5 research outputs found
An active strain electromechanical model for cardiac tissue
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
Segregated Algorithms for the Numerical Simulation of Cardiac Electromechanics in the Left Human Ventricle
We propose and numerically assess three segregated ( partitioned) algorithms for the numerical solution of the coupled electromechanics problem for the left human ventricle. We split the coupled problem into its core mathematical models and we proceed to their numerical approximation. Space and time discretizations of the core problems are carried out by means of the Finite Element Method and Backward Differentiation Formulas, respectively. In our mathematical model, electrophysiology is represented by the monodomain equation while the Holzapfel-Ogden strain energy function is used for the passive characterization of tissue mechanics. A transmurally variable active strain model is used for the active deformation of the fibers of the myocardium to couple the electrophysiology and the mechanics in the framework of the active strain model. In this work, we focus on the numerical strategy to deal with the solution of the coupled model, which is based on novel segregated algorithms that we propose. These also allow using different time discretization schemes for the core submodels, thus leading to the formulation of staggered algorithms, a feature that we systematically exploit to increase the efficiency of the overall computational procedure. By means of numerical tests we show that these staggered algorithms feature (at least) first order of accuracy. We take advantage of the efficiency of the segregated schemes to solve, in a High Performance Computing framework, the cardiac electromechanics problem for the human left ventricle, for both idealized and subject-specific configurations