Epilepsy control using a fixed time integral super twisting sliding mode control for Pinsky-Rinzel pyramidal model through ion channels with optogenetic method

Abstract

Background and objective: Epilepsy is a dynamic disease of neuronal networks and epileptic activity in the brain should be suppressed quickly in the shortest possible time with minimum control signal. Thus, a closed-loop feedback control by using the fixed-time integral super-twisting sliding-mode controller via an optogenetic method is employed for suppressing seizures in the Pinsky-Rinzel (PR) model as a dynamic model of the hippocampus CA3 region where epileptic seizures occur. The control signal is applied to the PR model through the ChR2 channel model in the form of light photons using the optogenetic method. The present study aimed to determine the controller robustness against parameter changes and disturbances in order to reduce the control time, approach the zero tracking error of the normal desired state in a fixed time, and finally, converge the epileptic state to the normal desired state.

Method: In order to apply the control signal to the Pinsky-Rinzel model in the optogenetic method, the dynamic model of the ion current generated by channelrhodopsin 2 (ChR2) as a light-sensitive protein model in the optogenetic method was first applied to the PR model. Then, a fixed-time integral super-twisting sliding-mode controller was designed for the system, which is the combination of PR and ChR2 models.

Results: After applying the proposed controller, the simulation results indicated that the control signal was -0.7 mV, the tracking error of the normal desired state could reach zero within 1.5 milliseconds, and the problems of singularity and chattering were solved.

Conclusions: A reduction occurred in the control signal reduced regarding the objectives of the study and comparing the proposed controller with the classical sliding-mode controller. Thus, this method can produce a safe control input for brain. In addition, both types of sliding mode controllers are robust against the parameters variations and external disturbances. Thus, they are superior to non-robust and simple controllers. Finally, based on the results, the validity of the fixed-time integral super-twisting sliding mode controller is confirmed for epilepsy control.

Keywords: Channelrhodopsin 2 model; Epilepsy; Fixed time integral super twisting sliding mode controller; Optogenetic method; Pinsky–Rinzel model.