Local Dynamic Stability Versus Kinematic Variability of Continuous Overground and Treadmill Walking

[+] Author and Article Information
J. B. Dingwell

Sensory Motor Performance Program, Rehabilitation Institute of Chicago, Chicago, IL 60611Center for Locomotion Studies, Penn State University, University Park, PA 16802

J. P. Cusumano

Department of Engineering Science and Mechanics, Penn State University, University Park, PA 16802

P. R. Cavanagh

Center for Locomotion Studies; Department of Kinesiology, Penn State University, University Park, PA 16802

D. Sternad

Department of Kinesiology, Penn State University, University Park, PA 16802

J Biomech Eng 123(1), 27-32 (Oct 16, 2000) (6 pages) doi:10.1115/1.1336798 History: Received September 30, 1999; Revised October 16, 2000
Copyright © 2001 by ASME
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Set-up of DataLogger data collection instrumentation
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Schematic representation of local stability analysis. (A) original time series data, x(t); (B) data embedded in a global 3-dimensional state space, X(t)=[x(t),x(t+T),x(t+2T)], with a local region outlined; (C) close-up view of the local region outlined in (B) showing divergence of neighboring trajectories resulting from local perturbations to the system; (D) average logarithmic divergence of neighboring trajectories, indicating the calculation of the short-term (λST*) and long-term (λLT*) finite-time Lyapunov exponents as the slopes of these curves in the ranges between 0 and 1 stride and between 4 and 10 strides, respectively.
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Average stride lengths (m), average stride times (s), and standard deviations of stride times (s) between OG and TM walking. Each line represents average results for one subject. ANOVA p-values for Condition effects are shown below each graph.
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Mean and maximum joint angle standard deviations for OG and TM walking. Each line represents average results for one subject. ANOVA p-values for Condition effects are shown for each comparison.
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Representative plots of the average logarithmic divergence, 〈ln[dj(i)]〉, as a function of normalized time for a typical subject for both OG and TM walking for all six sets of time series data. Within each subplot, five curves are drawn for each condition; one for each of the five two-minute intervals of data analyzed. Short-term (λST*) and long-term (λLT*) finite-time Lyapunov exponents were computed from each curve as described in Fig. 2. Similar results were obtained for all subjects.
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Short-term (λST*) and long-term (λLT*) finite-time Lyapunov exponents (〈ln[dj(i)]〉/Stride) for (A) upper body accelerations and (B) lower extremity kinematics. Each line represents average results for one subject. ANOVA p-values for differences between OG and TM walking are shown below each comparison.




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