T. Arbogast, Gravitational forces in dual-porosity systems: I. model derivation by homogenization, Transport in Porous Media [2] , Gravitational forces in dual-porosity systems: Ii. computational validation of the homogenized model, Transport in Porous Media, pp.179-203, 1993.

I. Aslund, A. Nowacka, M. Nilsson, and D. Topgaard, Filter-exchange PGSE NMR determination of cell membrane permeability, Journal of Magnetic Resonance, vol.200, issue.2, pp.291-295, 2009.
DOI : 10.1016/j.jmr.2009.07.015

Y. Assaf, T. Blumenfeld-katzir, Y. Yovel, and P. J. Basser, Axcaliber: A method for measuring axon diameter distribution from diffusion MRI, Magnetic Resonance in Medicine, vol.14, issue.6, pp.1347-1354, 2008.
DOI : 10.1002/mrm.21577

A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic analysis for periodic structures, de Studies in Mathematics and its Applications, 1978.

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

S. Chabert, N. Molko, Y. Cointepas, P. L. Roux, and D. L. Bihan, Diffusion tensor imaging of the human optic nerve using a non-CPMG fast spin echo sequence, Journal of Magnetic Resonance Imaging, vol.111, issue.2, pp.22-307, 2005.
DOI : 10.1002/jmri.20383
URL : https://hal.archives-ouvertes.fr/hal-00349673

H. Cheng and S. Torquato, Effective conductivity of periodic arrays of spheres with interfacial resistance, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.453, issue.1956, pp.145-161, 1997.
DOI : 10.1098/rspa.1997.0009

D. Cioranescu, A. Damlamian, and G. Griso, The Periodic Unfolding Method in Homogenization, SIAM Journal on Mathematical Analysis, vol.40, issue.4, pp.1585-1620, 2012.
DOI : 10.1137/080713148
URL : https://hal.archives-ouvertes.fr/hal-00693080

C. A. Clark and D. L. Bihan, Water diffusion compartmentation and anisotropy at high b values in the human brain, Magnetic Resonance in Medicine, vol.9, issue.6, pp.852-859, 2000.
DOI : 10.1002/1522-2594(200012)44:6<852::AID-MRM5>3.0.CO;2-A
URL : https://hal.archives-ouvertes.fr/hal-00349825

J. Coatléven, Mathematical justification of macroscopic models for diffusion MRI through the periodic unfolding method, Asymptotic Analysis, vol.93, issue.3, 2012.
DOI : 10.3233/ASY-151294

T. F. Coleman and Y. Li, On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds, Mathematical Programming, vol.51, issue.1, pp.189-224, 1994.
DOI : 10.1007/BF01582221

R. Dautray and J. Lions, Mathematical analysis and numerical methods for science and technology, 1993.

E. Fieremans, D. S. Novikov, J. H. Jensen, and J. A. Helpern, Monte Carlo study of a two-compartment exchange model of diffusion, NMR in Biomedicine, vol.436, issue.7, pp.711-724, 2010.
DOI : 10.1002/nbm.1577

K. D. Harkins, J. Galons, T. W. Secomb, and T. P. Trouard, Assessment of the effects of cellular tissue properties on ADC measurements by numerical simulation of water diffusion, Magnetic Resonance in Medicine, vol.60, issue.6, pp.1414-1422, 2009.
DOI : 10.1002/mrm.22155

D. P. Hasselman and L. F. Johnson, Effective Thermal Conductivity of Composites with Interfacial Thermal Barrier Resistance, Journal of Composite Materials, vol.21, issue.6, pp.508-515, 1987.
DOI : 10.1177/002199838702100602

B. Hellwig, A quantitative analysis of the local connectivity between pyramidal neurons in layers 2/3 of the rat visual cortex, Biological Cybernetics, vol.82, issue.2, pp.111-121, 2000.
DOI : 10.1007/PL00007964

A. Mark, D. K. Horsfield, and . Jones, Applications of diffusion-weighted and diffusion tensor mri to white matter diseases, a review, NMR Biomed, vol.15, pp.570-577, 2002.

J. H. Jensen, J. A. Helpern, A. Ramani, H. Lu, and K. Kaczynski, Diffusional kurtosis imaging: The quantification of non-gaussian water diffusion by means of magnetic resonance imaging, Magnetic Resonance in Medicine, vol.126, issue.6, pp.1432-1440, 2005.
DOI : 10.1002/mrm.20508

N. Sune, C. D. Jespersen, L. Kroenke, J. J. Stergaard, D. A. Ackerman et al., Modeling dendrite density from magnetic resonance diffusion measurements, NeuroImage, pp.34-1473, 2007.

J. Karger, H. Pfeifer, and W. Heinik, Principles and application of self-diffusion measurements by nuclear magnetic resonance, Advances in magnetic resonance, pp.1-89, 1988.

L. Latour, P. Svoboda, C. Mitra, and . Sotak, Time-dependent diffusion of water in a biological model system., Proceedings of the National Academy of Sciences, pp.91-1229, 1994.
DOI : 10.1073/pnas.91.4.1229

D. Le-bihan and H. , Diffusion MRI at 25: Exploring brain tissue structure and function, NeuroImage, vol.61, issue.2, pp.61-324, 2012.
DOI : 10.1016/j.neuroimage.2011.11.006

J. Lee and C. S. Springer, Effects of equilibrium exchange on diffusion-weighted NMR signals: The diffusigraphic ?shutter-speed?, Magnetic Resonance in Medicine, vol.41, issue.3, pp.450-458, 2003.
DOI : 10.1002/mrm.10402

R. L. Magin, O. Abdullah, D. Baleanu, and X. Zhou, Anomalous diffusion expressed through fractional order differential operators in the Bloch???Torrey equation, Journal of Magnetic Resonance, vol.190, issue.2, pp.255-270, 2008.
DOI : 10.1016/j.jmr.2007.11.007

S. E. Maier, P. Bogner, G. Bajzik, H. Mamata, Y. Mamata et al., Normal Brain and Brain Tumor: Multicomponent Apparent Diffusion Coefficient Line Scan Imaging, Radiology, vol.219, issue.3, pp.219-842, 2001.
DOI : 10.1148/radiology.219.3.r01jn02842

C. Meier, W. Dreher, and D. Leibfritz, Diffusion in compartmental systems. I. A comparison of an analytical model with simulations, Magnetic Resonance in Medicine, vol.40, issue.3, pp.500-509, 2003.
DOI : 10.1002/mrm.10557

R. V. Mulkern, H. Gudbjartsson, C. Westin, H. P. Zengingonul, W. Gartner et al., Multi-component apparent diffusion coefficients in human brain, NMR in Biomedicine, vol.112, issue.1, pp.12-51, 1999.
DOI : 10.1002/(SICI)1099-1492(199902)12:1<51::AID-NBM546>3.0.CO;2-E

T. Niendorf, R. M. Dijkhuizen, and D. G. Norris, Biexponential diffusion attenuation in various states of brain tissue: Implications for diffusion-weighted imaging, Magnetic Resonance in Medicine, vol.32, issue.6, pp.847-857, 1996.
DOI : 10.1002/mrm.1910360607

S. Dmitry, E. Novikov, J. H. Fieremans, J. A. Jensen, and . Helpern, Random walks with barriers, Nat Phys, vol.7, pp.508-514, 2011.

J. Pfeuffer, U. Flgel, W. Dreher, and D. Leibfritz, Restricted diffusion and exchange of intracellular water: theoretical modelling and diffusion time dependence of1H NMR measurements on perfused glial cells, NMR in Biomedicine, vol.11, issue.1, pp.19-31, 1998.
DOI : 10.1002/(SICI)1099-1492(199802)11:1<19::AID-NBM499>3.0.CO;2-O

W. S. Price, Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part 1. Basic theory, Concepts in Magnetic Resonance, vol.9, issue.5, pp.299-336, 1997.
DOI : 10.1002/(SICI)1099-0534(1997)9:5<299::AID-CMR2>3.0.CO;2-U

J. D. Quirk, G. L. Bretthorst, T. Q. Duong, A. Z. Snyder, C. S. Springer et al., Equilibrium water exchange between the intra- and extracellular spaces of mammalian brain, Magnetic Resonance in Medicine, vol.256, issue.3, pp.50-493, 2003.
DOI : 10.1002/mrm.10565

Y. Roth, . Ocherashvilli, . Daniels, . Ruizcabello, . Maier et al., Quantification of water compartmentation in cell suspensions by diffusion-weighted and T2-weighted MRI, Magnetic Resonance Imaging, vol.26, issue.1, pp.88-102, 2008.
DOI : 10.1016/j.mri.2007.04.013

D. Schnapauff, M. Zeile, M. B. Niederhagen, B. Fleige, P. Tunn et al., Diffusion-weighted echo-planar magnetic resonance imaging for the assessment of tumor cellularity in patients with soft-tissue sarcomas, Journal of Magnetic Resonance Imaging, vol.130, issue.6, pp.1355-1359, 2009.
DOI : 10.1002/jmri.21755

N. Pabitra, P. J. Sen, and . Basser, A model for diffusion in white matter in the brain, Biophys J, vol.89, pp.2927-2938, 2005.

G. J. Stanisz, G. A. Wright, R. M. Henkelman, and A. Szafer, An analytical model of restricted diffusion in bovine optic nerve, Magnetic Resonance in Medicine, vol.47, issue.1, pp.103-111, 1997.
DOI : 10.1002/mrm.1910370115

E. O. Stejskal and J. E. Tanner, Spin Diffusion Measurements: Spin Echoes in the Presence of a Time???Dependent Field Gradient, The Journal of Chemical Physics, vol.42, issue.1, pp.42-288, 1965.
DOI : 10.1063/1.1695690

T. Sugahara, Y. Korogi, M. Kochi, I. Ikushima, Y. Shigematu et al., Usefulness of diffusion-weighted MRI with echo-planar technique in the evaluation of cellularity in gliomas, Journal of Magnetic Resonance Imaging, vol.16, issue.1, pp.53-60, 1999.
DOI : 10.1002/(SICI)1522-2586(199901)9:1<53::AID-JMRI7>3.0.CO;2-2

S. Torquato and M. D. Rintoul, Effect of the Interface on the Properties of Composite Media, Physical Review Letters, vol.75, issue.22, p.4067, 1995.
DOI : 10.1103/PhysRevLett.75.4067

H. Torrey, Bloch Equations with Diffusion Terms, Physical Review, vol.104, issue.3, pp.563-565, 1956.
DOI : 10.1103/PhysRev.104.563

Y. Tsushima, A. Takahashi-taketomi, and K. Endo, Magnetic resonance (MR) differential diagnosis of breast tumors using apparent diffusion coefficient (ADC) on 1.5-T, Journal of Magnetic Resonance Imaging, vol.198, issue.2, pp.249-255, 2009.
DOI : 10.1002/jmri.21854

A. R. Waldeck, P. W. Kuchel, A. J. Lennon, and B. E. Chapman, NMR diffusion measurements to characterise membrane transport and solute binding, Progress in Nuclear Magnetic Resonance Spectroscopy, vol.30, issue.1-2, pp.39-68, 1997.
DOI : 10.1016/S0079-6565(96)01034-5

S. Warach, D. Chien, W. Li, M. Ronthal, and R. R. Edelman, Fast magnetic resonance diffusion-weighted imaging of acute human stroke, Neurology, vol.42, issue.9, pp.42-1717, 1992.
DOI : 10.1212/WNL.42.9.1717

J. Xu, J. Does, and . Gore, Numerical study of water diffusion in biological tissues using an improved finite difference method., Physics in medicine and biology, p.pp. ?, 2007.