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

## TL;DR

This paper introduces a comprehensive orthotropic electro-viscoelastic model for cardiac tissue that integrates nonlinear elasticity, stress-dependent electrical conductivities, and electrophysiological dynamics, validated through numerical simulations.

## Contribution

It presents a novel coupled electromechanical model with stress-assisted diffusion and a mixed-primal finite element scheme for cardiac tissue simulation.

## Key findings

- Model accurately describes cardiac action potential
- Stress influences electrical conductivities in the model
- Numerical validation confirms model's robustness

## 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.