On Gait Stability: Correlations between Lyapunov Exponent and Stride Time Variability

Abstract

Lyapunov exponent is a promising parameter to ascertain the stability of the human gait. In this work, we use a time-series model based on a second-order delay-system with inertial measurement units placed on the foot and wrist. Stability is analyzed in a localized sense, with the Lyapunov exponent computed in the temporal region between two heel-strike points, which are determined using a peak-detection algorithm. We have attempted to show correlations between variations in the stride time and stability of the gait under normal and abnormal conditions. In the latter case, we attach a weight on foot to emulate weakness. On comparison between both cases, we observe a statistical significance of p=0.0039 using Wilcoxon’s rank-sum test. Moreover, on observing the correlations between Lyapunov Exponent and Stride Time Variability, we notice a left-shift in the abnormal case, indicating a lower threshold for instability, with the Stride Time Variability being 0.07 as compared to 0.11 in the normal case.The results indicate that by exploiting the correlation between stride time variability and Lyapunov exponents, one can establish a threshold for gait stability.