Walking speed influences on gait cycle variability

Abstract

The purpose of this study was to investigate the influence of walking speed on the amount and structure of the stride-to-stride fluctuations of the gait cycle. Based on previous findings for both walking [Hausdorff JM, Purdon PL, Peng CK, Ladin Z, Wei JY, Goldberger AL. Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations. J Appl Physiol 1996;80:1448–57], and running [Jordan K, Challis JH, Newell KM. Long range correlations in the stride interval of running. Gait Posture 2006;24:120–5] it was hypothesized that the fractal nature of human locomotion is a reflection of the attractor dynamics of human locomotion. Female participants walked for 12 min trials at 80%, 90%, 100%, 110% and 120% of their preferred walking speed. Eight gait cycle variables were investigated: stride interval and length, step interval and length, and from the vertical ground reaction force profile the impulse, first and second peak forces, and the trough force. Detrended fluctuation analysis (DFA) revealed the presence of long range correlations in all gait cycle variables investigated. Speed related U-shaped functions occurred in five of the eight variables, with the minima of these curves falling between 100% and 110% of the preferred walking speed. These findings are consistent with those previously shown in running studies and support the hypothesis that reduced strength of long range correlations at preferred locomotion speeds is reflective of enhanced stability and adaptability at these speeds.

Introduction

Walking is one of the most practiced of all motor skills, thus, it is not surprising that there is a very low level of variability (e.g. coefficient of variation ≈ 3%) associated with many biomechanical measures of this task, e.g. [1], [3]. This low level of variability is generally taken to mean that a very repeatable movement pattern has been attained [3]. Traditionally this variability has been regarded as a (white) noise process, where any given fluctuation in the time series is independent of all other fluctuations. However, in the last decade it has become apparent that in both walking [1], [4] and running [2], that stride-to-stride fluctuations (i.e. stride interval variability) contain structure in the form of long range correlations. Statistically, this means that the stride interval at any point in the time series is related to or dependent upon the stride interval at remote previous times.

This type of long range dependence is common in physiological time series and has been used as an indicator of overall adaptability of particular systems. For example, the fluctuations of a healthy heart show complex multi-scale long range order, whereas heart disease results in a change in the scaling behavior such that the fluctuations are limited to either very few time scales (excessive predictability) or uncorrelated randomness (e.g. [5]). Similarly, it has been shown that the scaling behavior of the stride interval of human walking becomes more random-like with aging and disease [6]. One finding of relevance here is that the strength of the long range correlations of healthy young adults in both gaits appears to be speed dependent [1], [2], but there has been no systematic investigation of the speed-long range correlation function in walking.

Studies investigating variability of the step interval and length have revealed U-shaped patterns of change with speed for the coefficient of variation (CV) of both of these variables [7], [8]. It is also known that individuals exhibit a preference for a particular walking speed, which occurs at or close to the speed at which energy consumption (per unit distance) is minimized [9]. Results from both walking [10], and leg swinging [11] studies provide evidence that the metabolic cost of walking is minimized by taking advantage of the passive mechanical properties of the leg, which in turn reduces the required force contribution of muscle. When walking at a constant speed, preferred and predicted periods of oscillation are not significantly different, and these periods coincide with minimum metabolic expenditure [12]. Collectively, these findings support the idea of a preferred walking speed (PWS) which is related to the mechanical properties of the leg.

Within the dynamical systems motor control framework, the preferred parameterization of movement patterns (in this case PWS) is associated with the concept of an attractor [13]. An attractor can be regarded as a pattern of behavior towards which a system is drawn [14]. Preferred behavior of a system is regarded within this framework as being close to an attractor and hence stable. As the behavior of the system moves away from the attractor (for example by increasing or decreasing walking speed) it is expected that there will be a loss of stability. It follows from the results of Holt and coworkers [10], [12] that the preferred walking speed, related as it is to the eigenfrequency of the limb, is the most stable in terms of the attractor dynamics of the system. Here we examine the proposition that the apparent reduction in long range correlations at the preferred walking speed may be related to the attractor dynamics of walking.

The purpose of the current study was to investigate the influence of walking speed on the amount and structure of the stride-to-stride fluctuations of the gait cycle. Based on previous findings for both walking [1] and running [2], it was hypothesized that long range correlations would be present in gait cycle variables other than stride interval, that the effects of speed would be similar across these variables, and, that the preferred walking speed would be that at which the long range correlations were the weakest.