Citation

Zakynthinaki MS, Milla JM, de Durana AL, Martínez CA, Romo GR, Quintana MS, Molinuevo JS. Chaos Solitons Fractals 2010; 20(1): 013118.

Affiliation

Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, c/ Serrano 121, 28006 Madrid, Spain.

Copyright

(Copyright © 2010, Elsevier Publishing)

DOI

10.1063/1.3335460

PMID

20370273

Abstract

We show how asymmetries in the movement patterns during the process of regaining balance after perturbation from quiet stance can be modeled by a set of coupled vector fields for the derivative with respect to time of the angles between the resultant ground reaction forces and the vertical in the anteroposterior and mediolateral directions. In our model, which is an adaption of the model of Stirling and Zakynthinaki (2004), the critical curve, defining the set of maximum angles one can lean to and still correct to regain balance, can be rotated and skewed so as to model the effects of a repetitive training of a rotational movement pattern. For the purposes of our study a rotation and a skew matrix is applied to the critical curve of the model. We present here a linear stability analysis of the modified model, as well as a fit of the model to experimental data of two characteristic "asymmetric" elite athletes and to a "symmetric" elite athlete for comparison. The new adapted model has many uses not just in sport but also in rehabilitation, as many work place injuries are caused by excessive repetition of unaligned and rotational movement patterns.

Language: en