Spontaneous pattern formation and pinning in the primary visual cortex.

A mean field approach to the population activity of cortical neurons is used to provide a possible mechanism for the generation of geometric visual hallucinations. As was previously investigated, competition between short-range excitation and longer-range inhibition in the connectivity profile of neurons provides the difference of length scales necessary for spontaneous symmetry breaking in the form of the Turing mechanism to generate patterns of activity. This approach is expanded in order to be able to incorporate additional details of the cortical circuitry, namely that neurons are also weakly connected at long ranges to other neurons sharing a particular preference for a stimulus feature such as orientation, spatial frequency, motion, color or disparity. Since the layout of cortical feature maps is approximately crystalline, one can apply a study of nonlinear dynamics similar to the analysis of wave propagation in a crystalline lattice to demonstrate how the spatial pattern formed through the Turing instability can be pinned to the geometric layout of various feature preferences. The specific feature map used in the study presented here is that of orientation preference, although the model can be extended to include additional features. The perturbation analysis is analogous to solving the Schrödinger equation in a weak periodic potential. Competition between the local isotropic connections which produce patterns of activity via the Turing mechanism and the weaker patchy lateral connections that depend on a neuron's particular set of feature preferences create long wavelength affects analogous to commensurate-incommensurate transitions found in fluid systems under a spatially periodic driving force. Using the retinocortical map, spontaneously formed activity patterns generated by the model can then be overlayed on the feature maps to construct the corresponding image in the visual field. We thus describe a new approach that allows the incorporation of some of the above features into a comprehensive account of the origins of hallucinations.