A methodology for examining the chaotic behavior of CoP signal during quiet standing based on empirical mode decomposition method

Document Type : Article


1 Research Center of Biomedical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

2 Department of Electrical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Iran


A key parameter for analyzing the human balance dynamics during standing is the center of pressure (CoP). But, so far no conclusive idea has been posed with respect to elicited dynamics of the CoP signal during quiet standing. In this paper, a heuristic algorithm has been proposed to prove the chaotic behavior of the CoP signal with high confidence. In the proposed algorithm, at first the deterministic and non-deterministic (may be stochastic or may be chaotic) components of CoP signal are extracted using the empirical mode decomposition (EMD) method. Then the nonlinear features of the extracted components such as fractal dimension, Lyapunov exponent, correlation dimension, and alpha parameter are computed. Then according to the quantitative value of the computed features, the chaotic component is selected among the extracted components. Finally, using the recurrence quantitative analysis (RQA), the selected chaotic component is reanalyzed to give assurance of correct selecting the chaotic component. In this manner, the kind of CoP dynamics can be determined with high confidence. The analyzed CoP signals were recorded through some experiments on 12 healthy subjects being between 20 to 70 years old. The results of this study show that CoP is a chaotic signal whit high confidence.


1. Popovi_c, M.R., Pappas, I.P.I., Nakazawa, K., et al. Stability criterion for controlling standing in ablebodied subjects", J. Biomech., 33(11), pp. 1359{1368 (2000). 1568 R. Hajipour et al./Scientia Iranica, Transactions D: Computer Science & ... 28 (2021) 1560{1569 2. Rhea, C.K., Kiefer, A.W., Haran, F.J., et al. A new measure of the CoP trajectory in postural sway: dynamics of heading change", Med. Eng. Phys., 36(11), pp. 1473{1479 (2014). 3. Caballero, C., Barbado, D., and Moreno, F.J. What COP and kinematic parameters better characterize postural control in standing balance tasks?", J. Mot. Behav., 47(6), pp. 550{562 (2015). 4. Tan, A.M., Fuss, F.K., Weizman, Y., and Azari, M.F. Centre of pressure detection and analysis with a highresolution and low-cost smart insole", Procedia Eng., 112, pp. 146{151 (2015). 5. Pachori, R.B., Hewson, D.J., Snoussi, H., et al. Analysis of center of pressure signals using empirical mode decomposition and Fourier-bessel expansion", 2008 IEEE Region 10 Conference', TENCON 2008, pp. 1{6 (2008). 6. Liu, K., Wang, H., Xiao, J., et al. Analysis of human standing balance by largest lyapunov exponent", Comput. Intell. Neurosci., 2015, p. 158478 (2015). 7. Collins, J.J. and Luca, C.J.D. Open-loop and closedloop control of posture: A random-walk analysis of center-of-pressure trajectories", Exp. Brain Res., 95(2), pp. 308{318 (1993). 8. Pascolo, P.B., Marini, A., Carniel, R., et al. Posture as a chaotic system and an application to the Parkinson's disease", Chaos Solitons Fractals, 24(5), pp. 1343{1346 (2005). 9. Ladislao, L. and Fioretti, S. Nonlinear analysis of posturographic data", Med. Biol. Eng. Comput., 45(7), pp. 679{688 (2007). 10. Ghomashchi, H., Esteki, A., Sprott, J.C., et al. Identi- _cation of dynamic patterns of body sway during quiet standing: Is IT a nonlinear process?", J Bifurc. Chaos, 20, pp. 1269{1278 (2010). 11. Blaszczyk, J.W. and Klonowski, W. Postural stability and fractal dynamics", Acta Neurobiol. Exp. (Warsz.), 61(2), pp. 105{112 (2001). 12. Doyle, T.L.A., Dugan, E.L., Humphries, B., et al. Discriminating between elderly and young using a fractal dimension analysis of centre of pressure", Int. J. Med. Sci., 1(1), pp. 11{20 (2004). 13. Kuznetsov, N., Bonnette, S., Gao, J., et al. Adaptive fractal analysis reveals limits to fractal scaling in center of pressure trajectories", Ann. Biomed. Eng., 41(8), pp. 1646{1660 (2013). 14. Gurses, S. and Celik, H. Correlation dimension estimates of human postural sway", Hum. Mov. Sci., 32(1), pp. 48{64 (2013). 15. Bosek, M., Grzegorzewski, B., and Kowalczyk, A. Two-dimensional Langevin approach to the human stabilogram", Hum Mov Sci, 22(6), pp. 649{660 (2004). 16. Bosek, M., Grzegorzewski, B., Kowalczyk, A., et al. Degradation of postural control system as a consequence of Parkinson's disease and ageing", Neurosci. Lett., 376(3), pp. 215{220 (2005). 17. Lemons, D.S. and Gythiel, A. Paul Langevin's 1908 paper 'On the Theory of Brownian Motion' ['Sur la th_eorie du mouvement Brownien,' C. R. Acad. Sci. (Paris) 146, 530{533 (1908)]", American Journal of Physics, 65(11), pp. 1079{1081 (1997). 18. Snoussi, H., Hewson, D., and Duchene, J. Nonlinear chaotic component extraction for postural stability analysis", Conf. Proc. Annu. Int. Conf. IEEE Eng. Med. Biol. Soc. IEEE Eng. Med. Biol. Soc. Annu. Conf., 2009, pp. 31{34 (2009). 19. Torre, F.C.-D. la, Gonz_alez-Trejo, J.I., Real-Ramirez, C.A., et al. Fractal dimension algorithms and their application to time series associated with natural phenomena", J. Phys.: Conf. Ser., 475, pp. 1{10 (2013). 20. Ding, M., Grebogi, C., Ott, E., Sauer, T., et al. Estimating correlation dimension from a chaotic time series: when does plateau onset occur?", Phys. Nonlinear Phenom., 69(3), pp. 404{424 (1993). 21. Wu, Z. and Huang, N.E. Ensemble empirical mode decomposition: a noise-assisted data analysis method", Adv. Adapt. Data Anal., 1(1), pp. 1{41 (2009). 22. Goli_nska, A.K. Detrended uctuation analysis (DFA) in biomedical signal processing: Selected examples", Stud. Log. Gramm. Rhetor., 29, pp. 107{115 (2012). 23. Minamisawa, T., Takakura, K., and Yamaguchi, T. Detrended uctuation analysis of temporal variation of the center of pressure (COP) during quiet standing in parkinsonian patients", J. Phys. Ther. Sci., 21(3), pp. 287{292 (2009). 24. Bardet, J.M. and Kammoun, I. Asymptotic properties of the detrended uctuation analysis of long-rangedependent processes", IEEE Trans. Inf. Theory, 54(5), pp. 2041{2052 (2008). 25. Wolf, A., Swift, J.B., Swinney, H.L., et al. Determining Lyapunov exponent from a time series", Physica., 16D, pp. 285{317 (1984). 26. Zbilut, J.P. and Webber, C.L. Recurrence quanti_- cation analysis: introduction and historical context", Int. J. Bifurc. Chaos, 17(10), pp. 3477{3481 (2007). 27. Iwaniec, J., Klepka, A., and Uhl, T. Recurrence plots and RQA analysis for damage detection in mechanical systems", in 'Proceedings of the 8th International Conference on Structural Dynamics' EURODYN, 2011, pp. 2476{2482 (2011). 28. Negahban, H., Sanjari, M.A., Karimi, M., et al. Complexity and variability of the center of pressure time series during quiet standing in patients with R. Hajipour et al./Scientia Iranica, Transactions D: Computer Science & ... 28 (2021) 1560{1569 1569 knee osteoarthritis", Clin. Biomech., 32, pp. 280{285 (2016). 29. Masia, M., Bastianoni, S., and Rustici, M. Recurrence quanti_cation analysis of spatio-temporal chaotic transient in a closed unstirred Belousov{Zhabotinsky reaction", Phys. Chem. Chem. Phys., 3(24), pp. 5516{ 5520 (2001). 30. Apthorp, D., Nagle, F., and Palmisano, S. Chaos in balance: Non-linear measures of postural control predict individual variations in visual illusions of Motion", PLOS ONE, 9(12), p. e113897 (2014). 31. Torres-Oviedo, G. and Ting, L.H. Muscle synergies characterizing human postural responses", J. Neurophysiol., 98(4), pp. 2144{2156 (2007). 32. Hosseini, S.A.A. Chaos and bifurcation in nonlinear inextensional rotating shafts", Sci. Iran., 26(2), pp. 856{868 (2019).