An orthotropic electro-viscoelastic model for the heart with stress-assisted diffusion

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 (this is so 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.

References in corpus (6)

• A note on stress-driven anisotropic diffusion and its role in active deformable media
• Competing mechanisms of stress-assisted diffusivity and stretch-activated currents in cardiac electromechanics
• Nonlinear diffusion & thermo-electric coupling in a two-variable model of cardiac action potential
• A comparison between active strain and active stress in transversely isotropic hyperelastic materials
• A modeling framework for contact, adhesion and mechano-transduction between excitable deformable cells
• Modelling thermo-electro-mechanical effects in orthotropic cardiac tissue

Cited by in corpus (4)

• 3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics
• Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion
• Spatiotemporal Organization of Electromechanical Phase Singularities during High-Frequency Cardiac Arrhythmias
• Mechanochemical models for calcium waves in embryonic epithelia