A transversely isotropic thermo-hyperelastic constitutive model of myocardial tissue with a three-state cell death dynamics for cardiac radiofrequency ablation

Constitutive models of radiofrequency catheter ablation (RFCA) lack a reliable three-dimensional microstructural representation of the myocardium. Besides, complex multiphysics couplings arise during tissue heating. In light of procedure design and optimization, we propose a generalized, thermodynamically consistent, transverse isotropic thermo-hyperelastic constitutive model of the myocardium accounting for local anisotropies and multiscale dynamics. We advance, in particular, a biophysical rationale formulating a continuum damage approach based on a three-state hyperthermic cell death dynamical model. We further introduce a fully coupled thermo-mechanical model by means of the multiplicative decomposition of the deformation gradient and by defining phenomenological temperature dependencies of the material parameters consistent with the general theory of thermoelasticity. The overall multiphysics and multiscale model is numerically solved within an idealized tissue domain, adopting an accurate finite element scheme under the additional constraint of constant power control. Our modeling approach fills the gap of constitutive modeling of cardiac RFCA and results in a better matching of ablating volumes with respect to the current models in the literature. We show for the first time the elliptical shape of the lesion occurring because of anisotropic thermo-electric conduction and the occurrence of residual strains due to tissue phase changes after ablation. We conclude by discussing limitations, potential future applications and perspectives of our modeling approach towards generalized constitutive remodeling theories.