A NEURONAL TRANSITION-PROBABILITY MODEL FOR THE EVOLUTION OF POWER INTHE SIGMA-FREQUENCY AND DELTA-FREQUENCY BANDS OF SLEEP EEG

Although the time-courses of power in the delta and sigma frequency ba nds over the NREM episode in the human sleep EEG have been studied for several years, and their detailed forms have been well measured, no m athematical model has yet been formulated to account for the relation between them. The model presented here attempts to explain the form an d relative timing of these curves by a consideration of the behavior o f the thalamocortical neuronal populations that are believed to play a part in their generation The model applies the mathematics of the cas cade radioactive decay process, adapted to a finite population of thal amocortical neurons oscillating initially in the beta mode. At the beg inning of the NREM episode, each neuron of this population is assumed to acquire a constant probability of transitionning to the sigma oscil lation mode and, at the same time, each neuron of the newly created si gma population is assumed to acquire a constant probability of transit ionning to the delta oscillation mode. This simple model is sufficient to explain the main characteristics of the first half of the time-cou rses of the sigma and delta powers: the initial positive correlation a s they increase together, followed by the sigma peak and the subsequen t negative correlation At the end of this first phase, the model initi ates an identical, but reverse, process that reproduces the observed d elta maximum and sigma plateau, followed by the concomitant fall of bo th sigma and delta power. The time-course of the beta power and the ov erall negative correlation between beta and delta are also reproduced as integral consequences of the model. (C) 1997 Elsevier Science Inc.