V. Anaya, M. Bendahmane, D. Mora, and R. R. Baier, On a vorticity-based formulation for reaction-diffusion-Brinkman systems, Networks and Heterogeneous Media, vol.13, issue.1, pp.69-94, 2018.
DOI : 10.3934/nhm.2018004

URL : https://hal.archives-ouvertes.fr/hal-01407343

D. M. Bers, Excitation-contraction coupling and cardiac contractile force, 2001.

H. Brezis, Analyse fonctionnelle, théorie et applications, 1983.

R. M. Centor, J. J. Allison, N. W. Weissman, J. Canto, G. R. Heudebert et al., Diffusion of troponin testing in unstable angina patients: adoption prior to guideline release, Journal of Clinical Epidemiology, vol.56, issue.12, pp.1236-1243, 2003.

J. Chai, J. Hake, N. Wu, M. Wen, X. Cai et al., Towards simulation of subcellular calcium dynamics at nanometre resolution, The International Journal of High Performance Computing Applications, vol.29, issue.1, pp.51-63, 2013.
DOI : 10.1177/1094342013514465

J. Crank, The Mathematics of Diffusion. Brunel University Uxbridge second edition, 1975.

X. Chen, L. Guo, J. Kang, Y. Huo, S. Wang et al., Calcium waves initiating from the anomalous subdiffusive calcium sparks, Journal of The Royal Society Interface, vol.11, issue.91, p.20130934, 2013.
DOI : 10.1098/rsif.2013.0934

URL : http://rsif.royalsocietypublishing.org/content/11/91/20130934.full.pdf

B. S. Donahue and R. Abercrombie, Free diffusion coefficient of ionic calcium in cytoplasm, Cell Calcium, vol.8, issue.6, pp.437-448, 1987.
DOI : 10.1016/0143-4160(87)90027-3

E. Flauraud, F. Nataf, and F. Willien, Optimized interface conditions in domain decomposition methods for problems with extreme contrasts in the coefficients, Journal of Computational and Applied Mathematics, vol.189, issue.1, pp.539-554, 2006.

N. A. Gal and D. Weihs, Experimental evidence of strong anomalous diffusion in living cells Physical Review, vol.81, 2010.

J. Hake, A. G. Edwards, Z. Yu, P. M. Kekenes-huskey, A. P. Michailova et al., Modelling cardiac calcium sparks in a three-dimensional reconstruction of a calcium release unit, Journal of Physiology, vol.590, issue.18, pp.4403-4425, 2012.

D. E. Hurtado, S. Castro, and A. Gizzi, Computational modeling of non-linear diffusion in cardiac electrophysiology: A novel porous-medium approach, Computer Methods in Applied Mechanics and Engineering, vol.300, pp.70-83, 2016.

K. H. Jaeger, An Investigation of Necessary Grid Resolution for Numerical Simulations of Calcium Dynamics in Cardiac Cells, 2015.

T. Kenakin, The mass action equation in pharmacology, British Journal of Clinical Pharmacology, vol.81, issue.1, pp.41-51, 2016.
DOI : 10.1111/bcp.12810

URL : http://onlinelibrary.wiley.com/doi/10.1111/bcp.12810/pdf

O. A. Ladyzhenskaya, V. Solonnikov, and N. Uralceva, Linear and quasi-linear equations of parabolic type, Transl. AMS, vol.23, 1968.

J. E. Lagnese and G. Leugering, Dynamic Domain Decomposition in Approximate and Exact Boundary Control in Problems of Transmission for Wave Equations, Siam Journal on Control and Optimization, vol.38, issue.2, pp.503-537, 2000.

G. Langer and A. Peskoff, Calcium Concentration and Movement in the Diadic Cleft Space of the Cardiac Ventricular Cell, Biophysical Journal, vol.70, issue.3, pp.1169-1182, 1996.

S. E. Lehnart, X. H. Wehrnes, A. Kushnir, and A. R. Marks, Cardiac Ryanodine Receptor Function and Regulation in Heart Disease, Annals of the New York Academy of Sciences, vol.1015, issue.1, pp.144-59, 2004.

W. E. Louch, J. Hake, G. F. Jølle, H. K. Mørk, I. Sjaastad et al., Control of Ca2+ Release by Action Potential Configuration in Normal and Failing Murine Cardiomyocytes, Biophysical Journal, vol.99, issue.5, pp.1377-1386, 2010.

A. R. Marks, Calcium and the heart : a question of life and death, Journal of Clinical Investigation, vol.111, issue.5, pp.597-600, 2003.

U. M. Mayer, A. Gerstenberger, and W. A. Wall, Interface handling for three-dimensional higher-order XFEM-computations in fluidstructure interaction, International Journal for Numerical Methods in Engineering, vol.79, issue.7, pp.846-869, 2009.

L. Nilsson and . Stenström, Gas diffusion through sheets of fibrous porous media, Chemical Engineering Science, vol.50, issue.3, pp.361-371, 1995.

E. C. Perin, G. V. Silva, and T. J. Willerson, An Essential Guide to Cardiac Cell Therapy, 2006.

A. Peskoff and G. Langer, Calcium Concentration and Movement in the Ventricular Cardiac Cell during an ExcitationContraction Cycle, Biophysical Journal, vol.74, issue.1, pp.153-74, 1998.

A. Peskoff, J. Posit, and G. Langer, sarcolemmal calcium binding sites in heart: II. Mathematical model for diffusion of calcium released from the sarcoplasmic reticulum into the diadic region, Journal of Membrane Biology, vol.129, issue.1, pp.59-69, 1992.

E. Picht, A. V. Zima, T. R. Shannon, A. M. Duncan, L. A. Blatter et al., Dynamic calcium movement inside cardiac sarcoplasmic reticulum during release, Circulation Research, vol.108, issue.7, pp.847-856, 2011.

,. Pods, J. Schönke, J. Bastian, and P. , Electrodiffusion Models of Neurons and Extracellular Space Using the Poisson-NernstPlanck Equations-Numerical Simulation of the Intra and Extracellular Potential for an Axon Model, Biophysical Journal, vol.105, issue.1, pp.242-54, 2013.

I. Rubinstein, Electro-Diffusion of ions, Society for Industrial and Applied Mathematics, 1990.

N. J. Severs, A. F. Bruce, E. Dupont, and S. Rothery, Remodelling of gap junctions and connexin expression in diseased myocardium Cardiovascular research Review, vol.80, pp.9-19, 2008.

J. Simon, Compact sets in the space L p (0, T ; B), Ann. Mat. Pura Appl, vol.146, issue.4, pp.65-96, 1987.

E. A. Sobie, K. W. Dilly, J. Dos-santos-cruz, W. J. Lederer, and M. Saleet-jafri, Termination of Cardiac Ca2+ Sparks: An Investigation Mathematical Model of Calcium-Induced Calcium Release, Biophysical Journal, vol.83, issue.1, pp.59-78, 2002.

L. Tao and H. Yong, A generalization of discrete Gronwall inequality and its application to weakly singular Volterra integral equation of the second kind, Journal of Mathematical Analysis and Applications, vol.282, issue.1, p.62, 2003.

J. A. Vest, X. H. Wehrnes, S. R. Reiken, S. E. Lehnart, D. Dobrev et al., Defective cardiac ryanodine receptor regulation during atrial fibrillation, Circulation, vol.111, issue.26, pp.2025-2032, 2005.

G. Williams, A. Chikando, H. M. Tuan, E. Sobie, W. Lederer et al., Dynamics of Calcium Sparks and Calcium Leak in the Heart, Biophysical Journal, vol.101, issue.6, pp.1287-96, 2011.