Fully Eulerian finite element approximation of a fluid-structure interaction problem in cardiac cells

We propose in this paper an Eulerian finite element approximation of a coupled chemical fluid-structure interaction problem arising in the study of mesoscopic cardiac biomechanics. We simulate the active response of a myocardial cell (here considered as an anisotropic, hyperelastic, and incompressible material), the propagation of calcium concentrations inside it, and the presence of a surrounding Newtonian fluid. An active strain approach is employed to account for the mechanical activation, and the deformation of the cell membrane is captured using a level set strategy. We address in detail the main features of the proposed method, and we report several numerical experiments aimed at model validation.