Quantifying Chaotic Behavior in Treadmill Walking

Abstract

The authors describe an example of application of nonlinear time series analysis directed at identifying the presence of deterministic chaos in human motion data by means of the largest Lyapunov exponent (LLE). The research aimed at determination of the influence of gait speed on the LLE value with a view to verification of the belief that slower walking leads to increased stability characterized by smaller LLE value. Analyses were focused on the time series representing hip flexion/extension angle, knee flexion/extension angle and dorsiflexion/plantarflexion dimension of the ankle. Gait sequences were recorded in the Human Motion Laboratory (HML) of the Polish-Japanese Academy of Information Technology in Bytom by means of the Vicon system. Application of the AC5000M treadmill allowed recordings in three variants: at the preferred walking speed (PWS) of each subject, at 80% of the PWS and at 120% of the PWS. According to the recommendations from the literature the LLE value was estimated twice for every time series: as the short-term LLE$_1$ for the first stride and as the long-term LLE$_{4-10}$ over a fixed interval between the fourth and the tenth stride. In the latter case it was confirmed that the LLE value increases with walking speed for both limbs.