M. Musila et al., COMPUTATION OF FIRST PASSAGE TIME MOMENTS FOR STOCHASTIC DIFFUSION-PROCESSES MODELING NERVE MEMBRANE DEPOLARIZATION, Computer methods and programs in biomedicine, 49(1), 1996, pp. 19-27
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.