Abstract
We propose and analyse the properties of a new class of models for the electromechanics of cardiac tissue. The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law, for both active stress and active strain formulations of active mechanics, coupled with a four-variable phenomenological model for human cardiac cell electrophysiology, which produces an accurate description of the action potential. The conductivities in the model of electric propagation are modified according to stress, inducing an additional degree of nonlinearity and anisotropy in the coupling mechanisms, and the activation model assumes a simplified stretch–calcium interaction generating active tension or active strain. The influence of the new terms in the electromechanical model is evaluated through a sensitivity analysis, and we provide numerical validation through a set of computational tests using a novel mixed-primal finite element scheme.
Highlights
In order to effectively combat cardiovascular disease, we need a robust scientific understanding of the mechanisms of the heart and the nature of such health conditions
We have introduced a model for the active contraction of cardiac tissue
We focused on incorporating the mechanoelectric feedback through stress-assisted diffusion, accounting for a porous-media-type nonlinear diffusivity, and including inertial terms in the equations of motion
Summary
In order to effectively combat cardiovascular disease, we need a robust scientific understanding of the mechanisms of the heart and the nature of such health conditions. Even though the problem of cardiac electromechanics has been the focus of a large number of modelling and computational studies (see, for instance, Augustin et al 2016; Cherubini et al 2012; Franzone et al 2016; Costabal et al 2017; Gizzi et al 2015; Göktepe et al 2013; Nobile et al 2012; Quarteroni et al 2017; Sundnes et al 2014 and the references therein), there still remain many challenges in the development of more accurate and detailed models and the accompanying methods In such a context, the large majority of the proposed approaches rely on continuum formulations of the complex microstructural interactions occurring among the heart tissue components, e.g. cardiomyocytes, involving different scales (Quarteroni et al 2017).
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