Mexican hats and pinwheels in visual cortex

TLDR: An analytical study of a neuronal network model of the local cortical circuit in primary visual cortex that obtains a trade-off between the spatial range of inhibition and its time constant and concludes that local connections are isotropic.

Abstract: Many models of cortical function assume that local lateral connections are specific with respect to the preferred features of the interacting cells and that they are organized in a Mexican-hat pattern with strong “center” excitation flanked by strong “surround” inhibition. However, anatomical data on primary visual cortex indicate that the local connections are isotropic and that inhibition has a shorter range than excitation. We address this issue in an analytical study of a neuronal network model of the local cortical circuit in primary visual cortex. In the model, the orientation columns specified by the convergent lateral geniculate nucleus inputs are arranged in a pinwheel architecture, whereas cortical connections are isotropic. We obtain a trade-off between the spatial range of inhibition and its time constant. If inhibition is fast, the network can operate in a Mexican-hat pattern with isotropic connections even with a spatially narrow inhibition. If inhibition is not fast, Mexican-hat operation requires a spatially broad inhibition. The Mexican-hat operation can generate a sharp orientation tuning, which is largely independent of the distance of the cell from the pinwheel center.