Patient-Calibrated Dynamical Modeling and Embedded Trend-Zone Predictive Control for Closed-Loop Deep Brain Stimulation in Parkinson's Disease

Closed-loop deep brain stimulation (cDBS) for Parkinsons disease requires control strategies that tolerate noisy sensing, patient-specific stimulation responses, medication-related fluctuations, and embedded hardware constraints. We developed a patient-calibrated minute-scale dynamical model of subthalamic beta activity and an embedded explicit trend-zone predictive controller, eTZPC. The model combined a basal-ganglia mechanistic prior with stimulation-amplitude and medication-cycle recordings from five patients, and incorporated individualized stimulation-{beta}STN maps, fast- and slow-timescale stimulation responses, levodopa-related modulation, background drift, and observation noise. eTZPC was designed to maintain {beta}STN activity within a patient-specific target zone under stimulation-amplitude, step-size, and quantization constraints. Compared with dual-threshold (DT) and proportional-integral-derivative (PID) controllers across four disturbance scenarios, eTZPC achieved target-zone regulation close to PID while reducing stimulation-switching burden toward the low-switching profile of DT. Ablation analyses identified distinct contributions of smoothing, trend prediction, patient-specific action modeling, and embedded explicit implementation. Parameter-mismatch tests showed that eTZPC was relatively robust to dynamic and disturbance-parameter deviations, but remained sensitive to errors in the steady-state stimulation-{beta}STN map. Patient-in-the-loop recordings in five patients further confirmed execution consistency and compliance with stimulation-boundary and step-size constraints. These findings support patient-calibrated dynamical modeling combined with low-complexity explicit control as a feasible framework for further embedded cDBS evaluation.