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In this paper we introduce a new mathematical model for the activecontraction of cardiac muscle, featuring different thermo-electric andnonlinear conductivity properties. The passive hyperelastic response of thetissue is described by an orthotropic exponential model, whereas the ionicactivity dictates active contraction incorporated through the concept oforthotropic active strain. We use a fully incompressible formulation, and thegenerated strain modifies directly the conductivity mechanisms in the mediumthrough the pull-back transformation. We also investigate the influence ofthermo-electric effects in the onset of multiphysics emergent spatiotemporaldynamics, using nonlinear diffusion. It turns out that these ingredients have akey role in reproducing pathological chaotic dynamics such as ventricularfibrillation during inflammatory events, for instance. The specific structureof the governing equations suggests to cast the problem in mixed-primal formand we write it in terms of Kirchhoff stress, displacements, solid pressure,electric potential, activation generation, and ionic variables. We also proposea new mixed-primal finite element method for its numerical approximation, andwe use it to explore the properties of the model and to assess the importanceof coupling terms, by means of a few computational experiments in 3D.

Modelling thermo-electro-mechanical effects in orthotropic cardiac tissue