D. , L. Bihan, E. Breton, D. Lallemand, P. Grenier et al., MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders, Radiology, vol.161, pp.401-407, 1986.
URL : https://hal.archives-ouvertes.fr/hal-00349714

M. Moseley, J. Kucharczyk, J. Mintorovitch, Y. Cohen, J. Kurhanewicz et al., Diffusion-weighted MR imaging of acute stroke: correlation with T2-weighted and magnetic susceptibilityenhanced MR imaging in cats, AJNR Am J Neuroradiol, vol.11, pp.423-429, 1990.

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, p.1717, 1992.
DOI : 10.1212/WNL.42.9.1717

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

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

S. E. Maier, Y. Sun, and R. V. Mulkern, Diffusion imaging of brain tumors, NMR in Biomedicine, vol.199, issue.7, pp.849-864, 2010.
DOI : 10.1002/nbm.1544

D. , L. Bihan, and H. Johansen-berg, Diffusion MRI at 25: Exploring brain tissue structure and function, NeuroImage, vol.61, pp.324-341, 2012.

M. Lazar, Mapping brain anatomical connectivity using white matter tractography, NMR in Biomedicine, vol.7, issue.7, pp.821-835, 2010.
DOI : 10.1002/nbm.1579

D. Lebihan, S. Urayama, T. Aso, T. Hanakawa, and H. Fukuyama, Direct and fast detection of neuronal activation in the human brain with diffusion MRI, Proceedings of the National Academy of Sciences, vol.103, issue.21, pp.8263-8268, 2006.
DOI : 10.1073/pnas.0600644103

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

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. 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

L. L. Latour, K. Svoboda, P. P. Mitra, and C. H. Sotak, Time-dependent diffusion of water in a biological model system., Proceedings of the National Academy of Sciences 91, pp.1229-1233, 1994.
DOI : 10.1073/pnas.91.4.1229

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

A. Szafer, J. Zhong, and J. C. Gore, Theoretical Model for Water Diffusion in Tissues, Magnetic Resonance in Medicine, vol.46, issue.5, pp.697-712, 1995.
DOI : 10.1002/mrm.1910330516

D. A. Yablonskiy and A. L. Sukstanskii, Theoretical models of the diffusion weighted MR signal, NMR in Biomedicine, vol.57, issue.3, pp.661-681, 2010.
DOI : 10.1002/nbm.1520

T. Niendorf, R. M. Dijkhuizen, D. G. Norris, M. Van-lookeren-campagne, and K. Nicolay, Biexponential diffusion attenuation in various states of brain tissue: Implications for diffusion-weighted imaging, Magnetic Resonance in Medicine, vol.32, issue.6, pp.36-847, 1996.
DOI : 10.1002/mrm.1910360607

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.51-62, 1999.
DOI : 10.1002/(SICI)1099-1492(199902)12:1<51::AID-NBM546>3.0.CO;2-E

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

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.842-849, 2001.
DOI : 10.1148/radiology.219.3.r01jn02842

S. Chabert, N. Molko, Y. Cointepas, P. Le-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.307-310, 2005.
DOI : 10.1002/jmri.20383

URL : https://hal.archives-ouvertes.fr/hal-00349673

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

R. L. Magin, O. Abdullah, D. Baleanu, and X. J. 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

D. Yablonskiy, L. Bretthorst, and J. Ackerman, Statistical model for diffusion attenuated MR signal, Magnetic Resonance in Medicine, vol.49, issue.4, pp.664-669, 2003.
DOI : 10.1002/mrm.10578

D. S. Novikov and V. G. Kiselev, Effective medium theory of a diffusion-weighted signal, NMR in Biomedicine, vol.183, issue.24, pp.682-697, 2010.
DOI : 10.1002/nbm.1584

D. S. Novikov, E. Fieremans, J. H. Jensen, and J. A. Helpern, Random walks with barriers, Nature Physics, vol.303, issue.6, pp.508-514, 2011.
DOI : 10.1002/nbm.1577

D. S. Novikov, J. H. Jensen, J. A. Helpern, and E. Fieremans, Revealing mesoscopic structural universality with diffusion, Proceedings of the National Academy of Sciences, 2014.
DOI : 10.1073/pnas.1316944111

P. N. Sen and P. J. Basser, A Model for Diffusion in White Matter in the Brain, Biophysical Journal, vol.89, issue.5, pp.2927-2938, 2005.
DOI : 10.1529/biophysj.105.063016

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.59-1347, 2008.
DOI : 10.1002/mrm.21577

S. N. Jespersen, C. D. Kroenke, L. Stergaard, J. J. Ackerman, and D. A. Yablonskiy, Modeling dendrite density from magnetic resonance diffusion measurements, NeuroImage, vol.34, issue.4, pp.1473-1486, 2007.
DOI : 10.1016/j.neuroimage.2006.10.037

J. Karger, NMR self-diffusion studies in heterogeneous systems, Advances in Colloid and Interface Science, vol.23, pp.129-148, 1985.
DOI : 10.1016/0001-8686(85)80018-X

J. Coatléven, H. Haddar, and J. Li, A new macroscopic model including membrane exchange for diffusion MRI, SIAM Journal of Applied Mathematics, 2014.

T. Arbogast, Gravitational forces in dual-porosity systems: I. Model derivation by homogenization, Transport in Porous Media, pp.179-203, 1993.
DOI : 10.1007/BF00654409

T. Arbogast, Gravitational forces in dual-porosity systems: II. Computational validation of the homogenized model, Transport in Porous Media, pp.205-220, 1993.
DOI : 10.1007/BF00654410

A. 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

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

J. Pfeuffer, U. Flogel, 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

J. Lee and C. S. Springer, Effects of equilibrium exchange on diffusionweighted NMR signals: The diffusigraphic shutter-speed?, Magn. Reson. Med, pp.49-450, 2003.

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

Y. Roth, A. Ocherashvilli, D. Daniels, J. Ruizcabello, S. 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

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

M. Nilsson, J. Latt, E. Nordh, R. Wirestam, F. Stahlberg et al., On the effects of a varied diffusion time in vivo: is the diffusion in white matter restricted?, Magnetic Resonance Imaging, vol.27, issue.2, pp.176-187, 2009.
DOI : 10.1016/j.mri.2008.06.003

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

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

W. S. Price, A. V. Barzykin, K. Hayamizu, and M. Tachiya, A Model for Diffusive Transport through a Spherical Interface Probed by Pulsed-Field Gradient NMR, Biophysical Journal, vol.74, issue.5, pp.74-2259, 1998.
DOI : 10.1016/S0006-3495(98)77935-4

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.288-292, 1965.
DOI : 10.1063/1.1695690

J. Xu, M. Does, and J. Gore, Numerical study of water diffusion in biological tissues using an improved finite difference method, Physics in Medicine and Biology, vol.52, issue.7, 2007.
DOI : 10.1088/0031-9155/52/7/N01

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

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

R. , K. Jr, and I. Lowe, A modified pulsed gradient technique for measuring diffusion in the presence of large background gradients, Journal of Magnetic Resonance, pp.37-75, 1969.

D. V. Nguyen, J. Li, D. Grebenkov, and D. L. Bihan, A finite elements method to solve the Bloch???Torrey equation applied to diffusion magnetic resonance imaging, Journal of Computational Physics, vol.263, pp.283-302, 2014.
DOI : 10.1016/j.jcp.2014.01.009

URL : https://hal.archives-ouvertes.fr/hal-01111047