A 3D electro-mechanical continuum model for simulating skeletal muscle contraction

A thermodynamically consistent three-dimensional electro-mechanical continuum model for simulating skeletal muscle contraction is presented. Active and passive responses are accounted for by means of a decoupled strain energy function into passive and active contributions. The active force is obtained as the maximum tetanic force penalized by two functions that consider the external stimulus frequency and the overlap between actin and myosin filaments. Passive response is modelled by a transversely isotropic strain energy function. The robustness of the model is analyzed by means of finite element simulations that reproduce the one-dimensional isometric, concentric and eccentric contractions in a simplified model of a muscle. The model has also been implemented to reproduce isometric and concentric contractions on a three-dimensional finite element model of the rat tibialis anterior (TA) muscle. The finite element model was obtained from magnetic resonance imaging and the preferential directions associated with the collagen and muscular fibres were considered. The proposed model was able to reproduce the observed experimental response of the active force generated by the isolated rat TA muscle during isometric and concentric contractions. In addition, the predicted force-velocity relationship is in good agreement with experimental data reported for the fast-twitch extensor digitorum longus (e.d.l) muscle of male rats.