Control of state transitions in an in silico model of epilepsy using small perturbations

We propose the use of artificial neural networks in an in silica epilepsy model of biological neural networks: 1) to predict the onset of state transitions from higher complexities, possibly chaotic to lower complexity possibly rhythmic activities; and 2) to restore the original higher complexity activity. A coupled nonlinear oscillators model (Bardakjian and Diamant, 1994) was used to represent the spontaneous seizure-like oscillations of CA3 hippocampal neurons (Bardakjian and Aschebrenner-Scheibe, 1995) to illustrate the prediction and control schemes of these state transition onsets. Our prediction scheme consists of a recurrent neural network having Gaussian nonlinearities. When the onset of lower complexity activity is predicted in the in silica model, then our control scheme consists of applying a small perturbation to a system variable (i.e., the transmembrane voltage) when it is sufficiently close to the unstable higher complexity manifold. The system state can be restored back to its higher complexity mode utilizing the forces of the system's vector field.