Allometric Control of Human Gait

Abstract

The stride interval in normal human gait is not strictly constant, but fluctuates from step to step in a random manner. These fluctuations have traditionally been assumed to be uncorrelated random errors with normal statistics. Herein we show that, contrary to thes assumption 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 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 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 scales indicating long-time self-similar correlations extending for hundreds of steps, which is to say that the underlying process is a random fractal. Furthermore, the power-law index is related to the fractal dimension of the time series. To determine if walking is a nonlinear process the stride-interval time series were randomly shuffled and the differences in the fractal dimensions of the 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.