Allometric Control, Inverse Power Laws and Human Gait

The stride interval in normal human gait is not strictly constant, but fluctuates from step to step in a random manner. Herein we show that contrary to the traditional assumption of uncorrelated random errors, these fluctuations have long-time correlations. Further, these long-time correlations are interpreted in terms of a scaling in the fluctuations indicating an allometric control process. To establish this result we measure the stride interval of a group of 5 healthy men and women as they walked for 15 minutes at their usual pace. From these time series we calculate the relative dispersion, the ratio of the standard deviation to the mean, and show by systematically aggregating the data that the correlation in the stride-interval time series is an inverse power law similar to the allometric relations in biology. The inverse power-law relative dispersion shows that the stride-interval time series is a random fractal. The differences in the fractal dimensions of surrogate time series from those of the original time series were determined to be statistically significant. This difference indicates the importance of the long-time correlations in walking.