COMPUTATION OF FIRST PASSAGE TIME MOMENTS FOR STOCHASTIC DIFFUSION-PROCESSES MODELING NERVE MEMBRANE DEPOLARIZATION

For further understanding of neural coding, stochastic variability of interspike intervals has been investigated by both experimental and th eoretical neuroscientists. In stochastic neuronal models, the interspi ke interval corresponds to the time period during which the process im itating the membrane potential reaches a threshold for the first time from a reset depolarization. For neurons belonging to complex networks in the brain, stochastic diffusion processes are often used to approx imate the time course of the membrane potential. The interspike interv al is then viewed as the first passage time for the employed diffusion process. Due to a lack of analytical solution for the related first p assage time problem for most diffusion neuronal models, a numerical in tegration method, which serves to compute first passage time moments o n the basis of the Siegert recursive formula, is presented in this pap er. For their neurobiological plausibility, the method here is associa ted with diffusion processes whose state spaces are restricted to fini te intervals, but it can also be applied to other diffusion processes and in other (non-neuronal) contexts. The capability of the method is demonstrated in numerical examples and the relation between the integr ation step, accuracy of calculation and amount of computing time requi red is discussed.