Closed-Loop Proportion-Derivative Control of Suppressing Seizures in a Neural Mass Model

Abstract

In this work, we present an analytical approach of closed-loop Proportional-Derivative (PD) control to determine the stimulation parameters for suppressing high-amplitude epileptic activity in a neural mass model. Closed-loop PD control to suppress epileptic activity in the Jansen's neural mass model (Jansen's NMM) has been studied. This work shows that the output signal of the Jansen's NMM model without the PD control feedback is high amplitude epileptic seizure activity which turns into low amplitude activity with the intervention feedback of a PD controller. A graphical stability analysis method was employed to determine the stability region of the PD controller in the gain parameter space. Therefore, this approach draws a region of PD controller parameters that is empirically chosen to stabilize epileptic seizure activities in the chosen NMM. Furthermore, this approach allows us to explore the relationship between the model parameters of inducing epileptic activity and the feedback controller parameters to foster a better understanding of the mechanism to suppress epileptic seizure activity by applying closed-loop stimulation (pharmacology stimulation, electrical stimulation or optogenetic stimulation etc.).