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Computational and Mathematical Methods in Medicine
Volume 2015, Article ID 309756, 11 pages
Research Article

The Multivariate Largest Lyapunov Exponent as an Age-Related Metric of Quiet Standing Balance

1School of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China
2College of Electronic and Information Engineering, Hebei University, Baoding 071000, China

Received 24 January 2015; Revised 12 April 2015; Accepted 28 April 2015

Academic Editor: Luca Faes

Copyright © 2015 Kun Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The largest Lyapunov exponent has been researched as a metric of the balance ability during human quiet standing. However, the sensitivity and accuracy of this measurement method are not good enough for clinical use. The present research proposes a metric of the human body’s standing balance ability based on the multivariate largest Lyapunov exponent which can quantify the human standing balance. The dynamic multivariate time series of ankle, knee, and hip were measured by multiple electrical goniometers. Thirty-six normal people of different ages participated in the test. With acquired data, the multivariate largest Lyapunov exponent was calculated. Finally, the results of the proposed approach were analysed and compared with the traditional method, for which the largest Lyapunov exponent and power spectral density from the centre of pressure were also calculated. The following conclusions can be obtained. The multivariate largest Lyapunov exponent has a higher degree of differentiation in differentiating balance in eyes-closed conditions. The MLLE value reflects the overall coordination between multisegment movements. Individuals of different ages can be distinguished by their MLLE values. The standing stability of human is reduced with the increment of age.