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Computational and Mathematical Methods in Medicine
Volume 2012, Article ID 936243, 16 pages
http://dx.doi.org/10.1155/2012/936243
Research Article

A Meshfree Method for Simulating Myocardial Electrical Activity

1Shenzhen Institutes of Advanced Technology, Chinese Academy of Science, Shenzhen 518055, China
2Department of Optical Engineering, Zhejiang University, Hangzhou 310027, China
3Institute of Clinical Anatomy, Southern Medical University, Guangzhou 510515, China

Received 4 May 2012; Accepted 14 June 2012

Academic Editor: Huafeng Liu

Copyright © 2012 Heye Zhang 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

An element-free Galerkin method (EFGM) is proposed to simulate the propagation of myocardial electrical activation without explicit mesh constraints using a monodomain model. In our framework the geometry of myocardium is first defined by a meshfree particle representation that is, a sufficient number of sample nodes without explicit connectivities are placed in and inside the surface of myocardium. Fiber orientations and other material properties of myocardium are then attached to sample nodes according to their geometrical locations, and over the meshfree particle representation spatial variation of these properties is approximated using the shape function of EFGM. After the monodomain equations are converted to their Galerkin weak form and solved using EFGM, the propagation of myocardial activation can be simulated over the meshfree particle representation. The derivation of this solution technique is presented along a series of numerical experiments and a solution of monodomain model using a FitzHugh-Nagumo (FHN) membrane model in a canine ventricular model and a human-heart model which is constructed from digitized virtual Chinese dataset.