Responsible: Peter Deuflhard, Bodo Erdmann, Rainer Roitzsch, Martin Weiser

Cooperation: Jens Lang (Technical University, Darmstadt, Germany)
Piero Colli Franzone, Simone Scacchi (University Pavia, Italy)
Aslak Tveito, Glenn Terje Lines (Simula Research Laboratory, Norway)

Literature: P. Colli Franzone, P. Deuflhard, B. Erdmann, J. Lang, L. Pavarino, Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology, SIAM J. Sc. Comp.,  Vol .28,   942-962 (2006)
P. Deuflhard, B. Erdmann, R. Roitzsch, G.T. Lines, Adaptive Finite Element Simulation of Ventricular Dynamics, J. Computing and Visualization in Science (2007), accepted for publication

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 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.
Arrhythmic heart dynamics at 580ms
Adaptive mesh at 580ms

Last update: July 2007
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