ALLOMETRIC CONTROL OF HUMAN GAIT

The stride interval in normal human gait is not strictly constant, but fluctuates from step to step in a random manner. These fluctuations h ave traditionally been assumed to be uncorrelated random errors with n ormal statistics. Herein we show that, contrary to this assumption the se 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 measured the stride interval of a group of five healthy men and women as they walked for 5 to 15 minutes at their usual pace. From these ti me series we calculate the relative dispersion, the ratio of the stand ard deviation to the mean, and show by systematically aggregating the data that the correlation in the stride-interval time series is an inv erse power law similar to the allometric relations in biology. The inv erse power-law relative dispersion shows that the stride-interval time series scales indicating long-time self-similar correlations extendin g for hundreds of steps, which is to say that the underlying process i s a random fractal. Furthermore, the power-law index is related to the fractal dimension of the time series. To determine if walking is a no nlinear process the stride-interval time series were randomly shuffled and the differences in the fractal dimensions of the surrogate time s eries from those of the original time series were determined to be sta tistically significant. This difference indicates the importance of th e long-time correlations in walking.