An energy-preserving muscle tissue model: formulation and compatible discretizations

Dominique Chapelle (1) , Patrick Le Tallec (2) , Philippe Moireau (1) , Michel Sorine (3)

1 MACS - Modeling, analysis and control in computational structural dynamics
2 LMS - Laboratoire de mécanique des solides
3 SISYPHE - SIgnals and SYstems in PHysiology & Engineering

In this paper we propose a muscle tissue model -- valid for striated muscles in general, and for the myocardium in particular -- based on a multi-scale physiological description. This model extends and refines an earlier-proposed formulation by allowing to account for all major energy exchanges and balances, from the chemical activity coupled with oxygen supply to the production of actual mechanical work, namely, the biological function of the tissue. We thus perform a thorough analysis of the energy mechanisms prevailing at the various scales, and we proceed to propose a complete discretization strategy -- in time and space -- respecting the same balance laws. This will be crucial in future works to adequately model the many important physiological -- normal and pathological -- phenomena associated with these energy considerations.

Mots clés: muscle tissue modeling; myocardium; multi scale; energy balance; time and space discretizations

Domaines: Analyse numérique [math.NA]

Dominique Chapelle, Patrick Le Tallec, Philippe Moireau, Michel Sorine. An energy-preserving muscle tissue model: formulation and compatible discretizations. International Journal for Multiscale Computational Engineering, 2012, 10 (2), pp.189-211. ⟨10.1615/IntJMultCompEng.2011002360⟩. ⟨hal-00678772⟩