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

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

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

Obtaining Adequate Surgical Margins in Breast-Conserving Therapy for Patients with Early-Stage Breast Cancer: Current Modalities and Future Directions

Inadequate surgical margins represent a high risk for adverse clinical outcome in breast-conserving therapy (BCT) for early-stage breast cancer. The majority of studies report positive resection margins in 20% to 40% of the patients who underwent BCT. This may result in an increased local recurrence (LR) rate or additional surgery and, consequently, adverse affects on cosmesis, psychological distress, and health costs. In the literature, various risk factors are reported to be associated with positive margin status after lumpectomy, which may allow the surgeon to distinguish those patients with a higher a priori risk for re-excision. However, most risk factors are related to tumor biology and patient characteristics, which cannot be modified as such. Therefore, efforts to reduce the number of positive margins should focus on optimizing the surgical procedure itself, because the surgeon lacks real-time intraoperative information on the presence of positive resection margins during breast-conserving surgery. This review presents the status of pre- and intraoperative modalities currently used in BCT. Furthermore, innovative intraoperative approaches, such as positron emission tomography, radioguided occult lesion localization, and near-infrared fluorescence optical imaging, are addressed, which have to prove their potential value in improving surgical outcome and reducing the need for re-excision in BCT