Efficient simulation of cardiac electrical propagation using high order finite elements

Authors:
Christopher J. Arthurs;Martin J. Bishop;David Kay
Affiliations:
Department of Computer Science, University of Oxford, Oxford, United Kingdom;Department of Computer Science, University of Oxford, Oxford, United Kingdom and Department of Biomedical Engineering, King's College London, London, United Kingdom;Department of Computer Science, University of Oxford, Oxford, United Kingdom
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.