Robust Adaptive Deep Brain Stimulation Control of Non-Stationary Cortex-Basal Ganglia-Thalamus Network Models in Parkinson’s Disease

Closed-loop deep brain stimulation (DBS) is a promising therapy for Parkinson’s disease (PD) that works by adjusting DBS patterns in real time from the guidance of feedback neural activity. Current closed-loop DBS mainly uses threshold-crossing on-off controllers or linear time-invariant (LTI) controllers to regulate the basal ganglia (BG) beta band oscillation power. However, the critical cortex-BG-thalamus network dynamics underlying PD are nonlinear, non-stationary, and noisy, hindering the accurate and robust control of PD neural dynamics using current closed-loop DBS methods. Here, we develop a new robust adaptive closed-loop DBS method for regulating cortex-BG-thalamus network dynamics in PD. We first build an adaptive state-space model to quantify the dynamic, nonlinear, and non-stationary neural activity. We then construct an adaptive estimator to track the nonlinearity and non-stationarity in real time. We next design a robust controller to automatically determine the DBS frequency based on the estimated PD neural state while reducing the system’s sensitivity to high-frequency noise. We adopt and tune a biophysical cortex-BG-thalamus network model as a testbed to simulate various nonlinear and non-stationary neural dynamics for evaluating DBS methods. We find that under different nonlinear and non-stationary neural dynamics, our robust adaptive DBS method achieved accurate regulation of the BG beta band oscillation power with small control error, bias, and deviation. Moreover, the accurate regulation generalizes across different therapeutic targets and consistently outperforms state-of-the-art on-off and LTI DBS methods. These results have implications for future designs of clinically-viable closed-loop DBS systems to treat PD and other neurological and neuropsychiatric disorders.