Laparoscopic radical antegrade modular pancreatosplenectomy: preliminary experience with 10 cases.

BACKGROUND: The radical antegrade modular pancreatosplenectomy (RAMPS) which is a reasonable surgical approach for left-sided pancreatic cancer is emphasis on the complete resection of regional lymph nodes and tumor-free margin resection. Laparoscopic radical antegrade modular pancreatosplenectomy (LRAMPS) has been rarely performed, with only 49 cases indexed on PubMed. In this study, we present our experience of LRAMPS. METHODS: From December 2018 to February 2020, 10 patients underwent LRAMPS for pancreatic cancer at our department. The data of the patient demographics, intraoperative variables, postoperative hospital stay, morbidity, mortality, pathologic findings and follow-up were collected. RESULTS: LRAMPS was performed successfully in all the patients. The median operative time was 235 min (range 212-270 min), with an EBL of 120 ml (range 100-200 ml). Postoperative complications occurred in 5 (50.0%) patients. Three patients developed a grade B pancreatic fistula. There was no postoperative 30-day mortality and reoperation. The median postoperative hospital stay was 14 days (range 9-24 days).The median count of retrieved lymph nodes was 15 (range 13-21), and four patients (40%) had malignant-positive lymph nodes. All cases achieved a negative tangential margin and R0 resection. Median follow-up time was 11 months (range 3-14 m). Two patients developed disease recurrence (pancreatic bed recurrence and liver metastasis) 9 months, 10 months after surgery, respectively. Others survived without tumor recurrence or metastasis. CONCLUSIONS: LRAMPS is technically safe and feasible procedure in well-selected patients with pancreatic cancer in the distal pancreas. The oncologically outcomes need to be further validated based on additional large-volume studies.

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries.

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Hard harvesting of a stochastically changing population.

We consider a population whose size changes stochastically under a branching process, with the added modification that each generation a fixed number of individuals are removed, irrespective of the size of the population. We call removal that is independent of population size 'hard harvesting'. A key feature of hard harvesting occurs if the size of the population is smaller than the fixed number that are harvested. In such a case, the dynamics cannot continue and must terminate. We find that even for populations with a tendency to grow, there is a finite probability of termination. We determine the probability of termination, and given that termination occurs, we characterise the statistical properties of the random time to termination. We determine the impact of hard harvesting on the size of the population, in populations where termination has not occurred.

A statistical approach for detecting common features.

BACKGROUND: With increasing numbers of datasets in neuroimaging studies, it has become an important task to pool information, in order to increase the statistical power of tests and for cross validation. However, no robust global approach unambiguously identifies the common biological abnormalities in, for example, resting-state functional magnetic resonance imaging in a number of mental disorders, where there are multiple datasets/attributes. Here we propose a novel and efficient statistical approach to this problem that finds common features in multiple datasets. NEW METHOD: By collecting the statistics of each dataset into a vector, our method uses a 'multi-dimensional local false discovery' rate to pool information and make full use of the joint distribution of datasets. RESULTS: We have tested our approach extensively on both simulated and clinical datasets. By conducting simulation studies, we find that our approach has a higher statistical power than existing approaches, especially on correlated datasets. Employing our approach on clinical data yields findings that are consistent with the existing literature. COMPARISON WITH EXISTING METHODS: Conventional methods cannot determine the false discovery rate underlying multiple datasets/attributes. Our approach can effectively handle these datasets. It has a solid Bayesian interpretation, and a higher power than other approaches in numerical simulations. This can be explained by the incorporation of correlations, between different attributes, into the new method. CONCLUSIONS: In this work, we present a natural, novel and powerful statistical approach to tackle situations involving multiple datasets or attributes. This new method has significant advantages over existing approaches and wide applications.

Singular solution of the Feller diffusion equation via a spectral decomposition.

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.