Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations

Abstract

Fractal dynamics were recently detected in the apparently "noisy" variations in the stride interval of human walking. Dynamical analysis of these step-to-step fluctuations revealed a self-similar pattern: fluctuations at one time scale are statistically similar to those at multiple other time scales, at least over hundreds of steps, while healthy subjects walk at their normal rate. To study the stability of this fractal property, we analyzed data obtained from healthy subjects who walked for 1 h at their usual, slow, and fast paces. The stride interval fluctuations exhibited long-range correlations with power-law decay for up to 1,000 strides at all 3 walking rates. In contrast, during metronomically paced walking, these long-range correlations disappeared; variations in the stride interval were random (uncorrelated) and nonfractal. The long-range correlations observed during spontaneous walking were not affected by removal of drifts in the time series. Thus the fractal dynamics of spontaneous stride interval are normally quite robust and intrinsic to the locomotor system. Furthermore, this fractal property of neural output may be related to the higher nervous centers responsible for the control of walking rhythm.

Gait dynamics, fractals and falls: Finding meaning in the stride-to-stride fluctuations of human walking

“…We first studied the stride-to-stride fluctuations present in healthy adults in order to gain insight into normal locomotor function and its control mechanisms and thereby better appreciate pathological deviations (Hausdorff, Ashkenazy et al, 2001;Hausdorff et al, 1996). Variability, the magnitude of the stride-to-stride fluctuations, and stride dynamics, how the stride fluctuates with time, independent of the magnitude, may rely upon different control mechanisms.…”

“…In this case, the stride interval at any instant would 'depend' (in a statistical mechanics sense) on the interval at relatively remote times, and this dependence would decay in a scale-free (fractal-like), powerlaw fashion. We used spectral analysis and a modified random walk analysis, termed detrended fluctuation analysis (DFA) (Goldberger et al, 2002;Hausdorff, Peng et al, 1995;Hausdorff et al, 1996) to quantitatively characterize the stride interval fluctuations of healthy young men (aged: 20-30 years) as they walked continuously on level ground around a circular path.…”

“…To study the stability and extent of these unexpected long-range correlations, we asked another group of healthy young (ages 18-29 years) men to walk for one hour at their usual, slow and fast paces around an outdoor track (Hausdorff et al, 1996). This data (as well as other data sets described here) and further details can be found at www.physionet.org.…”

“…B) While there are subtle effects of gait speed, DFA shows that there is fractal scaling at all 3 gait speed. Adapted from (Hausdorff et al, 1996) Effects of healthy aging on gait: sensitivity of fractal dynamics. The average stride time, stride time variability, Timed Up and Go performance are similar in this group of healthy older adults and healthy young adults, while the fractal scaling index is reduced with aging.…”

Statistical quantifiers of memory for an analysis of human brain and neuro-system diseases

“…Despite its welldeveloped experimental methods this field still lacks good and reliable theoretical quantitative indicators for human gait disorders. Interesting results in this field have been derived before by Hausdorff et al [13][14][15][16][17][18][19][20][21]. They studied the dynamical changes of human gait, connected with various diseases [13][14][15][16], the increasing instability of gait in elderly people [13,[16][17][18], presence of long-range correlations in stride interval fluctuations [19,20], stride-to-stride variability and its temporal organization in children [21].…”