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### Stride Time Variability Measures

Representative examples of the effects of age on the stride time fluctuations are shown in Figure 1. The stride-to-stride variability is largest in the four year old, lower in the seven year old, and smaller still in the eleven year old child. As summarized in Table 2, there was a highly significant effect of age on variability (p < .0001). Both the standard deviation and coefficient of variation (CV) were significantly larger in the 3 and 4 year olds compared to the 6 and 7 year olds (p < .0001). In addition, these measures were significantly larger in the 6 and 7 year olds compared to the 11 to 14 year old children (p < .005). Of note, the stride-to-stride variability of the 11 to 14 year old children was closest to the values obtained in healthy, young adults (CV = 1.3 0.1 % in the young adults and 2.1 0.1 % in the 11 to 14 year olds).

In the representative examples shown in Figure 1, the local average of the stride time of the oldest child is relatively constant throughout the walk. In contrast, for the two younger children, the local average appears to change from time to time. Therefore, we next addressed two questions: 1) Is the increased variability in the younger children simply due to fatigue during this walk? 2) Is this increased variability due to a change in rate during the walk (e.g., long-term slowing down or speeding up), and not indicative of short-term, stride-to-stride unsteadiness per se?

To evaluate these questions, we detrended each time series to minimize the effects of any local changes in average stride. Figure 2 shows the results for the times series shown in Figure 1. Even after detrending, variability is largest for the four year old child and smallest for the oldest child. This inverse relationship between variability and age after detrending was found in general for all subjects as well. The standard deviation of the detrended time series, a measure of the dispersion or variability, was significantly larger in the 3 and 4 year olds compared to the 6 and 7 year old (p < .0001) and in the 6 and 7 year olds compared to the oldest children (p = .004).

As a further test of these findings, we analyzed sub-sections of each subject's time series to find the 30 consecutive strides with the lowest CV. (A data analysis window was moved forward 5 strides at a time across the time series and in each window the CV was calculated). Variability during this segment should be largely independent of a subject's speeding up or slowing down during the trial and reflects the ``best-effort'' of the neuromuscular control system. For the data shown in Figures 1 and 2, the CV calculated in this manner was 3.8, 1.9 and 1.1 % for the 4, 7 and 11 year old, respectively. Figure 3 shows the results of this lowest variability time segment for all subjects. Even during a relatively short time period, the fluctuations from one stride to the next were significantly increased in the 3 and 4 year olds compared to the 6 and 7 year olds (p < .0001) and in the 6 and 7 year olds compared to the oldest children (p < .0001). In fact, the CV of each of the oldest children was lower than that of all of the 3 and 4 year old children.

Finally, to confirm that the increased variability in the younger children was not simply due to fatigue or a change of speed during the walk, we studied the variability of only the first 30 strides. As was the case for the entire walk, both the standard deviation and coefficient of variation were significantly larger in the 3 and 4 year olds compared to the 6 and 7 year olds (p < .0001) and in the 6 and 7 year olds compared to the oldest children (p < .0003) (Table 2).

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