Free Access
Issue
ESAIM: M2AN
Volume 51, Number 4, July-August 2017
Page(s) 1279 - 1301
DOI https://doi.org/10.1051/m2an/2016060
Published online 30 June 2017
  1. Y. Achdou, O. Pironneau and F. Valentin, Effective boundary conditions for laminar flows over periodic rough boundaries. J. Comput. Phys. 147 (1998) 187–218. [CrossRef] [MathSciNet]
  2. B. Aslanyürek, H. Haddar and H.Şahintürk, Generalized impedance boundary conditions for thin dielectric coatings with variable thickness. Wave Motion 48 (2011) 681–700. [MathSciNet]
  3. Y. Assaf, R.Z. Freidlin, G.K. Rohde and P.J. Basser, New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter. Magn. Reson. Med. 52 (2004) 965–978. [CrossRef] [PubMed]
  4. W.Y. Aung, S. Mar and T.L. Benzinger, Diffusion tensor MRI as a biomarker in axonal and myelin damage. Imaging Med. 5 (2013) 427–440. [CrossRef] [PubMed]
  5. C. Beaulieu, The basis of anisotropic water diffusion in the nervous system – a technical review. NMR Biomed. 15 (2002) 435–455. [CrossRef] [PubMed]
  6. A. Bendali and K. Lemrabet, The effect of a thin coating on the scattering of a time-harmonic wave for the Helmholtz equation. SIAM J. Appl. Math. 56 (1996) 1664–1693. [CrossRef] [MathSciNet]
  7. I.E. Biton, I.D. Duncan and Y. Cohen, High b-value q-space diffusion MRI in myelin-deficient rat spinal cords. Magn. Reson. Imaging 24 (2006) 161–166. [PubMed]
  8. S. Chun, H. Haddar and J.S. Hesthaven, High-order accurate thin layer approximations for time-domain electromagnetics, Part II: transmission layers. J. Comput. Appl. Math. 234 (2010) 2587–2608. [CrossRef] [MathSciNet]
  9. J. Coatléven, H. Haddar and J. Li, A macroscopic model including membrane exchange for diffusion MRI. SIAM J. Appl. Math. 74 (2014) 516–546. [MathSciNet]
  10. B. Delourme, H. Haddar and P. Joly, Approximate models for wave propagation across thin periodic interfaces. J. Math. Pures Appl. 98 (2012) 28–71. [CrossRef] [MathSciNet]
  11. M. Duruflé, V. Péron and C. Poignard, Thin Layer Models for Electromagnetism. Commun. Comput. Phys. 16 (2014) 213–238.
  12. J. Farrell, Q-space Diffusion Imaging of Axon and Myelin Damage in the Human and Rat Spinal Cord. Johns Hopkins University (2009).
  13. R. Fox, T. Cronin, J. Lin, X. Wang, K. Sakaie, D. Ontaneda, S. Mahmoud, M. Lowe and M. Phillips, Measuring myelin repair and axonal loss with diffusion tensor imaging. Am. J. Neuroradiology 32 (2011) 85–91. [CrossRef]
  14. H. Haddar and P. Joly, Effective boundary conditions for thin ferromagnetic coatings. Asymptotic analysis of the 1D model. Asymptot. Anal. 2 (2001) 127–160.
  15. H. Haddar and P. Joly, Stability of thin layer approximation of electromagnetic waves scattering by linear and nonlinear coatings. J. Comput. Appl. Math. 143 (2002) 201–236. [CrossRef] [MathSciNet]
  16. H. Haddar, P. Joly and H.-M. Nguyen, Generalized impedance boundary conditions for scattering by strongly absorbing obstacles: the scalar case. Math. Models Methods Appl. Sci. 15 (2005) 1273–1300. [CrossRef] [MathSciNet]
  17. H. Haddar, P. Joly and H.-M. Nguyen, Generalized impedance boundary conditions for scattering problems from strongly absorbing obstacles: The case of Maxwell’s equations. Math. Models Methods Appl. Sci. 18 (2008) 1787–1827. [CrossRef] [MathSciNet]
  18. M.A. Horsfield and D.K. Jones, Applications of diffusion-weighted and diffusion tensor MRI to white matter diseases, a review. NMR Biomed. 15 (2002) 570–577. [CrossRef] [PubMed]
  19. W. Jäger and A. Mikelić, On the roughness-induced effective boundary conditions for an incompressible viscous flow. J. Differ. Equ. 170 (2001) 96–122.
  20. H. Johansen-Berg and T. Behrens, Diffusion MRI: From quantitative measurement to in vivo neuroanatomy. Elsevier Science (2013).
  21. D. Jones, Diffusion MRI: theory, methods, and applications. Oxford University Press, USA (2010).
  22. L.J. Lanyon, Neuroimaging – Methods, in: Diffusion tensor imaging: structural connectivity insights, limitations and future directions. Edited by Peter Bright. InTech (2012).
  23. D. Le Bihan and H. Johansen-Berg, Diffusion MRI at 25: Exploring brain tissue structure and function. NeuroImage 61 (2012) 324–34.
  24. D. LeBihan, The wet mind: water and functional neuroimaging. Phys. Med. Biol. 52 (2007).
  25. J.-L. Lions, Quelques remarques sur les équations différentielles opérationnelles du 1er ordre. Rend. Sem. Mat. Univ. Padova 33 (1963) 213–225. [MathSciNet]
  26. J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications, Vol. I. Translated from the French by P. Kenneth. Die Grundl. Math. Wiss., Band 181. Springer-Verlag, New York-Heidelberg (1972).
  27. S.E. Maier, Y. Sun and R.V. Mulkern, Diffusion imaging of brain tumors. NMR Biomed. 23 (2010) 849–864. [CrossRef] [PubMed]
  28. D.V. Nguyen, J.-R. Li, D. Grebenkov and D.L. Bihan, A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging. J. Comput. Phys. 263 (2014) 283–302. [MathSciNet]
  29. R. Perrussel and C. Poignard, Asymptotic expansion of steady- state potential in a high contrast medium with a thin resistive layer. Appl. Math. Comput. 221 (2013) 48–65. [MathSciNet]
  30. C. Poignard, Generalized impedance boundary condition at high frequency for a domain with thin layer: the circular case. Appl. Anal. 86 (2007) 1549–1568. [MathSciNet]
  31. R. Quarles, W. Macklin and P. Morell, Basic neurochemistry: molecular, cellular and medical aspects. In: Myelin formation, structure and biochemistry. Elsevier Science (2006).
  32. H. Si, TetGen, a Delaunay-based quality tetrahedral mesh generator. ACM Trans. Math. Softw. Art. 4 (2015) 11, 36.
  33. B.P. Sommeijer, L.F. Shampin and J.G. Verwer, RKC: an explicit solver for parabolic PDEs. J. Comput. Appl. Math. 88 (1998) 315–326. [CrossRef] [MathSciNet]
  34. E.O. Stejskal and J.E. Tanner, Spin diffusion measurements: Spin echoes in the presence of a time-dependent field gradient. J. Chem. Phys. 42 (1965) 288–292.
  35. H. Torrey, Bloch equations with diffusion terms. Phys. Rev. Online Archive (Prola) 104 (1956) 563–565.
  36. J.G. Verwer, W.H. Hundsdorfer and B.P. Sommeijer, Convergence properties of the Runge−Kutta−Chebyshev method. Numer. Math. 57 (1990) 157–178. [CrossRef] [MathSciNet]

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