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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Herzog,  W., Zatsiorsky,  V., Prilutsky,  B. I., and Leonard,  T. R., 1994, “Variations in Force–Time Histories of Cat Gastrocnemius, Soleus, and Plantaris Muscles for Consecutive Walking Steps,” J. Exp. Biol., 191, pp. 19–36.
Hausdorff,  J. M., Peng,  C. K., Ladin,  Z., Wei,  J. Y., and Goldberger,  A. L., 1995, “Is Walking a Random Walk? Evidence for Long-Range Correlations in Stride Interval of Human Gait,” J. Appl. Physiol., 78, pp. 349–358.
Dingwell,  J. B., and Cusumano,  J. P., 2000, “Nonlinear Time Series Analysis of Normal and Pathological Human Walking,” Chaos, 10, pp. 848–863.
Garcia,  M., Chatterjee,  A., Ruina,  A., and Coleman,  M., 1998, “The Simplest Walking Model: Stability, Complexity, and Scaling,” ASME J. Biomech. Eng., 120, pp. 281–288.
Goswami,  A., Thuilot,  B., and Espiau,  B., 1998, “A Study of the Passive Gait of a Compass-Like Biped Robot: Symmetry and Chaos,” Int. J. Robot. Res., 17, pp. 1282–1301.
Winter,  D. A., 1989, “Biomechanics of Normal and Pathological Gait: Implications for Understanding Human Locomotion Control,” J. Motor Behavior, 21, pp. 337–355.
Yack,  H. J., and Berger,  R. C., 1993, “Dynamic Stability in the Elderly: Identifying a Possible Measure,” J. Gerontol., 48, pp. M225–M230.
Holt,  K. G., Jeng,  S. F., Ratcliffe,  R., and Hamill,  J., 1995, “Energetic Cost and Stability During Human Walking at the Preferred Stride Frequency,” J. Motor Behavior, 27, pp. 164–178.
Maki,  B. E., 1997, “Gait Changes in Older Adults: Predictors of Falls or Indicators of Fear?” J. Am. Geriatr. Soc., 45, pp. 313–320.
Hausdorff,  J. M., Cudkowicz,  M. E., Firtion,  R., Wei,  J. Y., and Goldberger,  A. L., 1998, “Gait Variability and Basal Ganglia Disorders: Stride-to-Stride Variations of Gait Cycle Timing in Parkinson’s Disease and Huntington’s Disease,” Movement Disord., 13, pp. 428–437.
Hurmuzlu,  Y., and Basdogan,  C., 1994, “On the Measurement of Dynamic Stability of Human Locomotion,” ASME J. Biomech. Eng., 116, pp. 30–36.
Hurmuzlu,  Y., Basdogan,  C., and Stoianovici,  D., 1996, “Kinematics and Dynamic Stability of the Locomotion of Post-Polio Patients,” ASME J. Biomech. Eng., 118, pp. 405–411.
Pearce,  M. E., Cunningham,  D. A., Donner,  A. P., Rechnitzer,  P. A., Fullerton,  G. M., and Howard,  J. H., 1983, “Energy Cost of Treadmill and Floor Walking at Self-Selected Paces,” Eur. J. Phys., 52, pp. 115–119.
Arsenault,  A. B., 1986, “Treadmill Versus Walkway Locomotion in Humans: An EMG Study,” Ergonomics, 29, pp. 665–676.
Wank,  V., Frick,  U., and Schmidtbleicher,  D., 1998, “Kinematics and Electromyography of Lower Limb Muscles in Overground and Treadmill Running,” Int. J. Sports Med., 19, pp. 455–461.
White,  S. C., Yack,  H. J., Tucker,  C. A., and Lin,  H. Y., 1998, “Comparison of Vertical Ground Reaction Forces During Overground and Treadmill Walking,” Med. Sci. Sports Exercise, 30, pp. 1537–1542.
van Ingen Schenau,  G. J., 1980, “Some Fundamental Aspects of the Biomechanics of Overground Versus Treadmill Locomotion,” Med. Sci. Sports Exercise, 12, pp. 257–261.
Cavanagh,  P. R., and Kram,  R., 1989, “Stride Length in Distance Running: Velocity, Body Dimensions, and Added Mass Effects,” Med. Sci. Sports Exercise, 21, pp. 467–479.
Savelberg,  H. H. C. M., Vortenbosch,  M. A. T. M., Kamman,  E. H., van de Weijer,  J. G. W., and Schambardt,  H. C., 1998, “Intra-Stride Belt Speed Variation Affects Treadmill Locomotion,” Gait & Posture, 7, pp. 26–34.
Nelson,  R. C., Dillman,  C. J., Lagasse,  P., and Bickett,  P., 1972, “Biomechanics of Overground Versus Treadmill Running,” Med. Sci. Sports, 4, pp. 233–240.
Dingwell,  J. B., Ulbrecht,  J. S., Boch,  J., Becker,  M. B., O’Gorman,  J., and Cavanagh,  P. R., 1999, “Neuropathic Gait Shows Only Trends Toward Increased Variability in Sagittal Plane Kinematics During Treadmill Locomotion,” Gait & Posture, 10, pp. 21–29.
Takens, F., 1981, “Detecting Strange Attractors in Turbulence,” Dynamical Systems and Turbulence, D. Rand and L. S. Young, eds., Springer-Verlag, Berlin, Vol. 898, pp. 366–381.
Sauer,  T., Yorke,  J. A., and Casdagli,  M., 1991, “Embedology,” J. Stat. Phys., 65, pp. 579–616.
Fraser, A. M., 1986, “Using Mutual Information to Estimate Metric Entropy,” Dimensions and Entropies in Chaotic Systems, G. Mayer-Kress, ed., Springer-Verlag, Berlin, pp. 82–91.
Kennel,  M. B., Brown,  R., and Abarbanel,  H. D. I., 1992, “Determining Minimum Embedding Dimension Using a Geometrical Construction,” Phys. Rev. A, 45, pp. 3403–3411.
Rosenstein,  M. T., Collins,  J. J., and DeLuca,  C. J., 1993, “A Practical Method for Calculating Largest Lyapunov Exponents From Small Data Sets,” Physica D, 65, pp. 117–134.
Kantzi, H., and Schreiber, S., 1997, Nonlinear Time Series Analysis, Cambridge University Press, Cambridge, UK.
Dingwell, J. B., and Cavanagh, P. R., 2000, “Increased Variability of Continuous Overground Walking in Neuropathic Patients Is Only Indirectly Related to Sensory Loss,” Gait & Posture, in press.
Dingwell,  J. B., Cusumano,  J. P., Sternad,  D., and Cavanagh,  P. R., 2000, “Slower Speeds in Neuropathic Patients Lead to Improved Local Dynamic Stability of Continuous Overground Walking,” J. Biomech., 33, pp. 1269–1277.


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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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