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Application of Nonlinear Dynamics to Human Knee Movement on Plane and Inclined Treadmill

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New Trends in Medical and Service Robots

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 39))

Abstract

The objective of this study is to quantify and investigate nonlinear motion of the human knee joint for a sample of 7 healthy subjects on plane treadmill and inclined treadmill with an angle of 10° and for both knees of a sample of 3 patients who suffer of osteoarthritis, only on the plane treadmill, using nonlinear dynamics stability analysis. The largest Lyapunov exponent (LLE) and correlation dimensions are calculated as chaotic measures from the experimental time series of the flexion-extension angle of human knee joint. Larger values of LLEs obtained for patients group suffering by osteoarthritis are associated with more divergence and increase of knee variability, while smaller values obtained for healthy subjects reflect increase of local stability, less divergence and variability, less sensitivity to perturbations and higher resistance to stride-to-stride variability. The use of nonlinear tools may provide additional insight on the nature of the step-to-step fluctuations present in human and robotic locomotion.

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References

  1. Hausdorff, J.M., Rios, D.A., Edelberg, H.K.: Gait variability and fall risk in community-living older adults: a 1-year prospective study. Arch. Phys. Med. Rehabil. 82(8), 1050–1056 (2001)

    Article  Google Scholar 

  2. Dingwell, J.B., Cusumano, J.P., Cavanagh, P.R., Sternad, D.: Local dynamic stability versus kinematic variability of continuous overground and treadmill walking. J. Biomech. Eng. 123(1), 27–32 (2001)

    Article  Google Scholar 

  3. Hausdorff, J.M.: Gait dynamics, fractals and falls: finding meaning in the stride to-stride fluctuations of human walking. Hum. Mov. Sci. 26(4), 555–589 (2007)

    Article  Google Scholar 

  4. Menz, H.B., Lord, S.R., et al.: Age-related differences in walking stability. Age Ageing 32(2), 137–142 (2003)

    Article  Google Scholar 

  5. Owings, T.M., Grabiner, M.D.: Variability of step kinematics in young and older adults. Gait Posture 20(1), 26–29 (2004)

    Article  Google Scholar 

  6. Plitea, N., Pisla, D., et.al: On the kinematics of a new parallel robot for brachytherapy. Proc. Rom. Acad. Ser. A: Math. Phys. Tech. Sci. Inf. Sci. 15(4), 354–361 (2014)

    Google Scholar 

  7. Tarnita, D., Marghitu, D.: Analysis of a hand arm system. Robot. Comput.-Integr. Manuf. 29(6), 493–501 (2013)

    Article  Google Scholar 

  8. Pisla, D., Szilaghyi, A., Vaida, C., Plitea, N.: Kinematics and workspace modeling of a new hybrid robot used in minimally invasive surgery. Robot. Comput.-Integr. Manuf. 29(2), 463–474 (2013)

    Article  Google Scholar 

  9. Ottaviano, E., et al.: An experimental evaluation of human walking. In: International Congress Design and Modelling of Mechanical Systems, Hammamet, 16–18 Mar 2009

    Google Scholar 

  10. Winter, D.A.: Biomechanical motor patterns in normal walking. J. Mot. Behav. 15(4), 302–330 (1983)

    Article  Google Scholar 

  11. Moe-Nilssen, R., Helbostad, J.L.: Interstride trunk acceleration variability but not step width variability can differentiate between fit and frail older adults. Gait Posture 21(2), 164–170 (2005)

    Article  Google Scholar 

  12. Dingwell, J.B., Marin, L.C.: Kinematic variability and local dynamic stability of upper body motions when walking at different speeds. J. Biomech. 39(3), 444–452 (2006)

    Article  Google Scholar 

  13. Jordan, K., Challis, J.H., et al.: Walking speed influences on gait cycle variability. Gait Posture (2006). doi:10.1016/j.gaitpost.2006.08.010

    Google Scholar 

  14. Oberg, T., Karsznia, A., et al.: Joint angle parameters in gait: reference data for normal subjects, 10–79 years of age. J. Rehab. Res. Develop. 31(3), 199–213 (1994)

    Google Scholar 

  15. Terrier, Ph, Dériaz, O.: Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking. J. NeuroEngineering Rehabil. 8, 1–13 (2011)

    Article  Google Scholar 

  16. Winter, D.A.: The Biomechanics and Motor Control of Human Gait: Normal, Elderly and Pathological, 2nd edn. Waterloo, Canada (1991)

    Google Scholar 

  17. Davis, R., Ounpuu, S., Tyburski, D., Gage, J.: A gait analysis data collection and reduction technique. Hum. Mov. Sci. 10, 575–587 (1991)

    Article  Google Scholar 

  18. Tarnita, D., Catana, M., Tarnita, D.N.: Nonlinear analysis of normal human gait for different activities with application to bipedal locomotion. Ro. J. Tech. Sci. Appl. Mech. 58(1–2), 177–192 (2013)

    Google Scholar 

  19. Kawamura, K., Tokuhiro, A., Takechi, H.: Gait analysis of slope walking: a study of step length, stride width, time factors and deviation in the centre of pressure. Acta Med. Okayama 45(3), 179–184 (1991)

    Google Scholar 

  20. Leroux, A., Fung, J., Barbeau, H.: Postural adaptation to walking on inclined surfaces: I. Normal strategies. Gait Posture 15(1), 64–74 (2002)

    Article  Google Scholar 

  21. Sun, J., Walters, M., Svensson, N., Lloyd, D.: The influence of surface slope on human gait characteristics: a study of urban pedestrians walking on an inclined surface. Ergonomics 39(4), 677–692 (1996)

    Article  Google Scholar 

  22. Kang, H.G.: Kinematic and motor variability and stability during gait: effects of age, walking speed and segment height, Doctoral Thesis, The University of Texas, Dec 2007

    Google Scholar 

  23. Dingwell, J.B., Cusumano, J.P.: Nonlinear time series analysis of normal and pathological human walking. Chaos 10, 848–863 (2000)

    Article  MATH  Google Scholar 

  24. Yang, C., Wu, Q.: On Stabilization of bipedal robots during disturbed standing using the concept of Lyapunov exponents. Robotica 24(5), 621–624 (2006)

    Article  Google Scholar 

  25. Han, J., Moussavi, Z.: Application of nonlinear dynamics to human postural control system. Eng. Med. Biol. Soc. Conf. Shanghai, 1–4 Sept 2005

    Google Scholar 

  26. Abarbanel, H.D.: Analysis of Observed Chaotic Data. Springer, New York, Inc. (1996)

    Google Scholar 

  27. Wolf, A., Swift, J., Swinney, H., Vastano, J.: Determining Lyapunov exponents from a time series. Physica 16D (1995)

    Google Scholar 

  28. Nehmzow, U., Walker, K.: Quantitative description of robot-environment interaction using chaos theory. In: Proceedings of ECMR 03, Warsaw (2003)

    Google Scholar 

  29. Small, M., Tse, C.: Applying the method of surrogate data to cyclic time series. Physica D 164, 187–201 (2002)

    Article  MATH  Google Scholar 

  30. Packard, N.H., Crutchfield, J.P., et al.: Geometry from a time series. Phys. Rev. Lett. 45, 712–716 (1980)

    Article  Google Scholar 

  31. Nayfeh, A.H.: Introduction to Perturbation Techniques. Wiley-Interscience, NY (1981)

    MATH  Google Scholar 

  32. Takens, F.: Detecting strange attractors in turbulence. In: Rand, D.A., Young, L.S. (eds.) Lecture Notes in Mathematics, vol. 898, pp. 366–381 (1981)

    Google Scholar 

  33. Kennel, M.B., Brown, R., Abarbanel, H.D.I.: Determining embedding dimension for phase space reconstruction using a geometrical construction. Phys. Rev. A 45, 3403–3411 (1992)

    Article  Google Scholar 

  34. Perc, M.: The dynamics of human gait. Eur. J. Phys. 26, 525–530 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  35. Boccaletti, S., Valladares, et al.: Reconstructing embedding spaces of coupled dynamical systems from multivariate data. Phys. Rev. E 65(035204(R)), 1–4 (2002)

    Google Scholar 

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Tarnita, D., Georgescu, M., Tarnita, D.N. (2016). Application of Nonlinear Dynamics to Human Knee Movement on Plane and Inclined Treadmill. In: Wenger, P., Chevallereau, C., Pisla, D., Bleuler, H., Rodić, A. (eds) New Trends in Medical and Service Robots. Mechanisms and Machine Science, vol 39. Springer, Cham. https://doi.org/10.1007/978-3-319-30674-2_5

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  • DOI: https://doi.org/10.1007/978-3-319-30674-2_5

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-30674-2

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