Sensitivity of the wolf's and rosenstein's algorithms to evaluate local dynamic stability from small gait data sets

Annals of Biomedical Engineering

Volumn 40, Issue 5, 2012, Pages 1122-1130

  Cignetti, Fabien ^a   Decker, Leslie M ^a   Stergiou, Nicholas ^a,b  

^a UNIVERSITY OF NEBRASKA AT OMAHA   (United States)

^b UNIVERSITY OF NEBRASKA MEDICAL CENTER   (United States)

Author keywords

Aging; Delay embedding; Largest Lyapunov exponent; Walking

Indexed keywords

AGE-RELATED; ATTRACTOR TRAJECTORIES; DATA SETS; DELAY EMBEDDING; EMBEDDING DIMENSIONS; LARGEST LYAPUNOV EXPONENT; LOCAL DYNAMIC STABILITY; LORENZ ATTRACTOR; OLDER ADULTS; SMALL DATA SET; WALKING;

AGING OF MATERIALS; LYAPUNOV METHODS; STABILITY; TIME SERIES;

ALGORITHMS;

ADULT; AGED; AGING; ALGORITHM; ARTICLE; BIOLOGICAL MODEL; CLINICAL TRIAL; FEMALE; GAIT; HUMAN; MALE; PHYSIOLOGY;

ADULT; AGED; AGING; ALGORITHMS; FEMALE; GAIT; HUMANS; MALE; MODELS, BIOLOGICAL;

EID: 84862007648     PISSN: 00906964     EISSN: 15739686     Source Type: Journal    
DOI: 10.1007/s10439-011-0474-3     Document Type: Article

References (33)

1. Abarbanel, H. D. I., R. Brown, and J. B. Kadtke. Prediction in chaotic nonlinear systems: methods for time series with broadband Fourier spectra. Phys. Rev. A 41:1782-1807, 1990.
2. Bruijn, S. M., W. R. Ten Kate, G. S. Faber, O. G. Meijer, P. J. Beek, and J. H. van Dieën. Estimating dynamic gait stability using data from non-aligned inertial sensors. Ann. Biomed. Eng. 38:2588-2593, 2010.
3. Bruijn, S. M., J. H. van Dieën, O. G. Meijer, and P. J. Beek. Is slow walking more stable? J. Biomech. 42:1506-1512, 2009.
4. Bruijn, S. M., J. H. van Dieën, O. G. Meijer, and P. J. Beek. Statistical precision and sensitivity of measures of dynamic gait stability. J. Neurosci. Methods 178:327-333, 2009.
5. Buzzi, U. H., N. Stergiou, M. J. Kurz, P. A. Hageman, and J. Heidel. Nonlinear dynamics indicates aging affects variability during gait. Clin. Biomech. 18:435-443, 2003. (Pubitemid 36583590)
6. Cappozzo, A., F. Catani, A. Leardini, M. G. Benedetti, and U. Della Croce. Position and orientation in space of bones during movement: experimental artefacts. Clin. Biomech. 11:90-100, 1996. (Pubitemid 26062665)
7. Casdagli, M. Nonlinear prediction of chaotic time series. Physica D 35:335-356, 1989.
8. Dingwell, J. B., and J. P. Cusumano. Nonlinear time series analysis of normal and pathological human walking. Chaos 10:848-863, 2000.
9. Dingwell, J. B., J. P. Cusumano, D. Sternad, and P. R. Cavanagh. Slower speeds in neuropathic patients lead to improved local dynamic stability of continuous overground walking. J. Biomech. 33:1269-1277, 2000. (Pubitemid 30427323)
10. Dingwell, J. B., J. P. Cusumano, D. Sternad, and P. R. Cavanagh. Local dynamic stability versus kinematic variability of continuous overground and treadmill walking. J. Biomech. Eng. 123:27-32, 2001. (Pubitemid 32202575)
11. Dingwell, J. B., and L. C. Marin. Kinematic variability and local dynamic stability of upper body motions when walking at different speeds. J. Biomech. 39:444-452, 2006. (Pubitemid 43028507)
12. Eckmann, J. P., S. O. Kamphorst, D. Ruelle, and S. Ciliberto. Lyapunov exponents from time series. Phys. Rev. A 34:4971-4979, 1986.
13. Eckmann, J. P., and D. Ruelle. Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57:617-656, 1985.
14. Eckmann, J. P., and D. Ruelle. Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems. Physica D 56:185-187, 1992.
15. Ellner, S., A. R. Gallant, D. McCaffrey, and D. Nychka. Convergence rates and data requirements for Jacobianbased estimates of Lyapunov exponents from data. Phys. Lett. A 153:357-363, 1991.
16. England, S. A., and K. P. Granata. The influence of gait speed on local dynamic stability of walking. Gait Posture 25:172-178, 2007. (Pubitemid 46043427)
17. Fraser, A. M., and H. L. Swinney. Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33:1134-1140, 1986.
18. Gates, D. H., and J. B. Dingwell. Comparison of different state space definitions for local dynamic stability analyses. J. Biomech. 42:1345-1349, 2009.
19. Jordan, K., J. H. Challis, and K. M. Newell. Walking speed influences on gait cycle variability. Gait Posture 26:128-134, 2007. (Pubitemid 46617938)
20. Kang, H. G., and J. B. Dingwell. Intra-session reliability of local dynamic stability of walking. Gait Posture 24:386-390, 2006. (Pubitemid 44486043)
21. Kang, H. G., and J. B. Dingwell. Effects of walking speed, strength and range of motion on gait stability in healthy older adults. J. Biomech. 41:2899-2905, 2008.
22. Kang, H. G., and J. B. Dingwell. Dynamic stability of superior vs. inferior segments during walking in young and older adults. Gait Posture 30:260-263, 2009.
23. Kantz, H., and S. Schreiber. Nonlinear Time Series Analysis (2nded.). Cambridge, UK:CambridgeUniversityPress, 2004.
24. Kennel, M. B., R. Brown, and H. D. I. Abarbanel. Determining embedding dimension for phase space-reconstruction using a geometrical construction. Phys. Rev. A 45:3403-3411, 1992.
25. Kyvelidou, A., M. J. Kurz, J. L. Ehlers, and N. Stergiou. Aging and partial body weight support affects gait variability. J. Neuroeng. Rehabil. 19:5-22, 2008.
26. Mees, A. I., and K. Judd. Dangers of geometric filtering. Physica D 68:427-436, 1993.
27. Nigg, B. M., G. K. Cole, and W. Nachbauer. Effects of arch height of the foot on angular motion of the lower extremities in running. J. Biomech. 26:909-916, 1993. (Pubitemid 23220206)
28. Rosenstein, M. T., J. J. Collins, and C. J. De Luca. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65:117-134, 1993.
29. Sano, M., and Y. Sawada. Measurement of the Lyapunov spectrum from a chaotic time series. Phys. Rev. Lett. 55:1082-1085, 1985.
30. Strogatz, S. H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. New York, NY: Addison-Wesley, 1994.
31. Takens, F. Detecting strange attractors in turbulence. In: Dynamical Systems and Turbulence, Warwick 1980, Vol. 898, edited by D. Rand, and L. S. Young. Berlin: Springer, 1981, pp. 366-381.
32. Vaughan, C., B. Davis, and J. O'Connor. Dynamics of Human Gait. Cape Town, South Africa: Kiboho Publishers, 1999.
33. Wolf, A., J. B. Swift, H. L. Swinney, and J. A. Vastano. Determining Lyapunov exponents from a time series. Physica D 16:285-317, 1985.