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BioMed Research International
Volume 2015 (2015), Article ID 473279, 15 pages
http://dx.doi.org/10.1155/2015/473279
Research Article

Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements

1CRS4, Loc. Pixina Manna, Edificio 1, 09010 Pula, Italy
2Fujitsu Laboratories of Europe, Hayes Park Central, Hayes End Road, Hayes, Middlesex UB4 8FE, UK

Received 14 December 2014; Revised 20 March 2015; Accepted 9 April 2015

Academic Editor: Joakim Sundnes

Copyright © 2015 Gianmauro Cuccuru et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics. The solution of these equations requires solving multiple length scales due to the ratio of advection to diffusion that varies among the different equations. High order approximation of spectral elements provides greater flexibility in resolving multiple length scales. Furthermore, spectral elements are extremely efficient to model propagation phenomena on complex shapes using fewer degrees of freedom than its finite element equivalent (for the same level of accuracy). We illustrate a fully unstructured all-hexahedra approach implementation of the method and we apply it to the solution of full 3D monodomain and bidomain test cases. We discuss some key elements of the proposed approach on some selected benchmarks and on an anatomically based whole heart human computational model.