Theoretical and numerical modeling of nonlinear electromechanics with applications to biological active media

A general theoretical framework for the formulation of the nonlinear electromechanics of biological active media is presented. The approach is based on the additive decomposition of the Helmholtz free energy in elastic and inelastic parts and on the multiplicative decomposition of the deformation gradient in passive and active parts. The thermodynamical framework accounts for geometric and material nonlinearities. In view of numerical applications, the general approach is specialized to reproduce intracellular calcium spatio-temporal variations with the self-sustained contractions in cardiac myocytes. A finite element method based on a Taylor-Hood discretization is employed to approximate the nonlinear elasticity equations, whereas the calcium concentration and mechanical activation variables are discretized by piecewise linear finite elements. Numerical tests illustrate the ability of the model in predicting key experimentally established characteristics.