Possible biomechanical origins of the long-range correlations in stride intervals of walking

Abstract

When humans walk, the time duration of each stride varies from one stride to the next. These temporal fluctuations exhibit long-range correlations. It has been suggested that these correlations stem from higher nervous system centers in the brain that control gait cycle timing. Existing proposed models of this phenomenon have focused on neurophysiological mechanisms that might give rise to these long-range correlations, and generally ignored potential alternative mechanical explanations. We hypothesized that a simple mechanical system could also generate similar long-range correlations in stride times. We modified a very simple passive dynamic model of bipedal walking to incorporate forward propulsion through an impulsive force applied to the trailing leg at each push-off. Push-off forces were varied from step to step by incorporating both "sensory" and "motor" noise terms that were regulated by a simple proportional feedback controller. We generated 400 simulations of walking, with different combinations of sensory noise, motor noise, and feedback gain. The stride time data from each simulation were analyzed using detrended fluctuation analysis to compute a scaling exponent, a. This exponent quantified how each stride interval was correlated with previous and subsequent stride intervals over different time scales. For different variations of the noise terms and feedback gain, we obtained short-range correlations (α < 0.5), uncorrelated time series (α = 0.5), long-range correlations (0.5 < α < 1.0), or Brownian motion (α > 1.0). Our results indicate that a simple biomechanical model of walking can generate long-range correlations and thus perhaps these correlations are not a complex result of higher level neuronal control, as has been previously suggested.

Assessing the stability of human locomotion: a review of current measures

“…To the best of our knowledge, there are no model studies relating long-range correlations to the probability of falling. However, one study [154] showed that long-range correlations are present in a fairly simple model, indicating that no complex central nervous system is needed for them to arise.…”

Gait dynamics in Parkinson’s disease: Common and distinct behavior among stride length, gait variability, and fractal-like scaling

“…Conversely, some have suggested that correlation properties are merely a by-product of the fact that feedback occurs on multiple levels or that simple biomechanical properties cause the observed scaling in gait. 144 These theories are not consistent with the observed results and the effects of various "stresses" on long-range correlation properties; the stresses do not directly change biomechanics, yet fractal scaling may be altered ͑e.g., Table II͒. 145 More specifically with regard to gait dynamics, several explanations have been put forth.…”

Towards a “gold-standard” approach to address the presence of long-range auto-correlation in physiological time series

“…The alternative hypothesis suggested by Gates et al (2007) is that long-range correlations are due to a biomechanical filtering of the neural commands by the motor apparatus. However, the diversity of rhythmic patterns in which long-range correlation have been reported (heartbeat, saccades, spontaneous neural firing patterns, etc.)…”

“…Similarly, unstable gait has been associated with a random pattern in consecutive strides, suggesting that the loss of long-range correlation could be a precocious marker of fall risk (Hausdorff, 2007). However, Gates et al (2007) suggested that the long-range correlation in gait could result from white noise fluctuations in the neural motor commands that are somehow filtered by the biomechanical plant, and this remains an open question. Thus, the development of reliable methods for quantifying and analyzing the correlation function in physiological time series is essential for both fundamental and clinical applications.…”