Effects of the kinematic variable, time delay and data length on test–retest reliability of the maximal Lyapunov exponent of human walking

Abstract

The maximal Lyapunov exponent (MLE) has been used to quantify the dynamic stability of human locomotion. The method for estimating MLE requires selecting a proper time series of kinematic variables and reconstructing phase space using proper time delay. The data length also affects the reliability of the measured MLE. However, there has been no criterion for the choice of the time series, time delay or data length. Here, we quantified the effect of these factors on the test–retest reliability of MLE estimations. We recruited 15 young and healthy adults and let them walk on a treadmill three times. We calculated MLE employing various lengths of time series of 18 frequently used kinematic variables and two typical choices of time delay: fixed delay and delay selected by average mutual information algorithm. Then, we measured the intraclass correlation coefficient (ICC) of the measured MLE under each condition. Our results show that the choice of time delay does not affect reliability. Five among the 18 kinematic variables enabled excellent reliability with ICC above 0.9 within 450 strides and also enabled ICC above 0.75 even with 60 or less strides. These findings can contribute to establishing the criteria for measuring the dynamic stability of human walking.

Keywords

• maximal Lyapunov exponent
• test–retest reliability
• walking
• kinematic data
• data length
• time delay