A multiphysical computational model of myocardial growth adopted to human pathological ventricular remodelling

We present a novel three-dimensional constitutive model that describes an electro-visco-elastic-growth response on the myocardium with a fully implicit staggered solution procedure for the strong electromechanical coupling. The novel formulations of the myocardium allows us to simulate and analyze the remodelling of actively contracting human ventricular heart models which consist of growing viscoelastic myocardium where the growth direction is determined based on its mechanical state at each time step. The total deformation gradient is multiplicatively decomposed into a mechanical-active part and a growth part, where the mechanical-active part is further split into elastic, viscous, and active components. Unconditional stability of time integration is ensured by a backward Euler integration scheme. With the developed model, the myocardium can experience stretch-driven longitudinal (fibre) growth and stress-driven transverse (cross-fibre) growth. To validate the developed approach, two simulations regarding pathological ventricular remodelling are implemented: two divergent types of remodelling of a left ventricular model driven by hemodynamic overloads and ventricular remodelling triggered by acute myocardial ischemia in a biventricular heart model.