A new computational framework for electro-activation in cardiac mechanics

This paper presents a novel computational framework for the numerical simulation of the electromechanical response of the myocardium during the cardiac cycle. The paper presents the following main novelties. (1) Two new mixed formulations, tailormade for active stress and active strain coupling approaches, have been developed and used in conjunction with two different ionic models, namely Bueno-Orovio et al. (2008) and Ten Tusscher et al. (2004). Taking as a reference the mixed formulations introduced by Bonet et al. (2015) in the context of nonlinear elasticity, the proposed formulations include as unknown fields the geometry and the transmembrane potential (and possibly a Lagrange multiplier enforcing weakly the incompressibility constraint) as well as the deformation gradient tensor, its cofactor, its determinant, the gradient of the transmembrane potential and their respective work conjugates. The Finite Element implementation of these formulations is shown in this paper, where a static condensation procedure is presented in order to yield an extremely competitive computational approach. (2) A comprehensive and rigorous study of different ionic models (i.e Bueno-Orovio and Ten Tusscher) and electromechanical activation couplings (i.e active strain and active stress) has been carried out. (3) An analytical and numerical analysis of the possible loss of ellipticity and polyconvexity of one of the most widely used constitutive models in the context of cardiac mechanics is carried out in this paper, putting forward possible polyconvexifications of the existing model. (4) In addition, an invariant representation of Guccione's constitutive model is proposed. Finally, a series of numerical examples are included in order to demonstrate the applicability and robustness of the proposed formulations. (C) 2019 Elsevier B.V. All rights reserved.