Field Theory of the Epileptor

Epilepsy and seizure disorders are conditions that affect millions of people worldwide. The onset of seizures, as well as the effect of treatment, undergoes immense study, including approaches using theoretical, phenomenological models. In the model considered here, the dynamics of the EEG electrode activity and the excitability of brain regions are described using stochastic differential equations. The transition to the "epileptic" phase is characterized by the coexistence of a stable attractive fixed point, marking normal background brain activity, and an appearance of a stable limit cycle, which characterizes seizure-like dynamics. In this phase the transition between the two is activated by noise. Borrowing from neural field models, we promote this set of equations to a spatially continuous model. It is then a non-equilibrium dynamical system and the tools of field theory become available to study the transition and the correlation structure of the activity variable. Noise-induced transition to seizure-like behavior can also be analyzed in the context of escape-time statistics. We hope such an analysis of this system should describe the signatures of the onset of seizures as well as provide insights into making normal brain activity more robust against perturbations.