Symmetric path integrals for stochastic equations with multiplicative noise

A Langevin equation with multiplicative noise is an equation schematically of the form dq/dt = - F(q) + e(q) xi, where e(q) xi is Gaussian white noise whose amplitude e(q) depends on q itself. I show how to convert such equations into path integrals. The definition of the path integral depends crucially on the convention used for discretizing time, and I specifically derive the correct path integral when the convention used is the natural, time-symmetric one that time derivatives are (q_t - q_{t-\Delta t}) / \Delta t and coordinates are (q_t + q_{t-\Delta t}) / 2. [This is the convention that permits standard manipulations of calculus on the action, like naive integration by parts.] It has sometimes been assumed in the literature that a Stratanovich Langevin equation can be quickly converted to a path integral by treating time as continuous but using the rule \theta(t=0) = 1/2. I show that this prescription fails when the amplitude e(q) is q-dependent.Comment: 8 page

Prophylaxis and Early Detection for Breast Cancer

Abstract: Breast cancer is steadily increasing in number in Japan due to less child bearing, less breast-feeding, and more westernization of life style than ever. Cancer registration in Osaka reported the incidence of breast cancer in 1996 to 1998 to be 41.1/100,000, four-times higher than the value in 1966-1968. Avoiding overweight, animal fat intake and mental stresses is a basic and easy measure for prevention of breast cancer. A unique study performed in Japan shows that daily intake of 10 or more cups of green tea inhibits development of breast cancer. A large-scale study by National Surgical Adjuvant Breast and Bowel Project (NSABP) revealed that 5-year tamoxifen administration to high-risk women decreased the incidence of breast cancer to 1/2 of the value for control women. Early diagnosis of breast cancer is most effectively achieved by fine needle aspiration cytology if the tumor is palpable with joint work with capable cytologists. More recently, stereo-tactic biopsy devices are available for non-palpable lesions. Mammography is more frequently used in mass screening system though its essential merit is yet to be investigated

Association between Mammographic Breast Density and Lifestyle in Japanese Women

A high mammographic breast density is considered to be a risk factor for breast cancer. However, only a small number of studies on the association between breast density and lifestyle have been performed. A cross-sectional study was performed using a survey with 29 questions on life history and lifestyle. The breast density on mammography was classified into 4 categories following the BI-RADS criteria. The subjects were 522 women with no medical history of breast cancer. The mean age was 53.3 years old. On multivariate analysis, only BMI was a significant factor determining breast density in premenopausal women (parameter estimate, －0.403;p value, 0.0005), and the density decreased as BMI rose. In postmenopausal women, BMI (parameter estimate, －0.196;p value, 0.0143) and number of deliveries (parameter estimate, －0.388;p value, 0.0186) were significant factors determining breast density;breast density decreased as BMI and number of deliveries increased. Only BMI and number of deliveries were identified as factors significantly influencing breast density. BMI was inversely correlated with breast density before and after menopause, whereas the influence of number of deliveries on breast density was significant only in postmenopausal women in their 50 and 60s

Effects of lifestyle and single nucleotide polymorphisms on breast cancer risk: a case-control study in Japanese women

Background: Lifestyle factors, including food and nutrition, physical activity, body composition and reproductive factors, and single nucleotide polymorphisms (SNPs) are associated with breast cancer risk, but few studies of these factors have been performed in the Japanese population. Thus, the goals of this study were to validate the association between reported SNPs and breast cancer risk in the Japanese population and to evaluate the effects of SNP genotypes and lifestyle factors on breast cancer risk. Methods: A case-control study in 472 patients and 464 controls was conducted from December 2010 to November 2011. Lifestyle was examined using a self-administered questionnaire. We analyzed 16 breast cancer-associated SNPs based on previous GWAS or candidate-gene association studies. Age or multivariate-adjusted odds ratios (OR) and 95% confidence intervals (95% CI) were estimated from logistic regression analyses. Results: High BMI and current or former smoking were significantly associated with an increased breast cancer risk, while intake of meat, mushrooms, yellow and green vegetables, coffee, and green tea, current leisure-time exercise, and education were significantly associated with a decreased risk. Three SNPs were significantly associated with a breast cancer risk in multivariate analysis: rs2046210 (per allele OR = 1.37 [95% CI: 1.11-1.70]), rs3757318 (OR = 1.33[1.05-1.69]), and rs3803662 (OR = 1.28 [1.07-1.55]). In 2046210 risk allele carriers, leisure-time exercise was associated with a significantly decreased risk for breast cancer, whereas current smoking and high BMI were associated with a significantly decreased risk in non-risk allele carriers. Conclusion: In Japanese women, rs2046210 and 3757318 located near the ESR1 gene are associated with a risk of breast cancer, as in other Asian women. However, our findings suggest that exercise can decrease this risk in allele carriers

Acute Pancreatitis due to pH-Dependent Mesalazine That Occurred in the Course of Ulcerative Colitis

We report the case of a 26-year-old male who presented with acute pancreatitis during the course of treatment for pancolitic ulcerative colitis (UC) with a time-dependent mesalazine formulation, prednisolone and azathioprine (AZA). Despite a review of his clinical history and various tests, the cause of pancreatitis could not be determined. Since drug-induced pancreatitis was considered possible, administration of the time-dependent mesalazine preparation and AZA was discontinued, and conservative treatment for acute pancreatitis was performed. The pancreatitis promptly improved with these treatments, but drug lymphocyte stimulation test (DLST) for both the time-dependent mesalazine formulation and AZA was negative. A pH-dependent mesalazine formulation was given for maintenance therapy of UC. Subsequently, as the pancreatitis relapsed, drug-induced pancreatitis was strongly suspected. Administration of mesalazine was discontinued, and pancreatitis was smoothly in remission by conservative treatment. According to the positive DLST result for the pH-dependent mesalazine formulation and the clinical course, a diagnosis of pH-dependent mesalazine-induced pancreatitis due to this formulation was made. During the clinical course of UC, occurrence of drug-induced pancreatitis must always be considered

Recurrence dynamics does not depend on the recurrence site

Introduction: The dynamics of breast cancer recurrence and death, indicating a bimodal hazard rate pattern, has been confirmed in various databases. A few explanations have been suggested to help interpret this finding, assuming that each peak is generated by clustering of similar recurrences and different peaks result from distinct categories of recurrence. Methods: The recurrence dynamics was analysed in a series of 1526 patients undergoing conservative surgery at the National Cancer Institute of Milan, Italy, for whom the site of first recurrence was recorded. The study was focused on the first clinically relevant event occurring during the follow up (ie, local recurrence, distant metastasis, contralateral breast cancer, second primary tumour), the dynamics of which was studied by estimating the specific hazard rate.Results The hazard rate for any recurrence (including both local and distant disease relapses) displayed a bimodal pattern with a first surge peaking at about 24 months and a second peak at almost 60 months. The same pattern was observed when the whole recurrence risk was split into the risk of local recurrence and the risk of distant metastasis. However, the hazard rate curves for both contralateral breast tumours and second primary tumours revealed a uniform course at an almost constant level. When patients with distant metastases were grouped by site of recurrence (soft tissue, bone, lung or liver or central nervous system), the corresponding hazard rate curves displayed the typical bimodal pattern with a first peak at about 24 months and a later peak at about 60 months.Conclusions The bimodal dynamics for early stage breast cancer recurrence is again confirmed, providing support to the proposed tumour-dormancy-based model. The recurrence dynamics does not depend on the site of metastasis indicating that the timing of recurrences is generated by factors influencing the metastatic development regardless of the seeded organ. This finding supports the view that the disease course after surgical removal of the primary tumour follows a common pathway with well-defined steps and that the recurrence risk pattern results from inherent features of the metastasis development process, which are apparently attributable to tumour cells

Separate and combined analysis of successive dependent outcomes after breast-conservation surgery: recurrence, metastases, second cancer and death

<p>Abstract</p> <p>Background</p> <p>In the setting of recurrent events, research studies commonly count only the first occurrence of an outcome in a subject. However this approach does not correctly reflect the natural history of the disease. The objective is to jointly identify prognostic factors associated with locoregional recurrences (LRR), contralateral breast cancer, distant metastases (DM), other primary cancer than breast and breast cancer death and to evaluate the correlation between these events.</p> <p>Methods</p> <p>Patients (n = 919) with a primary invasive breast cancer and treated in a cancer center in South-Western France with breast-conserving surgery from 1990 to 1994 and followed up to January 2006 were included. Several types of non-independent events could be observed for the same patient: a LRR, a contralateral breast cancer, DM, other primary cancer than breast and breast cancer death. Data were analyzed separately and together using a random-effects survival model.</p> <p>Results</p> <p>LRR represent the most frequent type of first failure (14.6%). The risk of any event is higher for young women (less than 40 years old) and in the first 10 years of follow-up after the surgery. In the combined analysis histological tumor size, grade, number of positive nodes, progesterone receptor status and treatment combination are prognostic factors of any event. The results show a significant dependence between these events with a successively increasing risk of a new event after the first and second event. The risk of developing a new failure is greatly increased (RR = 4.25; 95%CI: 2.51-7.21) after developing a LRR, but also after developing DM (RR = 3.94; 95%CI: 2.23-6.96) as compared to patients who did not develop a first event.</p> <p>Conclusion</p> <p>We illustrated that the random effects survival model is a more satisfactory method to evaluate the natural history of a disease with multiple type of events.</p

Are ipsilateral breast tumour invasive recurrences in young (⩽40 years) women more aggressive than their primary tumours?

The characteristics of ipsilateral breast tumour recurrences (IBTRs) relative to those of their primary tumours (PTs) remain scarcely studied. Of 70 young (⩽40 years) premenopausal women with IBTRs, we studied a series of 63 with paired histological data. Median follow-up since IBTR was 10 years. Rates of histological types, grades or hormonal receptors were not significantly different in PTs and in IBTRs. The concordance between IBTRs and their PTs was good for histological types. IBTRs with conserved histological types tended to occur more locally, but not significantly sooner than others. These IBTRs had good concordance for hormone receptors. In discordant cases there were as many losses as appearances of the receptors. The concordance was weak for grades, with equivalent numbers of IBTRs graded lower as higher than their PTs. The 10-year overall survival rate was 70%. Neither the conservation of histological type, location, nor of the two combined were associated with deaths. Early (<2 years) IBTRs, tended to be associated with poorer survival (HR=2.24 (0.92–5.41); P=0.08). IBTRs did not display features of higher aggressiveness than PTs. Neither clinical nor histological definition of a true recurrence could be established other than the conservation of the histological type

Single nucleotide variations in CLCN6 identified in patients with benign partial epilepsies in infancy and/or febrile seizures

Nucleotide alterations in the gene encoding proline-rich transmembrane protein 2 (PRRT2) have been identified in most patients with benign partial epilepsies in infancy (BPEI)/benign familial infantile epilepsy (BFIE). However, not all patients harbor these PRRT2 mutations, indicating the involvement of genes other than PRRT2. In this study, we performed whole exome sequencing analysis for a large family affected with PRRT2-unrelated BPEI. We identified a non-synonymous single nucleotide variation (SNV) in the voltage-sensitive chloride channel 6 gene (CLCN6). A cohort study of 48 BPEI patients without PRRT2 mutations revealed a different CLCN6 SNV in a patient, his sibling and his father who had a history of febrile seizures (FS) but not BPEI. Another study of 48 patients with FS identified an additional SNV in CLCN6. Chloride channels (CLCs) are involved in a multitude of physiologic processes and some members of the CLC family have been linked to inherited diseases. However, a phenotypic correlation has not been confirmed for CLCN6. Although we could not detect significant biological effects linked to the identified CLCN6 SNVs, further studies should investigate potential CLCN6 variants that may underlie the genetic susceptibility to convulsive disorders.Toshiyuki Yamamoto, Keiko Shimojima, Noriko Sangu, Yuta Komoike, Atsushi Ishii, Shinpei Abe, Shintaro Yamashita, Katsumi Imai, Tetsuo Kubota, Tatsuya Fukasawa, Tohru Okanishi, Hideo Enoki, Takuya Tanabe, Akira Saito, Toru Furukawa, Toshiaki Shimizu, Carol J. Milligan, Steven Petrou, Sarah E. Heron, Leanne M. Dibbens, Shinichi Hirose, Akihisa Okumur

Standardized and reproducible methodology for the comprehensive and systematic assessment of surgical resection margins during breast-conserving surgery for invasive breast cancer

<p>Abstract</p> <p>Background</p> <p>The primary goal of breast-conserving surgery (BCS) is to completely excise the tumor and achieve "adequate" or "negative" surgical resection margins while maintaining an acceptable level of postoperative cosmetic outcome. Nevertheless, precise determination of the adequacy of BCS has long been debated. In this regard, the aim of the current paper was to describe a standardized and reproducible methodology for comprehensive and systematic assessment of surgical resection margins during BCS.</p> <p>Methods</p> <p>Retrospective analysis of 204 BCS procedures performed for invasive breast cancer from August 2003 to June 2007, in which patients underwent a standard BCS resection and systematic sampling of nine standardized re-resection margins (superior, superior-medial, superior-lateral, medial, lateral, inferior, inferior-medial, inferior-lateral, and deep-posterior). Multiple variables (including patient, tumor, specimen, and follow-up variables) were evaluated.</p> <p>Results</p> <p>6.4% (13/204) of patients had positive BCS specimen margins (defined as tumor at inked edge of BCS specimen) and 4.4% (9/204) of patients had close margins (defined as tumor within 1 mm or less of inked edge but not at inked edge of BCS specimen). 11.8% (24/204) of patients had at least one re-resection margin containing additional disease, independent of the status of the BCS specimen margins. 7.1% (13/182) of patients with negative BCS specimen margins (defined as no tumor cells seen within 1 mm or less of inked edge of BCS specimen) had at least one re-resection margin containing additional disease. Thus, 54.2% (13/24) of patients with additional disease in a re-resection margin would not have been recognized by a standard BCS procedure alone (P < 0.001). The nine standardized resection margins represented only 26.8% of the volume of the BCS specimen and 32.6% of the surface area of the BCS specimen.</p> <p>Conclusion</p> <p>Our methodology accurately assesses the adequacy of surgical resection margins for determination of which individuals may need further resection to the affected breast in order to minimize the potential risk of local recurrence while attempting to limit the volume of additional breast tissue excised, as well as to determine which individuals are not realistically amendable to BCS and instead need a completion mastectomy to successfully remove multifocal disease.</p