]. E. Acerbi, V. Chiadòpiat, G. Dal-maso, and D. Percivale, An extension theorem from connected sets, and homogenization in general periodic domains. Nonlinear Analysis: Theory, Methods & Applications, vol.18, issue.5, pp.481-496, 1992.
DOI : 10.1016/0362-546x(92)90015-7

R. Aliev and A. Panfilov, A simple two-variable model of cardiac excitation, Chaos, Solitons & Fractals, vol.7, issue.3, pp.293-301, 1996.
DOI : 10.1016/0960-0779(95)00089-5

G. Allaire, Homogenization and Two-Scale Convergence, SIAM Journal on Mathematical Analysis, vol.23, issue.6, pp.1482-1518, 1992.
DOI : 10.1137/0523084

URL : https://hal.archives-ouvertes.fr/hal-01111805

G. Allaire, A. Damlamian, and U. Hornung, Two-scale convergence on periodic surfaces and applications, Proceedings of the International Conference on Mathematical Modelling of Flow through Porous Media, 1995.

G. Allaire and F. Murat, Homogenization of the Neumann problem with nonisolated holes, Asymptotic Analysis, vol.7, issue.2, pp.81-95, 1993.

L. Ambrosio, P. Colli-franzone, and G. Savaré, On the asymptotic behaviour of anisotropic energies arising in the cardiac bidomain model. Interfaces and Free Boundaries, pp.213-266, 2000.

H. Ammari, J. Garnier, L. Giovangigli, W. Jing, and J. Seo, Spectroscopic imaging of a dilute cell suspension, Journal de Math??matiques Pures et Appliqu??es, vol.105, issue.5, pp.603-661, 2016.
DOI : 10.1016/j.matpur.2015.11.009

URL : https://hal.archives-ouvertes.fr/hal-01377780

M. Bendahmane and H. K. Karlsen, Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue. Networks and Heterogeneous Media, pp.185-218, 2006.

A. Bensoussan, J. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, 1978.
DOI : 10.1090/chel/374

M. Boulakia, M. A. Fernández, J. Gerbeau, and N. Zemzemi, A Coupled System of PDEs and ODEs Arising in Electrocardiograms Modeling, Applied Mathematics Research eXpress, vol.41, issue.5, 2008.
DOI : 10.1016/S0092-8240(03)00041-7

Y. Bourgault, Y. Coudì, and C. Pierre, Existence and uniqueness of the solution for the bidomain model used in cardiac electrophysiology, Nonlinear Analysis: Real World Applications, vol.10, issue.1, pp.458-482, 2009.
DOI : 10.1016/j.nonrwa.2007.10.007

URL : https://hal.archives-ouvertes.fr/hal-00865813

M. Briane, Three models of non periodic fibrous materials obtained by homogenization. RAIRO-Modélisation mathématique et analyse numérique, pp.759-775, 1993.

D. Cioranescu, A. Damlamian, P. Donato, G. Griso, and R. R. Zaki, The Periodic Unfolding Method in Domains with Holes, SIAM Journal on Mathematical Analysis, vol.44, issue.2, pp.718-760, 2010.
DOI : 10.1137/100817942

URL : https://hal.archives-ouvertes.fr/hal-00591632

D. Cioranescu and J. Saint-jean-paulin, Homogenization in open sets with holes, Journal of Mathematical Analysis and Applications, vol.71, issue.2, pp.590-607, 1979.
DOI : 10.1016/0022-247X(79)90211-7

D. Cioranescu and J. Saint-jean-paulin, Homogenization of Reticulated Structures, 1999.

P. Colli-franzone, L. F. Pavarino, and S. Scacchi, Mathematical Cardiac Electrophysiology , volume 13 of Modeling, Simulation and Applications, 2014.

P. , C. Franzone, and G. Savaré, Degenerate evolution systems modeling the cardiac electric field at micro and macroscopic level, Progress in Nonlinear Differential Equations and Their Applications, pp.49-78, 2002.

C. Corrado, J. Gerbeau, and P. Moireau, Identification of weakly coupled multiphysics problems. application to the inverse problem of electrocardiology, Journal of Computational Physics, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01091751

M. Courtemanche, R. J. Ramirez, and S. Nattel, Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model, American Journal of Physiology-Heart and Circulatory Physiology, vol.263, issue.32, pp.301-321, 1998.
DOI : 10.1016/S0006-3495(95)80271-7

K. Djabella, M. Landau, and M. Sorine, A two-variable model of cardiac action potential with controlled pacemaker activity and ionic current interpretation, 2007 46th IEEE Conference on Decision and Control, pp.5186-5191, 2007.
DOI : 10.1109/CDC.2007.4434970

S. S. Dragomir, Some Gronwall type inequalities and applications, Nova Science Pub Incorporated, 2003.

C. Lawrence and . Evans, Partial differential equations, 2010.

R. Fitzhugh, Impulses and Physiological States in Theoretical Models of Nerve Membrane, Biophysical Journal, vol.1, issue.6, pp.445-466, 1961.
DOI : 10.1016/S0006-3495(61)86902-6

S. Göktepe and E. Kuhl, Electromechanics of the heart: a unified approach to the strongly coupled excitation???contraction problem, Computational Mechanics, vol.104, issue.5, pp.227-243, 2010.
DOI : 10.1007/b96841

E. Grandi, S. V. Pandit, N. Voigt, A. J. Workman, D. Dobrev et al., Human Atrial Action Potential and Ca2+ Model: Sinus Rhythm and Chronic Atrial Fibrillation, Circulation Research, vol.109, issue.9, pp.1055-1066, 2011.
DOI : 10.1161/CIRCRESAHA.111.253955

E. Grandi, F. S. Pasqualini, and D. M. Bers, A novel computational model of the human ventricular action potential and Ca transient, Journal of Molecular and Cellular Cardiology, vol.48, issue.1, pp.112-121, 2010.
DOI : 10.1016/j.yjmcc.2009.09.019

P. E. Hand and C. S. Peskin, Homogenization of an Electrophysiological Model for??a??Strand of Cardiac Myocytes with Gap-Junctional and??Electric-Field Coupling, Bulletin of Mathematical Biology, vol.21, issue.8, pp.1408-1424, 2010.
DOI : 10.1016/0895-7177(91)90079-M

A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, vol.117, issue.4, pp.500-544, 1952.
DOI : 10.1113/jphysiol.1952.sp004764

O. Kavian, M. Legù-ebe, C. Poignard, and L. Weynans, ???Classical??? Electropermeabilization Modeling at the Cell Scale, Journal of Mathematical Biology, vol.1724, issue.4, pp.235-265, 2014.
DOI : 10.1016/j.bbagen.2005.05.006

J. Keener and J. Sneyd, Mathematical Physiology, 2004.
DOI : 10.1007/978-0-387-75847-3

J. T. Koivumäki, T. Korhonen, and P. Tavi, Impact of Sarcoplasmic Reticulum Calcium Release on Calcium Dynamics and Action Potential Morphology in Human Atrial Myocytes: A Computational Study, PLoS Computational Biology, vol.588, issue.1, p.1001067, 2011.
DOI : 10.1371/journal.pcbi.1001067.s008

K. Kunisch and A. Marica, Well-posedness for the Mitchell-Schaeffer model of the cardiac membrane, Research report, 2013.

J. Lions, Quelques méthodes de résolution desprobì emes aux limites non linéaires, 1969.

J. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, 1972.
DOI : 10.1007/978-3-642-65217-2

C. H. Luo and Y. Rudy, A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes, Circulation Research, vol.74, issue.6, pp.1071-1096, 1994.
DOI : 10.1161/01.RES.74.6.1071

M. M. Maleckar, J. L. Greenstein, N. A. Trayanova, and W. R. Giles, Mathematical simulations of ligand-gated and cell-type specific effects on the action potential of human atrium, Progress in biophysics and molecular biology, pp.161-170, 2008.
DOI : 10.1016/j.pbiomolbio.2009.01.010

Q. Marciniak-czochra and M. Ptashnyk, Derivation of a Macroscopic Receptor-Based Model Using Homogenization Techniques, SIAM Journal on Mathematical Analysis, vol.40, issue.1, pp.215-237, 2008.
DOI : 10.1137/050645269

W. Mclean, Strongly Elliptic systems and Boundary Integral equation, 2000.

C. C. Mitchell and D. G. Schaeffer, A two-current model for the dynamics of cardiac membrane, Bulletin of Mathematical Biology, vol.65, issue.5, pp.767-793, 2003.
DOI : 10.1016/S0092-8240(03)00041-7

Y. Mori, From three-dimensional electrophysiology to the cable model: an asymptotic study. arXiv preprint, 2009.

Y. Mori, J. W. Jerome, and C. S. Peskin, A three-dimensional model of cellular electrical activity, Bulletin of the Institute of Mathematics Academia Sinica, vol.2, issue.2, pp.367-390, 2007.

J. S. Nagumo, S. Arimoto, and S. Yoshizawa, An active pulse transmission line stimulating nerve axon, Proceedings of the IEEE, pp.2061-2071, 1962.
DOI : 10.1109/jrproc.1962.288235

J. C. Neu and W. Krassowska, Homogenization of syncytial tissues, Critical Reviews in Biomedical Engineering, vol.21, issue.2, pp.137-199, 1993.

M. Neuss-radu, Some extensions of two-scale convergence Comptes rendus de l'Académie des sciences, Mathématique, vol.1, issue.3229, pp.899-904, 1996.

G. Nguetseng, A General Convergence Result for a Functional Related to the Theory of Homogenization, SIAM Journal on Mathematical Analysis, vol.20, issue.3, pp.608-623, 1989.
DOI : 10.1137/0520043

D. Noble, A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action and pacemaker potentials, The Journal of Physiology, vol.160, issue.2, pp.317-352, 1962.
DOI : 10.1113/jphysiol.1962.sp006849

A. Nygren, C. Fiset, L. Firek, J. W. Clark, D. S. Lindblad et al., Mathematical Model of an Adult Human Atrial Cell : The Role of K+ Currents in Repolarization, Circulation Research, vol.82, issue.1, pp.63-81, 1998.
DOI : 10.1161/01.RES.82.1.63

T. O-'hara, L. Virág, A. Varró, and Y. Rudy, Simulation of the Undiseased Human Cardiac Ventricular Action Potential: Model Formulation and Experimental Validation, PLoS Computational Biology, vol.93, issue.Pt2, p.1002061, 2011.
DOI : 10.1371/journal.pcbi.1002061.s001

D. O-'regan, Existence Theory for Nonlinear Ordinary Differential Equations, 1997.

M. Pennacchio, G. Savaré, and P. Colli-franzone, Multiscale Modeling for the Bioelectric Activity of the Heart, SIAM Journal on Mathematical Analysis, vol.37, issue.4, pp.1333-1370, 2005.
DOI : 10.1137/040615249

M. Ptashnyk, Multiscale Modelling and Analysis of Signalling Processes in Tissues with Non-Periodic Distribution of Cells, Vietnam Journal of Mathematics, vol.91, issue.1-2, pp.295-316, 2017.
DOI : 10.1136/hrt.2005.072280

G. Richardson and J. Chapman, Derivation of the Bidomain Equations for a Beating Heart with a General Microstructure, SIAM Journal on Applied Mathematics, vol.71, issue.3, pp.657-675, 2011.
DOI : 10.1137/090777165

M. Rioux and Y. Bourgault, A predictive method allowing the use of a single ionic model in numerical cardiac electrophysiology, ESAIM: Mathematical Modelling and Numerical Analysis, vol.47, issue.4, pp.987-1016, 2013.
DOI : 10.1007/s11071-007-9202-9

J. Rogers and A. Mcculloch, A collocation-Galerkin finite element model of cardiac action potential propagation, IEEE Transactions on Biomedical Engineering, vol.41, issue.8, pp.41743-757, 1994.
DOI : 10.1109/10.310090

F. B. Sachse, Computational Cardiology: Modeling of Anatomy, Electrophysiology and Mechanics, 2004.
DOI : 10.1007/b96841

S. Sanfelici, Convergence of the Galerkin approximation of a degenerate evolution problem in electrocardiology, Numerical Methods for Partial Differential Equations, vol.5, issue.2, pp.218-240, 2002.
DOI : 10.1002/num.1000

R. E. Showalter, Monotone operators in Banach space and nonlinear partial differential equations, American Mathematical Soc, vol.49, 2013.
DOI : 10.1090/surv/049

J. Sundnes, G. T. Lines, X. Cai, B. F. Nielsen, K. A. Mardal et al., Computing the Electrical Activity in the Heart, of Monographs in Computational Science and Engineering, 2006.

K. H. Ten-tusscher, D. Noble, P. J. Noble, and A. V. Panfilov, A model for human ventricular tissue, American Journal of Physiology-Heart and Circulatory Physiology, vol.286, issue.4, pp.1573-1589, 2004.
DOI : 10.1152/ajpheart.2000.278.5.H1671

K. H. Tusscher and A. V. Panfilov, Alternans and spiral breakup in a human ventricular tissue model, American Journal of Physiology-Heart and Circulatory Physiology, vol.291, issue.3, pp.1088-1100, 2006.
DOI : 10.1016/j.jacc.2005.05.074

L. Tung, A bi-domain model for describing ischemic myocardial d-c potentials, 1978.

M. Veneroni, Reaction???diffusion systems for the microscopic cellular model of the cardiac electric field, Mathematical Methods in the Applied Sciences, vol.13, issue.14, pp.1631-1661, 2006.
DOI : 10.1007/978-1-4612-4838-5

M. Veneroni, Reaction???diffusion systems for the macroscopic bidomain model of the cardiac electric field, Nonlinear Analysis: Real World Applications, vol.10, issue.2, pp.849-868, 2009.
DOI : 10.1016/j.nonrwa.2007.11.008

M. Wilhelms, H. Hettmann, M. M. Maleckar, J. T. Koivumäki, O. Dössel et al., Benchmarking electrophysiological models of human atrial myocytes, Frontiers in Physiology, vol.3, issue.487, p.2013
DOI : 10.3389/fphys.2012.00487