This article is part of the series Gait Variability, edited by Jeffrey M Hausdorff.

Research

Fractional Langevin model of gait variability

Bruce J West¹ and Miroslaw Latka²

¹  Mathematical and Informational Sciences Directorate US Army Research Office, P.O. Box 12211 Research Triangle Park, NC 27709, USA

²  Physics Department Wroclaw University of Technology Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland

author email corresponding author email

Journal of NeuroEngineering and Rehabilitation 2005, 2:24doi:10.1186/1743-0003-2-24

Published:	2 August 2005

Abstract

The stride interval in healthy human gait fluctuates from step to step in a random manner and scaling of the interstride interval time series motivated previous investigators to conclude that this time series is fractal. Early studies suggested that gait is a monofractal process, but more recent work indicates the time series is weakly multifractal. Herein we present additional evidence for the weakly multifractal nature of gait. We use the stride interval time series obtained from ten healthy adults walking at a normal relaxed pace for approximately fifteen minutes each as our data set. A fractional Langevin equation is constructed to model the underlying motor control system in which the order of the fractional derivative is itself a stochastic quantity. Using this model we find the fractal dimension for each of the ten data sets to be in agreement with earlier analyses. However, with the present model we are able to draw additional conclusions regarding the nature of the control system guiding walking. The analysis presented herein suggests that the observed scaling in interstride interval data may not be due to long-term memory alone, but may, in fact, be due partly to the statistics.