Mathematical model for isometric and isotonic muscle contractions

A new mathematical model is presented to describe both the active and passive mechanics of muscles. In order to account for the active response, a two–layer kinematics that introduces both the visible and rest lengths of the muscle is presented within a rational mechanics framework. The formulation is based on an extended version of the principle of virtual power and the dissipation principle. By using an ac- curate constitutive description of muscle mobility under activation, details of microscopic processes that lead to muscle contraction are glossed over while macroscopic effects of chemical/electrical stimuli on muscle mechanics are retained. The model predictions are tested with isometric and isotonic experimen- tal data collected from murine extensor digitorum muscle. It is shown that the proposed model captures experimental observations with only three scalar parameters