Topological descriptors of foot clearance gait dynamics improve differential diagnosis of Parkinsonism

Differential diagnosis among parkinsonian syndromes remains a clinical challenge due to overlapping motor symptoms and subtle gait abnormalities. Accurate differentiation is crucial for treatment planning and prognosis. While gait analysis is a well established approach for assessing motor impairments, conventional methods often overlook hidden nonlinear and structural features embedded in foot clearance patterns. We evaluated Topological Data Analysis (TDA) as a complementary tool for Parkinsonism classification using foot clearance time series. Persistent homology produced Betti curves, persistence landscapes, and silhouettes, which were used as features for a Random Forest classifier. The dataset comprised 15 controls (CO), 15 idiopathic Parkinson's disease (IPD), and 14 vascular Parkinsonism (VaP). Models were assessed with leave-one-out cross-validation (LOOCV). Betti-curve descriptors consistently yielded the strongest results. For IPD vs VaP, foot clearance variables minimum toe clearance, maximum toe late swing, and maximum heel clearance achieved 83% accuracy and AUC=0.89 under LOOCV in the medicated (On) state. Performance improved in the On state and further when both Off and On states were considered, indicating sensitivity of the topological features to levodopa related gait changes. These findings support integrating TDA with machine learning to improve clinical gait analysis and aid differential diagnosis across parkinsonian disorders.