• Sjoerd M Bruijn, Jaap H van Dieën, Onno G Meijer, and Peter J Beek.
• Research Institute MOVE, Faculty of Human Movement Sciences, VU University Amsterdam, Van der Boechorststraat 9, NL-1081 BT Amsterdam, The Netherlands.
• J Biomech. 2009 Jul 22; 42 (10): 1506-1512.

AbstractSeveral efforts have been made to study gait stability using measures derived from nonlinear time-series analysis. The maximum finite time Lyapunov exponent (lambda(max)) quantifies how a system responds to an infinitesimally small perturbation. Recent studies suggested that slow walking leads to lower lambda(max) values, and thus is more stable than fast walking, but these studies suffer from methodological limitations. We studied the effects of walking speed on the amount of kinematic variability and stability in human walking. Trunk motions of 15 healthy volunteers were recorded in 3D during 2 min of treadmill walking at different speeds. From those time series, maximum Lyapunov exponents, indicating short-term and long-term divergence (lambda(S-stride) and lambda(L-stride)), and mean standard deviation (MeanSD) were calculated. lambda(S-stride) showed a linear decrease with increasing speed for forward-backward (AP) movements and quadratic effects (inverted U-shaped) for medio-lateral (ML) and up-down (VT) movements. lambda(L-stride) showed a quadratic effect (inverted U-shaped) of walking speed for AP movements, a linear decrease for ML movements, and a linear increase for VT movements. Moreover, positive correlations between lambda(S) and MeanSD were found for all directions, while lambda(L-stride) and MeanSD were correlated negatively in the AP direction. The different effects of walking speed on lambda(S-stride) and lambda(L-stride) for the different planes suggest that slow walking is not necessarily more stable than fast walking. The absence of a consistent pattern of correlations between lambda(L-stride) and MeanSD over the three directions suggests that variability and stability reflect, at least to a degree, different properties of the dynamics of walking.

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