Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter December 7, 2006

State-space analysis of joint angle kinematics in normal treadmill walking

  • Matthias Schablowski-Trautmann and Hans Jürgen Gerner

Abstract

By restricting analysis to single averaged strides considered to be characteristic for the individual under investigation, current methods in gait analysis do not exploit the full dynamics of continuous locomotion. Therefore, a novel approach is presented that is based on long-term measurements of kinematic data during treadmill walking. The method consists of reconstructing the system attractor in the embedding space and then analyzing its geometric structure. Estimating the dimension of movement trajectories correlates well with the notion of controlling multiple degrees of freedom during performance of complex movement tasks such as walking. The influence of walking speed on the complexity of physiologic walking was investigated in 10 healthy subjects walking on a treadmill at seven fixed speeds. The results suggest that human walking becomes more complex at slower speeds. This may be associated with results from EMG studies demonstrating more irregular EMG patterns at very slow walking speeds. This study emphasizes that tools from non-linear dynamics are well suited for providing more insight into motor control in humans.


Corresponding author: Dr.-Ing. Matthias Schablowski-Trautmann, Stiftung Orthopädische Universitätsklinik, Schlierbacher Landstraße 200a, 69118 Heidelberg, Germany

References

1 Abarbanel HDI, Kennel, MB. Local false neighbors and dynamical dimensions from observed chaotic data. Phys Rev E1993; 47: 3057–3068.10.1103/PhysRevE.47.3057Search in Google Scholar

2 Diedrich FJ, Warren WH. Why change gaits? Dynamics of the walk-run transition. J Exp Psychol Hum Percept Perform1995; 21: 183–202.10.1037/0096-1523.21.1.183Search in Google Scholar

3 Dingwell JB, Cusumano JP. Nonlinear time series analysis of normal and pathological human walking. Chaos2000; 10: 848–863.10.1063/1.1324008Search in Google Scholar

4 Dingwell JB, Cusumano JP, Sternad D, Cavanagh PR. Slower speeds in patients with diabetic neuropathy lead to improved local dynamic stability of continuous overground walking. J Biomech2000; 33: 1269–1277.10.1016/S0021-9290(00)00092-0Search in Google Scholar

5 Fraser AM, Swinney HL. Independent coordinates for strange attractors from mutual information. Phys Rev A1986; 33: 1134–1140.10.1103/PhysRevA.33.1134Search in Google Scholar

6 Grassberger P, Procaccia I. Characterization of strange attractors. Phys Rev Lett1983; 50: 346–349.10.1103/PhysRevLett.50.346Search in Google Scholar

7 Harris GF, Smith PA. Human motion analysis – Current applications and future directions. Piscataway, NJ: IEEE Press 1996.Search in Google Scholar

8 Hausdorff JM. Gait variability: Methods, modeling and meaning. J Neural Eng Rehab2005; 2: 19.10.1186/1743-0003-2-19Search in Google Scholar

9 Hausdorff JM, Ashkenazy Y, Peng CK, Ivanov PC, Stanley HE, Goldberger AL. When human walking becomes random walking: Fractal analysis and modeling of gait rhythm fluctuations. Physica A2001; 302: 138–147.10.1016/S0378-4371(01)00460-5Search in Google Scholar

10 Hegger R, Kantz H, Schreiber T. Practical implementation of nonlinear time series methods: The TISEAN package. Chaos1999; 9: 413–435.10.1063/1.166424Search in Google Scholar PubMed

11 Holt KG, Hamill J, Andres RO. Predicting the minimal energy costs of human walking. Med Sci Sports Exerc1991; 23: 491–498.10.1249/00005768-199104000-00016Search in Google Scholar

12 Kadaba MP, Ramakrishnan HK, Wootten ME. Measurement of lower extremity kinematics during level walking. J Orthopaed Res1990; 8: 383–392.10.1002/jor.1100080310Search in Google Scholar

13 Kantz H, Schreiber T. Dimension estimates and physiological data. Chaos1995; 5: 143–154.10.1063/1.166096Search in Google Scholar

14 Kantz H, Schreiber T. Nonlinear time series analysis. Cambridge, UK: Cambridge University Press 1997.Search in Google Scholar

15 Kennel MB, Brown R, Abarbanel HDI. Determining embedding dimension for phase-space reconstruction using a geometrical approach. Phys Rev A1992; 45: 3404–3411.10.1103/PhysRevA.45.3403Search in Google Scholar

16 Li L. Stability landscapes of walking and running near gait transition speed. J Appl Biomech2000; 16: 428–436.10.1123/jab.16.4.428Search in Google Scholar

17 Motion Analysis: OrthoTrak 5.0. Gait analysis software reference manual. Santa Rosa, CA: Motion Analysis 2001. http://www.motionanalysis.com/.Search in Google Scholar

18 den Otter AR, Geurts AC, Mulder T, Duysens J. Speed related changes in muscle activity from normal to very slow walking speeds. Gait Posture2004; 19: 270–278.10.1016/S0966-6362(03)00071-7Search in Google Scholar

19 Pandy MG. Computer modeling and simulation of human movement. Annu Rev Biomed Eng2001; 3: 245–273.10.1146/annurev.bioeng.3.1.245Search in Google Scholar

20 Perc M. The dynamics of human gait. Eur J Phys2005; 26: 525–534.10.1088/0143-0807/26/3/017Search in Google Scholar

21 Stein RB. What muscle variable(s) does the nervous system control in limb movements? Behav Brain Sci1982; 5: 535–577.10.1017/S0140525X00013327Search in Google Scholar

22 Sternad D. Debates in dynamics: A dynamical systems perspective on action and perception. Hum Mov Sci2000; 19: 407–423.10.1016/S0167-9457(00)00024-5Search in Google Scholar

23 Takens F. Dynamical systems and turbulence. In: Rand DA, Young LS, editors. Dynamical systems and turbulence. Lecture notes in mathematics 898. New York: Springer-Verlag 1981: 366–381.10.1007/BFb0091924Search in Google Scholar

24 Theiler J. Spurious dimensions from correlation algorithms applied to limited time-series data. Phys Rev A1986; 34: 2427–2432.10.1103/PhysRevA.34.2427Search in Google Scholar

25 Tsonis AA, Elsner JB. The weather attractor over very short time scales. Nature1988; 333: 545–547.10.1038/333545a0Search in Google Scholar

Published Online: 2006-12-07
Published in Print: 2006-12-01

©2006 by Walter de Gruyter Berlin New York

Downloaded on 1.6.2024 from https://www.degruyter.com/document/doi/10.1515/BMT.2006.060/html
Scroll to top button