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