Direction selectivity and spatiotemporal separability in simple cortical cells

Simple cells in mammalian visual cortex are quasi-linear mechanisms whose behavior departs from true linearity in a very consistent manner. Empirical research on direction selectivity (DS) clearly illustrates these characteristics. A linear DS cell will be DS for all stimuli, whereas a linear non-DS cell will not be DS for any stimuli. However, many simple cells have opposite preferred directions for stimuli of reversed polarity, and some cells are DS for some stimuli (e.g., moving bars) but not for others (e.g., drifting gratings). Also, linear non-DS cells must have separable spatiotemporal receptive fields (RFs), and linear DS cells must have inseparable RFs. Yet many actual DS cells have separable RFs. Here we present a nonlinear model of simple-cell behavior that reproduces all of these empirical behaviors. The model is a variant of the current linear model, amended to include an interleaved nonlinearity (half-wave rectification) that allows it to mimic the (im)balance of push-pull mechanisms. We present simulation results showing that balanced push-pull mechanisms result in linear behavior, while imbalanced push-pull arrangements produce all of the incongruent DS-related behaviors that have been reported for simple cells.