Long range correlations in the stride interval of running Kimberlee Jordan * , John H. Challis, Karl M. Newell Department of Kinesiology, The Pennsylvania State University, 266 Recreation Building, University Park, PA 16802, USA Received 13 May 2005; received in revised form 8 August 2005; accepted 14 August 2005 Abstract Fluctuations in the stride interval time series of unconstrained walking are not random but exhibit long range correlations that decay as a power law [Hausdorff JM, Peng CK, Ladin Z, Wei JY, Goldberger AL. Is walking a random walk? Evidence for long range correlations in stride interval of human gait. J Appl Physiol 1995;78:349–58]. Here, we examine whether the long range correlations are present in the stride interval time series of running. Recreational female runners ran 8 min trials at their preferred running speed as well as 10% and 20% slower and faster than their preferred speed. Both the average time and the amount of variability of the stride interval decreased with increasing speed. Detrended fluctuation analysis (DFA) showed that there were long range correlations present in the stride interval time series and these correlations followed a quasi U-shaped function, with the minimum at the preferred running speed. These results are consistent with the hypothesis that the preferred running speed, falling as it does between the upper and lower limits of possible running speeds, is the speed at which the most dynamical degrees of freedom are available for adaptive control of locomotion. # 2005 Elsevier B.V. All rights reserved. Keywords: Long range correlations; Running; Dynamical degrees of freedom; Variability 1. Introduction Locomotion is a complex act arising from the coordina- tion of multiple mechanisms and couplings of the neuromuscular system, including the motor cortex, cere- bellum, basal ganglia and feedback from vestibular, visual and peripheral receptors. It has been shown previously that the stride interval of walking is very stable and subject to only small variations about the mean stride interval (coefficient of variation, CV  4%), however, the distribu- tion of the stride interval is not normal and appears to be a fractal process [9,10,25,26]. The fluctuations present in the stride interval of human walking are persistent, self-similar and exhibit long range correlations, such that, any given stride interval is dependent on the stride interval at remote previous times, and that the dependence of stride intervals decays in a power law, fractal-like manner with time [9,10]. Processes with long range dependence are characterized by their autocorrelation function, coupling between points in the time series remains strong as the distance in time between points increases. In the case of human walking, long range correlations in the stride interval have been shown to extend over 1000 s of strides and are robust with respect to walking velocity [10]. Processes with long term correlations or 1/f -like processes have been observed in a number of different systems ranging from physics to sociology [3,14,21]. These types of processes are ubiquitous in nature yet they are not easily explained [2,24]. The key feature of such processes is an inverse power law scaling of fluctuation size with frequency, i.e., small fluctuations occur with high frequency whereas large fluctuations occur with low frequency. In addition to this, 1/f processes are self-similar, in that small irregularities at small time scales have the same statistical properties as large irregularities at large time scales. Thus, the inverse power law scaling of frequency with amplitude is a result of the self-similarity of the fluctuations. Of particular interest to movement scientists are the long range correlations found in the fluctuations of human movement time series such as the inter-tap interval in synchronization studies, e.g., [4] and the inter-stride interval in human walking, e.g., [9,10,25,26]. The finding that these fluctuations are not random but rather contain structure has www.elsevier.com/locate/gaitpost Gait & Posture 24 (2006) 120–125 * Corresponding author. Tel.: +1 814 863 4037; fax: +1 814 863 7360. E-mail address: kxj12@psu.edu (K. Jordan). 0966-6362/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2005.08.003