The visual cortex as a crystal

Abstract

A theory of pattern formation in primary visual cortex (V1) is presented that takes into account its crystalline-like structure. The cortex is partitioned into fundamental domains or hypercolumns of a lattice describing the distribution of singularities or pinwheels in the orientation preference map. Each hypercolumn is modelled as a network of orientation and spatial frequency selective cells organised around a pair of pinwheels, which are associated with high and low spatial frequency domains, respectively. The network topology of the hypercolumn is taken to be a sphere with the pinwheels located at the poles of the sphere. Interactions between hypercolumns are mediated by anisotropic long-range lateral connections that link cells with similar feature preferences. Using weakly nonlinear analysis, we investigate the spontaneous formation of cortical activity patterns through the simultaneous breaking of an internal O (3) symmetry and a discrete lattice symmetry. The resulting patterns are characterised by states in which each hypercolumn exhibits a tuned response to both orientation and spatial frequency and the distribution of optimal responses across hypercolumns is doubly periodic or quasi-periodic with respect to the underlying lattice.