A topological data analysis-based method for gait signals with an application to the study of multiple sclerosis

In the past few years, light, affordable wearable inertial measurement units have been providing to clinicians and researchers the possibility to quantitatively study motor degeneracy by comparing gait trials from patients and/or healthy subjects. To do so, standard gait features can be used but they fail to detect subtle changes in several pathologies including multiple sclerosis. Multiple sclerosis is a demyelinating disease of the central nervous system whose symptoms include lower limb impairment, which is why gait trials are commonly used by clinicians for their patients' follow-up. This article describes a method to compare pairs of gait signals, visualize the results and interpret them, based on topological data analysis techniques. Our method is non-parametric and requires no data other than gait signals acquired with inertial measurement units. We introduce tools from topological data analysis (sublevel sets, persistence barcodes) in a practical way to make it as accessible as possible in order to encourage its use by clinicians. We apply our method to study a cohort of patients suffering from progressive multiple sclerosis and healthy subjects. We show that it can help estimate the severity of the disease and also be used for longitudinal follow-up to detect an evolution of the disease or other phenomena such as asymmetry or outliers.