A modeling framework for electro-mechanical interaction between excitable deformable cells

Cardiac myocytes are the fundamental cells composing the heart muscle. The propagation of electric signals and chemical quantities through them is responsible for their nonlinear contraction and dilatation. In this study, a theoretical model and a finite element formulation are proposed for the simulation of adhesive contact interactions between myocytes across the so-called gap junctions. A novel multi-field interface constitutive law is proposed for their description, integrating the adhesive and contact mechanical response with their nonlinear electrophysiological behavior. From the computational point of view, the initial and boundary value problem is formulated as a structure-structure interaction problem, which leads to a straightforward implementation in the finite element software. Numerical tests are conducted on different couples of myocytes, characterized by different shapes related to their stages of growth, qualitatively capturing the experimental response in terms of tractions and displacement gaps at the interface. The proposed framework will represent a base reference model to investigate imperfect mechano-transduction between excitable deformable media and to understand how such complex nonlinear multiscale interactions affect the onset of emergent pathological scenarios, e.g. cardiac arrhythmias.