Calculation of interspike intervals for integrate-and-fire neurons with Poisson distribution of synaptic inputs

Abstract

We present a new technique for calculating the interspike intervals of integrate-and-fire neurons. There are two new components to this technique. First, the probability density of the summed potential is calculated by integrating over the distribution of arrival times of the afferent postsynaptic potentials (PSPs), rather than using conventional stochastic differential equation techniques. A general formulation of this technique is given in terms of the probability distribution of the inputs and the time course of the postsynaptic response. The expressions are evaluated in the gaussian approximation, which gives results that become more accurate for large numbers of small-amplitude PSPs. Second, the probability density of output spikes, which are generated when the potential reaches threshold, is given in terms of an integral involving a conditional probability density.

A.N. Burkitt and G.M. Clark, 'Calculation of Interspike Intervals for Integrate and Fire Neurons with Poisson Distribution of Synaptic Inputs ', Neural Computation, 12:8 (August, 2000), pp. 1789-1820. © 2000 by the Massachusetts Institute of Technology. http://www.mitpressjournals.org.ezp.lib.unimelb.edu.au/toc/neco/12/8