an:06059441
Zbl 1242.92016
Nobile, F.; Quarteroni, A.; Ruiz-Baier, R.
An active strain electromechanical model for cardiac tissue
EN
Int. J. Numer. Methods Biomed. Eng. 28, No. 1, 52-71 (2012).
00294957
2012
j
92C30 92C05 78A70 92C10 35K57 65N30 35Q92
cardiac electromechanical coupling; bidomain equations; reaction-diffusion problem; nonlinear elasticity; finite elements
Summary: We propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of the 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 there is a multiplicative decomposition of the deformation tensor into a passive and active part, 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 a 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.