A new model for force generation by skeletal muscle, incorporating work-dependent deactivation

Abstract

SUMMARY A model is developed to predict the force generated by active skeletal muscle when subjected to imposed patterns of lengthening and shortening, such as those that occur during normal movements. The model is based on data from isolated lamprey muscle and can predict the forces developed during swimming. The model consists of a set of ordinary differential equations, which are solved numerically. The model's first part is a simplified description of the kinetics of Ca2+ release from sarcoplasmic reticulum and binding to muscle protein filaments, in response to neural activation. The second part is based on A. V. Hill's mechanical model of muscle, consisting of elastic and contractile elements in series, the latter obeying known physiological properties. The parameters of the model are determined by fitting the appropriate mathematical solutions to data recorded from isolated lamprey muscle activated under conditions of constant length or rate of change of length. The model is then used to predict the forces developed under conditions of applied sinusoidal length changes, and the results compared with corresponding data. The most significant advance of this model is the incorporation of work-dependent deactivation, whereby a muscle that has been shortening under load generates less force after the shortening ceases than otherwise expected. In addition, the stiffness in this model is not constant but increases with increasing activation. The model yields a closer prediction to data than has been obtained before, and can thus prove an important component of investigations of the neural—mechanical—environmental interactions that occur during natural movements.