Fractal analyses reveal independent complexity and predictability of gait

Locomotion is a natural task that has been assessed for decades and used as a proxy to highlight impairments of various origins. So far, 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 α and the Minkowski fractal dimension D were computed and interpreted as indexes expressing predictability and complexity of stride interval time series, respectively. These holistic indexes can easily be interpreted in the framework of optimal movement complexity. We show that α and D accurately capture stride interval changes in function of the experimental condition. Walking forward exhibited maximal complexity (D) and hence, adaptability. In contrast, walking backward and/or stimulation of the vestibular system decreased D. Furthermore, walking backward increased predictability (α) 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. Our developments may have immediate applications in rehabilitation, diagnosis, and classification procedures

Mean ± standard deviations values for the parameters computed in the four experimental conditions.

<p>FW (BW) stands for forward (backward) walking and S0 (S+) for no GVS (GVS on).</p

Significance level (<i>p</i>–values) of the <i>post hoc</i> (Holm-Sidak) pairwise multiple comparisons between the different experimental conditions for the parameters analyzed.

<p>Statistically significant differences are written in bold font.</p

Median scores (in %) and interquartile range (IQR) results of the MSAQ.

<p>The first (Q1) and third quartiles (Q3) are shown between square brackets.</p

Typical stride interval time series in the different experimental conditions.

<p>FW or BW stand for forward and backward walking respectively. The indices <i>S</i>+ or <i>S</i>0 indicate the presence or absence of GVS.</p

Schematic representation of the body (circle) and the lower limb (solid lines) when the heel strikes the ground in forward direction (FW) or the toes in backward direction (BW).

<p>The red star encloses the contact point.</p

Evolution of the Hurst exponent (<i>α</i>) versus stride amplitude (<i>θ</i>₀) in the FW_<i>S</i>0 and BW_<i>S</i>0 conditions (empty open circles).

<p>Data from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0188711#pone.0188711.ref006" target="_blank">6</a>] (closed circles) are linked with dotted lines for clarity sake. Error bars represent SD. The notation (<i>NS</i>/*, <i>NS</i>/*) denotes statistically significant differences (*) or no (<i>NS</i>) in the (<i>α</i>, <i>θ</i>₀)–plane.</p

Typical logarithmic plots showing the linear regressions performed to find <i>α</i> (upper left panel), <i>γ</i> (upper right panel) and <i>D</i> (lower left panel) in the four conditions.

<p>Raw data are those of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0188711#pone.0188711.g001" target="_blank">Fig 1</a>.</p

Box plots of the mean stride time (<i>T</i>, upper left panel), the coefficient of variation (<i>CV</i>_<i>T</i>, upper right panel), the stride amplitude (<i>θ</i>₀, middle left panel), the mean step width (<i>w</i>, middle right panel), the Hurst exponent <i>α</i> (lower left panel), and the Minkowski fractal dimension <i>D</i> (lower right panel).

<p>Box plots of the mean stride time (<i>T</i>, upper left panel), the coefficient of variation (<i>CV</i>_<i>T</i>, upper right panel), the stride amplitude (<i>θ</i>₀, middle left panel), the mean step width (<i>w</i>, middle right panel), the Hurst exponent <i>α</i> (lower left panel), and the Minkowski fractal dimension <i>D</i> (lower right panel).</p

Evolution of the fractal dimension (<i>D</i>) versus the Hurst exponent (<i>α</i>) taken as complexity and predictability indices respectively for the four experimental conditions.

<p>Standard deviations have not been plotted for the sake of clarity. To guide the eyes, arrows indicate the four post-hoc comparisons performed with their significance or not. The notation (<i>NS</i>/*, <i>NS</i>/*) denotes statistically significant differences (*) or no (<i>NS</i>) in the (<i>α</i>, <i>D</i>)–plane.</p