Oscillatory Cortical Activity during Visual Hallucinations

Abstract

From a theoretical point of view we investigate cortical activity patterns causing dynamical visual hallucinations. For this reason we analyze an oscillatory instability of the dynamics of the activator-inhibitor model of Ermentrout and Cowan. Such an oscillatory instability occurs as a result of several disease mechanisms. We explicitly derive the order parameter equation. By means of the averaging theorem, we obtain the averaged order parameter equation. The latter enables us to determine stable and unstable bifurcating cortical activity patterns analytically in lowest order. Depending on model parameters as well as on initial conditions two types of cortical activity patterns occur: travelling waves and 'blinking rolls', i.e. standing waves oscillating with the same frequency and with a phase shift of π/2. In contrast to cortical activity patterns caused by non-oscillatory instabilities analyzed by Ermentrout and Cowan (1979) and by the author (1995) the travelling waves and the blinking rolls lead to a variety of dynamical visual hallucinations which are discussed in detail.