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.
Similar content being viewed by others
Notes
Not significant.
References
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.
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.
Bosek, M. Model of two noise source dependent Ornstein–Uhlenbeck processes applied to postural sway. BioSystems 94:282–284, 2008.
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.
Chow, C. C., and J. J. Collins. Pinned polymer model of posture control. Phys. Rev. E 52:907–912, 1995.
Chow, C.C., M. Lauk, and J.J. Collins. The dynamics of quasi-static posture control. Hum. Mov. Sci. 18:725–740, 1999.
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.
Collins, J. J., and C. J. DeLuca. Random walking during quiet standing. Phys. Rev. Lett. 73:764–767, 1994.
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.
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.
Costa, M., A. L. Goldberger, and C. K. Peng. Multiscale entropy analysis of complex physiologic time series. Phys. Rev. Lett. 89:068102, 2002.
Costa, M., A. L. Goldberger, and C. K. Peng. Multiscale entropy analysis of biological signals. Phys. Rev. E 71:021906, 2005.
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.
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.
Devaney, R. L. An Introduction to Chaotic Dynamical Systems (2nd ed.). Westview Press, 2003.
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.
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.
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.
Duarte, M., and V. M. Zatsiorsky. Long-range correlations in human standing. Phys. Lett. A 283:124–128, 2001.
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.
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.
Fraser, A. M., and H. L. Swinney. Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33:1134–1140, 1986.
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.
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.
Govindan, R. B., J. D. Wilson, H. Eswaran, C. L. Lowery, and H. Preißl. Revisiting sample entropy analysis. Phys. A 376:158–164, 2007.
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.
Inglin, B., and M. Wollacott. Age-related changes in anticipatory postural adjustments associated with arm movements. J. Gerontol. 43:M105–M113, 1988.
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.
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.
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.
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.
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.
Kantz, H., and T. Schreiber. Nonlinear Time Series Analysis (2nd ed.). Cambridge University Press, 2004.
Kaplan, D. T., and L. Glass. Direct test for determinism in a time series. Phys. Rev. Lett. 68:427–430, 1992.
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.
Ladislao, L., and S. Fioretti. Nonlinear analysis of posturographic data. Med. Biol. Eng. Comput. 45:679–688, 2007.
Ladislao, L., M. Guidi, G. Ghetti, and S. Fioretti. Chaos theory applied to posturagraphic data in parkinsonial patiens. J. Biomech. 39:S481, 2006.
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.
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.
Myklebust, J. B., T. Prieto, and B. Myklebust. Evaluation of nonlinear dynamics in postural steadiness time series. Ann. Biomed. Eng. 23:711–719, 1995.
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.
Ortega, G. J., C. Degli Esposti Boschi, and E. Louis. Detecting determinism in high-dimensional chaotic systems. Phys. Rev. E 65:16208, 2001.
Ortega, G. J., and E. Louis. Smoothness implies determinism in time series: a measure based approach. Phys. Rev. Lett. 81:4345–4348, 1998.
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.
Peterka, R. J. Postural control model interpretation of stabilogram diffusion analysis. Biol. Cybern. 82:335–343, 2000.
Pincus, S. M. Approximate entropy as a measure of system complexity. Proc. Natl. Acade. Sci. USA 88:2297–2301, 1991.
Prichard, D. The correlation dimension of differenced data. Phys. Lett. A 191:245–250, 1994.
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.
Pyykko, I., P. Jantti, and H. AAlto. Postural control in elderly subjects. Age Ageing 19:215–221, 1990.
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.
Ramdani, S., F. Bouchara, and J. Lagarde. Influence of noise on the sample entropy algorithm. Chaos 19:013123, 2009.
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.
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.
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.
Riley, M. A., R. Balasubramaniam, and M. T. Turvey. Recurrence quantification analysis of postural fluctuations. Gait Posture, 9:65–78, 1999.
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.
Sabatini, A. M. Analysis of postural sway using entropy measures of signal complexity. Med. Biol. Eng. Comput. 38:617–624, 2000.
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.
Schreiber, T., and A. Schmitz. Improved surrogate data for nonlinearity tests. Phys. Rev. Lett. 77:635–638, 1996.
Schreiber, T., and A. Schmitz. Surrogate time series. Physica D 142:346–382, 2000.
Seigle, B., S. Ramdani, and P. L. Bernard. Dynamical structure of center of pressure fluctuations in elderly people. Gait Posture 30:223–226, 2009.
Skinner, H. B., R. L. Barrack, and S. D. Cook. Age-related decline in proprioception. Clin. Orthop. 184:208–211, 1984.
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.
Theiler, J., and S. Eubank. Don’t bleach chaotic data. Chaos 3:771–782, 1993.
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.
Vaillancourt, D. E., and K. M. Newell. Changing complexity in human behavior and physiology through aging and disease. Neurobiol. Aging 23:1–11, 2002.
Yamada, N. Chaotic swaying of the upright posture. Hum. Mov. Sci. 14:711–726, 1995.
Yousefpoor, P., M. S. Esfahani, and H. Nojumi. Looking for systematic approach to select chaos tests. Appl. Math. Comput. 198:73–91, 2008.
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
Corresponding author
Additional information
Associate Editor Thurmon E. Lockhart oversaw the review of this article.
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10439-010-0137-9