A surface-based electrophysiology model relying on asymptotic analysis and motivated by cardiac atria modeling

Dominique Chapelle 1, * Annabelle Collin 1 Jean-Frédéric Gerbeau 2
* Corresponding author
1 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
2 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : Computational electrophysiology is a very active field with tremendous potential in medical applications, albeit leads to highly intensive simulations. We here propose a surface-based electrophysiology formulation, motivated by the modeling of thin structures such as cardiac atria, which greatly reduces the size of the computational models. Moreover, our model is specifically devised to retain the key features associated with the anisotropy in the diffusion effects induced by the fiber architecture, with rapid variations across the thickness which cannot be adequately represented by naive averaging strategies. Our proposed model relies on a detailed asymptotic analysis in which we identify a limit model and establish strong convergence results. We also provide detailed numerical assessments which confirm an excellent accuracy of the surface-based model -- compared with the reference 3D model -- including in the representation of a complex phenomenon, namely, spiral waves.
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Dominique Chapelle, Annabelle Collin, Jean-Frédéric Gerbeau. A surface-based electrophysiology model relying on asymptotic analysis and motivated by cardiac atria modeling. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2013, 23 (14), pp.2749-2776. ⟨10.1142/S0218202513500450⟩. ⟨hal-00723691v3⟩

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