Cortical pattern formation during visual hallucinations

We theoretically investigate pattern formation during simple visual hallucinations caused by epileptic activity. To this end we analyze the activator-inhibitor model of Ermentrout and Cowan [1]. In contrast to these authors we focus on a different disease mechanism: According to experimental findings (cf. [2]) we decrease the influence of the inhibitor on the activator. This causes spontaneous pattern formation due to a bifurcation. The model parameters determine whether one or two or four modes become unstable. By means of the center manifold theorem, in all cases the order parameter equation is derived, the stability of the solution is proofed, and the bifurcating activity pattern is calculated explicitely in lowest order. Taking into account terms up to third order in all cases the order parameter equation has a potential. For the two-modes and the four-modes instability this potential causes a winner-takes all dynamics. We integrate the order parameter equation numerically and plot the visual hallucinations which result from the bifurcating cortical activity. The theoretically derived hallucinations correspond to clinically observed visual hallucinations (cf. [3, 4]), which are, for instance, well-known from petit mal epilepsy [5].Finally we investigate the influence of noise on the activity patterns as well as the visual hallucinations.