Nonlinear dynamics and Poincaré sections to model gait impairments in different stages of Parkinson's disease

Parkinson’s disease is a progressive neurological disorder that affects the motor system and produces several problems to control muscles and limbs. One of the major manifestations of the disease appears in gait and typically causes disability in the most advanced stages of the disease. Gait assessment is suitable for the diagnosis and monitoring of the neurological state of the patients. Gait is mainly evaluated from signals collected with inertial sensors attached to the limbs, and kinematics features are commonly extracted. Besides the classical kinematic methods, there are nonlinear phenomena in the gait process that cannot be properly modeled with kinematic features. This study proposes the use of several nonlinear dynamics features to assess gait impairments of Parkinson’s patients. We consider classical nonlinear features including correlation dimension, largest Lyapunov exponent, Hurst exponent, and others. In addition, we propose a novel nonlinear analysis based on the construction of Gaussian mixture models to find clusters in Poincaré sections. The nonlinear dynamics features proposed here are used to discriminate between Parkinson’s patients and healthy subjects, and to classify patients in different stages of the disease. To the best of our knowledge, this is the first study that considers nonlinear dynamics analysis including Poincaré sections to assess gait impairments of patients with Parkinson’s disease