4.4 Article

ASYMPTOTIC AND NUMERICAL ANALYSIS OF A STOCHASTIC PDE MODEL OF VOLUME TRANSMISSION

期刊

MULTISCALE MODELING & SIMULATION
卷 18, 期 2, 页码 887-915

出版社

SIAM PUBLICATIONS
DOI: 10.1137/18M1230773

关键词

volume transmission; neuromodulation; stochastic hybrid system; piecewise deterministic Markov process; asymptotic analysis; radial basis functions; RBF-FD

资金

  1. National Science Foundation [DMS-1521748, CISE-CCF 1714844]

向作者/读者索取更多资源

Volume transmission is an important neural communication pathway in which neurons in one brain region influence the neurotransmitter concentration in the extracellular space of a distant brain region. In this paper, we apply asymptotic analysis to a stochastic partial differential equation model of volume transmission to calculate the neurotransmitter concentration in the extracellular space. Our model involves the diffusion equation in a three-dimensional domain with interior holes that randomly switch between being either sources or sinks. These holes model nerve varicosities that alternate between releasing and absorbing neurotransmitter according to when they fire action potentials. In the case that the holes are small, we compute analytically the first two nonzero terms in an asymptotic expansion of the average neurotransmitter concentration. The first term shows that the concentration is spatially constant to leading order and that this constant is independent of many details in the problem. Specifically, this constant first term is independent of the number and location of nerve varicosities, neural firing correlations, and the size and geometry of the extracellular space. The second term shows how these factors affect the concentration at second order. Interestingly, the second term is also spatially constant under some mild assumptions. We verify our asymptotic results by high-order numerical simulation using radial-basis-function-generated finite differences.

作者

我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。

评论

主要评分

4.4
评分不足

次要评分

新颖性
-
重要性
-
科学严谨性
-
评价这篇论文

推荐

暂无数据
暂无数据