Spontaneous pattern formation and pinning in the visual cortex

Bifurcation theory and perturbation theory can be combined with a knowledge of the underlying circuitry of the visual cortex to produce an elegant story explaining the phenomenon of visual hallucinations. A key insight is the application of an important set of ideas concerning spontaneous pattern formation introduced by Turing in 1952. The basic mechanism is a diffusion driven linear instability favoring a particular wavelength that determines the size of the ensuing stripe or spot periodicity of the emerging spatial pattern. Competition between short range excitation and longer range inhibition in the connectivity profile of cortical neurons provides the difference in diffusion length scales necessary for the Turing mechanism to occur and has been proven by Ermentrout and Cowan to be sufficient to explain the generation of a subset of reported geometric hallucinations. Incorporating further details of the cortical circuitry, namely that neurons are also weakly connected to other neurons sharing a particular stimulus orientation or spatial frequency preference at even longer ranges and the resulting shift-twist symmetry of the neuronal connectivity, improves the story. We expand this approach in order to be able to include the tuned responses of cortical neurons to additional visual stimulus features such as motion, color and disparity. We apply a study of nonlinear dynamics similar to the analysis of wave propagation in a crystalline lattice to demonstrate how a spatial pattern formed through the Turing instability can be pinned to the geometric layout of various feature preferences. The perturbation analysis is analogous to solving the Schrodinger 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. In this way we hope to better understand how the intrinsic architecture of the visual cortex can generate patterns of activity that underlie visual hallucinations.