Biomedical Engineering Reference
In-Depth Information
nization methods and asymptotic expansions. The models of cardiac tissue include
the anisotropic Bidomain and Monodomain models, as well as the Eikonal and vari-
ous relaxed approximations, while the ionic cellular models include Luo-Rudy-type
models as well as simpler FitzHugh-Nagumo variants. We have also presented ad-
vanced numerical methods for discretizing and solving numerically these complex
models on three-dimensional domains, using adaptive and parallel techniques. The
resulting solvers are able to reproduce complete normal heartbeat phenomena in
large ventricular volumes accurately, simulating e.g. various potential waveforms,
activation and recovery fronts, and action potential dispersion. The solvers can also
simulate re-entry phenomena such as spiral and scroll waves, their breakup and the
transition to electrical turbulence. In this work, we have applied the parallel Bido-
main solver to study the three-dimensional details of the mechanisms of cardiac exci-
tation elicited by unipolar extracellular stimuli of anodal type, yielding new insights
on the origin of excitation based on the virtual electrode polarization. Current work
is investigating the role of inhomogeneities of the tissue and heterogeneity of the
cellular membrane properties, due e.g. to ischemia, and the coupling of electrocar-
diological models with mechanical and fluid dynamic models, with the future goal
of integrating them with cardiovascular and circulatory models.
Acknowledgements.
The authors would like to thank Bruno Taccardi for introducing them to the
field of Mathematical Physiology and for many stimulating discussions.
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