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

Complex fluctuations of unknown origin appear in the normal gait pattern. These fluctuations might be described as being 1) uncorrelated white noise, 2) short-range correlations, or 3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series, we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that successfully accounts for the experimentally observed long-range correlations.

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

Journal of Applied Physiology ◽

10.1152/jappl.1996.80.5.1448 ◽

1996 ◽

Vol 80 (5) ◽

pp. 1448-1457 ◽

Cited By ~ 400

Author(s):

J. M. Hausdorff ◽

P. L. Purdon ◽

C. K. Peng ◽

Z. Ladin ◽

J. Y. Wei ◽

...

Keyword(s):

Long Range ◽

Healthy Subjects ◽

Fractal Property ◽

Dynamical Analysis ◽

Human Gait ◽

Locomotor System ◽

Long Range Correlations ◽

Power Law Decay ◽

Stride Interval ◽

The Stability

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.

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Peripheral neuropathy does not alter the fractal dynamics of stride intervals of gait

Journal of Applied Physiology ◽

10.1152/japplphysiol.00413.2006 ◽

2007 ◽

Vol 102 (3) ◽

pp. 965-971 ◽

Cited By ~ 45

Author(s):

Deanna H. Gates ◽

Jonathan B. Dingwell

Keyword(s):

Peripheral Neuropathy ◽

Spectral Density ◽

Power Spectral Density ◽

Long Range ◽

Sensory Loss ◽

Human Gait ◽

Time Variability ◽

Long Range Correlations ◽

Power Spectral ◽

Detrended Fluctuation

The purpose of this study was to determine the effect (if any) of significant sensory loss on the long-range correlations normally observed in the stride intervals of human gait. Fourteen patients with severe peripheral neuropathy and 12 gender-, age-, height-, and weight-matched nondiabetic controls participated. Subjects walked around an ∼200-m open-level walkway for 10 min at their comfortable pace. Continuous knee joint kinematics were recorded and used to calculate a stride interval time series for each subject. Power spectral density and detrended fluctuation analyses were used to determine whether these stride intervals exhibited long-range correlations. If the loss of long-range correlations indicates deterioration of the central control of gait, then changes in peripheral sensation should have no effect. If instead the loss of long-range correlations is a consequence of a general inability to regulate gait cycle timing, then a similar loss should occur in patients with peripheral locomotor disorders. Both power spectral density analyses and detrended fluctuation analyses showed that temporal correlations in the stride times of neuropathic and control subjects were statistically identical ( P = 0.954 and P = 0.974, respectively), despite slower gait speeds ( P = 0.008) and increased stride time variability ( P = 0.036) among the neuropathy patients. All subjects in both groups exhibited long-range correlations. These findings demonstrate that the normal long-range correlation structure of stride intervals is unaltered by significant peripheral sensory loss. This further supports the hypothesis that the central nervous system is involved in the regulation of long-range correlations.

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Assessing the stability of human locomotion: a review of current measures

Journal of The Royal Society Interface ◽

10.1098/rsif.2012.0999 ◽

2013 ◽

Vol 10 (83) ◽

pp. 20120999 ◽

Cited By ~ 271

Author(s):

S. M. Bruijn ◽

O. G. Meijer ◽

P. J. Beek ◽

J. H. van Dieën

Keyword(s):

Construct Validity ◽

Long Range ◽

Predictive Validity ◽

Observational Studies ◽

Convergent Validity ◽

Experimental Studies ◽

Maximum Lyapunov Exponent ◽

Floquet Multiplier ◽

Gait Stability ◽

Long Range Correlations

Falling poses a major threat to the steadily growing population of the elderly in modern-day society. A major challenge in the prevention of falls is the identification of individuals who are at risk of falling owing to an unstable gait. At present, several methods are available for estimating gait stability, each with its own advantages and disadvantages. In this paper, we review the currently available measures: the maximum Lyapunov exponent ( λ S and λ L ), the maximum Floquet multiplier, variability measures, long-range correlations, extrapolated centre of mass, stabilizing and destabilizing forces, foot placement estimator, gait sensitivity norm and maximum allowable perturbation. We explain what these measures represent and how they are calculated, and we assess their validity, divided up into construct validity, predictive validity in simple models, convergent validity in experimental studies, and predictive validity in observational studies. We conclude that (i) the validity of variability measures and λ S is best supported across all levels, (ii) the maximum Floquet multiplier and λ L have good construct validity, but negative predictive validity in models, negative convergent validity and (for λ L ) negative predictive validity in observational studies, (iii) long-range correlations lack construct validity and predictive validity in models and have negative convergent validity, and (iv) measures derived from perturbation experiments have good construct validity, but data are lacking on convergent validity in experimental studies and predictive validity in observational studies. In closing, directions for future research on dynamic gait stability are discussed.

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Tracking Performance Changes With Running-Stride Variability When Athletes Are Functionally Overreached

International Journal of Sports Physiology and Performance ◽

10.1123/ijspp.2015-0618 ◽

2017 ◽

Vol 12 (3) ◽

pp. 357-363 ◽

Cited By ~ 9

Author(s):

Joel T. Fuller ◽

Clint R. Bellenger ◽

Dominic Thewlis ◽

John Arnold ◽

Rebecca L. Thomson ◽

...

Keyword(s):

Long Range ◽

Prolonged Exposure ◽

Time Trial ◽

Training Load ◽

Fluctuation Analysis ◽

Long Range Correlations ◽

Stride Interval ◽

Fixed Order ◽

Detrended Fluctuation ◽

Heavy Training

Purpose:Stride-to-stride fluctuations in running-stride interval display long-range correlations that break down in the presence of fatigue accumulated during an exhaustive run. The purpose of the study was to investigate whether long-range correlations in running-stride interval were reduced by fatigue accumulated during prolonged exposure to a high training load (functional overreaching) and were associated with decrements in performance caused by functional overreaching.Methods:Ten trained male runners completed 7 d of light training (LT7), 14 d of heavy training (HT14) designed to induce a state of functional overreaching, and 10 d of light training (LT10) in a fixed order. Running-stride intervals and 5-km time-trial (5TT) performance were assessed after each training phase. The strength of long-range correlations in running-stride interval was assessed at 3 speeds (8, 10.5, and 13 km/h) using detrended fluctuation analysis.Results:Relative to performance post-LT7, time to complete the 5TT was increased after HT14 (+18 s; P < .05) and decreased after LT10 (–20 s; P = .03), but stride-interval long-range correlations remained unchanged at HT14 and LT10 (P > .50). Changes in stride-interval long-range correlations measured at a 10.5-km/h running speed were negatively associated with changes in 5TT performance (r –.46; P = .03).Conclusions:Runners who were most affected by the prolonged exposure to high training load (as evidenced by greater reductions in 5TT performance) experienced the greatest reductions in stride-interval long-range correlations. Measurement of stride-interval long-range correlations may be useful for monitoring the effect of high training loads on athlete performance.

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