Asymptotic and numerical analysis of a stochastic PDE model of volume transmission

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