Mathematical model of the frog skeletal muscle--analysis of non-linear mechanical properties

A mathematical model of the skeletal muscle, consisting of contractile and series elastic components of the contracting muscle as well as viscoelastic components of the resting muscle is presented, in which the contractile component obeying the force-load-velocity relation is expressed by two components, a force generator and a viscous-like component. Since it is one of the most significant properties of the muscle that the mechanical properties depend upon the contractile force (the intensity of the active state), detailed attention is given to the explanation of those non-linear properties. Parameters of the model are determined based on physiological observations obtained from fiber bundles prepared from the frog semitendinosus muscle. While viscoelasticity is constant at the resting state, the series elastic coefficient of the contracting muscle increases with an increase in tension and the viscous-like coefficient also increases linearly with increasing contractile force. This model is checked by digital simulation against responses to ramp stretch of the muscle of the steady and transient contractions. A close agreement is shown between the simulated results and the experimental ones. The model can explicitly account for the non-linear mechanical properties of the contracting muscle.