Open AccessSuccessive spike times predicted by a stochastic neuronal model with a variable input signal
Author(s) -
Giuseppe D’Onofrio,
Enrica Pirozzi
Publication year - 2016
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2016003
Subject(s) - first hitting time model , spike (software development) , ornstein–uhlenbeck process , mathematics , constant (computer programming) , signal (programming language) , probability density function , stochastic process , time constant , stochastic modelling , markov process , process (computing) , statistical physics , physics , statistics , computer science , software engineering , electrical engineering , programming language , engineering , operating system
Two different stochastic processes are used to model the evolution of the membrane voltage of a neuron exposed to a time-varying input signal. The first process is an inhomogeneous Ornstein-Uhlenbeck process and its first passage time through a constant threshold is used to model the first spike time after the signal onset. The second process is a Gauss-Markov process identified by a particular mean function dependent on the first passage time of the first process. It is shown that the second process is also of a diffusion type. The probability density function of the maximum between the first passage time of the first and the second process is considered to approximate the distribution of the second spike time. Results obtained by simulations are compared with those following the numerical and asymptotic approximations. A general equation to model successive spike times is given. Finally, examples with specific input signals are provided.