A 3D Reaction-Diffusion System Describing Bidomain Calcium Dynamics in Cardiac Cell

Mostafa Bendahmane (1) , Elmahdi Erraji (2) , Fahd Karami (2)

1 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
2 Ecole Supérieure de Technologie d'Essaouira

We are interested in modeling the interaction of calcium dynamics in a medium including sarcolemma and sarcoplasmic reticulum. The governing equations consist of a nonlinear reaction-diffusion system representing the various calcium fluxes and theirs buffers in the two media. We address the question of existence of weak solutions by using a fixed-point approach. We propose a finite element method for this system, we establish the existence of the discrete solution, and we show that the discrete solution generated by the given scheme converges to the corresponding weak solution for the model studied. Finally, we give some 2D and 3D numerical examples to our model. Mathematics Subject Classification. 92C50, 65M60, 65N12, 92C40. The dates will be set by the publisher.

Mots clés: Medical modeling; Interface problem; Convergence; Anomalous diffusion; Finite element; Calcium dynamics

Domaines: Mathématiques [math]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Sciences du Vivant [q-bio]; Médecine humaine et pathologie

Mostafa Bendahmane, Elmahdi Erraji, Fahd Karami. A 3D Reaction-Diffusion System Describing Bidomain Calcium Dynamics in Cardiac Cell. Mathematical Modelling of Natural Phenomena, 2019, 14 (2), pp.27. ⟨10.1051/mmnp/2018064⟩. ⟨hal-01680574⟩