We propose a finite element approximation of a system of
partial differential equations describing the coupling
between the propagation of electrical potential and large
deformations of the cardiac tissue. The underlying
mathematical model is based on the active strain
assumption, in which it is assumed that a multiplicative
decomposition of the deformation tensor into a passive
and active part holds, the latter carrying the
information of the electrical potential propagation and
anisotropy of the cardiac tissue into the equations of
either incompressible or compressible nonlinear
elasticity, governing the mechanical response of the
biological material. In addition, by changing from an
Eulerian to a Lagrangian configuration, the bidomain or
monodomain equations modeling the evolution of the
electrical propagation exhibit a nonlinear diffusion
term. Piecewise quadratic finite elements are employed to
approximate the displacements field, whereas for
pressure, electrical potentials and ionic variables are
approximated by piecewise linear elements. Various
numerical tests performed with a parallel finite element
code illustrate that the proposed model can capture some
important features of the electromechanical coupling, and
show that our numerical scheme is efficient and accurate.