Muscle elastance and the force-velocity relation arise from a new model of muscle contraction

Abstract

Striated muscle may be functionally described using a new analytical model that treats muscle as a time, length, and velocity dependent force generator. A single analytical function is able to describe a wide range of contractile phenomena, including isometric contractions, isotonic contractions, and transient behavior, as well as demonstrating a direct force-length relation for passive and active muscle, a direct relation between initial muscle length and amount of shortening, and an inverse relation between muscle load and shortening. Hill's famous force-velocity relation, typically embodied as the "contractile element" of lumped muscle models, arises from this equation without separate assumptions. A new description of muscle elastance also emerges by taking the derivative of muscle force with respect to length. Muscle dynamics develop from a single equation based on the formation and relaxation of crossbridge bonds within the muscle.