A Simplified Model of Skeletal Muscle Contraction Dynamics

The skeletal muscle contraction model as a complex of active motor units (sarcomeres) is discussed. The sarcomere model takes the fact into account that forces are generated by myosin bridges interacting with actin filaments in muscle myofibrils. The input of the model is the rate of calcium ion influx into muscle cells, which is assumed to be proportional to the motor neuron potential. The description of the muscle force as a whole uses averaging over an ensemble of motor units. The parameters of the model are adapted to describe contraction of a skeletal muscle sacromere. The transition from contraction of a single sarcomere to slow contraction of the whole muscle is constructed using motion separation methods. The model of “slow” contraction of a single muscle fiber excited by a single nerve impulse has no independent value because the characteristic time of change of the impulse potential is short. Nevertheless, for description of tetanic muscle contraction, when the change in the total action on the muscle is smooth enough, it seems acceptable to use such an approximate model. Approximate numerical estimates of the error of the constructed model for a simplified example are given.