Abstract
Closed-loop control is a promising deep brain stimulation (DBS) strategy that could be used to suppress high-amplitude epileptic activity. However, there are currently no analytical approaches to determine the stimulation parameters for effective and safe treatment protocols. Proportional-integral (PI) control is the most extensively used closed-loop control scheme in the field of control engineering because of its simple implementation and perfect performance. In this study, we took Jansen’s neural mass model (NMM) as a test bed to develop a PI-type closed-loop controller for suppressing epileptic activity. A graphical stability analysis method was employed to determine the stabilizing region of the PI controller in the control parameter space, which provided a theoretical guideline for the choice of the PI control parameters. Furthermore, we established the relationship between the parameters of the PI controller and the parameters of the NMM in the form of a stabilizing region, which provided insights into the mechanisms that may suppress epileptic activity in the NMM. The simulation results demonstrated the validity and effectiveness of the proposed closed-loop PI control scheme.
Highlights
Closed-loop control is a promising deep brain stimulation (DBS) strategy that could be used to suppress high-amplitude epileptic activity
The control scheme was developed based on the fact that epileptic activity can be characterized as high-amplitude limit cycle oscillation born in Hopf bifurcation[4,28,31,33,36,41,42,49,50,51,52,53], which indicates that the fixed point of the neural mass model (NMM) lost its stability
The design objective was to determine the PI controller parameter values that stabilized the unstable NMM caused by abnormally large excitatory or small inhibitory parameter values[32,42] such that homeostasis of the NMM was maintained and the high-amplitude epileptic activity was suppressed
Summary
Closed-loop control is a promising deep brain stimulation (DBS) strategy that could be used to suppress high-amplitude epileptic activity. Closed-loop control is a promising deep brain stimulation (DBS) strategy for suppressing abnormal neural activities, such as epilepsy and Parkinson’s disease, and it has become the focus of current experimental and theoretical studies[6,7,8,9,10,11,12,13,14,15,16,17,18]. A proportional-integral-derivative (PID) controller is the most extensively used closed-loop controller in the field of control engineering because of its simple implementation and robust performance[19] In this context, the PID-type controller was introduced to control various pathological neural activities[12,20,21,22,23]. Delayed feedback control is another representative control scheme that has been used to suppress pathological brain rhythms by desynchronizing the neural activities[30,31]
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