In this talk, we study how external inputs over an epileptic population, may promote or delay seizure emergence. To this aim, due to the increasingly adopted view of epileptic dynamics in terms of slow-fast systems, we study the phase response of a generic relaxation oscillator (RO). As ROs are effectively bistable at the fast time scale, perturbations of the non-seizing state with a suitable direction and amplitude may cause an immediate transition to seizure. By contrast, smaller perturbations have been found to delay the seizure initiation. By studying the isochrons of ROs, we show that this is a generic phenomenon, with the size of such delay depending on the slow flow component. Therefore, depending on the input amplitude, frequency and timing, the occurrence of seizures may increase, decrease or to be suppressed. We illustrate this phenomena by computing the isochrons, phase response curves and the response to perturbations in several epileptic models. While our theoretical results apply to any planar RO, in the context of epilepsy they elucidate mechanisms of triggering and abating seizures, thus suggesting stimulation strategies with effects ranging from mere delays to full suppression of seizures.
Tobias Galla 971 25 98 77 Contact form