Abstract
The authors describe an example of application of nonlinear time series analysis directed at identifying the presence of deterministic chaos in human motion data by means of the largest Lyapunov exponent (LLE). The research aimed at determination of the influence of gait speed on the LLE value with a view to verification of the belief that slower walking leads to increased stability characterized by smaller LLE value. Analyses were focused on the time series representing hip flexion/extension angle, knee flexion/extension angle and dorsiflexion/plantarflexion dimension of the ankle. Gait sequences were recorded in the Human Motion Laboratory (HML) of the Polish-Japanese Academy of Information Technology in Bytom by means of the Vicon system. Application of the AC5000M treadmill allowed recordings in three variants: at the preferred walking speed (PWS) of each subject, at 80% of the PWS and at 120% of the PWS. According to the recommendations from the literature the LLE value was estimated twice for every time series: as the short-term LLE\(_1\) for the first stride and as the long-term LLE\(_{4-10}\) over a fixed interval between the fourth and the tenth stride. In the latter case it was confirmed that the LLE value increases with walking speed for both limbs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Henry, B., Lovell, N., Camacho, F.: Nonlinear dynamics time series analysis. In: Akay, M.(ed.) Nonlinear Biomedical Signal Processing: Dynamic Analysis and Modeling, vol. 2, pp. 1–39. Wiley Online Library (2012) (published online)
Chen, C.-K., Lin, C.-L., Chiu, Y.-M.: Individual identification based on chaotic electrocardiogram signals. In: 6th IEEE Conference on Industrial Electronics and Applications, pp. 1765–1770 (2011)
Cohen, M.E.: Chaos. Wiley Encyclopedia of Biomedical Engineering (2006)
Osowski, S., Świderski, B., Cichocki, A., Rysz, A.: Epileptic seizure characterization by Lyapunov exponent of EEG signal. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 26(5), 1276–1287 (2007)
Mormann, F., Andrzejak, R.G., Elger, C.E., Lehnertz, K.: Seizure prediction: the long and winding road. Brain 130, 314–333 (2007)
Dingwell, J.B., Cusumano, J.P.: Nonlinear time series analysis of normal and pathological human walking. Chaos 10(4), 848–863 (2000)
Dingwell, J.B., Marin, L.C.: Kinematic variability and local dynamic stability of upper body motions when walking at different speeds. Journal of Biomechanics 39, 444–452 (2006)
Terrier, P., Deriaz, O.: Non-linear dynamics of human locomotion: effects of rhythmic auditory cueing on local dynamic stability. Frontiers in Physiology 4, 1–13 (2013)
England, S.A., Granata, K.P.: The influence of gait speed on local dynamic stability of walking. Gait & Posture 25, 172–178 (2007)
Look, N., Arellano, C.J., Grabowski, A.M., McDermott, W.J., Kram, R., Bradley, E.: Dynamic stability of running: The effects of speed and leg amputations on the maximal lyapunov exponent. Chaos 23, 043131 (2013)
Hurmuzlu, Y., Basdogan, C., Stoianovici, D.: Kinematics and Dynamic Stability of the Locomotion of Post-Polio Patients. Journal of Biomechanical Engineering 118(3), 405–411 (1996)
Dingwell, J.B., Kang, H.G.: Differences Between Local and Orbital Dynamic Stability During Human Walking. Journal of Biomechanical Engineering 129(4), 586–593 (2007)
Arif, M., Ohtaki, Y., Nagatomi, R., Inooka, H.: Estimation of the Effect of Cadence on Gait Stability in Young and Elderly People using Approximate Entropy Technique. Measurement Science Review 4(2), 29–40 (2004)
Stergiou, N., Moraiti, C., Giakas, G., Ristanis, S., Georgoulis, A.D.: The effect of the walking speed on the stability of the anterior cruciate ligament deficient knee. Clinical Biomechanics 19, 957–963 (2004)
Georgoulis, A.D., Moraiti, C., Ristanis, S., Stergiou, N.: A novel approach to measure variability in the anterior cruciate ligament deficient knee during walking: the use of the approximate entropy in orthopaedics. Journal of Clinical Monitoring and Computing 20, 11–18 (2006)
Perc, M.: The dynamics of human gait. European Journal of Physics 26, 525–534 (2005)
Takens, F.: Detecting Strange Attractor in Turbulence. Lecture Nodes in Mathematics, vol. 898, pp. 366–381 (1981)
Kugiumtzis, D.: State Space Reconstruction Parameters in the Analysis of Chaotic Time Series - the Role of the Time Window Length. Physica D: Nonlinear Phenomena 95(1), 13–28 (1996)
Kennel, M.B., Brown, R., Abarbanel, H.D.I.: Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A 45(6), 3403–3411 (1992)
Weisstein, E.W.: Attractor From MathWorld - A Wolfram Web Resource. http://mathworld.wolfram.com/Attractor.html
Rosenstein, M.T., Collins, J.J., De Luca, C.J.: A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65, 117–134 (1993)
Awrejcewicz, J., Mosdorf, R.: Numerical Analysis of Some Problems of Chaotic Dynamics. WNT (2003)
Webpage of the Human Motion Laboratory of the Polish-Japanese Academy of Information Technology. http://hm.pjwstk.edu.pl
Toebes, M.J.P., Hoozemans, M.J.M., Furrer, R., Dekker, J., van Dieën, J.H.: Local dynamic stability and variability of gait are associated with fall history in elderly subjects. Gait & Posture 36, 527–531 (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Josiński, H., Michalczuk, A., Świtoński, A., Mucha, R., Wojciechowski, K. (2015). Quantifying Chaotic Behavior in Treadmill Walking. In: Nguyen, N., Trawiński, B., Kosala, R. (eds) Intelligent Information and Database Systems. ACIIDS 2015. Lecture Notes in Computer Science(), vol 9012. Springer, Cham. https://doi.org/10.1007/978-3-319-15705-4_31
Download citation
DOI: https://doi.org/10.1007/978-3-319-15705-4_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15704-7
Online ISBN: 978-3-319-15705-4
eBook Packages: Computer ScienceComputer Science (R0)