low - grade chondrosarcoma . one was lost to follow - up , three had histologically proven act / cs1 and four had dynamic contrast mri findings consistent with benign enchondroma.conclusionsincidental cartilaginous tumours were relatively common on knee mri and may be regarded as a normal concurrent finding . however , more tumours than expected were act / cs1 . because further examination was performed only when suspicion of chondrosarcoma was high , the actual prevalence might be even higher.key points incidental cartilaginous tumours are relatively common on knee mri. most incidental cartilaginous tumours are small and lack suspicious features. small cartilaginous tumours without suspicious findings may be a normal concurrent finding. large tumours and/or those with suspicious findings should be further investigated. atypical cartilaginous tumour / chondrosarcoma grade 1 was found more often than expected .

None Introduction Materials and methods Study design and study population MRI of the right knee Lesion analysis Dynamic contrast MR Histological diagnosis Statistical analyses Results Lesion characteristics Association of BMI, age, sex and knee pain with presence of cartilaginous tumours Discussion Limitations Conclusion

diabetes therapies can negatively affect health status / health - related quality of life ( hrqol ) because of regimen complexity or rigidity , fear of injections , hypoglycaemia and fear of hypoglycaemia 1,2 . thus , reducing hypoglycaemia and providing a more predictable treatment regimen might be expected to improve hrqol . insulin degludec ( ideg ) is a new basal insulin that offers advantages over previous basal insulins . action profile , an ultra - long duration of action lasting beyond 42 h , and low within - patient variability 3 . seven randomised , open - label , controlled , phase 3 trials of 26- or 52-weeks duration using a treat - to - target non - inferiority design , all confirmed similar glycaemic control for ideg compared to insulin glargine ( iglar ) as expected in treat - to - target trials . however , individual trials , as well as a prospectively planned meta - analysis , showed advantages for ideg over iglar with respect to hypoglycaemia 4 . hrqol , another important treatment outcome , was measured in all of these trials using the sf-36 v2 questionnaire 5 and additional meta - analyses have shown that hrqol 6 , health utility 7 and mental health 8 are improved with ideg compared to iglar . the analysis presented here includes previously unreported data from insulin - nave patients with type 2 diabetes who were studied for a total of 2 years in a 52-week trial with a 52-week extension ; this was the largest of the phase 3 trials in the ideg clinical development programme 9 . as previously reported 10 , at 105 weeks , hba1c was similar for ideg and iglar ( estimated treatment difference [ etd ] 0.12%-points [ 0.01 to 0.25]95% ci , p = 0.078 ) . observed mean reductions in laboratory - measured fasting plasma glucose ( fpg ) were greater with ideg ( etd 0.38 mmol / l [ 0.70 to 0.06]95% ci , p = 0.019 ) . importantly , these improvements in glycaemic control were accompanied by a lower risk of hypoglycaemia over the entire treatment period . nocturnal confirmed hypoglycaemia was 43% lower with ideg than with iglar ( estimated rate ratio [ err ] , ideg / iglar : 0.57 [ 0.40 ; 0.81]95%ci , p = 0.002 ) and rate of severe hypoglycaemia was 69% lower with ideg ( err 0.31 [ 0.11 ; 0.85]95%ci , p = 0.023 ) . overall confirmed hypoglycaemia ( plasma glucose < 3.1 mmol / l or severe ) was similar between ideg and iglar ; estimated rate ratio ( ideg / iglar ) : err 0.84 [ 0.68 ; 1.04]95%ci , p = 0.115 10 . given that the clinical benefit of reduced hypoglycaemia occurred in conjunction with improved glucose control after 2 years of treatment , improvements in hrqol might also be expected . in the original 52-week trial , participants treated with ideg showed improvements in clinical measures and reported greater improvements in overall physical and physical functioning short form 36 ( sf-36 ) scores compared with iglar 9 . the aim of this subanalysis at 105 weeks was to compare ideg versus iglar with respect to change in health status from baseline ( initiation of basal insulin therapy ) in patients with type 2 diabetes , using the sf-36 v2 questionnaire . subjects provided informed consent and re - started treatment with ideg or iglar at the same dose levels at end - of - treatment in the main trial 9 with optional adjustment at the discretion of the investigator . at the end of the core trial , patients were transferred to neutral protamine hagedorn insulin for 7 days to allow for insulin antibody evaluation . the insulin dose at the end of the core trial was used as a starting point , and was titrated to a target fpg of 3.94.9 mmol / l based upon the mean pre - breakfast self - measured blood glucose for the preceding 23 consecutive days . all assessments for efficacy and safety in this extension trial were as described for the core trial 9 . health status was measured at baseline ( time of randomisation of the core trial ) , at 52 weeks , and at 105 weeks using the sf-36 v2 questionnaire . the sf-36 scale is a validated multi - purpose questionnaire that has raw , norm - based scores with a mean ( standard deviation ) of 50 ( 10 ) . the sf-36 questions are grouped into eight domains ( figure 1 ) , including a physical component summary ( pcs ) score and a mental component summary score . patients were provided with instructions and given privacy to complete the questionnaires , which were sealed in envelopes and not reviewed by local investigators or study nurses . scores from the intent - to - treat population were analysed using anova , with treatment , therapy at screening , sex and region as fixed factors , and age and relevant baseline values as covariates . the long study duration was considered sufficient to ensure that any initial patient reporting bias was minimal . as previously reported , 607 ( 79% ) of 773 patients randomised to ideg and 197 ( 77% ) of 257 randomised to iglar completed the core trial of 52 weeks 10 . a total of 551 ( 71% ) of those initially randomised to ideg and 174 ( 68% ) of those initially randomised to iglar continued into the extension study on the core phase treatment allocation , with 505 ( 65% ) of those continuing on ideg and 154 ( 60% ) continuing on iglar completing the entire 104 weeks of treatment . baseline characteristics have previously been reported , and were well - matched between treatment groups 10 . health status results for the full analysis set are summarised in table1 . at 105 weeks , the changes from baseline in overall pcs score , physical functioning score and bodily pain score were statistically significantly ( p < 0.05 ) in favour of ideg compared with iglar , with etds ( ideg / iglar ) of 1.1 [ 0.1 ; 2.1]95%ci , 1.1 [ 0.0 ; 2.3]95%ci and 1.5 [ 0.2 ; 2.9]95%ci , respectively . when only completers were used , scores tended to further improve in favour of ideg compared to the full analysis set , but because of the lower number of respondents and loss of statistical power , only the bodily pain domain remained statistically significant . short form 36 ( sf-36 ) scores at end - of - trial ci , confidence interval ; ideg , insulin degludec ; iglar , insulin glargine ; od , once daily . significantly better ( p < 0.05 ) . data are estimated mean standard error of the mean , full analysis set . the score and change from baseline in the score at 105 weeks were analysed using an ancova model . the statistically significant difference in pcs , physical functioning score in favour of ideg was maintained after 2 years treatment as also reported in the core 52 weeks of the trial 9 . in addition to sustaining the significant difference in pcs and physical functioning , the bodily pain domain also was significantly in favour of ideg after 2 years . these results are consistent with meta - analysis results of previous studies of ideg reporting improvements in sf-36 scores 6 and improvements in health utility versus iglar 7 . similarly , earlier studies have reported improvements in various patient - reported outcomes when iglar was compared against oral therapy or other basal insulins 11 . with respect to the clinical implications of these results , in diabetes , it has been estimated that a 1-point difference on pcs and physical functioning scores , for example , is associated with a 59% increase in mortality risk , a 24% increased risk of hospitalisation within 6 months and a 712% increased risk of being unable to work 12 . although the sf-36 does not have an established minimal important difference in diabetes , the sf-36 v2 user manual suggests that even small differences in these compressed scores ( < 1 ) are relevant in other chronic diseases . the precise reason for the improvement in sf-36 scores has not been determined . however , as mentioned earlier , ideg has been shown to have a beneficial effect on hypoglycaemia compared to iglar 4 . hypoglycaemic events , both non - severe and severe , are known to be a key marker for reduced hrqol in diabetes 1 . also , the sf-36 physical functioning score includes measures of vigorous activity , which may be enhanced if hypoglycaemia is less of a concern . given that clinical trials exclude people at high risk of hypoglycaemia , the benefit may be even greater in real - world settings . although an open - label design could have affected results of this study , the baseline values for sf-36 were collected prior to randomisation , and the long duration of the main trial plus extension study should have allowed any bias associated with initiation of a particular therapy to be minimised . this study emphasises that patient - reported outcomes , which are an important measure of any diabetes treatment , can be improved with ideg . h. w. r. has received grants / research support from amylin , eli lilly , merck and sanofi - aventis ; served as a consultant for biodel ; served on advisory panels of amylin pharmaceuticals , roche diagnostics , astrazeneca , biodel , novartis , novo nordisk , janssen , bristol - myers squibb and sanofi - aventis ; served on the speakers bureau for amylin pharmaceuticals , astrazeneca , bristol - myers squibb , boehringer ingelheim , eli lilly , merck and co. , and novo nordisk . b. c. has served on the advisory panel for eli lilly and company , genfit , novo nordisk and sanofi - aventis and received grants / research support from novo nordisk and sanofi - aventis . b. z. has served on the advisory panel for eli lilly and company , novo nordisk , and sanofi - aventis and received research support from novo nordisk . y. h. has received grants / research support from boehringer ingelheim , conjuchem , daiichi sankyo , glaxosmithkline , lexicon , novo nordisk , takeda , sanofi - aventis , xoma , and tolerx ; served as consultant for amylin pharmaceuticals , daiichi - sankyo , gilead , genetech , glaxosmithkline , novo nordisk , merck , xoma , tolerx , janssen , halozyme , amarin , liposcience and santarus ; served on speakers bureau for amylin , astrazeneca , boehringer ingelheim , bristol - myers squibb , daiichi - sankyo , eli lilly , glaxosmithkline , novo nordisk , and santarus ; and is president of the american association of clinical endocrinologists . m. l. w. and a. r. are employees of novo nordisk and own stock in the company . c. m. has served on the advisory panel for novo nordisk , sanofi - aventis , merck sharp and dohme ltd . , eli lilly and company , novartis , bristol - myers squibb , astrazeneca lp , pfizer , johnson and johnson , and mannkind ; has received research support from novo nordisk , sanofi - aventis , merck sharp and dohme ltd . , eli lilly and company , and novartis ; and has served on the speakers bureau for novo nordisk , sanofi - aventis , merck sharp and dohme , eli lilly and company , and novartis . all authors ( h. w. r. , b. c. , b. z. , y. h. , m. l. w. , a. r. and c. m. ) were involved in critical analysis and interpretation of the data , drafting / critically revising the article and shared in the final responsibility for the content of the manuscript and the decision to submit it for publication .

insulin degludec ( ideg ) is a new basal insulin with an ultra - long and stable glucose - lowering effect . we compared once - daily ideg and insulin glargine ( iglar ) , both in combination with metformin dipeptidyl peptidase-4 inhibitors , in a 52-week , open - label , treat - to - target trial in patients with type 2 diabetes followed by a 52-week extension trial in which subjects [ n = 725/1030 ( 70.4% ) ] maintained their initial randomised treatment . health status was assessed at baseline and 105 weeks using the short form-36 ( sf-36 v2 ) questionnaire . sf-36 scores were analysed ( itt population ) using anova , with adjustments for covariates . at 105 weeks , the overall physical component score was significantly better with ideg versus iglar [ treatment contrast ( tc ) : 1.1 ( 0.1 ; 2.1)95%ci , p < 0.05 ] . this was largely because of significantly better physical functioning [ tc : 1.1 ( 0.0 ; 2.3)95%ci , p < 0.05 ] and bodily pain sub - domain scores [ tc : 1.5 ( 0.2 ; 2.9)95%ci , p < 0.05 ] . improvements in health status with ideg compared to iglar were maintained after 2 years .

Introduction Methods Results Discussion Conflict of Interest Author declaration

currently , one of the biggest worries of our society is the future of the climate . common belief supported by an impressive 97% consensus is that our planet is heating up at an accelerated rate , caused by the rapid increase in carbon dioxide ( co2 ) concentration in the atmosphere , henceforth called [ co2 ] . this increased carbon dioxide finds its origin in human activity ; humans burn fossil fuels , thereby injecting large quantities of carbon into the troposphere by converting it into co2 . the co2 contributes to the greenhouse effect of our atmosphere and it is believed that the anthropogenic co2 will heat up the planet by up to six degrees during this century ( page 45 of ipcc 2007 report ) . here for that , while the subject is the atmosphere , we do not have to go into much detail of atmospheric science . there are observations one can make about climate systems , even without going into technical details . the model of anthropogenic global warming ( agw ) stands or falls with this idea that temperature t is strongly correlated to [ co2 ] by the so - called greenhouse effect . even though it is highly questionable to summarize the entire climate system in these two scalar properties both [ co2 ] and t show fractal - like variations in space and time this is often done . the contribution of co2 to the greenhouse effect can easily be estimated to be about 3.6% . the total greenhouse effect is also well known ; without our atmosphere our planet would be 32 degrees colder , as can be calculated on basis of a radiation balance and albedo of our planet . we arrive at a similar value if we use statistics and do a linear regression on contemporary [ co2 ] and temperature data , the maximum of the effect we can thus expect in a linear model when doubling the concentration artificially by burning up fossil fuels . this is below the global warming models even if we were to use a linear model . that is because the greenhouse effect is governed by absorption of light which is expected to follow the beer - lambert law : the absorption is highly sublinear ; twice as much co2 will not cause twice as much absorption . the classical arrhenius ' greenhouse law actually states that the forcing is logarithmic . yet , later models incorporating nonlinear positive - feedback effects as proposed by many climate scientists do predict a super - linear behavior and come up with an estimate of between 1.1 and 6.4 degrees heating for the next century as caused by our carbon dioxide injection into the atmosphere . the positive feedback can come from secondary effects such as an increase in water in the atmosphere , a strong greenhouse agent , or a co2-degassing of ground in the permafrost regions when these thaw . climate scientists are basing these conclusions mainly on research of the so - called finite - elements type , dividing the system in cells that interact , the same way the weather is studied . such systems are complicated , but by tuning the processes and parameters that are part of the simulations they manage to explain the actual climate data to an impressive accuracy , as evidenced by the quality of pictures presented in the official climate reports ; see , for example , the ipcc 2007 report where simulation and reality are as good as indistinguishable , and , moreover , alarmingly , they conclude that the recent rise in temperature can only be attributed to co2 . yet , the problem with such simulations is that even if they do simulate the past , no insight is gained into the system unless the simulations themselves are analyzed ; that is , we have just deferred the problem . this kind of simulations , if not properly analyzed and interpreted , could be in fact a devastating tool for the progress of understanding . from a philosophical point of view , the fact that the past was explained very accurately does not guarantee the same quality for the prediction of the future . small deviations in parameters and initial conditions or assumptions made in the simulations can cause huge changes in the outcome . if we have a chaotic circuit with , for instance , critical feedback , we can go to our spice or cadence simulator and find the parameters of our components that exactly explain the behavior of our circuit , so far so good . the problem is that if we now go back and switch on the same circuit , we will get a different result . ( just take an operational amplifier with 100% positive feedback , in the saturated state , the output voltage may reach the positive supply voltage as easily as the negative supply voltage , either case can be simulated . ) an additional problem is that even the parameters themselves are not constant and seem to change without any apparent reason , for instance , the el nio phenomena in the climate . this is one of the reasons electronic engineers talk about phase margins , the zone in nyquist plots , real versus imaginary parts of gain , that should be avoided because the circuit will become unpredictable even if it may be simulated perfectly . in fact , recent temperature data fall way out of the prediction margins of earlier models . in view of the discussion above , this does not come as a surprise . where extrapolation from the 2007 ipcc report predicted 2011 to be a year with an anomaly of close to one degree ( 0.95c is our personal estimate based on figure 2.5 of the ipcc 2007 report ) , in reality the anomaly is closer to zero . since 1998 , the hottest year in recent history , the planet has actually been cooling , something that was not foreseen by the predictions of 2007 where a continuing exponential increase in temperature was forecasted by the then generally accepted model . the scientific community is now going back to its drawing boards and fine - tunes its models to new perfection and manages to simulate the new data as well . the correctness of this statement is evidenced by the fact that there now apparently exist many models that explain the data up to a certain point in time ; every correction of the model that is still consistent with earlier data proves this . apparently , there is a manifold of models that can explain certain data quite satisfactorily ( but that diverge for future predictions ) . in view of this , one should be reluctant in making strong claims about the correctness of any model . just like in the weather , where the same simulation - evaluation techniques are used , we can only hope to get the predictions reasonably under control after thousands of iterations between predictions and reality . before we get it right , it will take at least some hundreds of centuries if we uniquely use the approach of finite - elements calculations on supercomputers . in the meantime , we should not see any climate models as proven indisputable facts . a skeptic approach to any scientific model is not an illness ; it is an essential ingredient in science . theories are correct until proven wrong . ideas that stand up to scrutiny are more likely to be correct than ideas one is supposed not to question . still , undeniably , a strong correlation is found between the co2 concentrations and the temperatures as measured by gas - analysis in drillings in ice shelves ; see , for example , the data of the pangaea project suggesting that one is the function of the other for the past hundreds of thousands of years . however , proving only statistical correlation , it is not clear from these data which one comes first . generally , correlation does not mean causation : in particular , in our case , are temperature variations the result of [ co2 ] variations , or vice versa ? while the data are consistent with the model of agw , they can not serve as proof of these models . in fact , upon closer scrutiny , the temperature always seems to be ahead of co2 variations . see figure 1 , where a detail of the temperature and [ co2 ] history as measured by ice - trapped gases is plotted , picturing the most blatant example of this effect . a simulation ( dashed line ) is also shown with an exponential - decay convolution of 15 kyr , quite adequately reproducing the results . indermhle and coworkers made a full statistical analysis and find a value of 900 yr for the delay and moreover note that this value is roughly in agreement with findings by fischer et al . who reported a time lag of co2 to the vostok temperature of ( 600 400 ) yr during early deglacial changes in the last 3 transitions glacial - interglacial . this is inexplicable in the framework of global warming models and we honestly start having some legitimate doubts . the apparent time lag may possibly be due to a calibration problem of the measurements , and indeed corrections have been made to the data since then , to make [ co2 ] variations and temperature variations coincide . while these corrections are the result of circular reasoning where the magnitude is found by modeling the behavior of ice based on climate models and the climate models are based on the ice behavior these corrections are not even sufficient to remove our doubts . if the correlations are true and we continue to claim that temperature variations are the result of [ co2 ] variations , something is still not correct . the vostok data of figure 1 show a sensitivity of 10 degrees for 50 ppm [ co2 ] . note that contemporary [ co2 ] variations are of the order of 80 ppm rise from the preindustrial value . we are thus in for a 16-degree temperature - rise . the fact that we did not reach that level means that either co2 is not climate forcing , or that there is a delay between [ co2 ] variations ( cause ) and temperature variations ( effect ) . to then get a rough idea of the magnitude of this delay , in 25 years , only 2.5% ( 0.4 of 16 degrees ) of this rise occurred . the relaxation time is thus ( 25 years)/ln(0.975 ) , which is about 1000 years . in other words , either the vostok plots should show a delay between [ co2 ] and t of the order of 1000 years , or the carbon dioxide is not climate forcing . the data , however , show a delay of 900 years or zero , the latter value resulting from questionable corrections . as far as we know , no correction was proposed to result in the + 1000 yr delay necessary to explain contemporary behavior . what is more , modern correlation figures such as those given in figure 1 also include methane ch4 ( available at noaa paleoclimatology ) and , remarkably , this methane shows the same correlation with [ co2 ] and t. this leaves us flabbergasted . we know that methane is also ( assumed to be ) a strong climate - forcing greenhouse agent . the enigma is , then , how did the information from the [ co2 ] variations percolate to [ ch4 ] variations ? was this information from [ co2 ] transmitted to the methane through the temperature variations ? in other words , [ ch4 ] variations are the result of t variations , rather than their cause ? then we may equally assume that [ co2 ] variations are the effect of t variations rather than their cause . there are several mechanisms that may explain such an inverse phase relation , such as outgassing of co2 ( and ch4 ) from the warming oceans and thawing permafrost ; the correlation between [ co2 ] and [ ch4 ] then stems from a common underlying cause . if that is the case , artificially changing the co2 in the atmosphere will not change the temperature of our planet , just like heating up a can of soda will liberate the gases contained therein into the atmosphere , while increasing the concentrations of gases above the can of soda will not raise its temperature . this unidirectional relation between temperature and gas concentrations is what is called henry 's law ; the ratio of concentrations of gas dissolved in the liquid and mixed in the air above it in equilibrium is a parameter that depends on temperature . al - anezi and coworkers have studied this effect in more detail in a laboratory setup under various conditions of salinity and pressure , and so forth . for co2 in and above water an increase in temperature will cause outgassing with a proportionality that is consistent with the correlation found by the historic correlations of global temperature and co2 in the atmosphere . also , fischer and coworkers find the delay of [ co2 ] relative to t , as discussed above , likely caused by this ocean outgassing effects and find that at colder times , the delay is longer , which is itself consistent with arrhenius - like behavior of thermally - activated processes , characteristic of the vast majority of chemical reactions occurring in nature . in the presence of an alternative explanation , there is room for doubt in the agw ideas that increased [ co2 ] will cause an increased temperature . inspired by this uncertainty in the ( anthropogenic ) global warming model , we tried to see if we can find more evidence for this failure of the cause - and - effect idea . we looked at the recent historic climate data ( from just before the agw model prevalence ) and meticulously measured [ co2 ] data and came to the same conclusion , as we will present here . we started with the data of a climate report from before the global warming claims . we deem these data more reliable since they were for sure not produced under the tutelage of a political committee ( ipcc ) . at least we are more convinced about the neutrality of the scientists reporting these data . moreover , the work contains all the useful data and these are even available online . the ideas presented here do not need recent data and thus we refrained from looking at them altogether . the authors of the work , balling and coworkers , analyzed the global warming ( without capitals because it is not the name of a model ) and concluded the following : our analysis reveal a statistically significant warming of approximately 0.5c over the period 1751 to 1995 . the period of most rapid warming in europe occurred between 1890 and 1950 , no warming was observed in the most recent half century . note that at the onset of the global warming ideas , no warming was observed that can be correlated to the ( accelerated ) increase of [ co2 ] . note also that since 1998 it has not warmed up at all , as confirmed by satellite data ( 1998 was the warmest year ) , in spite of the continuing exponential increase in atmospheric co2 . coworkers then went on to analyze the increase in temperature as a function of the time of the year for the data between 1851 and 1991 . the first thing we note is that , while there has been an average of warming , this is not spread equally over the year . in fact , summer months have become cooler . without knowing the underlying reason , this is remarkable , since [ co2 ] there are seasonal fluctuations of the co2 concentrations ; see the black dots which represent the monthly [ co2 ] fluctuations relative to the yearly average at the mauna loa site ( source : noaa , visited 2008 ) . these rapid fluctuations are mainly attributed to biological activity ( the northern hemisphere has more land and in colder times in winter more plants are converted into co2 and in warmer times in summer more photosynthesis takes place converting co2 into biomass , i.e. , [ co2 ] is a natural function of temperature ) . part of the fluctuations , however , is attributed to human activity ( in winter the northern hemisphere where more people live is cold and humans thus burn more fuel to warm their houses , i.e. , [ co2 ] is a function of temperature ) . as a side note , these two things show us that it is very straightforward to understand how [ co2 ] can be a function of temperature , in these cases through biological activity , including that of humans , in this case resulting in a rapid inverse proportionality ( warmer less co2 ) . other long - term processes such as degassing of oceans can have opposite effects , that is , warmer more co2 . while we bear this in mind , we will continue the reasoning of anthropogenic global warming and assume an opposite correlation , that is , temperature is a function of [ co2 ] , and analyze the oscillations . while the natural oscillations have always existed and thus do not result in seasonal oscillations of global warming , the human - caused fluctuations should be represented in the temperature fluctuations . what we would expect in the framework of agw is that all months have warmed up ( because of general injection of anthropogenic co2 into the atmosphere ) , but winter months a little bit more ( because of seasonal fluctuations of these injections ) . as a response to the sinusoidal [ co2 ] oscillations , a sinusoidal oscillation in temperature is to be expected that is ( i ) offset vertically by an amount to make it fully above the zero line ; ( ii ) offset ( delayed in time ) by a time that can be up to 3 months maximum , as will be discussed here . neither is the case . comparing the monthly fluctuations in temperature increase with monthly fluctuations in [ co2 ] we see again that the latter lags behind , this time by about 3 months ( to be precise , fitting sine curves to the data gives a difference of 2.9 months ) . after all , months are periodic but upon second thought , this is not possible . electronic engineers model things with electronic circuits and this case of temperature and co2 is also very adequately studied by such circuits . using an equivalent electronic circuit does not mean that the processes are electronic , but that they can be modeled by such circuits , as in an analog computer . ( the appendix gives the mathematical link between a relaxation model and the equivalent electronic circuit . ) in this case we have a model between driving force ( either [ co2 ] , as we are wo nt to believe , or temperature t ) and the response ( resp . , t or [ co2 ] ) . for instance , an increase in [ co2 ] will cause an increase in t by the greenhouse effect . this is necessarily a simple relaxation system , where the changes of the force cause the system to be off - equilibrium until a new equilibrium is reached . for instance , co2 has to diffuse to places where it can do its temperature effect . there can even be more than a single relaxation process , with a complex kinetics similar to a multistage nuclear decay . the fact is that one of the relaxation times is dominant , and we can describe the relaxation by a single relaxation time ( i.e. , the sum of all relaxation times ) . as long as there is no resonance in the system ( something that can only be achieved with positive feedback ) it will behave as described here . we will model our climate system with a simple electronic relaxation system consisting of a resistance and a capacitance , r and c , respectively ; see figure 3 . the product of the two yields the relaxation time , = rc . at the entrance of this system we connect our oscillating driving voltage vi(t ) ( representing , e.g. , [ co2 ] oscillations ) , in which t is time . the response is measured as the charge q(t ) in the capacitor which represents , for instance , the temperature variations . this charge is also measured by the output voltage by the standard capacitor relation v = q / c . thus our output voltage vo(t ) represents the response ( e.g. , temperature ) . applying a sinusoidal input signal , vi(t ) sin(2ft) [ co2 ] ( t ) ( with f the frequency of oscillation ) , we get a sinusoidal wave at the output , with the same frequency , but with a phase at the output that is not equal to the phase at the input signal , vo(t ) sin(2ft + ) . the phase difference is directly and uniquely determined by the relaxation time of the system and the oscillation frequency f ; see figure 3 . for very low oscillating frequencies , the system can easily relax and the phase of the output signal is equal to that of the input signal . for increased frequencies or for the maximum phase difference for infinite frequencies or infinite relaxation time is exactly one - quarter period . in our case one - quarter period is thus 3 months and that is the maximum delay we can expect between driving force and response . for relaxation times much longer than the oscillating period of one year , that is actually the delay one expects . , the comparable system of solar radiation and temperature comparable in that the oscillating period is one year and both deal with the weather and climate has a delay of one month ; the solar radiation and temperature oscillate with one year period , but the warmest day is nearly everywhere one month after the day with the most daylight and the on average coldest day is one month after the day with least daylight . in figure 3(c ) we see that the relaxation time of the { radiation temperature } system therefore must be about 0.1 year ( 1.2 months ) . in the plot we can get a similar estimation value of the relaxation time of the atmosphere temperature through daily oscillations . as a rough figure , the temperature drops by about 4 degrees at night in about 8 hours after the sun has set . assume that the relaxation upon this step - like solar radiation is a simple exponential ( situation b shown in the appendix ) and would finish eventually at close to absolute zero ( say 10 kelvin ) and starts at 290 k ( thus a total amplitude of 280 k ) : 4 degrees in 8 hours , we solve the equation ( 1)(280 k)exp(8 hours)=(2804)k , which yields 23 days , close to the value found above from yearly oscillations . going back to the data of [ co2 ] and temperature ( figure 2 ) we can now understand the behavior , that is , the phase difference , but only if we assume the temperature to be the driving force . for instance , for some reason the temperature has increased more in winter months , and , as a result , to the natural [ co2 ] oscillations has been added a component with a maximum in spring months . the alternative , [ co2 ] being the driving force and a delay of 9 months ( 3 quarter periods ) , is mathematically not possible . another explanation , which we do not consider as a valid alternative , is that the temperature might be lagging behind [ co2 ] if it has a negative gain , that is , [ co2 ] increments lower the temperature . this negative sign of the gain would add another 180 phase shift and a total apparent phase shift of 270 would be possible . this goes even more against agw models , although we do not see an easy physical explanation for how co2 might lower the temperature . this simple analysis opposes the hypothesis that [ co2 ] is causing serious temperature rises . as said , the model assumes that no resonance occurs that can possibly cause longer delay times . this , in our opinion , is a valid assumption since resonance is not likely . first of all , for this strong positive feedback , resonance effects should be observable , which experimentally is not the case . although many climate scientists have proposed positive feedbacks as discussed in the introduction and they make heavy use of them in order to explain and model the needed nonlinear behavior of the greenhouse effect , this goes against intuition . in a chaotic system scientists of any plumage , when making such simulations , know this : if they change their parameters just slightly ( sometimes even in the scale of the numerical resolution of their floating point numbers ) , the outcome can be hugely different . there is also an experimental argument against positive feedback factors , namely , the conscientious satellite measurements ; see , for instance , the work of lindzen and choi , spencer , or wielicki et al . . these , in fact , prove a negative feedback in the climate system . without feedback , in standard theory , if earth warms up ( by global warming in a radiation imbalance ) , the temperature rises and the outward earth radiation increases by a certain amount , until establishing a new equilibrium . in the agw model , a positive feedback of the the following form is used : if the temperature increases , the outward earth radiation is less than that predicted by standard theory or the incoming solar radiation increases because of reasons like cloud ( non)forming , thus increasing the temperature even further . the contrary can also happen : in negative feedback , if the planet heats up by a radiation imbalance for whatever reason , new channels of earth radiation can be opened or incoming solar radiation blocked ( for instance , by increased cloud cover ) , thus reducing the temperature with respect to standard theory . as demonstrated by the scientists mentioned above , the earth climate is a negative - feedback autostabilizing system , while they do not identify any specific feedback mechanisms . this is also in agreement with the fact that , whereas the conditions on our planet have significantly changed over the geological history ( the sun for instance has been 25% less bright than today ) , the climate has been rather stable , always restoring from climate perturbations to median values instead of saturating in extreme values ; the latter would be expected in a thermal - runaway positive - feedback climate system . note that , if large positive feedback exists , the temperature is unstable and will change until it saturates , that is , until negative feedback becomes important . in other words , it is technically not even possible that we are in a positive - feedback situation , considering the stable temperatures . ( compare this to the positive - feedback of a shopaholic buying always makes him buy even more his funds are acceleratingly depleted or his credit increasingly rising , until the banks put a lid on his spending , i.e. , negative feedback . ) we must be in a negative - feedback situation and lindzen and choi , spencer , and wielicki et al . have proven this by measurements . negative feedback was already argued to be significant when the consensus of the scientists was for a global cooling ; see the work of idso . additional arguments against positive feedback come from the fact that every day , and every year , the temperature is brought off equilibrium . at night these temperature disturbances are much larger and much faster than those that may have been produced by greenhouse gases ( 20 degrees / day or 30 degrees / year versus 0.7 degrees/100 years ) . the same accounts for co2 disturbances . the human - caused co2 seems insignificant compared to the large and noisy emissions naturally occurring on this planet ( only the accumulated effect of the tiny human - originated co2 is supposed to have an effect ) . to give an idea , segalstad established that of the current rise in [ co2 ] levels relative to the preindustrial level only 12 ppm is attributable to human activity while 68 ppm is attributed to natural phenomena . these fluctuations are also visible in the extensive summary of beck and show that even in recent history the [ co2 ] levels were sometimes higher than the modern values , while as everyone knows , the human emissions have monotonously increased , showing that these huge fluctuations can only have a natural origin . relevant for the discussion here , the fluctuations would rapidly push the climate off equilibrium if it were unstable . yet , in spite of these huge disturbances , both in temperature and co2 , the equilibrium is restored every day and every year and every century . had the earth climate been a positive - feedback system , in summer or in winter the temperature would have been in a runaway situation , unrecoverable in the following compensating half - period . the reason is that the climate is a negative - feedback system that stabilizes itself . one might think that the seasonal fluctuations are too fast to be causing a runaway scenario and that before the system runs away it already recovers . if starting oscillations are much faster than the response time of the system , the effective amplitude is reduced , but in a runaway system they will be amplified up to the point of saturation . the system can only be stable if the feedback factor at that specific frequency is not positive . look at it like this : in the first half of the year , it is hot and the system tries to runaway . in the second half of the year it is colder and it will restore , but it has a minute memory that the temperature has already run off a little in the first half and the second half therefore does not compensate completely . in the first year chance will determine which one , but if the system is unstable ( positive feedback ) , the system will run away . like the metastable system of a ball placed on top of a hill . it can only stay there in the absence of noise or any fluctuation in general . in conclusion relevant to the current work , such negative feedback will make any delay longer than 1/4 period impossible . thus , the fact that we find a delay close to a quarter period means that ( i ) the temperature signal is the origin for [ co2 ] signal ( or the two are uncorrelated ) and ( ii ) the relaxation time linking the two is ( much ) longer than the period ( 12 months ) of oscillation . moreover , even if positive feedback were present , for the resonance itself to be significant , the oscillating frequency needs to be close to the resonance frequency , that is , 12 months . it is highly unlikely that the natural frequency of the climate-[co2 ] system is close to the 12-month - periodic driving force , even more so since also the long - term ice - drilling data need to be explained somehow , where delays of several thousands of years are observed . in our analysis , relaxation times of several thousands of years will explain both the ice - drilling data and the yearly temperature and [ co2 ] oscillations . finally , the set of data we used is rather limited . future research should tell if the ideas presented here can stand up to scrutiny when more recent data and pan - global data are used . as a note in proof , humlum et al . have recently investigated correlation between temperature and [ co2 ] variations on the time scale of decades , similarly concluding that [ co2 ] changes are delayed in relation to temperature and can therefore not be the reason for temperature changes . in conclusion , the idea tested here that [ co2 ] is the cause of temperature changes does not pass our signal analysis . it goes a little too far to say that what we present here is proof for the opposite , namely , that [ co2 ] is the effect of temperature , but our analysis does not contradict this .

the primary ingredient of the anthropogenic global warming hypothesis , namely , the assumption that additional atmospheric carbon dioxide substantially raises the global temperature , is studied . this is done by looking at the data of temperature and co2 , both in the time domain and in the phase domain of periodic data . bicentenary measurements are analyzed and a relaxation model is introduced in the form of an electronic equivalent circuit . the effects of this relaxation manifest themselves in delays in the time domain and correlated phase shifts in the phase domain . for extremely long relaxation time constants , the delay is maximally one - quarter period , which for the yearly - periodic signal means 3 months . this is not in line with the analyzed data , the latter showing delays of 9 ( 3 ) months . these results indicate a reverse function of cause and effect , with temperature being the cause for atmospheric co2 changes , rather than their effect . these two hypotheses are discussed on basis of literature , where it was also reported that co2 variations are lagging behind temperature variations .

1. Introduction 2. Results 3. Discussion 4. Conclusion

uveitis occurs in 5070% of patients with behet 's disease ( bd ) typically within two years of disease onset in the majority of cases [ 1 , 2 ] . the course of the disease is characterized by the variable severity of recurrent symptomatic exacerbations of uveitis and spontaneous remission of the inflammatory signs . mild inflammatory episodes of anterior uveitis may go unnoticed by the patients as ciliary injection , pain or photophobia may be absent , and anterior chamber cells may resolve spontaneously . fluorescein angiography ( fa ) has been reported to be a useful tool in the detection of asymptomatic ocular involvement [ 5 , 6 ] . laser flare photometry ( lfp ) is also a very useful tool in monitoring behet 's uveitis . in clinical practice it is usually used as an auxiliary method to show disease activity in the followup of uveitis patients . presence of vitreous cells on slit - lamp examination is accepted as eye involvement according to international study group ( isg ) criteria for the diagnosis of bd . however , in case of mild cellular debris in anterior vitreous without any other ocular signs and symptoms , diagnosis of ocular involvement may be controversial . the present study was conducted to investigate if there is a prognostic implication of having cellular debris in anterior vitreous in the development of obvious ocular involvement in the followup of patients with bd without any ocular symptoms . to our knowledge this is the first study which investigates the importance of cellular debris in anterior vitreous in patients with bd without any ocular symptoms . the study included 120 eyes of 60 patients who were diagnosed as bd but had no history of ocular involvement and were found to have no ocular pathology or only cellular debris in the anterior vitreous on routine ocular examination at the uveitis services of two university hospitals between 2002 and 2013 . only patients who met the 1990 classification criteria of the isg for bd were included in the study . patient informed consent was obtained from all participants in accordance with the declaration of helsinki , and ethics approval was obtained from local ethical committee . all patients were referrals from the dermatology or rheumatology clinics for initial ocular examination after they were diagnosed as bd . a complete ocular examination was performed , including visual acuity , slit - lamp biomicroscopy , tonometry , and indirect ophthalmoscopy . patients who had a history of ocular involvement or who received any systemic treatment other than colchicum dispert and patients who had cells in the anterior chamber , posterior synechiae , cells or debris in the posterior vitreous , retinal vascular sheathing , retinal scars , or hyperemia or pallor of the optic disc were not included in the study . after a written informed consent was obtained , fa was performed on the day of initial visit . patients were divided into two groups according to the presence of cellular debris in the anterior vitreous detected at the slit - lamp examination . the groups were defined as cellular debris ( + ) ( group a ) and cellular debris ( ) ( group b ) . patients were followed up without any additional systemic or topical treatment unless they developed uveitis attacks later during their followup period . spss statistics software package version 15.0 for windows ( spss , chicago , il , usa ) was used for the statistical analysis . since the data did not follow gaussian 's distribution continuous variables were compared with mann - whitney u test . the kaplan - meier method was used to estimate survival curves of the patients followed up for at least 6 months . the log - rank test was used to perform comparisons of survival curves between the groups . cellular debris was seen in the anterior vitreous bilaterally in 22 patients and unilaterally in 10 patients . thus , there were 54 eyes in the cellular debris ( + ) group and 66 eyes in the cellular debris ( ) group . seven eyes ( 13% ) in group a and four eyes ( 6.1% ) in group b demonstrated optic disc hyperfluorescence ( staining of the disc ) on fa at initial examination . there was no statistically significant difference between the two groups in optic disc hyperfluorescence ( p = 0.2 ) . figure 1 shows fa images of two different patients , one having optic disc hyperfluorescence and the other being normal . forty - one patients were followed up for at least six months . among 82 followed up eyes there were 34 eyes in group a and 48 eyes in group b. table 1 shows that the patients experienced uveitis attacks during their followup period . kaplan - meier survival analysis estimated the risk of having uveitis attack within 3 years for group a and group b as 20.6% ( 7 eyes ) and 4.2% ( 2 eyes ) , respectively . the survival rates in terms of uveitis attacks were 35.7 2.8 and 56.7 2.1 in group a and group b , respectively ( log - rank = 6.85 , p = 0.009 ) ( figure 2 ) . none of the uveitis attacks occurred in the eyes that had disc hyperfluorescence on initial examination . fluorescein angiography has been an essential tool in both the diagnosis and followup of patients with behet 's uveitis . it has also been reported to be a useful method in the early detection of ocular involvement [ 9 , 10 ] . dye leakage from the retinal vessels may be found during remission periods in the eyes with the history of posterior uveitis attacks . in a previous study we found fluorescein leakage in 52 of 99 eyes ( 52.5% ) during clinical remission period following a documented posterior uveitis attack . fluorescein leakage from retinal vessels may be seen in eyes without ophthalmoscopic signs of vasculitis . in one study it has been reported to be the only ocular finding that confirmed the dermatological diagnosis of bd in 6.3% of 300 patients . laser flare photometry ( lfp ) is also a very useful tool in monitoring behet 's uveitis like fa . in a previous study from our clinic there was a strong correlation of flare values with fa leakage suggesting that lfp may be reliably used to quantify changes in the blood aqueous barrier functions in the followup of patients with bd . in another study from our clinic the risk of a recurrent uveitis attack was found higher in patients with flare readings more than 6 photons / msec than in patients with lower flare readings . this cut - off point would also be helpful in the differentiation of nonocular and ocular behet patients . but it does not give the risk of experiencing a uveitis attack for nonocular behet patients whom flare levels were very similar to those of normal population ( 3.5 photons / msec ) . the present study was designed before we had the lfp device so we could not be able to perform lfp to all patients . we previously found that 35% of unilateral behet uveitis patients became bilateral at the end of the 3-year followup period . however in the literature there is no study evaluating the risk of experiencing a uveitis attack in nonocular bd patients . in this study we performed fa to all patients at initial examination , and we found optic disc hyperfluorescence as the only fa finding in 11 of 120 eyes ( 9.1% ) . although this finding was more common in group a than in group b ( 13% versus 6.1% ) it was not statistically significant . we performed kaplan - meier survival analysis to the patients and found the risk of having uveitis attack within 3 years 5 times higher in group a than in group b. there was no such risk for the eyes with previous disc hyperfluorescence , and none of the uveitis attacks occurred in these eyes . subclinical ocular involvement might be detectable with fluorescein and/or ( if available ) indocyanine green angiography . because most of the patients did not accept to be followed up with fa , in their followup visits , we perform only slit - lamp biomicroscopy and ophthalmoscopic examinations to the patients . cellular debris in the anterior vitreous may implicate a subclinical anterior uveitis , and in the current study we found that it has prognostic implications in patients with bd screened for ocular involvement . additionally , periodic ocular examination is very important in all behet patients evenifthey are asymptomatic for ocular involvement , especially those with cellular debris in their anterior vitreous .

purpose . to investigate if there is a prognostic implication of the presence of cellular debris in the anterior vitreous in patients with behet 's disease ( bd ) without any ocular symptoms . methods . one hundred and twenty eyes of 60 patients with bd were included in the study . the eyes were divided into two groups according to the presence of cellular debris in the anterior vitreous . the first group included 54 eyes which were cellular debris ( + ) ( group a ) , and the second group included 66 eyes which were cellular debris ( ) ( group b ) . fluorescein angiography ( fa ) was performed to all patients following routine ocular examination . patients were called for the six monthly control visits to investigate possible new ocular involvement during followup . the kaplan - meier method was used to estimate survival curves . results . seven eyes ( 13% ) in group a and four eyes ( 6.1% ) in group b showed optic disc hyperfluorescence on fa ( p = 0.2 ) . none of the eyes with disc hyperflourescence on initial examination developed uveitis attacks in their followup . in kaplan - meier survival analysis there was a significant difference between the groups ( group a 20.6% and group b 4.2% ) by means of ocular involvement during their followup ( log - rank = 6.85 , p = 0.009 ) . conclusions . presence of cellular debris in the anterior vitreous may have prognostic implications in patients with bd screened for ocular involvement .

1. Introduction 2. Methods 3. Results 4. Discussion

granulosis rubra nasi is a rare disorder of the eccrine glands first described by jadassohn in 1901 . it is thought to be common in european countries . in the english literature maschkillesson and neradow ( 1935 ) have recorded 130 cases and the disease was not thought to be rare . although it is inherited as an autosomal dominant trait , it is rare to find the disease in two generations , although less commonly it is found in two children of same parents . granulosis rubra nasi is a focal form of hyperhidrosis that differs from the other forms in that it does not depend on the hypothalamic or emotional stimuli to develop . a 27-year - old man presented with erythema over the nose since childhood without sensitivity to sunlight . physical examination showed excessive sweating of the nose , erythema of the nose covered by beads of sweat , and multiple telangiectatic vesicles [ figures 1 and 2 ] . the skin biopsy showed dilatation of blood vessels , dilated sweat ducts with a discrete mononuclear cell infiltrate surrounding them [ figure 3 ] . beads of sweat seen on an erythematous base over the nose shows erythema more prominently . telangiectasias are appreciable histopathology section showing dilated blood vessels and eccrine ducts with surrounding lymphocytic infiltrate [ h & e , 10x ] the clinical picture is characterized by hyperhidrosis of the central part of the face , most conspicuous on the tip of the nose . this is followed by appearance of diffuse erythema over the nose , cheeks , chin , and upper lip . erythematous macules , papules , vesicles or even pustules may be seen over the sweat duct orifices . later histopathology shows a mild mononuclear cell infiltrate around the sweat ducts , blood vessels , and lymphatics . pilosebaceous units are normal and no heterotopic apocrine glands are found this disease usually remits after puberty , unlike the primary forms of localized hyperhidrosis but sometimes may continue into adulthood . some authors have suggested that it is a disorder of vasomotor and secretory function of the nose . eddowes had suggested that adenoids could be involved which can provide a source of irritation to the tip of the nose . reported a case of granulosis rubra nasi associated with phaeochromocytoma , surgical removal of which was followed by regression of the condition . the clinical picture is very distinctive and rarely there is a problem with the diagnosis . there is erythema of the cheeks and nose along with telangiectasias but no hyperhidrosis of the central part of the face . in the case of perioral dermatitis there are small monomorphic papules , pustules , erythema , and scaling involving the perioral area and no hyperhidrosis . treatment of granulosis rubra nasi has been described in the literature with topical indomethacin , oral corticosteroids , tetracycline , cryotherapy , and even x - rays . have recently described a treatment using botulinum toxin a that induced long - term remission in a patient with granulosis rubra nasi .

granulosis rubra nasi is a rare disorder of the eccrine glands , inherited as an autosomal dominant trait . it is clinically characterized by hyperhidrosis of the central part of the face , most conspicuous on the tip of the nose , followed by appearance of diffuse erythema over the nose , cheeks , chin , and upper lip . it is commonly seen in childhood , but can also occur in adults . this is a case report of a 27-year - old male patient who presented with excessive sweating over the nose . physical examination of the nose revealed erythema and multiple telangiectatic vesicles . biopsy findings supported the diagnosis of granulosis rubra nasi . this case is being reported for its rarity since to the best of our knowledge , it has not been reported in indian subjects so far .

INTRODUCTION CASE REPORT DISCUSSION

tmrna was discovered in 1995 , when simpson and coworkers overexpressed a mouse cytokine in escherichia coli and found truncated cytokine peptides each tagged at the carboxyl termini with the same 11-amino acid residue extension aandenyalaa . this tag sequence turned out to be encoded in a small stable rna that had been identified many years earlier as a 10s rna of unknown function . the 10s rna is now known as transfer messenger rna ( tmrna ) . as its name implies , tmrna has features of both transfer rna and messenger rna . one domain of the molecule , known as the transfer rna - like domain ( tld ) , has an amino acid acceptor stem chargeable with alanine and a t arm with modified nucleotides , just as in trna ( figure 1 ) . however , the d arm of the trna - like domain is degenerated , and there is no anticodon loop . a second domain , the mrna - like domain ( mld ) , is located in a pseudoknot - rich region and contains a short open reading frame that encodes aandenyalaa and is followed by a normal stop codon . comparison of the structures of ( a ) trna , ( b ) mrna and ( c ) tmrna . ( a , c ) the 3 ' and 5 ' termini , the amino acid acceptor stem ( ac ) and the anticodon ( a ) , d and t arms are indicated . ( b , c ) the shine - dalgarno sequence ( sd ) , the start codon ( s ) and the stop codon ( octagon ) , the locations of the trna - like ( tld ) and mrna - like domains ( mld ) as well as pseudoknots ( pk ) 1 to 4 , helix 5 ( h5 ) , and the + 1 resume codon ( r ) are indicated . these observations led to the proposal that the tmrna occupies the empty a site of the stalled ribosome which then jumps or slides from the 3 ' end of the truncated message onto the mld , at a triplet known as the resume codon ( in e. coli this is a gca triplet ) from where translation continues normally until an in - frame tmrna stop codon is encountered ( figure 2 ) . , bacteria use this seemingly complicated trick to proteolytically destroy proteins that are synthesized from damaged mrna templates and , perhaps more importantly , to reactivate and recycle needed ribosomes . in some bacteria , the gene for tmrna ( ssra ) is essential [ 5 - 7 ] , but in other species trans - translation is important only to survive challenging environmental growth conditions , and this is probably the reason for the relatively late discovery of this fundamental capability of every bacterial cell . a ribosome remains stalled near the 3 ' end of broken mrna , binds to alanine - charged tmrna ( orange ) , and switches from the broken message onto the open reading frame of the tmrna allowing regular translation to resume . upon reaching the tmrna stop codon , the ribosome releases a hybrid protein with a degradation tag and joins the pool of active ribosomes . because the tld of tmrna has no anticodon , it is not clear how it can recognize and bind to the empty a site of a stalled ribosome ( figure 2 ) . moreover , the mld has neither an aug start codon nor the shine - dalgarno sequence whereby bacterial mrna binds to a complementary region of the ribosomal rna at the start of translation . how then is the resume triplet properly positioned ? and what mechanism allows the ribosome to take off from the damaged mrna template and land precisely on the tmrna 's resume codon ? astonishingly , the ribosome performs this feat when a peptide bond forms between the partially synthesized protein and the alanine - charged tmrna , and while establishing the correct reading frame for continuing elongation . miller and colleagues have now carried out a systematic site - directed mutagenesis study in an attempt to establish the contribution of the nucleotide residues that precede the resume codon to the correct positioning of the mld . one problem in determining the critical elements of trans - translation in vivo has been that e. coli cells grow well without the ssra gene , so mutations can not be detected by their effects on growth . furthermore , the tagged proteins produced by trans - translation are degraded , and therefore can not be used to indicate whether it is occurring normally . luckily , however , a wide variety of tag templates are tolerated , and , upon removal of the natural stop codons , large additions can be engineered onto the tmrna and are then translated . the group of allen buskirk has used an ingenious assay in which proper tagging of truncated kanamycin resistance ( kanr ) gene products on stalled ribosomes produces full - length kanr protein , so that e. coli survives on kanamycin plates only when the tmrnp is functional . the nucleotides surrounding the resume codon have been the focus of several studies aimed at determining what enables the ribosome to switch templates ( reviewed in ) . the upstream region contains an adenosine - rich cluster of about seven residues adjacent to three nucleotides ( the -1 triplet ) immediately preceding the + 1 guanosine . downstream of the resume triplet , for unknown reasons , codons + 2 to + 4 prefer adenosine at the second position ( figure 3 ) . on the basis of sequence comparisons and the idea that the -1 triplet ( guc , at positions 8789 of e. coli tmrna , figure 3 ) should be in the a conformation for allowing tmrna to participate in the ribosomal elongation cycle , it was proposed that the -1 triplet has a crucial role in template switching . specifically , if the a conformation is required , 18 out of the 64 theoretically possible -1 triplets are prohibited , so they would yield tmrnas that could not function in trans - translation . rna structure logo displaying the information content surrounding the tmrna resume codon the height of each symbol is proportional to its frequency in 486 representative sequences from an alignment of 730 tmrnas . the resume codon ( + 1 ) , codons + 2 to + 4 and the -1 triplet are indicated . the new systematic in vivo study from the buskirk laboratory that has recently been published in bmc biology provides strong experimental evidence that the previously suspected -1 resume triplet has only a minor role in accommodating tmrna on the ribosome . in this paper , miller and colleagues constructed mutant tmrnas with all 64 possible permutations of the -1 triplet and determined their effect on survival in the kanamycin resistance assay . they found that eight of the 18 codons that were prohibited according to the -1 hypothesis were in fact fully functional , and other mutant tmrnas that were predicted by the -1 triplet rule to be functional were shown by experiment to be completely inactive . the results of this comprehensive study show that the proposed rule for the -1 triplet is invalid and suggest different nucleotides that are important for accommodation of tmrna on the ribosome . one alternative nucleotide is the highly conserved adenosine at position 86 of e. coli tmrna ( figure 3 ) , which was observed earlier to be important in trans - translation . indeed , by measuring survival in the kanamycin - resistance assay , the investigators confirmed that changing a86 to a pyrimidine yielded cells that were unable to trans - translate . because high - resolution structures of the ribosome - bound tmrna at various stages of trans - translation are currently unavailable , it is unclear why the conserved a86 has such a prominent role . although this adenosine residue may act independently to interact with the ribosome , the investigators suggest that the a86 interacts with a yet to be identified ligand that is primarily responsible for engaging the resume triplet and tmrna in the attachment and synthesis of the tag peptide . they speculate that a86 might bind to the smpb that is part of the transfer - messenger rna ribonucleoprotein , or to ribosomal protein s1 , two proteins that have been found by other investigators to be close to the decoding center of the ribosome - bound tmrna at some stage of trans - translation [ 14 - 18 ] . further studies at the atomic level will be required before the athletic potential of the ribosome is fully understood .

the transfer - messenger ribonucleoprotein ( tmrnp ) , which is composed of rna and a small protein , small protein b ( smpb ) , recycles ribosomes that are stalled on broken mrnas lacking stop codons and tags the partially translated proteins for degradation . although it is not yet understood how the ribosome gets from the 3 ' end of the truncated message onto the messenger portion of the tmrna to add the tag , a recent study in bmc biology has shed some light on this astonishing feat .

Discovery and properties of transfer messenger RNA Identifying determinants of template switching Acknowledgements

there is some evidence to suggest that working memory might be impaired in patients who show jtc compared to those who do not . a small study by ormrod et al69 found that visual working memory performance was affected in first - episode psychosis patients who showed a jtc response style . in addition , in sz patients with strong current delusions , working memory ( but not premorbid iq ) was worse in those who demonstrated jtc.70 as noted above , broome et al67 found that jtc in the prodrome was linked to working memory impairments . nevertheless , the presence of a memory aid during the urn task does not affect jtc in patient groups.51,53 this would appear to undermine any suggestion that jtc stems from a relative inability to maintain the task items in memory . working memory impairments might correlate with a tendency to jtc , but the relationship is unlikely to be causal . one explanation for the jtc response style observed in sz is that patients simply make decisions based on less evidence . this liberal acceptance account53,71 was founded on evidence that sz patients tend not to converge on one particular interpretation of a situation ( eg , when asked to judge the plausibility of multiple interpretations of a picture ) . healthy controls ruled out interpretations that patients continued to liberally entertain , giving higher ratings to a wide range of interpretations . sz patients are proposed to more readily accept a response option , while healthy participants are more cautious in doing so . in situations where only two ( mutually exclusive ) options moritz et al71 increased the number of jars to four to provide additional ambiguity : this was found to abolish the jtc in patients . although sz patients made a less systematic information search and were more likely to consider less valid information , they did not inspect fewer pieces of information compared to healthy controls and thus did not demonstrate jtc . effects were found on confidence ratings however , with patients more likely to be overconfident , using extreme confidence ratings under inappropriate circumstances . this is consistent with work showing that sz patients are less confident of their correct answers and overconfident when they make errors , during word recall tasks.72,73 although there were no overall differences between patients and controls , symptomatology in the patient group was linked to information search . a correlation was observed between symptom severity scores ( positive and negative syndrome scale [ panss ] positive , panss delusion ) and the degree of information search , with higher - scoring participants tending to gather less pieces of information . panss score did not predict use of extreme confidence ratings , but nevertheless this study would suggest that jtc can be largely abolished and can manifest as overconfidence only when information is presented in the right manner . impulsiveness is unlikely to be a factor because patients with sz show similar reaction times as healthy controls51,53 and draw more beads when the task is made harder.51,55,74 motivational factors are also unlikely to play a part : the possibility that the patients overestimate the cost of gathering more information ( possibly due to a greater need for closure ) has been discounted because patients do not seem to experience a greater cost for gathering more information.75 an alternative explanation is that jtc manifests not through a lowered threshold for making a decision but through each piece of evidence being relatively overvalued . when asked to report belief estimates after each draw , it has been shown that patients make more drastic updates after each piece of evidence.46,56,77 speechley et al78 found that delusional patients , when asked to give likelihood ratings for each urn on each trial , gave higher ratings for whichever urn matched the current evidence , while ratings for the nonmatching urn did not differ from those of the control groups . the authors argue that this provides evidence of a reasoning bias characterized by hypersalience of evidence that matches a hypothesis , but with reasoning that appears intact for nonmatches . the literature is inconsistent regarding patients responses to nonmatches ( disconfirmatory evidence ) . because delusions are maintained in the face of contradictory evidence , it is unsurprising that patients tend to show a bias against disconfirmatory evidence.79 it has been argued that hypersalience could underlie this effect : hypersalience of evidence hypothesis matches may lead to an enhancement of weak matches , leading to difficulties in integrating disambiguating information.80 some studies point to hypersalience of disconfirmatory , as well as confirmatory , evidence : deluded patients show a tendency to overadjust when presented with potentially disconfirmatory evidence,53,56 although this effect might be linked to miscomprehension of the task,81 especially because such a tendency would contradict the evidence of reversal - learning deficits discussed in the previous section . these findings are consistent with an aberrant salience account of sz,82 whereby dysregulated dopamine transmission generates context - inappropriate salience attributions , potentially due to aberrant signaling in the ventral striatal dopaminergic pathway , which is thought to regulate stimulus response pairings.83 moore and sellen84 built a simple network model in which the gain , or signal - to - noise , parameter ( which describes the likelihood of a node firing when presented with some input ) was varied . the gain parameter was assumed to represent striatal dopaminergic activity , and increasing this parameter meant that the model successfully mimicked the jtc response style seen in research data from delusional patients . this might be overly simplistic however , because imaging studies have shown that the striatum is downregulated in arms85 and sz patients.86 nevertheless , it is important to note that evidence for hypersalience has been observed across various other cognitive biases present in sz8789 and as such represents a convincing account of jtc . as mentioned previously , another suggestion concerning the development of delusions in sz focuses on impairments in theory of mind.42 langdon et al77 compared 35 sz patients with a history of delusions to healthy controls , on a battery of tasks that included two versions of the urn task , three theory - of - mind tasks , and a questionnaire on attributional biases . a jtc response style was found in the patient group , as well as impairments on the theory of mind tasks and evidence of an externalizing attributional bias . performance on the urn tasks correlated with that of the theory - of - mind tasks , while attributional bias scores did not correlate with other task measures . delusion proneness ( measured by the questionnaire ) correlated with probabilistic reasoning and theory - of - mind measures , while externalizing bias did not ; iq and memory ability were accounted for . although it was draws - to - decision that correlated most robustly with delusion proneness , these data prompted the authors to suggest that a common underlying mechanism might operate in sz to drive probabilistic reasoning and theory of mind deficits . they speculate that this could be a difficulty in inhibiting sensory input reflecting the immediate perceived reality , thus making patients more likely to be influenced by current data when making decisions on probabilistic reasoning tasks and making it harder to maintain an abstract viewpoint as required by theory - of - mind tasks . however , it should be noted that a large meta - analysis found no evidence for a link between theory of mind deficits and positive symptoms ; instead , deficits in theory of mind were correlated with negative symptoms , disorganization , and cognitive impairment.90 there is also some suggestion that poor emotion regulation might have a role to play . in one study , 90 healthy individuals with varying levels of psychosis vulnerability ( assessed by the community assessment of psychic experiences ) were recruited.74 half the sample received an anxiety induction procedure , the other half did not . paranoid delusions and jtc were then assessed during the session . the anxiety induction procedure promoted delusions and jtc , and participants with higher psychosis vulnerability showed greater increases in paranoid delusional ideation . furthermore , jtc appeared to mediate the association between anxiety and delusions , prompting the authors to suggest that paranoid delusions result from an interaction of anxiety and reasoning biases . in the glckner and moritz91 study , it was found that increasing stress ( through time pressure and the addition of affective valence ) led to diminished performance in patients . thus , improved self - monitoring in terms of better emotion regulation , combined with metacognitive training targeted at reasoning biases , could be beneficial in reducing delusion formation in sz . on balance , the explanations best supported by evidence are those of liberal acceptance and hypersalience . at present , it is hard to say which is best supported by the evidence available : this is possibly because these two explanations are by no means mutually exclusive . one difficulty in differentiating these explanations is that the urn task offers limited information regarding learning and decision - making processes . in one of our studies,92 we investigated performance in patients on a sequence - learning task ( sequences of four button presses were learnt using two buttons , feedback after each button press ) and the typical urn task . patients were able to learn the correct sequence , but learning was slower compared to that in healthy controls . interestingly , learning from positive ( but not negative ) feedback in the sequence task correlated with draws - to - decision in the urn task : patients who showed a jtc response style were impaired in learning from positive feedback . thus , these findings clearly favor a liberal acceptance account over hypersalience , but further work is needed to distinguish liberal acceptance and hypersalience , as well as to explore potential interactions with emotion regulation and other self - monitoring activities . in the next section , we discuss work aimed at elucidating the neural basis of jtc . various studies have attempted to induce the jtc bias in healthy controls using pharmacological manipulations ; others have used fmri . a drug model of jtc in healthy controls would be informative regarding the neurobiological underpinnings of jtc . there is some evidence that the noncompetitive n - methyl - d - aspartate ( nmda ) receptor antagonist ketamine could serve as such a model . because ketamine can be safely administered under clinical supervision and has relatively short - lived effects , the drug could represent a useful tool for studying processes underlying jtc . ketamine infusions in healthy controls can induce behavioral and cognitive disturbances that are somewhat similar to the symptoms of sz,9395 infusions induce delusional thinking,96,97 and ketamine use has been linked to increased delusional symptoms in recreational users.98 importantly , ketamine infusions in patients with sz cause a worsening of symptoms.99101 ketamine has been shown to affect both glutamatergic and dopaminergic systems,102,103 potentially mimicking the aberrant dopaminergic transmission posited to underlie the jtc effect seen in sz ; ketamine also increases basal ganglia and thalamic activation in a manner similar to that observed in sz patients.104 a recent study by corlett et al105 administered ketamine to healthy controls to investigate whether faulty prediction error signals could underlie delusion formation in sz . prediction error is defined by the mismatch between expectations and experience , and it is probably represented by activity in the mesostriatal dopamine system.106 the prediction error signal in frontostriatal regions has been shown to correlate with delusion - like beliefs in healthy people107 and to be predictive of the severity of delusions in sz patients.108 disrupted prediction error signals could cause individuals to attend to and make associations with inappropriate stimuli ( both internal and external ) , consequently developing beliefs that do not reflect real - world contingencies,108 causing a jtc style of responding . corlett et al105 found that ketamine could strengthen the memory trace of a previously conditioned stimulus when it was presented again , without reinforcement , offering tentative support for this hypothesis . however , another study failed to find a jtc response style during the urn task in healthy controls receiving ketamine . this suggests that although ketamine can induce delusions in healthy controls , delusion formation under ketamine might not be so closely linked to jtc as in sz,109 although possibly higher doses of ketamine might be required for jtc to manifest . interestingly , work investigating the effects of dopamine agonists and antagonists in healthy controls has also failed to induce jtc , suggesting that straightforward modulation of the dopaminergic system might not be sufficient to reproduce the jtc response style seen in sz . l - dopa , had no effect on draws - to - decision , or confidence , whereas a dopamine antagonist ( haloperidol ) was found to reduce overconfidence but had no effect on draws - to - decision.110 likewise , dopaminergic modulation with methamphetamine does not affect draws - to - decision.111 in sum , attempts to promote jtc in controls using pharmacological interventions have been largely unsuccessful . thus , it would seem that jtc can not be attributed solely to general dopaminergic overactivity , at least when induced acutely : the relationship might not be linear , or perhaps chronic aberrations in dopamine firing is required for jtc to manifest . alternatively , the disrupted interactions between several neurotransmitter systems might be critical . fmri can potentially indicate the neural mechanisms contributing to probabilistic reasoning in the urn task . studies in healthy controls implicate a distributed network of brain areas , including parietal cortex ( typically around intraparietal sulcus ) , prefrontal cortex ( typically dorsolateral ) , anterior insula , and striatum . these fmri studies use paradigms , including draw events ( stimuli for which participants choose to gather more information ) and urn events ( in which participants decide they have enough evidence and so select an urn ) . some of these studies compared urn task blocks ( which collapse over draw and urn decision events ) with blocks where participants performed a control task on the same stimuli . the most consistent finding across these block design studies are parietal responses near the intraparietal sulcus , which are larger for urn task blocks,112114 although some of these studies also report enhanced responses in the right dorsolateral prefrontal cortex113115 and anterior insula.113,115 one of these studies included a sz patient group and showed that the enhanced responses for the urn task blocks in the parietal and prefrontal cortices was reduced in these individuals , compared to the responses in healthy controls.113 this conclusion is tentative , however , as this study failed to replicate the classic jtc behavioral effect in sz . these block - design studies are limited , as they can not distinguish fmri responses to draw choice events ( decisions to gather more information ) from fmri responses associated with final choices of an urn . jtc occurs when data gathering is discontinued in favor of choosing an urn , so brain areas contributing to urn choice events are likely to be involved in jtc . studies that contrast fmri responses to urn choices versus draw choices yield similar results as the block - design contrasts . urn choices , compared to draw choices , activate anterior insula , striatum,115,116 acc , and parietal cortex , including the intraparietal sulcus.116 a near - identical network of brain areas has also been observed in the analogous contrast in the closely related best choice task.117 here , this network of areas was associated with deciding on an option currently available ( eg , a used car ) , compared to deciding to sample more possible options ( eg , viewing more cars ) . furl and averbeck116 found further roles for this parietal cortex area in the urn task . parietal cortex was more responsive during urn decisions for participants who tended to draw more and for participants who made greater adjustments to their draws - to - decision depending on prevalence of the minority bead color . these latter findings link parietal responses to individual differences in information - gathering behavior . however , this between - participant variability was within a nonclinical sample , and it remains to be confirmed whether it also extends to clinical cases such as sz . involvement of areas such as striatum , dorsolateral prefrontal cortex , and intraparietal sulcus in deciding on a probabilistic inference rather than continued evidence seeking ( as in jtc ) is perhaps not surprising . for example , measures of evidence accumulation for perceptual decisions have been associated with fmri responses in the prefrontal cortex of psychiatrically healthy participants118 and in neural recordings from the striatum119 and intraparietal sulcus in monkeys.120 measures of evidence accumulation for economic decisions in healthy participants are also associated with fmri responses in dorsolateral prefrontal cortex , striatum , and intraparietal sulcus.121 prefrontal cortex lesions are also associated with jtc.122 we hypothesize that this network of areas , which contributes to the urn task and other decision - making tasks in healthy participants , may be compromised in sz patients who show jtc behavior . the striatum , for instance , signals errors in reward prediction and predicts successful reward learning in healthy participants123 but shows aberrant responses during reward prediction tasks in schizophrenic individuals.124,125 aberrant prediction - related signaling in the dopaminergic striatum might also play a role in jtc behavior , as dopaminergic antipsychotic treatment abolishes jtc on an emotionally salient version of the urn task.64 in addition to the striatum , responses in the dorsolateral prefrontal cortex are also reduced in schizophrenics , compared to those in healthy individuals , when performing tasks requiring reward prediction.126 in sum , schizophrenic individuals appear to show reward - related response reductions in many of the brain areas activated by the urn task in healthy participants . dysfunctional interactions between the dopaminergic striatum and cortical areas , such as intraparietal sulcus and dorsolateral prefrontal cortex , might explain jtc behavior in sz patients . more brain - imaging studies using sz patients and the urn task are required to test this hypothesis . a drug model of jtc in healthy controls would be informative regarding the neurobiological underpinnings of jtc . there is some evidence that the noncompetitive n - methyl - d - aspartate ( nmda ) receptor antagonist ketamine could serve as such a model . because ketamine can be safely administered under clinical supervision and has relatively short - lived effects , the drug could represent a useful tool for studying processes underlying jtc . ketamine infusions in healthy controls can induce behavioral and cognitive disturbances that are somewhat similar to the symptoms of sz,9395 infusions induce delusional thinking,96,97 and ketamine use has been linked to increased delusional symptoms in recreational users.98 importantly , ketamine infusions in patients with sz cause a worsening of symptoms.99101 ketamine has been shown to affect both glutamatergic and dopaminergic systems,102,103 potentially mimicking the aberrant dopaminergic transmission posited to underlie the jtc effect seen in sz ; ketamine also increases basal ganglia and thalamic activation in a manner similar to that observed in sz patients.104 a recent study by corlett et al105 administered ketamine to healthy controls to investigate whether faulty prediction error signals could underlie delusion formation in sz . prediction error is defined by the mismatch between expectations and experience , and it is probably represented by activity in the mesostriatal dopamine system.106 the prediction error signal in frontostriatal regions has been shown to correlate with delusion - like beliefs in healthy people107 and to be predictive of the severity of delusions in sz patients.108 disrupted prediction error signals could cause individuals to attend to and make associations with inappropriate stimuli ( both internal and external ) , consequently developing beliefs that do not reflect real - world contingencies,108 causing a jtc style of responding . corlett et al105 found that ketamine could strengthen the memory trace of a previously conditioned stimulus when it was presented again , without reinforcement , offering tentative support for this hypothesis . however , another study failed to find a jtc response style during the urn task in healthy controls receiving ketamine . this suggests that although ketamine can induce delusions in healthy controls , delusion formation under ketamine might not be so closely linked to jtc as in sz,109 although possibly higher doses of ketamine might be required for jtc to manifest . interestingly , work investigating the effects of dopamine agonists and antagonists in healthy controls has also failed to induce jtc , suggesting that straightforward modulation of the dopaminergic system might not be sufficient to reproduce the jtc response style seen in sz . l - dopa , had no effect on draws - to - decision , or confidence , whereas a dopamine antagonist ( haloperidol ) was found to reduce overconfidence but had no effect on draws - to - decision.110 likewise , dopaminergic modulation with methamphetamine does not affect draws - to - decision.111 in sum , attempts to promote jtc in controls using pharmacological interventions have been largely unsuccessful . thus , it would seem that jtc can not be attributed solely to general dopaminergic overactivity , at least when induced acutely : the relationship might not be linear , or perhaps chronic aberrations in dopamine firing is required for jtc to manifest . alternatively , the disrupted interactions between several neurotransmitter systems might be critical . fmri can potentially indicate the neural mechanisms contributing to probabilistic reasoning in the urn task . studies in healthy controls implicate a distributed network of brain areas , including parietal cortex ( typically around intraparietal sulcus ) , prefrontal cortex ( typically dorsolateral ) , anterior insula , and striatum . these fmri studies use paradigms , including draw events ( stimuli for which participants choose to gather more information ) and urn events ( in which participants decide they have enough evidence and so select an urn ) . some of these studies compared urn task blocks ( which collapse over draw and urn decision events ) with blocks where participants performed a control task on the same stimuli . the most consistent finding across these block design studies are parietal responses near the intraparietal sulcus , which are larger for urn task blocks,112114 although some of these studies also report enhanced responses in the right dorsolateral prefrontal cortex113115 and anterior insula.113,115 one of these studies included a sz patient group and showed that the enhanced responses for the urn task blocks in the parietal and prefrontal cortices was reduced in these individuals , compared to the responses in healthy controls.113 this conclusion is tentative , however , as this study failed to replicate the classic jtc behavioral effect in sz . these block - design studies are limited , as they can not distinguish fmri responses to draw choice events ( decisions to gather more information ) from fmri responses associated with final choices of an urn . jtc occurs when data gathering is discontinued in favor of choosing an urn , so brain areas contributing to urn choice events are likely to be involved in jtc . studies that contrast fmri responses to urn choices versus draw choices yield similar results as the block - design contrasts . urn choices , compared to draw choices , activate anterior insula , striatum,115,116 acc , and parietal cortex , including the intraparietal sulcus.116 a near - identical network of brain areas has also been observed in the analogous contrast in the closely related best choice task.117 here , this network of areas was associated with deciding on an option currently available ( eg , a used car ) , compared to deciding to sample more possible options ( eg , viewing more cars ) . furl and averbeck116 found further roles for this parietal cortex area in the urn task . parietal cortex was more responsive during urn decisions for participants who tended to draw more and for participants who made greater adjustments to their draws - to - decision depending on prevalence of the minority bead color . however , this between - participant variability was within a nonclinical sample , and it remains to be confirmed whether it also extends to clinical cases such as sz . involvement of areas such as striatum , dorsolateral prefrontal cortex , and intraparietal sulcus in deciding on a probabilistic inference rather than continued evidence seeking ( as in jtc ) is perhaps not surprising . for example , measures of evidence accumulation for perceptual decisions have been associated with fmri responses in the prefrontal cortex of psychiatrically healthy participants118 and in neural recordings from the striatum119 and intraparietal sulcus in monkeys.120 measures of evidence accumulation for economic decisions in healthy participants are also associated with fmri responses in dorsolateral prefrontal cortex , striatum , and intraparietal sulcus.121 prefrontal cortex lesions are also associated with jtc.122 we hypothesize that this network of areas , which contributes to the urn task and other decision - making tasks in healthy participants , may be compromised in sz patients who show jtc behavior . the striatum , for instance , signals errors in reward prediction and predicts successful reward learning in healthy participants123 but shows aberrant responses during reward prediction tasks in schizophrenic individuals.124,125 aberrant prediction - related signaling in the dopaminergic striatum might also play a role in jtc behavior , as dopaminergic antipsychotic treatment abolishes jtc on an emotionally salient version of the urn task.64 in addition to the striatum , responses in the dorsolateral prefrontal cortex are also reduced in schizophrenics , compared to those in healthy individuals , when performing tasks requiring reward prediction.126 in sum , schizophrenic individuals appear to show reward - related response reductions in many of the brain areas activated by the urn task in healthy participants . dysfunctional interactions between the dopaminergic striatum and cortical areas , such as intraparietal sulcus and dorsolateral prefrontal cortex , might explain jtc behavior in sz patients . more brain - imaging studies using sz patients and the urn task are required to test this hypothesis . some studies have suggested that the jtc bias could represent an important therapeutic target . using an emotionally salient version of the urn task , menon et al64 found that within 2 weeks of initiating treatment with antipsychotics , patients demonstrated an increase in the number of trials - to - decision alongside attenuation of psychotic symptoms and delusions . although these measures were not correlated , baseline performance on the task had some predictive power over the individuals who would show improvements in symptomology in response to medication : jtc performance at baseline could therefore be useful in guiding treatment . moreover , treatment - related improvements in jtc can predict probability of regaining full employment , measured over a 6-month window . this was not the case for positive symptoms or neuropsychological performance , suggesting that jtc might act independently to influence real - world functioning.127 it is important to note that most studies have failed to show improvements in jtc on the standard urn task following antipsychotic treatment,64,128 although there is some evidence to dispute this.63,65 if jtc does indeed fluctuate with delusional symptoms , it would provide strong evidence of its importance as a treatment target : interventions that specifically target cognitive biases ( known as metacognitive training programs ) have already been shown to improve delusions and other positive symptoms.129,130 it is also important to note that most studies typically detect jtc in only approximately 50% of their patient samples . this heterogeneity needs to be explored further , to determine how it might relate to heterogeneity of symptomatology or whether it could be an issue of task sensitivity . again , individual differences in jtc performance could be useful in determining the best course of treatment . training programs that aim to ameliorate the jtc response style might prove to be an important adjunct to established therapies . in sum , jtc in sz seems to be a consistent finding and there is strong evidence linking jtc to delusion formation . both liberal acceptance and hypersalience accounts of jtc are well supported by the literature , but attempts to replicate jtc in healthy controls using pharmacological manipulations have largely failed , undermining attempts to develop a neurobiological account of jtc . fmri studies have implicated a network involved in making urn choices , which includes striatal , insula , parietal , and prefrontal areas ; further patient work is required , particularly in the context of evidence suggesting that jtc could represent a valuable therapeutic target .

schizophrenia is a mental disorder associated with a variety of symptoms , including hallucinations , delusions , social withdrawal , and cognitive dysfunction . impairments on decision - making tasks are routinely reported : evidence points to a particular deficit in learning from and revising behavior following feedback . in addition , patients tend to make hasty decisions when probabilistic judgments are required . this is known as jumping to conclusions ( jtc ) and has typically been demonstrated by presenting participants with colored beads drawn from one of two urns until they claim to be sure which urn the beads are being drawn from ( the proportions of colors vary in each urn ) . patients tend to make early decisions on this task , and there is evidence to suggest that a hasty decision - making style might be linked to delusion formation and thus be of clinical relevance . various accounts have been proposed regarding what underlies this behavior . in this review , we briefly introduce the disorder and the decision - making deficits associated with it . we then explore the evidence for each account of jtc in the context of a wider decision - making deficit and then go on to summarize work exploring jtc in healthy controls using pharmacological manipulations and functional imaging . finally , we assess whether jtc might have a role in therapy .

Working memory impairment Liberal acceptance Hypersalience of evidence Self-monitoring difficulties Remarks Methods of investigation Pharmacological interventions fMRI studies Role in therapy Conclusion

in october 2001 , the nordic cochrane centre published a cochrane review of mammography screening , which questioned whether screening reduces breast cancer mortality.1 within the same month , the centre published a more comprehensive review in lancet that also reported on the harms of screening and found considerable overdiagnosis and overtreatment ( a 30% increase in the number of mastectomies and tumourectomies).2 this resulted in a heated debate , which is still ongoing.3 the cochrane review was updated in 2006,4 to include overdiagnosis , and again in 2009.5 recently , several studies have questioned whether screening is as beneficial as originally claimed,68 and confirmed that overdiagnosis is a major harm of breast cancer screening.911 the us preventive services task force published updated screening recommendations in november 2009 and asserted that the benefit is smaller than previously thought and that the harms include overdiagnosis and overtreatment , but it did not quantify these harms.12 the task force changed its previous recommendations and now recommends that women aged 4049 years discuss with their physician whether breast screening is right for them , and it further recommends biennial screening instead of annual screening for all age groups.12 these recommendations were repeated in the 2011 canadian guidelines for breast screening.13 screening is likely to miss aggressive cancers because they grow fast , leaving little time to detect them in their preclinical phases.6 further , the basic assumption that finding and treating early - stage disease will prevent late stage or metastatic disease may not be correct , as breast cancer screening has not reduced the occurrence of large breast cancers14 or late - stage breast cancers,11 despite the large and sustained increases in early invasive cancers and ductal carcinoma in situ with screening . a systematic review from 2009 showed that the rate of overdiagnosis in organised breast screening programmes was 52% , which means that one in three cancers diagnosed in a screened population is overdiagnosed.9 it is quite likely that many screen - detected cancers would have regressed spontaneously in the absence of screening.15 16 we explored how the first comprehensive systematic review on mammography screening ever performed , the one from 2001 published in lancet,2 and the subsequent systematic cochrane reviews from 20064 and 20095 have been cited from 2001 to april 2012 . we investigated whether there were differences between general medical journals and specialty journals regarding which results were mentioned and how overdiagnosis , overtreatment , breast cancer mortality , total mortality , and the methods of the reviews were described . vested interests on behalf of both journals and contributing authors may be more pronounced in specialty journals , and this may influence views on specific interventions , such as mammography screening . we searched for articles quoting one of the three versions of the review2 4 5 ( date of last search 20 april 2012 ) . we used the source titles function in the institute for scientific information ( isi ) web of knowledge to count the number of times each review had been cited in individual journals . we only included journals in which four or more articles had cited one of the three versions of the review . this criterion led to the exclusion of specialty journals of little relevance for our study , for example , nephrology and research in gerontological nursing . we could not include the 2001 cochrane review1 because it was not indexed by the isi web of knowledge . this version of the review1 is not comparable to the other three versions,25 as the editors of the cochrane breast cancer group had refused to publish these data on overdiagnosis and overtreatment . a journal was classified as a general medical journal if it did not preferentially publish papers from a particular medical specialty . a journal was classified as a specialty journal if it preferentially published articles from a particular medical specialty or topic . when we rated how the papers cited the review , we looked for statements applicable to the following categories : breast cancer mortality methods used in the review we rated the quoting articles general opinions about the results and methods of the review using the labels accept , neutral , reject , unclear , or not applicable , using the following definitions : accept : the authors explicitly agreed with the results or methods , or quoted the numerical results without comments . neutral : the results or methods were mentioned and the author presented arguments both for and against them . reject : the authors explicitly stated that the results or methods were flawed , wrong , or false , or only presented arguments against them . only reporting a result from a favourable subgroup analysis unclear : the results or methods were mentioned , but it was not possible to tell if the authors agreed with them or not , or the results were only mentioned qualitatively . not applicable : the review was quoted for something else than its results or methods . the articles quoting the review were assessed in relation to the five categories ( overdiagnosis , overtreatment , breast cancer mortality , total mortality and methods ) separately , and no overall assessment of the articles general opinion about the review was made . texts classified as not applicable regarding any of the five categories were reread to determine and note which topics were discussed . two researchers ( kr , andreas brnden petersen , see acknowledgements ) assessed the text independently . disagreements were settled by discussion . in order to ensure blinded data extraction , an assistant ( mads clausen , see acknowledgements ) not involved with data extraction identified the text sections citing one of the three review versions and copied them into a microsoft word document . only this text was copied , and the two data extractors were therefore unaware of the author and journal names , time of publication and the title of the article . the fonts of the copied text were converted into times new roman , saved in a new document and the text labelled with a random number using the the key to matching the text with the articles was not available to data extractors until the assessments had been completed . the person responsible for copying the text made sure it did not contain any information that might reveal which of the three versions of the review had been cited . when there was more than one reference within the copied text , the reference to the review was highlighted to make it clear which statements referred to the review . all article types , as well as letters to the editor , were included and were classified as research papers , systematic reviews , editorials , letters , guidelines and narratives . p values were calculated using fisher 's exact test ( two - tailed p values ( http://www.swogstat.org/stat/public/fisher.htm ) ) . in total , 523 articles cited one of the three versions of the review : 360 cited the 2001 lancet review,2 123 the 2006 cochrane review4 and 40 the 2009 cochrane review.5 three articles cited both the 2001 and the 2006 versions of the review ; for these , we only used information related to the 2001 citation . including only journals that had published at least four articles , which cited one or more of the three versions of the review , the search identified 151 , 27 and 15 articles , respectively ( 193 in total , or 37% of the total of 523 articles ) . we excluded 22 additional articles , two because there was no reference to the review in the text , even though the review was listed as a reference,17 18 and 20 ( 10 , 5 and 5 citing the 2001 , 2006 and 2009 versions , respectively ) because they had one or more authors affiliated with the nordic cochrane centre . thus , 171 articles were included for assessment . in total , 63 articles ( 37% ) were from general medical journals and 108 ( 63% ) from specialty journals . a total of 80 ( 47% ) were from european journals and 91 ( 53% ) from north american journals . the general medical journals included were lancet ( 21 articles ) , bmj ( 13 articles ) , annals of internal medicine ( 13 articles ) , journal of the american medical association ( 7 articles ) , new england journal of medicine ( 5 articles ) and international journal of epidemiology ( 4 articles ) . the specialty journals included journal of the national cancer institute ( 13 articles ) , cancer ( 13 articles ) , american journal of roentgenology ( 7 articles ) and 15 others ( see box 1 ) . most of the included articles were either research papers ( n=63 , 37% ) or narrative articles ( n=44 , 26% ; table 1 ) . box 1the specialty journals included in this studyspecialty journals includedjournal of the national cancer institute ( 13)cancer ( 13)european journal of cancer ( 7)british journal of cancer ( 7)american journal of roentgenology ( 7)cancer causes and control ( 6)annals of oncology ( 6)european journal of surgical oncology ( 6)journal of medical screening ( 5)cancer epidemiology , biomarkers and prevention ( 5)ca : a cancer journal for clinicians ( 5)journal of clinical oncology ( 5)radiologic clinics of north america ( 5)oncologist ( 4)breast cancer research and treatment ( 4)breast ( 4)radiology ( 3)journal of surgical oncology ( 3 ) specialty journals included journal of the national cancer institute ( 13 ) european journal of cancer ( 7 ) british journal of cancer ( 7 ) american journal of roentgenology ( 7 ) cancer causes and control ( 6 ) annals of oncology ( 6 ) european journal of surgical oncology ( 6 ) journal of medical screening ( 5 ) cancer epidemiology , biomarkers and prevention ( 5 ) ca : a cancer journal for clinicians ( 5 ) journal of clinical oncology ( 5 ) radiologic clinics of north america ( 5 ) breast cancer research and treatment ( 4 ) journal of surgical oncology ( 3 ) the article types included in this study eu , european ; na , north american . the text of 32 of the 171 included articles ( 19% ) was rated as not applicable for all the five categories ( overdiagnosis , overtreatment , breast cancer mortality , total mortality and methods ) . in total , 15 of these 32 articles discussed the controversy when the first review was published , without specifically mentioning any of the categories . other subjects discussed were screening of women under the age of 50 ( two articles ) , and benefits of breast cancer screening other than those in our categories ( two articles ; see online supplementary appendix 1 for a full list of topics ) . the review s conclusions regarding overdiagnosis were not quoted in 87% ( 149/171 ) of the included articles and the results for breast cancer mortality were not quoted in 53% ( 91/171 ) of the included articles . general medical journals were more likely to accept the results or methods of systematic reviews than specialty journals , for example , overdiagnosis was classified as accepted in 11% ( 7/63 ) of articles in general medical journals , but in only 3% ( 3/108 ) of the articles in specialty journals ( p=0.05 ) , and the methods were accepted in 14% ( 9/63 ) of articles in general medical journals , but only in 1% ( 1/108 ) of articles in specialty journals ( p=0.001 ) . specialty journals were also more likely to reject the results for breast cancer mortality , namely for 26% ( 28/108 ) of articles compared with 8% ( 5/63 ; p=0.02 ) in general medical journals . the differences between general medical and specialty journals in relation to rejecting the categories overdiagnosis , overtreatment , total mortality and methods were small ( table 2 ) . the european and north american journals were equally likely to reject or accept the review 's methods or results ( data not shown ) . the number of citations of the three versions of the review differed a lot over time ( see table 3 ) . some years had very few citations , the lowest being 2012 and 2006 where the review was cited only 1 and 6 times , respectively . the highest number of citations was in 2002 ( 42 citations ) . there were no clear trends over time regarding the number of articles accepting or rejecting the methods and conclusions of the reviews , although the breast cancer mortality results may have received greater acceptance in recent years , for example , in 2002 , there was no acceptance of the breast cancer mortality results ( 0 of 42 ) , whereas 19% ( 3/16 ) explicitly accepted them in 2010 ( p=0.02 ; data not shown ) . number of citations of one of the three reviews per year the 2001 version of the review had more categories rejected and fewer categories accepted than the 2006 and 2009 versions , for example , 30% ( 3/10 ) accepted the results for breast cancer mortality presented in the 2009 version of the review , compared with 0 ( 0/140 ) in the 2001 version ( p=0.0002 ; see table 4 ) . comparison of the three versions of the review in terms of accepting or rejecting the five categories percentages in brackets are calculated from the total number of articles cited in that version of the review . the total number of articles cited in the 2006 version : 22 . the total number of articles cited in the 2009 version : 10 . although we deliberately reduced the sample size by requiring at least four citations for each included journal , we had enough articles that quoted the review for our comparisons . specialty journals were more likely to reject the estimate of the effect of screening on breast cancer mortality than the six general medical journals we included . articles in general medical journals were also more approving of four of the five individual categories we assessed ( overdiagnosis , overtreatment , total mortality and methods ) than the specialty journals were and the difference was statistically significant for all the categories , except for breast cancer mortality . we have previously found that scientific articles on breast screening tend to emphasise the major benefits of mammography screening over its major harms and that overdiagnosis was more often downplayed or rejected in articles written by authors affiliated with screening by specialty or funding , compared with authors unrelated with screening.19 recommendations in guidelines for breast screening are also influenced by the authors medical specialty.20 the difference we found between the general medical and specialty journals could be explained by conflicts of interest , which are likely to be more prevalent in specialty journals owned by political interest groups such as the american cancer society or by medical societies with members whose income may depend on the intervention . all the six general medical journals , but only 22% ( 4/18 ) of the specialty journals follow the international committee of medical journal editors ( icmje ) uniform requirements for manuscripts submitted to biomedical journals.21 even though journals have conflict of interest reporting policies , the conflicts of interest reported are not always reliable.22 all the general medical journals included are members of the world association of medical editors ( wame ) ; however , this is only the case for 22% ( 4/18 ) of the specialty journals included . wame aims to improve the editorial standards and , among other things , to ensure a balanced debate on controversial issues.23 being a member of wame helps with transparency in terms of their guidelines for conflicts of interest , but it also reminds editors to ensure that their journals are covering both sides of a debate . the results and conclusions on breast cancer mortality and overdiagnosis were more often accepted in 2010 than in any other year ( data not shown ) . the ongoing independent review of the national health service ( nhs ) breast screening programme announced by mike richards , the uk national clinical director for cancer and end of life care , department of health , in october 2011 is a further indication of this development.24 also , the us preventive services task force changed its recommendations for breast screening in 2009.12 though our data did not show strong time trends , we believe that these developments demonstrate a growing acceptance of the results and conclusions of our systematic review . in support of this , the 2009 version of the cochrane review has received more approval than disapproval , for example , 30% ( 3/10 ) accepted the results for breast cancer mortality presented in the 2009 version of the review , compared with 0 ( 0/140 ) in the 2001 version.2531 the us preventive services task force was heavily criticised after the publication of its new recommendations in 2009,29 32 but the criticism came from people with vested interests , and the independent canadian task force supported the conclusions of the us preventive services task force and the 2009 cochrane review5 in 2011.13 the 2001 review published in lancet was by far the most cited of the three reviews . it was 5 years older than the cochrane review from 2006 , but the vast majority of the citations came within the first year of publication . it was unique at the time , as it questioned whether mammography screening was effective , based on a thorough quality assessment of all the randomised controlled trials , and also was the first systematic review to quantify overdiagnosis . a minor part of the included articles ( 19% , 32/171 ) did not refer to any of our five specified outcomes . in nearly half of the cases ( 47% ) , this was due to the article referring only to the debate that followed the first review,33 and not its results or methods . the texts also dealt with topics such as false positives or screening women under the age of 50 years . this was the case for articles in both the general medical and specialty journals , and for articles in the european and north american journals . the text typically dealt with only one or two of our categories , for example , overdiagnosis , and did not mention overtreatment or any other categories . none of the articles rejected overdiagnosis ( 0 of 171 articles ) , which could be because they did not mention the issue at all . this was the case in 76% of scientific articles on breast screening in a previous study by jrgensen et al.19 our definition of rejection was that the author should explicitly state that the review 's estimate was flawed , wrong or false , or that they should in some way argue against it . with this strict definition , we did not capture authors who have consistently stated over the years in other articles than those we included that they do not believe that overdiagnosis is a problem , and we also did not present their views on the subject . numerous articles were classified as unclear for one or more of our categories . the texts in question did not allow an interpretation in any direction and we did not rate the articles as accepting or rejecting the review s results and methods unless it was perfectly clear what the authors meant . this reflects that authors often do not present clear opinions of the intervention which they discuss . an additional explanation for the many articles found to be unclear could be that we did not assess the entire article , and arguments could have been presented elsewhere in the text . letters were included in this study , which could explain why some of the articles were classified as not applicable in all the five categories . the specialists who read and respond to letters in their own journals might be more likely to react negatively towards the review because of conflicts of interest.19 specialists with a connection to mammography screening also reply to articles in general medical journals when they concern mammography screening . therefore , it is quite likely that there is a greater difference between the specialists involved with the screening programmes and the doctors not involved in breast cancer screening , in terms of accepting and rejecting the results and methods , than we have found in this study . the results and conclusions on breast cancer mortality and overdiagnosis were more often accepted in 2010 than in any other year ( data not shown ) . the ongoing independent review of the national health service ( nhs ) breast screening programme announced by mike richards , the uk national clinical director for cancer and end of life care , department of health , in october 2011 is a further indication of this development.24 also , the us preventive services task force changed its recommendations for breast screening in 2009.12 though our data did not show strong time trends , we believe that these developments demonstrate a growing acceptance of the results and conclusions of our systematic review . in support of this , the 2009 version of the cochrane review has received more approval than disapproval , for example , 30% ( 3/10 ) accepted the results for breast cancer mortality presented in the 2009 version of the review , compared with 0 ( 0/140 ) in the 2001 version.2531 the us preventive services task force was heavily criticised after the publication of its new recommendations in 2009,29 32 but the criticism came from people with vested interests , and the independent canadian task force supported the conclusions of the us preventive services task force and the 2009 cochrane review5 in 2011.13 the 2001 review published in lancet was by far the most cited of the three reviews . it was 5 years older than the cochrane review from 2006 , but the vast majority of the citations came within the first year of publication . it was unique at the time , as it questioned whether mammography screening was effective , based on a thorough quality assessment of all the randomised controlled trials , and also was the first systematic review to quantify overdiagnosis . a minor part of the included articles ( 19% , 32/171 ) did not refer to any of our five specified outcomes . in nearly half of the cases ( 47% ) , this was due to the article referring only to the debate that followed the first review,33 and not its results or methods . the texts also dealt with topics such as false positives or screening women under the age of 50 years . this was the case for articles in both the general medical and specialty journals , and for articles in the european and north american journals . the text typically dealt with only one or two of our categories , for example , overdiagnosis , and did not mention overtreatment or any other categories . none of the articles rejected overdiagnosis ( 0 of 171 articles ) , which could be because they did not mention the issue at all . this was the case in 76% of scientific articles on breast screening in a previous study by jrgensen et al.19 our definition of rejection was that the author should explicitly state that the review 's estimate was flawed , wrong or false , or that they should in some way argue against it . with this strict definition , we did not capture authors who have consistently stated over the years in other articles than those we included that they do not believe that overdiagnosis is a problem , and we also did not present their views on the subject . the texts in question did not allow an interpretation in any direction and we did not rate the articles as accepting or rejecting the review s results and methods unless it was perfectly clear what the authors meant . this reflects that authors often do not present clear opinions of the intervention which they discuss . an additional explanation for the many articles found to be unclear could be that we did not assess the entire article , and arguments could have been presented elsewhere in the text . letters were included in this study , which could explain why some of the articles were classified as not applicable in all the five categories . the specialists who read and respond to letters in their own journals might be more likely to react negatively towards the review because of conflicts of interest.19 specialists with a connection to mammography screening also reply to articles in general medical journals when they concern mammography screening . therefore , it is quite likely that there is a greater difference between the specialists involved with the screening programmes and the doctors not involved in breast cancer screening , in terms of accepting and rejecting the results and methods , than we have found in this study . articles in specialty journals were less approving of the results and methods of the systematic review of breast screening than those in general medical journals . this may be explained by conflicts of interest , as several specialty journals were published by groups with vested interests in breast screening , and several articles had authors with vested interests .

introductionin 2001 , a cochrane review of mammography screening questioned whether screening reduces breast cancer mortality , and a more comprehensive review in lancet , also in 2001 , reported considerable overdiagnosis and overtreatment . this led to a heated debate and a recent review of the evidence by uk experts intended to be independent.objectiveto explore if general medical and specialty journals differed in accepting the results and methods of three cochrane reviews on mammography screening.methodswe identified articles citing the lancet review from 2001 or updated versions of the cochrane review ( last search 20 april 2012 ) . we explored which results were quoted , whether the methods and results were accepted ( explicit agreement or quoted without caveats ) , differences between general and specialty journals , and change over time.resultswe included 171 articles . the results for overdiagnosis were not quoted in 87% ( 148/171 ) of included articles and the results for breast cancer mortality were not quoted in 53% ( 91/171 ) of articles . 11% ( 7/63 ) of articles in general medical journals accepted the results for overdiagnosis compared with 3% ( 3/108 ) in specialty journals ( p=0.05 ) . 14% ( 9/63 ) of articles in general medical journals accepted the methods of the review compared with 1% ( 1/108 ) in specialty journals ( p=0.001 ) . specialty journals were more likely to explicitly reject the estimated effect on breast cancer mortality 26% ( 28/108 ) , compared with 8% ( 5/63 ) in general medical journals , p=0.02.conclusionsarticles in specialty journals were more likely to explicitly reject results from the cochrane reviews , and less likely to accept the results and methods , than articles in general medical journals . several specialty journals are published by interest groups and some authors have vested interests in mammography screening .

Introduction Methods Results Discussion Development over time Limitations Conclusion Supplementary Material Supplementary Material

fl is the second most common form of nhl , accounting for approximately 30% of nhl cases . the disease is characterized by a slow progression and high response rates to therapy , that is the reason why it is considered the prototype of indolent lymphomas ; median survival is currently around 14 years , with most patients displaying an indolent form of the disease , slowly progressing over many years . nonetheless , most patients eventually develop increasingly resistant disease over time , and in up to 45% of cases , the original indolent subtype transforms into an aggressive subtype , an event that is associated with a poor outcome.1,2,3 the first hit of the oncogenic cascade leading to fl is attributed to the t(14;18 ) chromosomal translocation that occurs in an early b cell stage in the bone marrow . naive b cells , carrying the t(14;18 ) , exit the bone marrow and colonize secondary lymphoid tissue , where they undergo the germinal center reaction but have a survival advantage due to their constitutive expression of bcl2 , which is not normally expressed in the germinal center.4 apart from the t(14;18 ) , recurrent secondary genetic alterations including genomic gains , losses , and mutations ( i.e. alterations in mll2 , epha7 , tnfrsf14 , and ezh2 ) could provide a growth advantage to the neoplastic cells . moreover , the crosstalk between neoplastic b cells and the microenvironment plays an important role in sustaining tumor cell growth and eventually promoting transformation.5 current treatment strategies vary from the classical watch and wait approach to the use of anti cd20 monoclonal antibodies ( labeled or unlabeled with radioimmunoconjugates ) in combination with chemotherapy , while more aggressive treatment approaches including autologous or allogeneic stem cell transplantation are reserved to patients with more resistant disease.6 recently a large bulk of molecular and clinical research has been performed to better understand the molecular mechanisms of lymphomagenesis and to develop non - chemotherapeutic agents active in specific lymphoma subtypes ; in this field infectious agents could represent therapeutic targets for lymphoma treatment toward chemotherapy - free therapeutic approaches . despite huge advances in the comprehension of the genetic anatomy of fl , the potential epidemiologic role of environmental stimuli has not been clearly established ; this is somehow in contrast to the huge bulk of knowledge which has been accumulated in malt lymphomas . nevertheless , a number of biological and clinical observations suggests that interaction with physiological and pathological microbial populations might play a role also in fl . a classical model of the infection - driven lymphoproliferative disorder is helicobacter pylori - induced gastric malt lymphoma where antibiotic therapy allows eradication of both the infectious agent and the clonal b - cell expansion , leading to long - term complete remissions ( cr).7 the identification of this pathogen as the causative agent in gastric malt lymphomas have resulted in substantial progress in understanding the physiopathology of the disease permitting to develop new therapeutic strategies . the list of lymphomas evolving in response to antigen ( bacterial or viral ) has been growing rapidly in recent years , associated in some cases with similar therapeutic success.8 although no such association with infectious agents or other early specific therapeutic target has yet been identified for fl , this concept seems ideally suited to such an indolent disease . this review summarizes current evidence for a role of either physiological and pathological exogenous microbial species in the pathogenesis of fl . so , we underwent an extensive literature search focusing on clinical observations suggesting such correlations , and we tried to underline potential similarities between fl and other indolent lymphoproliferative processes where the role of microbial organisms is clearly established . in recent years , a growing number of exogenous microbial agents have been linked to nhl . the helicobacter pylori ( hp ) , chlamydia psittaci and hepatitis c virus are best - known examples , but other agents have been identified in the pathogenesis of more rare subtypes of nhl ; these associations are important because they have clinical and therapeutic implications and provide novel insights into the mechanisms that govern lymphoma development.9 hp is a proteobacteria epsilon bacterium known to cause stomach ulcers and chronic gastritis . its role in the pathogenesis of the majority of cases of gastric malt lymphoma was demonstrated nearly twenty years ago . hp affects about 50% of the world s population even if only 12% of infected individuals will develop a malignant disease . the pathogenetic role of hp is related to the oncogenic properties of the cytotoxin - associated antigen a ( cag - a ) , a protein that is able to activate the signaling pathway leading to the activation and upregulation of the antiapoptotic molecule bcl2.10,11 three major chromosomal translocations specific of malt lymphomas are reported , i.e. t(11;18 ) which is the most common ( found in nearly 30% of the cases ) , t(14;18 ) and t(1;14 ) . hp eradication using a combination of antibiotics and proton - pump inhibitors ( ppi ) , represents the standard treatment of hp - associated malt - lymphomas , leading to lymphoma regression in about 75% of patients.12 chlamydophila psittaci belongs to the family of chlamydiae and is the second most studied among bacteria having a pathogenetic role in malt - lymphomas . dna from this bacterium has been found in biopsies of malt lymphoma of the ocular adnexa . the finding that c. psittaci infection has been detected in up to approximately 80% of italian patients with ocular adnexa malt lymphoma provided the rationale for the antibiotic treatment of localized lesions . moreover , the eradication of c. psittaci infection with doxycycline for patients with ocular adnexa malt lymphoma resulted in lymphoma regression in approximately 50% of patients.9 epstein - barr virus ( ebv ) is the first human herpes virus found to be associated with the pathogenesis of cancer . ebv has a worldwide distribution , being able to establish a lifelong infection in more than 90% of individuals . primary infection is usually asymptomatic or could cause a benign lymphoproliferative disease , known as infectious mononucleosis . ebv has a successful strategy to reside in the hematopoietic system , including the establishment of a nonpathogenic latent infection of memory b lymphocytes that allows the virus to persist for the lifetime . according to current knowledge , latent antigens encoded by ebv interfere with a number of critical cellular pathways , thereby promoting oncogenesis . although human ebv infection may lead to the development of a variety of hematopoietic and epithelial cancers , most common cases result from the transformation of infected b cells into lymphoproliferative disorders:13 hodgkin lymphomas , diffuse large cell and burkitt lymphomas . moreover , ebv can cause a rare but potentially fatal complication in hematopoietic stem cell transplants , as well as in solid - organ recipients , known as ebv - associated post - transplant lymphoproliferative disease ( ptld).14,15,16 human immunodeficiency virus ( hiv ) is a lentivirus of the retroviridae family that integrates itself into host chromosomal dna . the increased risk for lymphoma appears related to multiple factors , including the transforming properties of the virus itself , the immunosuppression and , most importantly , opportunistic infections associated with other lymphotropic herpes viruses such as ebv and human herpesvirus 8 . the clinical outcome appears to be worse than in similar aggressive lymphomas in the general population . however , following the introduction of highly active antiretroviral therapy , the risk of developing lymphoma in the context of hiv infection has decreased , and the clinical outcome has improved.17 hepatitis c virus ( hcv ) is a small rna virus of the flaviviridae family ; is a hepatotropic and lymphotropic virus responsible for acute hepatitis and chronic liver disease ; the presence of hcv is associated with a spectrum of lymphoproliferative disorders , ranging from polyclonal b - cell expansion to overt malignant lymphoma . indeed , as well as small b - cell clones can be detected in bone marrow or liver biopsies , a higher frequency of lymphoid malignancies has been reported in hcv - positive patients . the association between hcv infection and nhl has been demonstrated by epidemiological studies , in particular in highly endemic geographical areas such as italy , japan , and southern parts of united states . in these countries , together with diffuse large b - cell lymphomas , marginal zone lymphomas are the histotypes most frequently associated with hcv infection . the most convincing argument for a causative link between hcv and lymphoproliferation is represented by studies demonstrating the eradication of the neoplastic clone by the antiviral treatment in hcv - positive patients affected by indolent nhl ( 18 ) . analogous to what has been observed in hp - associated gastric , the role of hcv infection in lymphomagenesis may be related to the chronic antigenic stimulation of b - cell immunologic response by the virus.19,20 adult t - cell leukemia - lymphoma ( atl ) is an aggressive lymphoid proliferation associated with the human lymphotropic virus type i ( htlv - i ) . atl usually occurs in people from htlv - i endemic regions , such as southern japan and the caribbean . htlv - i causes transformation and clonal expansion of t cells , resulting in atl in approximately 1%5% of the infected hosts , with a mean latency period of > 50 years . recently , a worldwide meta - analysis revealed that the combination of zidovudine and ifn- is highly effective in the leukemic subtypes of atl and should be considered as standard first - line therapy in this setting.21 human herpesvirus 8 ( hhv8 ) is a gammaherpesvirus associated with primary effusion lymphoma , a lymphoproliferative disease that is rarely observed in immunocompromised individuals . these neoplastic disorders that result from hhv8 infection are most commonly related to immunodeficiency states , including hiv infection and ebv infection . the lymphoma is characterized by the localization in one of the body cavities ( pleural , pericardial , or peritoneal cavity ) , without lymph node enlargement and lymphadenopathy . given the heterogeneous nature of lymphoma subtypes and their different clinical behavior , it is intriguing to identify the risk factors potentially responsible for the occurrence of nhl , so various occupational , environmental and chemical agents have been claimed by several epidemiological studies . however , although for some factors the correlation seems to exist , definite conclusions have not been drawn . several reports have also investigated the possible association between infection - related conditions and the occurrence of nhl ; in fact , several infectious agents have been identified as causative factors for the development of nhl , most likely due to their induction of dna damage , inflammatory cells proliferation , and cytokine release . to address this issue the international lymphoma epidemiology consortium ( interlymph ) , an open scientific forum for epidemiological research funded in 2001 , undertook the nhl subtypes project ; this is an international group of multidisciplinary specialists , who have worked together with the aim of identifying associations of several risk factors across different lymphoma subtypes.23 regarding fl , in 2013 a large pooled analysis carried on by the interlymph consortium made an attempt to assess associations between medical , hormonal , family history , lifestyle and occupational factors with the risk of developing fl . the incidence rate of fl was reported as higher in western countries , which comprises ~30% of nhl , with a white to black ratio of 2:3 , and relatively rare in developing and far eastern countries . moreover , fl risk was increased in subjects with a first - degree relative with non - hodgkin lymphoma in spray painters among women with sjgren and among cigarette smokers and obese subjects . no specific observation mentioned a link between infection and risk of fl.24 another large retrospective case control study using seer and medicare database investigated the role of infection - related conditions and different nhl subtypes.25 cases were defined as individuals with a seer diagnosis of primary lymphoid malignancy between 1992 and 2005 . the database identified respiratory and skin infections to be associated with an increased risk of nhl in individuals aged more than 66 years . claims for sinusitis , laryngitis and herpes zoster were present in the history of fl patients , sinusitis , laryngitis and herpes zoster were significant at longer latencies . most fl cases carried the t(14;18 ) , which was hypothesized to be transformed by exogenous antigen stimulation , such as from a viral infection.26 antigenic stimulation and/or subclinical immune deficiency , predisposing patients to both infections and lymphoma , were claimed as possible association between infection - related conditions and lymphoma . the gene sequence for the immunoglobulin ( ig ) heavy - chain ( h ) and light - chain ( l ) variable regions are assembled in the early stages of b - cell development in the bone marrow from distinct variable ( v ) , diversity ( d ) and joining ( j ) segments through a process of somatic dna rearrangement known as v(d)j recombination . in later stages , which takes place in the germinal center ( gc ) of the secondary lymphoid tissues , naive b - cells with low - affinity functional surface ig ( sig ) are induced to proliferate . the high proliferation rate is associated with somatic hypermutation of ig genes , a process that introduces a high incidence of mutations within the v region of genes . somatic hypermutation is thought to be a prerequisite for affinity maturation of antibody response . at this stage , normal b cells that are specific for an antigen are induced to operate a selection process that expands the population of b cells with an optimal binding affinity for the antigen . also , b cells carrying the t(14;18 ) exit the bone marrow and colonize the gc of secondary lymphoid tissue ; subsequently they undergo somatic hypermutations of igvh - genes , with mutational patterns very similar to their normal counterpart , but with a survival advantage due to the constitutive expression of bcl2 . recent studies by schneider et al . demonstrated that somatic hypermutations occurring in fl cells could introduce sugar moieties , like high - mannose - terminated glycan , into the variable domain of the surface ig antigen - binding sites , which create potential novel binding sites to mannose - specific lectins . in fl cells , b - cell receptor ( bcr ) expression is retained , despite the characteristic chromosomal translocation t(14;18 ) , because bcr is fundamental for the transduction of the signals that maintain the survival and growth of fl clones . bcr variable - region mannoses in fl are recognized by lectins of common opportunistic bacteria , such as burkholderia cenocepacia and pseudomonas aeruginosa , that are usually found in soil and water ; these lectins represent a potent stimulus for the proliferation of b cells expressing this kind of glycan - terminated glycan.27,28,29 therefore , these studies directly support the potential importance of microbial exposure in the proliferation and survival of fl clones , and they might be a key to a better understanding of the pathogenesis of fl . although an expanding literature has examined several risk factors potentially correlated with the occurrence of fl , the etiology of the proliferative stimulus is generally unknown , and the few relationships observed suggest a complex multifactorial etiology . a recent meta - analysis , selecting more than 20 articles , showed a more than two - times increase in the odds of developing nhl in patients with hbv infection . interestingly , regarding fl subtype , a trend toward statistical risk was observed in countries with a high prevalence of hbv infection while no statistical risk was seen in countries with a low prevalence of hbv infection.30 the conclusion of the study was that was difficult to determine if the increased risk of fl in areas of high prevalence of hbv infections is due simply to a larger number of hbv infections or a true causal relationship . in the latter case , hbv might be responsible for lymphomagenesis through a chronic stimulation of b - cells which may predispose to dna damage and transformation into neoplastic cells , or through an immunologic response to chronic local antigenic stimulation . as opposed to hbv , a case - control study carried on by the interlymph did not show an increased association between hcv infection and fl , that was restricted to other specific b - nhl subtypes like diffuse large b - cell lymphoma ( dlbcl ) , marginal zone lymphoma , and lymphoplasmacytic lymphoma.19 an interesting clinicopathological finding came up from a spanish study that analyzed a retrospective series of 58 patients with a diagnosis of hcv - positive b - cell lymphoproliferative disorder ; eight of them were affected by fl , and at least half of them expressed bcl2 and p53 . interestingly , the authors reported a cohort of 11 patients in which a clonal b cell expansion in the peripheral blood and bone marrow could be revealed , in the absence of conclusive histological evidence of neoplastic infiltration . these expanded clones make up a definite group of hcv - associated monoclonal b - cell lymphocytosis that should be monitored because a 10% risk of evolution to overt lymphoma has been demonstrated.31 currently , the association between ebv and follicular lymphoma is reported only in the form of isolated case reports in patients with various form of immunodeficiency or in the context of transformation to diffuse large cell lymphoma or classical hodgkin lymphoma . mackrides et al . analyzed 382 cases of fl consecutively diagnosed at the university of miami and stanford , in order to provide an estimated prevalence of ebv - positive fl ; all the cases were tested for the expression of ebv - encoded small rna ( eber ) as determined by in situ hybridization . they identified 10 cases of ebv - positive fl ( prevalence=2.6% ) with a significant prevalence of grades 3a3b fl ( 9 out of 10 ) and frequent strong coexpression of cd30 ; all cases demonstrated progression of the disease to a higher grade fl or diffuse large b - cell lymphoma . given the increased incidence of ebv in high - grade fl and the fact that the cases are clinically and morphologically indistinguishable from ebv - negative fl patients , the authors suggested the screening for eber in all high - grade cases.32 recently an intriguing association between coxiella burnetii / q fever and the incidence of b - cell lymphomas was proposed by melenotte et al . in a large scale study.33 starting from the observation of the occurrence of lymphoma in a patient with q fever , they screened over 1000 consecutive patients of the french national referral center for q fever database and examined if there was an association between the two diseases . an excess risk of dlbcl and fl was found in individuals who had q fever compared with the general population and above all patients with a persistent localized infection were found to have a greater risk of lymphoma . these results support the evidence that a novel factor should be added to the list of bacteria that promote human b - cell lymphomas , in particular , fl . the most relevant studies reporting a link between follicular lymphoma and infectious agents are summarized in table 1 . taken in mind the gastric malt as a well - accepted example of antigen - driven neoplastic cell proliferation , portlock et al . explored the association between infectious agents and nhl in a cohort of 56 patients with an untreated advanced non - bulky indolent lymphoma.34 all patients were tested for hp , hcv , borrelia burgdorferi , chlamydia psittaci and small bowel bacterial overgrowth ; in this series , a documented infection was found in 37% of the patients , with a prevalence of hp . starting from the observation of anecdotal lymphoma remissions after antibiotic therapy in a series of patients not requiring chemotherapy , they speculated that a prevention strategy would decrease the risk of future lymphoma progression driven by such antigens . therefore in 2007 , they launched a prospective clinical trial testing the role of prolonged clarithromycin antibiotic therapy as a first treatment in the same category of indolent advanced - stage lymphoma patients . although the small sample size , they reported lymphoma objective responses in 9 of 32 patients ( 28.1% ) with a long treatment - free survival for patients responding to antibiotics.35 the association between infectious agents and fl added new important information about the role played by the antigen stimulation in fl ; moreover , the possibility to treat the neoplastic disease in a simple and efficient way could be considered a step toward developing a lymphoma preventive strategy by reducing the antigen drive . in the last years , several infectious agents , like hepatitis c , human immunodeficiency , and epstein - barr viruses , and helicobacter pylori , chlamydia psittaci , and coxiella burnetii bacteria have been reported as involved in the malignant transformation of b or t lymphocytes , and therefore associated with the pathogenesis of lymphoproliferative disorders . while this hypothesis has been demonstrated for some rare subtypes of nhl , for the majority the evidence is uncertain . regarding fl , based on available data , evidence linking this lymphoma subtype and exogenous infectious agents are weak , and currently , fl can not be considered as an infection - driven disease . however , some clinical , epidemiologic studies and case reports indicate that it is still somehow premature to conclude that exogenous agents have a negligible role in the genesis of fl . it has been estimated that chronic infections caused by viruses , bacteria , and parasites are the causative agents of nearly 1015% of global cancers burden.36,37 these infectious agents promote a cascade of events culminating in chronic inflammatory responses . chronic antigenic stimulation has been postulated as a potential mechanism for carcinogenesis , thus predisposing target tissues to increased cancer susceptibility . in particular , in antigen - driven hematologic malignancies , like hp - associated with malt , the chronic stimulation of the innate immune system causes a clonal expansion of b - lymphocytes , which leads to the production of oxidative reactions ; these events result in genetic alterations , which eventually result in the development of a neoplastic monoclonal lymphoproliferation . as well as for malt lymphomas , also for fl could be postulated an inflammatory response secondary to an infectious - driven chronic antigenic stimulation , inducing t(14:18 ) translocation , leading to the transformation of a germinal center - derived b - cell . apart from hp and other few microorganisms that colonize the gastrointestinal tract , it should be kept in mind that little is known about the complex community of human microbiota which includes more than 10 procaryotic cells per individual . modern next generation sequencing tools for microbiome analysis are becoming widely available and intriguing correlations between the type of bacterial colonization in multiple districts , and some diseases have been established . of note , human microbiota has some well - established differences among different world areas as also observed in several indolent lymphoid disorders . it is , therefore , advisable to further investigate this potential link by performing careful case - control or population analyses aiming at verifying whether specific pathological or nearly physiological microbiota patterns might be responsible for a chronic antigen stimulation in those lymphomas where a clearly responsible microorganism has still not been identified . intestinal microbiota either directly or indirectly through the immune system can lead to aberrant dna replication , particularly in some b lymphocytes which are vulnerable to genetic instability and activation , eventually affecting several pathways associated with lymphomagenesis.38 finally , a chronic antigenic infectious stimulation was shown to be fundamental also in the cell perturbation of the microenvironment in sustaining the neoplastic cell growth . indeed , also this pathway could play a role in the oncogenic cascade leading to fl,39,40 and the encouraging results obtained by a novel panel of inhibitors of the signal transduction of the bcr , has led to further investigate the crosstalk between the downstream bcr signaling cascade and the microenvironment . the btk inhibitor ibrutinib and the pi3k inhibitor idelalisib have demonstrated good safety profile and promising clinical efficacy , affecting the survival of neoplastic b cells by preventing lymphocyte adhesion and homing , and inhibiting the microenvironment signals that commonly sustain the malignant clone.41,42 the pathogenesis of fl is a multistep process in which the t(14;18 ) translocation in a b lymphocyte appears to be fundamental for the initiation of the neoplastic cascade . even if still unclear , infectious agents could play a role as a first hit responsible for the b - cell malignant transformation and growth . precise elucidation of the mechanisms underlying lympho - proliferations may provide important clues for understanding how immune disturbance contributes to the development of this subtype of lymphoma . moreover , the responses shown by bcr inhibitors and by antibacterial treatments , which can have cytoprotection properties like rifaximin , considered a gut microenvironment modulator , provide an intriguing argument for a causative link between infectious agents and b - cell lymphoproliferation .

several infectious agents appear to provide a proliferative signal -- antigen - drive that could be implicated in the pathogenesis of various type of non - hodgkin lymphoma ( nhl ) . a classical model of the infection - driven lymphoproliferative disorder is helicobacter pylori - induced gastric malt lymphoma , where antibiotic therapy allows the eradication of both the infectious agent and the clonal b - cell expansion . following the footsteps of this example , several retrospective studies have found a correlation with other pathogens and b - cell lymphomas , adding new relevant information about pathogenesis and laying the groundwork for chemotherapy - free treatments.although no clear association has been found between infectious agents and follicular lymphoma ( fl ) , a growing number of biological and clinical observations suggests the interaction of physiological and pathological microbial populations also in this subtype of lymphoma . in the last few years , epidemiological studies investigating the association of known risk factors and fl found a potential correlation with viral or bacterial infections ; moreover , recent findings of the stimulation of fl clones support the importance of microbial exposure to lymphomagenesis and disease progression.in the following review we make an attempt to find tangible evidence for a role of either physiological and pathological exogenous microbial species in the pathogenesis of fl , and try to integrate the findings coming from epidemiological , biological and interventional studies to define future novel treatment and prevention strategies for fl .

Introduction Role of Infection in other Lymphomas Epidemiological Evidence Biological Evidence Clinical Evidence Discussion Conclusions

in the may issue of genome medicine , belmont and mcguire make the case for a ' uniform electronic health record ' ( ehr ) that includes both genotype and phenotype information . by uniform they mean a single data standard across different ehr databases and user interfaces , rather than a single database or a single user interface ( this has been confirmed by personal communication with the authors ) . it is certainly true that a clearer picture of a patient 's health is possible when their genotype data are combined with phenotype data . the quantity and quality of these data are improving , along with the analytical tools that allow us to interpret them . patients , clinicians and researchers can all benefit from a better understanding of these data , and belmont and mcguire 's article describes efforts in europe and the usa to unify the datasets . however , other parties that would benefit from better understanding include public health officials , government bureaucrats , insurance companies and employers . and in some cases , there are conflicts of interest ; for example , an insurance company could use genetic information to raise premiums or deny cover , whereas a patient might use the same information to seek increased cover when they learn of the risk for future diseases . there are ways to solve the conflicts of interest that can arise from the use and availability of patient data . first , as belmont and mcguire describe , efforts such as the personal genome project allow patients to opt in to fully disclose their genetic information for the benefit of researchers . patientslikeme.com has an openness policy alongside their privacy policy so that participants can agree to share all their data , and tens of thousands of people from around the world have already agreed to do so . the value to researchers is currently limited because the data are self - submitted rather than independently verified , but the proof that patients are willing to share their personal information is there . the principle must still stand , however , that data sharing begins with and is controlled by the patient . this favors a single personal health record ( phr ) as a database rather than a single electronic health record . phrs are records owned and controlled by the patient , as opposed to ehrs , which are owned and controlled by health care practitioners . useful data standards for phr and ehr communication should be expanded to fit the genomic vision that belmont and mcguire outline . in particular , the continuity of care record ( ccr ) data format is the digital equivalent of a referral letter from one clinician to another about a patient . it is supported by phr providers such as google health and microsoft healthvault ; pharmacies such as walgreens and cvs ; and providers such as minuteclinic . the department of health and human services at the national cancer institute unveiled a standard earlier this year for family history . de - identification is a better term than anonymization because the latter implies a binary process , which is misleading , while the former accurately conveys a spectrum . we know that de - identification algorithms are already in use when the public interest demands phenotype sharing but patient consent is not possible or practicable . examples include notifiable disease surveillance , public health planning and large - scale research . in these cases , looking after the patient 's privacy requires measures that ensure they can not be identified through illicit use of those data . illicit patient re - identification has three sources of risk : the research team , all other people who have access to these data and finally the inherent readability of the data itself . building a single system to be accessed by hundreds or thousands of researchers across tens or hundreds of projects such systems can therefore never be adequately private . what might work , when public interest demands but consent is not possible , are schemes that separately copy just the minimum of phenotype and genotype data from various health management systems for a specific group of vetted researchers working within a highly protective legal context . any change in project purpose would necessitate a re - assessment of the prevailing risks . a system in which highly vetted organizations were permitted to collect and link minimal data from all its various sources would be ideal . in addition , the architecture for a single ehr or phr is not a simple one . it is desirable and correct to view all the relevant data at the time of making a clinical decision or coming to a research conclusion . however , that does not mean all the data should be viewable . for the person viewing the data , their storage in a single place but for the people whose data are viewed , such a data warehouse is ripe for abuse . citizens have expressed their distrust of such systems on many occasions , and security experts have repeatedly pointed out the risks of data warehouses . federated architectures , where data are spread across multiple sites and queried as needed , have been deployed and are made easier by new approaches , such as service - oriented architecture . and knowing how much protection to put in place is made easier by couching privacy concerns in terms of the risk of illicit patient re - identification . all of the above discussion is not to say that a single ehr is a bad idea . belmont and mcguire make a good case for the need to unify data in the service of laudable aims , including providing good patient care and advancing medical research . however , just because something can be done does not mean that it should be done , and in health care it is patients who should decide what should be done . they will be the most affected by privacy breaches , so they must be the ones who decide which of the benefits to take advantage of . the good news is that mature technologies exist that do put patients in control . as professionals we need to earn their trust by using these technologies when we ask for data sharing that makes our jobs easier . ma is the ceo of patients know best , a company that makes and sells personal health record software . rn is the ceo of sapior , a company that makes and sells de - identification software for the private sharing of health data . ma wrote the sections on personal health records and rn wrote those on de - identification .

there is value to patients , clinicians and researchers from having a single electronic health record data standard that allows an integrated view , including genotype and phenotype data . however , it is important that this integrated view of the data is not created through a single database because privacy breaches increase with the number of users , and such breaches are more likely with a single data warehouse . furthermore , a single user interface should be avoided because each end user requires a different user interface . finally , data sharing must be controlled by the patient , not the other end users of the data . a preferable alternative is a federated architecture , which allows data to be stored in multiple institutions and shared on a need - to - know basis . the data sharing raises questions of ownership and stewardship that require social and political answers , as well as consideration of the clinical and scientific benefits .

None Conclusions Abbreviations Competing interests Authors' contributions

a challenge in medicinal chemistry is the appropriate evaluation of structure activity relations . if the assays fail to fully capture the critical features determining biological activity , then the impact from the synthetic effort is correspondingly diminished . the traditional model of drug action is of a ligand binding to a drug target , with response linked to target occupancy . the profound progress in our understanding of cellular biochemistry now affords detailed , albeit still developing , insights into the complexity of regulation of individual drug targets . incorporating these insights into the evaluation of structural analogues activity relationships ( csars ) , is illustrated here for a particular therapeutic target , protein kinase c ( pkc ) , which displays complex regulation in response to ligands directed at its regulatory c1 domain . we show that a series of ligands for the regulatory domain of pkc are not equivalent but can be distinguished by the isoelectric focusing signatures of pkc that they induce , as detected by a capillary isoelectric focusing immunoassay system . in this system , proteins and their phosphorylated isoforms are separated by charge , followed by target specific antibody probing and chemiluminescence detection . multiple phosphorylation isoforms can be simultaneously separated , detected , and quantified allowing fine dissection of molecular signaling events . pkc plays a central role in cellular signaling , responding to the lipophilic second messenger sn-1,2-diacylglycerol ( dag ) , and is a validated therapeutic target for cancer and a range of other conditions . dag , which is generated as one of the products of phosphoinositide turnover in response to activation of a wide variety of cellular receptors , binds to the c1 domains of pkc . the c1 domains function as hydrophobic switches . they possess a hydrophobic surface interrupted by a hydrophilic cleft . the dag , ultrapotent surrogates such as the phorbol esters , or synthetic ligands such as dag - lactones or benzolactams insert into this hydrophilic cleft , completing the hydrophobic surface as well as providing additional hydrophobic structural elements . driven by this increase in hydrophobicity , the c1 domain ligand complex associates with the membrane , bringing about conformational change in the pkc leading to enzymatic activation and a shift in its subcellular localization . both the pattern of membrane localization and the kinetics of the shift in localization markedly depend on the structure of the ligand . more lipophilic ligands , such as phorbol 12-myristate 13-acetate ( pma ) , initially cause pkc to move to the plasma membrane , after which it slowly shifts in part to internal membranes . more hydrophilic ligands , such as phorbol 12,13-dibutyrate , in contrast , cause the initial localization to the internal membranes . the pattern of localization , moreover , correlates in part with the pattern of biological response . thus , the tumor promoting derivative 12-deoxyphorbol 13-tetradecanoate behaves like pma , whereas the antipromoting derivative 12-deoxyphorbol 13-phenylacetate acts like phorbol 12,13-dibutyrate . marquez and co - workers evaluated , in a range of biological systems , combinatorial libraries of dag - lactones that only varied in their hydrophobic substituents . zip codes to membrane subdomains , at a level of resolution beyond that revealed by imaging of gfp - tagged pkc constructs . a further critical level of regulation for pkc is by phosphorylation ( figure 1 ) , where phosphorylation at serine / threonine sites in the activation loop , the turn motif , and the hydrophobic motif of the kinase domain are required for rendering the enzyme capable of being activated upon binding of ligands to its c1 regulatory domain , as well as controlling its stability within the cell . additional regulation , although not as well understood , is exerted by phosphorylation of tyrosine residues . in the case of pkc , different tyrosine residues are required for the function of pkc for different biological end points . thus , mutation to phenylalanine of tyrosine residues at positions 64 and 187 of pkc blocks its contribution to apoptosis of c6 glioma cells in response to etoposide , whereas mutation of residues at positions 52 , 64 , and 155 enhanced apoptosis of the c6 cells in response to sindbis virus . additionally , phosphorylation at tyrosine 311 has been reported to change its selectivity for the substrate cardiac troponin i. multiple additional phosphorylation sites on pkc have been characterized ( figure 1 ) . ser 299 is of particular interest in that it has been suggested that this site provides a marker of the enzymatically active pkc , as distinct from the enzyme simply being in a state capable of being activated by ligands . for most of the sites of phosphorylation , however , neither is their regulatory impact known nor are reagents available for assessing their phosphorylation . sites of phosphorylation on pkc. sites of phosphorylation on ser / thr and on tyr of human pkc are indicated ( numbering for the mouse / rat isoforms is in italic ) . the pattern of pkc phosphorylation will necessarily reflect an integrated measure of ligand binding , conformational change , and colocalization with kinases such as pdk1 , with tyrosine kinases such as abl or src , or with protein phosphatases such as phlpp . in elegant studies using fret . showed marked differences in the level of phosphatase activity as a function of the particular membrane compartment . furthermore , the pattern of phosphorylation itself influences localization of pkc. in the present study , we direct particular attention to three pkc ligands with different biology . although pkc isoforms are activated by binding of diacylglycerol , phorbol esters , and related ligands to their c1 domains , downstream consequences are not necessarily the same . bryostatin 1 is a complex macrocyclic lactone that binds with high affinity to the same site on the c1 domain as do the phorbol esters , leading to enzymatic activation . paradoxically , however , bryostatin 1 fails to induce many of the responses typical of the phorbol esters and , when added in combination with the phorbol ester , suppresses the phorbol ester response . of particular note , whereas the phorbol esters represent the paradigm for tumor promotion , bryostatin 1 fails to be tumor promoting and indeed suppresses the tumor promotion induced by phorbol ester . given the extensive involvement of pkc in cancer , bryostatin 1 is being extensively evaluated in cancer clinical trials . exciting advances in the chemistry of the bryostatins are now making it possible to explore which structural features confer their unusual pattern of response . the bryostatin derivative merle 23 has been of particular interest . in the u937 human leukemia cell line , the phorbol ester pma induces attachment and inhibits proliferation ; bryostatin 1 shows little effect in either assay and suppresses the action of pma ; the bryostatin derivative merle 23 acts like pma , highlighting the structural features that distinguish merle 23 from bryostatin 1 . in the lncap human prostate cancer cell line , pma induces tumor necrosis factor ( tnf ) secretion and inhibits cell growth ; bryostatin 1 again shows little effect on either end point ; merle 23 , in contrast to its behavior in the u937 cells , now acts more like bryostatin 1 , showing reduced induction of tnf secretion and little inhibition of cell growth . detailed analysis of its actions in the lncap cells , however , shows that merle 23 may be more or less pma - like in this system , depending on the specific response . single measures of ligand interaction with pkc , such as in vitro ligand binding or enzymatic activation , while a clear first level of characterization , necessarily can not capture this degree of complexity found in the intact cell . chromatographic fractionation of stimulated pkc by fplc yields a broad profile , with different functional characteristics in different portions of the profile , but lacks resolution . western blotting of pkc with an ppkcy311 antibody reveals that bryostatin 1 fails to induce phosphorylation at this site in lncap cells , unlike pma , but addresses neither the absolute level of substitution at this site nor the status at the other sites of phosphorylation . here , we explore the potential of high resolution isoelectric focusing with immunoassay detection to provide a signature of the pattern of phosphorylation ( or other charge altering modifications ) of pkc as a function of ligand . charge - based simple western technology is a capillary - based isoelectic focusing ( ief ) immunoassay system , which employs high - resolution ief separation of proteins by charge followed by target - specific immune - probing to simultaneously detect and quantify multiple protein phosphorylation ( or other post - translational modification ) isoforms . the charge - based simple western apparatus and associated software provide a robust platform for sample evaluation and have the potential to detect signals that are not accessible by conventional western blot . analyzing a series of ligands for pkc that differ in the patterns of response that they induce in the lncap human prostate cell line , we show that these ligands likewise induce different isoelectric focusing signatures for pkc. the concept of function - oriented synthesis is that the modern medicinal chemist seeks to capture the relevant functional activity of a lead compound while reducing synthetic complexity . for pkc , the isoelectric focusing signature provides an integrated window into the complex consequences of ligand binding and localization in the intact cell , as reflected in its pattern of regulatory phosphorylations or other modifications . this more detailed picture provides an additional layer of insight into contextual structure activity relationships ( csars ) for pkc ligands . such a signature has value even if , like a gene expression microarray , the individual elements contributing to the signature remain to be dissected . analysis by immunoblotting of pkc and pkc in the lncap cells upon treatment for 30 min with pma , bryostatin 1 , and merle 23 showed only modest differences ( figure 2 ) , consistent with our findings as reported previously . with all three ligands , pkc showed a limited increase in staining for pt638 , a regulatory phosphorylation in the turn motif . pkc displayed a reduction in mobility together with phosphorylation detected with an antibody directed at ps299 , a site associated with pkc activation . as shown both by the similar intensities of the bands detected with the pkc antibody and by the lack of appearance of lower molecular weight forms ( data not shown ) , proteolytic degradation of pkc was not evident under these conditions . in contrast to the similar effects of pma , bryostatin 1 , and merle 23 on phosphorylation of pkc at s299 , the three ligands had differential effects , as revealed by staining with an antibody directed at py311 , as previously reported . strong staining was seen with pma , very little with bryostatin 1 , and intermediate staining with merle 23 . similar levels of erk1/2 phosphorylation were observed with all three ligands , confirming that all three ligands were being used at effective concentrations . because of different affinities of the different antibodies , the absolute levels of modification as detected by the various antibodies could not be compared . lncap cells were treated with pma , bryostatin 1 , or merle 23 ( 1000 nm ) for 30 min . total cell lysates were prepared and evaluated by western blotting with the indicated antibodies . by use of antibody directed against total pkc , a complex pattern of peaks was already evident for the dmso control ( figure 3a ) . in the illustrated experiment , 38.8% of total pkc had a pi of 6.66 ( peak 18 ) , 19.2% and 17.35% had pi s of 6.31 and 6.94 , respectively ( peaks 13 and 19 ) and 10.1% had a pi of 6.61 ( peak 17 ) . as discussed below ( see figure 6 ) , peak 18 is detected with antibodies directed against the phosphorylated activation loop ( t505 ) and turn motifs ( s643 ) , and , based on its abundance as the major pkc peak in the absence of stimulation , it is plausibly the triphosphorylated pkc described as being the mature protein capable of activation ( there was not a suitable antibody for the phosphorylated hydrophobic motif of pkc ) . peak 19 is also phosphorylated at the activation loop and turn motifs . because it has a higher pi ( is less phosphorylated ) than peak 18 , it is possible that it is lacking phosphorylation on the hydrophobic motif . peak 13 , based on its pi , is more highly phosphorylated than is peak 18 and is detected with the antibody for ppkcs299 . it is most like the tetraphosphorylated pkc containing the activation loop , turn , and hydrophobic motif phosphorylations . this is not so clear in figure 6 but is supported by other experiments in which peak 13 is more prominent . in any case , as emphasized in our discussion regarding figure 6 , considerable additional work will be required before the modifications responsible for the various peaks are fully identified . complex pattern of pkc modification measured by the charge - based simple western system . lncap cells were treated with pma , bryostatin 1 , or merle 23 ( 1000 nm ) for 30 min . total cell lysates were prepared as described in experimental section and evaluated by the charge - based simple western system using total pkc antibody ( from santa cruz ) ( a ) or ppkcs299 antibody ( b ) . peaks with different isoelectric focusing points ( pi ) were numbered for easier comparison between runs . upon pma treatment , there was a dramatic reduction in most of these baseline peaks and the emergence of a highly complex pattern at lower pi , consistent with phosphorylation of pkc. although an overall similar pattern was observed upon treatment with bryostatin 1 or merle 23 as was seen with pma , closer examination revealed both the absence of some bands and the emergence of others ( figure 3a ) . for identification , the pattern of response was reproducible between different runs for the different treatments , but minor shifts in the pi values for the different peaks were observed and the region around peaks 810 showed more variability . the above pattern was detected with an antibody that detects total pkc independent of its state of phosphorylation . we similarly compared the patterns using the ppkcs299 antibody , which has been described as being selective for the active enzyme ( figure 3b ) . here , the pattern is somewhat simplified , representing a subset of the bands detected with the antibody to total pkc , but the multiplicity of peaks is still dramatic . comparison between the patterns with pma , bryostatin 1 , and merle 23 reveals appreciable differences , with bryostatin 1 treatment leading to a relative deficiency in the more acidic bands seen with pma , e.g. , peak 3 , and with merle 23 yielding a pattern intermediate between that of bryostatin 1 and pma . differences in the relative abundance of specific peaks within the profile were also evident . thus , peak 6 in the pma treatment profile was markedly diminished upon bryostatin 1 treatment whereas peak 7 was elevated . conceptually important , all of these peaks were being detected with the ppkcs299 antibody , so this single antibody was detecting a multiplicity of different modification states of activated pkc , which presumably are not functionally equivalent but which all are combined into a single band on immunoblotting and interpreted as activated pkc. as discussed in more detail later , we do not know the specific modifications accounting for most elements of the isoelectric focusing profiles in the presence of pma , bryostatin 1 , or merle 23 . all the peaks detected with ppkcs299 would be expected to contain this phosphorylation and most presumably would contain the phosphorylations at the activation loop ( t505 ) , the turn motif ( s643 ) , and the hydrophobic motif ( s662 ) . profiles were dependent not only on the ligand but also on the time of treatment . with time , not only is the absolute level of the pkc signal diminished but shifts in the pattern are also observed ( figure 4 ) . this was most evident with pma and least evident with bryostatin 1 . the pattern of pkc phosphorylation changes with time . lncap cells were treated with pma , bryostatin 1 , or merle 23 ( 1000 nm ) for 30 or 150 min . total cell lysates were prepared and evaluated by the charge - based simple western system using total pkc antibody . asterisks denote that peaks 9 and 10 show variability compared to peaks labeled 9 and 10 in figure 3 . elsewhere , we have described differences in the extents to which different phorbol esters and related derivatives inhibit proliferation in lncap cells or induce tumor necrosis factor secretion , an important mediator of the inhibitory response . similarly , tested at concentrations at or above those giving maximal response for these end points , these ligands had different capacities to induce phosphorylation of pkc at s299 or y311 ( figure 5a ) . we therefore examined this series of compounds for their effects on the pkc signature in the lncap cells , as detected with the ppkcs299 antibody ( figure 5b ) and total pkc antibody ( figure 5c ) . levels of individual peaks for the various ligands were expressed as percent of the total pma signal observed in the case of the ppkcs299 antibody ( to better compare the level of signal activation by different compounds ) or as percent of the total signal of that sample in the case of total pkc antibody and presented as a heat map ( figure 5b and figure 5c ) . the average values sem of all points on the heat map are presented in supporting information ( supplementary data 1a and 1b ) . a partial correlation with lipophilicity was observed as well as marked differences among ligands . lncap cells were treated with different pkc activators ( 10 000 nm for phorbol 13-acetate and prostratin , 1000 nm for others ) for 150 min . total cell lysates were prepared and evaluated by western blotting ( a ) , by the charge - based simple western system using ppkcs299 antibody ( b ) , or by the charge - based simple western system using total pkc antibody ( c ) . ( a ) immunoblot analysis of total cell lysates using the indicated antibodies . a representative image of three independent experiments is shown . for analysis using the charge - based simple western system the areas under peaks were calculated and expressed as % of the total peaks for pma in the same set of runs ( b ) or % of total peaks in the sample ( c ) . the heat map represents the average % values for each detected peak ( n = 3 except for phorbol 13-acetate , phorbol 12,13-diacetate , phorbol 12,13-dibenzoate , and phorbol 13-decanoate where n = 2 ) . although deconvolution of the various pkc modifications responsible for the multiplicity of peaks will be a highly laborious undertaking beyond the scope of the present analysis , it is possible to begin to approach this question using those phospho - specific antibodies that are available ( and sensitive enough to detect the responses ) . this is illustrated for the dmso control sample , detected with another antibody directed against total pkc ( antibody from bd biosciences ) , as well as those directed against ppkct505 , ppkcs643 , and ppkcs299 ( figure 6 ) . the peak profiles detected using the two different total pkc antibodies are very similar ( figure 3a , figure 6 , supporting information figure 2 ) . peaks 18 and 19 detected with the total pkc antibody also show phosphorylation on sites t505 and s643 ( 81.35% of total pkc is phosphorylated on t505 and s643 ) , whereas about 12.53% of total pkc is phosphorylated at s299 under these basal conditions in this experiment ( peaks 12 , 13 , and 17 ) ( figure 6 ) . the slide also illustrates that the level of basal pkc phosphorylation at s299 showed some variation with different batches of cells ( compare figure 3a and figure 6 ) . importantly , the figure illustrates that the relative proportions of the peaks with the antibodies directed against total pkc permit an estimate of the relative proportions of the modified peaks , whereas their relative contributions could not be inferred from the absolute signal strengths with the various antibodies . unfortunately , the sensitivities of the antibodies directed against t505 and s643 were not adequate for analysis once the pkc profile was spread over the multiple bands upon phorbol ester treatment . detection of changes in pkc phosphorylation by the charge - based simple western system using different pkc antibodies . the total cell lysate of dmso treated lncap cells used in figure 3 was analyzed by the charge - based simple western system using the indicated antibodies . single experiments were performed with total pkc , ppkct505 , and ppkcs643 . to evaluate the role of pkc activity in the subsequent phosphorylation changes , we examined the effect of the general pkc inhibitor g6983 ( 3000 nm ) on the phosphorylation response . under these conditions , this concentration of g6983 largely but not entirely blocked the pma stimulated pkc activity , as revealed by immunoblotting ( figure 7a ) , with a reduction in erk1/2 phosphorylation and ppkcs299 staining . by charge - based simple western analysis , treatment with g6983 alone had no effect on the pattern of peaks ( figure 7b ) . in contrast , a marked reduction in the overall magnitude of the profile from the pma stimulated cells was observed upon detection with the ppkcs299 antibody with the residual bands predominantly at higher pi . lncap cells were treated with pma ( 1000 nm ) with or without pretreatment with pkc inhibitor ( g6983 , 3000 nm for 30 min ) . the total cell lysates were examined by immunoblotting ( a ) and by the charge - based simple western system using ppkcs299 antibody ( b ) . data presented are representative of four ( a ) or two ( b ) independent experiments . asterisks in ( b ) denote that peaks 9 and 10 show variability compared to the peaks labeled 9 and 10 in figure 3 we have described earlier that treatment with pma or bryostatin 1 causes different distribution between a nuclear enriched fraction and the cytoplasm . we confirm here that pma treatment causes enhanced phosphorylation on y311 of pkc and this species is predominantly found in the nuclear enriched fraction ( figure 8a ) . likewise , the ps299 signal upon pma treatment is predominantly in the nuclear enriched fraction whereas that upon bryostatin 1 treatment is predominantly in the cytoplasmic fraction ( figure 8a ) . analysis by the charge - based simple western system emphasizes the difference in the profile of pkc between these two fractions , with the nuclear enriched fraction enriched in the lower pi forms upon pma treatment , which is not observed with bryo 1 treatment ( figure 8b ) . the ppkcy311 antibody did not yield a sufficiently strong signal for analysis of the multiple bands generated upon phorbol ester treatment . although we do not know if phosphorylation at s299 and at y311 are found in some of the same peaks , it seems highly likely that they would be at least partially coincident because y311 phosphorylation is associated with pkc that is active and s299 phosphorylation presumably reflects the active conformation of the pkc exposing the hinge region , where s299 is located . lncap cells were treated for 60 min with pma , bryostatin 1 ( 1000 nm ) , or dmso as control . pkc phosphorylation in the total cell lysates , the cytoplasmic fraction , and the nuclear fraction was detected by immunoblotting ( a ) and by the charge - based simple western system using the ppkcs299 antibody ( b ) . asterisks in ( b ) denote that peaks 9 and 10 show variability compared to the peaks labeled 9 and 10 in figure 3 in marked contrast to the complex pattern of modification of pkc upon ligand addition , analysis of pkc by the charge - based simple western system showed only minor changes . treatment with pma , bryostatin 1 , or merle 23 caused similar , quantitatively minor changes with the appearance of three bands at lower pi ( figure 9 ) . the same simple pattern was detected with the pkc antibody from epitomics ( data not shown ) . simple phosphorylation pattern of pkc measured by the charge - based simple western system . the total cell lysates used in figure 3 were evaluated by the charge - based simple western system using pkc antibody ( santa cruz ) . our findings have impact at multiple levels . we find that different c1 domain - targeted pkc ligands have qualitatively different effects on pkc phosphorylation ( or other modifications affecting the isoelectric point ) . the isoelectric focusing signature can thus be used as a guide to synthesis , reporting how congeners may retain or diverge in their pattern of action , as reflected through this signature . the charge - based simple western resolution of pkc isoelectric states revealed both the great complexity and extensiveness of pkc modification . finally , our analysis of pkc provided an initial glimpse into the methodological issues and exciting potential of the approach . it is essential to emphasize that the isoelectric focusing patterns obtained yield a signature for pkc modification . individual peaks within the pattern may represent several combinations of phosphorylation events , provided that each combination results in the same isoelectric point for the protein . indeed , although the individual peaks are interpreted for convenience as representing different phosphorylation states of pkc , the results could also incorporate any changes in isoelectric point arising through other mechanisms . although degradation can not be excluded as a contributor to such complexity , we failed to see significant degradation at these early times of treatment upon size fractionation on sds polyacrylamide gels , either as a decrease in the signal at the size of the intact protein or as the appearance of lower molecular weight bands under our detection conditions . in any case , while we have developed some insights through the use of antibodies of different specificities , full deconvolution of the identities of the combinations of underlying sites and types of modifications constitutes a formidable future challenge . just as patterns of gene expression provide a signature of the systems biology of a cell or tissue , with different signatures being associated with different underlying perturbations of cellular control , so the pattern of modification of protein kinase c provides a signature for the integrated consequences of activation , of autophosphorylation , of heterophosphorylation by both serine / threonine specific kinases and tyrosine kinases , and of dephosphorylation by phosphatases . these in turn will have been influenced not only by pkc activation but also by changes in its subcellular localization and interaction with anchoring proteins as well as the kinetics of these changes . speculatively , a further potential element may be intermediate conformational states of pkc . in the case of pkc ii , recent elegant crystallographic studies indicate that one of the twin c1 domains , the c1b domain , is involved in intramolecular contacts with the kinase domain . activity relations for the two c1 domains , and occupancy of just one c1 domain may yield a different conformation for pkc than does occupancy of both . the lncap cells show very complicated behavior in response to treatment with phorbol esters or related derivatives . in response to the typical phorbol ester phorbol 12-myristate 13-acetate ( pma ) this response reflects both stimulation of secretion of tumor necrosis factor and modulation of downstream signaling . like pma , bryostatin 1 binds to the c1 domains of pkc and leads to pkc activation . paradoxically , however , bryostatin 1 fails to induce many of the responses typically induced by the phorbol esters , and for those responses that it fails to induce , it inhibits response to the phorbol ester upon cotreatment . correspondingly , in the lncap cells bryostatin 1 fails to inhibit cell growth and induces only minimal tumor necrosis factor secretion . pkc appears to be the primary pkc isoform determining the outcome in this system . this is consistent with our finding that the expression level of pkc is at least 20 times higher than other pkc isoforms in lncap cells . bryostatin 1 is of great interest as a therapeutic agent for cancer and dementia , as reflected in multiple clinical trials . because of the formidable obstacles to supply of this complex natural product , there has been intense interest in the development of synthetic congeners , retaining the same pattern of biological activity as bryostatin 1 while eliminating those structural features that complicate synthesis but are unnecessary for activity . using the lncap cell system as a potential cellular model for evaluating such congeners , we found that the simplified synthetic bryostatin 1 derivative merle 23 appeared to act like bryostatin 1 in this system , failing to inhibit proliferation and stimulating only a low level of tumor necrosis factor secretion . further examination of the behavior of merle 23 in the lncap cells , however , revealed appreciable differences between it and bryostatin 1 . for example , addition of a proteosome inhibitor shifted the behavior of merle 23 to that of pma , whereas the response to bryostatin 1 remained largely the same . in further studies , we showed that a series of other phorbol esters and indolactams likewise did not all behave like pma but showed variable extents of lesser response , in partial similarity to bryostatin 1 . analysis in the lncap cells of compounds drawn from this series thus seemed well suited for detecting potential differences in pkc phosphorylation in response to different ligands . consistent with the different patterns of biological response , we observed that different ligands indeed caused different signatures of modification of pkc ( as summarized in figure 5b ) . consistent with the response to merle 23 not fully resembling that to bryostatin 1 , we observed an intermediate pattern of modification . it was also clear that , considering all of the ligands , the patterns could not be simply ordered in parallel with their extents of induction of tumor necrosis factor or inhibition of proliferation . for example , indolactam v was among the most effective for growth inhibition of the lncap cells whereas sapintoxin d was among the least effective . conversely , phorbol 13-decanoate and phorbol 12-myristate 13-acetate showed similar maximal levels of growth inhibition . we suggest that examination of pkc isoelectric focusing signatures for mimicry of the pattern observed for bryostatin 1 may afford a stringent test for synthetic bryostatin derivatives that capture its unique pattern of biological response . one striking aspect of the difference between the effects of pma and bryostatin 1 was the presence upon pma treatment of the more acidic pkc bands , as detected with the ppkcs299 antibody , in the nuclear extract fraction . while this nuclear extract fraction was not characterized in detail and thus could also include some other cellular elements , it showed dramatic contrast between the effects of pma and bryostatin 1 . we have speculated that this difference between pma and bryostatin 1 may be an important contributor to the differential action of these two agents . although our goal was to compare signatures of phosphorylation ( plus other modifications of isoelectric point ) rather than to identify the particular sets of phosphorylated residues represented by each peak , we were able to develop some insights by comparison of the patterns detected with antibodies directed against total pkc and against pkc phosphorylated at s299 , t505 , and ser643 . ps299 has been described as a marker of pkc activation in response to ligand binding . pt505 represents phosphorylation of the activation loop , leading to pkc being converted to a more active state , and ps643 represents phosphorylation of the turn motif . we could detect and quantify a basal level of s299 phorphorylation in the absence of external activation . while not characterized in detail , this basal s299 phosphorylated pkc displayed a lower pi consistent with additional phosphorylations , presumably those at the activation loop , the turn motif , and the hydrophobic motif . although y311 phosphorylation would have been of particular interest to evaluate , the quality of py311 antibodies was not sufficient for analysis with the charge - based simple western system . although the focus of our analyses was pkc , since this residue has been centrally implicated in the unique patterns of response to bryostatin 1 both in lncap cells and in other systems , we conducted an initial examination of the response of pkc , one of the other functionally important pkc isoforms in the lncap cells . in comparison with pkc , a similar situation was observed for pkd1 , a kinase that is positionally regulated through its intrinsic c1 domains as well as activated by phosphorylation by pkc isoforms . the complexity of pkc phosphorylation is yet another example of its exceptional behavior among pkc isoforms , along with its differential localization by different ligands and the function of its c2 domain as a novel phosphotyrosine binding motif . one potential basis for its complexity of phosphorylation could be through complex formation of pkc with other kinases . through its c2 domain it can bind to phosphotyrosine residues on other kinases ; through its own phosphotyrosine groups it could interact with kinases possessing sh2 domains ; through either mechanism it further could interact with adapter proteins bringing it into proximity with other kinases . the particular value of the isoelectric focusing signatures enabled by the charge - based simple western system for analysis of contextual structure activity relationships probably lies in targets such as pkc , which reflect such complexity . the current analysis of pkc response to ligands using the charge - based simple western system represents an early stage in the evaluation of the utility of this approach . signatures such as observed in the treated cellular systems could be extended to define signatures in dissected tumor samples , reporting on signaling pathway regulation in the tissue sample . modifications , such as the use of a validated detection tag , which could be coupled to any target of interest , would facilitate its generalized application to a wide range of targets , without needing to identify and validate specific antibodies for each target . an efficient system for subsequent identification of the specific sites of phosphorylation represented would move the analysis to the next step from response signature toward dissected phosphorylation pathway . nonetheless , the methodology has already proven to be highly informative for our understanding of pkc pharmacology and regulation . all phorbol esters were purchased from lc laboratories ( woburn , ma ) unless otherwise specified ( purity for all > 99% ) . sapintoxin d ( purity > 98% by hplc ) was from enzo life sciences international inc . bryostatin 1 was provided by the developmental therapeutics program , nci ( frederick , md ) . bryostatin 1 was judged to be greater than or equal to 95% purity , as determined by h and c nmr , as well as hplc analysis . merle 23 was isolated as single observable tlc spot in 40% etoac / hexanes , appeared as a single peak by reverse phase hplc using a waters 4.5 m 150 m c18 column and was judged to be > 95% pure by 500 mhz h nmr and 125 mhz c nmr . the lncap human prostate cancer cell line , fetal bovine serum ( fbs ) , and rpm1 - 1640 medium were obtained from atcc ( manassas , va ) . precast 10% sds gels and pbs were from invitrogen ( carlsbad , ca ) . the primary antibody against pkc ( sc-208 ) was from santa cruz biotechnology ( santa cruz , ca ) and that against pkc was from santa cruz biotechnology ( sc-937 ) or bd biosciences ( san jose , ca ) . the primary antibodies against phosphorylated pkc ( ppkcy311 , ppkct505 , ppkcs643 ) and phosphorylated pkc ( ppkct638 ) , perk1/2 ( no . those against pkc ( no . 1510 - 1 ) , pkc ( no . 2222 - 1 ) , and phosphorylated pkc ( ppkcs299 and another antibody against ppkcy311 ) were from epitomics ( burlingame , ca ) . the mouse monoclonal antibody against -actin was from sigma ( st . louis , mo ) . the horseradish peroxidase conjugated secondary anti - rabbit antibodies , the nonfat dry milk , tween-20 , and the triton x-100 solution were from bio - rad ( hercules , ca ) . the ecl ( electrochemiluminescence ) reagent and the films were from ge healthcare ( piscataway , nj ) . the following reagents were from proteinsimple ( santa clara , ca ) : 1 fluorescent pi standard 6.4 , 7.0 and ladder 4 ( no . 040 - 031 , and no . 040 - 647 , respectively ) , 1 g2 premix 5 - 8 ampholyte ( no . 040 - 973 ) , luminol ( no . the secondary goat anti - rabbit antibody ( no . 111 - 035 - 144 ) and donkey anti - mouse antibody ( no . 715 - 035 - 150 ) used for charge - based simple western analysis were from jackson immunoresearch ( west grove , pa ) . cell culture , treatment of cells , preparation of total cells lysates and nuclear extracts , and the western blotting were performed as described earlier . except for cell fractionation samples , cells were lysed with ripa buffer ( 20 mm hepes , ph 7.5 , 150 mm nacl , 1% np 40 alternative , 0.25% sodium deoxycholate ) containing phosphatase and protease inhibitors ( emd millipore catalog no . cell lysates ( approximately 20 ng of protein ) were mixed with 1 g2 premix 5 - 8 ampholyte , and 1 fluorescent pi standard 6.4 , 7.0 , and ladder 4 before being loaded into the nanopro1000 system ( proteinsimple , santa clara , ca ) for analysis . during isoelectric focusing electrophoresis , proteins were separated by charge and concentrated at their respective isoelectric focusing points in the capillaries . separated proteins were immobilized on the capillary wall using uv light , followed by immunoprobing with the indicated primary antibodies and hrp - conjugated goat anti - rabbit ( 1:100 diluted ) or donkey anti - mouse ( 1:100 diluted ) secondary antibody . the primary antibodies used in the study were the following : ppkcs299 ( 1:50 diluted ) , pkc ( 1:100 diluted , santa - cruz sc-937 ) , pkc ( 1:50 diluted , santa - cruz sc-208 ) , pkc ( 1:100 diluted , bd biosciences no . luminol and peroxide were added to generate chemiluminescence , which was captured by a ccd camera . the digital image was analyzed by compass software ( proteinsimple , santa clara , ca ) . the software calculates the height and area under the curve ( auc ) of the separated / individual peaks . for quantitative analysis of pkc signals the auc value of peaks was expressed as % of total auc ( sum of auc of all peaks for that sample ) . for ppkcs299 signals the auc of individual peaks was expressed as % of total auc of the pma treated sample from the same set of runs to reflect the differences in pkc activation induced by the different treatments .

protein kinase c ( pkc ) , a validated therapeutic target for cancer chemotherapy , provides a paradigm for assessing structure activity relations , where ligand binding has multiple consequences for a target . for pkc , ligand binding controls not only pkc activation and multiple phosphorylations but also subcellular localization , affecting subsequent signaling . using a capillary isoelectric focusing immunoassay system , we could visualize a high resolution isoelectric focusing signature of pkc upon stimulation by ligands of the phorbol ester and bryostatin classes . derivatives that possessed different physicochemical characteristics and induced different patterns of biological response generated different signatures . consistent with different patterns of pkc localization as one factor linked to these different signatures , we found different signatures for activated pkc from the nuclear and non - nuclear fractions . we conclude that the capillary isoelectric focusing immunoassay system may provide a window into the integrated consequences of ligand binding and thus afford a powerful platform for compound development .

Introduction Results Discussion Experimental Section

different studies in animal models have demonstrated that the combination of vrb and cape has a synergistic activity against breast cancer cells , due to their different mechanism of action . these results have been subsequently confirmed in numerous studies conducted in metastatic breast cancer patients , heavily pretreated with taxanes and anthracyclines , in which vrb was administered as iv formulation . subsequent trials showed that there was a substantial equivalence between the iv and the oral formulations of vrb , even if this latter was characterized by a higher rate of haematological toxicity [ 35 ] . in all these studies , vrb and cape were administered on days 1 and 8 , according to the approved standard schedule . metronomic chemotherapy refers to the frequent , even daily , administration of drugs at doses significantly lower than the maximum tolerated dose ( mtd ) , with no prolonged drug - free breaks . a recent study by dellapasqua et al . showed that the metronomic combination of cyclophosphamide and cape with bevacizumab was effective and minimally toxic in advanced breast cancer patients . this study fixed the dose of cape as 500 mg thrice a day , continuously . different studies have evaluated the possibility to administer vrb in a metronomic way [ 8 , 9 ] , trying to establish the mtd of the drug , both as single agent or as part of a multidrug regimen . these studies fixed the mtd of oral metronomic therapy with vrb at 4060 mg / tot thrice a week . no studies to our knowledge investigated the administration of an all - oral metronomic combination of the two drugs . aim of the present trial was to determine the mtd of metronomic vrb in combination with a fixed dose of cape in locally advanced or metastatic breast cancer patients . after defining the mtd , we conducted a phase ii study in order to verify the activity and the tolerability of the schedule . patients aged 18 years or more , with histological proven locally advanced ( inoperable ) or metastatic breast cancer with the following characteristics were eligible : pre- or postmenopausal , pretreated with anthracyclines and taxanes or not suitable for each of these drugs or both due to clinical conditions , her2-negative or her2-positive not suitable or no longer suitable to anti - her2 agents due to cardiac impairment , measurable or evaluable disease , life - expectancy > 12 weeks , ecog ps 2 , adequate ( bone ) marrow , liver , and renal function ( absolute neutrophil count > 1.5 10/l , platelets > 100 10/l , haemoglobin > 10 g / dl ; total bilirubin within the normal institutional limits , ast / alt < 2.5 unl , or < 5 unl in the case of liver involvement , creatinine within normal institutional limits , or creatinine clearance 50 ml / min , according to cockroft - gault formula ) , inr < 3 at the screening for patients taking warfarin , and absence of cerebral or leptomeningeal metastases . the starting dose ( level i ) of vrb was 20 mg thrice a week for 3 consecutive weeks ( 1 cycle ) . the first cohort started with level i dose ( 20 mg ) , receiving the drug for 1 cycle . if no grade 3 - 4 toxicity was observed during the 1st cycle , the first cohort escalated to level ii ( 30 mg ) in the 2nd cycle , together with the initiation of the second cohort , which started with level ii directly in the 1st cycle . both groups of patients received 1 cycle ( 3 weeks ) ; if no grade 3 - 4 toxicity was observed , they could increase the vrb dose to level iii ( 40 mg ) , together with the initiation of the third cohort , which directly began with 30 mg . all patients who reached the level of 40 mg continued to be treated with the same dose up to disease progression , up to refusal to continue the study , and in any case up to 9 cycles of therapy ( 27 weeks overall ) . all toxicities were graduated according to the national cancer institute common terminology criteria of adverse events ( nci - ctc , version 3 ) . the baseline evaluation included complete history and physical examination , assessment of performance status , cbc and differential , metabolic profile , coagulation studies , and serum pregnancy test in women with childbearing potential . baseline staging was performed with total body ct scan , ultra sound for abdomen , standard chest x - ray , or clinical examination . haematological toxicity was evaluated by cbc count every week and renal and liver function by biochemistry at the beginning of each subsequent cycle . thus , for each mtd common toxicities ( occurring in 30% of patients ) would rarely be unobserved ( p = 0.11 ) , and very common toxicities ( occurring in 50% of patients ) would almost never be missed . standard descriptive statistics were used for describing baseline characteristics and relevant safety and activity endpoints . median age was 72 years ( 4981 ) , 2 patients were metastatic d'emble at the time of enrolment , but they could not be treated with anthracyclines or taxanes due to cardiac impairment in the first case and refusal to have hair loss in the second one . two patients were her2 + , but one has been already treated with trastuzumab , developing a cardiac heart failure which precluded any other therapy with anti - her2 agents ; the second could not receive any anti - her2 treatment due to the presence of severe cardiomyopathy . in 3 patients her2 status was not assessable due to little available histological material in 2 cases and paraffin block too old in another one . all patients but 3 had been treated with previous therapies , which were endocrine therapy in 2 patients , sequential chemotherapy and endocrine therapy in 6 , and chemotherapy plus trastuzumab in 1 case . nine patients presented 2 or more metastatic sites ; the remaining patients had just one organ involved . seven out of 12 ( 58.3% ) patients received anthracyclines , of whom 6 were treated with anthracycline plus paclitaxel combination and 7 received taxanes , alone ( 1 patient ) or in combination with anthracyclines ( 6 patients ) . four patients received vrb plus cape as first - line treatment of their metastatic disease because of their comorbidities , which precluded the use of other drugs . three cycles have been conducted at level i ( 20 mg ) , 6 cycles at level ii , and 16 cycles at level iii . all 3 patients of the first cohort completed the planned cycle of 3 weeks ; no delay or dose reduction was required . in level i we observed 4 adverse events per cycle : 2 constipation g2 , 1 nausea g1 , and 1 dyspnoea g1 . six patients were treated at level ii for a total of 6 cycles , without any delay , dose reduction , or suspension . we observed a total of 15 adverse events per cycle , of which 11 were classified g1 ( 73.3% ) ; abdominal pain was reported in 3 cases , nausea in 4 , and gastric pain , stomatitis , and asthenia in 1 . grade 2 adverse events were reported in 4 cases : nausea 2 and constipation 2 . eight patients were treated with vrb 40 mg for a total of 16 cycles . one patient of the second cohort did not complete the planned treatment because of death due to liver metastases at the end of level ii dose . we observed a total of 46 adverse events , grade 1 in 38 cases ( 82.6% ) ; the majority of them concerned the gastrointestinal area ( 33 events , 86.8% ) . regarding haematological toxicity , we observed 2 events of leukopenia and 2 cases of anaemia , in all cases grade 1 . the mtd dose of metronomic vrb in combination with fixed doses of cape was established at 40 mg days 1 , 3 , and 5 of each week . in order to confirm the toxicity profile observed in the dose - finding part of the study , we further treated 22 patients with vrb 40 mg and cape 500 mg thrice a day , for a total of 187 cycles . we observed 90 grade 1 events ( 48.1% ) , 29 grade 2 ( 15.5% ) , 7 grade 3 ( 0.03% ) , and 4 grade 4 events ( 0.02% ) per cycle . among grade 3 events , grade 3 neutropenia was associated to grade 1 leukopenia , which required 1-week delay in chemotherapy administration ; the event spontaneously recovered and the patients continued her therapy at the same dose . one case of hand - foot syndrome was described , which required the reduction of cape to 500 mg bid . grade 3 neurological toxicity occurred in 1 patient and vrb was reduced to 20 mg / tot . among grade 4 events , 2 neutropenia events of which 1 of febrile neutropenia , and 2 leukopenia events occurred . febrile neutropenia was complicated by the presence of erysipelas and required hospitalization and antibiotic treatment with amoxicillin and clindamycin , together with g - csf administration for 5 days . in this case , tumour restaging was performed every 3 cycles ( 9 weeks ) . at the 3rd evaluation ( 27 weeks of treatment ) , patients who did not progress accounted for the clinical benefit . thirty - one patients were evaluable for efficacy : 3 patients in the phase i part did not reach the timing of tumour evaluation due to rapid progression in 2 patients and development of febrile neutropenia which determined definitive suspension of the treatment in the reaming one . clinical benefit defined as cr + pr + sd 24 weeks the present study was designed to establish the mtd of oral metronomic vrb in association with fixed metronomic doses of cape . to our knowledge , this is the first study which investigates the combination of a full oral , metronomic schedule of vrb and cape . assuming that vrb and cape have different toxicity profiles and no enhanced toxicity should be expected from the combination , we initially designed a study to evaluate the clinical activity of the combination . vrb was planned to be administered at the dose of 50 mg every other day , which was the recommended dose coming from the studies of briasoulis et al . , whereas cape dose was 500 mg , tid , which was the dose used by dellapasqua et al . . despite the results of the above - mentioned study , we excluded this dose from the combination with cape 500 mg tid continuously , because of the occurrence of one event of g4 neutropenia and one event of g3 neurological toxicity , clearly related to vrb instead of cape , in 2 out of the first 3 patients . considering that these toxicities were strongly related to the administration of vrb instead of cape , we reviewed our initial intention by designing the present intrapatient , dose - finding study , with no modifications of cape dose and assuming 50 mg thrice a week of vrb as the limit dose . in the study by briasoulis et al . , the dose of vrb 50 mg determined just 3 adverse events , all of them being g1 - 2 ( anaemia 1 and nonhaematological 2 ) . the patient who developed g4 neutropenia has received 6 cycles of epirubicin and paclitaxel as first - line treatment for the metastatic disease and her blood reserve could have been compromised by that treatment . the patient who developed 3 neurological pain events was in excellent general condition at the beginning of the protocol , without any preclinical neurological condition . during the 25 cycles delivered in the dose - finding part of the study , no grade 3 - 4 adverse events occurred in our patients . a total of 51 grade 1 events were described , most of them regarding the gastrointestinal area ( 45 events , 88.2% ) and 14 grade 2 , 8 of them were concerning the same area . different studies [ 5 , 1014 ] have evaluated the efficacy and the safety of oral vrb in combination with cape ; most of them used vrb at doses ranging from 60 to 80 mg / mq , administered on days 1 and 8 every 21 days , as the classical regimen . in all those studies , cape was administered at a dose ranging from 800 to 1250 mg / mq bid , from day 1 to day 14 , every 21 days . five trials [ 5 , 1012 ] studied the combination of vrb 60 mg / mq ( days 18 ) and cape 2000 mg / mq / day , days 114 , every 3 weeks . in the study by lorusso et al . , 38 advanced breast cancer patients received a total of 228 courses . the authors observed grade 2 - 3 neutropenia in 18.9% and grade 4 in 2.7% , thrombocytopenia grade 3 in 2.7% , and nausea / vomiting grade 3 in 2.7% of the patients , concluding that that regimen was safe and easy to administer in an outpatient setting . tubiana - mathieu et al . reported a 49% of grade 3 - 4 neutropenia treating 54 patients for a median number of 7 cycles ( range 158 ) ; in addiction , 2 patients experienced febrile neutropenia ( 3.8% ) and 3 additional patients had documented infection associated with grade 3 - 4 neutropenia , one of them producing a fatal septicaemia . a similar but larger phase ii study was conducted by finek et al . reporting a 0.8% incidence of grade 4 neutropenia in approximately 115 patients . nol et al . treated 44 patients with metastatic breast cancer with the same dose of oral vrb 6080 mg / mq and escalating doses of cape from 1650 to 2500 mg / mq / day , days 14 every 3 - 4 weeks . neutropenia was the main dose - limiting toxicity of the combination ; it was reported in 40 patients ( 90.0% ) , with grade 3 in 14 patients ( 31.8% ) and 6.2% of the cycles and grade 4 in 12 patients ( 27.3% ) and 4.3% of the cycles . the authors also reported a frequent gastrointestinal toxicity , even if the incidence of grade 3 was low , with no episode of grade 4 . nevertheless , cycle delay occurred in 61.4% of the patients and 26.12% of the cycles . day 1 oral vrb administration was cancelled in 38.6% of the patients and 7.7% of the cycles and dose reduction occurred in 22 patients ( 50% ) and 7.4% of the cycles . in the study by jones et al . , forty patients received a median number of 4 cycles ( range 131 ) ; main toxicity was haematological , with 7.9% of grade 3 and 3.5% of grade 4 neutropenia per cycles . febrile neutropenia occurred in 0.4% of the cycles . comparing to the standard administration of the combination of vrb and cape , we observed a significantly lower incidence of grade 3 - 4 events ; this could be explained by the metronomic schedule of administration , which , by definition , consists of low , repeated doses of the same drug without rest period . this kind of administration warrants the delivery of similar , if not superior , dose intensity than the 18 schedule of vrb : if we consider the definition of a cycle as a 3-week period and a median body surface area ( bsa ) of 1.6 for women , the standard schedule provides the administration of approximately 192 mg / tot / cycle , in comparison to 360 mg / tot / cycle of the metronomic regimen . the delivered dose of cape in the standard schedule would be 44800 mg / tot , in comparison to 31500 mg / tot of the metronomic schedule . one could argue that the dose of cape delivered in the metronomic schedule is below the standard accepted dose , but some data would suggest that lower doses of cape could have a more favourable therapeutic index in metastatic breast cancer because of a less incidence of suspension or delay . the study by saridaki et al . described the results of a phase i trial of the all - oral combination of metronomic vrb ( starting dose 30 ) and cape ( starting dose 800 mg / mq , bid on days 114 every 21 days ) . the dose - limiting - toxicity ( dlt ) level was reached at oral metronomic vrb 70 mg and cape 1250 mg / mq . dlts were febrile neutropenia grades 3 and 4 , diarrhoea grade 4 , and treatment delays due to unresolved neutropenia . the incidence of grade 3 gastrointestinal adverse events was 16.5% ( nausea / vomiting 11% and diarrhoea 5.5% ) , whereas grade 4 diarrhoea was observed in 2.7% of the patients . the administration of cape with a metronomic schedule could reduce the incidence of gastrointestinal disorders , increasing the compliance of the patients and assuring the best dose intensity of the drug . in our study , as well in the one by dellapasqua et al . , the incidence of diarrhoea and nausea / vomiting was very low ( 4 and 16 events , resp . ) with any reporting of grade 3 - 4 events . the major limit of the dose - finding part of the study was the low number of administered cycles . in order to assess the toxicity of prolonged treatment , 22 additional patients were treated with the recommended dose of 40 mg of vrb and cape 500 mg tid . the low incidence of haematological toxicity observed in the dose - finding part of the study was confirmed . in conclusion , the mtd of oral metronomic vrb was 40 mg / tot on days 135 of a week and it is the recommended dose for the ongoing phase ii trial . the all - oral combination of vrb 40 mg thrice a week and cape 500 mg tid continuously was feasible and well tolerated also during prolonged treatment .

background . vinorelbine ( vrb ) and capecitabine ( cape ) are demonstrated to be active in pretreated metastatic breast cancer patients . different studies have demonstrated that the metronomic treatment is active with an acceptable toxicity profile . we designed a phases i - ii study to define the mtd of oral metronomic , vrb , and cape . patients and methods . phase i : fixed dose of cape was 500 mg thrice a day , continuously . level i of vrb was 20 mg / tot thrice a week for 3 weeks ( 1 cycle ) . subsequent levels were 30 mg / tot and 40 mg / tot ( level iii ) , respectively , if no grades 3 - 4 toxicity were observed in the previous level . phase ii : further 32 patients received the mtd of vrb plus cape for a total of 187 cycles to confirm toxicity profile . results . 12 patients were enrolled in phase i and 22 in phase ii . phase i : the mtd of vrb was 40 mg . phase ii : 187 cycles were delivered , observing 5.9% of grades 3 - 4 toxicity . 31 patients are evaluable for efficacy , obtaining a clinical benefit rate of 58.1% . conclusion . mtd of vrb with fixed dose of cape was 40 mg thrice a week and was the recommended dose for the ongoing phase ii multicenter study .

1. Background 2. Patients and Methods 3. Results 4. Discussion

the sibling bond is the marathon runner of human relationships ; it is the longest lasting relationship , enduring from the birth of the youngest sibling to the death of the first to go . it is therefore reasonable to assume the importance of this relationship across the lifespan . it has been established that the younger siblings of individuals with autism spectrum disorder ( asd ) are at heightened risk of developmental problems in comparison to the general population . some of these developmental difficulties include : social and cognitive deficiencies , and neurocognitive and behavioural delays , specifically executive function and repetitive behaviours . the above examples of sibling research are commonly used to provide evidence for the genetic basis of asd with elevated levels of autistic traits in siblings representing potential markers of a broader autism phenotype ( bap ; ) . the nurture side of the debate how are these siblings and families impacted by the disorder in regard to their quality of life ( qol ) and psychosocial outcomes ? the american psychiatric association describes the essential features of autistic disorder as the presence of markedly abnormal or impaired development in social interactions and communication and a markedly restricted repertoire of activity and interests this is commonly referred to as the triad of autism diagnosis , representing delays or deficits in three essential categories : social interaction , communication , and restricted interests . characteristic symptoms may include self - stimulation behaviours ( e.g. , hand flapping and rocking ) , self - injury behaviours ( e.g. , head banging , skin picking , hair pulling ) , lack of emotional and social reciprocity , and inflexible adherence to routines or rituals . in addition to common comorbidity with other medical , psychiatric , and developmental disorders , these asd characteristics can be difficult for families to manage . epilepsy , allergies , sleep disorders , conduct disorder , attention deficit / hyperactivity disorder ( adhd ) , gastro - intestinal disorders , anxiety disorders , intellectual disability and language disorders often cooccur with a diagnosis of asd . furthermore , asd requires substantial financial investment in therapy , medical treatment , and early intervention education ; increased vigilance of the individual with autism ; micromanagement of the family environment to ensure minimal sensory discomfort and maintenance of a highly predictable routine ; often limited communication with the family member with autism ; and many other family disturbances . ensuring that an individual with asd lives in an environment that caters for their complex needs requires a large commitment from the family . it is empirically intuitive to assume that quality of life ( qol ) is impacted in these families . this has yet to be supported by research , with a lack of studies focusing on qol outcomes in asd families . a review of the sibling literature reveals both positive and negative effects of growing up with an individual with a disability . siblings of children with autism have been shown to do more poorly on a number of outcome measures in comparison to siblings of other developmental disabilities and those with only typically developing siblings . this distinct population of siblings has been shown to exhibit higher levels of internalising and externalising disorders [ 5 , 6 ] , social and behavioural adjustment problems , hassles with sibling behaviour , and distressing emotions such as guilt . in contrast , other researchers have found no difference in levels of adjustment between siblings of individuals with asd and those with only typically developing siblings or those with siblings with other developmental diagnoses . even more promising , the positive impacts of growing up with a sibling with asd are becoming known . siblings of individuals with autism have been reported to have less conflict in the sibling relationship , family resilience , and increased self - perceived competence [ 6 , 13 , 14 ] . they have also been shown to have a more positive opinion of the sibling relationship , positive psychosocial and emotional development conditional upon limited demographic risk factors , feelings of empathy for their sibling , and increased maturity . the autism sibling literature is yet to reach consensus ; however , macks and reeve [ 14 , page 1065 ] succinctly conclude that having a sibling with autism may not be a risk factor in and of itself , and children with autism may even have a positive influence on the life of the nondisabled sibling . however , when multiple demographic risk factors are present , it becomes more difficult for the nondisabled sibling to deal with the child with autism , both emotionally and psychologically . macks and reeve consider the contribution this potentially makes to the inconsistency currently plaguing sibling research . if those studies reporting positive influences included samples of demographically stable families , while those samples that exhibited negative impacts consisted of participants experiencing a high number of demographic risk factors , the true effects of growing up with a sibling with autism would be masked , justifying continued exploration of sibling outcome . in order to investigate this masking effect at surface level , the author conducted closer inspection of the studies listed above that showed no difference between siblings of individuals with asd and comparison siblings . study were part of high - income families ( 25 out of 27 families ) . a large proportion of the sample in the kaminsky and dewey study reported receiving high levels of social support . the majority of bayat 's resilient families used in his 2007 study were intact families with average incomes of 81,000 usd per year . although the study included families with low income ( 23% ) , over 60 percent were in the high - income category . had these samples included more demographically disadvantaged siblings , their outcome may have been poorer than comparison siblings . the low level of demographic risk may have contributed to the healthy levels of adjustment reported in these studies , a consideration that further supports macks and reeve 's proposal . recent literature reviews report mixed results and emphasise the large gaps in our current knowledge of sibling outcome , due in large part to inconsistency in methodology and a lack of rigorous sampling procedures [ 18 , 19 ] . the purpose of this literature review was to summarise studies of the psychosocial impacts of growing up with a sibling with asd , identify gaps in the literature , and propose future directions for sibling research in the autism spectrum field . although it is recognised that genetic factors play an integral part in any research regarding asd , the current paper focuses on psychosocial rather than biological components of sibling outcome . in the context of the multitude of challenging behaviours exhibited by an individual with autism , it is intuitively appealing to predict that the well - being of siblings in these homes may be compromised ; this literature review attempted to summarise this impact . electronic databases including pubmed , psycinfo , google scholar , psycarticles , medline , scopus , wiley online library , and proquest psychology journals were reviewed for studies published in peer - reviewed journals within the last decade . a large number of the identified studies were published in 2003 , signalling an increase in focus on siblings around this time and a suitable start point for this historical investigation . fourteen articles were accessed using key words to identify research within the sibling well - being field and further filtered in order to critically appraise the most relevant studies . due to the small number of robust and empirically sound studies focussing specifically on siblings of children with autism , a number of studies focussing on the functioning of the whole family in addition to studies targeting a range of developmental disabilities were considered . relevant studies were also identified if they were cited within the articles accessed through the above database search . within the sibling field a number of pertinent concepts were identified ; the current article will discuss the outcome of siblings of children with autism according to psychological health , overall quality of life , emotional intelligence , family coping , and child and family factors . the original criteria used to filter relevant articles allowed for inclusion of databased articles that were asd - specific and included a control comparison group . however , these criteria needed to be relaxed as only 4 studies met this stringent category . siblings of individuals with autism appear to be socially and emotional well adjusted according to a study that compared them to siblings of individuals with developmental language disorders ( specific learning disability ) and intellectual disability . despite the absence of a typically developing sibling control comparison , these findings are still promising due to the low number of the siblings of individuals with asd that fell into the clinical diagnostic range ( 13.4% ) on a number of behavioural adjustment measures . kaminsky and dewey . with the advantage of including comparison groups of siblings of individuals with another disability ( down syndrome ) and those with only typically developing siblings , kaminsky and dewey reported low levels of loneliness in siblings of individuals with asd . they also reported that siblings of individuals with asd were no more likely to have adjustment problems than comparison siblings . despite all of the sibling groups falling into the normal range for adjustment , kaminsky and dewey concluded that it is more likely for siblings of individuals with asd who live in larger families to be well - adjusted . the addition of other typically developing children in the family appeared to buffer the negative impacts of growing up with autism in the home . many siblings reported high levels of social support , a promising finding that may have buffered against the adjustment problems reported in other studies . children and adolescent 's self - concepts appear to benefit from them having a sibling with asd , when demographic risk factors are limited . the risk factors that are important for psychological well - being were not detailed in the study ; however , birth order , family size , gender , and socioeconomic status ( ses ) were considered in their analyses . it is not clear which gender or birth order constitutes a risk for psychosocial and emotional maladjustment or whether a small family constituted a risk as reported previously ; however , other studies reported below have investigated these variables . the important finding to note is that demographic factors may have a cumulative effect in producing poorer outcome . the social , behavioural , academic , and psychological adjustment of siblings was investigated in families with and without a child with asd . there was an interaction effect , however , between maternal well - being and sibling adjustment . both teacher and parent reports suggested that higher levels of daily stress and depression in the mother correlated with higher ratings of problem behaviours in siblings . ross and cuskelly . in a study that categorised 40 percent of siblings of individuals with autism in the borderline or clinical range for behavioural and emotional dysfunction , ross and cuskelly concluded that the risk of developing internalising behaviour problems is heightened in siblings of individuals with asd . an interaction between the number of stressful life events experienced by siblings of individuals with asd and their level of subthreshold asd characteristics was used as evidence to partially support a diathesis - stress model of sibling adjustment . genetic vulnerability to asd ( broad autism phenotype ) was found to increase depressive and anxious traits only in the presence of high levels of stress , such as in maternal depression and challenging behaviours in the individual with asd . the adolescent sisters in the sample reported more depression and anxiety symptoms than brothers but were comparable to community samples . it was reported that maternal depression was related to increased risk of depression in the adolescent siblings of individuals with asd . behaviour problems and social competence in siblings of individuals with high - functioning asd were found to be comparable to a control group of siblings of typically developing individuals . siblings appear to be capable of adapting to the environmental demands of high - functioning autism . siblings of individuals with asd were rated higher on measures of behavioural dysfunction and exhibiting fewer prosocial behaviours . maternal stress and behaviour problems in the child with autism were not predictive of sibling adjustment ; however , the low sample size reduces predictive power , a common difficulty in sibling research . the siblings with asd were all recruited from one school , reducing demographic variability and lowering ability to generalise these results . the study also failed to control for bap ( as does the majority of the sibling studies ) , so it is unclear whether these behaviour problems have genetic or environmental basis , particularly when the outcome measure selected is based on two important components of the triad of autism diagnosis ( challenging behaviours and social dysfunction ) . hastings provides only a brief report and recognises the limitations of his data ; however , his contribution is important , particularly as his analyses took into account important variables such as age , gender , gender matches , birth order , and living arrangements of siblings . a case study methodology revealed a number of stressful life conditions that siblings of individuals face regularly . a number of emotional reactions were identified within the seven domains of the sibling experience : empathy , sympathy , fear , anxiety ; and social isolation . the siblings revealed that : ( 1 ) they felt obligated under a sense of precocious responsibility for protecting the individual with asd and helping their parents ; ( 2 ) they felt sorry for their sibling with asd ; ( 3 ) they were exposed to frightening and abnormal behaviour ; ( 4 ) they held empathetic feelings for their sibling with asd ; ( 5 ) they hoped and wished that their family , and the individual with asd may have some relief with the individual in a group home ; ( 6 ) impulsive and uncontrolled physical violence made the siblings feel anxious and unsafe ; and ( 7 ) their relationships with friends were negatively affected . despite some positive emotions , the overwhelming feel of the sibling experience was negative . moyson and roeyers . in a recent qualitative investigation into the quality of life of siblings of children with asd ( sibqol ) , moyson and roeyers identified a number of integral domains within this concept . an important theme contributing to sibqol appeared to be the apparent invisibility of asd ( page 46 ) . a heterogeneous disorder , asd does not always present uniformly and there are no physical features distinguishing individuals with asd from their typically developing peers . it may also ensure that others do not stare at the individual with asd or express their negative opinions . it does , however , lessen the likelihood that the outside world can accurately assess the impact of a child with asd on their sibling / s , possibly lessening the likelihood that the sibling 's feelings will be validated and that they will receive appropriate services . the siblings felt it was important that the individual with asd could communicate with them ; they were disappointed that their sibling did not always want to talk , and they consistently felt misunderstood . moyson and roeyers suggested that the characteristic behaviour of an individual with asd , reported by their siblings as being sometimes bizarre , aggressive , or annoying , siblings do appear to eventually develop awareness that the individual with asd is often unable to control their behaviour , resulting in some forbearance on the part of the sibling . the qualitative findings of the study suggested that the siblings developed patience and tolerance to these challenging behaviours . longitudinal studies would provide important information about the common trajectories across the lifespan for siblings . quality of life in families of children with a disability was significantly accounted for by a number of family variables . these variables included : parental perceptions of the disability ; experiences of family - centred professional support ; perceived intensity of child behavioural problems ; and support from extended family members . this has important implications for providing parents with the skills and opportunities to apply positive meaning to disability and model this to their family . it has been reported that parents use both positive and negative appraisals of childhood developmental disability . these findings also suggest that disability services should focus on family approaches to intervention . siblings of individuals with asd have been reported to conceptualise the self in a positively enhanced manner in comparison to the general population . siblings of individuals with asd were more likely to have developed positive perspectives towards their behaviour , intelligence , academic ability , and levels of anxiety . they also held a more positive view of their overall personal characteristics than siblings of typically developing individuals . furthermore , qualitative reports revealed empathetic feelings towards siblings with autism , showing an emotional maturity also reported by gray . a diagnosis of asd often brings with it a period of family loss : feelings of loss for the individual with the disorder , parental ideas and plans for their family 's future , and the loss of the normal sibling relationship for the typically developing child . once the period of grieving is over , however , families often show great resilience in the face of adversity . bayat identified a number of coping strategies used by families facing asd that fit nicely with the foundational concepts of the resilience theoretical framework [ 25 , 26 ] . using qualitative and quantitative investigations , bayat reported evidence of family unity , mobilisation of resources , greater life appreciation , and spiritual and personal growth . qualitative data was used to identify adolescent perceptions and coping responses towards a sibling with a disability . adolescent siblings resisted expressing feelings about the individual with the disability ; however , they did express emotions related to guilt . unfortunately this study was not specific to asd , but it gives justification that qualitative studies should be pursued in the asd field as the findings may have important implications for what components of their experience siblings feel comfortable in expressing . quintero and mcintyre . maternal well - being correlated negatively with higher problem behaviours in siblings of individuals with asd ; however , there was no significant difference between siblings of individuals with asd and those with typically developing siblings on measures of adjustment ( behavioural outcome and socialisation skills ) . ses ; past attendance at a sibling group ; parent stress ; family time and routines ; family problem - solving and communication ; and family hardiness were found to be important predictors of sibling adjustment in families of children with a disability . the study consisted of children with intellectual , sensory , physical , or developmental disabilities , with 30.6 percent of participating families including a child with asd . more positive effect has been reported within sibling relationships in which the member with asd had fewer problem behaviours . the present study aimed to determine the extent of negative and positive impacts of growing up with a sibling with asd . the scarce research available on psychosocial outcome points to some promising outcomes ; the review revealed positive impacts of growing up with a sibling with asd contingent upon limited risk factors . only four studies met the more rigorous criteria of : quantitative study , focused exclusively on siblings of individuals with asd with comparisons to controls with only typically developing siblings , and targeting behavioural and emotional psychosocial adjustment rather than the quality of the sibling relationship [ 10 , 13 , 14 , 20 ] . all of these studies suggested that the sample siblings were well adjusted under optimal environmental conditions ( limited demographic risk factors , large family , no compromised maternal well - being , sibling has high - functioning asd ) . this suggests that the focal mechanism for poor outcome may not be the autism spectrum disorder but a number of other child and family variables . these studies , however , still involved a mixture of children and adolescents , or in the case of quintero and mcintyre , primary school - aged children only ; this creates a challenge in attempting to make conclusive remarks regarding adolescent sibling outcome and a complete lack of ability to comment on the adult experience . furthermore , none of the databased studies explicitly measured qol , and they all involved less than one hundred participants . the majority of studies involved children and adolescent samples , leading to confounding results and an inability to draw accurate insights and conclusions about the distinct life stages of childhood and adolescence . this is concerning due to the large changes that occur during transition through these life periods . siblings play a vital role in each other 's lives within the family system . during childhood , children rely heavily on siblings for a multitude of functions : as role models ; in the development of theory of mind ; in seeking personal identity and their niche in the family and then the world ; and in developing socialisation skills . during this period siblings may fail to understand a complex disability like asd and may not understand why their brother or sister will not play with them , why their brother or sister gets different rules , and why their parents spend more time with their brother or sister . during adolescence , teenagers begin to spend less time with siblings and family and more time with friends ; they may begin to understand the diagnosis of asd more and feel guilt for any of their previous behaviours toward their sibling . they have usually formed strong social awareness and may become embarrassed by disability in the family , potentially resulting in a conflict between loyalty to their sibling and a desire to fit in with their peers . with such different concerns , child and adolescent siblings need to be studied separately . out of the two studies that focussed exclusively on an adolescent sample , one was not autism - specific and included multiple severe disabilities . limited family interaction and uncomfortable emotions were some concerning results that arose from this qualitative study . the other study concluded with a strong genetic environment interaction as a basis for the depressive and anxious traits found in the siblings of individuals with asd , whereas the current literature review was more concerned with the psychosocial components of sibling outcome . when qol was investigated using qualitative measures , communication within the sibling relationship and the invisibility of autism emerged as important themes . the severity of communication deficits in the individual with asd may be a mediating factor in qol outcome studies and should be investigated in future research . in regard to behavioural and emotional adjustment , internalising difficulties appear to be a concern for siblings of individuals with autism but perhaps mostly in sisters and in the presence of high levels of stress or maternal depression [ 20 , 21 ] . on a more positive note , bayat reported evidence of family unity , mobilisation of resources , greater life appreciation , and spiritual and personal growth . the families of individuals with asd also appeared to attach positive meaning to the disability in many instances . opperman and alant did find , however , that siblings of individuals with a disability felt that they could not express their feelings regarding the disability . this needs to be investigated in asd - specific samples , with implications for service providers to give siblings the opportunity to express emotions such as guilt . investigations into how we can foster resilience in our most at - risk families seem important . asd may be conceptualised as a developmental disorder that is particularly disruptive to the family unit . this is supported by reports that siblings of individuals with intellectual disability without asd were emotionally and behaviourally better adjusted than those siblings of individuals with intellectual disability and comorbid asd . this supports the notion that autism contributes to environmental stress that a sibling needs to adapt to , that it produces a unique set of circumstances for the sibling to navigate , and that autism specific studies , in the midst of such mixed results , need to become more prevalent in addition to disability studies . despite reports that the large majority of siblings of individuals with asd may be well adjusted , a significant proportion of the research indicates some vulnerability for behavioural and emotional dysfunction . this suggests that siblings need to be considered when planning interventions for asd , as important units within whole family functioning . the current review helps to identify potentially at - risk siblings , such as those in small families and those with little external support . furthermore , while sisters appear to internalise the stress of growing up with a sibling with asd , brothers and younger siblings appear to be at heightened risk for externalising disorders and antisocial behaviours . in summarising current knowledge of sibling outcome in asd research and identifying the gaps in this knowledge , the current literature review provides a theoretical and empirical basis from which to develop a conceptual framework to test the important research questions that have yet to be answered . what impact does having a sibling with asd have on children , adolescents , and adults as distinct life stages ? what transitions are important in the life of the typically developing sibling and the individual with asd ? most importantly , how can we lessen the impact of autism on siblings and families ? with findings that suggest the true impacts of growing up with a sibling with a disability may be masked by samples containing too many confounding factors such as age and gender [ 14 , 21 , 30 ] , further studies are vital in presenting conclusive findings . studies using systematic sampling procedures to identify participants within a narrow age range and controlling for confounding variables such as gender and birth order need to become more common in the sibling literature . according to hodapp et al . , research into the siblings of individuals with disabilities needs to meet certain vital criteria before the sibling community can reach a consensus . they identified six themes that appeared to be creating challenges in the sibling literature , providing a framework for guiding future research in this field . methodological challenges , measurement inconsistencies , developmental and life - course perspectives , factors and predictors , cultural issues , and balanced views were revealed as potential challenges in presenting conclusive data . ( 1 ) methodological challenges included the need to consider genetic and environmental influences , the use of systematic sampling procedures that take important characteristics into account ( age , gender , and birth order ) , and the need for matched control groups . these difficulties present significant potential for confounding yet are common in the sibling literature to date . ( 3 ) a developmental perspective is yet to be arrived at due to the use of both children and adolescents within sibling samples . ( 4 ) explicit research on mediators and moderators of sibling outcome specifically for asd is scarce and has been identified by hodapp et al . as an important consideration for future researchers . ( 5 ) furthermore , there is a complete paucity of studies examining cultural factors in sibling research . ( 6 ) lastly , hodapp et al . valued the presentation of both positive and negative aspects of sibling adjustment . there is a need within the literature to further define well - being , a term that currently appears to encompass a large range of sibling outcome measures , as being distinct from adjustment and qol , two potentially separate components of the well - being construct . it has been shown that psychosocial outcome and qol are related , but distinct constructs and that psychosocial outcome may be a necessary but insufficient component of overall qol . a clearer distinction is needed of the terms used to represent the outcome measures used in future research . despite normal levels of psychosocial adjustment in adolescents following childhood traumatic brain injury ( tbi ) , this suggests that qol can still be affected in the presence of normal levels of psychosocial health . this justifies further investigation into qol in disability studies , even if sibling adjustment appears normal , which is still debatable at this point . as it is yet to be explored empirically , it is only theoretically pertinent to propose at this point that siblings of individuals with asd may be behaving well and reporting no ill effects of their home environment due to empathy for their sibling and a desire to assist their parents , despite implicitly suffering compromised satisfaction with life . the studies that reported that siblings of individuals with asd were well adjusted included mostly demographically stable samples ; hence , future research using demographically disadvantaged siblings is warranted . many family and child factors have been linked to poorer outcome in siblings of individuals with a disability . these factors need to be considered in future studies so we can begin to make conclusive remarks on sibling outcome . these mediating variables do suggest , however , that there is the potential for siblings of individuals with asd to become well adjusted and happy adults under the right conditions . these conditions need to be rigorously studied so we can optimise sibling well - being . it appears that quantitative examples of the sibling experience , in which researchers categorise siblings into clinical and nonclinical or rate their symptom level in the desired emotional and behavioural domains , show that siblings may be well adjusted if not for a small proportion of vulnerable children . qualitative data , however , reveals some disturbing emotional and cognitive challenges for siblings of individuals with asd , justifying further investigation into subjective well - being outcomes .

objective . the purpose of this review of the literature was to summarise studies regarding the psychosocial impact of growing up with a sibling with autism and to identify gaps in the related literature . methods . electronic databases were reviewed in order to critically appraise the 14 articles relevant to the topic . the search included a combination of the following key words : autism , quality of life , well - being , sibling , asd , asd sibling , family , adjust , psychological functioning . results . the majority of studies involved mixed children and adolescent samples , leading to confounding results and an inability to draw accurate conclusions about these distinct life stages . autism appears to contribute to unique environmental stressors for the typically developing sibling . when experienced in the context of additional demographic risk factors , these stressors can result in difficulties adjusting to the demands of a special - needs child . despite some vulnerability to behavioural and emotional dysfunction in at - risk children , siblings have the potential to not only adjust but to thrive in the face of disability adversity . conclusion . growing up with a sibling with autism appears to manifest in both positive and negative outcomes for siblings , depending upon important demographical , family , and individual variables .

1. Introduction 2. Method 3. Results 4. Discussion 5. Conclusions

a number of bacteria resist axenic ( i.e. cell - free ) culture in the laboratory . those include obligate parasites causing serious human diseases , such as rickettsia ( 1,2 ) and mycobacterium leprae ( 3 ) . they adapt to a limited environment that provides appropriate physical conditions , nutriments and other factors required for their replication and growth . current culture systems of obligate parasitic bacteria depend on eukaryotic cells ( e.g. for rickettsia ) or even entire living animals ( e.g. for m.leprae ) . the lack of cell - free culture media poses a critical problem in studying these bacteria . without cell - free culture , it is impossible to use modern experimental approaches ( e.g. transcriptomics , proteomics ) that depend on non - contaminated rna or protein extractions . thus , the establishments of axenic culture media for those pathogens would have a significant impact on the medical and biological research communities working on these diseases . in a more fundamental way , this type of study might help to unraveling various type of signals involved in their host parasite relationships . with the recent development of metabolic databases ( 4,5 ) , genome - based metabolic reconstruction has become an efficient approach to tackle this problem ( 6,7 ) . by examining the metabolic pathways predicted from genomic sequence analyses we recently analyzed the complete genome sequence of a human pathogen , tropheryma whipplei strain twist , and identified significant deficiencies in the biosynthesis of nine amino acids ( 8) . remarkably , this knowledge effectively guided the development of the first axenic culture medium to grow this fastidious microorganism ( 7 ) that had been previously cultured only in association with a fibroblast cell line ( hel ) ( 9 ) . we believe that this type of approach should be generalized and could allow more obligate parasitic bacteria to be grown in a cell - free culture medium . it is clear that explicit hypotheses ( e.g. required nutriments ) and supporting evidences ( e.g. deficiencies of the de novo synthesis ) are determinants for this type of study . however , such a biological knowledge is usually dispersed in literature and various biological databases . till date , no existing database exhaustively collects and systematically provides biological knowledge about the cultivation of obligate parasites . this prompted us to gather evidences and hypotheses that are relevant to the improvement of the culture conditions of obligate parasites and make them available in a knowledgebase named metagrowth ( http://igs-server.cnrs-mrs.fr/axenic/ ) . in this paper , we describe the source of the data accessible in metagrowth as well as its web interface guiding the user to design new cell - free culture media of obligate parasites . hypotheses relevant to the improvement of the culture conditions of parasitic bacteria as follows : example 1 . evidence : the genome does not encode enzymes for the biosynthesis of compound x , but encodes a transporter for x. hypothesis : adding x may improve the growth.example 2 . evidence : the genome encodes enzymes requiring cofactor y , but does not encode genes for the biosynthesis of cofactor y. hypothesis : adding y may improve the growth. these kinds of information are collected from the published literature , genomic sequence databases ( 4 ) , metabolic databases ( 4,5,10,11 ) and transporter databases ( 12 ) . table 1 shows a tentative metagrowth entry describing the supplementation of s - adenosyl - l - methionine for the improvement of rickettsia culture conditions . evidence and hypothesis records are the two main components of the database entry . the evidence record is a free text describing experimentally validated facts or predicted metabolic features . associated hypotheses for the improvement of the culture condition are stored in the hypothesis record . in the hypothesis record , we currently describe the supplementation of organic or inorganic compounds in the medium , or appropriate physical conditions such as oxygen concentration . a prefix in= in the hypothesis record designates a preferential input ( a compound or a physical condition ) to the culture medium that could be experimentally tested . hyperlinks to relevant genes , pathways and literature in the source databases are provided to direct the users to the original data . currently , we have accumulated 220 metagrowth entries for 6 species of bacteria ( 5 genera ) : rickettsia prowazekii and rickettsia conorii ( agents of typhus and spotted fever , respectively ; 40 entries ) , t.whipplei ( whipple 's disease ; 38 entries ) , treponema pallidum ( 13 ) ( syphilis ; 42 entries ) , m.leprae ( leprosy ; 63 entries ) and coxiella burnetii ( 14 ) ( q - fever ; 37 entries ) . evidence : the genome does not encode enzymes for the biosynthesis of compound x , but encodes a transporter for x. hypothesis : adding x may improve the growth. example 2 . evidence : the genome encodes enzymes requiring cofactor y , but does not encode genes for the biosynthesis of cofactor y. hypothesis : adding y may improve the growth. rating of the reliability of collected scientific evidences is an important issue in constructing a database of biological hypotheses ( 15 ) . in metagrowth , the relationships between evidences and hypotheses were classified into several categories . the evidence types could be used for the prioritization of different hypotheses supported by different kinds of evidences . class i evidences describe the inability to synthesize a compound , either by metabolic deficiencies or by general incapability of biosynthesis ( e.g. inorganic molecules such as metal ions ) . class ii evidences refer to the importing capability of a compound , either by active transporters or by passive membrane permeability . class iii evidences refer to the requirement or utilization of a compound by the bacteria . those include cofactors required for known or predicted enzymatic reactions in the cell , and basic building blocks of macromolecules such as the 20 amino acids . class iv evidences refer to the other type of evidences , mostly experimentally validated facts . the precise definitions of these evidence classes and subclasses are provided in the supplementary material ( table s1 ) . figure 1 shows the current status of the number of hypotheses supported by different types of evidences . browsing metagrowth entries , users can easily obtain a list of nutriment compounds and the corresponding list of evidences suggesting the supplementation of the medium by these compounds . an important practical issue is the determination of the concentrations of those supplemented molecules . to help the users with this respect the ranges were determined according to the roles of molecules in bacterial cells and the concentrations of the molecules of the same role in several reference culture media . as reference culture media , we selected two complex culture media for fastidious ( i.e. difficult to grow ) bacteria : bsk - h medium designed to support the growth of the lyme disease spirochete borrelia burgdorferi ( 16 ) , and twh medium supporting the growth of t.whipplei ( 7 ) . the concentrations of the components in the two media and the upper and lower limits of the concentrations within each compound category are provided in the supplementary material ( figure s1 ) . the users may specify one or more values within the suggested range of concentration of each molecule . if the users specify more than one concentration in the range , the combination of different concentrations for different molecules could lead to a huge number of experiments even if the number of molecules remains relatively small . the full combinatorial testing of 20 different nutriments , at two concentrations each , corresponds to 2 10 . such a large number of screening experiments can be avoided by the use of the incomplete factorial design approach . incomplete factorial design is a mathematical method to effectively reduce the number of experiments required by a full combinatorial - screening of parameters ( 17 ) . samba is an implementation of the incomplete factorial design , which has been extensively used for the determination of protein crystallization conditions ( 18 ) , and more recently for optimizing recombinant protein experiments ( 19 ) . metagrowth outputs the list of molecules and their concentrations in a format compatible with the samba program ( http://igs-server.cnrs-mrs.fr/samba/ ) . in the above example with 20 compounds , , the incomplete factorial design provides a minimal set of experiments in which the influence of each parameter can be examined rationally by statistical methods such as a multiple linear regression analysis . many evidences in metagrowth originate in metabolic analyses described in the literature such as whole genome sequencing papers . the use of in silico simulation studies with more sophisticated mathematical metabolic models ( 2023 ) than those available in the current metabolic databases ( 4,5 ) is clearly the next improvement in the generation of metabolic hypotheses . with these approaches , one may , more precisely , examine metagrowth evidences and derived hypotheses such as a metabolic pathway from x to y lacks an enzyme , thus the addition of y in the medium may improve the culture of bacteria. in silico simulation studies may reveal an alternative pathway to the metabolite y bypassing the missing reaction steps . in the current metagrowth , we only present predictions for preferential inputs to the culture conditions ( designated by the in= prefix ) . . compound nomenclature in metagrowth is based on ligand ( 10 ) , in which hierarchical relationships between individual and generic compound names are not well treated . standardization of the compound name in metagrowth will be required to facilitate data update and to automatically detect data redundancies . genome sequence analysis and metabolic reconstruction of t.whipplei led to the establishment of the first cell - free culture medium allowing this fastidious bacteria to grow outside its cellular host . further improvement of the culture condition using metagrowth may lead to an even faster growth , which would further facilitate the manipulation and study of this microorganism . the development of an axenic culture medium for other bacteria could be more challenging . for m.leprae and t.pallidum , a large body of research has been carried out to explore the possibility of axenic cultivation as can be seen in metagrowth . the study of bacterial culture conditions offers new testable and valuable challenges for the whole cell metabolic modeling and simulation studies . it helps better characterization of host parasite relationships , eventually giving us clues about new therapeutic targets . we hope to help the scientific community working on those pathogens by providing comprehensive information about their culture conditions through metagrowth . table s1 gives the definition of the classes and the subclasses of the relationships between evidences and hypotheses . we thank dr didier raoult for helpful discussions and dr guillaume blanc for carefully reading the manuscript .

metagrowth is a new type of knowledge base developed to guide the experimental studies of culture conditions of obligate parasitic bacteria . we have gathered biological evidences giving possible clues to the development of the axenic ( i.e. cell - free ) growth of obligate parasites from various sources including published literature , genomic sequence information , metabolic databases and transporter databases . the database entries are composed of those evidences and specific hypotheses derived from them . currently , 200 entries are available for rickettsia prowazekii , rickettsia conorii , tropheryma whipplei , treponema pallidum , mycobacterium tuberculosis and coxiella burnetii . the web interface of metagrowth helps users to design new axenic culture media eventually suitable for those bacteria . metagrowth is accessible at http://igs - server.cnrs - mrs.fr / axenic/.

INTRODUCTION DATA IN METAGROWTH DESIGN OF A NEW CELL-FREE CULTURE MEDIUM FUTURE DIRECTIONS AND CONCLUSIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS

each origin generates a pair of sister replication forks that subsequently move along parental dna in a bidirectional manner to undergo dna replication . replication forks then terminate when they encounter forks from the adjacent replication origins moving in the opposite direction . thus , replication initiated at each origin leads to duplication of a discrete dna region , which is called replicon . in budding yeast saccharomyces cerevisiae , dna replication origins are defined by a 200-bp dna sequence called an autonomously replicating sequence , which was originally identified based on its ability to support the replication of plasmid dna ( newlon and theis 1993 ) . the budding yeast genome ( about 14 mb ) contains 300 replication origins at average intervals of 50 kb ( raghuraman et al . 2001 ; yabuki et al . 2002 ; feng et al . 2006 ; nieduszynski et al . 2006 ) . in fission yeast schizosaccharomyces pombe , replication origins lack a consensus dna sequence but consist of at - rich sequences ( robinson and bell 2005 ) . it is estimated that at least half of the approximately 2,500 intergenic regions have potential origin activity ( dai et al . 2005 ) , and 460 of these are actually licensed for replication ( hayashi et al . metazoan cells also lack any dna consensus sequence for replication origins ( robinson and bell 2005 ) , but intriguingly , the initiation points of replication at the nucleotide level show very similar distribution patterns within the origin regions in budding yeast , fission yeast , and humans ( bielinsky and gerbi 2001 ) . despite the difference in the dna sequences of replication origins between yeast and metazoa , the protein components assembling at replication origins and replication forks the prereplicative complex ( prerc ) is a large protein complex , comprised of the origin recognition complex ( orc ) , cdc6 , cdt1 , and mcm27 ( blow and dutta 2005 ) . the prerc is formed at replication origins from telophase and throughout g1 phase to license the origins for dna replication initiation . at the onset of s phase , more proteins such as dna polymerases and a sliding clamp called proliferating cell nuclear antigen ( pcna ) are loaded at origins , establishing a protein complex called the replisome , which subsequently moves with a replication fork to undergo dna replication ( johnson and o'donnell 2005 ) . dna replication initiation at various origins ( origin firing ) occurs by a coordinated temporal program ; some origins fire early and others late during s phase . inside the nuclei , duplication of chromosomal dna is physically organized into replication factories , consisting of dna polymerases and other replication proteins . in this review article , we examine the spatial organization and regulation of dna replication within the nucleus and discuss how this spatial organization is linked to temporal regulation . we focus on dna replication in budding yeast and fission yeast and , in chosen topics , compare yeast dna replication with that in bacteria and metazoans . in this context , we briefly touch upon spatial regulation of dna damage and replication checkpoints , which are , however , reviewed in more detail in herrick and bensimon ( 2008 ) and branzei and foiani ( 2009 ) . when replication origins are isolated and placed on minichromosomes , they normally replicate in early s phase in budding yeast ( ferguson and fangman 1992 ) . however , in their normal chromosomal context , some origins show delayed firing within s phase . this delay is due to proximal cis - acting chromosomal elements , telomeres , and other dna sequences for subtelomeric and nontelomeric late - firing origins , respectively ( ferguson and fangman 1992 ; friedman et al . so far , among such cis - acting chromosomal elements , no consensus dna sequences , apart from telomeres , have been identified . it has been shown that both subtelomeric and nontelomeric late - firing origins localize preferentially in the nuclear periphery during g1 phase ( heun et al . does this nuclear periphery localization have a causative role in the late firing of replication origins during s phase ? indeed , in various conditions , the nuclear periphery localization of origins is correlated with their delayed replication . for example , cis - acting chromosomal elements , which determine the late firing of the origins , are also required for nuclear periphery localization ( friedman et al . 1996 ; heun et al . 2001 ) . moreover , after a subtelomeric late - firing origin was excised from its chromosome locus prior to g1 phase ( in g1 , telomeres localize preferentially at the nuclear periphery ) ; the origin advanced the timing of its firing to early s phase ( raghuraman et al . 1997 ) . however , in some circumstances , late firing of replication origins is not correlated with their nuclear periphery localization during g1 . for example , after a normally early - firing origin was tethered to the nuclear periphery by targeted interaction with an integral membrane protein , the origin did not show late firing ( zappulla et al . 2002 ) . moreover , genetic screening identified mutants that disrupt telomere localization at the nuclear periphery but still maintain late firing of subtelomeric origins ( hiraga et al . therefore , nuclear periphery localization of replication origins is neither sufficient nor required for their late firing . it seems that chromatin states and structures , such as silencing by sir proteins and chromosome - end binding of the ku complex , affect more directly the initiation timing of subtelomeric origins ( stevenson and gottschling 1999 ; cosgrove et al . sir proteins and the ku complex also regulate the nuclear periphery localization of telomeres ( hediger et al . 2002 ; taddei and gasser 2004 ) ; however , the nuclear periphery localization is probably not a direct determinant of their replication timing . perhaps a similar argument can be also applied for nontelomeric late - firing origins , although regulators other than sir and ku proteins may be involved in delaying their replication . for example , it was shown that histone deacetylase rpd3 is important for delaying their replication ( vogelauer et al . 2009 ) ; it is known that rpd3 is targeted to promoters and coding regions and regulates their transcription ( kadosh and struhl 1997 ; carrozza et al . , it does not seem that the subnuclear localization of replication origins per se determines their timing of replication initiation in yeast ; however , underlying chromatin states and structures probably regulate both their localization and initiation timing . nonetheless , it is still possible that the subnuclear localization assists maintenance of underlying chromatin states and structures in a feedback and thereby affects replication timing moderately even if it is not an essential determinant . for example , euchromatin and heterochromatin undergo dna replication in early and late s phase , respectively ( gilbert 2002 ) . replication timing of a chromosomal region is correlated with its subnuclear localization and with chromatin states such as histone modifications ( hiratani et al . upon replication initiation , dna polymerases and other replication proteins such as pcna and replication factor c assemble at a licensed replication origin , forming a replisome , which subsequently moves together with a replications fork to undergo dna replication ( johnson and o'donnell 2005 ) . a range of evidence suggests that each replisome synthesizes both leading and lagging strands of dna simultaneously ( baker and bell 1998 ; waga and stillman 1998 ; johnson and o'donnell 2005 ) . in bacteria , one type of dna polymerase ( e.g. , dna polymerase iii in escherichia coli ) synthesizes both leading and lagging strands . in contrast , in eukaryotes , the identity of dna polymerases that synthesize each strand had been unclear until recently . the mutation rates were evaluated using polymerase mutants with reduced replication fidelity in budding yeast , and it was discovered that dna polymerase and primarily synthesize lagging and leading strands , respectively ( pursell et al . 2007 ; nick mcelhinny et al . 2008 ) . it was originally thought that the two replisomes at sister forks ( i.e. , initiated from the same origin ) would behave separately since they travel in opposite directions along template dna . however , it was found that on bacterial circular chromosomes where dna replication starts from a single defined origin , sister forks move along dna and normally complete dna replication with similar timing at a defined region on the chromosome ( bussiere and bastia 1999 ) . to explain this coordinated termination of dna replication , it was proposed that two replisomes at sister forks ( sister replisomes ) remain attached during dna replication ( dingman 1974 ; falaschi 2000 ) . this model predicts that template dna moves into two associated replisomes , and newly replicated sister dna strands are extruded as replication proceeds . such dna motion relative to centrally located stationary replisomes ( lemon and grossman 1998 ) was indeed confirmed in bacteria bacillus subtilis and caulobacter crescentus ( lemon and grossman 2000 ; jensen et al . furthermore , electron microscopy of large tumor antigen ( t antigen ) in simian virus 40 , which functions as a dna helicase at replication forks ( herendeen and kelly 1996 ) , showed that unwound dna from viral replication origins forms two loops which are pinched by the same pair of associated t - antigen hexamers ( wessel et al . on the other hand , in e. coli , sister replisomes separate shortly after dna replication initiation and undergo dna replication independently ( bates and kleckner 2005 ; reyes - lamothe et al . in contrast to bacteria and viruses , it remained unknown until recently whether sister replisomes are associated together in eukaryotes . in budding yeast , live - cell imaging was used to analyze the replication timing of chromosome loci ( fig . 1 ) ( kitamura et al . 2006 ) , at which bacteria - derived teto and laco arrays were integrated ( straight et al . 1996 ; michaelis et al . these arrays bound tetr and laci proteins , fused with fluorescent proteins , and were thus visualized as small fluorescent dots . the fluorescent dots increased their intensity upon their dna replication when the number of teto and laco arrays was doubled , which defined their replication timing by microscopy ( kitamura et al . two loci were selected and visualized within a single replicon so that they locate at the opposite sides of the relevant replication origin and show similar replication timing ( based on a genome - wide replication timing data : raghuraman et al . remarkably , these two loci came close to each other , increased their intensity , and subsequently diverged from each other during s phase ( kitamura et al . such behavior of the two loci suggests that sister replisomes are associated together during replication of the replicon . furthermore , in a separate study , nascent dna segments were pulse - labeled and observed by electron microscopy . this study suggested that human sister replisomes are also associated with each other during dna replication ( ligasov et al . 1sister replisomes are associated with each other during replication in budding yeast . a model of a closely associated double replisome and expected behavior of two chromosomal loci , teto , and laco , which bound tetr-3cfp and gfp - laci , respectively ( top ) . b two loci come close to each other upon dna replication . cfp ( red ) , gfp ( green ) , and bright field images of a representative cell are shown . the teto and laco are visualized as small fluorescent of dots of cfp and gfp , respectively . two loci came close to each other , increased their intensity ( 3 to 1 min ) and subsequently diverged from each other during s phase . scale bar represents 1 m . the figure is adapted from kitamura et al . ( 2006 ) with permission ( copyright elsevier 2006 ) sister replisomes are associated with each other during replication in budding yeast . a model of a closely associated double replisome and expected behavior of two chromosomal loci , teto , and laco , which bound tetr-3cfp and gfp - laci , respectively ( top ) . b two loci come close to each other upon dna replication . cfp ( red ) , gfp ( green ) , and bright field images of a representative cell are shown . the teto and laco are visualized as small fluorescent of dots of cfp and gfp , respectively . two loci came close to each other , increased their intensity ( 3 to 1 min ) and subsequently diverged from each other during s phase . scale bar represents 1 m . the figure is adapted from kitamura et al . why do cells keep sister replisomes closely associated during replication ? what benefits can cells reap from it ? one possibility is that the close association enables temporal coordination of dna replication between sister replisomes . indeed , such temporal coordination was revealed in human cells : by labeling nascent dna on single - molecule dna fibers ( michalet et al . 1997 ; herrick et al . 2000 ) ; it was possible to measure the velocity of replication fork movements along template dna , and it was found that the majority pairs of sister forks showed very similar velocity ( conti et al . if one fork changed its speed , its sister also changed its speed in a similar way . given that replication forks in the adjacent replicon also shows similar velocity ( conti et al . 2007 ) , this temporal coordination may help replication forks in the same and neighboring replicons change their speed collaboratively and promptly , responding to replication stress such as the reduced amount of deoxy - nucleotides available in the nucleus . the velocity of sister replication forks also show significant correlation in budding yeast ( fig . 2 ) ; thus , the temporal coordination seems to be conserved in evolution . we used the genome - wide replication profile ( black line ; yabuki et al . 2002 ) , which represents the time ( minutes ) after release from factor arrest at which 50% of cells complete dna replication , along the chromosomes ( 1-kb intervals ) . peaks and valleys ( rectangles pointing down and up , respectively ) of the profile represent replication origins and termini , respectively . to measure the velocity , first , we excluded a 5-kb region on each side of peaks and valleys in order to avoid errors due to smoothing when drawing the replication profile in that region . second , the regions were selected for measurement of the velocity of the leftward and rightward forks ( red lines ) so that they end with the same replication timing ; for example , if the right valley goes deeper than the left , the selected region for the right terminated when the left one ended . third , we chose replicons for the analysis only when their defined regions for measurement span more than 8 kb along a chromosome both at left and right sides , as smaller ones may give larger errors . the replicon , locating at 508 kb on chromosome viii ( from the left telomere ) , was excluded from the analysis as it showed much larger fork velocity ( 1117 kb / min ) than others . b as described in a , we chose 67 replicons out of 260 identified in yabuki et al . the graph indicates that the velocity of replication fork movements shows significant correlation between sister forks ( pearson s correlation , r = 0.4725 , p < 0.0001 , n = 67 ) the velocity of replication fork movements is correlated between sister forks in budding yeast . we used the genome - wide replication profile ( black line ; yabuki et al . 2002 ) , which represents the time ( minutes ) after release from factor arrest at which 50% of cells complete dna replication , along the chromosomes ( 1-kb intervals ) . peaks and valleys ( rectangles pointing down and up , respectively ) of the profile represent replication origins and termini , respectively . to measure the velocity , first , we excluded a 5-kb region on each side of peaks and valleys in order to avoid errors due to smoothing when drawing the replication profile in that region . second , the regions were selected for measurement of the velocity of the leftward and rightward forks ( red lines ) so that they end with the same replication timing ; for example , if the right valley goes deeper than the left , the selected region for the right terminated when the left one ended . third , we chose replicons for the analysis only when their defined regions for measurement span more than 8 kb along a chromosome both at left and right sides , as smaller ones may give larger errors . the replicon , locating at 508 kb on chromosome viii ( from the left telomere ) , was excluded from the analysis as it showed much larger fork velocity ( 1117 kb / min ) than others . b as described in a , we chose 67 replicons out of 260 identified in yabuki et al . the graph indicates that the velocity of replication fork movements shows significant correlation between sister forks ( pearson s correlation , r = 0.4725 , p < 0.0001 , n = 67 ) the temporal coordination between associated sister replisomes would be indeed useful for replisomes to respond promptly to replication stress if this stress affects the whole genome . on the other hand , it may be rather harmful if the replication stress is imposed locally on particular chromosome loci . for example , when dna damage on a chromosomal region halts or terminates the motion of a fork ( branzei and foiani 2005 ) , the behavior of its sister fork would be also affected , widening the adverse effects of the dna damage . intriguingly , however , it was shown that in yeast cells , a replication fork continues to move while its sister fork is halted or terminated due to a dna double - strand break ( doksani et al . similarly , within yeast rdna regions , halting of a replication fork by a replication - fork barrier did not stop or slow down the progression of its sister fork ( brewer and fangman 1988 ; linskens and huberman 1988 ) . taken together , when a replication fork is stalled upon the encounter on a local replication obstacle , its sister can behave independently . thus , there might be a mechanism that senses a stalled replication fork and uncouples it functionally from its sister fork ( herrick and bensimon 2008 ) . are there any other functional consequences or benefits of the association of sister replisomes ? once a replication origin is unwound and replication forks are generated , the origin loses its ability to initiate replication , which requires prerc formation at the origin in eukaryotes ( see introduction ) and the origin methylation on both dna strands in bacteria ( boye et al . 2000 ) . therefore , a half replicon might fail to replicate if one replisome could initiate without waiting for the other replisome to be loaded onto the origin . if avoidance of this problem is a major benefit of associated sister replisomes , this association might not be necessary once both of them start dna replication from an origin . indeed , at least in bacterium e. coli , sister replisomes separate shortly after initiation and undergo dna replication independently ( bates and kleckner 2005 ; reyes - lamothe et al . nonetheless , in other bacteria such as b. subtilis and c. crescentus , or in eukaryotes such as budding yeast and humans , sister replisomes seem to be associated for a longer time , perhaps throughout replication of the whole replicon ( see above ) . the associated sister replisomes may coordinate the dna polymerase operation for two leading and two lagging strands to avoid chromosome entanglement and to facilitate smooth reeling in and out of unreplicated and replicated dna strands . this spatial coordination might be particularly important in eukaryotic cells , in which more complex spatial regulation may be required as their multiple replicons are processed for dna replication in a single replication factory ( see below ) . when mammalian cells are pulse - labeled with nucleoside analogs ( such as bromodeoxyuridine ( brdu ) ) or tagged nucleotides during s phase , dna replication appears to start at several discrete sites called replication foci ( nakamura et al . studies with different mammalian cell lines showed that 1001,000 foci are observed in early s - phase nuclei ( berezney et al . it is estimated that each focus contains 10100 replicons , which together represent a chromatin territory , a stable unit maintained until the next cell cycle ( jackson and pombo 1998 ) . the average replication focus is estimated to contain 1 mbp of genomic dna in mouse cells ( ma et al . similar replication foci were also observed in budding yeast nuclei . in vitro experiments using isolated yeast nuclei showed that a tagged nucleotide was incorporated as 1520 discrete foci in an orc - dependent and origin - specific manner ( pasero et al . because yeast cells lack a thymidine kinase ( tk ) , they can not utilize brdu or isotope - labeled thymidine , which is widely used to visualize sites of dna replication in intact mammalian cells . however , introduction of heterogeneous tk enabled yeast cells to incorporate brdu in vivo ( mcneil and friesen 1981 ; lengronne et al . , several studies have shown that brdu is incorporated as discrete foci into nuclei using immunostaining ( lengronne et al . , however , it is unlikely that replication foci represent stable chromatin units maintained to the next cell cycle , in contrast to mammalian cells ( see above ) . in fact , a chromosome arm locus can move vigorously covering a wide area of the yeast nucleus in a single cell cycle ( berger et al . 2008 ; our unpublished results ) . this is presumably due to the small size of the yeast nucleus ( see fig . 3 ) and may also reflect potentially different chromatin organization between yeast and mammalian cells . fig . 3comparing the size of replication factories and the nucleus between budding yeast and mammalian cells . the subnuclear localization of pcna fused with gfp during s phase in a mouse cell ( top left ; scale bar 1 m ; adapted from leonhardt et al . ( 2000 ) with permission ) and in budding yeast ( top right , asterisks ; scale bar 1 m ) . a magnified image of the yeast nucleus is also shown ( bottom right ) . the nuclei of yeast and mouse cells are outlined in yellow for comparison of their sizes . note that a large factory is composed of several small ones in a mouse cell ( leonhardt et al . 2000 ; z series , bottom left ) comparing the size of replication factories and the nucleus between budding yeast and mammalian cells . the subnuclear localization of pcna fused with gfp during s phase in a mouse cell ( top left ; scale bar 1 m ; adapted from leonhardt et al . ( 2000 ) with permission ) and in budding yeast ( top right , asterisks ; scale bar 1 m ) . a magnified image of the yeast nucleus is also shown ( bottom right ) . the nuclei of yeast and mouse cells are outlined in yellow for comparison of their sizes . note that a large factory is composed of several small ones in a mouse cell ( leonhardt et al . 2000 ; z series , bottom left ) when replisome components such as dna polymerase a and pcna are visualized by immunolabeling in mammalian cells , they show discrete punctate signals in the nucleus during s phase ( frouin et al . 2003 ) . these punctate signals are called replication factories as they colocalize with replication foci , i.e. , the sites of ongoing dna replication ; thus , replisome components are concentrated into discrete foci , in which multiple replicons are processed for replication ( hozk et al . 1993 ) . the organization and dynamics of replication factories were also examined in live mammalian cells that expressed pcna , fused with a fluorescent protein , ( leonhardt et al . live - cell imaging revealed that replication factories show dynamic assembly and disassembly throughout s phase . replication factories are also formed in the nucleus of budding yeast , as revealed by immunostaining and live - cell imaging ( ohya et al . for example , when pcna or dna polymerases and were visualized with fluorescent proteins , yeast cells showed 1015 globular signals in their nuclei during s phase ( kitamura et al . the size of each globular signal , i.e. , replication factory , was up to 200 nm in diameter , which is smaller than the 0.52-mm diameter replication factories of mammalian cells ( leonhardt et al . 2000 ; fig . 3 ) . however , given that large factories are composed of several small ones in mammalian cells ( leonhardt et al . 2000 ) , yeast factories may correspond to the small units of mammalian factories in terms of the size and mode of function . replication factories in yeast change their shapes and show dynamic assembly and reassembly , similarly to mammalian cells . these replication factories at least partially colocalize with replication foci , visualized with pulse - labeled brdu , in fixed cells ( hiraga et al . 2005 ; kitamura et al . , when a teto array ( bound by tetr fusion with a fluorescent protein ) was visualized as a small fluorescent dot on a chromosome locus , the dot increased its intensity specifically upon colocalization with a replication factory , thus , confirming de novo dna replication at factories in live cells ( kitamura et al . fission yeast nuclei also show globular signals of pcna and dna polymerase during s phase ( meister et al . is a replication factory a preformed complex , inside of which replication is initiated ? alternatively , only after replication initiation , is the factory formed as a result of assembly of replisomes undergoing replication ? a number of evidences suggest that the factory is formed only after dna replication initiation . for example , the factory formation is dependent on the activity of cyclin - dependent kinase ( cdk ) 2 that triggers dna replication initiation in vertebrate cells ( cardoso et al . 1993 ; jackson et al . 1995 ; yan and newport 1995 ) . on the other hand , punctate signals of replication protein a ( rpa ) appear prior to dna replication in xenopus egg extract system ( adachi and laemmli 1992 , 1994 ) . however , it turns out that rpa , which binds single - strand dna with dependence on prerc ( and therefore , directly relevant to dna replication ) , forms factories only after replication initiation in s phase ( jackson et al . replication factories are also formed after replication initiation in yeast cells , where the factory formation is delayed if the activation of s - phase cdk is retarded ( kitamura et al . if the origin licensing becomes defective in yeast cells by depletion of cdc6 , the factory formation is abolished even if other s - phase events such as s - phase cdk activation takes place normally . these results suggest that in cells ranging from yeast to vertebrates , the assembly of active replisomes undergoing dna replication leads to the formation of replication factories . as discussed above , replication factories show dynamic assembly and disassembly during s phase . as a result , in mammalian cells , a large number of factories are distributed throughout the nucleus , except for the nucleolus , during early s phase . during mid s phase then , in late s phase , large factories , composed of several independent small ones ( see fig . 3 ) , are formed inside the nucleus ( leonhardt et al . the change in the distribution of replication factories was also examined in fission yeast ( meister et al . 2007 ) . after the onset of s phase , factories appear throughout the nucleus except for the nucleolus . later in s phase , interestingly , this temporal pattern is regulated by cds1 ( chk2 ) kinase , a regulator of s - phase checkpoint , even in the absence of replication stress ( meister et al . , it was shown that another checkpoint kinase chk1 is involved in temporal pattern of origin firing during unperturbed s phase ( maya - mendoza et al . when dna replication is halted due to replication stress , the replication checkpoint pathway is also required to maintain the organization of replication factories ( dimitrova and gilbert 2000 ) . in mammalian cells , a replication focus is considered to represent a cluster of multiple replicons ( 10100 ) that synchronously fire in s phase , although the number of replicons per focus and its synchrony seem to be highly heterogeneous ( berezney et al . 2000 ) . what group of replicons forms a replication focus that is processed for replication in a single replication factory ? intriguingly , as s phase proceeds , a replication focus appears in close proximity to a focus replicating earlier , suggesting that replication may proceed to neighboring regions by a domino effect involving local changes of chromatin states ( sporbert et al . 2004 ) . in budding yeast , neighboring replicons along a chromosome region can be grouped into clusters , each of which comprises several origins that initiate replication with similar timing and behave similarly after deletion of an s - phase cyclin ( yabuki et al . the origins in the same cluster might be processed in the same replication factory . on the other hand , replicons on different chromosomes , such as those at centromere or telomere regions ( see below ) , might be processed in the same factory due to their proximity in the nucleus . are there any benefits of forming replication factories and undergoing replication at discrete sites ? one possible benefit might be that by concentrating replisome components and dna - building materials such as deoxy - nucleotides , cells may increase the efficiency of dna replication . in addition , a group of replicons processed in each replication factory may form a unit that responds coordinately to a replication stress or dna damage . for example , it is suggested that under a replication stress , the replication initiation from dormant origins is promoted within the factories that have been already formed while replication initiation is suppressed outside of these factories ( ge et al . moreover , when the speed of replication forks changes , this affects the programming of origin firing in the next cell cycle ( courbet et al . 2008 ) , in which replication factories may signal a change of the fork speed . in this section , we briefly discuss dna replication at centromeres and telomeres as examples of spatial regulation of replication in particular chromosome contexts . in budding yeast , spindle pole bodies ( spbs ; microtubule - organizing centers in yeast ) are embedded in the nuclear envelope , which remains intact throughout the cell cycle ( closed mitosis ; heath 1980 ) , and kinetochores are tethered to spbs by microtubules during most of the cell cycle . however , it was revealed that , upon centromere dna replication , kinetochores are transiently disassembled , causing centromere detachment from microtubules for 12 min ( kitamura et al . subsequently kinetochores are reassembled and interact with microtubules again . because centromeres are replicated in early s phase in budding yeast ( mccarroll and fangman 1988 ; raghuraman et al . the timing of these events is presumably crucial to make a time window sufficient ( even in the absence of g2 phase ; see below ) for establishment of proper kinetochore telomeres in budding yeast tend to localize at the nuclear periphery from the end of mitosis to g1 phase , and this localization depends on the ku- and sir - mediated anchoring mechanisms ( hediger et al . 2002 ; taddei and gasser 2004 ) . prior to anaphase , however , telomeres localize randomly within the nucleus ( laroche et al . it was demonstrated that the delocalization of telomeres from the nuclear periphery is triggered by their dna replication , which suppresses the ku - mediated anchoring mechanism in late s phase ( ebrahimi and donaldson 2008 ) . the detachment of telomeres from the nuclear periphery probably enhances telomere mobility in the nucleus , which has an advantage in subsequent chromosome segregation . thus , replication at centromeres and telomeres is closely linked to chromosome segregation in mitosis . this link is probably crucial in budding yeast as it is thought that s phase and mitosis are overlapped , and g2 phase is absent in this organism ( kitamura et al . dna replication is a spatially regulated process at multiple levels ; i.e. , from replisome architecture to subnuclear chromosome organization . the spatial regulation of dna replication is closely linked to its temporal regulation . both spatial and temporal regulations seem to be important for efficient duplication of chromosomes , for proper responses to replication stresses and for coupling dna replication with other cellular events such as chromosome segregation . several new methods have been developed and widely applied over the last decade , making considerable contribution to the research field . for example , genome - wide approaches have introduced unbiased and thorough landscapes of genome replication in yeast and other organisms ( raghuraman et al . 2004 ) . single - cell and single - molecule assays have enabled analyses of dna replication in high spatial and temporal resolution and have opened a window into how dna replication differs from cell to cell and from chromosome to chromosome ( michalet et al . 1997 ; herrick et al . further development of these methods and other biochemical , genetic , and cell biological approaches will advance further the research of chromosome duplication .

duplication of chromosomal dna is a temporally and spatially regulated process . the timing of dna replication initiation at various origins is highly coordinated ; some origins fire early and others late during s phase . moreover , inside the nuclei , the bulk of dna replication is physically organized in replication factories , consisting of dna polymerases and other replication proteins . in this review article , we discuss how dna replication is organized and regulated spatially within the nucleus and how this spatial organization is linked to temporal regulation . we focus on dna replication in budding yeast and fission yeast and , where applicable , compare yeast dna replication with that in bacteria and metazoans .

Introduction Subnuclear localization of replication origins and timing of their firing Replisome architecture and association of sister replisomes Possible benefits of the association of sister replisomes Replication foci and replication factory Replication factories: regulation, organization, and possible benefits DNA replication at centromeres and telomeres Conclusions and perspectives

deficient capacity can cause tissue hypoperfusion , microcirculation dysfunction , and vital organ failure . however , excess liquid expansion may also cause cardiac insufficiency , pulmonary edema , and other adverse clinical consequences . although it is essential to optimize cardiac preload immediately to maintain tissue perfusion in patients with severe sepsis , it is difficult to appropriately evaluate the status of cardiac preload in patients during the early phase of severe sepsis . however , monitoring vital signs and blood biochemical indices for predicting capacity in septic patients is not precise because they are influenced by various clinical conditions . measurements of central venous pressure ( cvp ) and pulmonary capillary wedge pressure ( pawp ) through central venous and pulmonary artery catheters are based on pressure and affected by many factors , such as cardiovascular adaptability , chest cavity pressure , valvular regurgitation , and intra - abdominal pressure . in recent years , more reliable parameter for cardiac preload has been elucidated and use of minimally invasive methods to evaluate capacity in septic patients has become especially popular . these methods include pulse indicates continuous cardiac output ( picco ) to measure general end - diastolic volume index ( gedvi ) and ultrasound to measure the degree of variation of the vena cava . global end - diastolic volume index ( gedvi ) , a static volumetric parameter , is considered to be better than cvp or pawp at determining cardiac preload in patients with septic shock . evidence from clinical trials of septic patients confirms that picco measurements can guide capacity treatment and markedly reduce mortality . however , in clinical practice , it is hard to immediately do the measurement of gedvi , which necessitates an expansive picco device and a specific monitor during the early phase of sepsis . moreover , 3 recent high - quality controlled trials reported that invasive hemodynamic monitoring is not associated with better outcome at the early phase of septic shock [ 810 ] . bedside ultrasound is a non - invasive and immediate hemodynamic evaluation , and can identify capacity status just like picco , and it is more convenient for clinicians to use in evaluating response to fluid resuscitation . therefore , we attempted to evaluate inferior vena cava collapsibility index ( ivcci ) as an indicator for capacity . because there are no studies correlating ivcci and picco monitoring index , we monitored the change in ivcci before and after fluid treatment in septic shock patients . use of human data in this observational clinical study was first approved by the local ethics committee of our hospital on 23 september 2013 . all of the patients provided informed consent . in total , 45 patients were admitted to the intensive care unit with septic shock between october 2013 and march 2014 according to the following definition : ( a ) evidence of clinical infection ; ( b ) presence of systemic inflammatory response syndrome ; ( c ) systolic blood pressure lower than 90 mm hg or decreased more than 40 mm hg from the original values for at least 1 h , or depending on vasopressor infusion to maintain blood pressure ; ( d ) tissue hypoperfusion phenomenon , such as decreased urine output ( < 30 ml / h ) for more than 1 h. all the patients were enrolled with an onset of sepsis syndrome 24 h. three patients were excluded from analysis for not meeting study criteria . exclusion criteria were : combination of portal hypertension and severe peripheral vascular disease ; cardiac disease , including valvular heart disease and arrhythmia ; and respiratory disease , including ards , pneumothorax , and copd . obese or postoperative patients were also excluded because of the difficulty in measuring inferior vena cava diameter . the general data of 42 patients are included in table 1 . a central venous catheter ( arrow , asheboro , nc , usa ) was inserted in the subclavian vein , and was confirmed to be placed in the superior vena cava by bedside echo exam for analysis . the zero point was corrected and the cvp read . the picco catheter ( 4f , pulsion , feldkirchen , germany ) after the monitor was ready , mean arterial pressure ( map ) , ci , gedvi , and itbvi were recorded . during measurement , 20 ml of saline in 4c was injected quickly ( within 5 s ) , measuring at least 3 times in a row , and using measurements whose variation was less than 15% . a sonosite m - turbo ultrasound machine with a 3.5-mhz frequency probe was used to detect ivc diameter . the probe was placed in the subxiphoid location when the patient was supine . to standardize measurements , the ivc was measured 2 cm caudal to the junction point of the hepatic vein and ivc , choosing the 2-d mode every 10 s ( and including 23 respiratory cycles ) . the inspiratory ( ivci ) and respiratory ( ivce ) diameters of the ivc were detected by measuring the vein lumen at 1 respiratory cycle , from 1 interior wall to the opposite interior wall ( figure 1 ) . the ivcci ( ivcci=[(ivce ivci)/ivce]100% ) was calculated as the ivc provided respiratory variation . hr , map , cvp , ci , gedwi , itbvi , ivce , and ivcd were monitored as baseline parameters . during volume expansion with 500 ml of 6% hydroxyethyl starch ( he s , 130/0.4 ) over 30 min , ventilator setting and dosages of inotropic and vasopressor drugs were held constant . after intravenous fluid patients were divided into 2 groups depending on change in ci after volume expansion , including the positive response group ( prg , whose ci increased 15% or more compared with baseline ) and the negative response group ( nrg , whose ci increased less than 15% compared with baseline ) . we assumed that a 15% change in ci was needed for clinical significance according to previous studies [ 1113 ] . therefore , patients with a ci increase induced by > 15% and < 15% were classified as responders and non - responders , respectively . the paired t - test was used to compare variables that gave a normal pre - treatment and post - treatment distribution in the patient group , whereas an independent t - test was used to compare variables that gave a normal distribution between prg and nrg . the relationship between variables a receiver operating characteristic ( roc ) curve was plotted to determine the threshold values of ivcci , which provided the prediction of the response to volume expansion with the best sensitivity and specificity . use of human data in this observational clinical study was first approved by the local ethics committee of our hospital on 23 september 2013 . all of the patients provided informed consent . in total , 45 patients were admitted to the intensive care unit with septic shock between october 2013 and march 2014 according to the following definition : ( a ) evidence of clinical infection ; ( b ) presence of systemic inflammatory response syndrome ; ( c ) systolic blood pressure lower than 90 mm hg or decreased more than 40 mm hg from the original values for at least 1 h , or depending on vasopressor infusion to maintain blood pressure ; ( d ) tissue hypoperfusion phenomenon , such as decreased urine output ( < 30 ml / h ) for more than 1 h. all the patients were enrolled with an onset of sepsis syndrome 24 h. three patients were excluded from analysis for not meeting study criteria . exclusion criteria were : combination of portal hypertension and severe peripheral vascular disease ; cardiac disease , including valvular heart disease and arrhythmia ; and respiratory disease , including ards , pneumothorax , and copd . obese or postoperative patients were also excluded because of the difficulty in measuring inferior vena cava diameter . a central venous catheter ( arrow , asheboro , nc , usa ) was inserted in the subclavian vein , and was confirmed to be placed in the superior vena cava by bedside echo exam for analysis . the zero point was corrected and the cvp read . the picco catheter ( 4f , pulsion , feldkirchen , germany ) was placed via the femoral artery prior to connecting the monitor . after the monitor was ready , mean arterial pressure ( map ) , ci , gedvi , and itbvi were recorded . during measurement , 20 ml of saline in 4c was injected quickly ( within 5 s ) , measuring at least 3 times in a row , and using measurements whose variation was less than 15% . a sonosite m - turbo ultrasound machine with a 3.5-mhz frequency probe was used to detect ivc diameter . the probe was placed in the subxiphoid location when the patient was supine . to standardize measurements , the ivc was measured 2 cm caudal to the junction point of the hepatic vein and ivc , choosing the 2-d mode every 10 s ( and including 23 respiratory cycles ) . the inspiratory ( ivci ) and respiratory ( ivce ) diameters of the ivc were detected by measuring the vein lumen at 1 respiratory cycle , from 1 interior wall to the opposite interior wall ( figure 1 ) . the ivcci ( ivcci=[(ivce ivci)/ivce]100% ) was calculated as the ivc provided respiratory variation . before the start of treatment , hr , map , cvp , ci , gedwi , itbvi , ivce , and ivcd were monitored as baseline parameters . during volume expansion with 500 ml of 6% hydroxyethyl starch ( he s , 130/0.4 ) over 30 min , ventilator setting and dosages of inotropic and vasopressor drugs were held constant . after intravenous fluid patients were divided into 2 groups depending on change in ci after volume expansion , including the positive response group ( prg , whose ci increased 15% or more compared with baseline ) and the negative response group ( nrg , whose ci increased less than 15% compared with baseline ) . we assumed that a 15% change in ci was needed for clinical significance according to previous studies [ 1113 ] . therefore , patients with a ci increase induced by > 15% and < 15% were classified as responders and non - responders , respectively . the paired t - test was used to compare variables that gave a normal pre - treatment and post - treatment distribution in the patient group , whereas an independent t - test was used to compare variables that gave a normal distribution between prg and nrg . a receiver operating characteristic ( roc ) curve was plotted to determine the threshold values of ivcci , which provided the prediction of the response to volume expansion with the best sensitivity and specificity . hr increased after treatment in the prg group , whereas map was higher in the nrg group . other measurements ( cvp , ci , gedvi , and itbvi ) improved in both groups , while only ivcci decreased ( table 2 ) . further analysis showed that ivcci was negatively correlated with cvp , ci , and gedvi in the 2 groups . the correlation coefficient of gedvi was stronger than the correlation coefficient of cvp and ci in the prg and nrg groups , respectively ( table 3 ) . therefore , we concluded that gedvi had the strongest negative correlation with ivcci in both groups . as gedvi had the strongest correlation with ivcci , we further assessed the exact relationship between gedvi and ivcci in the prg group . the roc curve demonstrated that ivcci had the best area under the curve ( auc ) , with 100% sensitivity and 100% specificity for a cut - off value of 0.129 to detect a gedvi below 600 ml / m ( figure 2 , table 4 ) . to further evaluate the clinical usefulness of ivcci in predicting volume expansion , we examined the change of ivcci relationships in 7 patients in whom serial measurements of ivcci and gedvi were obtainable . figure 3 shows that the initial gedvi of all 7 patients was < 600 ml / m with a corresponding ivcci higher than 12.9% . importantly , 2 patients whose gedvi increased to 600 ml / m in the second measurements had concomitant decreases in ivcci to < 12.9% . these data further support the validity of ivcci for predicting elevated gedvi in sepsis patients . hr increased after treatment in the prg group , whereas map was higher in the nrg group . other measurements ( cvp , ci , gedvi , and itbvi ) improved in both groups , while only ivcci decreased ( table 2 ) . further analysis showed that ivcci was negatively correlated with cvp , ci , and gedvi in the 2 groups . the correlation coefficient of gedvi was stronger than the correlation coefficient of cvp and ci in the prg and nrg groups , respectively ( table 3 ) . therefore , we concluded that gedvi had the strongest negative correlation with ivcci in both groups . as gedvi had the strongest correlation with ivcci , we further assessed the exact relationship between gedvi and ivcci in the prg group . the roc curve demonstrated that ivcci had the best area under the curve ( auc ) , with 100% sensitivity and 100% specificity for a cut - off value of 0.129 to detect a gedvi below 600 ml / m ( figure 2 , table 4 ) . to further evaluate the clinical usefulness of ivcci in predicting volume expansion , we examined the change of ivcci relationships in 7 patients in whom serial measurements of ivcci and gedvi were obtainable . figure 3 shows that the initial gedvi of all 7 patients was < 600 ml / m with a corresponding ivcci higher than 12.9% . importantly , 2 patients whose gedvi increased to 600 ml / m in the second measurements had concomitant decreases in ivcci to < 12.9% . these data further support the validity of ivcci for predicting elevated gedvi in sepsis patients . cardiac preload refers to the initial length of myocardial fibers when the heart begins to shrink . moreover , gedvi is not based on pressure , which may be influenced by many factors in volume expansion . however , picco monitoring requires placement of a central venous catheter and a set of transducers , which is often difficult in urgent resuscitation , or impossible if the clinician is inexperienced . it also increases risk of complications , which makes it unsuitable for routine use during the care of septic shock patients . therefore , bedside ultrasound is an alternative approach to estimate intravascular status and the need for fluid resuscitation . the ivc is a highly collapsible major vein whose diameter is altered by respiration , blood volume , and right heart function . therefore , it reflects volume status and acts as a reservoir . the quality of the ivc evaluation does not depend greatly on operator experience . it has already been shown that a 4-h course on ultrasound analysis of the inferior vena cava ( 20 clinical cases ) can significantly improve clinical diagnosis of vascular overload by internal medicine residents . therefore , bedside ultrasound of the ivc is a valuable , noninvasive , and rapid hemodynamic monitoring tool for use in the intensive care unit . our data show that both gedvi and ivc distensibility index , termed ivcci , were good predictors of low volume expansion . the results of our pilot study suggest that an elevated ivcci ( greater than 12.9% ) may represent a new index to detect decreased gedvi , with a sensitivity of 100% and specificity of 100% in ill septic patients . specifically , the increase in gedvi during volume expansion is proportional to the measured value of ivcci . therefore , a qualitative assessment of ivcci in our study should be able to detect most patients with an ivcci of greater than 0.129 and an increase in cardiac output of more than 15% during a fluid challenge test . even after volume expansion therapy , the gedvi of the 4 patients with an ivcci of greater than 0.129 was lower than 600 ml / m . therefore , the ivcci can also serve as an index to ensure lower gedvi levels , which can be easily integrated into an overall hemodynamic assessment , as mentioned previously . future studies with a larger sample size are warranted to test this hypothesis . first , ivc diameter varies widely and moves relative to the ultrasound transducer secondary to respiratory activity . moreover , movement off the midline of the ivc results in an artificial decrease in measured diameter along the long axis . second , we only enrolled 42 patients in this study and the range of subjects was narrower than expected . diseases ( e.g. , right heart disease , portal hypertension , and obstructive lung disease ) that effect ivc diameter prevent use of this technique and limit the results of our study . therefore , it is better to perform serial measurements to evaluate volume status more precisely , and to investigate its effect on outcomes . although the present study yielded some interesting results , there are also a few limitations . actually , the same findings may be also result from hypovolemic shock . the present study is only a preliminary investigation of the role of inferior vena cava collapsibility in septic shock . in our next study , we plan explore the role of inferior vena cava collapsibility in both septic shock and hypovolemic shock . an ivc distensibility index above 12.9% is a good argument in favor of volume expansion in circulatory failure during severe sepsis . ultrasonographically - derived ivcci is potentially useful for the management of circulation in septic shock patients .

backgroundthis study aimed to investigate the relationship between the inferior vena cava respirophasic variation ( ivc collapsibility index [ ivcci ] ) and the general heart end - diastolic volume index ( gedvi ) . by determining the above relationship , we could evaluate the utility of ivcci as an indicator.material/methodsforty-two septic patients were finally enrolled in this study . the inferior vena cava s diameter was measured with the largest at the end of expiration ( ivc3 ) and with the smallest at the end of inspiration ( ivci ) on the ultrasound ( ivcci=[(ivcd e ivcd i)/ivcd e ] 100% ) . the central venous pressure ( cvp ) , cardiac index ( ci ) , and gedvi were also measured at least 3 times . after fluid resuscitation therapy , the patients with a ci increase induced by more than 15% and less than 15% were classified as the positive response group ( prg ) and the negative response group ( nrg ) , respectively.resultsafter treatment , the average levels of cvp , ci , and gedvi were significantly higher ( p<0.01 ) in both groups , whereas the ivcci was reduced . cvp , ci , and gedvi were negatively correlated with ivcci in both groups . the correlation coefficient between ivcci and gedvi was the greatest ( correlation coefficient in the prg group was 0.889 and in the nrg group it was 0.672 ) . the roc curve analysis indicated that ivcci illustrated the best area under the curve , with a sensitivity of 100% and specificity of 100% , and a cut - off value of 12.9% to predict gedvi < 600 ml / m2 in the prg group.conclusionsivcci was a good predictor of low - volume state . the ivcci appears to be a valuable and non - invasive index for the estimation of elevated gedvi during fluid resuscitation in septic shock patients .

Background Material and Methods Demographicdata Administration of PiCCO Bedside ultrasound Volume expansion Statistical analysis Results GEDVI had the strongest negative correlation with IVCCI after fluid resuscitation in both the NRG and PRG groups The initial IVCCI, which was higher than 12.9%, acted as a cut-off value to discriminate a GEDCI below 600 mL/m Discussion Conclusions

pollens are important allergens which trigger symptoms in patients with allergic diseases such as allergic rhinitis ( ar ) and asthma . pollens during pollination period generally trigger asthma . at the time of seasonal peaks , large number of pollen grains are liberated from the trees and remain suspended in the air . in various studies , it was observed that number of patients attending hospital increases with higher pollen count in that period . therefore , knowledge about pollen season of the area may prove an important tool for a doctor treating asthmatic patients . pollen count varies at different places and is affected by the topographical factors , local vegetation of the area , and meteorological factors . pollen calendar is a useful tool in the diagnosis and management of allergic disorders . during pollination season , sensitive subjects develop symptoms of the disease , therefore , chances of getting new patients increases . however , we could not find significant indian data relating pollen counts with clinical symptoms except a jaipur study carried out in 19571958 . therefore , we conducted this study to characterize main types of pollens in jaipur and to find a correlation with the hospital visit of new patients of asthma and ar . the study was carried out at asthma bhawan , located in the western part of jaipur . new patients of ar and asthma who were residents of jaipur were included in the study . skin prick tests ( spts ) were performed using allergen extracts , saline as negative control and histamine as positive control . it was considered positive when wheal diameter was more than 3 mm of size , or it was with pseudopodia formation . pollen sampling was carried out from january 1 , 2011 , to december 31 , 2012 . the aerobiological samples of pollens were collected through burkard 24 h spore trap system , which is a type of suction sampler . although sampling collected at multiple places is desirable yet pollen sampling carried at one place is also shown be representative of 30 km radius area . the method of pollen collection , preparation of slide and analysis of sample had been described . the counts represent number of pollens per cubic meter of air in 24 h. traditionally different species of poaceae and cheno - amaranthaceae family are not described separately . however , we were able to differentiate some of the species from the poaceae family . these include cynodon , hordeum vulgare , pennisetum glaucum , saccharum munja , sorghum vulgare , triticum aestivum , and zea mays . similarly , the identifiable pollens of cheno - amaranthaceae family were amaranthus spinosus , spinacia oleracea , and chenopodium album . most of the pollens of chenopodiaceae and amaranthaceae family which could not be differentiated were grouped under the heading of cheno - amaranthaceae . the total number of new patients attending the hospital during 12 months was averaged for 2 years . pollen counts of various species were also used in making the pollen calendar of the jaipur . an average monthly pollen count of trees , weeds , and grasses were correlated with an average number of new patients during that month . correlation of the spt with the pollen counts of both years was also done using pearson correlation coefficient . an average monthly pollen count of trees , weeds , and grasses were correlated with an average number of new patients during that month . correlation of the spt with the pollen counts of both years was also done using pearson correlation coefficient . during 2011 and 2012 , the average number of new patients of asthma and ar per year attending asthma bhawan outpatient department was 1692.5 . during these years the numbers of pollen trapped were 13,738 and 15,183 respectively with yearly average of 14,460.5 pollens [ table 1 ] . analysis of pollen data of 2 years showed 37 types of pollen species or families . since many of these pollens were identified only after this study therefore during this period , spt tests were carried out for only 17 pollens as identified in the earlier study . average pollen counts and number of new outpatient department patients during 12 months and their correlation two seasonal peaks of pollen count were observed . the first peak was mainly due to trees pollens while the second peak was due to weeds and grasses pollens . major part of the first peak was in march , and it had holoptelea ( 65% ) as the major contributor . while major part of the second peak was contributed by grasses family . in the second season , september had the highest number , and the grasses ( 38% ) contributed the most . the main contributors of the total pollen counts for 2 years were poaceace family ( 42% ) and cheno - amaranthaceae family ( 30% ) . during january and cheno - amaranthaceae , poaceace , and holoptelea integrifolia are the highest pollen generating plant family / species [ table 2 ] . top ten pollen generating plant families / species during 2 years in this study , 37 types of pollen species / families were identified in the 2 years duration . out of these 25 species / families were having a limited period of pollination in the year and 12 species / families had their pollens in the aerobiology of jaipur throughout the year . pollen calendar was prepared based on the presence of different pollens in specific part of the year [ figure 1 ] . pollen calendar of the pollens in jaipur when average monthly pollen counts were correlated with the number of new patients during that period , a positive correlation was found with grass pollens . the correlation of the individual pollen with the spt of patients gave the correlation in only one of the species that is c. album , a weed . pollen count peaks were observed during march to april and august to october in both years . many studies have demonstrated that peak pollen counts were associated with higher number of hospital visits by new asthmatic or ar patients . in our study also a significant positive correlation was demonstrated between number of monthly new asthmatic and ar patients and grass pollen count . however , correlation was not significant with weeds and trees . although in the study done in kuwait , the number of new patients of ar were significantly correlated with weeds but not to grass and trees . in yet another study , episodes of asthma exacerbations in children were significantly correlated with pollen counts . the cause and effect relationship was further established in a study wherein a cohort of asthmatic patients exacerbations were monitored at monthly interval , and these were significantly correlated with the pollen counts in the environment . similarly , an earlier study done in jaipur in 19571958 showed that the number of respiratory allergy patients in allergy clinic were proportional to the fluctuation in the pollen count . all these evidence suggest strong association between the presence of respiratory symptoms and presence of pollens in the environment . it emphasizes the need of proper knowledge of pulmonologists about the environmental pollens and vegetations of the area . a proper pollen calendar may prove a useful tool for clinicians involved in the treatment of patients with respiratory allergy . we could not compare data of absolute number of pollen counts of our study with that of earlier study because of variation in the methodology . however , the proportion of various types of vegetation can be compared which showed interesting differences . have published that in jaipur tree pollens were 50% while grass pollens were only 14% . in the present study , tree pollens constituted only 17% while proportion of grass is much higher ( 42% ) [ figure 2 ] . probably urbanization has replaced trees by concrete jungles thereby causing reduced pollen counts . in our study , grass pollens were present throughout the year and peak was present during postmonsoon period . in earlier jaipur study grass pollens were limited only during postmonsoon period . probably with urbanization in jaipur during last seven decades density of trees proportion of pollens of trees , weeds and grasses during 19571958 and 20112012 in jaipur a similar study was conducted in delhi from september 1990 to august 1997 . during the 7-year period , this was attributed to the large clearance of vegetation from the city . in their study studies done in different parts of india showed that there is wide variation in number of pollens and most frequent pollen . in gwalior , pollen grains mainly belonged to families of poaceae and amaranth - chenopodiacae similar to our study , while in lucknow , grasses and holoptelea were main pollens . in the majority of places , two peaks of pollen seasons were observed but in north kashmir peak pollen counts were observed during march september period . number of new patients of asthma and ar attending hospital were significantly correlated with grass pollen counts . knowledge of pollen calendar may prove useful in the evaluation of patients with seasonal exacerbation of symptoms of respiratory allergy .

aims and objectives : environmental pollens are known to cause exacerbation of symptoms of patients with allergic rhinitis ( ar ) and asthma . during pollen months , number of patients visiting hospital has been shown to increase in some studies . however , in india , such studies are lacking . therefore , we aimed to study pollen counts and to find its correlation with number of new patients attending asthma bhawan for 2 years.materials and methods : aerobiological sampling was done using burkard 24 h spore trap system . the site selected for the entrapment of the air spore was the building of asthma bhawan situated at vidhyadhar nagar , jaipur . new patients coming with problems of respiratory allergy such as ar or asthma were recruited in the study . skin prick tests ( spts ) were carried out after obtaining consent in these patients . monthly pollen counts of trees , weeds and grasses were correlated with the number of new patients . pollen calendar was prepared for 2 years.results:average annual pollen count during 2011 and 2012 were 14,460.5 . in the analysis , 37 types of species or families were identified . pollen count showed two seasonal peaks during march april and from august to october . january and june showed the lowest pollen counts in 2 years . average monthly count of grass pollens showed significant correlation with number of new patients ( r = 0.59 ) . however , monthly pollen count of trees and weeds did not correlate . the correlation of the pollen count of individual pollen with the spt positivity to that pollen showed significant correlation with chenopodium album only.conclusions:it can be concluded that there were two peaks of pollen count in a year during march april and august october . average monthly pollen counts of grass were significantly correlated with the number of hospital visits of new patients .

INTRODUCTION MATERIALS AND METHODS Statistical analysis RESULTS DISCUSSION CONCLUSIONS Financial support and sponsorship Conflicts of interest

mantle cell lymphoma ( mcl ) is a b - cell malignant lymphoid tumor which is defined as a separate entity and included in lymphoma classification by world health organization ( who ) . mcl includes small - medium sized lymphoid cells and accounts for 610% of all b - cell lymphomas . mcl patients are predominantly older males and usually present as stage iv ( ann arbor ) disease . the prognosis of mcl is reported to be poor with a mean survival of 3 years . in most of the cases however , extra - nodal sites of involvement such as oral cavity , gastrointestinal tract , waldeyer 's ring , peripheral blood are well documented . palatal mcl is mostly seen in elderly people and may be masked with the presence of prosthesis . in this study , a case of palatal mcl is presented with treatment outcome and a literature analysis was performed to analyze the importance of dental examination in the primary diagnosis of the disease . a 71-year - old male patient was referred to eskiehir osmangazi university , faculty of dentistry , department of oral and maxillofacial surgery with a complaint of ill - fitting dentures . an intra - oral examination was performed and symmetric mucosal enlargements were observed on hard palate [ figure 1 ] . patient was uncomfortable about the mobility of his dentures and had tried to fix them by sticking dish rags or other foreign materials into the prosthesis . therefore , a provisional diagnosis of reactive mucosal lesion was made and incisional biopsy was performed under local anesthesia . ulcerated palatal symmetric mucosal swelling responsible for the mobility of maxillary dentures microscopic examination revealed diffuse abundant small cells with hyperchromatic nuclei in the subepithelial region [ figure 2 ] . glandular structures can be seen at the upper - right quadrant ( h&e stain , 100 ) nuclei of small cells have distinct hyperchromatism . mild nuclear pleomorphism is also evident ( h&e stain , 400 ) after the immunohistochemistry , tumoral cells showed strong positive staining with cd20 ( l26 , ventana , tucson ) [ figure 4 ] , pax-5 ( sp34 , ventana , tucson ) , cd5 ( sp19 , ventana , tucson ) , cyclin d1 ( sp4-r , ventana , tucson ) [ figure 5 ] , bcl-2 ( 124 , ventana , tucson ) and igm ( poliklnal , ventana , tucson ) . cd21 ( sp104 , ventana , tucson ) and cd23 ( sp23 , ventana , tucson ) immunostaining showed follicular dendritic cells . cd10 ( sp67 , ventana , tucson ) and igd ( policlonal , ventana , tucson ) were negative . patient was referred to hematology department of eskiehir osmangazi university , faculty of medicine for further evaluation and treatment . tumoral cells stained diffusely positive with cd20 ( ihc stain , 200 ) tumoral cells showed nuclear positivity with cyclin d1 staining ( ihc stain , 200 ) ultrasonography of abdomen revealed multiple lymphoadenopathies at mesenteric and para - aortic regions . after informed consent was taken , patient underwent cyclophosphamide , oncovin , prednol ( cop ) chemotherapy regimen . english dental and medical literature search was conducted using the combination of terms such as hard palate , mcl , lymphoma and extra - nodal lymphoma in pubmed . cases which were reported under the strict diagnosis of mcl and primarily located on the hard palate were extracted and data regarding treatment , follow - up and demographics was reviewed . nine publications with 14 cases defining primary hard palate mcls published between 1990 and 2014 were identified . mcl is a counterpart of non - hodgkin lymphoma family and was first included in lymphoma classification in 2001 . although mcl is mainly located in the lymph nodes , involvement of extra - nodal sites such as waldeyer 's ring , peripheral blood , bone marrow and gastrointestinal tract are also reported . definite diagnosis of mcl is achieved with immunohistochemical staining with or without the assistance of molecular techniques . mcl tumoral cells commonly express cd20 , cd5 , cd43 antigens and bcl2 and cyclin d1 protein . however , they are cd10 and bcl6 negative and show negativity / weak positivity for cd23 antigen expression . histologic examination reveals abundant monomorphic small - medium sized lymphoid cells with slightly / markedly irregular nuclear contours . blastoid and pleomorphic subtypes of mcl have been defined by who and it is suggested that blastoid or pleomorphic morphology are aggressive variants ; similar histology may be seen in some cases at relapse . hard palate is an unusual site for primary mcl and this has been reported in the english literature several times . reported that long term use of maxillary prosthesis might have provoked the lymphoid tissue accumulation and proliferation leading to a mass of mcl in the submucosal region of the hard palate . guggisberg and jordan reported that most oral mcls occur in an elderly male population and have a predilection for the palate . the duration of the prosthesis usage of mcl patients could not be analyzed in the current literature review due to the unavailable data in the case reports . in the current case , patient was using total prosthesis for 10 years and the only complaint of the patient was the mobility of his dentures . the clinical appearance of the tumor suggested that the palatal accumulation of lymphoid mass might have been initiated by the long term use of the total prosthesis . milgrom and yahalom reported nine cases of primary indolent lymphomas of the hard palate including mcl , follicular lymphoma and marginal zone lymphoma . there were two cases of mcl in their series and it is suggested that mcl cases showed more aggressive behavior compared to other lymphomas of the hard palate . ( chop ; cyclophosphamide , doxorubicin , vincristine , prednisolone ) chang et al . reported a polychemotherapy regimen consisting of cytoxan , doxorubicin , vincristine and prednisone , in conjunction with meusers et al . reported that the chop regimen did not show superiority to cop regimen in the treatment of mcl . although chop - like antracycline containing chemotherapeutic combinations do not have distinct advantage on survival , they are currently chosen for standard therapuetic approach . radiation therapy is still a therapeutic option in low - stage disease ( ann - arbor stage 1,2 ) in advance stage disease , the combination of radiotherapy and chemotherapy can be used , however , the efficacy of this combination have not been proven yet . primary mcl of the hard palate is a rare entity which is mostly seen in elder people . in this study , a case of palatal primary mcl which presents with ill - fitting total prosthesis is reported with clinical and histopathological features . dental total prosthesis may mask the existing lesion on the hard palate , therefore , dental practitioner should be alert at the time of the clinical examination of patients with total or partial prosthesis .

mantle cell lymphoma ( mcl ) is a subtype of b - cell non - hodgkin 's lymphoma seen predominantly in males . common extra - nodal sites of involvement of mcl are waldeyer 's ring , gastrointestinal tract , bone marrow and peripheral blood . the extra - nodal palatal localization of mcl is quite uncommon . mcl is seen in predominantly older patients , therefore undiagnosed mcl patients are likely to have total prosthesis . in this study , a case of mcl , initially presenting as palatal swelling was reported with relevant literature review and the possible role of dental professionals in the diagnosis of this rare entity was discussed .

INTRODUCTION CASE REPORT MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSION Financial support and sponsorship Conflicts of interest

the international continence society defines nocturia as the need to void one or more times during the night , with each of the voids preceded and followed by sleep . nocturia has the following two main causes : increased nocturnal urine volume and vesical instability.1 as one of the most common complaints in patients with lower urinary tract symptoms ( luts ) , nocturia is reported to negatively affect the quality of life and quality of sleep.2,3 since its prevalence and severity increase with age,4 the negative effect of nocturia on the elderly requires more attention . jensen et al5 reported that 25% of falls experienced by older individuals occur during the night and 25% of these occur when the individual is waking up to void . studies have shown a significant association between nocturia and sleep quality , but most of these investigations were among the general elderly population.68 obayashi et al used objective actigraphy and subjective questionnaires to quantitatively evaluate the association between nocturnal voiding frequency and sleep quality in the general elderly population.9,10 considerable number of patients with benign prostate hyperplasia , bladder outlet obstruction , overactive bladder , or other diseases that affect urinary function may suffer from nocturia , and there are some reports focusing on nocturia and sleep.6,11,12 however , studies on the quantitative effect of nocturia on both sleep quality and daytime function , specifically in adult patients with luts , are sparse . in this cross - sectional study of 728 individuals with luts , we used three survey tools to evaluate the effect of nocturia on sleep quality and daytime sleepiness . our study is a cross - sectional and questionnaire - based survey conducted among patients with luts and nocturia . inclusion criteria were as follows : patients who visited our urologic department from march 1 , 2015 to december 31 , 2015 due to luts and experienced nocturia at least once per night were enrolled in this study . exclusion criteria were as follows : patients with a history of drug treatment for luts and those with concomitant urinary tract infection or urolithiasis were excluded . we conducted our face - to - face survey based on three internationally validated , reliable , and widely used questionnaires , namely pittsburgh sleep quality index ( psqi ) questionnaire,10,13 epworth sleepiness scale ( ess ) questionnaire,14,15 and international prostate symptom score ( ipss ) questionnaire . after obtaining their written informed consents , the patients were asked to complete the questionnaires at their first visit before medications for luts were prescribed , with the assistance of trained research assistants . the psqi questionnaire was used to evaluate sleep quality and disturbance over the past month . the first four items are open questions , and 519 items are rated on a four - point scale . the item scores yield the following seven subscores ranging from 0 to 3 : sleep quality , sleep latency , sleep duration , sleep efficiency , sleep disturbance , sleep medication use , and daytime dysfunction due to sleepiness . the total scores ranging from 0 to 21 were obtained by summing up the seven subscores . most studies have consistently stated that a total psqi score of 5 suggests a good sleep quality , whereas a total psqi score of > 5 suggests a poor sleep quality.10,13,16,17 the ess questionnaire consists of eight questions that are rated on a four - point scale ranging from 0 to 3 . a total score between 0 and 24 is used to evaluate our participants general level of daytime sleepiness or the average sleep propensity over the past month . an ess score of > 8 suggests significant sleepiness.14,16,17 we used the ipss questionnaire to evaluate their voiding dysfunction . it contains the seven - item american urological association ( aua ) symptom index and one question on the quality of life , which is used to evaluate male luts , such as benign prostate hyperplasia - related voiding problem . the seven - item aua symptom index , developed and psychometrically validated by an aua measurement committee in 1992 , reliably assesses the severity of luts and is responsive to changes in treatment.18 the world health organization in 1993 adopted the eight - item ipss , which uses the same seven questions assessing luts severity as the aua symptom index and an eighth disease - specific quality of life question that assesses the pain associated with luts . it has also been proven reliable for the evaluation of female patients with lower urinary tract dysfunction.19 the seven questions are divided into the following two parts : ipss voiding scores and ipss storage scores.20 the ipss voiding scores consist of weak stream , intermittency , straining , and feeling of incomplete bladder emptying , whereas the ipss storage scores consist of frequency , urgency , and nocturia . the eighth question on voiding - related quality of life is assigned a score of 06 . nocturia number was defined as the number of voids during the time from going to bed at night to waking up next morning , excluding the last void before bedtime and the first void after waking up in the morning . patients basic characteristics , including age , sex , height , weight , and body mass index , were collected from their medical charts . the statistical analyses were performed on a personal computer using the statistical package spss for windows ( version 17.0 , spss inc . we used generalized linear model to perform multivariate analysis between several parameters versus psqi and ess scores . we used the independent samples t - test to compare the differences of age , nocturia number , ess score , psqi score , and ipss score between subgroups dividing by sex and age ( < 65 and 65 years ) . the associations between nocturia number and sleep quality ( psqi scores c1c7 and total score ) and daytime dysfunction ( ess score ) were analyzed by pearson s correlation test . the analysis was performed not only for the overall patient group but also for the patients divided into subgroups according to age ( older than and younger than 65 years ) and sex ( male and female ) . our study is a cross - sectional and questionnaire - based survey conducted among patients with luts and nocturia . inclusion criteria were as follows : patients who visited our urologic department from march 1 , 2015 to december 31 , 2015 due to luts and experienced nocturia at least once per night were enrolled in this study . exclusion criteria were as follows : patients with a history of drug treatment for luts and those with concomitant urinary tract infection or urolithiasis were excluded . we conducted our face - to - face survey based on three internationally validated , reliable , and widely used questionnaires , namely pittsburgh sleep quality index ( psqi ) questionnaire,10,13 epworth sleepiness scale ( ess ) questionnaire,14,15 and international prostate symptom score ( ipss ) questionnaire . after obtaining their written informed consents , the patients were asked to complete the questionnaires at their first visit before medications for luts were prescribed , with the assistance of trained research assistants . the psqi questionnaire was used to evaluate sleep quality and disturbance over the past month . the first four items are open questions , and 519 items are rated on a four - point scale . the item scores yield the following seven subscores ranging from 0 to 3 : sleep quality , sleep latency , sleep duration , sleep efficiency , sleep disturbance , sleep medication use , and daytime dysfunction due to sleepiness . the total scores ranging from 0 to 21 were obtained by summing up the seven subscores . most studies have consistently stated that a total psqi score of 5 suggests a good sleep quality , whereas a total psqi score of > 5 suggests a poor sleep quality.10,13,16,17 the ess questionnaire consists of eight questions that are rated on a four - point scale ranging from 0 to 3 . a total score between 0 and 24 is used to evaluate our participants general level of daytime sleepiness or the average sleep propensity over the past month . an ess score of > 8 suggests significant sleepiness.14,16,17 it contains the seven - item american urological association ( aua ) symptom index and one question on the quality of life , which is used to evaluate male luts , such as benign prostate hyperplasia - related voiding problem . the seven - item aua symptom index , developed and psychometrically validated by an aua measurement committee in 1992 , reliably assesses the severity of luts and is responsive to changes in treatment.18 the world health organization in 1993 adopted the eight - item ipss , which uses the same seven questions assessing luts severity as the aua symptom index and an eighth disease - specific quality of life question that assesses the pain associated with luts . it has also been proven reliable for the evaluation of female patients with lower urinary tract dysfunction.19 the seven questions are divided into the following two parts : ipss voiding scores and ipss storage scores.20 the ipss voiding scores consist of weak stream , intermittency , straining , and feeling of incomplete bladder emptying , whereas the ipss storage scores consist of frequency , urgency , and nocturia . each scoring ranges from 1 to 5 for a total of maximum 35 points . the eighth question on voiding - related quality of life nocturia number was defined as the number of voids during the time from going to bed at night to waking up next morning , excluding the last void before bedtime and the first void after waking up in the morning . patients basic characteristics , including age , sex , height , weight , and body mass index , were collected from their medical charts . the statistical analyses were performed on a personal computer using the statistical package spss for windows ( version 17.0 , spss inc . , we used generalized linear model to perform multivariate analysis between several parameters versus psqi and ess scores . we used the independent samples t - test to compare the differences of age , nocturia number , ess score , psqi score , and ipss score between subgroups dividing by sex and age ( < 65 and 65 years ) . the associations between nocturia number and sleep quality ( psqi scores c1c7 and total score ) and daytime dysfunction ( ess score ) were analyzed by pearson s correlation test . the analysis was performed not only for the overall patient group but also for the patients divided into subgroups according to age ( older than and younger than 65 years ) and sex ( male and female ) . the patients characteristics and detailed subscale scores of ipss , ess , and psqi are presented in table 1 . the mean age of the patients was 61.413.7 years , with a male - to - female ratio of 2.7 . of the 728 patients , 101 ( 13.9% ) patients reported one nocturia episode , 188 ( 25.8% ) patients reported two nocturia episodes , 170 ( 23.4% ) patients reported three nocturia episodes , 124 ( 17.0% ) patients reported four nocturia episodes , and 145 ( 19.9% ) patients reported five or more nocturia episodes . the mean ipss total score , psqi total score , and ess score were 17.568.62 , 8.353.66 , 3.232.48 , and 8.225.07 , respectively . the results revealed that our participants have both poor sleep quality and daytime dysfunction compared to the normal population.10,1316 the result of multivariate analysis using the generalized linear model is disclosed in table 2 . taking the ess total score as a dependent variable , we found that it is positively correlated with psqi score with statistical significance , and the 95% confidence interval does not cover zero . while using the psqi score as a dependent variable , we found that it is positively correlated with nocturia number and ess score with statistical significance , and the 95% confidence interval does not cover zero . , we divided our participants into subgroups ( male and female , < 65 years and 65 years ) . the mean age , nocturia number , ipss storage score , and voiding - related quality of life were similar between different sex groups , whereas a higher psqi total score , a lower ipss voiding score , and a lower ipss total score were found in female group with significant difference . among subgroups of patients < 65 and 65 years old , patients older than 65 years had significantly worse performance in all parameters , including nocturia number , psqi total and subscores , ipss total and subscores , and voiding - related quality of life , except for ess score . the effects of nocturia number on sleep quality and daytime function , which were analyzed using pearson s correlation test , are revealed in table 4 . in the overall group , the higher nocturia number was significantly correlated with the higher ess score and the higher psqi scores c1c6 and total score but not for score c7 . in subgroups divided by age , nocturia number was still significantly correlated with the higher ess score in patients younger than 65 years , but it had no significant effect on ess score in patients older than 65 years . the severity of nocturia significantly correlated with higher psqi total score in both subgroups . for patients divided by sex , more nocturia number was still significantly correlated with ess score in male patients but not in female patients . in both subgroups , the relationships between nocturia numbers and ess score and psqi score respectively are shown in figure 1 . nocturia is a persistent luts and is often regarded as a natural consequence of aging.21 however , the negative effect of nocturia has been underestimated until recently , not only for its underreported prevalence7,22,23 but also for the resulting physical and psychiatric problems.2,3,24,25 increasing numbers of studies are now describing the negative effect of nocturia on sleep quality , associated diseases , and mortality in the aging population . most of the previous studies have reported an association between nocturia that was categorized using cutoff points but have not quantified its severity.9 in this study , we investigated the correlation of nocturia number with sleep quality and daytime dysfunction in patients with luts . in this study , we also compared the differences of each parameter between males and females and patients older than or younger than 65 years . female patients had similar nocturia number and daytime dysfunction but had significant worse sleep quality than male patients . such a correlation was revealed by multivariate analysis in our study shown in table 2 . the average of psqi total score was 9.80 in female and 7.80 in male patients , which is shown in table 3 . this is consistent with the relatively higher frequency of prescription sleep aids use in the female population,26 and in our data , the psqi c6 scores were 0.69 and 0.43 among females and males , respectively ( psqi c6 score refers to use of sleeping medication : never = 0 ; < 1 per week = 1 ; 12 per week = 2 ; and 3 per week = 3).10 the ipss storage score for females was similar to that for males , but the ipss voiding score was significantly lower for females than for males . the high prevalence of prostatic disorder - related voiding dysfunction in aging males could explain this finding.20 as for age , in patients older than 65 years , all parameters were significantly worse than those in the younger group , except for similar ess scores , which were compatible with some published study results.79 in multivariate analysis , psqi score was positively correlated with age , but the ess score was not . nocturia has been recognized as a potential risk for sleep disturbance.27 our study also found that the severity of nocturia increased significantly with age in patients with luts . , score c7 ( daytime dysfunction ) is not correlated with higher nocturia number ( table 4 ) , which is not compatible with other published studies.28 this inconsistency with ess score could be explained by the fact that the score c7 ranges from 0 to 3 while the ess score ranges from 0 to 24 . we suggested that ess score is a more definite and detailed evaluation for daytime dysfunction . we found that the negative effect of nocturia on daytime dysfunction ( ess score ) among patients older than 65 years and female patients was not statistically significant . this phenomenon could be explained by the fact that the subjective perception of daytime dysfunction is more obvious and stronger in people with jobs who need higher concentration and focus . most patients older than 65 years were retired from active work , and the impact of nocturia on daytime function is easily overlooked . foley et al28 reported that frequent napping is common among older adults or patients without employment to compensate their sleep disruption . a similar situation exists for the female subgroup of our participants . a considerably high proportion ( 68% ) of our female participants were housewives , for whom working hours are more flexible and who have less need to concentrate for a long time . such result suggested that nocturia plays an important role in patients younger than 65 years in daytime dysfunction , and hence treating nocturia might improve their work performance . clinically , this blunt perception of the effect of nocturia on daytime spirit and dysfunction among aging people might also be one of the causes of nocturia being underestimated or regarded as a natural consequence of getting older and resulting in delays in seeking treatment . we used questionnaires to quantify the negative effect of nocturia not only on sleep quality but also on daytime function among patients with luts . we also evaluated the severity of nocturia , rather than using a binary yes - or - no measure , and found a significant correlation . however , the evaluations of sleep quality and daytime dysfunction were based on subjective perception only . more objective tools , such as actigraphy and polysomnography , may provide more accurate information on actual sleep quality in future studies . the male - to - female ratio was 2.7 , reflecting the fact that our patients were sourced mainly from the urologic department . the relatively small size of the female population may have affected the statistical analysis . in table 4 , pearson s correlation coefficients are not high but still with statistical difference , which might result from the large number of our participants . in order to emphasize on the effect of nocturia numbers , in patients with luts , nocturia number increased with age and was significantly correlated with poor sleep quality . nocturia plays an important role in patients younger than 65 years in daytime dysfunction , which should not be overlooked . with similar nocturia number ,

backgroundnocturia has been proven to have a negative impact on the quality of life and sleep quality in general elderly population . however , there are limited studies on the quantitative effect of nocturia on sleep quality and daytime dysfunction , specifically in patients with lower urinary tract symptoms.patients and methodsduring march 1 , 2015 to december 31 , 2015 , a total of 728 patients who visited our urology department due to voiding dysfunction and experienced nocturia at least once per night were enrolled . three questionnaires were administered to them after obtaining their written consents . pittsburgh sleep quality index ( psqi ) questionnaire , epworth sleepiness scale ( ess ) questionnaire , and international prostate symptom score ( ipss ) questionnaire were applied to evaluate their sleep quality , daytime dysfunction , and voiding problems , respectively . statistical analysis of the impact of nocturia on sleep quality and daytime dysfunction was performed.resultsthe mean age of patients was 61 years , with a male - to - female ratio of 2.7 . the mean nocturia number was 3.03 . the ipss , psqi , and ess scores were 17.56 , 8.35 , and 8.22 , respectively . the nocturia number increased with age and was significantly correlated to ess score ( daytime dysfunction ) and psqi total score ( sleep quality ) in overall group . among subgroups divided by age and sex , there was a significant correlation between nocturia number and daytime dysfunction in male patients or patients younger than 65 years.conclusionin patients with lower urinary tract symptoms , nocturia number increased with age and was significantly correlated with poor sleep quality . nocturia plays an important role in patients younger than 65 years in daytime dysfunction .

Introduction Patients and methods Participants and study protocol Data collection Measuring sleep quality and daytime dysfunction Measuring LUTS Other parameters Statistical analyses Results Discussion Conclusion

in january 2007 , the american college of obstetricians and gynecologists ( acog ) practice bulletin number 77 recommended screening and invasive diagnostic testing should be available to all women who present for prenatal care before 20 weeks of gestation regardless of maternal age . several strategies for screening have been proposed based on the first trimester combined test ( nuchal translucency ( nt ) measurement and biochemical markers ) and second trimester maternal serum quadruple ( quad ) screen . the highest detection rates and lowest screen positive rates have been reported for integrated screening . this includes first trimester nuchal translucency , pregnancy - associated plasma protein a ( papp - a ) and human chorionic gonadotropin ( hcg ) plus maternal serum quad screening in the mid - trimester , with the results provided only after all tests are completed . patient anxiety during the delay between presentation for screening and results make this an unacceptable option for many patients . proposed alternative screening options include stepwise sequential screening and contingent sequential screening based on classifying women as high- or low - risk using a predetermined threshold ( american college of obstetricians and gynecologists acog 2007 ) . stepwise sequential screening is first trimester combined testing plus maternal serum quad screening with results provided after each test . contingent sequential screening is first trimester combined testing with only women having a risk between 1:30 and 1:1,500 for trisomy 21 ( t21 ) proceeding to maternal serum quad screening . prenatal aneuploidy screening results are often reported or framed as positive or negative based on a defined threshold . this is usually the risk of a 35-year old woman having a child with t21 or trisomy 18 ( t18 ) . however , there is little information about the effects of using verbal descriptions of risk versus numerical data . in a survey of 169 british antenatal clinics about the method of communicating down syndrome screen negative results , 44 % used a verbal phrase ( low risk , screen negative , within normal limits , not needing further action , among others ) , 16 % gave a numeric risk figure and 40 % used both a verbal phrase and numeric risk ( marteau 1999 ) . the goals of this study were to examine : 1- the uptake of stepwise sequential screening in our primarily urban , midwestern population , 2- the potential affects of ethnicity , education and proximity to the medical center on willingness to proceed with further testing , and 3- our method of risk reporting , which emphasized a woman s age - risk for t21 and adjusted risk after screening , rather than classifying a result as positive or negative , or high - risk , or low - risk . this is a retrospective cohort study of all patients who completed first trimester nt and biochemical screening at our institution between june 2007 and february 2010 . this study was approved by the washington university human research protection office , which waived informed consent . inclusion criteria included women with singleton gestations who completed combined first trimester screening with nt and the serum markers papp - a and hcg . for the first 3 months of the study period , the laboratory utilized at this institution used total beta - hcg . exclusion criteria included multiple gestations , blood testing not performed or analyzed and inability to obtain a nt measurement . all nt measurements were performed by physicians or sonographers certified in nt measurement by either the fetal medicine foundation or the nuchal translucency quality review ( ntqr ) program . patient s were categorized at the time of their first trimester screening visit into one of three groups as follows : u = undecided as to whether they wished to proceed with stepwise sequential screening ; y = yes , they planned to pursue stepwise sequential screening ; or n = no , they do not plan to have stepwise sequential screening . results of first trimester screening were not reported as positive or negative . the phone call and/or letter informing patients of their first trimester screen results indicated the patient s age - risk for ( t21 ) and trisomy 18 ( t18 ) and their revised risks for same based on the nt and biochemical markers . the determination of whether a patient was of high enough risk to warrant further screening or testing was at the patient s discretion . all phone calls and/or result letters also again reviewed the patient s subsequent options , including no further screening , maternal serum quad screening , mid - trimester ultrasound and invasive testing via chorionic villus sampling ( cvs ) or amniocentesis . the patient s decision about whether to proceed with stepwise sequential screening ( both before and after their first trimester screening results ) were recorded in a computerized database for subsequent correlation with variables including ethnicity , level of education , distance from our medical center , nt measurement , crown rump length , age- and screen - risks for t21 , results of invasive testing and pregnancy outcomes . in order to assess the impact of non - invasive first trimester screening and stepwise sequential screening ( first trimester screening plus maternal serum quad screening ) on the utilization of amniocentesis and cvs , the number of these procedures was compared as follows : for a 2-year period prior to the initiation of first trimester screening ( january 2000december 2001 ) , for a 2-year period when first trimester screening was utilized but prior to the availability of stepwise sequential screening ( june 2005may 2007 ) and for the 2-year period following initiation of stepwise sequential screening ( july 2007june 2009 ) . relationship between decision status ( yes , no , undecided ) and various characteristics were compared using the chi - square test or fisher s exact test , as appropriate . differences in the counts of invasive procedures performed across time periods were evaluated using simple poisson regression models , where time period ( 20002001 , 20052007 , and 20072009 ) was included using indicator variables . the study population consists of 2,643 patients who met inclusion criteria during the study period ( june 2007february 2010 ) . during this time , an acceptable nt measurement was unable to be obtained in 8 patients ( 0.3 % of the initial study population ) . at the time of the first trimester examination , 1,926 ( 72.8 % ) were undecided regarding stepwise sequential screening ( u group ) pending their first trimester results . 434 patients ( 16.4 % ) indicated they planned to return for stepwise sequential screening , regardless of their results ( y group ) and 283 patients ( 10.7 % ) declined stepwise sequential screening at the time of their first trimester screening ( n group ) . the numbers of patients who actually pursued stepwise sequential screening are listed in table 1 . this included a minority of the undecided and no groups ( 14.9 % and 1.4 % , respectively ) and only 56.4 % of those who originally intended to have stepwise sequential screening . overall , 79.8 % of the study population elected not to pursue follow - up screening.table 1stepwise sequential screening following first trimester combined screengroupnno ss screeningfollow - up ss screening p undecided1,926 ( 72.9 % ) 1,639 ( 85.1 % ) 287 ( 14.9 % ) < 0.0001yes434 ( 16.4 % ) 190 ( 43.8 % ) 244 ( 56.2 % ) no283 ( 10.7 % ) 279 ( 98.6 % ) 4 ( 1.4 % ) 2,643 ( 100 % ) 2,108 ( 79.8 % ) 535 ( 20.2 % ) u vs y<0.0001u vs n<0.0001y vs n<0.0001 stepwise sequential screening following first trimester combined screen the relation between education level and choice of screening is presented in table 2 . in the group of women who did not plan to pursue stepwise sequential screening there were a significantly greater number who were not high school graduates and significantly fewer who were college graduates compared to women in the other two groups . table 3 demonstrates that women who declined stepwise sequential screening were more likely to be black and hispanic and less likely to be white , than women in the other groups . table 4 indicates that distance from the medical center did not correlate with the decision to pursue or decline stepwise sequential screening.table 2eduction level and decision to pursue stepwise sequential screeninggroupnsome high schoolhs grad some collegecollege grad post grad p < 0.0001undecided1,92368 ( 3.5 % ) 501 ( 26.1 % ) 1,354 ( 70.4 % ) yes43411 ( 2.5 % ) 115 ( 26.5 % ) 308 ( 71.0 % ) no28222 ( 7.8 % ) 111 ( 39.4 % ) 149 ( 52.8 % ) 2,639101 ( 3.8 % ) 727 ( 27.5 % ) 1,811 ( 68.6 % ) u vs. y0.58u vs. n<0.0001y vs n<0.0001table 3ethnicity and decision to pursue stepwise sequential screeningethnicitygroupnwhiteblackasianhispother p < 0.0001undecided1,9261,395 ( 72.4 % ) 293 ( 15.2 % ) 106 ( 5.5 % ) 49 ( 2.5 % ) 83 ( 4.3 % ) yes434326 ( 75.1 % ) 50 ( 11.5 % ) 18 ( 4.1 % ) 8 ( 1.8 % ) 32 ( 7.4 % ) no283165 ( 58.3 % ) 71 ( 25.1 % ) 10 ( 3.5 % ) 17 ( 6.0 % ) 20 ( 7.1 % ) 2,6431,886 ( 71.4 % ) 414 ( 15.7 % ) 134 ( 5.1 % ) 74 ( 2.8 % ) 135 ( 5.1 % ) u vs. n0.01u vs. n<0.0001y vs. n<0.001table 4distance from medical center and decision to pursue stepwise sequential screeningmiles p groupn0202150>500.14undecided1,9261,293 ( 67.1 % ) 507 ( 26.3 % ) 126 ( 6.5 % ) yes434284 ( 65.4 % ) 114 ( 26.4 % ) 36 ( 8.3 % ) no283170 ( 60.1 % ) 88 ( 31.1 % ) 25 ( 8.8 % ) 2,6431,747 ( 66.1 % ) 709 ( 26.8 % ) 187 ( 7.1 % ) u vs. y0.42u vs. n0.05y vs. n0.32 eduction level and decision to pursue stepwise sequential screening ethnicity and decision to pursue stepwise sequential screening distance from medical center and decision to pursue stepwise sequential screening tables 5 and 6 demonstrate that the percentages of women at risk for t21 were similar between the groups.table 5age risk for t21 and decision to pursue stepwise sequential screeninggroup1:501:511:270>1:270 p*undecided ( n-1,926)44 ( 2.3 % ) 896 ( 46.5 % ) 986 ( 51.2 % ) 0.26yes ( n-434)17 ( 3.9 % ) 204 ( 47.0 % ) 213 ( 49.1 % ) no ( n-283)9 ( 2.6 % ) 140 ( 49.5 % ) 134 ( 47.3 % ) u vs. y0.14u vs. n0.37y vs. n0.75*fishers exact testtable 6screen risk for t21 and decision to pursue stepwise sequential screeninggroup1:501:511:270>1:270 p * 0.63undecided ( n-1,926)26 ( 1.3 % ) 86 ( 4.5 % ) 1,814 ( 94.2 % ) yes ( n-434)7 ( 1.6 % ) 21 ( 4.8 % ) 406 ( 93.5 % ) no ( n-283)7 ( 2.5 % ) 13 ( 4.6 % ) 263 ( 92.9 % ) uvs . y0.79u vs. n0.30yvsn.0.74*fishers exact test age risk for t21 and decision to pursue stepwise sequential screening screen risk for t21 and decision to pursue stepwise sequential screening the number of patients whose first trimester screen - risk for t21 exceeded their age - risk , and their choice of follow - up , is depicted in table 7 . overall , 126 patients ( 4.8 % of the study population ) had a first trimester screen - risk for t21 which was greater than their age - risk . of these , 73(57.9 % ) women elected not to have follow - up stepwise sequential screening or diagnostic testing , 24(19.8 % ) had stepwise sequential screening only and 29(23.0 % ) had invasive testing via cvs ( n = 11 ) or amniocentesis ( n = 18 ) . there was one case of 47 , xy , + 21 and one apparently balanced robertsonian translocation between chromosomes 13 and 14 . women who originally declined stepwise sequential screening were significantly less likely to pursue invasive testing than women in the other two groups.table 7screen risk for t21 greater than age risk and choice of follow - upgroupsr > ar p no further testingss screen onlyinvasive testing p*undecided ( n-1,926)91 ( 4.7 % ) 0.9852 ( 57.9 % ) 15 ( 19.0 % ) 24 ( 26.4 % ) yes ( n-434)21 ( 4.8 % ) 8 ( 38.1 % ) 9 ( 42.9 % ) 4 ( 19.0 % ) no ( n-283)14 ( 4.6 % ) 13 ( 92.9 % ) 01 ( 7.1 % ) 2,643126 ( 4.8 % ) 73 ( 57.9 % ) 24 ( 19.0 % ) 29 ( 23.0 % ) u vs. y0.92u vs. y0.05u vs. n0.87u vs n0.04y vs. n0.99y vs. n0.002*fisher 's exact test screen risk for t21 greater than age risk and choice of follow - up a total of 91(3.4 % of the study population ) women had invasive testing by amniocentesis ( n = 76 ) or cvs ( n = 15 ) during the study period . in 59(64.8 % ) , the age - risk for t21 was greater than the screen - risk . there were three cases of t21 and the aforementioned translocation . in two of the three t21 cases , the maternal age risk was greater than the screen risk ( the age risks were 1:43 and 1:235 versus screen risks of 1:96 and 1:246 , respectively ) . the number of invasive procedures performed prior to the availability of first trimester screening , following initiation of first trimester screening and following the availability of stepwise sequential screening is indicated in table 8 . the indications for invasive testing were varied and included ama , abnormal ultrasound findings , abnormal screening , and family history of aneuploidy . the number of amniocenteses in our center declined by 51.4 % following the availability of first trimester screening with a further 17.4 % reduction upon initiation of stepwise sequential screening . the number of cvs procedures declined by 19.2 % following availability of first trimester screening . there was a significant reduction in the number of cvs procedures from pre - first trimester screening and its utilization . however , there was no significant difference in the number of cvs procedures between availability of first trimester screening and stepwise sequential screening.table 8number of invasive procedures before and after first trimester and stepwise sequential screening availabilityprocedurepre - ftsfts onlyss availp , pre - fts vs fts onlyp , fts only vs. ss availamniocentesis1,632793655 p < 0.0001 p < 0.0001cvs494399371 p < 0.001 p = 0.31 first trimester screening sequential screening number of invasive procedures before and after first trimester and stepwise sequential screening availability first trimester screening sequential screening in our population , only 20 % of women having first trimester screening , elected to pursue stepwise sequential screening with 3.4 % undergoing invasive testing . proximity to the medical center women of lower education level and black or hispanic ancestry were least likely to desire further screening or testing following their first trimester screen results . it is possible this represents lower health literacy in these groups with less of an appreciation or even misinterpretation of the consequences and benefits of stepwise sequential screening . the amount of information to be collected and conveyed at the initial prenatal visit , in addition to decisions regarding aneuploidy screening , can be overwhelming even for relatively medically sophisticated women . perhaps women of lower education and minorities should be offered pre - conception counseling so that they have more time to consider the benefits and risks of genetic screening and testing . it may also be that women in these groups are more conservative in their approach to prenatal screening overall , and consider themselves less likely to act on the basis of a positive result . additionally , it is possible that their perception and tolerance of risk may be different than women in other groups due to differences in their own frame of reference . how results are reported , and its potential impact on how a woman interprets this information was a focus of this work . a woman whose screen - risk of t21 is 1:310 will be considered to have a negative result and may well be reassured even if this is higher than her age - related risk . by the same token , a woman with a screen - risk of 1:260 will have a result reported as positive or elevated risk even if it is a significant reduction compared to her age - related risk . the difference between 0.32 % ( 1:310 ) and 0.38 % ( 1:260 ) is not great but the implications for a woman s attitude , anxiety and subsequent plans for screening and testing may be significant . for many patients , interpretation of risk the manner in which risk information is presented or framed assumes special importance when it involves communication of genetic testing results . negative framing , in this case the designation of a test result as indicating elevated risk , may have a greater impact on the perceived need for follow - up testing , than the numerical description of risk , which is more understandable to many patients . this is consistent with evidence that numeric communication of risk is often preferred by individuals when making major medical decisions ( lipkus 2007 ) . the intent of our approach was that the women s perceptions of their risks would be based on their screen - risk for t21 relative to their age - risk , and not necessarily relative to the risk of a 35-year old woman . with respect to implications for genetic counselors , an appreciation of the potential impact of framing as it relates to prenatal screening results is appropriate . it is important that the magnitude of the increase in risk , whether increased or decreased , be presented as simply and effectively as possible . classifying a result as positive because the t21 risk exceeds that of a 35-year old , may be less useful and more frightening than expressing the screen - risk relative to a woman s age - risk . verbal communication of risk is commonly used in other areas of life ( it is likely to rain , a certain condition is common , etc . ) . the limitations of this approach when applied to medical screening is that it lacks precision due to variability in interpretation of what represents increased risk . describing a result as negative has the effect of providing maximum reassurance , even is cases where the screen related - risk is similar to a woman s age - related risk . conversely , informing a woman her result is positive is often associated with great stress , which may be ameliorated when the numeric risk is placed in the context of a woman s age - related risk . because of the imprecision associated with terms like positive , negative , high - risk , and low - risk , it is our recommendation that when screen results are discussed , numeric risks should be stressed over verbal description of risks . additionally , an absolute number as expressed by the screen - risk provides the patient with an estimate not only of the risk for t21 , but also the chance the pregnancy is not at risk . a screen - risk of 1:1,000 or less , not an unusual result , predicts not only a 1:1,000 chance for t21 , but roughly a 999:1,000 a fetus does not have t21 . the numerical expression of risk allows not only a precise estimate of the risk of a problem , but also the likelihood of normalcy or absence of a condition . in this way , risks can be presented in a balanced manner , not merely focusing on whether a result is positive or negative . unlike other forms of medical screening , which are designed to predict or prevent disease , prenatal screening provides women with information allowing them to make informed choices regarding their prenatal care as well as continuation or interruption of their pregnancy . in our approach , positive test can be defined practically as one which prompts further screening and/or diagnostic testing . similarly , a negative test provides sufficient reassurance to obviate further testing or to allow diagnostic testing via amniocentesis rather than cvs . as demonstrated by the first and second trimester evaluation of risk ( faster ) trial , detection rates and screen positive rates are modestly improved with the addition of maternal serum quad screening ( ball , et al . however , the majority of our population did not require or desire this information to make informed choices regarding their pregnancy . while this may reflect the generally conservative nature of our population , it may also indicate the information , when presented as described , facilitates women s understanding of the change in absolute risk for fetal trisomy relative to their baseline , age - related risk . this is consistent with evidence that responses to risk often depend on that to which the calculated risk is being compared ( johnson 2004 ) . it also reflects the contextualized nature of prenatal risk assessment and the observation that objective risk and perceived risk are often dissimilar ( marteau 1999 ) . the influence of other factors , including religious , economic , and the perceived effects of a child with aneuploidy on the existing family structure also play an important role in the patient interpretation of and response to screening results ( garcia et al . the availability of first trimester screening and stepwise sequential screening were each associated with a significant decline in the number of amniocenteses performed at our institution . the smaller decrease between first trimester and stepwise sequential screening can be at least partially attributed to the fact only 20 % of our population elected sequential screening . first trimester screening was also associated with a significant reduction in the number of cvs procedures performed . the option of stepwise sequential screening did not further reduce the number of cvs s . this is not unexpected as most pregnancies at increased risk for fetal aneuploidy are identified earlier with the option for first trimester diagnostic testing , obviating the need for mid - trimester testing . this also reflects some cases where the screen risk was lower than the maternal age risk but the reduction was not adequately reassuring , resulting in the decision to proceed with earlier diagnostic testing . with respect to the utilization of invasive procedures , our findings are similar to those described by others . wray , et al . reported that availability of first trimester screening coincided with more women of advanced maternal age ( ama ) referred for early genetic counseling . in 2001 , 68 women were seen for early genetic counseling versus 172 in 2003 . the rates of invasive testing dropped significantly from pre- to post - first trimester screening availability ( 71 % vs 26 % , p < 0.01 ) . the types of invasive testing were not specified ( wray et al . 2005 ) . benn , et al . reviewed a series of nearly 2000 amniocentesis and cvs samples from 1991 to 2002 . they reported a 50 % reduction in the number of invasive procedures over this time . however , this was before the widespread application of first trimester screening and it was not stipulated whether nuchal translucency or first trimester serum markers were included in this analysis . additionally , cvs specimens comprised only 4.3 % of their samples ( benn , et al . it is felt that first trimester screening is the major reason for the decrease in invasive procedures . in our experience , prenatal care providers have embraced this technology and routinely offer this option even to at - risk women , ahead of invasive testing . it is possible this predisposes women to have confidence in first trimester screening sufficient to obviate the need for absolute reassurance via invasive testing with its attendant risks . it is also possible the risks of invasive testing are exaggerated in many womens minds . if you have a result you like , why seek additional information which may detract from your peace of mind ? in our opinion , receiving a very low risk early in pregnancy gives many women the reassurance that their pregnancies are normal . it may be that this makes it easier for some to believe that further testing is unnecessary . similar reassurance can be provided by maternal serum quad screening , but not until later in the pregnancy . the main limitation of our study is that it reflects a local population whose attitudes regarding screening and testing and thresholds for pursuing follow - up may not be reflective of women in other parts of the country . additionally , while most cases of t21 and t18 are reliably diagnosed postnatally , the majority of women did not have cytogenetic testing and postnatal follow - up was unavailable for 64 patients . other limitations include the fact that there is no control population of women who did not receive results reported as positive or negative . it is also plausible that both health care providers and patients are used to considering medical test results as normal or abnormal , and may be less familiar with the notion of comparative quantitative risk assessment . lastly , while noninvasive prenatal testing with cell free fetal dna is presently limited , the anticipated expanded application of such technology will likely limit the utilization of current screening paradigms . therefore , other risk communication and counseling strategies will ultimately need to be developed to suit different circumstances . in summary , communication of risk for aneuploidy is especially important and challenging in the prenatal setting . following the performance of first trimester screening , 80 % of our study population ultimately declined follow - up testing , including nearly one - half of those who initially planned to pursue stepwise sequential screening . the policy of providing patients with their results by specifying their age - related risk , their revised screen - related risk and further options , without classifying results as positive or negative , seemed to communicate risk in a manner which was understandable and clinically useful , with minimal bias . this also resulted in far fewer stepwise sequential screens being performed than would be predicted using most current sequential screening paradigms . the introduction and increasing utilization of first trimester combined screening has been accompanied by a steady decrease in the number of invasive diagnostic procedures , which is more pronounced for amniocentesis than cvs .

the types , interpretation , and use of first- and second - trimester aneuploidy screening are often unclear for many women . this impairs appropriate decision making and understanding of the implications of prenatal genetic testing options . the purpose of this study was to examine the utilization of stepwise sequential screening in our midwestern population , demographic factors associated with choice of screening and method of risk reporting and it s potential impact on women s choices . first trimester screening was performed for 2,634 women during the study period . results were not reported or framed as positive or negative . rather , the specific age - risk and screen - risk for t21 were relayed , along with options for follow - up stepwise sequential screening and invasive testing . nearly 80 % of women declined stepwise sequential screening . minorities and women of lower education were least likely to pursue further screening . less than 4 % of the study population elected invasive testing . first trimester screening was associated with a 53 % reduction in amniocenteses and 20 % fewer cvs s compared to pre - first trimester screening availability . reporting age - and screen - risks for t21 , rather than classifying results as positive or negative based on a pre - determined threshold , was associated with a low uptake of further testing .

Introduction Methods Results Discussion Conclusion

non - alcoholic fatty liver disease ( nafld ) is a condition characterized by the accumulation of large fat droplets in hepatocytes ( hepatic steatosis ) that usually appear in those without a history of alcohol abuse or known liver disease ( 1 ) . nafld is a metabolic disorder affecting obese or overweight individuals in particular , and is considered the main cause of chronic liver disease with an increasing incidence worldwide ( 2 ) . nafld is considered to be the hepatic component of metabolic syndrome , which includes features such as obesity , hyperinsulinemia , peripheral insulin resistance , diabetes , dyslipidemia , and hormonal disturbances secondary to interaction between this syndrome and reproductive axis ( 3 ) . in women with ovarian dysfunction , such us polycystic ovary syndrome ( pcos ) and acne , the possibility of nafld occurrence is much higher , and approximately 7% of obese patients with pcos also develop nafld associated with insulin resistance ( 4,5 ) . environmental pollutants , particularly pesticides or solvents represent tangible nafld risk factors ( 68 ) . studies have demonstrated that nafld is an important risk factor for the development of primary liver cancer , mostly due to nafld - associated cirrhosis ( cryptogenic cirrhosis ) ( 9,10 ) . a high prevalence of naflds occurs in hepatitis c virus infections where double antiviral therapy with peginterferon and ribavirin can have a significant impact on the progression of the disease ( 11,12 ) . understanding the pathogenesis , biochemical parameters , histological grading and staging , and the management of nafld , are vital in clinical practice today . nafld is the most common liver disorder in western industrialized countries , affecting 2040% of the population . the major risk factors for nafld are abdominal obesity , type 2 diabetes mellitus , dyslipidemia and metabolic syndrome ( 13 ) . some studies also demonstrate an association between cardiovascular disease and development of nafld ( 14 ) . nafld is also associated with metabolic syndrome , insulin resistance being considered as the key mechanism leading to hepatic steatosis ( 15 ) . therefore , it is important to actively search for nafdl in other conditions associated with insulin resistance , such as pcos , acromegaly and psoriasis , and to consider liver function when treating the primary disorder . in the management of patients with nafld there is a need for a multidisciplinary system , as apart from the standard treatment for liver disease , and also a need for the specific treatment of associated metabolic disturbances , such as obesity , hyperlipidemia , insulin resistance and type 2 diabetes mellitus . the aim of this planned , prospective and uncontrolled study was to evaluate the efficacy of atorvastatin and pentoxifylline in treating nafld . the present study included 98 patients with histologically confirmed nafld , admitted between october 2012 and january 2016 at the department of internal medicine at filantropia university hospital ( craiova , romania ) upon admission , a comprehensive medical history and full physical examination was carried out , including the determination of body mass index ( mean bmi , 31.455.54 kg / m ) . there were 2 groups of patients : group i ( 57 dyslipidemic patients and group ii ( 41 non - dyslipidemic patients ) . the results of biochemical tests upon admission are shown in table i. this study was carried out in accordance with the helsinki declaration of 1975 , and was approved by the review ethics board of the university medicine and pharmacy of craiova and of the filantropia university hospital . taking into consideration ethical concerns and the overall poor consent to hepatic biopsies , we decided not to use placebos or controls in the present study ; this is primarily due to the fact that it would involve a large number of patients having to undergo two liver biopsies while receiving no active treatment . the patients were divided into 2 therapeutic groups as follows : group i , 57 dyslipidemic patients receiving atorvastatin 20 mg / day ; and group ii , 41 non - dyslipidemic patients treated with pentoxifylline 800 mg / day ( 400 mg twice daily ) . , the patients were subjected to a medical examination upon admission ( t0 ) , two regular medical examinations ( t1 and t2 ) at 10 and 20 weeks after the initial medical examination and one medical examination at the end of treatment at week 30 ( t3 ) . all patients ( 51 males/47 females ) were caucasians with a mean age of 54/52 years and no active viral hepatitis and no history of drug and/or alcohol abuse . the study group was selected using inclusion and exclusion criteria as follows : patients were included in the study if they were able to provide written informed consent , had been histologically confirmed to suffer from nafld and had no history of drug and/or alcohol abuse . the exclusion criteria were represented by the history of chronic intake or abuse of alcohol or active viral hepatitis . in monitoring alcohol intake , we used a questionnaire ( which was slightly modified ) based on the behavioral risk factor surveillance system 2006 questionnaire ( 16 ) taken at each medical examination . the infrequent consumption of small amounts of alcohol amounts was permitted , in the condition that this did not exceed > 2 drinks per week , with each drink being defined as one standard us alcoholic drink ( approximately 14 g ethanol i.e. , 12 oz of beer , 5 oz of wine , or 1.5 oz of liquor ; 1 us oz = approximately 30 ml ) . no restriction or modifications in lifestyle or diet were enforced on any patient , apart from any current recommendations made by their endocrinologist or cardiologist . bmi , serum levels of alanine aminotransferase ( alt ) , aspartate aminotransferase ( ast ) , gamma - glutamyl transpeptidase ( ggt ) , alkaline phosphatase ( alp ) , total cholesterol ( tc ) and triglycerides ( tg ) , and blood glucose levels were determined for all patients upon admission , at each visit and at the end of treatment . the patients were sampled after at least 8 h of overnight fasting by standard venipuncture . the patients underwent liver biopsy at the beginning and end of the present study ; we deemed 2 weeks before or after the first and last visit to be a respectable and acceptable time interval for biopsy . hepatic biopsy was carried out using the menghini technique , using braun melsungen sonocan 20 g needles ( b. braun medical s.r.l . , biopsy fragments with a minimum length of 12 mm were considered adequate and delivered for pathological analysis . histological staining techniques were carried out to determine inflammation , steatosis and hepatic fibrosis using the nafld activity score ( nas or the brunt score ) for each case , upon admission into the study and at the end of the treatment , as previously described ( 17 ) . in this study , we used the nash recognized lesion evaluation system developed by kleiner et al ( 17 ) . using these criteria , the nash clinical research network pathology committee designed and validated a histological system of scoring which addresses the entire spectrum of nafld lesions and proposed a nas to use in clinical trials ( 17 ) . the scoring system is made up of 14 histological features , of which 4 were evaluated semi - quantitatively : lobular inflammation ( 02 ) , steatosis ( 03 ) , fibrosis ( 04 ) and hepatocellular ballooning ( 02 ) . nas is the sum of lobular inflammation , steatosis and hepatocellular ballooning scores , a nas score > 5 correlates with a nash diagnosis and scores of 3 are considered as not nash. the nas admission scores at t0 ( score 1 ) and at the termination of the study at t3 ( score 2 ) were database - stored and compared between the therapeutic groups . redmond , wa , usa ) , along with the xlstat suite for ms excel ( addinsoft sarl , paris , france ) . for statistical comparisons between the 2 groups at admission ( t0 ) and at the end of the treatment period ( t3 ) , variance analysis ( one way anova ) was used , and for comparisons within the groups themselves , variant analysis and the kruskall - wallis and wilcoxon tests were used . during the analysis of our results , we noted that the tg and tc levels were higher in group i compared with group ii at t0 , while the alt , ast , ggt and alp values were comparable between the groups ( table i ) . bmi and blood glucose levels were also higher in the dyslipidemic patients than in the patients with normal lipid levels ( table i ) . the mean nas score upon admission ( nas score t0 ) was 5.261.82 in group i and 5.061.48 in group ii , with no significant differences between the 2 therapeutic groups ( p=0.5639 , p>0.05 ) ( table ii ) ; likewise , there were no significant differences observed between the 2 groups as regards steatosis , necroinflammation , ballooning and fibrosis upon admission ( data not shown ) . the importance of evaluating patients at t1 and t2 , respectively , consisted of the information obtained on the direct and comparative effects of administering atorvastatin or pentoxifylline after 10 and 20 weeks following the different treatments ( table iii ) . during treatment , the results of biochemical parameters after 30 weeks from the beginning of the present study revealed a significant decrease ( p=0.018 ) in the glucose levels in patients from study group i and a non - significant decrease in patients from study group ii . a significant a decrease was observed in group i in the levels of alt ( p<0.0001 ) , ast ( p<0.0001 ) , ggt ( p<0.0001 ) , tc ( p<0.0001 ) and alp ( p<0.0001 ) . in group ii , the decrease in the alt , ast and ggt levels was similar to that of group i ( p<0.05 ) ; however , the levels of tc and tg in group ii were only slightly and non - significantly decreased ( tables iii and iv , and fig . 1 ) .. no significant alteration was noticed regarding the levels of glucose and bmi within the groups . after the first 10 weeks of treatment , a significant decrease in the alt levels in both groups was observed ( table iii ) . in both groups , a significant decrease was observed in the alt and ast levels ; the alt and ast levels markedly decreased after 20 weeks of treatment . for ggt values , a similar descending trend was observed during treatment with the difference that lower rates were noted between t2 and t3 . histopathological evaluation for group i presented a mean nas score at termination of 3.131.62 , which is highly significantly lower than score 1 ( p=0.0007 ) . group ii exhibited a mean nas score at termination of 3.981.48 , which is borderline significant compared to the initial nas score ( p=0.04073 ) . the lowest nas score at termination was achieved by the patients in group i treated with atorvastatin ( table iii ) . nas components improvement ( one or more ) was noticed only in group i ; however , no attenuation of fibrosis was observed in either group . the steatosis score was significantly decreased in patients from group i , but only group ii experienced an improvement of necroinflammation that was statistically significant . a comparison between the nas scores at admission vs. termination in both groups is shown in fig . the pharmacological treatment of nafld includes vitamin e , insulin sensitisers and other metabolic agents aiming an antioxidant or hypolipemic activity , such as atorvastatin , while pentoxifylline inhibits the production of tumor necrosis factor- ( tnf- ) , which stimulates nash development . the results of the present study are in agreement with those of other trials . in short , both drugs atorvastatin also led to a significant reduction in the levels of alp ( p<0.0001 ) , tc ( p<0.0001 ) and tg ( p=0.002 ) . the lack of a control group imposed limits on the ability of determining the real pharmacotherapy impact , but when considering that these parameters failed to improve treatment previously , it is possible that the positive effects observed in the present study were caused by pentoxifylline and atorvastatin . on the other hand , the histological evaluation showed significant improvement in 2 of the 4 nas components of both groups . the dyslipidemic patients exhibited a highly statistically significant difference between the initial and final nas scores , resulting in a p - value of 0.00007 . the difference in the initial and final nas scores of patients from the non - dyslipidemic group administered pentoxifylline was of marginal significance ( p=0.04073 ) . atorvastatin is a hmg - coa reductase inhibitor which catalyzes the hmg - coa conversion into mevalonate , an early and rate - limiting step in the cholesterol biosynthesis , leading to low cholesterol production by the liver , high ldl cholesterol plasmatic clearance and up - regulation of hepatocyte ldl - receptors ( 18 ) . kiyici et al observed that the use of atorvastatin for 6 months on a number of 27 dyslipidemic patients , for whom nash diagnosis was histopathologicaly verified , was both effective and safe ( 19 ) , while balistreri observed that atorvastatin normalized serum alt levels , tc and tg levels in patients with nash ( 20 ) . in 2011 , as part of the saint francis heart study , 80 patients with nafld confirmed by computer tomography were administered 20 mg / day atorvastatin combined with 1 g vitamin c , and 1,000 iu vitamin e. after 4 years of therapy , the reduction of hepatic steatosis was 71% ( or=0.29 , p<0.001 ) . however , the fact that the patients received a combination of vitamins c and e along with atorvastatin , and that the nafld diagnosis was based on imaging and not on histology , limited the power of the conclusions ( 21 ) . gmez - domnguez et al examined the way in which atorvastatin in doses of 1080 mg / day affects lipid metabolism and transaminases levels in 22 patients for whom nafld diagnosis was established through ultrasonography . following 6 months of treatment , 36.3% of the patients presented normal levels of transaminases and tc and after 12 months of treatment , a statistically noticeable decrease in transaminases levels and tc ( from 268.544.2 to 186.814.4 mg / dl ) were present , confirming the effect of atorvastatin in nafld and dyslipidemic patients without notable side - effects for daily doses of 1080 mg ( 22 ) . pentoxifylline is an inhibitor of tnf-. it is evident that tnf- is associated with hepatic inflammatory cell recruitment , which represents a key step in the initiation and perpetuation of nash liver injury ( 23 ) . several pilot studies have demonstrated biochemical improvement , and in some cases histological improvement following the administration of pentoxifylline to patients with nash ( 2426 ) . satapathy et al observed in 18 histopathologicaly verified nafld patients with elevated transaminases levels , that after 6 months of pentoxifylline administration in 800 mg / day doses , the serum transaminases levels were significantly reduced ( ast : 6629 to 3311 iu / l , p<0.0001 and alt : 10944 vs. 4720 iu / l , p<0.0001 ) . moreover , alt was normalized for 23% of the patients within the first month ( p=0.125 ) , 35% after the second month and 60% of the patients after 6 months of treatment . the same authors , reported in 2007 of nine patients that administered 800 mg pentoxifylline daily doses and after an average of 12 months treatment , a decrease in transaminase values was achieved ( alt : 11153 to 4519 iu / l , p=0.003 and ast : 6127 to 3312 iu / l , p=0.005 ) accompanied by steatosis and lobular inflammation reduction in 55% of the cases , as well as decreased histological fibrosis in 4 out of 9 patients with baseline fibrosis ( 25 ) . in another study , on 55 patients with nash confirmed by biopsy who received 400 mg pentoxifylline 3 times per day or the placebo for 1 year , patients treated with pentoxifylline were more likely than those treated with the placebo to present a decrease in histological nafld . the nas score decreased by 2 points in 38.5% of the patients treated with pentoxifylline compared to only 13.8% of the patients receiving the placebo . in this study , the administration of pentoxifylline improved the liver fibrosis scores , lobular inflammation and steatosis . in 3 patients receiving pentoxifylline , the dose of medication was decreased from 3 times daily to twice daily due to nausea , which resulted in adequate symptom control ( 26 ) . in another study by van wagner et al , in 30 patients treatesd with pentoxifylline , in doses of 1,200 mg / day , or placebo , for a period of 12 months . at the completion of the study , iu / l and ast : 676 to 476 iu / l , p<0.05 ) , as well as in the degree of steatosis and lobular inflammation ( p<0.05 ) were observed in the group administed pentoxifylline ( 27 ) . in other studies , pentoxifylline at doses of 400 mg / day twice daily , administered to 20 patients for 12 months , was associated with the normalization of serum levels of alt and ast ( 8464 vs. 13876 , p=0.002 and 5837 vs. 10262 , p=0.003 , respectively ) . a total of 9 patients withdrew from the study , due to nausea ( 28 ) and in another pilot study , similar biochemical improvements under pentoxifylline treatment were demonstated ( 29 ) . ll patients studied presented elevated levels of tnf-. hepatic damage is associated with tnf- production that triggers the production of various cytokines ( 31 ) , recruiting inflammatory cells , that affect hepatocytes and induce fibrogenesis ( 32,33 ) . the main mechanism through which pentoxifylline improves hepatic histology ( decreasing steatosis and necroinflammation ) is the reduction of lipopolysaccharide stimulated tnf- production . in conclusion , statins are well known for their lipid lowering properties , but they may have the potential to diminish some of the histological features of nafld . dyslipidemia is common among patients with nafld and atorvastatin proved to be efficient in the treatment of both disorders , by improving biochemical parameters and steatosis . pentoxifylline was well - tolerated and showed similar efficacy in patients with non - dyslipidemia by decreasing the degree of steatosis / lobular inflammation and improving liver function .

in this study , we aimed to evaluate the efficacy of pentoxifylline and atorvastatin in the treatment of non - alcoholic fatty liver disease ( nafld ) . the study included 98 patients with histologically confirmed nafld divided into 2 groups as follows : group i ( 57 dyslipidemic patients , receiving atorvastatin 20 mg / day and group ii ( 41 non - dyslipidemic patients , treated with pentoxifylline , 800 mg / day ) . the present study was conducted for a mean of 32.83.4 weeks . for all patients , we determined the body mass index , a liver biopsy was performed , and we measured the serum levels of alanine aminotransferase ( alt ) , aspartate aminotransferase ( ast ) , gamma - glutamyl transpeptidase ( ggt ) , alkaline phosphatase ( alp ) , total cholesterol ( tc ) and triglycerides ( tg ) at the beginning and at the end of the study period . the nafld activity score ( nas ) was used to evaluate the liver biopsies for steatosis , fibrosis and necroinflammation . the patients in group i exhibited a considerable reduction in alt , ast , ggt , tc , ap and tg levels ( p<0.0001 ) . histologically , there were no changes in fibrosis and necroinflammation , although the extent steatosis was reduced . the improvement in the alt , ast and ggt values ( p<0.05 ) in group ii were similar to those in group i ; however , no statistically significant decrease was noted in the levels of alp , tc and tg in this group . our results thus demonstrated that atorvastatin attenuated steatosis and improved liver function parameters in patients with nafld associated with dyslipidemia . similar results were obtained in the non - dyslipidemic patients administered pentoxifylline .

Introduction Materials and methods Results Discussion

it is essencial to localize the toxic region accurately in hyperthyroid patients before making a decision to remove with operation . here we report a cese of an intrathoracic toxic thyroid nodule causing hyperthyroidism with a multinodular normal functional cervical thyroid gland . a 62-year - old female presented with a 2 years history of weakness , weight loss , tremulousness palpitations , and heat intolerance . physical examination revealed a normal weight female in no distress ; blood pressure was 120/80 mmhg supine , pulse 96 , and regular . laboratory examination results from complete blood cell count , urinalysis , electrocardiography , and biochemical tests were within the normal limits . thyroid function tests revealed hyperthyroidism ; free t3 : 4.5 ng / ml l ( normal : 1.85 ng / ml ) , free t4 : 1.83 ng / ml ( normal : 0.81.9 ng / ml ) , and thyroid - stimulating hormone : 0.016 u / ml ( normal : 0.44 u / ml . radionuclide tc-99 m pertechnetate ( mtc04 ) thyroid scan images obtained [ figure 1a and c ] from neck and mediastinum 20 min after intervenes . administration of 3 mci tc99 m pertechnetate using a parallel hole low energy all - purpose collimator . the scan showed a normoactive cervical thyroid gland and a hyperactive intrathoracic area on the left side of thyroid . thyroid radioactive iodine uptake ( raiu ) measured over the neck and the uptake after oral administration of 7 ci i-131 was 15% at 2 h and 34% at 24 h. a thyroid scan was also obtained with gamma camera at 24 h [ figure 1b ] using a parallel hole high - energy collimator . planar images of neck and mediastinum and cervicothoracic single photon emission computed tomography images were taken . images showed a normal functioning cervical thyroid gland and a hyperfunctioning intrathoracic thyroid tissue on the left side of thyroid . chest roentgenogram [ figure 2 ] revealed widened upper mediastinum with no tracheal displacement and fibrotic changes in the basal regions that suggested bronchiectasis . ultrasonographic assessment of thyroid bed showed a normal sized multinodular cervical goiter ( right lobe : 43 mm 17 mm 22 mm , left lobe : 46 mm 31 mm 22 mm and isthmus : 5 mm ) and did not define a substernal enlargement . thoracic computed tomographic scans [ figure 3 ] showed a 6 cm 6 cm 4.5 cm diameter , smooth edge mass in the left superior portion of the anterior mediastinum with patchy calcification and heterogeneous contrasting which is related with the left thyroid lobe in a small area . . tc-99 m pertechnetate images of anterior and posterior thorax and mediastinum ( a ) showed a normoactive cervical thyroid gland and an activity accumulation in the intrathoracic area on the left side of thyroid ( a , arrowheads ) . anterior i-131 thyroid scan ( b ) revealed a normal functioning cervical thyroid gland and a hyperfunctioning intrathoracic thyroid tissue on the left side ( b , arrow ) and support the accumulation in the upper thoracic area . anterior tc-99 m pertechnetate images ( c , arrow ) showed that it was a thyroid tissue , and a marker was located in inferior isthmus region chest x - ray revealed widened upper mediastinum ( arrow ) with no tracheal displacement and fibrotic changes on the basal regions that suggested bronchiectasis in thoracic computed tomography scans ; axial images of lung window showed a smooth edge mass in the left superior anterior mediastinum ( upper arrows ) , and patchy calcification and heterogeneous contrasting were seen in axial images of the bone window ( lower arrows ) . there was no significant tracheal and esophageal compression or displacement due to a hyperfunctioning intrathoracic goiter with a normal multinodular functional cervical thyroid gland , the patient was diagnosed as hyperthyroidism . the patient was treated with graded doses of propylthiouracil , but partial response was provided . radionuclide scintigraphy is valuable in confirming suspected or clinically evident thyroid tissue that is extending into mediastinum . although mtc04 has been used for routine thyroid scintigraphy , i-131 is preferred for imaging of substernal goiter because mtc04 activity in goiter remains lower comparing with high level of background activity in the heart and great vessels . moreover , for imaging structures behind sternum , higher energy photons of i-131 are needed . in this case , our patient has high raiu values indicating clinical hyperthyroidism ; however , her cervical thyroid was in normal size without enlargement and abnormal uptake . the possibility of the existence of external thyroidal tissue should be kept in mind in such suspicious cases . the case we present , a hyperthyroid patient with high radioiodine uptake without cervical thyroid enlargement suggest that the radiation is coming from intrathoracicgoiter which was detected recently . intrathoracic goiter ( retrosternal or substernal ) is one of the major diagnostic consideration in evaluation of upper anterior mediastinal masses . because of iodine trapping of thyroid tissue , radioiodine scintigraphy remains an excellent confirmatory test . however , few cases of i-131 accumulations in thoracic region confirmed to be bronchogenic cyst or carcinoma have been reported were confirmed as . park et al . analyzed 54 patients and demonstrate that most intrathoracic goiters can be diagnosed by thyroid scintigraphy with a sensitivity of 93% . they conclude that most intrathoracic goiters have thyroid function , and radioiodine scintigraphy is a definitive and cost - effective test for diagnosis . in addition , they recommend that radioiodine scintigraphy should be the first study for further evaluation of upper anterior mediastinal masses . reported a hyperthyroid patient with intrathoracic goiter that was cured after excision of the mass . they stated that radioactive iodine treatment may be used unless the patient has compression symptoms . also mentioned the importance of radionuclide scintigraphy with either mtc04 or i-123 in their study including children with thyroid dysgenesis . they use those scintigraphic modalities as a diagnostic tool averting invasive procedure such as biopsy and providing both functional and anatomic information to show where the thyroid tissue is and how effective it works . aydin et al . reported a case underlining the value of mtc04 scintigraphy with and without potassium perchlorate administration . disappearance of tracer accumulation after applying potassium perchlorate suggests that mediastinal mass was an intrathoracic goiter . pathological improvement supports this technique as a simple , accurate , and cost - effective imaging . in our case , high thyroid hormone levels and isotopic uptake in the intrathoracic goiter with normal uptake of the cervical thyroid were diagnostic for toxic intrathoracic goiter . higher accumulation in thoracic mass than cervical thyroid in both mtc04 and i-131 scintigraphy reminds us the development of hyperthyroidism in the intrathoracic goiter which had not yet produced feedback suppression of the cervical thyroid . our patient was cured after excision of mediastinal mass despite the absence of compression symptoms or mass effect . intrathoracic goiters are generally considered an indication for surgery ; radioiodine therapy remains a choice for those who can not be operable because of advanced systemic disease or other reasons . our patient did not have significant tracheal deviation or compression symptoms but her hyperthyroidism can not be controlled by antithyroid drugs and symptomatic improvement was incomplete . this case highlights the importance of mediastinal imaging using i-131 and mtc04 scintigraphy in thyroid detection . patients should not only be imaged with a pinhole collimator but also their mediastinal region should be viewed with parallel hole collimators .

radionuclide scintigraphy with i-131 and tc-99 m pertechnetate ( 99mtc04 ) has been widely used in detecting toxic nodules . intrathoracic goiter usually presents as an anterior mediastinal mass . mostly the connection between intrathoracic mass and the cervical thyroid gland is clearly and easily identified occurring as a result of inferior extension of thyroid tissue in the neck , which is called as secondary intrathoracic goiter . completely separated , aberrant or in other words primary intrathoracic goiters arise as a result of abnormal embryologic migration of ectopic thyroid closely associated with aortic sac and descend into the mediastinum . intrathoracic goiters are generally nontoxic nodules existing with mass effect without causing hyperthyroidism . however , mostly reported cases had enlarged thyroid glands in the neck . this report demonstrates the usefulness of i-131 and 99mtc04 scintigraphy for detecting intrathoracic goiter causing hyperthyroidism with a normal functioned cervical thyroid gland .

INTRODUCTION CASE REPORT DISCUSSION Financial support and sponsorship Conflicts of interest

advances in biomedical research have given way to new enthusiasm surrounding the expectation that medical treatment will be informed by an individual 's genetic information . as knowledge of the genetic factors underlying complex diseases such as cancer advances , new tools for disease risk assessment , screening , prognosis , and therapeutics incorporating this knowledge are continuing to emerge at an increasingly rapid pace . tailoring medical treatment decisions to an individual 's genetic profile using their own genetic information to guide medical decisions will optimize patient care by allowing for the personalized assessment of disease risk , and prescription of treatments with higher likelihoods of success . for society , integrating the use of personal genetic information into health - care delivery is hoped to result in significant cost savings by administering treatments only to those most likely to benefit . should the use of individual genetic information in the delivery of health care be a cause for concern ? fears regarding the potential for misuse of genetic information have given rise to the concept of genetic discrimination ' , directed against an individual based solely on an apparent or perceived genetic variation from the normal human genotype ' . dialog surrounding genetic discrimination has predominately occurred in relation to use of genetic information contained in a patient 's medical file by third parties with access to the information : namely employers and private insurance companies providing disability or life insurance ( see eg ) . so prevalent is public concern over the possibility of genetic discrimination , legislation exists prohibiting it in many jurisdictions ( reviewed in ) . but the rise of personalized medicine raises questions as to whether the use of an individual 's genetic information to inform medical decision making by health - care professionals collecting the information could be inequitable , perhaps amounting to discrimination . by discrimination , we mean the possibility of indirect discrimination , whereby policies or practices surrounding the use of genetic information in medical decision making could have the unintended effect of denying individuals access to health care on non - medical grounds . we ask whether exclusion based on genetic information could result in inequitable access to health care , where equal medical need does not result in equal access . here , we examine this question from legal and socioethical perspectives . indeed , these questions are timely as stakeholders worldwide have acknowledged that establishing fair access to genomic medicine is a priority as they contemplate translation strategies . the practice of oncology has been revolutionized by the use of individual genetic information to identify those most at risk or likely to benefit from increased surveillance , therapeutic , and risk reduction measures for cancer . among the many new developments , genetic risk assessment models that calculate cancer risk represent an excellent case study from which to ask whether inequitable access to health care can result from the use of individual genetic information . indeed , risk assessment that includes individual genetic information is one of the fastest growing areas of personalized medicine and promises to be a prominent component of health - care delivery going forward . presently , clinical risk assessment for complex disease is predominantly based on family history , lifestyle , and shared environmental factors and the predictive value of non - genomic - based risk assessment is considered variable or low . further , while genetic models have been in existence for nearly 20 years for breast cancer , the advent of genome - wide association scans and whole genome sequencing has led to the forecast that new risk prediction tools will emerge capable of using genomics to calculate an individual 's risk of developing not only cancer , but numerous other complex diseases . proposed risk assessment tools that include individual genomic information , however , promise to raise distinct concerns , as the analytic validity of such risk assessment is , arguably , higher than family history , justifying a greater number of medical decisions to be based on it . with a greater number of risk assessment tools with increased predictive value expected to emerge , genomic - based risk assessment promises to have a profound impact on the delivery of health care by using genetic information to identify and intervene for those at risk , prior to development of disease . breast cancer genetic risk assessment models are clinical tools that calculate a patients ' individual risk for developing cancer or harboring a cancer predisposing genetic mutation . these tools seek to identify patients likely to benefit from increased cancer surveillance , prophylactic treatments , and other cancer risk reducing interventions . in existence for nearly 20 years , the models are based on cancer prevalence in particular populations . by mapping individual factors from the patient such as family history of cancer , age , etc . , into the models , a patients ' individual cancer risk can be expressed numerically . countries worldwide have established particular risk thresholds required before a patient is eligible for additional screening , or cancer risk reduction measures . as a result , patient stratification regarding access to health care occurs through the use of their genetic information . on the surface , use of breast cancer genetic risk prediction models to select patients for additional health care should not raise concerns for equitable access . indeed , they are tools that have the purpose of improving the delivery health care . strong medical , legal , ethical , and economic arguments exist favoring their use to maintain or improve equitable access to health care . from a medical perspective , decisions based on the best available scientific evidence is part of evidence - based medicine , a widely adopted practice in health - care systems worldwide . hence , the use of risk assessment scores to select patients for additional care is consistent with evidence - based medicine . use of risk assessment scores to prioritize patients can be justified from a legal perspective in the context of a publically funded health - care system . for example , in canada , the canada health act , specifies the conditions for public funding of health care stipulating that universal public funding is provided for services that are deemed medically necessary for the purpose of maintaining health , preventing disease or diagnosing or treating an injury , illness or disability ' . thus use of cancer risk assessment scores as a medical tool to identify those patients in need of further medical intervention is consistent with the legislated purpose of the public health insurance program to provide funding for medically necessary care . use of risk assessment scores can also be justified from ethical perspectives . indeed , selecting only patients likely to benefit from additional interventions spares those unlikely to benefit from the burden of additional medical treatment , consistent with the principle of non - malfeasance . in publically funded health - care systems , limiting access to additional screening and testing by establishing thresholds through the use of risk assessment represents a fair distribution of limited resources , by prescribing additional treatment only to those in need . while use of breast cancer genetic risk prediction models has advantages , the technology has limitations . increasingly , researchers and decision makers have come to realize that successful implementation of genomic - based technologies requires consideration of not only benefits , but also drawbacks , medical , and otherwise . thus , the clinical application of breast cancer genetic risk prediction models provides an opportunity to identify limitations and examine the consequences for equitable access to health care . two categories of limitations can potentially give rise to the unintended effect of perpetuating inequities in access to health care : ( i ) limitations inherent to the models themselves and ( ii ) the means by which the models are implemented and used . first , underlying limitations of the models themselves raise the question as to whether their use could be inequitable when applied across a general population . indeed , variability exists within individual models in their ability to assess risk among different age and ethnic groups . age under 40 has been shown to be a factor resulting in reduced accuracy of the models . moreover , ethnicity has been shown to affect validity of the resulting risk assessment . in effect , some models have a high level of accuracy among some groups , such as italian or french canadian populations , while at the same time underestimating risk among other groups such as african - american , turkish , iranian , or hispanic populations . concerns over accuracy among african americans , hispanics , and asians have led to questions from the medical community as to whether individuals in these groups receive optimal care when medical decisions are based on risk assessment scores . more than a dozen models assessing breast cancer risk exist , and inconsistencies have been reported with respect to which model provides the most accurate degree of risk assessment . as new data about the risk factors for cancer are continually incorporated into the models , understanding of the models becomes a moving target . finally , despite the clinical use of breast cancer risk prediction models for over 20 years , systematic reviews of their performance have raised questions regarding their ability to consistently and accurately predict breast cancer risk across different populations , while the need for ongoing validation of the models as they are modified has been recognized . . clinical collection of patient information upon which risk assessment is based is one example that illustrates the potential for inequities to occur during implementation . family history , which provides insight into the shared genetic information of individuals , is considered the largest risk factor after age and gender for a number of cancers and other chronic conditions . as breast cancer risk prediction models rely heavily on family history , it follows that accuracy of family history can significantly affect the validity of the resulting risk assessment . despite the potential value of family history in cancer treatment and prevention , barriers have been reported in its clinical collection . indeed , it is widely accepted that accuracy of family history is considered inadequate to fully assess familial cancer risk . underlying inequities are known to exist emanating from both patients and health - care professionals . from patients , knowledge , socioeconomic , and cultural barriers are each factors that have been shown to influence patient 's accuracy of their family history . older age , lower education , and membership in a minority group have also been shown to be associated with lower accuracy of personal and family history of cancer . health - care providers also contribute to the inaccuracy of family history . as no standard medical definition of family member exists , health - care providers have reported being unclear themselves regarding information that should be collected . further , health - care provider knowledge of cancer incidence among minority populations is purported to be a barrier to accurate collection of family history . this has led to the recognition of the need to routinize and educate health - care professionals in clinical family history collection , and develop distinct family history tools targeting underserved groups . however , at present , such tools are only in the preliminary stages of development and still require validation . limitations with respect to age , race , and underlying variability across breast cancer genetic risk prediction models , as well as limitations arising during their implementation , raise the possibility that some populations are excluded , or are sent for superfluous testing , not as a result of actual medical risk , but as a result of inequities arising from the limitations inherent to the models themselves or through the inadequate collection of family history . such use of risk assessment scores to determine access to health care would not be discriminatory on the surface , but could represent a more insidious means through which use of genetic information could create or perpetuate inequities in accessing health care . further , as the patient inputs and the means of collecting information for breast cancer risk prediction models are similar for risk prediction models for other diseases , similar questions can be asked of other genetic - based risk prediction tools . the possibility for inequitable access resulting from the use of genetic information thus raises the following questions : what are the challenges for implementing genomic technology as a result of these limitations ? limitations of breast cancer genetic risk prediction models highlight the challenges that exist for health - care professionals and governments seeking to maintain equitable access to health care when implementing technologies that use genetic information to inform medical decision making . for health - care professionals , how are they educated about underlying limitations in the tools , and how are these limitations taken into account when selecting or administering a model to a given patient ? for governments and hospitals administering a publically funded health - care system , how are these limitations taken into account when selecting which models will be relied upon , and what risk thresholds will be required to establish eligibility for subsequent health care ? in countries with diverse immigrant populations , how is the variable performance across ethnic groups taken into account when setting population - based thresholds ? at what point is the evidence gathered on risk prediction models considered sufficient for governments and health - care professionals to rely on their use in the clinic ? simply put , how can evidence demonstrating their medical value be reconciled with the possibility of inequities arising during implementation ? failure to consider these issues during implementation would increase the likelihood that inequities could be created or perpetuated by the use of risk prediction models in medical decision making . consequently , it becomes important to consider the consequences , legal and ethical , of possible inequities . could inequities arising through the use of risk prediction models result in legal consequences ? from an international law perspective , article 12 of the united nations international covenant on economic , social and cultural rights , for which 160 nations are party , states that everyone has the right to the enjoyment of the highest attainable standard of physical and mental health ' . this has been interpreted by the un committee on economic , social and cultural rights to mean that the covenant proscribes any discrimination in access to health care and underlying determinants of health , as well as to means and entitlements for their procurement ' . similarly , article 3 of the council of europe convention on human rights and biomedicine , provides that parties , taking into account health needs and available resources , shall take appropriate measures with a view to providing , within their jurisdiction , equitable access to health care of appropriate quality ' . while neither provision creates enforceable rights for individuals alleging inequitable access to health care , nevertheless such provisions have persuasive value by imposing obligations on governments to consider equitable access in their political and legislative agendas surrounding health care . moreover , in jurisdictions with publically funded health - care systems , legal mechanisms can exist that allow individuals to pursue the government on questions of equitable access to health care . for example in canada , two normative regimes exist which together have the purpose of ensuring that all canadians have equitable access to publically funded health care . citizens have the right under the canadian charter to challenge government decisions and have done so with respect to choice and availability of health - care services under the public system on the grounds that such decisions are indirectly discriminatory . given the national and international norms that exist surrounding equitable access to health care , it becomes prudent for nations having public and/or private health - care delivery models , to consider whether the use of genetic risk assessment scores could have for effect to deny individuals access to health care on non - medical grounds , and how to mitigate such effects during their implementation . beyond legal questions , the effect of excluding or testing individuals on non - medical grounds raises ethical questions of the harm that would be caused to individuals as a result . further , inequities arising from their use raises the question as to whether such use could be inconsistent with the principle of fair distribution of resources . indeed , scientific advances underlying personalized medicine genetic - based technologies are the result of enormous public investment in basic genomic sciences . the public is justified to expect that these discoveries will translate into products and services accessible to all , a sentiment echoed by the us national advisory council for human genome research stating that genetic - based personalized medicine will only achieve its full potential to improve health when the advances it engenders become accessible to all ' . others have expressed that genomic - based advances represent tools to be used to address underlying health disparities , by identifying those at risk , while those most in need should not be the last to benefit . thus , if new personalized medicine genetic technologies have the effect of inequitably excluding individuals , thereby becoming vehicles through which disparities are perpetuated , we can ask whether the decision to rely on information from them is ethical , in light of the significant public investment underlying their development . health technology assessments and other implementation strategies are recognizing the need to improve implementation of genomic - based technologies and as a result , are integrating perspectives beyond scientific including ethical , legal , and social perspectives . indeed , part of the center for disease control acce framework for evaluating genetic tests involves considering the potential for discrimination and stigmatization as impediments to their implementation . however , as discussion surrounding genetic discrimination has been predominantly focused around employment or private insurance , we suggest that there is a need to consider a broader view of genetic discrimination , one which departs from the categorical conception of genetic discrimination , where it is either present or absent . our case study of breast cancer genetic risk prediction models illustrates how using individual genetic information in medical decision making could give rise to inequities capable of creating or perpetuating disparities in accessing health care . further it raises legal , ethical , and implementation challenges distinct from those raised in relation to employment or private insurance . as an increasing number of medical decisions are based on individual genetic information , the potential for inequities arising from the medical use of this information also increases and it becomes important to consider this possibility . thus , we suggest acknowledging the potential for inequitable access as occurring along a continuum ranging from inequities that could be tolerated in varying degrees , to intolerable , possibly amounting to discrimination . challenges have been recognized related to evaluating the ethical , legal , and social concerns raised by genetic technologies and the need to improve upon methods to identify these concerns . we advocate investment in research to assess the potential for inequitable access to occur from the use of emerging genetic technologies that are used in part to determine access to health care . such research would be conducted early on to mitigate identified concerns and would address the following questions : we suggest examining new genetic technologies to assess whether limitations exist such that their use as medical decision making tools could have the effect of creating or perpetuating inequitable access to health care . for this , evidence is needed to better understand these technologies from the perspective of the potential for inequities to occur . for example , early assessment of the accuracy of breast cancer genetic risk prediction models compared among multiple age , socioeconomic , and ethnic backgrounds would provide an opportunity to ask whether a one size fits all ' approach is appropriate or to consider the extent to which subsequent medical decisions will be based on a risk assessment . further , we ask whether the use of genetic information in a given genetic technology for medical decision making is compatible with existing legislative regimes surrounding equitable access to health . a key remaining question is whether legislative regimes are appropriate tools to safeguard against possible inequities . moreover , beyond legal questions raised , successful implementation requires that evidence of potential inequities arising through the use of individual genetic information be brought to the attention of and taken into consideration by health - care professionals using the technology , and by decision makers conducting health technology assessments . the continuum approach to characterizing inequities as advocated above would recognize the need to adjust implementation efforts so as to address the potential for inequities according to the tolerance level and the likelihood that it will occur . the use of genomic information to inform medical decision making raises significant social , ethical , and legal questions . however , delaying implementation of tools that use genomic information until they are sufficiently perfected does not represent a realistic solution . as discussed , strong medical , rather , our example points to the need to continue to invest in parallel at improving upon the limitations of these tools , as well as identifying when to supplement information from genetic - based tools with other sources of information for clinical decision making . early identification of the potential for inequities lends an opportunity to take proportionate proactive steps to minimize the risks of inequities during implementation . by anticipating and addressing the potential for inequitable access to health care to occur from the use of genetic information , we will move closer to realizing the goal of personalized medicine : to improve health care for individuals .

personalized medicine promises that an individual 's genetic information will be increasingly used to prioritize access to health care . use of genetic information to inform medical decision making , however , raises questions as to whether such use could be inequitable . using breast cancer genetic risk prediction models as an example , on the surface clinical use of genetic information is consistent with the tools provided by evidence - based medicine , representing a means to equitably distribute limited health - care resources . however , at present , given limitations inherent to the tools themselves , and the mechanisms surrounding their implementation , it becomes clear that reliance on an individual 's genetic information as part of medical decision making could serve as a vehicle through which disparities are perpetuated under public and private health - care delivery models . the potential for inequities arising from using genetic information to determine access to health care has been rarely discussed . yet , it raises legal and ethical questions distinct from those raised surrounding genetic discrimination in employment or access to private insurance . given the increasing role personalized medicine is forecast to play in the provision of health care , addressing a broader view of what constitutes genetic discrimination , one that occurs along a continuum and includes inequitable access , will be needed during the implementation of new applications based on individual genetic profiles . only by anticipating and addressing the potential for inequitable access to health care occurring from using genetic information will we move closer to realizing the goal of personalized medicine : to improve the health of individuals .

Using genetic information in medical decision making Case study: breast cancer risk prediction models Limitations of risk prediction models Consequences for equitable access to health care Challenges for implementation Legal consequences Ethical consequences Conclusion

the reductions in leg strength have been observed during concentric and isometric actions . moreover , positive correlations between lower leg strength and walking tolerance have been identified , suggesting that interventions to improve leg strength might increase exercise tolerance in these patients.5 however , basic locomotor tasks involve not only concentric and isometric , but also eccentric action,6 which is defined as the force exerted by muscles while lengthening . lower eccentric strength and endurance might also be related to exercise intolerance in patients with ic . therefore , interventions to improve eccentric strength and endurance might also be useful in improving exercise tolerance in these patients . nevertheless , this is the first study to analyze the effect of peripheral arterial disease in eccentric strength . we hypothesized that reduced muscle strength and endurance would be observed during both concentric and eccentric actions . eleven male patients with unilateral peripheral arterial disease ( 11 symptomatic and 11 asymptomatic legs ) and stable symptoms of ic were recruited from a tertiary center specializing in vascular disease . patients were included if they had fontaine stage ii peripheral arterial disease,7 ankle / brachial index ( abi ) at rest 0.90 in one leg , abi > 1.0 in the other leg , and symptoms of calf claudication . moreover , since the assessment of strength and endurance was performed on the gastrocnemius and soleus muscles , the arterial obstruction had to be present in femoral - popliteal and/or iliac - femoral sites as determined by arterial palpation . patients were excluded under the following conditions : abi measurement could not be obtained , presence of chronic lung disease , exercise tolerance limited by factors other than claudication ( e.g. , dyspnea or poorly controlled blood pressure ) , presence of electrocardiogram response suggestive of myocardial ischemia during the exercise test , or history of revascularization in the previous year . this study was approved by the ethics committee for research involving human trials , in compliance with helsinki declaration of 1975 , as revised in 1989 . arm and leg blood pressures were measured using a mercury column ( unitec ) and doppler ultrasound ( martec dv600 ) . the abi was obtained by dividing the highest value of systolic blood pressure recorded in the legs ( in the dorsalis pedis artery or in the posterior tibial artery ) by the highest brachial systolic blood pressure ( right or left arm ) . the tests were carried out using a cybex 6000 isokinetic dynamometer ( cybex , division of lumex , ronkonkoma , new york ) in both concentric and eccentric modes . both action modes were tested in the supine position with the knee flexed at 90 and with the thigh supported by a custom apparatus . the axis of rotation of the dynamometer arm was aligned with the ankle joint , and the foot was stabilized in a specific support apparatus using velcro straps.8 patients were tested unilaterally . the order of leg testing ( symptomatic or asymptomatic ) and action types ( concentric or eccentric ) were randomly determined . patients were allowed to practice three submaximal and two maximal trials before each test . during all procedures , concentric and eccentric peak torque ( pt ) and total work ( tw ) during plantar flexion was measured during maximal voluntary contractions at a speed of 120/s . the highest pt assessed over five consecutive repetitions was considered for analysis , while tw was obtained during 60 consecutive repetitions . we employed a rest period of 30 s between warm up and testing , and 1 min between testing pt and tw . the rest period between legs and action types was 10 min . to analyze the quality of pt and tw data , the reliability was assessed in all patients during two different test sessions separated by at least three days . the obtained intraclass correlation coefficient ranged from 0.94 to 0.98 without any differences in the means between sessions for both pt and tw , confirming the reliability of the data . the statistically required sample size was calculated using data from a previous study.1 for a desired power of 80% and an alpha error of 5% , a total of 20 legs were needed to detect differences between symptomatic and asymptomatic limbs . shapiro - wilks and levene tests confirmed the normal distribution and the homogeneity of variance of the data , respectively . the comparisons between symptomatic and asymptomatic legs in concentric and eccentric pt and tw were performed using the two - tailed t test for dependent samples . significance was established at an alpha level of p 0.05 , and data are expressed as means standard deviation . eleven male patients with unilateral peripheral arterial disease ( 11 symptomatic and 11 asymptomatic legs ) and stable symptoms of ic were recruited from a tertiary center specializing in vascular disease . patients were included if they had fontaine stage ii peripheral arterial disease,7 ankle / brachial index ( abi ) at rest 0.90 in one leg , abi > 1.0 in the other leg , and symptoms of calf claudication . moreover , since the assessment of strength and endurance was performed on the gastrocnemius and soleus muscles , the arterial obstruction had to be present in femoral - popliteal and/or iliac - femoral sites as determined by arterial palpation . patients were excluded under the following conditions : abi measurement could not be obtained , presence of chronic lung disease , exercise tolerance limited by factors other than claudication ( e.g. , dyspnea or poorly controlled blood pressure ) , presence of electrocardiogram response suggestive of myocardial ischemia during the exercise test , or history of revascularization in the previous year . this study was approved by the ethics committee for research involving human trials , in compliance with helsinki declaration of 1975 , as revised in 1989 . arm and leg blood pressures were measured using a mercury column ( unitec ) and doppler ultrasound ( martec dv600 ) . the abi was obtained by dividing the highest value of systolic blood pressure recorded in the legs ( in the dorsalis pedis artery or in the posterior tibial artery ) by the highest brachial systolic blood pressure ( right or left arm ) . the tests were carried out using a cybex 6000 isokinetic dynamometer ( cybex , division of lumex , ronkonkoma , new york ) in both concentric and eccentric modes . both action modes were tested in the supine position with the knee flexed at 90 and with the thigh supported by a custom apparatus . the axis of rotation of the dynamometer arm was aligned with the ankle joint , and the foot was stabilized in a specific support apparatus using velcro straps.8 patients were tested unilaterally . the order of leg testing ( symptomatic or asymptomatic ) and action types ( concentric or eccentric ) were randomly determined . patients were allowed to practice three submaximal and two maximal trials before each test . during all procedures , the inactive leg was immobilized using a specific support as recommended by manufacturer . concentric and eccentric peak torque ( pt ) and total work ( tw ) during plantar flexion was measured during maximal voluntary contractions at a speed of 120/s . the highest pt assessed over five consecutive repetitions was considered for analysis , while tw was obtained during 60 consecutive repetitions . we employed a rest period of 30 s between warm up and testing , and 1 min between testing pt and tw . the rest period between legs and action types was 10 min . to analyze the quality of pt and tw data , the reliability was assessed in all patients during two different test sessions separated by at least three days . the obtained intraclass correlation coefficient ranged from 0.94 to 0.98 without any differences in the means between sessions for both pt and tw , confirming the reliability of the data . the statistically required sample size was calculated using data from a previous study.1 for a desired power of 80% and an alpha error of 5% , a total of 20 legs were needed to detect differences between symptomatic and asymptomatic limbs . shapiro - wilks and levene tests confirmed the normal distribution and the homogeneity of variance of the data , respectively . the comparisons between symptomatic and asymptomatic legs in concentric and eccentric pt and tw were performed using the two - tailed t test for dependent samples . significance was established at an alpha level of p 0.05 , and data are expressed as means standard deviation . the abis of the symptomatic legs were lower than those of the asymptomatic legs ( p < 0.05 ) . the concentric and eccentric pt and tw of symptomatic and asymptomatic legs are presented in table 2 . concentric pt and tw in symptomatic legs were lower than in asymptomatic legs ( p < 0.05 ) . this study is one of the few to analyze strength and endurance during concentric action , and it is the first to evaluate eccentric action in patients with ic . the main findings of this study were ( i ) patients with unilateral ic exhibited significantly lower concentric pt and tw in the symptomatic compared with the asymptomatic leg ; and ( ii ) there were no differences in eccentric pt or tw between symptomatic and asymptomatic legs . peak torque is considered the most important indicator of muscle strength that can be obtained using an isokinetic dynamometer.9 it can be used to identify any early impairment in muscular performance as well as to assess maximal strength levels . total work represents the work performed by the muscular group during the whole test , indicating the muscle endurance capacity of muscle groups.9 it is considered the most sensitive parameter for evaluating muscle fatigue.10 reduced concentric strength in patients with ic has been observed in previous studies . impaired concentric strength in the gastrocnemius and tibial muscles was observed in 26 men with ic compared with six age - matched controls.4 the effects of the disease in terms of muscle strength and endurance were confirmed by other studies using isometric11,12 and concentric10 actions . moreover , a significant relationship was observed between lower extremity strength , abi , and walking tolerance , suggesting that strength levels are associated with disease severity.5 the mechanisms underlying the strength impairments in patients with peripheral arterial disease are not completely understood and remain controversial . it has been hypothesized that type i and ii fiber atrophy and denervation of muscle fibers are the main causes of decreased muscle function in such patients.4,13 the lower tw in the symptomatic leg compared with the asymptomatic leg during concentric action in patients with ic was previously observed in studies analyzing lower10 and upper leg regions.1 these results may be due to the aerobic nature of the endurance test protocol ( 60 actions ) , which results in maximum flow demands to the leg . therefore , once the symptomatic leg has an arterial obstruction , a lower level of performance is expected in symptomatic as compared with asymptomatic legs . no previous study has evaluated eccentric strength in ic patients , despite the importance of this contraction in the daily activities of elderly people.6 several factors inherent to eccentric action might explain the lack of influence of the disease in terms of the strength and endurance of this action mode . the reduction in eccentric strength with aging seems to be less pronounced than that in concentric strength,1416 suggesting that strength and endurance are better preserved during disease process in eccentric than in concentric action . the similar tw between symptomatic and asymptomatic legs during eccentric action may be partly caused by the lower caloric cost of this mode of contraction.1719 some authors have reported a 14% to 20% lower energy cost in eccentric compared with concentric action.17 thus , the limited blood flow observed in patients with ic has fewer muscle endurance effects in eccentric as compared with concentric action . however , this hypothesis must be analyzed carefully , because no prior study has investigated the net caloric cost of eccentric isokinetic contractions in this population . the reduced muscle strength and endurance have been associated with impaired walking tolerance in ic patients.5 therefore , interventions to improve muscle strength and endurance , such as strength training , might be useful to minimize the effects of the disease on strength and to improve exercise tolerance in patients with unilateral ic . previous studies analyzing the effects of strength training in ic patients that used both concentric and eccentric action during training showed improvements in walking tolerance20 and in quality of life.21 the results of the present study suggest that a strength training program that focuses on concentric strength would probably be most effective for patients with ic . however , the effects of different strength training programs for patients with ic remain unknown . this study highlights the need for future studies to analyze the effects of different strength training programs on concentric muscle strength and endurance , as well as on functional limitations of these patients . since the design of this study did not include a control group , it was not possible to compare muscle strength and endurance of subjects with and without peripheral arterial disease however , it is well known that strength and endurance are influenced by several factors , including both physical activity levels22,23 and associated diseases.24,25 therefore , the inclusion of a control group with different physical activity levels and diseases would not have allowed us to determine the specific effects of ic on strength and endurance . therefore , the use of the asymptomatic leg as the control permitted us to determine the specific effects of the disease in terms of strength and endurance while controlling other possible variables . the present study showed that strength and endurance in the symptomatic leg of patients with intermittent claudication is reduced in concentric , but not in eccentric action as compared to the asymptomatic leg . future studies are recommended to investigate the mechanisms underlying these responses and to analyze the effects of interventions to improve concentric strength and endurance in the context of functional limitations in patients with intermittent claudication .

objective : to analyze concentric and eccentric strength and endurance in patients with unilateral intermittent claudication.introduction:basic motor tasks are composed of concentric , isometric , and eccentric actions , which are related and contribute to physical performance . in previous studies of patients with intermittent claudication , the disease - related reduction in concentric and isometric muscular strength and endurance resulted in poorer walking performance . to date , no study has evaluated eccentric muscle action in patients with intermittent claudication.methods:eleven patients with unilateral intermittent claudication performed isokinetic concentric and eccentric actions at the ankle joints to assess peak torque and total work in both symptomatic and asymptomatic legs.results:concentric peak torque and total work were lower in the symptomatic than in the asymptomatic leg ( 80 32 vs. 95 41 n / m , p = 0.01 ; 1479 667 vs. 1709 879 j , p = 0.03 , respectively ) . there were no differences in eccentric peak torque and total work between symptomatic and asymptomatic legs ( 96 30 vs. 108 48 n / m ; 1852 879 vs. 1891 755 j , respectively).conclusion : strength and endurance in the symptomatic leg were lower during concentric compared to eccentric action . future studies are recommended to investigate the mechanisms underlying these responses and to analyze the effects of interventions to improve concentric strength and endurance on functional limitations in patients with intermittent claudication .

INTRODUCTION MATERIALS AND METHODS Patients Ankle Brachial Index Assessment of muscular strength and endurance Statistical analysis RESULTS DISCUSSION CONCLUSION

descemet s membrane tearing is often attributable to surgical procedures , and is usually confined to the incision site . early in the postoperative period , patients can be asymptomatic , and clinical signs might be difficult to detect . when apparent , descemet s membrane tears and detachments may cause decreased vision and corneal edema in the first days or weeks after surgery . few cases of descemet s detachments occurring late in the postoperative period have been reported , and very rarely months after surgery . wong et al reported a case of a patient who developed a descemet s detachment 8 months after thc : yag ( thulium , holmium , chromium - doped yttrium aluminum garnet crystal ) laser sclerostomy.1 stewart et al reported a case of a descemet s detachment that occurred 5 months after uncomplicated cataract surgery.2 to our knowledge , this is the first report of delayed descemet s tear and detachment occurring 11 months after cataract surgery . a 51-year - old hispanic male was referred to the bascom palmer eye institute cornea service with a complaint of sudden onset of blurred vision in the left eye 3 weeks prior . he had undergone uncomplicated phacoemulsification ( alcon ) with posterior chamber intraocular lens insertion 11 months prior in the left eye and 5 years prior in the right eye . he had been using topical prednisolone acetate 1% and sodium chloride 5% for 3 weeks with no improvement in his symptoms . the exam revealed best - corrected visual acuity of 20/20 in the right eye and 20/40 in the left eye , with a 2.50 sphere at 61. intraocular pressures were 10 mmhg in both eyes by tono - pen . slit - lamp exam ( zeiss ) of the left eye revealed a healed temporal corneal incision wound and abnormal descemet s membrane wrinkling with irregular edges . stromal edema was noted just nasally to this site , which extended centrally through the visual axis ( figure 1 ) . the view of the fundus was hazy in the left eye , but both retinas appeared flat and without lesions , and the optic nerves were unremarkable ( topcon indirect ophthalmoscope ; alcon ma60 posterior chamber lens ) . orbscan pachymetry revealed central corneal thickness of 614 m in the right eye and 878 m in the left eye ( 1,093 m temporally , 702 m nasally ) . topcon keratometry readings of the left eye revealed 2.5 d of astigmatism at 61. specular endothelial microscopy and cell count showed no significant difference between the two eyes ( 2,427 cells / mm oculus dexter , 2,320 cells / mm oculus sinister ; topcon ) . the patient was diagnosed with a spontaneous descemet s dehiscence at the site of the clear cornea cataract incision . as the corneal edema was mild , medical treatment was continued with hyperosmotic saline ointment at bedtime , hyperosmotic drops in the morning , timolol 0.5% daily , and tapering off the prednisolone . he was also instructed to use a hair dryer to the eye in the morning , avoid eye rubbing , and use a protective shield at bedtime . in the subsequent months of follow - up , the corneal edema and visual acuity remained the same . at 7 months after our initial evaluation , the patient reported decreased vision in the left eye associated with pain . the exam revealed a best - corrected visual acuity of 20/200 in the left eye , intraocular pressure of 18 mmhg , and microcystic corneal edema extending from the site of the descemet s tear ( figure 2 ) . a low - lying descemet s detachment could not be ruled out , so surgical intervention with 0.25 ml of 100% sulfur hexafluoride gas injection was elected . one month after the intracameral gas injection , the vision remained at 20/200 and there was no improvement in the corneal edema . penetrating keratoplasty the best surgical option at that time since descemet s stripping endothelial keratoplasty was not available was discussed with the patient , but he decided to continue medical therapy and observation . four months later , he presented with vision of 20/400 in the left eye , persistent corneal edema , and descemet s disruption the remainder of descemet s membrane was partially detached from the corneal stroma ( figure 3 ) . ten years after surgery , the best - corrected visual acuity in the left eye was 20/25 , and the graft remained clear . we report a case of delayed descemet s membrane detachment and tear leading to hydrops 11 months after uncomplicated phacoemulsification using a temporal clear cornea approach . the proximity of the edema to the corneal wound suggests this as the source , despite the fact that the wound had been made 11 months prior , appeared well healed , and had been asymptomatic until 3 weeks prior . known risk factors that may increase the likelihood of traumatic entry into the anterior chamber include oblique angle of entry , anterior and shelved incisions , use of a blunt knife , injection of viscoelastic or antibiotics anteriorly to descemet s membrane , a shallow anterior chamber , soft eye , previous surgery , and recent episode of corneal edema.35 the location of the incision may have contributed to the development of the descemet s membrane tear in this patient . we noted an anterior temporal corneal entry incision wound to the anterior chamber , leading to a descemet s membrane prone to detachment and tear after phacoemulsification . kansal and sugar explored the possibility of an underlying anatomic predisposition for the development of descemet s membrane detachment after phacoemulsification , possibly explained by an abnormality in the fibrillary stromal adhesion to descemet s membrane.6 some patients may have an abnormal attachment between the stroma and descemet s membrane caused by dysfunction of the anchoring protein ig - h3.7,8 the predisposition is more evident in cases of bilateral descemet s membrane detachment after cataract surgery9 and among siblings.10 many mechanisms have been easily attributable to the occurrence of early detachments after cataract surgery . however , the scarce literature on the very few late presentations does not methodically discuss mechanisms responsible for delayed cases , especially when they present with tears . a logical explanation for this unusually late presentation is that he might have traumatized his cornea , eg , by eye rubbing or unnoticed trauma , to a point that he caused further disruption of an already - susceptible descemet s membrane and acute onset of edema in this area . in patients with keratoconus , the central corneal thickness in the right eye appeared relatively high at the time of presentation . however , based on previous readings from the patient , we considered the pachymetry results to be symmetrically conserved , except for the area of edema in the left eye , which was thicker . interestingly , preexistent endothelial dysfunction has been reported as the only significant preoperative risk factor by ti et al.11 the endothelium in both eyes appeared to be normal by specular microscopy , excluding endothelial dysfunction and pseudophakic bullous keratopathy as the cause of hydrops . it is important to be aware of the potential causes of corneal edema months after cataract surgery , in order that they may be diagnosed and treated appropriately . instructing patients to avoid eye rubbing or any other type of trauma to the cornea

a 51-year - old male who had undergone phacoemulsification in his left eye 11 months prior presented with complaint of sudden onset of blurred vision in the same eye . review of his clinical course , slit - lamp exam , pachymetry , and specular endothelial microscopy led to the diagnosis of acute hydrops caused by descemet s membrane dehiscence at the site of the incision . he was initially managed with medical treatment and observation . in the subsequent months of follow - up , the corneal edema and the patient s visual acuity did not improve . intracameral gas injection was performed 7 months after presentation , but because of persistent corneal edema and nonattached descemet s membrane , penetrating keratoplasty was performed . histopathologic examination confirmed the diagnosis . the patient has had a clear corneal graft since then . although descemet s membrane detachment is a rather common complication after intraocular surgery , its unusually delayed presentation can also occur , and should not be confused with pseudophakic bullous keratopathy . many mechanisms have been studied for the development of early tears and detachments after cataract surgery , but little is known about late presentations . the authors explore possible causes , and highlight the importance of instructing patients to avoid eye rubbing and any other type of trauma to the cornea after intraocular surgery .

Introduction Case report Discussion

rasa shastra means the science of mercury but also refers to the preparation of minerals / metals suitable for the body so that they can be used as medicines . minerals such as mercury and arsenic are considered toxic but with proper shodhana ( detoxification ) process , they can be turned into therapeutic medicines . the formulation was prepared and processed properly , the mercury balances all three doshas , has a soothing effect and protects the body from diseases and aging process . it is a vrishya ( aphrodisiac ) , balya ( tonic ) , rasayana ( rejuvenating ) , vrana shodhana , ropana ( wound cleaner and wound healer ) , and krimighna ( anthelmintic and antimicrobial ) . mercury compounded with herb , the mercury heightens the medicinal potential of the particular herb . mercury is said to give a firm physique , a stable mind , and considered to be the destroyer of diseases . herbs were used in the combination with rasa , the efficacy spectrum of herbs increases to a great extent enabling them to treat complicated diseases . rasa shastra has been placed with great importance in ayurveda . shwas kuthar rasa a reputed preparation of ayurveda valued for the treatment of asthma and allergy is a herbomineral formulation contains herbs , purified aconitum ferox ( aconite ) , piper longum ( long pepper ) , piper nigrum ( black pepper ) , and zingiber officinale ( ginger ) , and minerals that is , parada ( mercury ) , gandhaka ( sulfur ) , tankana ( borax ) , and manahsila ( arsenic disulfide ) in purified form as per ayurvedic text . p. longum have a traditional claims of ayurveda for antiallergic and antiasthmatic activity p. nigrum suppressed and reduced the infiltration of eosinophils , hyper responsiveness , and inflammation in mice . z. officinale are capable of inhibiting allergic reactions and is useful for the treatment and prevention of allergic diseases review of literature revealed that shwas kuthar rasa , apart from treating asthma and allergy , is used for the cure of cough , laryngitis , tuberculosis , unconsciousness , mental disorders , comma , chest burn , and heart diseases . none of the work presents the elemental and structural characterization of herbomineral formulation which is an essential requirement to discuss the therapeutic value of mercurial preparations . the present study aims to study the composition and the structure of shwas kuthar rasa a herbomineral formulation using various techniques , viz . , transmission electron microscopy ( tem ) , x - ray diffraction ( xrd ) , far infrared spectroscopy ( fir ) , fourier transform infrared spectroscopy ( ftir ) , energy dispersive x - ray analysis ( edax ) , and inductively coupled plasma - mass spectroscopy ( icp - ms ) . the dried fruit of p. longum and p. nigrum , root of a. ferox , and rhizome of ginger officinale were obtained from amruth kesari herbs , bangalore in february . k. prabhu , botanist , s. c. s. college of pharmacy , harapanahalli ( karnataka ) , india . the herbs voucher specimens ( no : scscop / ph.cog / herb-652 , 717 , 691 , and 572 , respectively ) were deposited in the botany herbarium of the institute . shwas kuthar rasa was prepared using herbal and mineral ingredients as prescribed in ayurvedic text , initially detoxifying the parada ( mercury ) , manahsila ( arsenic disulfide ) , gandhaka ( sulfur ) , tankana ( borax ) , and a. ferox ( vastanabha ) as per given ayurvedic text . equal quantities of shodhit ( detoxified and pure ) parada and gandhaka were taken ( 1:1 ) in a stone mortar in reference amount , triturated for 40 h or until it attained the required kajjalabha ( blackish appearance ) and nishchandra ( lusterless ) state , that is , shining of parada is lost . kajjali was then triturated , with the reference amount of powdered manahsila , vastanabha , tankana , and trikatu ( equal part of black pepper , long pepper , and ginger ) , for 72 h to obtain fine powdered herbomineral formulation shwas kuthar rasa and it was allowed for drying and stored in glass jar . shwas kuthar rasa was subjected to evaluation for physicochemical characters such as loss on drying , ash value , and acid insoluble ash followed by tem ( philips , cem , cm-12 ) was used to study the particle size of shwas kuthar rasa whereby a beam of electrons transmits through an ultrathin specimen , interacting with the formulation . as the beam passes through , an image was formed from the interaction of the electrons transmitted through the specimen , the image was magnified and focused on fluorescent screen , on a layer of photographic film ( saif , chandigarh , punjab ) . the powder xrd patterns of the shwas kuthar rasa were recorded on xpert pro panalytical x - ray diffractometer with cuk radiation ( = 1.5406 a ) operating at 45 kv and 40 ma for the angle ( 2 ) ranging from 5 to 50 at a scanning rate of 3/s . a representative portion of shwas kuthar rasa was placed in an alumina crucible , and the temperature was varied from 40c to 400c . mahwah , nj , usa ) attached to tem ( cem , cm-12 ) was used for the detection of various elements in shwas kuthar rasa ( saif , chandigarh , punjab ) . for the quantitative determination of heavy metals in shwas kuthar rasa in parts per million ( ppm ) , an icp - ms , perkinelmer elan-6000 was used . the infrared ( ir ) spectrum in the low- frequency region ( 50400/cm ) was recorded on a bruker ifs 66 v / s vacuum fourier transform interferometer ; whereas the spectra from 400 to 4000/cm region were recorded using ftir spectrophotometer ( spectrum rxi , perkinelmer ) . for ir spectra , powdered samples were mixed in kbr to make translucent pellet and spectrum was recorded ( saif , chandigarh , punjab ) . the dried fruit of p. longum and p. nigrum , root of a. ferox , and rhizome of ginger officinale were obtained from amruth kesari herbs , bangalore in february . k. prabhu , botanist , s. c. s. college of pharmacy , harapanahalli ( karnataka ) , india . the herbs voucher specimens ( no : scscop / ph.cog / herb-652 , 717 , 691 , and 572 , respectively ) were deposited in the botany herbarium of the institute . shwas kuthar rasa was prepared using herbal and mineral ingredients as prescribed in ayurvedic text , initially detoxifying the parada ( mercury ) , manahsila ( arsenic disulfide ) , gandhaka ( sulfur ) , tankana ( borax ) , and a. ferox ( vastanabha ) as per given ayurvedic text . equal quantities of shodhit ( detoxified and pure ) parada and gandhaka were taken ( 1:1 ) in a stone mortar in reference amount , triturated for 40 h or until it attained the required kajjalabha ( blackish appearance ) and nishchandra ( lusterless ) state , that is , shining of parada is lost . kajjali was then triturated , with the reference amount of powdered manahsila , vastanabha , tankana , and trikatu ( equal part of black pepper , long pepper , and ginger ) , for 72 h to obtain fine powdered herbomineral formulation shwas kuthar rasa and it was allowed for drying and stored in glass jar . shwas kuthar rasa was subjected to evaluation for physicochemical characters such as loss on drying , ash value , and acid insoluble ash followed by tem ( philips , cem , cm-12 ) was used to study the particle size of shwas kuthar rasa whereby a beam of electrons transmits through an ultrathin specimen , interacting with the formulation . as the beam passes through , an image was formed from the interaction of the electrons transmitted through the specimen , the image was magnified and focused on fluorescent screen , on a layer of photographic film ( saif , chandigarh , punjab ) . the powder xrd patterns of the shwas kuthar rasa were recorded on xpert pro panalytical x - ray diffractometer with cuk radiation ( = 1.5406 a ) operating at 45 kv and 40 ma for the angle ( 2 ) ranging from 5 to 50 at a scanning rate of 3/s . a representative portion of shwas kuthar rasa was placed in an alumina crucible , and the temperature was varied from 40c to 400c . mahwah , nj , usa ) attached to tem ( cem , cm-12 ) was used for the detection of various elements in shwas kuthar rasa ( saif , chandigarh , punjab ) . for the quantitative determination of heavy metals in shwas kuthar rasa in parts per million ( ppm ) , an icp - ms , perkinelmer elan-6000 was used . the infrared ( ir ) spectrum in the low- frequency region ( 50400/cm ) was recorded on a bruker ifs 66 v / s vacuum fourier transform interferometer ; whereas the spectra from 400 to 4000/cm region were recorded using ftir spectrophotometer ( spectrum rxi , perkinelmer ) . for ir spectra , powdered samples were mixed in kbr to make translucent pellet and spectrum was recorded ( saif , chandigarh , punjab ) . evaluation of shwas kuthar rasa for organoleptic characters revealed that preparation possess no metallic sound , it is black colored , tasteless , and odorless with no coarse particle . the data of loss on drying , ash value , and acid insoluble ash values were recorded [ table 1 ] . physicochemical characters of shwas kuthar rasa modern analytical techniques were used to observe the effect of the procedure employed in processing of shwas kuthar rasa . particle shape and size from the tem photograph of shwas kuthar rasa shows spongy structure with the irregular particle size lying in the submicron range [ figure 1 ] . from the image , it is clear that nanosize crystallites are agglomerated giving rise to micro sized particles with the loss of grain boundaries . these studies confirm that shwas kuthar rasa is nanocrystallite with submicron size particle ( 1.22 ) . transmission electron microscopy image of shwas kuthar rasa xrd pattern of kajjali [ figure 2a ] shows the peaks due to the presence of free sulfur , mercuric oxide , and mercuric sulfide ( hgs ) ( joint committee on powder diffraction standards [ jcpds ] file number-20 - 1227 , 01 - 0896 , and 02 - 461 , respectively ) while the xrd pattern of shwas kuthar rasa [ figure 2b ] shows the peaks due to major presence of hgs ( jcpds file number-02 - 461 ) , mercuric oxide ( jcpds file number-01 - 0896 ) , and very low intensity of sulfur ( jcpds file number-20 - 1227 ) . no extra diffraction peaks were observed in case of final shwas kuthar rasa formulation confirming that while in the initial stages of the processing of the formulation free sulfur is present in significant amount ; however , after trituration process , the major amount of hgs and mercuric oxide remains in the product . the diffraction peaks in the xrd pattern of shwas kuthar rasa corresponding to hgs become sharper and intense compared to kajjali sample as well as some new peaks appeared due to hgs , which were not present in the kajjali sample . this observation confirms that the trituration of kajjali helps in the formation of hgs and increases the crystallinity in the sample . the crystallite size was calculated from xrd pattern following the scherrer equation t = 0.9/( cos ) . here t is the crystallite size for ( h k l ) plane , is the wavelength of the incident x - radiation ( cuk [ = 1.5406 a ] ) , is the full width at half maximum ( fwhm ) in radians , and is the diffraction angle for ( h k l ) plane . it is notable , here , the fwhm in case of kajjali is high in comparison to the finally prepared shwas kuthar rasa confirms that the size of the crystallite increases . x - ray diffraction pattern of ( a ) kajjali and ( b ) shwas kuthar rasa in addition , the metal hg and as used as ingredients , other metals like calcium is also expected in the drug that enters in it during its trituration process while carryout the detoxification of individual herbs and metals . edax has been used to detect the presence of elements in considerable amount , whereas icp - ms was used to detect elements hg and as in trace amount . chemical compositions of shwas kuthar rasa using edax and trace metal composition of shwas kuthar rasa using icp - ms have been listed [ table 1 ] . abundance of c ( 31.24% ) , n ( 12.40% ) , and o ( 42.63% ) in the drug was observed which is obviously from the herbs used in the preparation of the formulation . ca ( 1.62% ) conducive to healthy metabolism and preventive for stomach lesions was also found to be present in the final shwas kuthar rasa product . na ( 2.37% ) needed for maintaining normal fluid balance is also present in the final product [ table 1 ] . these elements ( ca , na , and s ) act as additional supplement improving the curative properties of the formulation . other elements such as h ( 4.65% ) and cl ( 3.46% ) were also found in the formulation . concentration of heavy metals was found 0.94 ppm for hg and 8.78 ppm for as , which were well within the safe limits recommended by who . thus , the additional element present in the drug is clearly due to the botanical origin . it is notable that the proportion / concentration of mercury in shwas kuthar rasa does not seem to follow a consistent trend , and some of mercury is certainly lost during the preparation through direct trituration process . this raises the safety concerns pertaining to the use of mercury and may require additional work on the processing technique employed in the preparation of rasas . fir spectrum of shwas kuthar rasa in the region from 50 to 400/cm was studied [ figure 3 ] . crystalline hgs is known to have absorption at 83 , 92 , and 100/cm and their presence in the present fir spectra indicate that shwas kuthar rasa is essentially hgs . ftir spectrum of shwas kuthar rasa in the region from 400 to 4000/cm is shown [ figure 4 ] . there are fairly sharp peaks at 708 , 1080 , 1131 , 1253 , 1346 , 1440 , 1634 , 2930 , and 3363/cm which indicate the presence of the organic compounds in the formulation . the presence of appreciable concentrations of c , h , o , and n [ table 1 ] also suggests the presence of organic molecules in the drug . it would not be unexpected if the organic molecules also play an important role in the medicinal properties of these drugs . far infrared spectroscopy spectrum of shwas kuthar rasa fourier transform - infrared spectrum of shwas kuthar rasa macro particle size of the preparation may be attributed to the trituration of detoxified metals , nonmetals , and herbs for a long duration which causes the change in the chemical nature of materials . this could be due to the formation of organometallic complexes in the drug sample that can sustain even at the high processing temperature of herbomineral drugs . several significant possibilities and future prospects of the drug could be debated with these results . the macro particle size of the drug matches well with the colloidal size and this suggest the possibility that these colloidal particles are get attached to the human intestine and provide a large surface area thereby increasing the absorption of other nutrients and drugs , which are added to it during the process of preparation or prescribed to the patient along with them . further , metal ingredients act as the carrier of the herb derived organic matter used during the pharmaceutical processing . in short , metals as a carrier for the organic contents from a. ferox , p. nigrum , p. longum , and z. officinale are known to be useful in the treatment of asthma , allergy , cough , inflammation , etc . from xrd studies , shwas kuthar rasa concluded that hgs in nanocrystalline range ( 3156 nm ) , in association with organic molecules probably plays an important role in making it biocompatible and nontoxic at therapeutic doses . other elements present in shwas kuthar rasa act as additional supplement and possibly help in increasing the efficacy of the formulation . shwas kuthar rasa herbomineral formulation revealed the presence of crystalline hgs associated with several organic macromolecules derived from the herbs as basic ingredients of formulation . in addition , several elements were also found in varying concentrations , which bioavailability enhanced and thus responsible for therapeutic value addition of shwas kuthar rasa .

background : shwas kuthar rasa is a prestigious and potential herbomineral formulation of ayurveda tested on 100 years of time scale for the treatment of asthma , allergy , and other respiratory problems . however , there is a lack of scientific work on shwas kuthar rasa.objective:to prepare and physicochemically evaluate mercury - based shwas kuthar rasa herbomineral formulation of ayurveda for asthma and allergy.materials and methods : shwas kuthar rasa was prepared as per ayurvedic text and characterized by various modern analytical techniques , viz . , transmission electron microscopy ( tem ) , x - ray diffraction ( xrd ) , far infrared ( ir ) spectroscopy , fourier transform ir spectroscopy , energy dispersive x - ray analysis , and inductively coupled plasma - mass spectroscopy.results:study clearly revealed that prepared shwas kuthar rasa formulation shows several crystallites agglomerate into a single particle . it yields submicron size particle structure ( 1.22 ) with tem analysis . the usage of mercury in the formulation found in the form of mercuric sulfide ( hgs ) and reaching to nanocrystalline ( 3156 nm ) size by xrd analysis.conclusion:the present study indicates shwas kuthar rasa is nanocrystallite with submicron size particle . trituration of kajjali helps in the formation of hgs and increases the crystallinity in the formulation .

INTRODUCTION MATERIALS AND METHODS Plant materials Preparation of Structural and physicochemical characterization RESULTS DISCUSSION CONCLUSION Financial support and sponsorship Conflicts of interest

alagille syndrome is clinically defined by neonatal cholestatic jaundice with intrahepatic bile duct hypoplasia associated with additional findings , including a characteristic facies , peripheral pulmonary artery stenosis , butterfly - like vertebral anomalies , and ocular abnormalities . ocular findings include posterior embryotoxon , iris abnormalities , optic disc anomalies , and fundus changes ( irregular pigmentation at the level of the retinal pigment epithelium , diffuse hypopigmentation , and punched out chorioretinal atrophy).1,2 to our knowledge , there are no cases in the literature presenting with alagille syndrome and chorioretinal atrophy involving the macula , as examined by optical coherence tomography ( oct ) and fundus autofluorescence . herein , we report oct and fundus autofluorescence changes in a patient with this syndrome . an 11-year - old girl with alagille syndrome was referred to the jichi medical university hospital before a liver biopsy during observation after liver transplantation . liver transplantation was performed at the age of 20 months , and left pulmonary artery balloon dilation was performed at the age of 8 years . she had an unusual triangular facies characterized by a broad overhanging forehead , deep - set hyperteloric eyes , and a small pointed chin . best - corrected visual acuity in the right eye was 12/20 with 6.25 d 1.0d 90 , and in the left eye was 8/20 with 4.25 d 2.0 d 90. the patient was orthophoric and showed normal ocular movements . on slit lamp examination , funduscopy showed diffuse choroidal hypopigmentation with increased visibility of the choroidal blood vessels and symmetric well circumscribed macular discoloration ( figure 1 ) . decreased retinal thickness was seen on oct ( rs-3000 , nidek , japan ) . on the basis of macular etdrs ( early treatment diabetic retinopathy study ) sectors , thickness of the center ( central fovea ) , inner ring ( 13 mm from the central fovea ) and outer ring ( 36 mm from the central fovea ) were 222 m , 254.8 m , and 241.0 m , respectively , in the right eye . in the left eye , in particular , the outer retinal ( nuclear ) layer and the photoreceptor inner segment / outer segment junctions were irregular and discontinuous , corresponding to macular discoloration ( figures 2 and 3 ) . foveal architecture was preserved in both eyes with thinning . in high - magnification oct images , the border between the chorioretinal atrophy and the hypopigmented area of the macula was clearly defined . the outer retinal thickness in the chorioretinal atrophic area was thinner than that in the hypopigmented area . fundus autofluorescence imaging ( heidelberg retina angiograph 2 , heidelberg , germany ) showed hypofluorescent areas in the peripapillary regions extending along the macula corresponding to the chorioretinal atrophy . these had an appearance similar to a sleep mask ( figure 4 ) . a mottled pattern of hyperautofluorescent areas was also detected in the macula . visual field testing with goldmann perimetry only showed enlargement of the blind spots in both eyes . serum vitamin a and vitamin e levels were 94 ( normal range 97316 ) iu / dl and 0.51 ( normal range 0.751.41 ) mg / dl , respectively . in the largest series of patients with alagille syndrome , hingorani et al1 evaluated 22 patients with the condition . the most common ocular abnormalities in alagille syndrome were posterior embryotoxon ( 95% ) , iris abnormalities ( 45% ) , diffuse fundus hypopigmentation ( 57% ) , speckling of the retinal pigment epithelium ( 33% ) , and optic disc anomalies ( 76%).1 in studying retinal changes in alagille syndrome , hingorani et al1 reported that irregular pigmentation at the level of the retinal pigment epithelium , most often manifested as a speckling or granularity of the retinal pigment epithelium , was distributed diffusely in the mid peripheral / peripheral zone.1 the few reports concerning macular changes in alagille syndrome describe symmetric , well circumscribed , horizontally oval areas of speckled reddish brown macular discoloration,2 pigment clumping in the macula,3 and circumpapillary geographic chorioretinal atrophy with half - moon shapes involving the macular area.4 however , chorioretinal atrophy involving the macular area is rare . in this case , diffuse choroidal hypopigmentation with increased visibility of the choroidal vessels and a sleep mask - like hypofluorescent area corresponding to chorioretinal atrophy as examined by fundus autofluorescence were detected . to our knowledge , there are no similar cases in the literature of alagille syndrome presenting a chorioretinal atrophy involving the macula with a sleep mask appearance as examined by oct and fundus autofluorescence . a possible explanation for chorioretinal atrophy in alagille syndrome is failure of absorption of fat - soluble vitamins . romanchuk et al5 suggested that failure of fatsoluble vitamin absorption plays a major role in the evolution of retinopathy in alagille syndrome . the retinoid cycle is a vitamin a - linked metabolic circuit which occurs between the outer segment of the photoreceptor and the retinal pigment epithelium to maintain visual function . low serum vitamin e levels have been well documented in children with malabsorption due to cholestatic liver diseases.6 the role of vitamin e in vision is less clear , but it is believed to have an important protective function as a lipid antioxidant for the extremely high concentrations of polyunsaturated fatty acids found in the outer segments . increases in the number of lipofuscin granules in the cytoplasm of retinal pigment epithelium in vitamin e - deficient rats were observed.7 the retinal pigment epithelium cells of the peripheral and equatorial zone contain large numbers of lipofuscin granules within their cytoplasm.8 thus , both of these vitamins are believed to be important in maintaining the integrity of the photoreceptor outer segments and the retinal pigment epithelium cells . fundus autofluorescence has been investigated in various fundus diseases associated with changes in the retinal pigment epithelium . fundus autofluorescence is presumed to derive from lipofuscin in retinal pigment epithelium cells and to represent metabolic activity of retinal pigment epithelium involving turnover of photoreceptor outer segments . hypofluorescence is thought to correspond to areas of decreased metabolism resulting from photoreceptor and/or retinal pigment epithelium atrophy , and has been used as a marker of the integrity of the retinal pigment epithelium / photoreceptor complex . the peculiar findings in this patient were abnormalities of the inner segment / outer segment junction and the outer segments of photoreceptors , suggestive of loss of structural integrity of the photoreceptors . therefore , we suggest that transient hypovitaminosis due to alagille syndrome early in life might contribute to the retinal degeneration seen in this case . finally , anatomic evidence of retinal degeneration induced by vitamin a or e deficiencies suggests that the structural disruption of photoreceptors is more advanced in cones and most pronounced in the macula , with lesser involvement of the peripheral retina.9 however , it is not clear whether our case represents a congenital or acquired change due to alagille syndrome .

we report the first case in the literature of chorioretinal atrophy involving the macula in an 11-year - old girl with alagille syndrome , as examined by optical coherence tomography , and fundus autofluorescence imaging . funduscopy revealed diffuse choroidal hypopigmentation with increased visibility of the choroidal vessels and symmetric , well circumscribed macular discoloration . anomalous oblique configuration of the optic disc and peripapillary tortuous vessels were also detected . optical coherence tomography demonstrated decreased retinal thickness , especially the outer retinal layer , and the photoreceptor inner segment / outer segment junctions were irregular and discontinued , corresponding to macular discoloration . fundus autofluorescence imaging clearly defined hypofluorescent areas in the peripapillary regions that extended along the macula and had a sleep mask appearance . we suggest that transient hypovitaminosis due to alagille syndrome early in life might contribute to the retinal degeneration seen in this case .

Introduction Case report Discussion

animals studies and preparations : all animal procedures were performed in accordance with the guidelines of the institutional animal care and use committee of seoul national university ( snu-111115 - 4 ) . both eyes of 25 clinically normal laboratory beagle dogs were used in this study . complete ophthalmic examinations were performed before the experiment using a rebound tonometer ( tonovet , tiolat , helsinki , finland ) , schirmer tear test ( schirmer tear test , schering - plough animal health , kenilworth , nj , u.s.a . ) , slit - lamp biomicroscope ( topcon sl - d7 , topcon corp . , tokyo , japan ) and indirect ophthalmoscope ( vantage , keeler instruments inc . , broomall , pa , u.s.a . ) with a 30-diopter indirect lens ( classic bio lens , volk optical inc . , mentor , oh , u.s.a . ) . to investigate changes in cct according to stepwise increases in iop compared with a fixed normal iop , 30 eyes of 15 dogs were used . the remaining eyes were used to investigate changes in cct according to a fixed increase in iop ( 30 , 45 , 60 and 75 mmhg ) . before induction of anesthesia , atropine eye drops ( ocutropine , samil , gyeonggi , south korea ) , a combination of phenylephrine and tropicamide eye drops ( mydrin - p , saten pharmaceutical , osaka , japan ) , a combination of dexamethasone , polymyxin b and neomycin eye drops ( maxitrol , s.a . , puurs , belgium ) and flurbiprofen eye drops ( ocufen , allergan sales llc , waco , tx , u.s.a . ) were all applied twice to achieve mydriasis and reduce inflammation induced by anterior chamber paracentesis . acepromazine 0.03 mg / kg ( sedaject , samwoo medical , chungnam , south korea ) , cefazoline 30 mg / kg ( ckd cefazolin inj . , chong kun dang , gyeonggi , south korea ) and dexamethasone 0.3 mg / kg ( je il dexamethasone inj . , je il pharmaceutical , daegu , south korea ) were administered intravenously 5 min before anesthesia induction using propofol ( provive 1% , claris lifesciences , ahmedabad , india ) . co. , ltd . , gyeonggi , south korea ) and oxygen . during anesthesia , ecg , pulse oxymetry , noninvasive blood pressure , end tidal co2 , capnography and temperature ( with a digital thermometer ) were monitored . after induction of anesthesia , the dog was laid in a dorsoventral position during the experiment . to induce extraocular muscle akinesia and prevent pain , retrobulbar injection of 2 ml of 2% lidocaine ( je il lidocaine injection ( 2% ) , je il pharmaceutical ) was performed with a 23-gauge retrobulbar needle in each eye using the inferior - temporal palpebral technique . in cases with inadequate extraocular muscle akinesia , a second injection of 1 ml of 2% lidocaine was performed 10 min after the first injection . an eye speculum was placed to expose the cornea after induction of extraocular muscle akinesia . the exposed cornea was frequently lubricated with 0.5% sodium carboxymethyl cellulose ( refresh plus , allergan sales llc ) to prevent corneal desiccation during the experiment . the anterior chamber was entered with two 26-gauge needles through the limbus ( 2 and 10 oclock positions ) for each eye . cyanoacrylate glue ( 3 m vetbond , 3 m animal care products , st . paul , mn , u.s.a . ) was used to prevent leakage from the entry site after needle insertion . one needle was connected to a normal saline reservoir containing 5 iu per milliliter of heparin through a polypropylene line . the other needle was connected to a pressure transducer system for iop measurement through a polypropylene line and contained normal saline with 5 iu per milliliter of heparin . the system comprised a pressure monitoring kit ( transpac iv monitoring kit , icu medical , inc . , san clemente , ca , u.s.a . ) with a transducer , polyethylene tubes , monitoring cable ( transpac reusable cable , hospira , inc . , lake forest , il , u.s.a . ) and a monitor ( datex - ohmeda s/5 , helsinki , finland ) for continuous monitoring of iop ( fig . 1fig . the transducer was positioned at eye level . before each experiment , the transducer was calibrated to a mercury manometer , and a zero balance was set using the manufacturer s instructions . procedures for stepwise increase of iop and fixed normal iop : thirty eyes of 15 dogs were randomly assigned to groups t and c15 . in group t , the iop of 1 eye per dog was adjusted to 10 mmhg immediately after cannulation and was then raised in increments of 10 mmhg until a maximum iop of 70 mmhg . cct was measured with an ultrasonic pachymeter ( pachmate dgh 55 , dgh technology , exton , pa , u.s.a . ) the iop in the other eye was adjusted to 15 mmhg ( group c15 ) immediately after cannulation , which was maintained throughout the experiment . an ultrasonic pachymeter was also applied every 10 min in the same manner as for group t. procedures for fixed increase of iop : twenty eyes of 10 dogs were randomly assigned to groups c30 , c45 , c60 and c75 . the iop was respectively adjusted to 30 , 45 , 60 and 75 mmhg in these groups immediately after cannulation and was maintained throughout the experiment . an ultrasonic pachymeter was also applied every 10 min in the same manner as for groups t and c15 . ind . , gyeonggi , south korea ) and gentamicin 8 mg / kg ( kukje gentamicin inj . ind . ) were injected into the subconjunctiva to reduce inflammation and infection after the experiment . a combination eye drop comprising dexamethasone , polymyxin b and neomycin statistical analysis : statistical analysis was performed using pasw statistics 18 for windows ( spss inc . , cct data were expressed as the mean se ( standard error ) , and the level of significance used was p<0.05 . in one - way repeated measures anova following pairwise comparison , bonferroni adjustment was performed to evaluate the variation in cct values against time in the same group and to evaluate variation in the difference in cct ( dcct ) from baseline ( 10 min after cannulation ) against time , which was compared with dcct at the same time point between groups . tables 1 and 2table 1.central corneal thickness ( cct ; microns ) changes according to experimental adjustment of iopthe timeafter cannulation ( min)iop of t group(mmhg)tc15*c30*c45*c60*c75 * 1010519.8 15.0513.9 15.0508.1 23.3487.7 23.3513.3 23.3480.2 23.32020516.3 15.1513.6 15.1500.4 23.1479.5 23.1519.4 23.1490.8 23.13030512.2 14.9514.2 14.9494.2 22.9482.5 22.9531.5 22.9504.7 22.94040511.7 15.1513.9 15.1494.7 23.0486.8 23.0544.9 23.0512.2 23.05050519.1 15.6513.6 15.6494.3 23.4498.5 23.4557.3 23.4524.1 23.46060529.8 15.4512.3 15.4494.3 23.4504.1 23.4561.9 23.4532.7 23.47070535.3 15.2515.3 15.2495.3 23.4513.3 23.4581.1 23.4545.5 23.4data for cct are expressed as the mean se ( standard error ) . a ) values in the same column with this superscript are significantly different ( p<0.05 ) compared with the cct at 10 min . b ) values in the same column with this superscript are significantly different ( p<0.05 ) compared with the cct at 20 min from 30 min onward . c ) values in the same column with this superscript are significantly different ( p<0.05 ) compared with the cct at 30 min from 40 min onward . d ) values in the same column with this superscript are significantly different ( p<0.05 ) compared with the cct at 40 min from 50 min onward . e ) values in the same column with this superscript are significantly different ( p<0.05 ) compared with the cct at 50 min from 60 min onward . f ) values in the same column with this superscript are significantly different ( p<0.05 ) in cct at 70 min compared with that at 60 min . * the iops of groups c15 , c30 , c45 , c60 and c 75 were maintained at 15 , 30 , 45 , 60 and 75 mmhg , respectively , during the experiment . show the results of one - way repeated measures anova following pairwise comparison with bonferroni adjustment of the cct and dcct , respectively . there was a significant difference in the effect of time on cct ( p<0.001 ) and dcct ( p<0.001 ) between groups . there was no significant difference in the effect of time on cct in group c15 ( p=0.729 ) . however , there was a significant difference in the effect of time on cct in group t ( p<0.001 ) . the cct in group t initially decreased until 40 min and then began to increase . the cct in group t was unchanged at 20 min compared with at 10 min . however , the ccts at 30 ( p=0.006 ) and 40 min ( p=0.028 ) were significantly thinner than that at 10 min in group t. furthermore , the ccts at 50 , 60 and 70 min were significantly thicker than those at 30 and 40 min in group t. there was a significant difference in the effect of time on cct in group c30 ( p=0.032 ) . the cct in group c30 was unchanged at 20 min compared with at 10 min . however , the ccts at 30 ( p=0.003 ) and 40 min ( p=0.045 ) were significantly thinner than that at 10 min in group c30 . there was a significant difference in the effect of time on cct in group c45 ( p<0.001 ) . the cct in group c45 was unchanged at 40 min compared with at 10 min and then showed a significant increase . the ccts in group c45 at 20 , 30 and 40 min were significantly thinner than those at 50 , 60 and 70 min there was a significant difference in the effect of time on cct in group c60 ( p<0.001 ) and group c75 ( p<0.001 ) . the cct in group c60 was unchanged at 20 min compared with at 10 min and then showed a significant increase , except at 50 min to 60 min . the cct in group c75 showed a steady significant increase after cannulation , except at 30 min to 40 min . a ) values in the same column with this superscript are significantly different ( p<0.05 ) compared with the cct at 10 min . b ) values in the same column with this superscript are significantly different ( p<0.05 ) compared with the cct at 20 min from 30 min onward . c ) values in the same column with this superscript are significantly different ( p<0.05 ) compared with the cct at 30 min from 40 min onward . d ) values in the same column with this superscript are significantly different ( p<0.05 ) compared with the cct at 40 min from 50 min onward . e ) values in the same column with this superscript are significantly different ( p<0.05 ) compared with the cct at 50 min from 60 min onward . f ) values in the same column with this superscript are significantly different ( p<0.05 ) in cct at 70 min compared with that at 60 min . * the iops of groups c15 , c30 , c45 , c60 and c 75 were maintained at 15 , 30 , 45 , 60 and 75 mmhg , respectively , during the experiment . there was a statistically significant difference in dcct between groups c15 and c70 at 20 min ( p=0.040 ) . the dccts in groups c60 ( p=0.031 ) and c75 ( p=0.001 ) were significantly thicker than that in group c30 at 20 min . the dccts in groups c60 and c75 were also significantly thicker than those in groups t , c15 , c30 and c45 at 30 , 40 , 50 , 60 and 70 min . there was a statistically significant difference in dcct between groups c15 and c30 at 30 min ( p=0.010 ) . there were also statistically significant differences in dcct between groups t and c30 at 60 ( p=0.012 ) and 70 min ( p=0.016 ) . there were statistically significant differences in dcct between groups c30 and c45 at 50 ( p=0.024 ) , 60 ( p=0.008 ) and 70 min ( p=0.005 ; table 2table 2.difference in cct ( dcct ; microns ) from baseline value according to experimental adjustment of iopthe timeafter cannulation ( min)iop of t group(mmhg)tc15*c30*c45*c60*c75 * 10(baseline)1000000020203.5 1.70.3 1.77.7 3.08.2 3.06.1 3.010.6 3.030307.6 1.90.3 1.913.9 3.45.1 3.418.1 3.424.4 3.440408.1 2.40.0 2.413.4 4.10.9 4.131.5 4.132.0 4.150500.7 3.00.3 3.013.8 5.110.8 5.244.0 5.243.8 5.2606010.0 3.31.5 3.313.8 5.716.4 5.748.6 5.752.5 5.7707015.5 4.01.4 4.012.9 7.025.6 7.067.7 7.065.2 7.0data for dcct are expressed as the mean se ( standard error ) . a ) values in the same row with this superscript are significantly different ( p<0.05 ) compared with the group t. b ) values in the same row with this superscript are significantly different ( p<0.05 ) compared with the group c15 . c ) values in the same row with this superscript are significantly different ( p<0.05 ) compared with the group c30 . d ) values in the same row with this superscript are significantly different ( p<0.05 ) compared with the group c45 . e ) values in the same row with this superscript are significantly different ( p<0.05 ) compared with the group c60 . f ) values in the same row with this superscript are significantly different ( p<0.05 ) compared with the group c75 . * the iops of groups c15 , c30 , c45 , c60 and c75 were maintained at 15 , 30 , 45 , 60 and 75 mmhg , respectively , during the experiment . ) . a ) values in the same row with this superscript are significantly different ( p<0.05 ) compared with the group t. b ) values in the same row with this superscript are significantly different ( p<0.05 ) compared with the group c15 . c ) values in the same row with this superscript are significantly different ( p<0.05 ) compared with the group c30 . d ) values in the same row with this superscript are significantly different ( p<0.05 ) compared with the group c45 . e ) values in the same row with this superscript are significantly different ( p<0.05 ) compared with the group c60 . f ) values in the same row with this superscript are significantly different ( p<0.05 ) compared with the group c75 . * the iops of groups c15 , c30 , c45 , c60 and c75 were maintained at 15 , 30 , 45 , 60 and 75 mmhg , respectively , during the experiment . although iop can be a factor in cct variation , there are few experimental studies that have investigated this relationship in either animals or humans [ 12 , 24 ] . the current study showed that cct varied according to different experimental adjustments of iop . also , a significant decrease in dcct in group c30 compared with c15 was identified at 30 min . however , in groups t , c45 , c60 and c75 , it appears that the cct ultimately increased after passing the critical pressure . comparing groups c45 , c60 and c75 , there is evidence to say the duration and degree of increase in iop was a factor contributing to the increase in cct . in previous human studies , there was no obvious change in cct when the iop was increased by approximately 10 mmhg , although the duration of the increase in iop was only 5 min . a similar result was found in the current study with no statistical difference in cct values between 10 and 20 mmhg in group t. however , a significant difference in cct was shown in this group when the iop was elevated above 30 mmhg , which is adjacent to the upper limit of the physiologically normal iop . olsen suggested that iop showed a dual effect on corneal thickness according to corneal endothelium conditions in human patients with acute glaucoma . first , cct decreases in response to an increase in iop in the intact corneal endothelium , and second , it increases in the acutely damaged corneal endothelium . ehlers et al . documented that cct in eyes with a low iop was thicker than that in contralateral normal eyes in human patients with retinal detachment . initially , cct gradually decreased with an increase in iop until 40 min ( 40 mmhg ) in group t. the ccts at 30 and 40 min were significantly different from that at 10 min in group t. however , cct was increased from 50 min ( 50 mmhg ) to 70 min ( 70 mmhg ) in group t. the ccts at 30 and 40 min were significantly different from those at 50 , 60 and 70 min in group t. the initial decrease in cct according to elevated iop is associated with microsturctural changes in the corneal anterior stroma . the anterior stroma is more resistant to corneal hydration , and the transverse collagen lamellae of the anterior stroma are short [ 3 , 23 ] . an initial decrease in cct can be caused by immediate loss of anterior stromal interlamellar gaps with increasing iop in rabbits . abnormal thickening of the cornea presents as corneal edema , which can appear when the iop is above 40 mmhg in human glaucoma patients . in this study , cct increased after iop passed the lowest point of 40 mmhg ( 40 min ) in group t , and significant differences in cct were also observed between ccts in group c45 at 20 min and 50 min . therefore , it can be proposed that corneal endothelial decompensation was initiated at an iop of 40 to 45 mmhg in normal canine eyes . the duration and degree of increased iop should also be considered when assessing the initiation of thickening of the cct . in group c45 also , there were significant increases in cct beginning at 30 min and 20 min in groups c60 and c75 , respectively . furthermore , there were significant increases in dcct compared with group c15 beginning at 30 min and 20 min in groups c60 and c75 , respectively . therefore , the initiation of thickening of the cct was influenced by the duration and degree of iop increase . a high degree of iop may cause thickening of the cct to occur rapidly . in humans , a thin cct was considered a risk factor for glaucoma in the ocular hypertension treatment study . this relationship might be partially explained when considering the effect of cct on iop measurement . although the effect of cct was different with each type of tonometer used , the measured iop can be lower than the real iop in both humans and dogs with a thin cct [ 2 , 10 , 19 ] . therefore , glaucoma patients with a thin cct can be measured as having a normal iop when using tonometry . cct is also correlated with the development of glaucomatous visual field loss in humans [ 9 , 13 , 16 ] . although this study was performed over a short duration ( 70 min ) , the results support that thin cct can be a promising source for diagnosis and monitoring of glaucoma in dogs . thinning of the cornea was not correlated with tonometer readings in this study , because manometric values were used . although the reductions in cct were quite small , there were significant differences in cct between 10 min and 30 min in groups t and c30 . cct itself changed with an increased iop , exhibiting an initial decrease and then a subsequent increase . in this study , changes in cct according to experimental adjustment of iop were documented , and the possibility of using cct as a diagnostic and monitoring factor for canine glaucoma was suggested . this study provides basic data to enable further investigation of the relationship between cct and iop in dogs .

abstractcentral corneal thickness ( cct ) can be a promising source of glaucoma monitoring and diagnosis . this study evaluated changes in cct according to experimental adjustment of intraocular pressure ( iop ) in canine eyes . to adjust and measure iop , each eye was cannulated with two 26-gauge needles under inhalant anesthesia . one needle was connected to a pressure transducer , and the other was connected to an adjustable bag of physiologic saline . iop was stepwise increased from 10 mmhg to 70 mmhg in 10 mmhg increments ( group t ) . iop was maintained at 15 mmhg ( group c15 ) , 30 mmhg ( group c30 ) , 45 mmhg ( group c45 ) , 60 mmhg ( group c60 ) and 75 mmhg ( group c75 ) during the experiment . cct was measured with an ultrasonic pachymeter every 10 min after cannulation . there was a significant difference in the effect of time on cct ( p<0.001 ) and difference in cct ( dcct ; p<0.001 ) between groups . the cct of group c15 remained constant during the experiment . however , group t showed an initial decrease and then an increase after passing the lowest point . group c30 showed decreasing values for 30 min , after which the values remained constant . the values in group c45 showed no changes for 40 min and then increased . the values in group c60 showed no change for 20 min and then increased . group c75 showed a steady increase . in conclusion , the cct showed two core changes according to increased iop . this study provides essential basic data to enable further investigation into the association of iop and cct in dogs .

MATERIALS AND METHODS RESULTS DISCUSSION

f. mangiferae isolated from malformed floral tissues of dashehri cultivar of mango demonstrated light purple in addition white colony color . microscopic study f. mangiferae revealed the presence of micro- and macro - conidia , however chlamydospores were entirely absent . both the micro- and macro - conidia may germinate at a suitable temperature ( 27 c ) and reproduce mycelial mat consisting of long septate hyphae ( fig . 3-septate and 4-celled macroconidia were 34.8% , whereas 45 septate and 56 celled macroconidia were 4.2% . the oval - to - elliptical shaped aseptate microconidia were present in large numbers ( 73.7% ) , however few microconidia partitioned with septa ( 1 septate ) ( 11.2% ) were also observed ( fig . the length and width of micro- and macro - conidia were 7.5 , 55 , 3.2 , and 3.5 , respectively ( fig . a ) the pure colony of f. mangiferae obtained from malformed floral tissues of mango cv dashehri via single spore isolation technique depicting light purple along with white color . the crescent - shaped and usually 3-septate or rarely 45 septate macroconidia , as well as oval- to elliptical - shaped microconidia , either devoiding of septum or a few consisting one septum , were present . both the conidia showing germination in vitro at suitable temperature ( 27 c ) leading to the development of mycelial mat showing a long septate hyphae . ( b ) the type and number of conidia may vary in axenic suspension culture of f. mangiferae . ( c ) the length of micro- and macro - conidia was 7.5 and 55 , respectively . ( d ) the width of micro- and macro - conidia was confined to 3.2 and 3.5 , respectively . the plant growth regulators viz . , naphthalene acetic acid ( naa ) and gibberellic acid ( ga3 ) naphthalene acetic acid ( naa ) and gibberellic acid glutathione ( ga3 ) were observed to have stimulatory effect on conidia germination of f. mangiferae after 12h of incubation at 27 c . with increasing concentration of naa ( 0500 ppm ) , germination of conidia of f. mangiferae were recorded at 500 ppm ( 69.62% ) with respect to control , as well as 25 ppm naa ( 69.49% ) ( fig . likewise , the treatment of ga3 resulted into inductive response on condial germination of f. mangiferae . conidia germination was progressively increased with raising the ga3 concentration ( 0500 ppm ) , and the response was higher at 500 ppm ( 89.66% ) as compared with control ( 70.86% ) ( fig . similar trends were observed in the case of 6-benzylaminopurine ( bap ) and ethylene releasing agent ( ethrel ) applied to conidia of f. mangiferae , where conidia germination were steadily increased with elevated concentration of bap and ethrel and were greatest ( 100% and 99.86% ) at 400 , 500 ppm bap and 150 ppm ethrel with respect to untreated ( control ) ( fig . evaluation of conidia germination of f. mangiferaein vitro under varying concentration of plant growth regulators . ( a ) naphthalene acetic acid ( naa ) ( 500 ppm ) promotes conidia germination to 82.47% from 69.49% and 69.62% at 25 ppm and untreated control , respectively after 12 h. ( b ) the stimulatory effect of gibberellic acid ( ga3 ) was detected and the germination was highest ( 89.66% ) in conidia treated with 500 ppm gibberellic acid ( ga3 ) , whereas it was least ( 70.79% ) at 25 ppm ga3 , after 12 h. ( c d ) the 6-benzylaminopurine ( bap ) and ethylene - releasing compounds , such as ethrel , consistently induced conidial germination of f. mangiferae with their increasing concentrations . condial germination was 100% beyond 300 ppm bap , while ethrel at 150 ppm was highly effective ( 99.86% conidia germination ) , after 12 h. a role of antimolformin chemicals , such as silver nitrate ( agno3 ) and glutathione , were evaluated in vitro for their effect on conidial germination of f. mangiferae . silver nitrate ( agno3 ) in varying concentrations ( 25 , 50 , 75 , 100 , 150 , 200 , 250 , 300 , 400 , and 500 ppm ) showed inhibitory effect on conidia germination of f. mangiferae . however , inhibition was maximum with 400 ppm ( 1.8% ) and conidia germination was nil over 500 ppm , as compared with control ( 70.02% ) after 24h ( fig . the effect of glutathione on conidia germination of f. mangiferae was assessed and found that it stimulates the conidial germination of f. mangiferae with increasing concentration of glutathione ranging from 25 ppm to 1200 ppm . the conidial germination was highest at 1200 ppm ( 92.7% ) after 24h ( fig . the response of germination of f. mangiferaein conidia in vitro under defined concentration of antimalformins after 24h . ( a ) the maximum inhibition was recorded at silver nitrate ( agno3 ) above 400 ppm ( 1.8% ) and conidia germination was nil over 500 ppm . ( b ) glutathione stimulates the conidial germination from untreated control ( 70.4% ) to 1200 ppm ( 92.7% ) . f. mangiferae isolated from malformed floral tissues of dashehri cultivar of mango demonstrated light purple in addition white colony color . microscopic study f. mangiferae revealed the presence of micro- and macro - conidia , however chlamydospores were entirely absent . both the micro- and macro - conidia may germinate at a suitable temperature ( 27 c ) and reproduce mycelial mat consisting of long septate hyphae ( fig . 3-septate and 4-celled macroconidia were 34.8% , whereas 45 septate and 56 celled macroconidia were 4.2% . the oval - to - elliptical shaped aseptate microconidia were present in large numbers ( 73.7% ) , however few microconidia partitioned with septa ( 1 septate ) ( 11.2% ) were also observed ( fig . the length and width of micro- and macro - conidia were 7.5 , 55 , 3.2 , and 3.5 , respectively ( fig . a ) the pure colony of f. mangiferae obtained from malformed floral tissues of mango cv dashehri via single spore isolation technique depicting light purple along with white color . the crescent - shaped and usually 3-septate or rarely 45 septate macroconidia , as well as oval- to elliptical - shaped microconidia , either devoiding of septum or a few consisting one septum , were present . both the conidia showing germination in vitro at suitable temperature ( 27 c ) leading to the development of mycelial mat showing a long septate hyphae . ( b ) the type and number of conidia may vary in axenic suspension culture of f. mangiferae . ( c ) the length of micro- and macro - conidia was 7.5 and 55 , respectively . ( d ) the width of micro- and macro - conidia was confined to 3.2 and 3.5 , respectively . naphthalene acetic acid ( naa ) and gibberellic acid ( ga3 ) were tested for their effect on conidia germination of f. mangiferae . naphthalene acetic acid ( naa ) and gibberellic acid glutathione ( ga3 ) were observed to have stimulatory effect on conidia germination of f. mangiferae after 12h of incubation at 27 c . with increasing concentration of naa ( 0500 ppm ) , germination of conidia of f. mangiferae were recorded at 500 ppm ( 69.62% ) with respect to control , as well as 25 ppm naa ( 69.49% ) ( fig . likewise , the treatment of ga3 resulted into inductive response on condial germination of f. mangiferae . conidia germination was progressively increased with raising the ga3 concentration ( 0500 ppm ) , and the response was higher at 500 ppm ( 89.66% ) as compared with control ( 70.86% ) ( fig . similar trends were observed in the case of 6-benzylaminopurine ( bap ) and ethylene releasing agent ( ethrel ) applied to conidia of f. mangiferae , where conidia germination were steadily increased with elevated concentration of bap and ethrel and were greatest ( 100% and 99.86% ) at 400 , 500 ppm bap and 150 ppm ethrel with respect to untreated ( control ) ( fig . evaluation of conidia germination of f. mangiferaein vitro under varying concentration of plant growth regulators . ( a ) naphthalene acetic acid ( naa ) ( 500 ppm ) promotes conidia germination to 82.47% from 69.49% and 69.62% at 25 ppm and untreated control , respectively after 12 h. ( b ) the stimulatory effect of gibberellic acid ( ga3 ) was detected and the germination was highest ( 89.66% ) in conidia treated with 500 ppm gibberellic acid ( ga3 ) , whereas it was least ( 70.79% ) at 25 ppm ga3 , after 12 h. ( c d ) the 6-benzylaminopurine ( bap ) and ethylene - releasing compounds , such as ethrel , consistently induced conidial germination of f. mangiferae with their increasing concentrations . condial germination was 100% beyond 300 ppm bap , while ethrel at 150 ppm was highly effective ( 99.86% conidia germination ) , after 12 h. a role of antimolformin chemicals , such as silver nitrate ( agno3 ) and glutathione , were evaluated in vitro for their effect on conidial germination of f. mangiferae . silver nitrate ( agno3 ) in varying concentrations ( 25 , 50 , 75 , 100 , 150 , 200 , 250 , 300 , 400 , and 500 ppm ) showed inhibitory effect on conidia germination of f. mangiferae . however , inhibition was maximum with 400 ppm ( 1.8% ) and conidia germination was nil over 500 ppm , as compared with control ( 70.02% ) after 24h ( fig . the effect of glutathione on conidia germination of f. mangiferae was assessed and found that it stimulates the conidial germination of f. mangiferae with increasing concentration of glutathione ranging from 25 ppm to 1200 ppm . the conidial germination was highest at 1200 ppm ( 92.7% ) after 24h ( fig . the response of germination of f. mangiferaein conidia in vitro under defined concentration of antimalformins after 24h . ( a ) the maximum inhibition was recorded at silver nitrate ( agno3 ) above 400 ppm ( 1.8% ) and conidia germination was nil over 500 ppm . ( b ) glutathione stimulates the conidial germination from untreated control ( 70.4% ) to 1200 ppm ( 92.7% ) . the severity of malformation disease is the highest in mango growing areas of the world where the mean temperature preceding flowering is between 1015 c . recently , f. mangiferae was found to be associated with mango malformation . here , we morphologically characterized fusarium sp from mango cv , dashehri ( fig . 1a d ) and found that features ( light purple plus white colony colors , shape and size of microconidia and macroconidia , partitionate hyphae with septa and absence of chlamydospores ) were in accord with the reported standard features of species f. mangiferae . at present , several attempts have proved futile to find out the exact causal agent and the etiology of disease has not yet been determined . currently , a role of low temperature stress ethylene has been implicated in mango malformation , whereas involvement of f. mangiferae in causing disease either via toxic principle ( tp ) or malformation induction principle ( mip ) is not definite at low temperature range where malformation is most sever . in the present study , in vitro conidia germination technique was made to evaluate the degree tolerance or susceptibility of f. mangiferae at favorable temperature range . plants , during their growth , development and cellular differentiation , secrete different kinds of growth regulators . it is well known that these secretions may affect the growth and development of f. mangiferae . here , we observed stimulatory effect of plant growth regulators on conidia germination of f. mangiferae and found that conidia germination increases with increasing concentration of naa , ga3 , bap and ethrel ( fig . the role of hormonal imbalance in mango malformation was pointed out by majumder et al . , who achieved a significant decrease in floral malformation by exogenously applying the naa ( 100200 ppm ) to the affected branches of mango cv dashehri , chausa , and bobay green . naphthaleneacetic - acid ( 200 ppm ) treated malformed panicles were reported to grow like healthy panicles of mango and produced fruits . similarly , exogenous application of ga3 enhanced the early flowering and improved the number of healthy panicles and resulted into the reduced incidence of floral malformation . the number , nature , and kind of cytokinins varied in healthy and malformed inflorescence during different developmental stages were studied and cytokinin content was detected to be elevated in malformed inflorescence with respect to healthy ones . the higher infection of fusaium and the malformation symptoms were explained to be mediated via consequence of cytokinin production and metabolism . ethylene is a well known stress hormone that may affect the extent and magnitude of spore germination . ethylene was reported to promote the conidial germination and involved in the establishment of plant all these reports reveal that higher population of fusarium sp in diseased tissues could be due to the higher level of ethylene . , silver nitrate , ascorbic acid , potassium metabisulfite , and glutathione caused the disappearance of malformin from panicle , which fruited like healthy controls . in the present study , the effect of silver nitrate and glutathione were evaluated on conidia germination of f. mangiferae in vitro ( fig . 3a b ) malformed panicles sprayed with 600 ppm agno3 were found to grow into fruit - bearing healthy panicles . the effect may certainly be due to the inhibitory effect of ag in ethylene action . furthermore , inhibitory effect of silver nitrate ( concentrations between 400 ppm to 500 ppm ) on conidial germination of f. mangiferae ( fig . 3a ) could explain the fact that silver nitrate may reduce the population of f. mangiferae contributing ethylene to stress ethylene pool in malformed panicles . on the other hand , glutathione was highly effective in stimulating the conidial germination of f. mangiferae at concentration exceeding the 1000 ppm ( fig . . exogenous application of gluthione to malformed panicles resulted in normal panicles and these panicles fruited like the healthy control . the response of glutathione to reduce the disease incidence may explain the fact that it plays a part in reducing ascorbate required in the last step of ethylene biosynthesis catalyzed by acc synthase . the resulted lower level of ethylene in malformed tissues may help in nullifying the malformed symptoms in mango panicles caused by over production of stress ethylene . naa and ga3 resulted into the recovery of malformed panicles to normal panicles reported earlier is not correlated with the finding of present study where such treatment cause induction of conidial germination of f. mangiferae . on the other hand , bap and ethrel response to positively modulate the germination of conidia of f. mangiferae , explain that a higher population of f. mangiferae in malformed tissue might be the result of higher endogenous content of these hormones . the role of antimolformin chemicals , such as silver nitrate and glutathione in reducing floral malformation reported earlier , was found to be correlated with ethylene effects and probably not fusarium in causing the malformation in the present study . the exogenous application of bap and ethrel to mango panicle to reproduce disease symptoms was not succeeded . further , naa and ga3 treated mango plants expected to reduce the population of f. mangiferae resulting in a decline infection may lead to diminish the disease incidence , but this is not the case of present in vitro study where naa and ga3 favored the f. mangiferae infection by stimulating conidia germination . the findings of present investigation do not authenticate the involvement of f. mangiferae in mango malformation , however hormonal imbalance might be responsible for deformed functional morphology of mango inflorescence . further study is required to trace out the mechanism involved in triggering the endogenous level of a particular hormone by the signal of various external stimuli at full bloom and prior to the full - bloom stage of flower buds and transmission of these signals via signaling cascade leading to various cellular response that in fact is responsible for loss in functional morphology of mango inflorescence . a single conidia isolation technique was used for producing pure cultures of the fusaria from mango cultivars . single conidia were transferred from the axenic suspension culture to sterilized petri plates of pda . from these parent cultures , mycelial growth from the margin of the culture the colonies of f. mangiferae were purified on cla medium and the identification was done on the basis of typical macro and microconidia . the harvested conidia from mycelial mat of f. mangiferae were placed separately into the cavity of glass slides and were treated with varying concentrations of plant growth regulators , such as naphthalene acetic acid ( naa ) , gibberellic acid ( ga3 ) , 6-benzylaminopurine ( bap ) , ethylene releasing agent ( ethrel ) , and anti - malformin chemicals viz . , silver nitrate and glutathione at the rate of 10 l solution volume . the cavity glass slides were subsequently placed onto the moist blotting sheets of petriplates to maintain the humidity . the condia of f. mangiferae were then allowed to germinate at suitable temperature ( 27 c ) . the number of conidi germinating after 12h and 24h was counted under the compound microscope . a single conidia isolation technique was used for producing pure cultures of the fusaria from mango cultivars . single conidia were transferred from the axenic suspension culture to sterilized petri plates of pda . from these parent cultures , mycelial growth from the margin of the culture the colonies of f. mangiferae were purified on cla medium and the identification was done on the basis of typical macro and microconidia . the harvested conidia from mycelial mat of f. mangiferae were placed separately into the cavity of glass slides and were treated with varying concentrations of plant growth regulators , such as naphthalene acetic acid ( naa ) , gibberellic acid ( ga3 ) , 6-benzylaminopurine ( bap ) , ethylene releasing agent ( ethrel ) , and anti - malformin chemicals viz . , silver nitrate and glutathione at the rate of 10 l solution volume . the cavity glass slides were subsequently placed onto the moist blotting sheets of petriplates to maintain the humidity . the condia of f. mangiferae were then allowed to germinate at suitable temperature ( 27 c ) . the number of conidi germinating after 12h and 24h was counted under the compound microscope .

mango malformation is the most important and threatening disease of recent times , primarily because of persistent lacuna in complete understanding of its nature . diverse fusarium spp , including f. mangiferae , were found to be associated with the disease . here , f. mangiferae from mango cv dashehri was morphologically characterized . typically , oval - shaped microconidia without septum and crescent - shaped macroconidia with 3-septate were more often observed , whereas not a single chlamydospore was detected . the length and width of micro- and macro - conidia were 7.5 , 55 , 3.2 , and 3.5 , respectively . the plant growth regulators such as naa , ga3 , bap and ethrel were found to induce in vitro germination of conidia of f. mangiferae after 12 h. in contrast , antimalformin silver nitrate ( agno3 ) inhibits conidial germination in vitro and none of conidia was germinated beyond 500 ppm , however antimalformin glutathione was highly effective in stimulating conidial germination of f. mangiferae in vitro at > 1000 ppm after 24 h. we observed that the response of f. mangiferae to germinate the conidia in vitro under influence of plant growth regulators and antimalformins is not coincided with earlier findings of reduced disease incidence by exogenous application of these compounds . the present findings do not authenticate the involvement of f. mangiferae in the disease , however hormonal imbalance , most probably ethylene , might be responsible for deformed functional morphology of panicle . further , a signal transduction mechanism of stress - stimulated ethylene imbalance causing physio - morphological changes in reproductive organs of mango flower and thereby failure of fertilization and fruit set , which needs to be investigated .

Results Isolation and morphological characterization of Effect of naphthalene acetic acid, gibberellic acid, 6-benzylaminopurine, and ethrel on conidia germination of Anti-malformin chemicals affect the germination of Discussion Materials and Methods Isolation, purification, and morphological identification of Plant growth regulators and antimalformins affect the conidia germination of

the effects of smoking habits of mother during pregnancy have been studied in the past century or so in various communities and different cultures . one of the earliest studies ( 1 ) in birmingham , uk , reported in 1959 shows that infants of mothers who smoked regularly during pregnancy were on the average more than 170 g lighter than the infants of those who never smoked during pregnancy . despite the association of the children s health with the smoking habits of mother during pregnancy have been investigated for many years and well - documented , the topic is still being studied by various research groups . ( 2 ) estimated that about 5% of infant deaths in the united states are attributable to maternal smoking while pregnant , with variations by race / ethnicity . a recently published study ( 3 ) reported that an experimental citywide smoking ban in pueblo , colorado , usa , improved maternal and fetal outcomes . ( 4 ) discussed not only the relationship of smoking habits of mothers and fetal risks , but the importance of negative impact of smoking on the health of mothers as well . they suggested that smokers have a higher chance of experiencing cardiovascular problems ( deep vein thrombosis , myocardial infarction , and stroke ) and pulmonary disorders ( bronchitis , asthma , pneumonia , influenza ) than non - smokers . in the united states , mateja et al . ( 5 ) investigated the data from the pregnancy risk assessment monitoring survey ( prams ) for nine states over a 10-year period ( 19962005 ) , and revealed the risk factor of maternal alcohol use and smoking habits , in early pregnancy , and congenital heart defects . ( 6 ) also suggested the importance of preconception prevention efforts for women who are at dual risk for alcohol and smoking habits . ( 7 ) investigated the healthy lifestyle behaviors during pregnancy , from 2001 to 2009 , in a survey from 22,604 american pregnant women aged 1844 years , and pointed out the importance of reducing alcohol use , binge drinking , and smoking and increasing fruit and vegetable consumption during pregnancy . this paper describes the association of maternal smoking habits with stillbirths , abortions , neonatal deaths , birth weights , placental weights and the outcomes on the 28 day of life . during 2001 and 2002 , the first author had a fellowship at the division of clinical and metabolic genetics , hospital for sick children , toronto , canada , in the late prof . a questionnaire was developed and completed with the hospitals recorded data which have been collected over a period of 5 years from about 47,000 babies born in several hospitals in ontario . the designed questionnaire covered a comprehensive range of information on both mothers and their babies health , which were and will be the source for a series of other articles . the babies , whose records had missing data on any of the maternal or infant variables under study , were excluded from the analyses . for the purpose of this study , the mothers were classified into four categories : non - smokers , light smokers ( less than 10 cigarettes per day ) , moderate smokers ( between 10 and 19 cigarettes per day ) and heavy smokers ( 20 or more cigarettes per day ) . other groups such as sportive smoking , ex - smokers and mothers who have smoked before pregnancy and ceased during pregnancy were out of the scope of present study . throughout this study statistical analysis was performed using the spss statistical package , version 15.0 for windows ( spss , chicago , usa ) and the chi - square test was used to estimate the probable association between the variables , and a p value less than 0.05 was considered statistically significant for all the tables . the odds ratios ( or ) the present analysis is a cohort study where the maternal smokers during pregnancy are compared with the maternal non - smokers during pregnancy . during 2001 and 2002 , the first author had a fellowship at the division of clinical and metabolic genetics , hospital for sick children , toronto , canada , in the late prof . a questionnaire was developed and completed with the hospitals recorded data which have been collected over a period of 5 years from about 47,000 babies born in several hospitals in ontario . the designed questionnaire covered a comprehensive range of information on both mothers and their babies health , which were and will be the source for a series of other articles . the babies , whose records had missing data on any of the maternal or infant variables under study , were excluded from the analyses . for the purpose of this study , the mothers were classified into four categories : non - smokers , light smokers ( less than 10 cigarettes per day ) , moderate smokers ( between 10 and 19 cigarettes per day ) and heavy smokers ( 20 or more cigarettes per day ) . other groups such as sportive smoking , ex - smokers and mothers who have smoked before pregnancy and ceased during pregnancy were out of the scope of present study . throughout this study statistical analysis was performed using the spss statistical package , version 15.0 for windows ( spss , chicago , usa ) and the chi - square test was used to estimate the probable association between the variables , and a p value less than 0.05 was considered statistically significant for all the tables . the odds ratios ( or ) the present analysis is a cohort study where the maternal smokers during pregnancy are compared with the maternal non - smokers during pregnancy . previous stillbirths were consisted of three subgroups of no previous stillbirths , 1 previous stillbirth and 2 or more previous stillbirths . previous abortions were divided into four subgroups of no previous abortions , 1 previous abortion , 2 previous abortions and 3 or more previous abortions . table 1 shows the incidence of previous stillbirths and previous abortions in regard to smoking habits . it was found , that mothers who smoke have significantly more previous stillbirths ( = 60.98 , p < 0.0001 ) and also previous abortions ( = 290.77 , p < 0.0001 ) than mothers who do not smoke . our data shows that there is no significant difference between non - smokers and light smokers with regard to the number of previous stillbirths ( = 2.38 , p > 0.30 ) and also to the number of previous abortions ( = 8.51 , p > 0.036 ) . the frequency of previous neonatal deaths in relation to smoking habits is given in table 2 . in this study neonatal deaths were scored as being absent or 1 , 2 or more . early neonatal mortality refers to a death of a live - born baby within the first 7 days of life . late neonatal mortality refers to a death of a live - born baby after 7 days until before 28 days of life . our results revealed that the proportion of previous neonatal deaths was significantly higher amongst smoker mothers than non - smokers ( = 45.02 , p < 0.0001 ) . the results show that there is no significant difference between no - smokers and light smokers in regard to previous neonatal deaths ( = 1.22 , p > 0.50 ) . birth weight was consisted of six subgroups of 2.5 kg or less , ( 2.6 2.9 ) kg , ( 3.0 3.3 ) kg , ( 3.4 3.7 ) kg , ( 3.8 4.1 ) kg , and 4.2 kg or more . the data from the present study suggest that mothers who smoke have lighter babies than mothers who do not smoke . the differences were statistically highly significant ( = 1689.11 , p < 0.0001 ) . placental weight was divided into four subgroups of 400 g or less , ( 400 599 ) g , ( 600 799 ) g , and 800 g or more . the pattern of results is similar to that found for birth weight results and indicates that those babies born to smoking mothers have significantly lighter placental weight than those born to non - smokers ( = 145.20 , p < 0.0001 ) . the result of smoking habits and outcome with respect to mortality up to 28th days after birth is given in table 5 . this outcome mortality consisted of the perinatal deaths plus the deaths after 7 days until 28th days after birth . it was found that babies born to heavy smokers have the highest mortality rate , and the rate , gradually increases as smoking increases . our results show that there is no significant difference between non - smokers and light smokers ( = 0.01 , p > 0.90 ) and also no significant difference between moderate and heavy smokers ( = 0.15 , p > 0.60 ) . kllen ( 8) reported that maternal smoking during pregnancy is associated with a number of effects such as pre - term birth , intrauterine growth retardation , a small head circumference , and stillbirths and neonatal deaths . the smoking habits of the mothers were recorded in three categories : non - smokers , < 10 cigarettes / day and 10 cigarettes / day . the results showed the stillbirths risk estimates are 0.42% and 0.32% for smokers and non - smokers , respectively . hgberg and cnattingius ( 9 ) reported that maternal smoking during pregnancy is causally associated with stillbirth risk . they showed that compared with nonsmokers , women who smoked during the first pregnancy but not during the second do not have an increased risk of stillbirth ( or 1.02 ; 95% ci 0.791.30 ) , while corresponding risk among women who smoked during both pregnancies was 1.35 ( 95% ci 1.151.58 ) . gray et al . ( 10 ) studied the contribution of smoking during pregnancy to inequalities in stillbirth in scotland from 1994 to 2003 and reported that smoking during pregnancy accounted for 38% of the inequality in stillbirths . it was found that ( 1 ) . there is no significant difference between moderate and heavy smoking mothers with respect to previous stillbirths where the odds ratios vary from 1.20 ( 95% ci : 0.64 2.25 ) to 1.42 ( 95% ci : 0.69 2.94 ) for 2 or more previous stillbirths , and ( 2 ) there was no significant difference between non - smokers and light smokers ( < 10 cigs / day ) with any previous stillbirths.( = 2.38 , p > 0.30 ) in a study ( 11 ) conducted in montreal , quebec , canada , the researchers interviewed approximately 56,000 women who had had a delivery or a spontaneous abortion in 11 montreal hospitals during the two - year period 19821984.the researchers found that 22% of the women had had previous pregnancies that ended in spontaneous abortion . compared with women who abstained during pregnancy , women who smoked cigarettes had a 20% increase in spontaneous abortion ( odds ratio of 1.20 ) for each 10 cigarettes smoked per day . ( 12 ) shows that they found no association between maternal smoking and the risk of spontaneous abortion . nielsen et al . ( 13 ) has also reported that smoking status was only weakly related to spontaneous abortion after adjustment for maternal age . the results of the present study show that the previous abortion is a significant factor for women who smoke 20 or more cigarettes per day . the odds ratios for the previous number of abortions of 1 , 2 and 3 are 1.54 ( 95% ci , 1.42 1.67 ) , 1.97 ( 95% ci , 1.70 2.28 ) and 2.86 ( 95% ci , 2.30 3.55 ) , respectively . no significant difference was observed between the light smokers ( < 10 cigs / day ) and non - smokers ( = 8.51 , p > 0.036 ) . one of the early studies on smoking and pregnancy ( 14 ) reports the prospective survey of almost 7000 women from 11 paris hospitals between 1963 and 1969 . the results show while smokers had a stillbirth rate more than three times as high ( 28 versus 8 per 1000 births ) they found that the neonatal death rates were almost the same for smokers and nonsmokers . in a study ( 15 ) conducted in sweden between 1983 and 1985 , significant relative risks for early neonatal mortality were found for multiple births ( 4.9 ) and smoking ( 1.2 ) . they concluded that maternal cigarette smoking may be the most important preventable risk factor for late fetal death . the study ( 16 ) based on the number of stillbirths or neonatal deaths among infants born in sweden from 1983 to 1995 showed that maternal smoking seems to aggravate the placental abruption because the death risk in the presence of abruption increases when mother smoked ( or = 1.74 , 95% ci 1.45 2.08 ) . the present results show that there is no significant difference between non - smokers and light smokers with < 10 cigarettes per day ( = 1.22 , p > 0.50 ) . for moderate and heavy smokers the odds ratios are up to or = 1.84 , 95% ci 1.05 3.23 . in a study reported by dsouza ( 17 ) a total of 452 mothers who attended antenatal clinics regularly at st mary s hospital , manchester , uk , were selected with a normal singleton pregnancy . at each visit the mothers were asked about the number of cigarettes smoked per day , and they were grouped as follows : ( a ) non - smokers , ( b ) light - to - moderate smokers , ( 114 cigarettes / day ) , and ( c ) heavy smokers ( 15 or more cigarettes/ day ) . in both sexes babies born to non - smokers were heavier , longer , and had larger head circumferences than those born to heavy smokers . smoking during pregnancy appears to have caused a general retardation in intrauterine growth , resulting in babies born with lower birth weights , shorter lengths , and smaller head circumferences . dickute ( 18 ) reported a case - control study involved 851 newborns with low birth weight ( < 2500 g ) and 851 normal weight newborns . the study started 1 february 2001 and ended 31 october 2002 in six main maternity hospitals in lithuania . the results showed that smoking during pregnancy in combination with the socioeconomic inequalities is significantly associated with the higher risk of low birth weight . the association of socioeconomic status with heath and birth weight has been discussed by some authors ( 1922 ) . in a study in illinois , usa , keeton et al . ( 23 ) suggested that the family case management program may be effective in reducing very low birth weight and low birth weight rates among infants born to low - income women . ( 24 ) reported the prenatal smoking status of west virginia , usa , women and the associated changes in infant birth weights . a population - based secondary data analysis was conducted for all singleton infant siblings born between 1989 and 2006 . they found that infants born to women who smoked during pregnancy had significantly lower birth weights than infants born to non - smokers . the results showed that maternal prenatal smoking was the strongest predictor of low birth weight ( < 2500 g ) with an odds ratio of 3.29 ( 95% ci 2.87 , 3.77 ) for smoking during the recent pregnancy . the odds ratio is significantly reduced from the birth weight of < 2.5 kg to = > 4.2 kg for smoking mothers . the variation of odds ratio is from 0.95 ( 95% ci 0.85 1.06 ) to 0.18 ( 95% ci 0.14 0.23 ) . jones et al . ( 25 ) reported a study with the objective of determining whether maternal smoking during pregnancy is associated with bone mass and other growth variables in pre - pubertal children in tasmania , australia . they showed that the mothers who smoked during pregnancy had lower placental weight ( 56 g , 95% ci 95 to 17 ) . ( 26 ) reported the study conducted in the county of north jutland , denmark . they examined the association between mothers smoking habits during pregnancy , taking the sex of the offspring into consideration , and the risk and prognosis of placental abruption , placenta previa , and preeclampsia . the results showed that smoking was associated with the risk of placental abruption ( or=1.99 , 95% ci 1.722.30 ) and placenta previa ( or=1.88 , 95% ci 1.153.07 ) . the effect of maternal smoking on placental volume was studied ( 27 ) in 80 pregnancies categorized according to cigarette consumption : group a never smoked , b smoking < 10 cigarettes / day , c smoking 1020 cigarettes / day , and d smoking > 20 cigarettes / day . the three - dimensional power doppler ultrasonography of the placenta was performed in this study and the results showed no differences in placental volume among different groups . the odds ratios for heavy smokers ( > 20 cigs / day ) are 0.81 ( 95% ci : 0.69 0.95 ) , 0.67 ( 95% ci : 0.57 0.79 ) and 0.59 ( 95% ci : 0.49 0.71 ) for the placental weight groups of 400 599 g , 600 799 g and = > 800 g , respectively . the perinatal mortality ( pnm ) has been defined ( 28 ) as the total number of stillbirths and deaths in the first week of life ( early neonatal deaths ) . the sudden infant death syndrome ( sids ) happens usually with no known illness and typically affecting sleeping infants between the ages of two weeks to six months . schoendorf and kiely ( 29 ) reported the results of a case - control analysis performed on data from the 1998 us national maternal and infant health survey ( nmihs ) . they showed that sudden infant death syndrome ( sids ) is associated with maternal smoking during pregnancy . ( 30 ) have shown that maternal smoking during pregnancy remains the most important risk factor for sids in sweden . in the present study we defined the outcome of pregnancy as whether the infant was alive on the 28 day of life . we considered the total number of infants deaths as the sum of stillbirths and neonatal deaths ( early neonatal : within the first 7 days of life and late neonatal : after 7 days until 28 day ) . the outcomes on the 28 day were 45923 ( 97.66% ) lives and 1100 ( 2.34% ) deaths . the odds ratios were 1.01 ( 95% ci 0.82 1.24 ) , 1.43 ( 95% ci 1.23 1.66 ) and 1.49 ( 95% ci 1.24 1.79 ) for light smokers ( < 10 cigs / day ) , moderate smokers ( 10 19 cigs / day ) and heavy smokers ( 20 cigs / day ) , respectively . it was found , firstly , that babies born to moderate and heavy smokers have the highest mortality rate . secondly , there were no significant differences between non - smokers and light smokers ( = 0.01 , p > 0.90 ) or between moderate and heavy smokers ( = 0.15 , p > 0.60 ) . kllen ( 8) reported that maternal smoking during pregnancy is associated with a number of effects such as pre - term birth , intrauterine growth retardation , a small head circumference , and stillbirths and neonatal deaths . the smoking habits of the mothers were recorded in three categories : non - smokers , < 10 cigarettes / day and 10 cigarettes / day . the results showed the stillbirths risk estimates are 0.42% and 0.32% for smokers and non - smokers , respectively . hgberg and cnattingius ( 9 ) reported that maternal smoking during pregnancy is causally associated with stillbirth risk . they showed that compared with nonsmokers , women who smoked during the first pregnancy but not during the second do not have an increased risk of stillbirth ( or 1.02 ; 95% ci 0.791.30 ) , while corresponding risk among women who smoked during both pregnancies was 1.35 ( 95% ci 1.151.58 ) . gray et al . ( 10 ) studied the contribution of smoking during pregnancy to inequalities in stillbirth in scotland from 1994 to 2003 and reported that smoking during pregnancy accounted for 38% of the inequality in stillbirths . it was found that ( 1 ) . there is no significant difference between moderate and heavy smoking mothers with respect to previous stillbirths where the odds ratios vary from 1.20 ( 95% ci : 0.64 2.25 ) to 1.42 ( 95% ci : 0.69 2.94 ) for 2 or more previous stillbirths , and ( 2 ) there was no significant difference between non - smokers and light smokers ( < 10 cigs / day ) with any previous stillbirths.( = 2.38 , p > 0.30 ) in a study ( 11 ) conducted in montreal , quebec , canada , the researchers interviewed approximately 56,000 women who had had a delivery or a spontaneous abortion in 11 montreal hospitals during the two - year period 19821984.the researchers found that 22% of the women had had previous pregnancies that ended in spontaneous abortion . compared with women who abstained during pregnancy , women who smoked cigarettes had a 20% increase in spontaneous abortion ( odds ratio of 1.20 ) for each 10 cigarettes smoked per day . ( 12 ) shows that they found no association between maternal smoking and the risk of spontaneous abortion . nielsen et al . ( 13 ) has also reported that smoking status was only weakly related to spontaneous abortion after adjustment for maternal age . the results of the present study show that the previous abortion is a significant factor for women who smoke 20 or more cigarettes per day . the odds ratios for the previous number of abortions of 1 , 2 and 3 are 1.54 ( 95% ci , 1.42 1.67 ) , 1.97 ( 95% ci , 1.70 2.28 ) and 2.86 ( 95% ci , 2.30 3.55 ) , respectively . no significant difference was observed between the light smokers ( < 10 cigs / day ) and non - smokers ( = 8.51 , p > 0.036 ) . one of the early studies on smoking and pregnancy ( 14 ) reports the prospective survey of almost 7000 women from 11 paris hospitals between 1963 and 1969 . the results show while smokers had a stillbirth rate more than three times as high ( 28 versus 8 per 1000 births ) they found that the neonatal death rates were almost the same for smokers and nonsmokers . in a study ( 15 ) conducted in sweden between 1983 and 1985 , significant relative risks for early neonatal mortality were found for multiple births ( 4.9 ) and smoking ( 1.2 ) . they concluded that maternal cigarette smoking may be the most important preventable risk factor for late fetal death . the study ( 16 ) based on the number of stillbirths or neonatal deaths among infants born in sweden from 1983 to 1995 showed that maternal smoking seems to aggravate the placental abruption because the death risk in the presence of abruption increases when mother smoked ( or = 1.74 , 95% ci 1.45 2.08 ) . the present results show that there is no significant difference between non - smokers and light smokers with < 10 cigarettes per day ( = 1.22 , p > 0.50 ) . for moderate and heavy smokers the odds ratios are up to or = 1.84 , 95% ci 1.05 3.23 . in a study reported by dsouza et al . ( 17 ) a total of 452 mothers who attended antenatal clinics regularly at st mary s hospital , manchester , uk , were selected with a normal singleton pregnancy . at each visit the mothers were asked about the number of cigarettes smoked per day , and they were grouped as follows : ( a ) non - smokers , ( b ) light - to - moderate smokers , ( 114 cigarettes / day ) , and ( c ) heavy smokers ( 15 or more cigarettes/ day ) . in both sexes babies born to non - smokers were heavier , longer , and had larger head circumferences than those born to heavy smokers . smoking during pregnancy appears to have caused a general retardation in intrauterine growth , resulting in babies born with lower birth weights , shorter lengths , and smaller head circumferences . dickute ( 18 ) reported a case - control study involved 851 newborns with low birth weight ( < 2500 g ) and 851 normal weight newborns . the study started 1 february 2001 and ended 31 october 2002 in six main maternity hospitals in lithuania . the results showed that smoking during pregnancy in combination with the socioeconomic inequalities is significantly associated with the higher risk of low birth weight . the association of socioeconomic status with heath and birth weight has been discussed by some authors ( 1922 ) . in a study in illinois , usa , keeton et al . ( 23 ) suggested that the family case management program may be effective in reducing very low birth weight and low birth weight rates among infants born to low - income women . ( 24 ) reported the prenatal smoking status of west virginia , usa , women and the associated changes in infant birth weights . a population - based secondary data analysis was conducted for all singleton infant siblings born between 1989 and 2006 . they found that infants born to women who smoked during pregnancy had significantly lower birth weights than infants born to non - smokers . the results showed that maternal prenatal smoking was the strongest predictor of low birth weight ( < 2500 g ) with an odds ratio of 3.29 ( 95% ci 2.87 , 3.77 ) for smoking during the recent pregnancy . the odds ratio is significantly reduced from the birth weight of < 2.5 kg to = > 4.2 kg for smoking mothers . the variation of odds ratio is from 0.95 ( 95% ci 0.85 1.06 ) to 0.18 ( 95% ci 0.14 0.23 ) . jones et al . ( 25 ) reported a study with the objective of determining whether maternal smoking during pregnancy is associated with bone mass and other growth variables in pre - pubertal children in tasmania , australia . they showed that the mothers who smoked during pregnancy had lower placental weight ( 56 g , 95% ci 95 to 17 ) . ( 26 ) reported the study conducted in the county of north jutland , denmark . they examined the association between mothers smoking habits during pregnancy , taking the sex of the offspring into consideration , and the risk and prognosis of placental abruption , placenta previa , and preeclampsia . the results showed that smoking was associated with the risk of placental abruption ( or=1.99 , 95% ci 1.722.30 ) and placenta previa ( or=1.88 , 95% ci 1.153.07 ) . the effect of maternal smoking on placental volume was studied ( 27 ) in 80 pregnancies categorized according to cigarette consumption : group a never smoked , b smoking < 10 cigarettes / day , c smoking 1020 cigarettes / day , and d smoking > 20 cigarettes / day . the three - dimensional power doppler ultrasonography of the placenta was performed in this study and the results showed no differences in placental volume among different groups . the odds ratios for heavy smokers ( > 20 cigs / day ) are 0.81 ( 95% ci : 0.69 0.95 ) , 0.67 ( 95% ci : 0.57 0.79 ) and 0.59 ( 95% ci : 0.49 0.71 ) for the placental weight groups of 400 599 g , 600 799 g and = > 800 g , respectively . the perinatal mortality ( pnm ) has been defined ( 28 ) as the total number of stillbirths and deaths in the first week of life ( early neonatal deaths ) . the sudden infant death syndrome ( sids ) happens usually with no known illness and typically affecting sleeping infants between the ages of two weeks to six months . schoendorf and kiely ( 29 ) reported the results of a case - control analysis performed on data from the 1998 us national maternal and infant health survey ( nmihs ) . they showed that sudden infant death syndrome ( sids ) is associated with maternal smoking during pregnancy . ( 30 ) have shown that maternal smoking during pregnancy remains the most important risk factor for sids in sweden . in the present study we defined the outcome of pregnancy as whether the infant was alive on the 28 day of life . we considered the total number of infants deaths as the sum of stillbirths and neonatal deaths ( early neonatal : within the first 7 days of life and late neonatal : after 7 days until 28 day ) . the outcomes on the 28 day were 45923 ( 97.66% ) lives and 1100 ( 2.34% ) deaths . the odds ratios were 1.01 ( 95% ci 0.82 1.24 ) , 1.43 ( 95% ci 1.23 1.66 ) and 1.49 ( 95% ci 1.24 1.79 ) for light smokers ( < 10 cigs / day ) , moderate smokers ( 10 19 cigs / day ) and heavy smokers ( 20 cigs / day ) , respectively . it was found , firstly , that babies born to moderate and heavy smokers have the highest mortality rate . secondly , there were no significant differences between non - smokers and light smokers ( = 0.01 , p > 0.90 ) or between moderate and heavy smokers ( = 0.15 , p > 0.60 ) . the association of smoking habits of mother during pregnancy investigated with the stillbirths , abortions , neonatal deaths , birth weights , placental weights and the outcomes on the 28 day of life . the smoker mothers were classified as light smokers ( less than 10 cigarettes per day ) , moderate smokers ( between 10 and 19 cigarettes per day ) and heavy smokers ( 20 or more cigarettes per day ) . the results show that even the light smoking habit has an effect on the birth weight and the placental weight but for other characteristics , stillbirth , abortion , and the outcomes on the 28 day of life , there is no significant difference between light smokers and non - smokers . while quit smoking must be the ultimate goal for any smoker , the present study concludes that moderate and heavy smokers should reduce their number of cigarettes per day to at least the level of light smokers to achieve the same results for non - smokers . ethical issues ( including plagiarism , informed consent , misconduct , data fabrication and/or falsification , double publication and/or submission , redundancy , etc . ) have been completely observed by the authors .

background : the objectives of this work were to study the association of maternal smoking habits with stillbirths , abortions , neonatal deaths , birth weights , placental weights and the outcomes on the 28th day of life.methods:a questionnaire was developed and completed with the hospitals recorded data collected over a period of 5 years from 47,000 babies born in several hospitals in ontario , canada . the mothers were classified into four categories : non - smokers , light smokers ( less than 10 cigarettes per day ) , moderate smokers ( between 10 and 19 cigarettes per day ) and heavy smokers ( 20 or more cigarettes per day ) . the population surveyed was of mixed ethnicity from both rural and urban areas . statistical analysis was performed using the spss statistical package.results:even the light smoking habit has an effect on the birth weight and the placental weight but for other characteristics , stillbirth , abortion , and the outcomes on the 28th day of life , no significant difference observed between light smokers and non-smokers.conclusion:while quit smoking must be the ultimate goal for any smoker , the present study concludes that moderate and heavy smokers , if they will not be able to quit , they should reduce their number of cigarettes per day to at least the level of light smokers to achieve the same results for non - smokers . all characteristics show significant difference between non - smokers and moderate and heavy smokers .

Introduction Materials and Methods Research Design Data Collection Statistical Analysis Results Discussion Smoking Habits and Previous Stillbirths and Previous Abortions Smoking Habits and Previous Neonatal Deaths Smoking Habits and Birth Weight Smoking Habits and Placental Weight Smoking Habits and Outcomes on the 28 Conclusions Ethical considerations

amyloid pet can identify fibrillar amyloid- ( a ) deposition , a core aspect of alzheimer s disease ( ad ) pathology , in vivo . however , cost , availability , and paucity of evidence that it changes management are factors that limit its clinical use . proposed appropriate use criteria suggest that amyloid pet may be used in unexplained mild cognitive impairment , young - onset dementia , and atypical dementia syndromes [ 2 , 3 ] . csf measures of amyloid and tau provide an alternate means of substantiating a molecular diagnosis of ad , with broadly similar diagnostic performance to amyloid pet when either is used in isolation . in many clinical centers , while previous studies assessing the use of amyloid pet in the clinical setting have found it to provide added diagnostic value , patients included in these studies have often had incomplete prior investigative work - up , in some cases without mri , neuropsychometry , and/or csf [ 69 ] . few studies have assessed the utility of amyloid pet in circumstances where it may prove most useful , i.e. , in cases fulfilling good use criteria in whom a csf has been performed and an equivocal / uncertain result is obtained and there remains clinical equipoise as to whether the patient has ad pathology or not . in this study , we aimed to determine in a real life clinical setting whether amyloid pet can provide added diagnostic value beyond csf measurements alone ; and in what specific clinical circumstances the addition of amyloid pet is likely to provide the most benefit . twenty patients with a range of different dementia syndromes were recruited from a specialist cognitive disorders service ( supplementary table 1 ) . ten had memory - led syndromes ; the remainder had a range of other presentations including posterior cortical atrophy ( n = 5 ) , primary progressive aphasia ( ppa ) ( n = 4 ) , and behavioral change ( with the patient becoming impulsive and socially disinhibited ) ( n = 1 ) . as part of their routine clinical evaluation , each patient had been seen by an experienced cognitive neurologist , and been investigated with neuropsychological testing , mr brain imaging and lumbar puncture , with samples analyzed for a42 , total tau , and p - tau ( innotest elisas , fujirebio , ghent belgium ) . at the time of testing , the normal clinical ranges for csf measures in use were : a42 > 450 ng / l , tau : a42 ratio < 1 , p - tau < 68 ng / l . tau and a42 cut - points were those in use clinically at our center at the time of the study , and were based on reference ranges of healthy controls and ability to distinguish clinically diagnosed ad from ftd ; the p - tau cut - point was that determined by the kit manufacturer . as part of a research study , each patient subsequently had an f18 florbetapir pet scan on a siemens 3 t pet / mr unit , with a 50-min dynamic acquisition commencing immediately after intravenous injection of 370 mbq of florbetapir . a single static pet image , reconstructed from the last 10 min of the pet acquisition , was used for analysis . three nuclear medicine physicians , blinded to the diagnosis , visually rated the images as positive / negative according to standard criteria . with the benefit of the psychology , mri , and csf results , but prior to the pet scan , the treating clinician was asked to give their diagnosis and degree of diagnostic certainty ( on a percentage scale ) . the clinician was subsequently provided with the pet scan result , which with their consent was also shared with the patient , and asked again to give the diagnosis / diagnostic certainty . the patients had a meansd age of 65.57.6 , and age of symptom onset of 59.26.2 . csf examination preceded scanning , with a median delay of 145 days ( range 32427 ) . across all subjects , csf a42 ranged between 3431127 ng / l , tau / a42 ratio 0.242.54 , and p - tau 24227 ng / l . prior to the amyloid pet , 13 patients had a diagnosis of ad , and seven of non - ad dementia . based on the visual pet results , 18 patients were amyloid positive and 2 patients amyloid negative , with no disagreement between the three readers for any scan . the amyloid pet result led to a change in diagnosis in 7/20 patients ( 5 non - amnestic , 2 amnestic ) ( table 1 ) . six patients diagnoses changed from non - ad to ad ; and 1 from ad to non - ad . the pet scan result led to an increase in diagnostic certainty in 18/20 patients ( to a mean 8414% ) . management was changed in 8/20 patients : an acetylcholinesterase inhibitor was started / stopped ( n = 4 ) ; memantine was started ( n = 1 ) ; immune suppression was stopped ( n = 1 ) ; and ad genetic testing was requested ( n = 2 ) . of the seven individuals in whom the pet led to a change in diagnosis , all had young - onset dementia ( age - at - onset < 65 y ) , and five had non - amnestic syndromes , particularly primary progressive aphasia ( n = 4 ) ( table 1 , supplementary table 1 ) . clinically , the ppa cases had each been felt to be most consistent with progressive non - fluent aphasia ( pnfa ) , although three of the four cases did not fulfill one of the canonical ppa syndromes , having some features additionally consistent with a logopenic aphasia ( e.g. , anomia and word finding pauses ) . the seven cases in whom the pet scan altered the diagnosis had a rather lower pre - pet diagnostic certainty than the rest of the group ( 55% versus 76% ) . also , the csf results for these cases were generally close to the pre - determined csf diagnostic cut - points , particularly for the tau : a42 ratio ( table 1 , fig . 1 ) . providing molecular evidence to support / refute a diagnosis of ad will become ever more important as we move toward an era of disease - modifying therapies . in many centers , csf measurements remain the first - line molecular biomarker of choice . here , we show that in certain situations , amyloid pet provides added diagnostic value above and beyond csf measurements , leading not only to increased diagnostic certainty but also to changes in management . we found that amyloid pet had most benefit in two particular scenarios , ( 1 ) in patients with young onset , atypical clinical syndromes ; and ( 2 ) in those where there was diagnostic uncertainty despite otherwise comprehensive investigation . these findings are consistent with appropriate use criteria , but also extend on the previous guidelines by assessing the use of amyloid pet in patients who have already had csf amyloid and tau measurements ; which in most clinical centers is likely to be the situation where amyloid pet may most commonly be used . atypical ( i.e. , non - amnestic ) syndromes may be underpinned by a variety of different underlying pathologies and this is particularly the case for ppa , where a tauopathy , tdp-43 proteinopathy , and ad are all possibilities . although consensus clinical diagnostic criteria describe three major forms ( pnfa , logopenic aphasia , and semantic dementia ) , in many cases patients do not easily fulfill any one criteria [ 10 , 11 ] . additionally , while there is good clinico - pathological correspondence in some of the ppa syndromes , notably semantic dementia and logopenic aphasia ( tdp43 and ad , respectively ) , in nosyndrome is this perfect ; and in non - fluent aphasia and undetermined aphasias ascribing a particular pathology is notoriously difficult [ 12 , 13 ] . while previous studies have found relatively high concordance between csf measures and amyloid pet [ 14 , 15 ] , atypical ad syndromes may have less clear - cut csf profiles than would normally be seen in typical ad . this subtle variability between the csf profiles of different ad syndromes , combined with the high proportion of atypical cases in our cohort , may have contributed in some cases to diagnostic uncertainty and the discrepancy between the csf and pet results . cases where there was most diagnostic uncertainty were often those where the csf levels were equivocal , lying close to or even outside diagnostic cut - points . no csf cut - point is perfect , and it is possible that the csf cut - points in clinical use at the time of this study were overly conservative . csf values can vary substantially if not taken , handled , and stored appropriately ; and establishing csf cut - points is difficult , as evidenced by the wide differences in normal ranges used at different clinical centers , leading us and others to propose the adoption of diagnostic grey - zones , and to suggest that comparing csf and amyloid pet results may be useful in refining csf cut - point use . this study reinforces that it is just such equivocal cases with atypical phenotypes and borderline csf results that addition of an amyloid brain scan may be most useful , and that so doing can alter clinical management . given the known incidence of cerebral amyloid deposition within the asymptomatic aging population , it is always necessary to consider whether a positive amyloid pet scan reflects the primary cause of a patient s symptoms , or if it is merely reflective of a second coincident pathology . however , particularly considering the patients relatively young ages of symptom onset , the possibility of dual pathology was felt to be unlikely , again in keeping with the inclusion of young - onset dementia as an appropriate use criterion for amyloid pet . however , as a load is thought to plateau prior to the onset of ad symptoms , this delay is unlikely to have had a significant effect on the relative diagnostic utility of the two tests , and also reflects what is likely to happen in real life clinical practice . and , without pathological confirmation , we can not know whether any diagnostic or management changes following the amyloid pet were correct or not . this study demonstrates that amyloid pet scanning has clinical utility is some cases in addition to csf examination , and provides evidence to support its use particularly in young - onset , atypical dementias , where csf results are borderline and diagnostic uncertainty remains . demographic and clinical information on the study participants : clinical presentation refers to the most prominent symptom at initial presentation . family history is considered positive if at least one first order relative had a diagnosis of dementia , with young onset classed as an onset of symptoms before the age of 65 . those with a family history of young onset dementia were tested for known autosomal dominant mutations of neurodegenerative dementias , but none were found . the addenbrook 's cognitive examination ( ace ) iii gives a score out of 100 , incorporating a range of cognitive domains including attention , memory , verbal fluency , language , and visuospatial skills . those seven participants for whom the pet scan led to a change in diagnosis are indicated by an . further information on these seven individuals can be found in table 1 of the main paper .

cerebrospinal fluid ( csf ) measures of amyloid and tau are the first - line alzheimer s disease biomarkers in many clinical centers . we assessed if and when the addition of amyloid pet following csf measurements provides added diagnostic value . twenty patients from a cognitive clinic , who had undergone detailed assessment including csf measures , went on to have amyloid pet . the treating neurologist s working diagnosis , and degree of diagnostic certainty , was assessed both before and after the pet . amyloid pet changed the diagnosis in 7/20 cases . amyloid pet can provide added diagnostic value , particularly in young - onset , atypical dementias , where csf results are borderline and diagnostic uncertainty remains .

INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION Supplementary Material

the effects of exogenous administration of neurotrophic molecules on neurorestoration of lesioned central nervous system have been largely evaluated . pigment epithelium derived factor ( pedf ) has emerged as a potential candidate to promote behavioral gain and neurorestorative events in the spinal cord injury because pedf receptor is concentrated in ventral motor region of the spinal cord and the molecule is highly expressed and it is able to trigger trophic actions to motor neurons [ 1 , 2 ] . the potential capacity of pedf to promote motor restoration may involve its ability to modulate neurotrophic / neuroplasticity events and its capacity to interfere with endothelial and glial reactions to injury , cells that are also important actors in the scenario of neurorestoration [ 25 ] . despite the great effort to understand the inhibitory nature of neuronal environment to regenerating fibers , recent results have pointed out neuronal plasticity in the lesioned spinal cord as the major event leading functional recovery in that pathological condition [ 610 ] . in fact , studies have identified and characterized molecular signals related to axonal growth and functional target innervation in the lesioned spinal cord . much of the functional restoration observed in the experimental models of spinal cord lesion has been triggered however by the neuroplasticity - related molecules that are expressed by rescued neurons nearby injury , especially in the regions of the central pattern generators ( cpg ) [ 1114 ] . furthermore , the apoptotic and neurotrophic responses in neurons that are not enrolled by primary lesion as well as the paracrine glial mechanisms may modify the functional outcome [ 1517 ] . those events occurred in several rostral / caudal spinal levels in the subsequent periods after lesion [ 18 , 19 ] . molecular signaling plays a central role in the cell communication - mediated neuroplasticity in the lesioned nervous system , especially those that are involved in neuroprotection , neovascularization , glial activation , and extracellular matrix regulating neuronal fiber growth . in that context , neurotrophin 3 ( nt-3 ) , glial derived neurotrophic factor ( gdnf ) , brain derived neurotrophic factor ( bdnf ) , fibroblast growth factor 2 ( fgf-2 ) , and pedf have been described as proteins that are able to exert autocrine / paracrine trophic actions to spinal cord neurons and also able to modulate wound repair events that are triggered by nonneuronal cells [ 5 , 16 , 20 ] . furthermore , the ephrin system may also play important action on neurorestoration , remarkably in the lesioned spinal cord , due to its actions on multiple cellular regenerative events . for instance , ephrins could modulate axonal guidance [ 2123 ] , target reinnervation , synaptic plasticity [ 2426 ] , neurotrophic factor signaling - induced neuroprotection / neuroplasticity , and endothelial / glial reaction - induced wound repair [ 2729 ] . the large range of actions of ephrin system is favored by the spread distribution of the receptor tyrosine kinase eph and its membrane - bound ligand ephrin in astrocytes , endothelial cells as well as in presynaptic and postsynaptic neurons [ 3032 ] . remarkably , the above mentioned intercellular signaling events that mediate the outcome of a spinal cord injury are modulated by molecules of the extracellular matrix specially the members of the chondroitin sulfate proteoglycan ( cspg ) family . two molecules , which were revealed by immunoblot analysis after chondroitinase treatment , are in the context of neuroregeneration . the 70 kda chondroitin sulfate / dermatan sulfate hybrid chain and also the 150 kda neurocan - derived c - terminal product , a proteolytic and biological activity fraction of the full - length neurocan [ 34 , 35 ] , seem to play a role in neurotrophic factor binding and neuronal fiber growth . among the vast , complex , and imbricate cellular and molecular events driving neurorestorative functional outcome , the local ischemia is a pathological condition that appears not only as a consequence of lesion reaction to a spinal cord injury but also as a disorder that is able to interfere with local wound repair and neurotrophic / neuroplasticity mechanisms [ 36 , 37 ] . the effects of a pedf injection in the epicenter of an ischemic lesion applied in a low thoracic level of the rat spinal cord were investigated behaviorally and also at cellular and molecular levels . regulations of molecules related to neuroplasticity , neurotrophism , and neovascularization and also those of the growth cone inhibitor chondroitin sulfate proteoglycans ( cspg ) family and ephrin system were analyzed in the lumbar spinal cord cpg . specific pathogen - free adult male wistar rats from the university of so paulo school of medicine ( n = 42 , weighting 350400 g ) were used in the present study . rats were kept under controlled temperature and humidity conditions with a standardized light / dark cycle ( light on at 7 : 00 a.m. and off at 7 : 00 p.m. ) with free access to food pellet and tap water . the study was conducted according to protocols approved by the animal care and use ethic committee at the university of so paulo and in accordance with the guide for the care and use of laboratory animals adopted by the national institutes of health . rats were anesthetized intraperitoneally with a mixture of ketamine chlorhydrate ( 62.5 mg / kg ) and xylazine chlorhydrate ( 10 mg / kg ) . . rose bengal dye ( aldrich chemical , 40 mg / kg , diluted in 0.9% nacl in a final concentration of 20 mg / ml ) was administered slowly in the rat dorsal vein ( n = 30 ) . the rat back was shaved and disinfected with an iodopovidone solution . immediately after dye injection , a midline longitudinal incision was made over the thoracic 8- to the lumbar l1 ( t8-l1 ) vertebrae ; the skin was retracted and paravertebral muscles were dissected . the spinal process and the vertebral lamina of thoracic 12 ( t12 ) spinal cord level were removed with a complete exhibition of circular regional dura mater ( laminectomy ) . a 5 mm diameter - fiber - optic linked to a xenon lamp device ( schott kl 1500 , mainz , germany ) , which produces a 560 nm wavelength irradiation , was placed on the surface of the dura - exposed spinal cord ( thoracic level ) illuminating it for 20 minutes . the fiber - optic was attached to a stereotaxic device ( kopf , usa ) , attempting to maintain a 2 mm distance between the fiber - optic and the dorsal spinal cord to be lesioned . the procedure induced an excitation of the systemically injected dye , triggering a local thrombosis and ischemia [ 38 , 39 ] . sham operated rats ( n = 12 ) were submitted to microsurgical procedures and light exposure , without receiving the dye intravenous injection . immediately after spinal cord ischemia or sham surgery , the animals received a stereotaxical injection of the neurotrophic factor pedf ( 10 l , 100 ng / ml ; hs300210 , kindly supplied by dr . joyce tombran - tink , university of missouri - kansas city ) or solvent ( 10 l , phosphate buffered saline , ph 7.4 ) at the epicenter of the lesion . the spinal injections were made with 100 m outer diameter glass needles , which were obtained by means of a pipette puller ( kopf ) . the needle was connected to a hamilton syringe ( 50 l ) and to a stereotaxical apparatus adapted with a spinal cord unit ( kopf ) in order to promote the mechanical injection , which lasted 35 minutes . were submitted to a sham surgery and a local injection of solvent ( n = 12 ) . in the saline group rats received an ischemic lesion and a local injection of solvent ( n = 14 ) . in the pedf group rats received an ischemic lesion and a local injection of pedf ( n = 16 ) . at the end of the procedure the animals received preventive antibiotic therapy ( ceftriaxone , 40 mg / kg , i m . daily ) for 15 days and also accompanied for bladder evacuation using the crede method until bladder functional recovery . animals submitted to photothrombotic spinal cord injury or sham operation were evaluated behaviorally using the inclined plane test 24 , 48 , and 72 hours after surgery and then weekly until the end of week 6 . animals were placed head down on an adjustable inclined plane covered by a rubber mat . the angle of the plane was increased from 0 to the point where the rat could not maintain its position for 5 seconds . normal uninjured rats remained on the plane to an angle of 50 to 60 inclination . the inclined plane test was chosen because the performance on the inclined plane correlates with the integrity of the rubrospinal tract and other nonpyramidal pathways that could be compromised at week 6 after ischemic injury . the test can be also used as an index of animal strength and it has been shown to be a sensitive and reliable test for clip compression injury . half of the animals in each group ( n = 68 ) were processed for immunohistochemistry six weeks after spinal cord injury . the rats were anesthetized with sodium pentobarbital and euthanized by a transcardiac perfusion with 100 ml isotonic saline at room temperature , followed by 500 ml of fixation fluid ( 4c ) over a period of 6 minutes [ 20 , 43 , 44 ] . the fixative consisted of 4% paraformaldehyde ( w / v , merck , darmstadt , germany ) in 0.1 m phosphate buffer , ph 6.9 . the spinal cords were removed , kept in the fixative solution at 4c for 90 minutes , and then rinsed in 10% sucrose ( merck ) dissolved in 0.1 m phosphate - buffered saline ( pbs ) , ph 7.4 , for 48 hours . the spinal cords were cut into pieces of 0.8 cm long at the lumbar intumescence level . the segments were then frozen in dry ice - cooled ( 40c ) isopentane ( sigma , milwaukee , wi ) and stored at a 70c freezer until use . adjacent serial 14 m thick frozen sections were obtained with a cryostat ( leica , cm3000 , germany ) from the spinal cord lumbar segment ( l2l5 ) , containing the cpg region . series in a cranial - caudal order including every 100th sections were used for tissue labeling . thus , three sampling sections / animal were submitted to each immunolabeling procedure ( see below ) . immunoreactivity was detected by the avidin - biotin peroxidase technique [ 46 , 47 ] . sections were washed for 2 10 minutes in pbs and incubated with 5% normal goat serum for 30 minutes at room temperature . the series of sections were then incubated for 48 hours at 4c with the mouse monoclonal microtubule associated protein-2 antibody ( map-2 , diluted 1 : 2,500 , sigma ) . the antibody was diluted in pbs containing 0.5% triton x-100 ( sigma ) and 1% bovine serum albumin ( sigma ) . the sections were washed again in pbs ( 2 10 minutes ) and incubated with biotinylated horse anti - mouse immunoglobulins ( vector , burlingame , ca , usa ; diluted 1 : 250 ) for 2 hours . after rinsing in pbs , sections were incubated with an avidin - biotin peroxidase complex ( both diluted 1 : 125 , vectastain , vector , usa ) for 45 minutes . immunoreactivity was visualized using 3 - 3-diaminobenzidine tetrahydrochloride ( sigma ) as a chromogen and h2o2 ( 0.05% , v / v , sigma ) for 8 minutes . to standardize the immunohistochemical procedure , we used a dilution of the primary antibody , a dab concentration , and an incubation time , all adjusted so that the darkest elements in the spinal cord sections were below saturation . to further analyze the specificity of the immunostainings , sections were incubated with the solvent of the primary and secondary antibodies or with the solvent of the avidin - biotin solution and processed at the same time with the experimental sections . the sections submitted for measurements were selected from those three of sampling regime described above that represented better the cranial ( l2-l3 ) and caudal ( l4-l5 ) regions of the lumbar rat spinal cord . the means of the data of the two regions were presented because there is no description of functional differences between two regions of the cpg . the map-2 immunoreactivity was measured in two spinal cord sections per rat by means of semiquantitative morphometric image analysis . the measurements were done in the ventral horn of lumbar intumescence ( caudal to the injury site ) , where the lumbar cpg is located and the spinal cord showed a preserved morphology . the image analysis procedures , implemented on a kontron - zeiss ks400 image analyzer ( germany ) , have been described previously [ 19 , 43 , 46 , 4850 ] . briefly , a television camera from the microscope ( 40 objective ) acquired the image . the mean gray value ( mgv ) and s.e.m . of gray matter in areas of the spinal cord devoid of specific labeling ( background , bg ) were measured . gray values darker than bgmgv , 3 s.e.m . were considered as belonging to specific labeling and thus discriminated . the specific ( sp ) mgv was subsequently defined as the difference between the bgmgv value and the mgv of discriminated profiles . the procedure was repeated for each section to correct every measurement of specific labeling for its background value . the morphometric and microdensitometric ( spmgv ) measurements indicate the amount of immunoreactive cell profiles and the intensity of immunolabeling in the sampled fields , respectively . the map-2 immunoreactive dendritic and cell body profiles were quantified individually by means of a stereological method . the point intercepts stereological tool was employed to obtain the areal fraction in the sampled region of the ventral horn of the spinal cord rats , bilaterally , as described elsewhere [ 20 , 43 , 44 ] . a point - grid with an area per point of 400 m was used to estimate the area of the counted profiles . the aa was calculated [ 20 , 43 , 44 ] ( aa = pstructure/psection ) . a 40x oil - immersion objective was used to acquire the images that were used to quantify the profiles in the gray matter sampled fields . all map-2 immunoreactive processes that emerged from the cell perikarya ( first level processes ) were not considered in the discrimination procedures so that axons and axon hillock were not included in the measurements . the sections were initially washed for 3 10 minutes in pbs and then were incubated for 48 hours at 4c with a mixture of one of the antibodies to receptor eph or ephrin subtypes ( the descriptions of the antibodies and the employed dilutions are shown in table 1 ) and one of the following antibodies to neuronal and astroglial markers : mouse monoclonal neurofilament-200 antibody ( nf-200 , diluted 1 : 200 , sigma ) , rabbit polyclonal glial fibrillary acidic protein antibody ( gfap , diluted 1 : 200 , sigma ) , or goat polyclonal gfap antibody ( diluted 1 : 50 , dako ) . the antibodies were diluted in pbs containing 0.5% triton x-100 ( sigma ) and 1% bovine serum albumin ( sigma ) . after the incubation of the primary antibodies , sections received two washes of 10 minutes in pbs and were incubated for 2 hours in the dark at 37c with a mixture of fluorescein isothiocyanate ( fitc ) and texas red ( both diluted 1 : 40 , jackson , west grove , usa ) . the sections were rinsed in pbs and were examined in an ax70 olympus epifluorescence photomicroscope . the other half of the animals ( n = 68 ) were euthanatized by decapitation and processed to western blot and real - time polymerase chain reaction ( rt - pcr ) techniques . the spinal cords were rapidly removed and a 0.8 cm fragment was cut from the lumbar intumescence as described previously . the ventral part ( motor area ) was carefully separated from the dorsal part ( sensory area ) in each fragment . the caudal portion was then submitted to western blot technique and the cranial one to the rt - pcr procedures . the material of rt - pcr was frozen in dry ice and stored at 70c freezer until processing . the samples were homogenized in lyses buffer containing 1% np40 ( sigma ) , 0.5% sodium deoxycholate ( sigma ) , 1% sodium dodecyl sulfate ( biorad ) , 1 mm ethylenediaminetetraacetic acid ( sigma ) , 1 mm ethylene glycol tetraacetic acid ( sigma ) , and 1% protease inhibitor cocktail ( sigma ) , diluted in phosphate buffered ( ph 7.4 ) . after centrifugation ( 14,000 rpm ) for 20 min at 4c , as described previously , the supernatants were transferred into new tubes and stored at 70c until use . the samples ( 60 g of protein / lane ) were separated on a 12% sodium dodecyl sulfate ( sds ) polyacrylamide ( biorad ) gel electrophoresis at 100 v for 1 h. proteins ( 120 g ) were transferred to polyvinylidenefluoride ( pvdf ) membrane at 100 v during one hour . membranes were then blocked with 10% milk diluted in tbs - t ( mixture of tris - buffered saline and 0.05% tween 20 ) for 30 minutes under slight agitation at room temperature . then , all membranes were incubated overnight at 4c with the respective antibodies : a mouse monoclonal antibody to map-2 ( 1 : 1,000 ; novus biological ) , a mouse monoclonal antibody to brain core protein of cspg ( 1 : 500 , millipore ) , a rabbit polyclonal antibody to laminin ( 1 : 1,000 ; sigma ) , and a rabbit polyclonal antibody to b - cell lymphoma protein-2 ( bcl-2 , diluted 1 : 1,000 ; santa cruz ) . membranes were also submitted to specific labeling of subtypes a and b of eph receptors and ephrins . the concentration used and the descriptions of the antibodies are shown in table 1 . membranes were washed 2 times for 10 minutes in tbs - t and incubated at room temperature for 1 hour with anti - mouse ( 1 : 6,000 ; ge ) , anti - rabbit ( 1 : 10,000 ; ge ) , or anti - goat ( 1 : 2,000 ; ge ) igg ecl conjugated secondary antibodies . in the sequence , after final washes , the membranes were incubated with western lightning chemiluminescence reagent plus ( perkinelmer life science , usa ) for 1 minute . the membranes were exposed to an x - ray film for imaging ( hyperfilmtm ecl , ge healthcare , usa ) to visualize protein bands . the membranes of every blot were then washed and incubated individually with a mouse monoclonal antibody to alpha - tubulin ( 1 : 30,000 ; sigma ) diluted in tbs - t containing 1% bsa for 1 hour at room temperature and developed as described previously . the densitometry of the bands was quantified by means of a computer assisted image analyzer and a software developed by imaging research ( brock university , canada ) as described elsewhere . dividing the density of the protein signal by the correspondent alpha - tubulin signal value performed data normalization . total rna from spinal cord fragments was extracted with rnaspin mini kit ( ge healthcare , uk ) according to the manufacturer 's instructions . rna quantity and integrity were assessed by spectrophotometry ( nanodrop ) and microfluidics - based electrophoresis ( bioanalyzer , agilent 2100 ) , respectively . only rna samples with od 260/280 1.8 and rin ( rna integrity number ) > 7 were used for quantitative rt - pcr . for rt - pcr reactions , total rna was converted into cdna in the presence of reverse transcriptase ( multiscribe , applied biosystems ) and random hexamer primers ( applied biosystems ) , according to manufacturers ' instructions . quantitative pcrs reactions were performed on a step one plus sequence detection system ( applied biosystems ) using taqman universal pcr master mix ( applied biosystems ) in a total volume of 20 l . the gene expression of the following molecules was analyzed : the neurotrophic factors nt-3 ( rn00579280_m1 ) , gdnf ( rn00569510_m1 ) , bdnf ( customized , forward 5tggttatttcatacttcgg ttgcatga3 , reverse 5tgtccgtggacgtttgctt3 , and probe 5ctgcgcccatgaaag3 ) , and fgf-2 ( rn00570809_m1 ) , the eph receptors epha6 ( rn01474859_m1 ) and ephb2 ( rn01181017_m1 ) , and the small gtpase rhoa ( rn04219610_g1 ) . the amplification protocol included 3 minutes at 95c , followed by 45 cycles of 10 seconds at 95c for denaturation and 45 seconds at 60c for annealing and extension . statistical analysis for the behavioral data consisted of a two - way analysis of variance and followed the bonferroni posttest . a second analysis was performed including only the saline and pedf groups , in order to obtain data related to motor recovery of the injured animals . in the western blot , immunohistochemistry and rt - pcr analyses , the one - way anova was applied with tukey 's multiple comparisons posttest to identify statistical significances between groups . data were presented as means s.e.m . and significance level was set at p < 0.05 . the motor evaluation of animals submitted to ischemic spinal cord injury was performed by the inclined plane test . the statistical analysis by the two - way anova showed effects of time ( p < 0.0001 ; f = 101.4 ) , treatment ( p < 0.0001 ; f = 32.99 ) , and interaction time / treatment ( p < 0.0001 ; f = 7.516 ) when the three groups were analyzed together , as well as when only the saline and pedf groups were included in the evaluation ( effects of time p < 0.0001 , f = 99.14 ; of treatment p = 0.002 , f = 9.543 ; and of interaction time / treatment p = 0.004 , f = 5.80 ) . therefore , differences between the saline and pedf groups ( p < 0.001 ) were seen at week 4 to week 6 of assessment , according to the bonferroni posttest ( figure 1 ) . furthermore , although sham and saline groups differed at all evaluated periods , sham and pedf groups were different only at 13 days time - interval ( figure 1 ) . the effects of photothrombotic ischemic injury and treatment with pedf on the neuroplasticity in the ventral horn of the lumbar spinal cord were analyzed by means of map-2 detection . western blot revealed an increase ( 87.78% ) of map-2 protein level in the ventral region of lumbar spinal cord of pedf treated group compared to sham ( p < 0.05 , figure 2(a ) , also illustrated in figure 2(c ) ) . moreover , map-2 immunoreactivity was elevated ( p < 0.001 ) in the ventral horn of lumbar spinal cord in rats of pedf group compared with the sham ( 35.99% ) and saline ( 33.81% ) groups ( figure 2(a ) ) . the qualitative analysis showed an increased map-2 immunoreactivity in the neuronal cell bodies and fibers of the spinal cord ventral horn of pedf rats , compared to saline rats ( figure 2(b ) ) . furthermore , the stereological tool point intercepts revealed that pedf injection elevated ( 11.71% , values expressed as areal fraction ) the amount of map-2 immunoreactive dendritic processes in the ventral horn of the lumbar spinal cord in relation of saline injected rats ( figure 3 ) . the stereological method revealed no alterations in the areal fraction of the map-2 immunoreactive perikarya among experimental groups . the values of areal fraction of map-2 immunoreactive perikarya were 31.69 1.61 , 34.79 2.17 , and 38.94 4.39 of sham , saline , and pedf groups , respectively ( mean s.e.m . , p > 0.05 ) . the increased map-2 immunoreactive dendritic profiles in the ventral horn of pedf treated rats are illustrated in higher magnification microphotographs of representative rats of the three studied groups ( figure 4 ) . the stereological tool , named point intercepts ( red frame ) , that was projected on the digital image of map-2 immunoreactive profiles for quantification of neuronal dendrites and cell bodies of ventral horn were illustrated in figure 4 . it should be mentioned that the sections incubated with the solvent of the primary or secondary antisera as well as with the solvent of the avidin - biotin solution showed no reaction ( data not shown ) . rt - pcr for relative gene expression of neurotrophic factors in the ventral region of lumbar spinal cord revealed a decrease of nt-3 in the pedf group compared to sham ( 38.52% , p < 0.05 , table 2 ) . moreover , gdnf gene expression was found to be elevated in the pedf group compared to sham ( 38.21% , p < 0.05 ) and also to saline ( 94.0% , p < 0.01 ) groups ( table 2 ) . no differences were seen in the analyses of bdnf and fgf-2 gene expression ( table 2 ) . no differences were observed among the experimental groups at the postoperative periods performed in this study ( data not shown ) , thus representing no autocrine regulation of that neurotrophic factor in the present experimental conditions . western blot of the growth cone inhibitor cspg levels in the ventral region of lumbar spinal cord showed two bands of molecular weights 70 and 150 kda ( figures 5(a ) and 5(b ) ) . the chondroitinase treatment allowed the identification of a 70 kda chondroitin sulfate / dermatan sulfate hybrid chain and also a 150 kda neurocan - derived c - terminal product [ 34 , 35 ] . decreases in the cspg level were found in the 70 kda band ( p < 0.05 ) of the pedf ( 12.92% ) and also saline ( 18.33% ) groups compared to sham rats ( figure 5(a ) , also illustrated in figure 5(b ) ) . laminin and bcl-2 proteins were used as markers for angiogenesis and antiapoptosis regulator , respectively , and were quantified by means of western blot in the ventral region of lumbar spinal cord of the rats ( figures 6(a ) and 6(b ) ) . laminin level was elevated ( 66.23% ) in the saline group compared to sham ( p < 0.01 ) and a decrease ( 24.97% ) in the level of laminin was found in the pedf group compared to saline ( p < 0.5 ) . regarding the bcl-2 analysis , no changes were demonstrated among groups at the postoperative studied periods ( figure 6 ) . the protein levels of subtypes a and b of the eph receptors and ephrins were quantified by western blot in the ventral region of lumbar spinal cord of the rats ( figure 7 ) . the epha4 level increased in the saline ( 122.16% ) and pedf ( 127.93% ) groups compared to sham ( p < 0.01 ) , and no changes were observed in protein levels of the receptors epha2 , a3 , a5 , and a7 ( figure 7(a ) ) . regarding the levels of type - a ephrins , ephrin a2 increased ( 64.28% ) in the pedf group compared to sham ( p < 0.05 ) , and no changes were seen in the ephrins a1 , a3 , a4 , and a5 ( figure 7(b ) ) . the representative bands of ephs a and ephrins a illustrated the effect described above ( figures 7(c ) and 7(d ) ) . furthermore , regarding the ephs b1 , b4 , and b6 ( figure 7(e ) ) , no differences were found among the experimental groups . moreover , increases of ephrin b1 levels were observed in the saline ( 71.78% ) and pedf ( 53.51% ) groups compared to sham ( p < 0.05 , figure 7(f ) ) . ephrin b2 level was elevated in the pedf group compared to sham ( 49.67% ) and saline ( 43.54% ) groups ( p < 0.05 ) , and the ephrin b3 level was increased in the pedf group ( 87.55% ) compared to sham ( p < 0.05 ) , ( figure 7(f ) ) . the representative bands of ephs b and ephrins b illustrated the effects described above ( figures 7(g ) and 7(h ) ) . some members of studied eph receptors , particularly the epha1 , a6 , a8 , a10 , b2 , and b3 , showed no specific signal bands at the western blot assay . finally , the relative gene expression analyses of epha6 and ephb2 receptors as well as the small gtpase rhoa , performed by rt - pcr in an adjacent region , showed no differences among the experimental groups ( table 2 ) . the cellular analysis of the two - color immunofluorescence in ventral horn of the rat spinal cord showed a colocalization of the epha1 , epha2 , epha7 , epha8 , ephb1 , ephb4 , and ephb6 receptors , as well as the ephrin a5 with the nf-200 positive motor neurons of this region . the type b ephrins ( b1 , b2 , and b3 ) are colocalized with astrocytes of that region ( data not shown ) . the presence of ephrin b2 in astrocytes of ventral horn of pedf treated rat is illustrated in figure 8 . the qualitative analysis of immunofluorescence allowed the recognition of cellular component of the labeling signals but did not lead the identification of differences among groups . spinal cord ischemia is considered the most relevant event present in a series of pathological situations , including trauma , tumor , infection , and circulatory disorders , contributing to the deleterious secondary mechanisms that amplify initial injury [ 5255 ] . ischemia might also influence injury outcome and neurorestorative events due to its ability to modify neurotrophic and neuroplasticity responses of nearby lesion [ 56 , 57 ] . experimental models of spinal cord trauma are largely employed [ 5862 ] ; however , analyses have failed to attempt the circumstances of related ischemia . this work performed a spinal cord injury photothrombotic ischemia using the rose bengal method , as first described by watson et al . reproducible lesion with regard to its size , localization , and behavioral response is achieved because the method allows a precise control of dye concentration and irradiation settings thus leading , in rats , to a nonrecovery of blood flow , an absence of short term behavioral recovery , and a 3-month - old circumscribed lesion in the dorsal half of the cord as described previously [ 6668 ] . importantly , the photothrombotic injury applied at the low thoracic levels of rat spinal cord of the present work preserved the lumbar segments caudally where rat lumbar cpg is located . neuroplasticity in the lumbar cpg has been addressed as the major source of motor recovery , spontaneously or after treatments , following spinal cord lesion [ 7072 ] . the understanding of the neuroplasticity potential of the lesioned spinal cord would favor the translation of spinal cord regeneration to clinical practice ( http://www.clinicaltrial.gov , nct00406016 ) [ 73 , 74 ] . neurotrophic factors have been tested on spinal cord injury experimentally , especially those with actions on several aspects of neurorestoration , for instance , wound repair , neuronal trophism , and neuroplasticity [ 7577 ] . pedf has been pointed out as a potential candidate mainly in terms of motor recovery because the molecule is highly expressed and triggered trophic actions to motor neurons and because its receptor is concentrated in ventral motor region of the spinal cord [ 1 , 2 ] . in fact , we described motor behavior improvements and neuroplasticity responses in the low thoracic lesioned rats after a pedf injection in the epicenter of the injury . the rats that were submitted to the experimental procedures were accompanied behaviorally by means of the inclined plane test , which evaluates muscle strength and endurance parameters required to keep the animal in a static position when its plane is submitted to a progressive increase of the inclination angle [ 78 , 79 ] . the possibility of pedf injection in the epicenter of a spinal cord photothrombotic injury to trigger neuroplasticity events in the lumbar regions of the organ was evaluated by means of the responses of structural protein map-2 . the regulation of that neuronal microtubule protein in the lesioned nervous system has been associated with dendritic branching and synaptic plasticity . western blot analysis revealed increases of map-2 levels in ventral regions of the lumbar spinal cord after the ischemic lesion applied cranially , remarkably in the rats treated with pedf , indicating that the neurotrophic factor is able to stimulate neuronal plasticity in the regions of the spinal cord distant to the wound . quantitative microdensitometric image analysis of map-2 immunoreactivity revealed , at cellular level , increases of map-2 immunoreactivity in the perikarya and neuropil of large motoneurons in the ventral horn of the lumbar region , caudal to ischemic injury site , of rats treated with pedf . image analysis is not able to separate map-2 positive dendrites from the cell bodies profiles . the stereological method however allowed us to show the neuroplasticity responses taking place in the dendritic process of map-2 positive neurons of the ventral horn of pedf treated rats . these results are in agreement with previous publication which treated a traumatic spinal cord injury with another neurotrophic factor , thus revealing the potential of spinal cord plasticity to lead a higher behavioral recovery after organ injury . neuroplasticity is favored by a complex intracellular signaling that takes place in the rescued regions of the lesioned nervous tissue . in fact , the unaltered levels of the antiapoptotic factor bcl-2 [ 8183 ] in lumbar ventral region indicate the absence of local neuronal death , favoring further neuronal plasticity in that region . neuroplasticity is a result of events specially addressed by the responsive neurons , their neighbor nonneuronal cells , and extracellular matrix molecules [ 8486 ] . regarding that , pedf seems to be a promising candidate to spinal cord repair due to its actions on spinal cord neurons and ability of signaling to the endothelial and glial cells , the main actors of neurorestorative events in nervous tissue [ 3 , 87 ] . remarkable pedf actions include those that are inhibitory to angiogenesis and astrogliogenesis [ 87 , 88 ] , thus with substantial impact to extracellular matrix elements . although neovascularization is required for neuronal fiber growth in regions close to injury acutely , to our knowledge , there is no publication referring to a long lasting possible interaction of vasculature regulation and neuronal plasticity in regions distant to lesion . nevertheless , a recent publication correlated a local pedf expression to opposite responses of nerve fibber growth and neovessels in the cornea treated with the neurotrophic factor fgf-2 , which is in agreement with our results on pedf - induced downregulation of laminin , a marker of small blood vessels , in lumbar spinal cord neuroplasticity responsive region that is distant from the injury . inhibitory actions of pedf to astrocytes may have not interfered with ability of reactive astrocytes of the lesioned spinal cord to secrete cspg in the neuroplasticity responsive region caudally . inhibitory influence of extracellular matrix molecules , especially cspg , to fiber growth close to the spinal cord injury site has been described [ 92 , 93 ] ; however , there is a lack of descriptions on the regulation of cspg in the neuroplasticity responsive spinal cord regions . the decreased level of 70 kda cspg in the motor ventral region of the lumbar levels , far from the photothrombotic injury site , in animals treated or not with pedf and at a chronic period after surgery ( 6 weeks ) already emphasizes the ability of the lesioned spinal cord to last a permissive microenvironment for neuronal plasticity [ 94 , 95 ] . all in all , pedf actions to nonneuronal actors of neurorestorative events seem to favor neuronal plasticity in the lesioned spinal cord . additional feature of pedf is its capability to modulate the expression of other neurotrophic factors , thus amplifying neurorestorative events triggered by specific trophic molecules in the lesioned nervous system [ 9699 ] . there are actually several neurotrophic factors that play paracrine / autocrine actions on the spinal cord motor neurons . based on that , we evaluated gene expression of nt-3 , gdnf , bdnf , and fgf-2 by means of rt - pcr in the neuroplasticity responsive lumbar motor region of the spinal cord injury rats . we do not know whether photothrombotic ischemia in the low thoracic level of the rat spinal cord has triggered gene expression of studied neurotrophic factors in the neuroplasticity responsive lumbar region acutely ; however , at the later week 6th time point , pedf treatment modulated the differentially nt-3 and gdnf gene regulation . the pedf - induced downregulation of nt-3 gene expression in the late period after injury might be related to a fine tuning of neuroplasticity responses in the cord [ 100 , 101 ] by an action on the descending corticospinal motor fibers [ 102 , 103 ] . furthermore , such a regulation that was induced by pedf treatment might have favored the expression of a neurotrophic factor with stronger actions to postsynaptic spinal cord motor neurons . that would be actually the case for gdnf [ 5 , 76 , 97 , 104 ] . the absence of a late gene regulation of bdnf and fgf-2 might be explained for their ability to modulate early events after injury like neuronal rescue , progenitor cell proliferation , glial reactivity , and wound repair [ 14 , 105 ] . the bidirectional signaling system provided by the eph receptors and their ligands was recently mentioned as a key regulator of neuroplasticity in central nervous system . ephrin signaling plays important actions regarding axonal guidance and synaptogenesis during development [ 107 , 108 ] . the role of ephrin on the lesioned spinal cord has been the subject of recent investigation [ 29 , 109 ] . the ephrin function is highlighted on neurorestorative events mainly because of its ability to prompt communication between neuronal and nonneuronal cells [ 110 , 111 ] . we have analyzed at biochemical and cellular levels several members of the ephrin a and b families as well as the receptor subtypes of the eph a and b families that could play a role in the lesioned spinal cord . the epha6 and ephb2 signals that were not shown by western blot and immunohistochemistry were evaluated at molecular levels by employing rt - pcr . upregulations of ephrins and their eph receptors have been described in reactive astrocytes close to rat spinal cord injury [ 29 , 31 , 113 ] . the regulation of ephrin system close to spinal cord injury has been associated with its ability to interfere with cell activation related to wound repair and also to inhibit neurite outgrowth and axonal regeneration close to a wound repair region [ 114 , 115 ] . remarkably , increases of epha4 in reactive astrocytes close to a scar region of the lesioned spinal cord were correlated to inhibition of axonal regeneration [ 116 , 117 ] , event that gained importance after the description of the improvement of axonal regeneration and reduction of glial scar in the epha4-deficient spinal cord injury mouse . furthermore , epha4 antagonist was able to block retrograde axonal degeneration , to increase axonal regeneration , and to improve motor behavior in lesioned spinal cord rats [ 109 , 116 ] . the present analysis demonstrated regulation of ephrin system in the neuroplasticity responsive lumbar motor region after a chronic spinal cord low thoracic injury , remarkably the ephrins a2 , b1 , and b3 and the receptor epha4 . the details of their contribution to neuronal plasticity in the lesioned spinal cord must be further evaluated . nevertheless , changes in the levels of ephrin b system were correlated to neuropathic pain due to their ability to regulate neuronal excitability at spinal cord . important finding of the present study was the upregulation of ephrin b2 in the neuroplasticity responsive region of pedf treated rats compared to nontreated lesioned animals , thus with a special relevance to motor recovery . in fact , the epha4/ephrin b3 bidirectional signaling in developing spinal motor neurons seems to be involved in locomotion function [ 119122 ] . because ephrin b2 is specifically present in astrocytes of neuroplasticity responsive area , as demonstrated by the double immunofluorescence analyses , that ephrin signalling may contribute to well describe the ability of glial cells to promote neuronal plasticity . all in all , it is likely that long term spinal cord injury might employ ephrin signaling for spontaneous motor recovery , event that could be amplified by neurotrophic factor - induced regulation of specific ephrin molecules , as it is the case of pedf . finally , long term ephrin regulation in the neuroplasticity responsive region of the lesioned spinal cord does not seem to require the transcription factor rhoa . rhoa impairs neurite outgrowth , by means of growth cone collapse , an event that could be restricted to wound areas [ 124 , 125 ] where upregulation of rhoa mrna and protein last on reactive astrocytes of the lesion site of a cord injury [ 126128 ] . further analyses are required for a further understanding of the rhoa function in the neuroplasticity areas after a long period after injury . pedf injection in the epicenter of a low thoracic rat spinal cord photothrombotic ischemic injury improved motor behavior and triggered neuroplasticity responses in the motor regions of lumbar levels far from the lesion site . changes in the expression of extracellular matrix protein , neurotrophic factors , and molecules of the ephrin system may have favored neuroplasticity .

pigment epithelium derived factor ( pedf ) exerts trophic actions to motoneurons and modulates nonneuronal restorative events , but its effects on neuroplasticity responses after spinal cord ( sc ) injury are unknown . rats received a low thoracic sc photothrombotic ischemia and local injection of pedf and were evaluated behaviorally six weeks later . pedf actions were detailed in sc ventral horn ( motor ) in the levels of the lumbar central pattern generator ( cpg ) , far from the injury site . molecules related to neuroplasticity ( map-2 ) , those that are able to modulate such event , for instance , neurotrophic factors ( nt-3 , gdnf , bdnf , and fgf-2 ) , chondroitin sulfate proteoglycans ( cspg ) , and those associated with angiogenesis and antiapoptosis ( laminin and bcl-2 ) and eph ( receptor)/ephrin system were evaluated at cellular or molecular levels . pedf injection improved motor behavioral performance and increased map-2 levels and dendritic processes in the region of lumbar cpg . treatment also elevated gdnf and decreased nt-3 , laminin , and cspg . injury elevated epha4 and ephrin - b1 levels , and pedf treatment increased ephrin a2 and ephrins b1 , b2 , and b3 . eph receptors and ephrins were found in specific populations of neurons and astrocytes . pedf treatment to sc injury triggered neuroplasticity in lumbar cpg and regulation of neurotrophic factors , extracellular matrix molecules , and ephrins .

1. Introduction 2. Materials and Methods 3. Results 4. Discussion 5. Conclusion

additionally , the obturating materials seal within the canal system any irritants that are not removed during chemomechanical preparation . gutta - percha has been considered as the gold standard filling material and for many years has been used as a core material with zinc oxide eugenolbased or ca(oh)2 based sealers . however , leakage and recontamination of the root - canal system continue to cause post - treatment complications . recently endodontic sealers have been developed to improve the sealing and bonding to root dentin . one such epoxy - resin based sealer is ah plus ( dentsply , mailleffer ) that has been extensively used because of its good handling characteristics and the potential for better wettability of dentin and gutta - percha surfaces . manufacturers have further incorporated adhesive dentistry in endodontics by introducing obturation systems with a specific focus on obtaining a monoblock in which the core material , sealer and root canal dentin form a single cohesive unit . the introduction of resilon ( resilon research , north branford , conn . ) resilon is a thermoplastic synthetic resin material that is based on polymers of polyester and contains difunctional methacrylate resin , bioactive glass and radiopaque fillers . it can couple to a variety of dentin adhesives and resin - type sealers , including epiphany . recently , epiphanyself - etch ( se ) was introduced with the promise of optimizing the clinical performance with a simplified application procedure . another is the endorez ( ultradent , south jordan , ut ) system that establishes a bond between a methacrylate resin - coated gutta - percha core material and a urethane dimethacrylate - based sealer . an improved bond and the creation of a monoblock root canal obturation are claimed to be the main advantages of these materials . thus the present in - vitro study is an attempt to evaluate and compare the push - out bond strength of gutta - percha / ah plus , resilon / epiphany se and gutta - percha / endorez to dentin . the null hypothesis tested was that there are no differences in the bond strength between obturation groups tested . sixty extracted single - rooted , single - canal anterior teeth were collected and stored in 0.1%thymol solution until use . the teeth were decoronated at cementoenamel junction ( cej ) with diamond disc and standardized to 10 mm + 1 mm length . working length was established by placing # 15 stainless steel k - file into the canal until it was seen at the apical foramen and then subtracting 1 mm . cleaning and shaping was done by using 0.06 taper k3niti rotary instruments in a gear reduction handpiece ( rotary master , j.morita , usa ) upto size # 40 . the canals were irrigated with 3% sodium hypochlorite during instrumentation with a final rinse of 17% ethylene diamine tetraacetic acid . the canals were dried with sterile paper points , and specimenwere then randomly assigned into three experimental groups of 20 teeth each based on the obturation material used . in group i , ah plus sealer was mixed on a paper pad and applied to the root canal walls using a lentulospiral . pre - fitted # 40/0.06 tapergutta - percha cone was coated with ah plus sealer and pumped a few times . the cone was removed , re - coated with sealer , and then inserted upto the working length . in group ii , epiphany se sealer was dispensed into the canal using intra - oral tips supplied with the system . then , a pre - fitted # 40/0.06 taper resilon cone was inserted upto the working length . in group iii , endorez sealer was dispensed into the canal through navitip and then a pre - fitted # 40/.06 taper endorez cone was placed in the canal as in group ii . all the samples were coronally sealed with cavit g. they were then wrapped in moist gauze piece and stored in incubator at 37c for 2 weeks . then , each slice was placed under a micrometer microscope where the diameter of each obturation site was measured and recorded . this measurement and thickness measurements were used to calculate the bonded area of the filling material . on the coronal side of the slices , the larger diameter was measured to select a support jig with a hole large enough to provide clearance for the obturating material when it will be dislodged from the tooth slices . on the apical side of the slices , the smallest diameter was measured to select a punch to be used to supply load with that side , making sure that the punch would not contact the dentin around the obturating material , causing a crack and erroneous results . each specimen was subjected to push - out test using universal testing machine where the plunger moved in an apical to coronal direction at a crosshead ] speed of 1 mm / min , which resulted in displacement of filling material . the push - out bond strength was calculated using the formula : debond stress ( mpa ) = debonding force ( n)/area ( mm ) where debonding force is the maximum force before debonding and area is the average value of the perimeter times the thickness . the data obtained was subjected to two way analysis of variance and scheffe 's test . sixty extracted single - rooted , single - canal anterior teeth were collected and stored in 0.1%thymol solution until use . the teeth were decoronated at cementoenamel junction ( cej ) with diamond disc and standardized to 10 mm + 1 mm length . working length was established by placing # 15 stainless steel k - file into the canal until it was seen at the apical foramen and then subtracting 1 mm . cleaning and shaping was done by using 0.06 taper k3niti rotary instruments in a gear reduction handpiece ( rotary master , j.morita , usa ) upto size # 40 . the canals were irrigated with 3% sodium hypochlorite during instrumentation with a final rinse of 17% ethylene diamine tetraacetic acid . the canals were dried with sterile paper points , and specimenwere then randomly assigned into three experimental groups of 20 teeth each based on the obturation material used . in group i , ah plus sealer was mixed on a paper pad and applied to the root canal walls using a lentulospiral . pre - fitted # 40/0.06 tapergutta - percha cone was coated with ah plus sealer and pumped a few times . the cone was removed , re - coated with sealer , and then inserted upto the working length . in group ii , epiphany se sealer was dispensed into the canal using intra - oral tips supplied with the system . then , a pre - fitted # 40/0.06 taper resilon cone was inserted upto the working length . in group iii , endorez sealer was dispensed into the canal through navitip and then a pre - fitted # 40/.06 taper endorez cone was placed in the canal as in group ii . all the samples were coronally sealed with cavit g. they were then wrapped in moist gauze piece and stored in incubator at 37c for 2 weeks . then , each slice was placed under a micrometer microscope where the diameter of each obturation site was measured and recorded . this measurement and thickness measurements were used to calculate the bonded area of the filling material . on the coronal side of the slices , the larger diameter was measured to select a support jig with a hole large enough to provide clearance for the obturating material when it will be dislodged from the tooth slices . on the apical side of the slices , the smallest diameter was measured to select a punch to be used to supply load with that side , making sure that the punch would not contact the dentin around the obturating material , causing a crack and erroneous results . each specimen was subjected to push - out test using universal testing machine where the plunger moved in an apical to coronal direction at a crosshead ] speed of 1 mm / min , which resulted in displacement of filling material . the push - out bond strength was calculated using the formula : debond stress ( mpa ) = debonding force ( n)/area ( mm ) where debonding force is the maximum force before debonding and area is the average value of the perimeter times the thickness . the data obtained was subjected to two way analysis of variance and scheffe 's test . the mean push - out bond strength for each group were as follows : group i ( gutta - percha / ah plus ) : 1.49 + 0.16mpa , group ii ( resilon / epiphany se ) : 0.95 + 0.13mpa and group iii ( endorezobturation system ) : 0.56 + 0.15mpa [ table 1 ] . group i shows significantly highest bond strength whereas group iii showed the lowest bond strength . table 2 lists the group - by - location push - out bond strength values . the interactions between different groups was found to be significant ( p < 0.05 ) while the group - by - location interaction was not found to be significant ( p > 0.05 ) . mean and standard deviation values of bond strength in megapascal for different groups mean and standard deviation values of bond strength in megapascal at different locations within each group for the three groups mean bond strength for the three groups mean bond strength at different locations within a group for three groups the bond strength of root canal sealers to dentin is important for maintaining the integrity of the seal in root canal filling . although sealers can form close adhesion to the root canal wall , none is able to bond to gutta - percha ; leaving a gap through which bacteria may pass . an improved bond and creation of monoblockare considered to be the main advantages of resilon / epihanyse and endorez oburation system . these properties should be reflected by improvements in interfacial strength between root - filling material and intraradicular dentin , which may be evaluated using thin - slice push - out tests . in this study , 60 single - rooted , single - canal anterior teeth were used , which were decoronated at cej and standardized to 10 mm + 1 mm length to serve as stable and equivocal reference for all measurements . cleaning and shaping was carried out with 0.06 taper k3 till an apical size of 40 . also its asymmetrical flutes provide superior canal tracking and eliminate transportation thus preventing the file from screwing into the canal . sodium hypochlorite was not used as the final irrigating solution since it is an oxidizing agent that leads to oxidation of some component of the dentin matrix . furthermore , oxygen has been shown to inhibit polymerization of resins , thus leading to reduced resin bond strengths . this passive - fit single - cone obturation protocol , without any type of condensation , was used to maintain experimental consistency among all groups . though manufacturers of resilon / epiphany se and endorez recommend light curing of coronal aspect for 40 s ; but it was not done since then only the most coronal portion would likely be influenced by light activation . samples were then incubated for 2 weeks at 37c to simulate clinical conditions and allow the sealer to set . furthermore , samples with non - circular filling material were discarded as it would result in non - uniform stress distributions during testing and thus inaccurate measurements . this resulted in variance of sample size per group , which was accounted for during statistical analysis . when instrumentation was done with 0.06 taper k3 rotary niti files to an international organization for standardization size 40 , the root section obtained after discarding apical 3 mm had an apical diameter 0.58 mm . the push - out bond strength was then calculated using the formula : debond stress ( mpa ) = debonding force ( n)/area ( mm ) in the present study , group i ( gutta - percha / ah plus ) showed highest bond strength , which was greater than both group ii ( resilon / epiphany se ) and group iii ( endorezobturation system ) . group ii ( resilon / epiphany se ) showed lower bond strength compared to group i ( gutta - percha / ah plus ) but higher than group iii ( endorezobturation system ) . the results of the present study correlate well with that of other studies who also used push - out test design and found higher bond strengths in teeth obturated with gutta - percha and ah plus sealer compared with those filled with resilon / epiphany or endorez obturation system . a plausible explanation for the significantly lower bond strengths detected in the groups containing methacrylate resin - based sealer is the effect of cavity configuration factor ( c - factor ) . c - factor is found to be extremely high in long , narrow root canals . in these situations , there is very limited unbonded surface area to provide relief from the stresses created by polymerization shrinkage . it is likely that the bond between sealer core and sealer dentin is not adequate enough to resist this debilitating stress that develops during polymerization resulting in gap formation . despite using the similar methodology , the results of resilon / epiphany se group in the present study did not correspond well with that of skidmore et al . who found a significantly higher mean bond strength to root dentin in the resilon / epiphany ( 1.51 + 1.22mpa ) compared with gutta - percha / kerr extended working time ( 0.66 + 0.39mpa ) . a potential factor that may have accounted for this dissimilarity includes the difference in obturation technique . the use of single - cone obturation in the present study results in a greater sealer thickness when compared with warm vertical compaction used in their study . this can negatively influence the sealing ability of the root canal filling except when using ah plus sealer . this phenomenon , along with its inherent volumetric expansion , may have contributed to the superior bond strength found with this epoxy resin - based sealer in the present study . research on endorez obturation system disclosed good hydrophilic properties , thus helping create long resin tags in radicular dentin . however , these tags appeared unbonded and exhibited insufficient adhesive strength to resist polymerization shrinkage , resulting in gap formation between sealer and canal wall . this may help explain the very low bond strength inthis group in the present study . the results of the present study challenge the claim of monoblock formation by the new resin - based sealers . the adhesiveness quality to root dentin promoted by both resin - based sealers is compromised even when teeth with simple anatomic features were obturated under well - monitored laboratory conditions . the higher push - out bond strength found in the gutta - percha / ah plus root fillings reiterate the fact that the era of conventional nonbonding root filling has not yet come to an end .

aim : to evaluate and compare the push - out bond strengths of three obturation materials ; gutta - percha / ah plus , resilon / epiphany self - etch ( se ) and endorez obturation system to intraradicular dentin.materials and methods : sixty single - canal anterior teeth were prepared and assigned to experimental groups ( n = 20 ) , designated as group i : gutta - percha / ah plus , group ii : resilon / epiphany se and group iii : endorez sealer / endorez points . after obturation , each tooth was prepared for push - out assessment with root slices of 2 mm thickness using universal testing machine.statistical analysis : two way analysis of variance and scheffe 's test.results:gutta-percha/ah plus root fillings showed significantly highest bond strength . also , root segment location did not have a significant influence on bond strength.conclusion:the adhesiveness quality to root dentin promoted by newer methacrylate resin - based obturation systems like resilon / epihany se and endorez is compromised even when teeth with simple anatomic features were obturated under well - monitored laboratory conditions .

INTRODUCTION MATERIALS AND METHODS Sample selection and specimen preparation Canal filling Push-out assessment RESULTS DISCUSSION CONCLUSION

coronary artery aneurysm is a rare clinical entity with an estimate incidence of 0.35% among patients who undergo coronary angiography . giant coronary artery aneurysm is defined as a coronary dilatation that exceeds by four times or has a diameter exceeding 8 mm , and is under controversies in the literature . giant coronary aneurysm is even less common in only 0.02% of all atherosclerotic patients . due to lack of clinical trials and its rarity , clinical presentations and the best strategic management of it a 43-year - old male patient was admitted to our hospital for a new sensation of tightness in his chest . he also complained of chest pain in retrosternal region radiating to his left arm and aggravated with walking , lasting 30 min . he did not have any medical history of hypertension or diabetes in his last check - up visit , but he was smoker . he had family history of coronary artery diseases in his father who died in the age of 62 years . on clinical examination , he was hemodynamically stable without any pathological findings . the electrocardiogram initially showed an st elevation of > 0.2 mv in anterior chest leads from isoelectric baseline . reciprocal changes were seen in inferior limb leads , consistent with st elevation myocardial infarction ( fig . 1 ) . during monitoring in the next 10 min of arrival , st elevation in anterior chest leads subsided , and the patient was treated as an ordinally unstable angina . routine lab tests showed positive troponin , and echocardiography showed an ejection fraction of 55% without any valvular abnormalities . figure 1:electrocardiogram of the patient during the early time of admission showed st elevation myocardial ischemia . electrocardiogram of the patient during the early time of admission showed st elevation myocardial ischemia . it revealed a large ( 1.5 cm 3 cm ) aneurysm in the proximal part of left anterior descending coronary artery ( lad ) with significant stenosis at its mid part ( fig . 2 ) . the patient underwent successful resection of the giant aneurysm by coronary artery bypass surgery , using left internal mammary artery to bypass lad . the patient had a usual course of hospitalization and discharged without any complications . at 6 months of follow - up figure 2:coronary angiography showing giant coronary aneurysm originating from the proximal part of left anterior descending coronary artery . coronary angiography showing giant coronary aneurysm originating from the proximal part of left anterior descending coronary artery . giant coronary artery aneurysm is defined as a coronary dilatation that exceeds at least four times of the reference diameter or has a diameter exceeding 8 mm . only a few cases have been reported , and due to its rarity , clinical manifestations and the best strategic management are under discussion in the literature . up to one - third of the patients with coronary artery aneurysms may present with angina pectoris or myocardial infarction or sudden cardiac death and congestive heart failure . in our case , we found st elevation changes in the electrocardiogram during the early time of the admission , consistent with st elevation myocardial infarction . emergent thrombolysis in this case could be detrimental as ruptures of coronary artery aneurysms also have been described . although such cases have not been assumed , it could bring challenges in recent guidelines for treatment of such patients . surgery is the best preferred management for giant coronary artery aneurysms , which requires median sternotomy and coronary revascularization [ 3 , 4 ] . due to lack of controlled trials , prognosis of giant coronary artery aneurysm giant coronary artery aneurysm is a rare pathology of coronary vessels due to atherosclerosis or other causes . for the exact diagnosis , coronary angiography should be required , and emergent surgical management should be planned for the best outcomes . written informed consent was obtained from the patient for publication of this case report including the pictures .

coronary artery aneurysm is a rare clinical entity encountered incidentally 0.35% among patients who undergo coronary angiography . even giant coronary artery aneurysm is much rarer with an incidence of 0.02% among all atherosclerotic cases . due to rare occurrence and lack of controlled trials , clinical presentation , prognosis and management of giant coronary artery aneurysm are under controversies in the literature . we report a 43-year - old male patient admitted to our hospital with a typical chest pain associated with st elevation changes in anterior chest leads and elevated cardiac enzymes . coronary angiography of the patient revealed a large ( 1.5 cm 3 cm ) aneurysm of proximal left anterior descending coronary artery . we performed a successful surgical excision and coronary bypass surgery . the patient had an uncomplicated course .

INTRODUCTION CASE REPORT DISCUSSION CONFLICT OF INTEREST STATEMENT