Towards Dead Time Inclusion in Neuronal Modeling

TL;DR

This paper introduces a mathematical framework for incorporating dead time into neuronal models, providing explicit formulas for moments and analyzing key features of neuronal firing times.

Contribution

It presents a novel mathematical description of refractoriness in neuronal diffusion models, with explicit moment calculations and analysis for common neuronal models.

Findings

Explicit formulas for moments of refractoriness period

Analysis of mean and variance of first passage times

Comparison across Wiener, Ornstein-Uhlenbeck, and Feller models

Abstract

A mathematical description of the refractoriness period in neuronal diffusion modeling is given and its moments are explicitly obtained in a form that is suitable for quantitative evaluations. Then, for the Wiener, Ornstein-Uhlenbeck and Feller neuronal models, an analysis of the features exhibited by the mean and variance of the first passage time and of refractoriness period is performed.