On Bi-Laminar Neural Field Models of Electrical Activity in the Primary Visual Cortex

Abstract

We investigate the modelling framework for studying electrical activity in the primary visual cortex of the brain based on a bi-laminar neural field equation. The deep layer of the neural field models the orientation-independent electrical activity, whereas the orientation-dependent superficial layer captures the selectivity to spatially oriented stimuli of the orientation columns in the primary visual cortex. We verify the solvability of a Cauchy problem for the bi-laminar neural field equation with both sigmoidal and Heaviside-type neuronal activation. We also construct connections between the solutions that correspond to these types of neuronal activation, which justifies the use of the Heaviside-type neuronal activation functions that is crucial in the problems of computer simulations involving vast ensembles on neurons. We prove the possibility of a correct approximation of the bi-laminar neural field model with a two-layer neuronal network. We also highlight some perspectives opened by the results of the present research related to the studies of travelling waves of evoked electrical activity in the visual cortex as well as the neural activity control problems in the framework of the neurofeedback paradigm.