Is walking a random walk? Evidence for long-range correlations in stride interval of human gait

Abstract

Complex fluctuations of unknown origin appear in the normal gait pattern. These fluctuations might be described as being 1) uncorrelated white noise, 2) short-range correlations, or 3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series, we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that successfully accounts for the experimentally observed long-range correlations.