Is walking a random walk? Evidence for long-range correlations in stride interval of human gait. J. Appl. Physiol. 78(l): 349-358, 1995.-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. fluctuation analysis; locomotion; pattern generator; fractal computer modeling; central HUMAN GAIT is a Complex process. The locomotor system incorporates input from the cerebellum, the motor cortex, and the basal ganglia, as well as feedback from visual, vestibular, and proprioceptive sensors. Under healthy conditions, this multilevel control system produces a remarkably stable walking pattern; the kinetics, kinematics, and muscular activity of gait appear to remain relatively constant from one step to the next, even during unconstrained walking (12, 13,23, 24,40). Nevertheless, closer examination reveals fluctuations in the gait pattern, even under stationary conditions (7, 10, 23, 41, 42). We (11) and others (7,10,41,42) have observed considerable "noise" in one of the outputs of the locomotor system, the stride interval, defined as the time between the heel strike of one foot and the next heel strike of the same foot. A representative example of these complex fluctuations is shown in Fig. 1. One possible explanation for these stepto-step variations is that they simply represent uncorrelated (white) noise superimposed on a basically regular process. Alternatively, there could be short-range correlations in the stride interval such that the current value is influenced by only the most recent stride intervals, but over the long term, the fluctuations are random. A third, less intuitive, possibility is that the fluctuations in the stride interval exhibit long-range correlations, as seen in a wide class of scale-free phenomena (6, 14, 17, 28, 34, 38, 43). In this case, the stride interval at any instant would depend on the interval at relatively remote times, and this dependence woul...

Fluctuations in the duration of the gait cycle (the stride interval) display fractal dynamics and long-range correlations in healthy young adults. We hypothesized that these stride-interval correlations would be altered by changes in neurological function associated with aging and certain disease states. To test this hypothesis, we compared the stride-interval time series of 1) healthy elderly subjects and young controls and of 2) subjects with Huntington's disease and healthy controls. Using detrended fluctuation analysis we computed alpha, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. The scaling exponent alpha was significantly lower in elderly subjects compared with young subjects (elderly: 0.68 +/- 0.14; young: 0.87 +/- 0.15; P < 0.003). The scaling exponent alpha was also smaller in the subjects with Huntington's disease compared with disease-free controls (Huntington's disease: 0.60 +/- 0.24; controls: 0.88 +/-0.17; P < 0.005). Moreover, alpha was linearly related to degree of functional impairment in subjects with Huntington's disease (r = 0.78, P < 0.0005). These findings demonstrate that strike-interval fluctuations are more random (i.e., less correlated) in elderly subjects and in subjects with Huntington's disease. Abnormal alterations in the fractal properties of gait dynamics are apparently associated with changes in central nervous system control.

The basal ganglia are thought to play an important role in regulating motor programs involved in gait and in the fluidity and sequencing of movement. We postulated that the ability to maintain a steady gait, with low stride-to-stride variability of gait cycle timing and its subphases, would be diminished with both Parkinson's disease (PD) and Huntington's disease (HD). To test this hypothesis, we obtained quantitative measures of stride-to-stride variability of gait cycle timing in subjects with PD (n = 15), HD (n = 20), and disease-free controls (n = 16). All measures of gait variability were significantly increased in PD and HD. In subjects with PD and HD, gait variability measures were two and three times that observed in control subjects, respectively. The degree of gait variability correlated with disease severity. In contrast, gait speed was significantly lower in PD, but not in HD, and average gait cycle duration and the time spent in many subphases of the gait cycle were similar in control subjects, HD subjects, and PD subjects. These findings are consistent with a differential control of gait variability, speed, and average gait cycle timing that may have implications for understanding the role of the basal ganglia in locomotor control and for quantitatively assessing gait in clinical settings.

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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