A continuous statistical-geometric framework for normative and impaired gaits

A quantitative analysis of human gait patterns in space-time provides an opportunity to observe variability within and across individuals of varying motor capabilities. Impaired gait significantly affects independence and quality of life, and thus a large part of clinical research is dedicated to improving gait through rehabilitative therapies. Evaluation of these paradigms relies on understanding the characteristic differences in the kinematics and underlying biomechanics of impaired and unimpaired locomotion, which has motivated quantitative measurement and analysis of the gait cycle. Previous analysis has largely been limited to a statistical comparison of manually selected pointwise metrics identified through expert knowledge. Here, we use a recent statistical-geometric framework, elastic functional data analysis (FDA), to decompose kinematic data into continuous 'amplitude' (spatial) and 'phase' (temporal) components, which can then be integrated with established dimensionality reduction techniques. We demonstrate the utility of elastic FDA through two unsupervised applications to post-stroke gait datasets. First, we distinguish between unimpaired, paretic and non-paretic gait presentations. Then, we use FDA to reveal robust, interpretable groups of differential response to exosuit assistance. The proposed methods aim to benefit clinical practice for post-stroke gait rehabilitation, and more broadly, to automate the quantitative analysis of motion.