Functional Requirements of a Mathematical Model of Muscle Contraction

Muscle modeling has a long history. Models typically belong to the class of lumped models built around Hill's contractile element, or to crossbridge models at the ultrastructure level. Lumped models built on the contractile element are not sufficiently dynamic, since the muscle's contractile properties are set a priori by the force-velocity relation. We have shown that the force-velocity relation is not a unique descriptor of muscle's contractile state [1]. Alternatively, description of muscle as a time and length dependent force generator may be used to model muscle dynamics. This paper defines the functional requirements of a mathematical model of muscle contraction and evaluates how closely a lumped model based on ultrastructural dynamics resembles muscle. This single model was found able to describe isometric and isotonic contractions, the force-length relation, the force-velocity relation, and changes in contractile state and contraction rate. This approach may help link macro contractile properties, such as the force-velocity relation, to micro dynamics of crossbridge bonds. It may also be useful as a component of larger physiological models and simulations.