title: Improved integral equation solution for the first passage time of leaky integrate-and-fire neurons.
abstract: An accurate calculation of the first passage time probability density (FPTPD) is essential for computing the likelihood of solutions of the stochastic leaky integrate-and-fire model. The previously proposed numerical calculation of the FPTPD based on the integral equation method discretizes the probability current of the voltage crossing the threshold. While the method is accurate for high noise levels, we show that it results in large numerical errors for small noise. The problem is solved by analytically computing, in each time bin, the mean probability current. Efficiency is further improved by identifying and ignoring time bins with negligible mean probability current.
authors.affiliation: Zanvyl Krieger Mind/Brain Institute and Solomon Snyder Department of Neuroscience, Johns Hopkins University, Baltimore, MD 21218, USA. doyen@pha.jhu.edu
authors.forename: Yi
authors.initials: Y
authors.lastname: Dong
authors.forename: Stefan
authors.initials: S
authors.lastname: Mihalas
authors.forename: Ernst
authors.initials: E
authors.lastname: Niebur
mesh_terms: D000200:Action Potentials / Q000502:physiology; D000818:Animals; D006801:Humans; D008564:Membrane Potentials / Q000502:physiology; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*