The influence of gait speed on local dynamic stability of walking

Abstract

The focus of this study was to examine the role of walking velocity in stability during normal gait. Local dynamic stability was quantified through the use of maximum finite-time Lyapunov exponents, lambda(Max). These quantify the rate of attenuation of kinematic variability of joint angle data recorded as subjects walked on a motorized treadmill at 20%, 40%, 60%, and 80% of the Froude velocity. A monotonic trend between lambda(Max) and walking velocity was observed with smaller lambda(Max) at slower walking velocities. Smaller lambda(Max) indicates more stable walking dynamics. This trend was evident whether stride duration variability remained or was removed by time normalizing the data. This suggests that slower walking velocities lead to increases in stability. These results may reveal more detailed information on the behavior of the neuro-controller than variability-based analyses alone.

Fig. 1

(A) Reconstructed state-space kinematics of knee angle with three embedded dimensions. Fifteen contiguous strides are illustrated. (B) Divergence of nearest neighbors with temporal variability permitted.

Fig. 2

Plot of x(t) = sin(2πt) + cos(πt) with embedding dimension n = 3 (A) and n = 2 (B). Note the false-nearest-neighbor illustrated by the intersection at [−0.25, 0.25] when n =2.

Fig. 3

Average logarithmic divergence vs. time. The best fit linear slope of the logarithmic relation from 0 to 1 stride represents λ^Max. In this example the stride duration was 0.74 s.

Fig. 4

Average λ^Max increased with walking velocity. This trend was observed when data were re-sampled to 3000 samples per 30 strides (A) and similarly when temporal variability was removed by re-sampling the data to 100 samples per stride (B).