Skip to main content
Log in

Characterizing the Dynamics of Postural Sway in Humans Using Smoothness and Regularity Measures

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

We investigate human postural sway velocity time series by computing two dynamical statistics quantifying the smoothness (the central tendency measure or CTM) and the regularity (the sample entropy or SampEn) of their underlying dynamics. The purpose of the study is to investigate the effect of aging and vision on the selected measures and to explore the nature of postural dynamics by performing surrogate data tests. A group of 14 young subjects was compared to a group of 11 older healthy subjects in two visual conditions: with eyes open (EO) and with eyes closed (EC). The results suggest that vision and age do not influence the two statistics of the velocity data in the same way. More specifically, the smoothness statistic is able to detect the aging effect. The regularity measure is sensitive to the visual feedback removal. In contrast with some findings in the literature, the results of the surrogate data tests indicate that the center of pressure velocity dynamics are stochastic and are not produced by a purely determinisitic behavior. Finally, we discuss some potential implications of our results in terms of postural control mechanisms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

Notes

  1. Not significant.

References

  1. American Academy of Neurology. Assessment: posturography. Report of the therapeutics and technology assessment subcommittee of the American Academy of Neurology. Neurology 43:1261–1264, 1993.

    Google Scholar 

  2. Basafa, E., Z. Heidari, H. Tamaddoni, A. Mirbagheri, O. Haddad, and M. Parnianpour. The effect of fatigue on recurrence parameters of postural sway. J. Biomech. 40:S362, 2007.

    Article  Google Scholar 

  3. Bosek, M. Model of two noise source dependent Ornstein–Uhlenbeck processes applied to postural sway. BioSystems 94:282–284, 2008.

    Article  PubMed  Google Scholar 

  4. Cao, L. Y., B. G. Kim, J. Kurths, and S. Kim. Detecting determinism in human posture control data. Int. J. Bifurcation Chaos 8:179–188, 1998.

    Article  Google Scholar 

  5. Chow, C. C., and J. J. Collins. Pinned polymer model of posture control. Phys. Rev. E 52:907–912, 1995.

    Article  CAS  Google Scholar 

  6. Chow, C.C., M. Lauk, and J.J. Collins. The dynamics of quasi-static posture control. Hum. Mov. Sci. 18:725–740, 1999.

    Article  Google Scholar 

  7. Collins, J. J., and C. J. DeLuca. Open-loop and closed-loop control of posture: a random-walk analysis of center-of-pressure trajectories. Exp. Brain Res. 95:308–318, 1993.

    Article  CAS  PubMed  Google Scholar 

  8. Collins, J. J., and C. J. DeLuca. Random walking during quiet standing. Phys. Rev. Lett. 73:764–767, 1994.

    Article  PubMed  Google Scholar 

  9. Collins, J. J., and C. J. DeLuca. The effects of visual input on open-loop and closed-loop postural control mechanisms. Exp. Brain Res. 103:151–163, 1995.

    Article  CAS  PubMed  Google Scholar 

  10. Collins, J. J., C. J. DeLuca, A. Burrows, and L. A. Lipsitz. Age-related changes in open-loop and closed-loop postural control mechanisms. Exp. Brain Res. 104:480–492, 1995.

    Article  CAS  PubMed  Google Scholar 

  11. Costa, M., A. L. Goldberger, and C. K. Peng. Multiscale entropy analysis of complex physiologic time series. Phys. Rev. Lett. 89:068102, 2002.

    Article  PubMed  Google Scholar 

  12. Costa, M., A. L. Goldberger, and C. K. Peng. Multiscale entropy analysis of biological signals. Phys. Rev. E 71:021906, 2005.

    Article  Google Scholar 

  13. Costa, M., A. A. Priplata, L. A. Lipsitz, Z. Wu, N. E. Huang, A. L. Goldberger, and C. K. Peng. Noise and poise: enhancement of postural complexity in the elderly with a stochastic resonance-based therapy. Europhys. Lett. 77:68008, 2007.

    Article  PubMed  Google Scholar 

  14. Deffeyes, J. E., R. T. Harbourne, S. L. DeJong, W. A. Stuberg, A. Kyvelidou, and N. Stergiou. Approximate entropy is robust to non-stationarity in analysis of infant sitting postural sway. In: The Conference of the American Society of Biomechanics, Stanford University, 22–25 August 2007.

  15. Devaney, R. L. An Introduction to Chaotic Dynamical Systems (2nd ed.). Westview Press, 2003.

  16. Donker, S., A. Ledebt, M. Roerdink, G. Savelsbergh, and P. Beek. Children with cerebral palsy exhibit greater and more regular postural sway than typically developing children. Exp. Brain Res. 184:363–370, 2008.

    Article  PubMed  Google Scholar 

  17. Donker S. F., M. Roerdink, A. J. Greven, and P. J. Beek. Regularity of center-of-pressure trajectories depends on the amount of attention invested in postural control. Exp. Brain Res. 181:1–11, 2007.

    Article  PubMed  Google Scholar 

  18. Duarte, M., and D. Sternad. Complexity of human postural control in young and older adults during prolonged standing. Exp. Brain Res. 191:265–276, 2008.

    Article  PubMed  Google Scholar 

  19. Duarte, M., and V. M. Zatsiorsky. Long-range correlations in human standing. Phys. Lett. A 283:124–128, 2001.

    Article  CAS  Google Scholar 

  20. Ehlers, C. L., J. Havstad, D. Prichard, and J. Theiler. Low doses of ethanol reduce evidence for nonlinear structure in brain activity. J. Neurosci. 18:7474–7486, 1998.

    CAS  PubMed  Google Scholar 

  21. Frank, T.D., A. Daffertshofer, and P.J. Beek. Multivariate Ornstein–Uhlenbeck processes with mean-field dependent coefficients: application to postural sway. Phys. Rev. E 63:11905, 2000.

    Article  Google Scholar 

  22. Fraser, A. M., and H. L. Swinney. Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33:1134–1140, 1986.

    Article  PubMed  Google Scholar 

  23. Goldberger, A. L., L. A. N. Amaral, L. Glass, J. M. Hausdorff, P. C. Ivanov, R. G. Mark, J. E. Mietus, G. B. Moody, C. K. Peng, and H. E. Stanley. PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals. Circulation 101:215–220, 2002. Available at http://circ.ahajournals.org/cgi/content/full/101/23/e215.

  24. Goldberger, A. L., C. K. Peng, and L. A. Lipsitz. What is physiologic complexity and how does it change with aging and disease? Neurobiol. Aging 23:23–26, 2002.

    Article  PubMed  Google Scholar 

  25. Govindan, R. B., J. D. Wilson, H. Eswaran, C. L. Lowery, and H. Preißl. Revisiting sample entropy analysis. Phys. A 376:158–164, 2007.

    Article  Google Scholar 

  26. Haddad, J. M., R. E. A. van Emmerik, J. Wheat, and J. Hamill. Chaos theory applied to posturagraphic data in parkinsonial patiens. J. Biomech. 40:S247, 2007.

    Article  Google Scholar 

  27. Inglin, B., and M. Wollacott. Age-related changes in anticipatory postural adjustments associated with arm movements. J. Gerontol. 43:M105–M113, 1988.

    CAS  PubMed  Google Scholar 

  28. Jeka, J., T. Kiemel, R. Creath, F. Horak, and R. Peterka. Controlling human upright posture: velocity information is more accurate than position or acceleration. J. Neurophysiol. 92:2368–2379, 2004.

    Article  PubMed  Google Scholar 

  29. Jeong, J., J. C. Gore, and B. S. Peterson. A method for determinism in short time series, and its application to stationary EEG. IEEE Trans. Biomed. Eng. 49:1374–1379, 2002.

    Article  PubMed  Google Scholar 

  30. Jeong, J., J. C. Gore, and B. S. Peterson. Detecting determinism in short time series, with an application to the analysis of a stationary EEG recording. Biol. Cybern. 86:335–342, 2002.

    Article  PubMed  Google Scholar 

  31. Kang, H. G., M. Costa, A. A. Priplata, O. V., Starobinets, A. L. Goldberger, C. K. Peng, D. K. Kiely, L. A. Cupples, and L.A. Lipsitz. Frailty and the degradation of complex balance dynamics during a dual-task protocol. J. Gerontol. A Biol. Sci. Med. Sci. 64A:1304–1311, 2009.

    Google Scholar 

  32. Kantz, H., and E. Olbrich. Scalar observations from a class of high-dimensional chaotic systems: limitations of the time delay embedding. Chaos 7:423–429, 1997.

    Article  PubMed  Google Scholar 

  33. Kantz, H., and T. Schreiber. Nonlinear Time Series Analysis (2nd ed.). Cambridge University Press, 2004.

  34. Kaplan, D. T., and L. Glass. Direct test for determinism in a time series. Phys. Rev. Lett. 68:427–430, 1992.

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  36. Ladislao, L., and S. Fioretti. Nonlinear analysis of posturographic data. Med. Biol. Eng. Comput. 45:679–688, 2007.

    Article  PubMed  Google Scholar 

  37. Ladislao, L., M. Guidi, G. Ghetti, and S. Fioretti. Chaos theory applied to posturagraphic data in parkinsonial patiens. J. Biomech. 39:S481, 2006.

    Article  Google Scholar 

  38. Lake, D. E., J. S. Richman, M. P. Griffin,and R. Moorman. Sample entropy analysis of neonatal heart rate variability. Am. J. Physiol. Regul. Integr. Comp. Physiol. 283:789–797, 2002.

    Google Scholar 

  39. Maurer, C., and R. J. Peterka. A new interpretation of spontaneous sway measures based on a simple model of human postural control. J. Neurophysiol. 93:189–200, 2005.

    Article  PubMed  Google Scholar 

  40. Myklebust, J. B., T. Prieto, and B. Myklebust. Evaluation of nonlinear dynamics in postural steadiness time series. Ann. Biomed. Eng. 23:711–719, 1995.

    Article  CAS  PubMed  Google Scholar 

  41. Newell, K. M. Degrees of freedom and the development of postural center of pressure profiles. In: Applications of Nonlinear Dynamics to Development Process Modeling, edited by K. M. Newell and P. C. M. Molenaar. New Jersey: Lawrence Erlbaum Associates, 1998, pp. 63–84.

  42. Ortega, G. J., C. Degli Esposti Boschi, and E. Louis. Detecting determinism in high-dimensional chaotic systems. Phys. Rev. E 65:16208, 2001.

    Article  Google Scholar 

  43. Ortega, G. J., and E. Louis. Smoothness implies determinism in time series: a measure based approach. Phys. Rev. Lett. 81:4345–4348, 1998.

    Article  CAS  Google Scholar 

  44. Packard, N. H., J. P. Crutchfield, J. D. Farmer, and R. S. Shaw. Geometry of a time series. Phys. Rev. Lett. 45:712–716, 1980.

    Article  Google Scholar 

  45. Peterka, R. J. Postural control model interpretation of stabilogram diffusion analysis. Biol. Cybern. 82:335–343, 2000.

    Article  CAS  PubMed  Google Scholar 

  46. Pincus, S. M. Approximate entropy as a measure of system complexity. Proc. Natl. Acade. Sci. USA 88:2297–2301, 1991.

    Article  CAS  Google Scholar 

  47. Prichard, D. The correlation dimension of differenced data. Phys. Lett. A 191:245–250, 1994.

    Article  Google Scholar 

  48. Prieto, T. E., J. B. Myklebust, R. G. Hoffmann, E. G. Lovett, and B. M. Myklebust. Measures of postural steadiness: differences between healthy young and elderly adults. IEEE Trans. Biomed. Eng. 43:956–966, 1996.

    Article  CAS  PubMed  Google Scholar 

  49. Pyykko, I., P. Jantti, and H. AAlto. Postural control in elderly subjects. Age Ageing 19:215–221, 1990.

    Article  CAS  PubMed  Google Scholar 

  50. Ramdani, S., F. Bouchara, and J.-F. Casties. Detecting determinism in short time series using a quantified averaged false nearest neighbors approach. Phys. Rev. E 76:36204, 2007.

    Article  Google Scholar 

  51. Ramdani, S., F. Bouchara, and J. Lagarde. Influence of noise on the sample entropy algorithm. Chaos 19:013123, 2009.

    Article  PubMed  Google Scholar 

  52. Ramdani, S., B. Seigle, J. Lagarde, F. Bouchara, and P. L. Bernard. On the use of sample entropy to analyze human postural sway data. Med. Eng. Phys. 31:1023–1031, 2009.

    Article  PubMed  Google Scholar 

  53. Ramdani, S., B. Seigle, J. Lagarde, F. Bouchara, and P. L. Bernard. Exploring the dynamics of postural sway in humans using recurrence quantification analysis. In: The 11th Experimental Chaos and Complexity Conference, Lille, France, 1–4 June 2010.

  54. Richman, J. S., and J. R. Moorman. Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol. 278:2039–2049, 2000.

    Google Scholar 

  55. Riley, M. A., R. Balasubramaniam, and M. T. Turvey. Recurrence quantification analysis of postural fluctuations. Gait Posture, 9:65–78, 1999.

    Article  CAS  PubMed  Google Scholar 

  56. Roerdink, M., M. De Haart, A. Daffertshofer, S. F. Donker, A. C. Geurts, and P. J. Beek. Dynamical structure of center-of-pressure trajectories in patients recovering from stroke. Exp. Brain Res. 174:256–269, 2006.

    Article  CAS  PubMed  Google Scholar 

  57. Sabatini, A. M. Analysis of postural sway using entropy measures of signal complexity. Med. Biol. Eng. Comput. 38:617–624, 2000.

    Article  CAS  PubMed  Google Scholar 

  58. Schmit, J. M., M. A. Riley, A. Dalvi, A. Sahay, P. K. Shear, K. D. Shockley, and R. Y. Pun. Deterministic center of pressure patterns characterize postural instability in Parkinson’s disease. Exp. Brain Res. 168:357–367, 2006.

    Article  PubMed  Google Scholar 

  59. Schreiber, T., and A. Schmitz. Improved surrogate data for nonlinearity tests. Phys. Rev. Lett. 77:635–638, 1996.

    Article  CAS  PubMed  Google Scholar 

  60. Schreiber, T., and A. Schmitz. Surrogate time series. Physica D 142:346–382, 2000.

    Article  Google Scholar 

  61. Seigle, B., S. Ramdani, and P. L. Bernard. Dynamical structure of center of pressure fluctuations in elderly people. Gait Posture 30:223–226, 2009.

    Article  PubMed  Google Scholar 

  62. Skinner, H. B., R. L. Barrack, and S. D. Cook. Age-related decline in proprioception. Clin. Orthop. 184:208–211, 1984.

    PubMed  Google Scholar 

  63. Takens, F. Detecting strange attractors in turbulence. In: Dynamical Systems and Turbulence. Lectures Notes in Mathematics, edited by D. A. Rand and L. S. Young. Berlin: Springer, 1981, p. 888.

  64. Theiler, J., and S. Eubank. Don’t bleach chaotic data. Chaos 3:771–782, 1993.

    Article  PubMed  Google Scholar 

  65. Theiler, J., 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.

    Article  Google Scholar 

  66. Vaillancourt, D. E., and K. M. Newell. Changing complexity in human behavior and physiology through aging and disease. Neurobiol. Aging 23:1–11, 2002.

    Article  PubMed  Google Scholar 

  67. Yamada, N. Chaotic swaying of the upright posture. Hum. Mov. Sci. 14:711–726, 1995.

    Article  Google Scholar 

  68. Yousefpoor, P., M. S. Esfahani, and H. Nojumi. Looking for systematic approach to select chaos tests. Appl. Math. Comput. 198:73–91, 2008.

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by a grant from the french Ministère de l’Education Nationale, de l’Enseignement Supérieur et de la Recherche. The authors would like to thank the anonymous reviewers for their useful comments and suggestions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sofiane Ramdani.

Additional information

Associate Editor Thurmon E. Lockhart oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ramdani, S., Seigle, B., Varoqui, D. et al. Characterizing the Dynamics of Postural Sway in Humans Using Smoothness and Regularity Measures. Ann Biomed Eng 39, 161–171 (2011). https://doi.org/10.1007/s10439-010-0137-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-010-0137-9

Keywords

Navigation