Maximum Lyapunov exponent revisited: Long-term attractor divergence of gait dynamics is highly sensitive to the noise structure of stride intervals

TL;DR

This study reveals that the long-term maximum Lyapunov exponent in gait analysis is highly sensitive to stride interval noise structure, suggesting it reflects gait complexity rather than stability, unlike the short-term exponent.

Contribution

It demonstrates that long-term DE is a gait complexity index sensitive to noise structure, proposing the term attractor complexity index (ACI) for it.

Findings

Long-term DE varies significantly with noise structure.

Short-term DE remains relatively unaffected by noise structure.

Long-term DE may serve as an index of gait complexity.

Abstract

The local dynamic stability method (maximum Lyapunov exponent) can assess gait stability. Two variants of the method exist: the short-term divergence exponent (DE), and the long-term DE. Only the short-term DE can predict fall risk. The significance of long-term DE has been unclear so far. Some studies have suggested that the complex, fractal-like structure of fluctuations among consecutive strides correlates with long-term DE. The aim, therefore, was to assess whether the long-term DE is a gait complexity index. The study reanalyzed a dataset of trunk accelerations from 100 healthy adults walking at preferred speed on a treadmill for 10 minutes. By interpolation, the stride intervals were modified within the acceleration signals for the purpose of conserving the original shape of the signal, while imposing a known stride-to-stride fluctuation structure. 4 types of hybrid signals with different noise structures were built: constant, anti-correlated, random, and correlated (fractal). Short- and long-term DEs were then computed. The results show that long-term DEs, but not short-term DEs, are sensitive to the noise structure of stride intervals. It was that observed that random hybrid signals exhibited significantly lower long-term DEs than hybrid correlated signals did (0.100 vs 0.144, i.e. a 44% difference). Long-term DEs from constant hybrid signals were close to zero (0.006). Short-term DEs of anti-correlated, random, and correlated hybrid signals were closely grouped (2.49, 2.50, and 2.51). The short- and long-term DEs, although they are both computed from divergence curves, should not be interpreted in a similar way. The long-term DE is very likely an index of gait complexity, which may be associated with gait automaticity or cautiousness. To better differentiate between short- and long-term DEs, the use of the term attractor complexity index (ACI) is proposed for the latter.