On a Generalized Leaky Integrate-and-Fire Model for Single Neuron Activity

Motivated by some experimental results of C.F. Stevens and A.M. Zador, the standard stochastic Leaky Integrate-and-Fire model for single neuron firing activity is generalized in a way to include evolutionary instantaneous time constant and resting potential. The main features of the ensuing Gauss-diffusion process are disclosed by making use of a space-time transformation leading to the Ornstein-Uhlenbeck process. On the grounds of simulations of the time course of the membrane potential, we are led to conclude that our generalized model well accounts for a variety of experimental recordings that appear to indicate that the standard model is inadequate to reproduce statistically reliable features of spike trains generated by certain types of cortical neurons.