# Fractal Analyses Reveal Independent Complexity and Predictability of Gait

## TL;DR

This study applies advanced non-linear analysis techniques to gait time series, revealing that complexity and predictability indexes can distinguish different walking conditions and may improve clinical assessments.

## Contribution

It introduces the combined use of Hurst exponent and Minkowski fractal dimension to analyze gait, providing more sensitive indexes for detecting locomotion abnormalities.

## Key findings

- Walking forward shows highest complexity and adaptability.
- Perturbations decrease gait complexity.
- Gait predictability varies with walking direction and vestibular stimulation.

## Abstract

Locomotion is a natural task that has been assessed since decades and used as a proxy to highlight impairments of various origins. Most studies adopted classical linear analyses of spatio-temporal gait parameters. Here, we use more advanced, yet not less practical, non-linear techniques to analyse gait time series of healthy subjects. We aimed at finding more sensitive indexes related to spatio-temporal gait parameters than those previously used, with the hope to better identify abnormal locomotion. We analysed large-scale stride interval time series and mean step width in 34 participants while altering walking direction (forward vs. backward walking) and with or without galvanic vestibular stimulation. The Hurst exponent $\alpha$ and the Minkowski fractal dimension $D$ were computed and interpreted as indexes expressing predictability and complexity of stride interval time series, respectively. We show that $\alpha$ and $D$ accurately capture stride interval changes in function of the experimental condition. Walking forward exhibited maximal complexity ($D$) and hence, adaptability. In contrast, any perturbation (walking backward and/or stimulation of the vestibular system) decreased it. Furthermore, walking backward increased predictability ($\alpha$) through a more stereotyped pattern of the stride interval and galvanic vestibular stimulation reduced predictability. The present study demonstrates the complementary power of the Hurst exponent and the fractal dimension to improve walking classification. These holistic indexes can easily be interpreted in the framework of optimal movement complexity. Our developments may have immediate applications in rehabilitation, diagnosis, and classification procedures.