An adaptive Hybridizable Discontinuous Galerkin approach for cardiac electrophysiology

Julia Hoermann 1 Cristóbal Bertoglio 1, 2 Martin Kronbichler 1 Martin Pfaller 1 Radomir Chabiniok 3, 4, 5 Wolfgang Wall 1
1 TUM - Technische Universität München [München]
2 University of Groningen [Groningen]
3 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
4 Imaging Sciences and Biomedical Engineering Division [London]
5 Université Paris-Saclay
Abstract : Cardiac electrophysiology simulations are numerically challenging due to the propagation of a steep electrochemical wave front and thus require discretizations with small mesh sizes to obtain accurate results. In this work, we present an approach based on the Hybridizable Discontinuous Galerkin method (HDG), which allows an efficient implementation of high-order discretizations into a computational framework. In particular using the advantage of the discontinuous function space, we present an efficient p-adaptive strategy for accurately tracking the wave front. HDG allows to reduce the overall degrees of freedom in the final linear system to those only on the element interfaces. Additionally, we propose a rule for a suitable integration accuracy for the ionic current term depending on the polynomial order and the cell model to handle high-order polynomials. Our results show that for the same number of degrees of freedom coarse high-order elements provide more accurate results than fine low-order elements. Introducing p-adaptivity further reduces computational costs while maintaining accuracy by restricting the use of high-order elements to resolve the wave front. For a patient-specific simulation of a cardiac cycle p-adaptivity reduces the average number of degrees of freedom by 95% compared to the non-adaptive model. In addition to reducing computational costs, using coarse meshes with our p-adaptive high-order HDG method also simplifies practical aspects of mesh generation and postprocessing.
Keywords : finite element method Hybridizable Discontinuous Galerkin cardiac electrophysiology
Document type :
Journal articles
Liste complète des métadonnées

Cited literature [36 references]  Display  Hide  Download
https://hal.archives-ouvertes.fr/hal-01672964
Contributor : Radomir Chabiniok <>
Submitted on : Wednesday, December 27, 2017 - 10:30:58 PM
Last modification on : Wednesday, March 27, 2019 - 4:16:24 PM

File

ep_hdg_171213.pdf
Files produced by the author(s)

Identifiers

Données associées

Collections

INSMI | INSTITUT-TELECOM | TDS-MACS | ENSMP_LMS | X-LMS | INRIA | PSL | ENSMP | X | UNIV-PARIS-SACLAY | PARISTECH | X-DEP-MECA

Citation

Julia Hoermann, Cristóbal Bertoglio, Martin Kronbichler, Martin Pfaller, Radomir Chabiniok, et al.. An adaptive Hybridizable Discontinuous Galerkin approach for cardiac electrophysiology. International Journal for Numerical Methods in Biomedical Engineering, John Wiley and Sons, 2018, 34 (5), e2959 (20 p.). ⟨10.1002/cnm.2959⟩. ⟨hal-01672964⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

506

Files downloads

207

Contact

support.ccsd.cnrs.fr
hal.support@ccsd.cnrs.fr
Logo CCSD