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Biol Cybern. 1999 Sep;81(3):249-61.

A comparison of models explaining muscle activation patterns for isometric contractions.

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Department of Medical Physics and Biophysics, University of Nijmegen, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands.


One of the main problems in motor-control research is the muscle load sharing problem, which originates from the fact that the number of muscles spanning a joint exceeds the number of degrees of freedom of the joint. As a consequence, many different possibilities exist for the activation of muscles in order to produce a desired joint torque. Several models describing muscle activation have been hypothesized over the last few decades to solve this problem. This study presents theoretical analyses of the various models and compares the predictions of these models with new data on muscle activation patterns for isometric contractions in various directions. None of the existing models fitted the experimental data in all aspects. The best fit was obtained by models based on minimization of the squared sum of muscle forces ( summation operator(m)φ(2)(m), which is almost equivalent to the Moore-Penrose pseudo-inverse solution), muscle stress sigma ( summation operator(m)sigma(m)(2)) or muscle activation alpha ( summation operator(m)alpha(m)(2)). Since muscle activation patterns are different for isometric contractions and for movements, it could well be that other models or optimization criteria are better suited to describe muscle activation patterns for movements. The results of our simulations demonstrate that the predicted muscle activation patterns do not depend critically on the parameters in the model. This may explain why muscle activation patterns are highly stereotyped for all subjects irrespective of differences between subjects in many neuro-anatomical aspects, such as, for example, in the physiological cross-sectional area of muscle.

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