A Nonlinear Model of the Behavior of Simple Cells in Visual Cortex

Despite their structured receptive fields (RFs) and the strong linear components in their responses, most simple cells in mammalian visual cortex exhibit nonlinear behaviors. Besides the contrast-response function, nonlinearities are evident in various types of failure at superposition tasks, in the disagreement between direction indices computed from drifting and counterphase flickering gratings, in various forms of response suppression (including end- and side-stopping, spatial-frequency-specific inhibition and cross-orientation inhibition), in the advance of phase with increasing contrast, and in phase-insensitive and frequency-doubled responses to counterphase flickering gratings. These behaviors suggest that nonlinearities are involved in the operation of simple cells, but current models fail to explain them. A quantitative model is presented here that purports to describe basic and common principles of operation for all visual cortical cells. Simple cells are described as receiving afferents from multiple subunits that differ in their individual RFs and temporal impulse responses (TIRs). Subunits are independent and perform a spatial integration across their RFs followed by halfwave rectification and temporal convolution with their TIRs. This parallel operation yields a set of temporal functions representing each subunit's contribution to the membrane potential of the host cell, whose final form is given by the weighted sum of all subunits' contributions. By varying the number of subunits and their particular characteristics, different instances of the model are obtained each of which displays a different set of behaviors. Extensive simulation results are presented that illustrate how all of the reported nonlinear behaviors of simple cells arise from these multi-subunit organizations.