Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology

Please always quote using this URN: urn:nbn:de:0297-zib-8649
  • Adaptive numerical methods in space and time are introduced and studied for multiscale cardiac reaction-diffusion models in three dimensions. The evolution of a complete heartbeat, from the excitation to the recovery phase, is simulated with both the anisotropic Bidomain and Monodomain models, coupled with either a variant of the simple FitzHugh-Nagumo model or the more complex phase-I Luo-Rudy ionic model. The simulations are performed with the {\sc kardos} library, that employs adaptive finite elements in space and adaptive linearly implicit methods in time. The numerical results show that this adaptive method successfully solves these complex cardiac reaction-diffusion models on three-dimensional domains of moderate sizes. By automatically adapting the spatial meshes and time steps to the proper scales in each phase of the heartbeat, the method accurately resolves the evolution of the intra- and extra-cellular potentials, gating variables and ion concentrations during the excitation, plateau and recovery phases.

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Author:Piero Colli Franzone, Peter Deuflhard, Bodo Erdmann, Jens Lang, Luca Franco Pavarino
Document Type:ZIB-Report
Tag:adaptive finite elements; adaptive time integration; cardiac Bidomain and Monodomain models; reaction-diffusion equations
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Bxx Mathematical biology in general / 92B05 General biology and biomathematics
CCS-Classification:G. Mathematics of Computing / G.4 MATHEMATICAL SOFTWARE
Date of first Publication:2005/05/20
Series (Serial Number):ZIB-Report (05-30)
Published in:Appeared in: SIAM Journal on Scientific Computing vol. 28, issue 3, 2006, pp. 942-962