Math. Model. Nat. Phenom.
Volume 14, Number 2, 2019
Mathematical modelling in cardiology
|Number of page(s)||27|
|Published online||15 February 2019|
A 3D reaction–diffusion system describing calcium dynamics in cardiac cell★
Institut de mathématique de Bordeaux (IMB) et l’institut de rythmologie et modélisation cardiaque (Liryc), université de Bordeaux et INRIA-Carmen Bordeaux Sud-Ouest,
2 Ecole Supérieure de Technologie d’Essaouira, Université Cadi Ayyad, B.P. 383 Essaouira El Jadida, Essaouira, Morocco, Morocco.
* Corresponding author: firstname.lastname@example.org
Accepted: 10 October 2018
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
Key words: Finite element / calcium dynamics / anomalous diffusion / convergence / interface problem / medical modeling
© EDP Sciences, 2019
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.