Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements

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 di erential equations coupled with a system of ordinary di erential equations representing cell membrane dynamics. e solution of these equations requires solving multiple length scales due to the ratio of advection to di usion that varies among the di erent equations. High order approximation of spectral elements provides greater exibility in resolving multiple length scales. Furthermore, spectral elements are extremely e cient to model propagation phenomena on complex shapes using fewer degrees of freedom than its nite 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.

@Article{CFMS15,
  author       = {Cuccuru, G. and Fotia, G. and Maggio, F. and Southern, J.},
  title        = {Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements},
  journal      = {Biomed Research International, Special Issue on Simulation of Heart Function, Guest Editors: Rodrigo W. dos Santos, Sergio Alonso, Elizabeth M. Cherry, Joakim Sundnes},
  volume       = {2015},
  month        = {october},
  year         = {2015},
  publisher    = {Hindawi Publishing Corporation},
  keywords     = {cardiac simulation, high performance computing, finite elements, spectral elements, , linear algebra},
  doi          = {10.1155/2015/473279},
  url          = {https://publications.crs4.it/pubdocs/2015/CFMS15},
}