Modelling of force production in skeletal muscle undergoing stretch

Many human movements involve eccentric contraction of muscles. Therefore, it is important that a theoretical model is able to represent the kinetic response of activated muscle during lengthening if it is to be applied to dynamic simulation of such movements. The so-called Hill and Distribution Moment models are two commonly used models of skeletal muscle. The Hill model is a phenomenological model based on experimental observations; the Distribution Moment model is based on the cross-bridge theory of muscle contraction. The ability of each of these models to predict the force-velocity relation has been considered previously; however, few attempts have been made to evaluate the force response of each model with respect to time during stretches at different velocities. The purpose of this study was to compare the predicted force-time responses of the Hill and Distribution Moment models to the actual force produced by the cat soleus during experimental iso-velocity stretches at maximal activation. Two stretch velocities were simulated: 7.2 and 400 mm s-1. Model parameters were derived from the literature where possible. In addition, model parameters were optimized to provide the best possible fit between model force predictions and experimental results at each velocity. The results of the study showed that using the Hill model, it was possible to describe qualitatively the force-time response of the muscle at both velocities of stretch using parameters derived from the literature. It was also possible to optimize a set of parameters for the Hill model to provide a quantitative description of the force-time response at each velocity. Using the Distribution Moment model, it was not possible to describe the force-time response of the muscle for both velocities using a single set of rate constants, suggesting that the cross-bridge theory, upon which the model is based, may have to be further evaluated for lengthening muscle. Further research is required to determine if the model results can be generalized to other muscles and other velocities of stretch.