A Pseudo-Markov Model for Series of Neuronal Spike Events

Abstract

Spike trains of spontaneous neuronal activity in the rabbit brain are submitted to statistical analyses based on the following pseudo-Markov model. The nerve cell is supposed to alternate between a bursting and a resting state. The numbers of consecutive spikes within each state are assumed to be independent integer-valued random variables with discrete probability distributions. Given the state, the interspike intervals are independent real-valued random variables. The two state semi-Markov model is obtained as a special case when the discrete distributions are geometrical. Statistical second-order properties of recorded spike trains are compared with those predicted by the model on the basis of known first-order properties. For that purpose, serial correlation coefficients and intensity functions for spike trains produced by the model are computed. A comparison between observed and predicted results for the spontaneous activity of 17 brain cells yields a good fit in eight cells and discloses some salient features of the statistical structure in the activity of six other cells. By making it feasible to compute theoretical correlograms, the model may advance the understanding of empirical correlograms. The possibilities for integrating this statistical model of spike trains with a model of the mechanism of spike train production are discussed.