title: 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 (FEs). The technique generates macro FEs (MFEs) based on the local decomposition of elements into tetrahedral subelements with linear shape functions. Such an approach necessitates the direct use of hybrid meshes (HMs) composed of different types of elements. MFEs are compared to classic standard FEs with respect to accuracy and RAM memory usage under different scenarios of cardiac modeling, including bidomain and monodomain simulations in 2-D and 3-D 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 FEs. However, MFEs offer a significant decrease in memory requirements. We conclude that HMs composed of MFEs are well suited for solving problems in cardiac computational electrophysiology.
authors.affiliation: Institute of Biophysics, Medical University of Graz, Graz 8010, Austria. bernardosk@gmail.com
authors.forename: Bernardo M
authors.initials: BM
authors.lastname: Rocha
authors.forename: Ferdinand
authors.initials: F
authors.lastname: Kickinger
authors.forename: Anton J
authors.initials: AJ
authors.lastname: Prassl
authors.forename: Gundolf
authors.initials: G
authors.lastname: Haase
authors.forename: Edward J
authors.initials: EJ
authors.lastname: Vigmond
authors.forename: Rodrigo Weber
authors.initials: RW
authors.lastname: dos Santos
authors.forename: Sabine
authors.initials: S
authors.lastname: Zaglmayr
authors.forename: Gernot
authors.initials: G
authors.lastname: Plank
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D018780:Body Surface Potential Mapping / Q000379:methods*; D003198:Computer Simulation; D020342:Finite Element Analysis; D006329:Heart Conduction System / Q000503:physiopathology*; D006801:Humans; D008955:Models, Cardiovascular