Interpretable Machine Learning Evaluates Differential Therapy Effects in Parkinsonian Gait

Parkinson's disease therapy is usually adjusted based on extensive clinical examinations, but the effects of medication and deep brain stimulation (DBS) on gait dynamics remain difficult to quantify precisely. We use interpretable probabilistic machine learning to measure therapy-related gait changes in a repeated-measures motion-capture dataset comprising 376 walking trials from 19 patients with Parkinson's disease. Patients were recorded under four therapy conditions: medication off/stimulation off, medication off/stimulation on, medication on/stimulation off, and medication on/stimulation on. They performed natural and fast walking, and a study neurologist scored motor severity using UPDRS-III. From 1.0 s sliding windows of foot-marker motion, we compute short-window largest Lyapunov exponent (LLE)-derived local divergence features that capture local changes in gait trajectory dynamics. We summarize these features as two LLE-derived digital biomarkers: left-right asymmetry and left-right coupling. Bayesian hierarchical regression then estimates medication, stimulation, and task effects while accounting for repeated measurements within the same patients and patient-specific baseline differences. The main result is that during natural walking, LLE asymmetry decreased under combined therapy with a large paired effect size ($d_z=-0.83$). Coupling features changed with therapy in a complementary way, especially for stimulation-related changes in bilateral coordination. These findings suggest that short-window LLE asymmetry tracks therapy-related reduction of lateralized gait dysregulation, while LLE coupling tracks treatment-dependent reorganization of left-right coordination. By modeling novel LLE-derived biomarkers across controlled medication and DBS states, we show that the two therapies are expressed through distinct gait-dynamics signatures, supporting interpretable nonlinear gait biomarkers for objective therapy-response assessment.