I. Babu?ka, Error-bounds for finite element method, Numerische Mathematik, vol.3, issue.1-3, pp.322-333, 1971.
DOI : 10.1007/BF02165003

F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers, Revue fran??aise d'automatique, informatique, recherche op??rationnelle. Analyse num??rique, vol.8, issue.R2, pp.129-151, 1974.
DOI : 10.1051/m2an/197408R201291

D. Chapelle, J. Gerbeau, and J. , A poroelastic model valid in large strains with applications to perfusion in cardiac modeling, Computational Mechanics, vol.130, issue.5, pp.91-10110, 2010.
DOI : 10.1007/s00466-009-0452-x

URL : https://hal.archives-ouvertes.fr/hal-00592688

R. Cimrman and E. Rohan, On modelling the parallel diffusion flow in deforming porous media, Mathematics and Computers in Simulation, vol.76, issue.1-3, pp.34-43, 2007.
DOI : 10.1016/j.matcom.2007.01.034

A. N. Cookson, J. Lee, C. Michler, R. Chabiniok, E. Hyde et al., A novel porous mechanical framework for modelling the interaction between coronary perfusion and myocardial mechanics, Journal of Biomechanics, vol.45, issue.5, pp.1-6, 1992.
DOI : 10.1016/j.jbiomech.2011.11.026

N. Smith, euHeart: personalized and integrated cardiac care using patient-specific cardiovascular modelling, Interface Focus, vol.41, issue.10, 2011.
DOI : 10.1016/j.jbiomech.2008.04.035

URL : https://hal.archives-ouvertes.fr/inria-00616189

A. Goyal, J. Lee, P. Lamata, J. Van-den-wijngaard, P. Van-horssen et al., Model-Based Vasculature Extraction From Optical Fluorescence Cryomicrotome Images, IEEE Transactions on Medical Imaging, vol.32, issue.1
DOI : 10.1109/TMI.2012.2227275

T. J. Hughes, A. Masud, and J. Wan, A stabilized mixed discontinuous Galerkin method for Darcy flow, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.25-28, pp.3347-3381, 2006.
DOI : 10.1016/j.cma.2005.06.018

J. M. Huyghe, T. Arts, D. H. Van-campen, and R. S. Reneman, Porous medium finite element model of the beating left ventricle, American Journal of Physiology -Heart and Circulatory Physiology, vol.262, pp.1256-1267, 1992.

G. S. Kassab, C. A. Rider, N. J. Tang, and Y. C. Fung, Morphometry of pig coronary arterial trees, American Journal of Physiology -Heart and Circulatory Physiology, vol.265, issue.1, pp.350-365, 1993.

J. Lee, S. Niederer, D. Nordsletten, I. Le-grice, B. Smail et al., Coupling contraction, excitation, ventricular and coronary blood flow across scale and physics in the heart, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.192, issue.Pt 2, pp.2311-2331, 2009.
DOI : 10.1152/physrev.00029.2005

A. F. Loula, F. A. Rochinha, and M. A. Murad, Higher-order gradient post-processings for second-order elliptic problems, Computer Methods in Applied Mechanics and Engineering, vol.128, issue.3-4, pp.361-381, 1995.
DOI : 10.1016/0045-7825(95)00885-3

S. M. Malta, A. F. Loula, and E. L. Garcia, Numerical analysis of a stabilized finite element method for tracer injection simulations, Computer Methods in Applied Mechanics and Engineering, vol.187, issue.1-2, pp.119-136, 2000.
DOI : 10.1016/S0045-7825(99)00113-9

A. Masud and T. J. Hughes, A stabilized mixed finite element method for Darcy flow, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.39-40, pp.4341-4370, 2002.
DOI : 10.1016/S0045-7825(02)00371-7

E. Rohan, R. Cimrman, and V. Luke?, Numerical modelling and homogenized constitutive law of large deforming fluid saturated heterogeneous solids, Computers & Structures, vol.84, issue.17-18, pp.1095-1114, 2006.
DOI : 10.1016/j.compstruc.2006.01.008

N. P. Smith, A computational study of the interaction between coronary blood flow and myocardial mechanics, Physiological Measurement, vol.25, issue.4, p.863, 2004.
DOI : 10.1088/0967-3334/25/4/007

N. P. Smith and G. S. Kassab, Analysis of coronary blood flow interaction with myocardial mechanics based on anatomical models, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.359, issue.1783, pp.1251-1262, 2001.
DOI : 10.1098/rsta.2001.0829

J. A. Spaan, R. Ter-wee, J. W. Van-teeffelen, G. Streekstra, M. Siebes et al., Visualisation of intramural coronary vasculature by an imaging cryomicrotome suggests compartmentalisation of myocardial perfusion areas, Medical and Biological Engineering and Computing, vol.71, issue.4, pp.431-435, 2005.
DOI : 10.1007/BF02344722

P. Van-horssen, M. Siebes, I. Hoefer, J. A. Spaan, and J. P. Van-den-wijngaard, Improved detection of fluorescently labeled microspheres and vessel architecture with an imaging cryomicrotome, Medical & Biological Engineering & Computing, vol.269, issue.8, pp.735-744, 2010.
DOI : 10.1007/s11517-010-0652-8

W. J. Vankan, J. M. Huyghe, M. R. Drost, J. D. Janssen, and A. Huson, A FINITE ELEMENT MIXTURE MODEL FOR HIERARCHICAL POROUS MEDIA, International Journal for Numerical Methods in Engineering, vol.96, issue.2, pp.193-210, 1997.
DOI : 10.1002/(SICI)1097-0207(19970130)40:2<193::AID-NME55>3.0.CO;2-9

N. Westerhof, C. Boer, R. R. Lamberts, and P. Sipkema, Cross-Talk Between Cardiac Muscle and Coronary Vasculature, Physiological Reviews, vol.86, issue.4, pp.1263-1308, 2006.
DOI : 10.1152/physrev.00029.2005