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.

Assessing the impact of gait speed on gait stability using multi-scale entropy fused with plantar pressure signals

“… Warlop et al (2016) found that the variation in the duration of strides affects the stability of gait in patients with Parkinson’s disease. Chandrasekaran et al (2022) used the Lyapunov exponent to analyze the stride intervals, found that it was correlated with variations in the duration of strides, and used this to obtain the threshold of gait stability. Aziz and Arif (2006) claimed that the stride interval of the gait reflects a law of the human gait, and analyzed the complex stability of gait in patients with neurodegenerative diseases based on the symbolic entropy of the stride interval.…”

Dynamic Stability of Human Walking in Response to Sudden Speed Changes

“…To address these gaps, this study employs nonlinear dynamics methods, including the Maximum Lyapunov Exponent (MLE), Sample Entropy (SaEn), and Detrended Fluctuation Analysis (DFA), to quantitatively analyze the relationship between gait pattern characteristics and dynamic stability. These methods offer a holistic perspective on gait behavior, capturing intricate dynamics throughout the entire gait cycle [10,[17][18][19][20][21][22]. Unlike previous studies focusing on individual variables, the utilization of nonlinear dynamics tools allows us to delve into the complex interactions that shape gait stability during sudden speed changes [23,24].…”