Nonlinear time series analysis of normal and pathological human walking

Jonathan B.  Dingwell; Joseph P.  Cusumano

doi:10.1063/1.1324008

ABSTRACT

Characterizing locomotor dynamics is essential for understanding the neuromuscular control of locomotion. In particular, quantifying dynamic stability during walking is important for assessing people who have a greater risk of falling. However, traditional biomechanical methods of defining stability have not quantified the resistance of the neuromuscular system to perturbations, suggesting that more precise definitions are required. For the present study, average maximum finite-time Lyapunov exponents were estimated to quantify the local dynamic stability of human walking kinematics. Local scaling exponents, defined as the local slopes of the correlation sum curves, were also calculated to quantify the local scaling structure of each embedded time series. Comparisons were made between overground and motorized treadmill walking in young healthy subjects and between diabetic neuropathic (NP) patients and healthy controls (CO) during overground walking. A modification of the method of surrogate data was developed to examine the stochastic nature of the fluctuations overlying the nominally periodic patterns in these data sets. Results demonstrated that having subjects walk on a motorized treadmill artificially stabilized their natural locomotor kinematics by small but statistically significant amounts. Furthermore, a paradox previously present in the biomechanical literature that resulted from mistakenly equating variability with dynamic stability was resolved. By slowing their self-selected walking speeds, NP patients adopted more locally stable gait patterns, even though they simultaneously exhibited greater kinematic variability than CO subjects. Additionally, the loss of peripheral sensation in NP patients was associated with statistically significant differences in the local scaling structure of their walking kinematics at those length scales where it was anticipated that sensory feedback would play the greatest role. Lastly, stride-to-stride fluctuations in the walking patterns of all three subject groups were clearly distinguishable from linearly autocorrelated Gaussian noise. As a collateral benefit of the methodological approach taken in this study, some of the first steps at characterizing the underlying structure of human locomotor dynamics have been taken. Implications for understanding the neuromuscular control of locomotion are discussed.

REFERENCES
Section:

1. M. E. Tinetti, J. Doucette, E. Claus, and R. Marottoli, “Risk factors for serious injury during falls by older persons in the community,” J. Am. Geriatr. Soc. 43(11), 1214–1221 (1995). Google ScholarCrossref
2. A. J. Blake, K. Morgan, M. J. Bendall, H. Dallosso, S. B. Ebrahim, T. H. Arie, P. H. Fentem, and E. J. Bassey, “Falls by elderly people at home: Prevalence and associated factors,” Age Ageing 17(6), 365–372 (1988). Google ScholarCrossref
3. D. A. Winter, “Biomechanics of normal and pathological gait: Implications for understanding human locomotion control,” J. Motor Behav. 21, 337–355 (1989). Google ScholarCrossref
4. J. Yackand R. C. Berger, “Dynamic stability in the elderly: Identifying a possible measure,” J. Gerontol.: Med. Sci. 48(5), M225–M230 (1993). Google ScholarCrossref
5. K. G. Holt, S. F. Jeng, R. Ratcliffe, and J. Hamill, “Energetic cost and stability during human walking at the preferred stride frequency,” J. Motor. Behav. 27(2), 164–178 (1995). Google ScholarCrossref
6. B. E. Maki, “Gait changes in older adults: Predictors of falls or indicators of fear?” J. Am. Geriatr. Soc. 45(3), 313–320 (1997). Google ScholarCrossref
7. J. S. Bayand H. Hemami, “Modeling of a neutral pattern generator with coupled nonlinear oscillators,” IEEE Trans. Biomed. Eng. BME-34(4), 297–306 (1987). Google ScholarCrossref
8. J. J. Collinsand I. N. Stewart, “Coupled nonlinear oscillators and the symmetries of animal gaits,” J. Nonlinear Sci. 3, 349–392 (1993). Google ScholarCrossref
9. J. J. Collinsand I. N. Stewart, “A group-theoretic approach to rings of coupled biological oscillators,” Biol. Cybern. 71, 95–103 (1994). Google ScholarCrossref
10. G. Taga, “A model of the neuro-musculo-skeletal system for human locomotion I: Emergence of basic gait,” Biol. Cybern. 73(2), 97–111 (1995). Google ScholarCrossref
11. G. Taga, “A model of the neuro-musculo-skeletal system for human locomotion II: Real-time adaptability under various constraints,” Biol. Cybern. 73(2), 97–111 (1995). Google ScholarCrossref
12. T. Zielinska, “Coupled oscillators utilized as gait rhythm generators of a two-legged walking machine,” Biol. Cybern. 74(3), 263–273 (1996). Google ScholarCrossref
13. M. Garcia, A. Chatterjee, A. Ruina, and M. Coleman, “The simplest walking model: Stability, complexity, and scaling,” J. Biomech. Eng. 120(2), 281–288 (1998). Google ScholarCrossref
14. A. Goswami, B. Thuilot, and B. Espiau, “A study of the passive gait of a compass-like biped robot: Symmetry and chaos,” Int. J. Robot. Res. 17(12), 1282–1301 (1998). Google ScholarCrossref
15. Y. Hurmuzluand C. Basdogan, “On the measurement of dynamic stability of human locomotion,” J. Biomech. Eng. 116(1), 30–36 (1994). Google ScholarCrossref
16. Y. Hurmuzlu, C. Basdogan, and D. Stoianovici, “Kinematics and dynamic stability of the locomotion of post-polio patients,” J. Biomech. Eng. 118(3), 405–411 (1996). Google ScholarCrossref
17. M. T. Rosenstein, J. J. Collins, and C. J. DeLuca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D 65, 117–134 (1993). Google ScholarCrossref
18. H. Kantz and S. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 1997). Google Scholar
19. R. C. Nelson, C. J. Dillman, P. Lagasse, and P. Bickett, “Biomechanics of overground versus treadmill running,” Med. Sci. Sports 4(4), 233–240 (1972). Google Scholar
20. G. M. Strathy, E. Y. S. Chao, and R. K. Laughman, “Changes in knee function associated with treadmill ambulation,” J. Biomech. 16(7), 517–522 (1983). Google ScholarCrossref
21. J. Pailhousand M. Bonnard, “Stead-state fluctuations of human walking,” Behav. Brain Res. 4, 181–190 (1992). Google ScholarCrossref
22. M. E. Pearce, D. A. Cunningham, A. P. Donner, P. A. Rechnitzer, G. M. Fullerton, and J. H. Howard, “Energy cost of treadmill and floor walking at self-selected paces,” Euro. J. Physiol. 52(1), 115–119 (1983). Google ScholarCrossref
23. J. Isacson, L. Gransberg, and E. Knutsson, “Three-dimensional electrogoniometrical gait recording,” J. Biomech. 19(8), 627–635 (1986). Google ScholarCrossref
24. A. B. Arsenault, “Treadmill versus walkway locomotion in human: An EMG study,” Ergonomics 29(5), 665–676 (1986). Google ScholarCrossref
25. J. B. Dingwell, J. S. Ulbrecht, J. Boch, M. B. Becker, J. O’Gorman, and P. R. Cavanagh, “Neuropathic gait shows only trends toward increased variability in sagittal plane kinematics during treadmill locomotion,” Gait Post. 10(1), 21–29 (1999). Google ScholarCrossref
26. J. B. Dingwell, J. P. Cusumano, D. Sternad, and P. R. Cavanagh, “Local dynamic stability versus kinematic variability of continuous overground and treadmill walking,” J. Biomech. Eng. (in revision). Google Scholar
27. D. A. Greene, A. A. F. Sime, J. W. Albers, and M. A. Pfeifer, “Diabetic Neuropathy,” in Diabetes Mellitus: Theory and Practice, 4th ed. (Elsevier Science, New York, 1990), pp. 710–755. Google Scholar
28. A. I. Vinik, M. T. Holland, J. M. LeBeau, F. J. Liuzzi, K. B. Stansberry, and L. B. Colen, “Diabetic neuropathies,” Diabetes Care 15(12), 1926–1975 (1992). Google ScholarCrossref
29. P. R. Cavanagh, J. A. Derr, J. S. Ulbrecht, R. E. Maser, and T. J. Orchard, “Problems with gait and posture in neuropathic patients with insulin-dependent diabetes mellitus,” Diabet Med. 9, 469–474 (1992). Google ScholarCrossref
30. J. K. Richardson, C. Ching, and E. A. Hurvitz, “The relationship between electromyographically documented peripheral neuropathy and falls,” J. Am. Geriatr. Soc. 40, 1008–1012 (1992). Google ScholarCrossref
31. J. K. Richardsonand E. A. Hurvitz, “Peripheral neuropathy: A true risk factor for fall,” J. Gerontol. A Biol. Sci. Med. Sci. 50(4), M211–M215 (1995). Google ScholarCrossref
32. M. J. Mueller, S. D. Minor, S. A. Sahrmann, J. A. Schaf, and M. J. Strube, “Differences in the gait characteristics of patients with diabetes and peripheral neuropathy compared with age-matched controls,” Phys. Ther. 74(4), 299–313 (1994). Google ScholarCrossref
33. R. Courtemanche, N. Teasdale, P. Boucher, M. Fleury, Y. Lajoie, and C. Bard, “Gait problems in diabetic neuropathic patients,” Arch. Phys. Med. Rehabil. 77(9), 849–855 (1996). Google ScholarCrossref
34. J. B. Dingwell and P. R. Cavanagh, “Increased variability of continuous overground walking in neuropathic patients is only indirectly related to sensory loss,” Gait Post. (in revision). Google Scholar
35. D. A. Winter, “Biomechanical motor patterns in normal walking,” J. Motor Behav. 15(4), 302–330 (1983). Google ScholarCrossref
36. T. Öberg, A. Karsznia, and K. Öberg, “Basic gait parameters: Reference data for normal subjects, 10–79 years of age,” J. Rehabil. Res. Dev. 30(2), 210–223 (1993). Google Scholar
37. L. M. Nashner, “Balance adjustments of humans perturbed while walking,” J. Neurophysiol. 44(4), 650–664 (1980). Google ScholarCrossref
38. S. C. Gandeviaand D. Burke, “Does the nervous system depend on kinesthetic information to control natural limb movements?” Behav. Brain Sci. 15, 614–632 (1992). Google Scholar
39. J. M. Hausdorff, C. K. Peng, Z. Ladin, J. Y. Wei, and A. L. Goldberger, “Is walking a random walk? Evidence for long-range correlations in stride interval of human gait,” J. Appl. Physiol. 78(1), 349–358 (1995). Google ScholarCrossref
40. J. M. Hausdorff, S. L. Mitchell, R. Firtion, C. K. Peng, M. E. Cudkowicz, J. Y. Wei, and A. L. Goldberger, “Altered fractal dynamics of gait: Reduced stride interval correlations with aging and Huntington’s disease,” J. Appl. Physiol. 82(1), 262–269 (1997). Google ScholarCrossref
41. B. J. Westand L. Griffin, “Allometric control, inverse powers laws and human gait,” Chaos, Solitons, Fractals 10(9), 1519–1527 (1999). Google ScholarCrossref
42. Y. Chen, M. Ding, and J. A. S. Kelso, “Long memory processes ${(1/f}^{α}$ type) in human coordination,” Phys. Rev. Lett. 79(22), 4501–4504 (1997). Google ScholarCrossref
43. D. T. Kaplan and L. Glass, Understanding Nonlinear Dynamics (Springer-Verlag, New York, 1995). Google Scholar
44. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer, “Testing for nonlinearity in time series: The method of surrogate data,” Physica D 58, 77–94 (1992). Google ScholarCrossref
45. F. Takens, “Detecting strange attractors in turbulence,” in Dynamical Systems and Turbulence, Warwick 1980 (Springer-Verlag, Berlin, 1981), pp. 366–381. Google Scholar
46. R. Mañé, “On the dimension of the compact invariant sets of certain non-linear maps,” in Dynamical Systems and Turbulence, Warwick 1980 (Springer-Verlag, Berlin, 1981), pp. 230–242. Google Scholar
47. T. Sauer, J. A. Yorke, and M. Casdagli, “Embedology,” J. Stat. Phys. 65(3/4), 579–616 (1991). Google ScholarCrossref
48. A. M. Fraserand H. L. Swinney, “Independent coordinates for strange attractors from mutual information,” Phys. Rev. A 33, 1134–1140 (1986). Google ScholarCrossref
49. M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining minimum embedding dimension using a geometrical construction,” Phys. Rev. A 45, 3403–3411 (1992). Google ScholarCrossref
50. J.-P. Eckmann, S. O. Kamphorst, and D. Ruelle, “Recurrence plots of dynamical systems,” Europhys. Lett. 4(9), 973–977 (1987). Google ScholarCrossref
51. A. Babloyantz, “Some remarks on nonlinear data analysis of physiological time series,” in Measures of Complexity and Chaos (Plenum, New York, 1989). Google Scholar
52. M. C. Casdagli, “Recurrence plots revisited,” Physica D 108(1), 12–44 (1997). Google ScholarCrossref
53. P. Grassbergerand I. Procaccia, “Measuring the strangeness of strange attractors,” Physica D 9, 189–208 (1983). Google ScholarCrossref
54. J. Theiler, “Estimating fractal dimensions,” J. Opt. Soc. Am. A 7(6), 1055–1073 (1990). Google ScholarCrossref
55. H. Kantzand T. Schreiber, “Dimension estimates and physiological data,” Chaos 5(1), 143–154 (1995). Google ScholarScitation
56. H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65, 1331–1392 (1993). Google ScholarCrossref
57. J. Timmer, S. Häussler, M. Lauk, and C.-H. Lücking, “Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?” Chaos 10(1), 278–288 (2000). Google ScholarScitation
58. F. L. Ramsey and D. W. Schafer, The Statistical Sleuth: A Course in Methods of Data Analysis (Duxbury, Wadsworth, Belmont, CA, 1997). Google Scholar
59. J. F. Hair, R. E. Anderson, R. L. Tatham, and W. C. Black, Multivariate Data Analysis, 5th ed. (Prentice Hall, Englewood Cliffs, NJ, 1998). Google Scholar
60. J. B. Dingwell, 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(10), 1269–1277 (2000). Google ScholarCrossref
61. E. N. Lorenz, “Deterministic non-periodic flows,” J. Atmos. Sci. 7, 130–141 (1963). Google ScholarCrossref
62. J. B. Dingwell, J. P. Cusumano, D. Sternad, and P. R. Cavanagh, “Using Lyapunov exponents to quantify dynamic stability during continuous overground locomotion,” in Proceedings of the Third North American Congress on Biomechanics (University of Waterloo, Waterloo, Ontario, Canada, 1998), pp. 125–126. Google Scholar
63. M. J. Pavol, T. M. Owings, K. T. Foley, and M. D. Grabiner, “The sex and age of older adults influence the outcome of induced trips,” J. Gerontol. A Biol. Sci. Med. Sci. 54(2), M103–M108 (1999). Google ScholarCrossref
64. M. J. Pavol, T. M. Owings, K. T. Foley, and M. D. Grabiner, “Gait characteristics as risk factors for falling from trips induced in older adults,” J. Gerontol. A Biol. Sci. Med. Sci. 54(11), M583–M590 (1999). Google ScholarCrossref
65. N. Bernstein, The Coordination and Regulation of Movements (Pergamon, New York, 1935). Google Scholar
66. R. J. Fulland D. E. Koditschek, “Templates and anchors: Neuromechanical hypothesis of legged locomotion,” J. Exp. Biol. 202(23), 3325–3332 (1999). Google Scholar
67. S. Ellnerand P. Turchin, “Chaos in a noisy world: New methods and evidence from time-series analysis,” Am. Nat. 145(3), 343–375 (1995). Google ScholarCrossref

Nonlinear time series analysis of normal and pathological human walking

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