Thermodynamic properties of muscle contraction models and associated discrete-time principles

François Kimmig (1, 2) , Dominique Chapelle (1, 2) , Philippe Moireau (1, 2)

1 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
2 Université Paris-Saclay

Considering a large class of muscle contraction models accounting for actin-myosin interaction, we present a mathematical setting in which solution properties can be established, including fundamental thermodynamic balances. Moreover, we propose a complete discretization strategy for which we are also able to obtain discrete versions of the thermodynamic balances and other properties. Our major objective is to show how the thermodynamics of such models can be tracked after discretization, including when they are coupled to a macroscopic muscle formulation in the realm of continuum mechanics. Our approach allows to carefully identify the sources of energy and entropy in the system, and to follow them up to the numerical applications.

Mots clés: muscle contraction; sliding filaments; Clausius-Duhem inequality; thermodynamically consistent time-discretization

Domaines: Analyse numérique [math.NA]; Biomécanique [physics.med-ph]

François Kimmig, Dominique Chapelle, Philippe Moireau. Thermodynamic properties of muscle contraction models and associated discrete-time principles. Advanced Modeling and Simulation in Engineering Sciences, In press, ⟨10.1186/s40323-019-0128-9⟩. ⟨hal-02065957v3⟩