Figure 1.
Step-by-step variability of overground walking.
(A) Step length and width are observed to vary, apparently randomly, over many overground steps (different color for each subject). (B) Walking speed also fluctuates, albeit more slowly. Examination of speed and step length together (scaled and overlaid in inset diagram) reveals that the two may in fact co-vary. Data shown are all trials performed by six representative subjects.
Figure 2.
Representative step lengths and step widths as a function of walking speed.
Step lengths are shown along with subject-specific curve fits (Eqn. 1) for the preferred step length vs. speed (s vs. v) relationship, s = α · vβ [19], with typical values of β ranging 0.27–0.55. Step width exhibits little dependence on walking speed, and appears to have greater variability than step length. Data shown are trials from six subjects, with a different color for each subject.
Figure 3.
Decomposition of step lengths into a speed-related trend and variations from that trend.
(A) Actual step lengths are hypothesized to vary according to the preferred step length vs. speed relationship, as walking speed fluctuates slowly during over-ground walking (see Eqn. 1). (B) The speed-related trend fluctuates in close correspondence to the low-frequency, long-term components of step length (solid line), found by low-pass filtering. (C) Variations from the speed trend, or de-trended step length, appear similar to random noise. This example shows one trial from a representative subject over about 90 steps. Variability of both the speed-related trend and de-trended step length are comparable in magnitude (mean and s.d. shown as error bars at right).
Figure 4.
Overall variance of step length and step width.
(A) Step length and (B) step width are each decomposed by de-trending and by filtering (N = 14). In each panel, the average total variability (labeled “Total” at left, with error bars for standard deviation across subjects) is contrasted with the variability of the components determined by the “Speed-related” trend and the “Filtered” components (middle and right of each panel). The speed-related trend and the de-trended step lengths (lighter and darker bars respectively) have similar variances whose sum is nearly equal to total variance. The long- and short-term components (lighter and darker bars respectively) of step length, separated by filtering, yield variances comparable to the speed-related components. In contrast, step width exhibits little speed-related trend, and little low-frequency content. The speed-related trend accounted for about half of the total variance in step length, but a negligible amount of width. De-trended step width variability was over 4 times the de-trended step length variability (P = 4.2 · 10−8).
Figure 5.
Difference in step length and width variability between walking with eyes open and eyes closed.
(A) Eyes open. (B) Eyes closed. Each panel shows total variance of step length and width (left and right bars of each pair), speed-related length and width components, and filtered length and width components. When walking with eyes closed, subjects walked with 56% greater step length variance, and 103% greater step width variance (P < 0.05). Speed-related trends do not account for the increased gait variability with eyes closed.
Figure 6.
Autocorrelation of walking speed, step length and step width as a function of lag in steps.
Autocorrelation of speed decreases gradually with lag (solid line denotes mean, shaded region denotes ± 1 s.d.), comparable to the long-term correlations of low-frequency noise (dashed line; 6 step correlation time constant). Total step length autocorrelation also exhibits a long-term trend, whereas de-trended step length has an autocorrelation resembling white noise. Step width autocorrelation exhibits very little long-term correlation, and de-trending has little effect on the autocorrelation. (White noise has an autocorrelation of 1 at zero lag, and 0 at all other lags.).