Cardiac muscle strip model parameters and muscle elastance

A recent functional model of the left ventricle as a pressure generator that is time and volume dependent [1] was adapted to describe the mechanical aspects of heart muscle contraction. Muscle's complex dynamics develop from a single equation based on the formation and relaxation of crossbridge bonds. Muscle is modeled as a force generator that is time and length dependent. This equation permits the calculation of muscle elastance via E_m = ∂f_m/∂l_m from muscle force and length, both as functions of time. This muscle model is defined independently from load properties, and elastance is dynamic and reflects changing numbers of crossbridge bonds. The model parameters were extracted from measured force and length data from cat papillary muscle experiments in the literature [2]. The purpose of this paper is to present in some detail how to describe a particular muscle strip from measured data. The resulting model is tested under a wide range of mechanical conditions, such as isometric and isotonic contractions for normal and varied inotropic state, and muscle velocity is computed for different loads. Computed results compare favorably with similar measurements from the literature. The resulting lumped muscle model is a compact, yet comprehensive functional description of muscle dynamics.