A four-state cross bridge model for muscle contraction. Mathematical study and validation

A mathematical model of contracting skeletal muscle is studied. The model is composed by an elastic element (SE) in series with a contractile element (CE) that describes the cross bridge kinetics with a formulation derived by that proposed by Eisenberg and Hill (1978). An analytical study of the system of nonlinear partial differential equations of the model allows the existence and the uniqueness of the solution to be proved. A suitable approach to the numerical solution is defined and a series of numerical tests are performed. These tests lead to select an appropriate set of parameters and allow to compare model predictions and experimental observations on frog skeletal muscle.