Topological Gait Analysis: A New Framework and Its Application to the Study of Human Gait

Abstract

Objective: This study introduces a physiologically driven topological gait analysis (TGA) framework to gain insights into pathological gait. Methods: A publicly available gait dataset consisting of four groups: healthy adults, people with Parkinson's disease (PD), Huntington's disease (HD), and amyotrophic lateral sclerosis (ALS) was used. The topological properties of the configuration space of three gait parameters were studied by approximating the underlying distribution through a Gaussian kernel-based density estimation technique. Thereafter, sublevel sets of the density estimate were analyzed using cubical persistence homology. Results: Three new features were constructed: 1. Probability density estimates (PDEs) that characterize the distribution of gait parameters over their configuration space. Healthy adults exhibited a unimodal distribution, while people with neurodegenerative disorders displayed a multi-modal distribution. 2. Persistence entropy plots that summarize changes in the PDEs and characterize the uncertainty in the underlying distribution. Gait of healthy adults was concentrated at higher entropy values as opposed to neurodegenerative gait. 3. A number $\alpha _{s}$ that captures disease severity trends. Conclusions: Topological features in PD and HD indicate a ‘bias’ to a certain set of gait configurations. This lack of exploration may reflect poor planning of the underlying topology, resulting in outward manifestations of impaired gait. The lower variegations in PDEs in ALS compared to PD and HD suggest that the planning of the topology of gait may occur at higher levels of the neural architecture. Significance: TGA offers characterization of gait at a hitherto uncharted level, potentially serving neuromotor markers for early diagnosis and personalized rehabilitation protocols.