Theory of ocular dominance column formation. Mathematical basis and computer simulation

Abstract

A general theory previously proposed by the author which describes synaptic stabilization on the basis of three basic assumptions is employed for the understanding of ocular dominance column formation. A reduced mathematical model is constructed based on the thermodynamics in the Ising spin variables representing the afferent synaptic connection distribution. The results of Monte Carlo simulations on the segregation of ipsilateral and contralateral synaptic terminals in the input layer of the primary visual cortex suggest the existence of phase transition phenomena. Three types of ocular dominance column patterns--stripe, blob, and uniform--are visualized according to the values of the correlation strength and the degree of imbalance in activity between the left and right retinas. The theory presented here successfully explains how ocular dominance columns are developed.