A Macro Finite-Element Formulation for Cardiac Electrophysiology Simulations Using Hybrid Unstructured Grids

Abstract

Electrical activity in cardiac tissue can be described by the bidomain equations whose solution for large scale simulations still remains a computational challenge. Therefore, improvements in the discrete formulation of the problem which decrease computational and/or memory demands are highly desirable. In this study, we propose a novel technique for computing shape functions of finite elements. The technique generates macro finite elements (MFEs) based on the local decomposition of elements into tetrahedral sub-elements with linear shape functions. Such an approach necessitates the direct use of hybrid meshes composed of different types of elements. MFEs are compared to classic standard finite elements with respect to accuracy and RAM memory usage under different scenarios of cardiac modeling including bidomain and monodomain simulations in 2D and 3D for simple and complex tissue geometries. In problems with analytical solutions, MFEs displayed the same numerical accuracy of standard linear triangular and tetrahedral elements. In propagation simulations, conduction velocity and activation times agreed very well with those computed with standard finite elements. However, MFEs offer a significant decrease in memory requirements. We conclude that hybrid meshes composed of MFEs are well suited for solving problems in cardiac computational electrophysiology.

Tachycardia in Post-Infarction Hearts: Insights from 3D Image-Based Ventricular Models

“…The mesh of the infarcted canine ventricles consisted of 3,177,732 nodes (2,185,112 nodes in the ventricles) and 3,981,196 (2,603,624 in the ventricles) mixed-type elements [21] with an average element edge length of 396 µm. Finally, fiber orientations were assigned to each element by calculating the primary eigenvector from the corresponding DT-MRI (Fig.…”

Modeling Defibrillation of the Heart: Approaches and Insights

“…Typically, monolithic meshes consist of one element type only, but exception exist [52], [53], where hybrid meshes consisting of tetrahedra, hexahedra, pyramids and prisms were used. Furthermore, most FEM studies relied on the Galerkin FEM where linear test functions with tetrahedral elements [39], [54], [55], isoparametric trilinear test functions with hexahedral elements [51] or cubichermite hexahedral elements [38], [56] were employed.…”

Modeling Defibrillation

“…With the FVM, quadrilaterals in 2D (Harrild & Henriquez, 1997) and hexahedral elements in 3D (Harrild & Henriquez, 2000;Trew, Le Grice, Smaill & Pullan, 2005) have been preferred, whereas with the FEM, triangles and quadrilaterals were used in 2D and tetrahedral or hexahedral elements in 3D (Munteanu et al, 2009;Seemann et al, 2006). Typically, monolithic meshes consisting of one element type only were used, but exception exist Rocha et al, 2011) where hybrid meshes consisting of tetrahedra, hexahedra, pyramids and prisms were used. Further, most FEM studies relied on the Galerkin FEM where linear test functions with tetrahedral elements (Franzone et al, 2006;Sundnes et al, 2006;Vigmond et al, 2002), isoparametric trilinear test functions with hexahedral elements (Munteanu et al, 2009) or cubic-hermite hexahedral elements (Rogers & McCulloch, 1994;Saucerman et al, 2004) were used.…”