Nous introduisons les concepts et modèles de base en résonance magnétique nucléaire (RMN). Nous décrivons une expérience d'imagerie simple ainsi que la réduction du problème d'excitation sélective à un problème de scattering inverse.
The basic concepts and models used in the study of nuclear magnetic resonance are introduced. A simple imaging experiment is described, as well as, the reduction of the problem of selective excitation to a classical problem in inverse scattering.
@article{AIF_2004__54_5_1697_0,
author = {Epstein, Charles L.},
title = {Introduction to magnetic resonance imaging for mathematicians},
journal = {Annales de l'Institut Fourier},
volume = {54},
year = {2004},
pages = {1697-1716},
doi = {10.5802/aif.2063},
mrnumber = {2127862},
zbl = {02162438},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2004__54_5_1697_0}
}
Epstein, Charles L. Introduction to magnetic resonance imaging for mathematicians. Annales de l'Institut Fourier, Tome 54 (2004) pp. 1697-1716. doi : 10.5802/aif.2063. http://gdmltest.u-ga.fr/item/AIF_2004__54_5_1697_0/
[AKNS] , , & , The inverse scattering transform-Fourier analysis for nonlinear problems, Studies Appl. Math. 53 (1974) p. 249-315 | MR 450815 | Zbl 0408.35068
[Ab] , Principles of Nuclear Magnetism, Clarendon Press, 1983
[BC] & , Scattering and inverse scattering for first order systems, CPAM 37 (1984) p. 39-90 | MR 728266 | Zbl 0514.34021
[Bl] , Nuclear induction, Phys. Review 70 (1946) p. 460-474
[Cal] , Principles of nuclear magnetic resonance microscopy, Clarendon Press, 1993
[Ca1] , Exact solutions for selective-excitation pulses, J. Magn. Res. 94 (1991) p. 376-386
[Ca2] , Exact solutions for selective-excitation pulses. II. Excitation pulses with phase control, J. Magn. Res. 97 (1992) p. 65-78
[Ep] , Minimum power pulse synthesis via the inverse scattering transform, J. Magn. Res. 167 (2004) p. 185-210
[EBW] , & , Principles of nuclear magnetic resonance in one and two dimensions, Clarendon, 1987
[FT] & , Hamiltonian Methods in the Theory of Solitons, Springer Verlag, 1987 | MR 905674 | Zbl 0632.58004
[Gr1] , Trying to beat Heisenberg, Lecture Notes in Pure and Applied Math. vol. 122, Marcel Dekker, 1989, p. 657-666 | Zbl 0702.35199
[Gr2] , Concentrating a potential and its scattering transform for a discrete version of the Schrödinger and Zakharov-Shabat operators, Physica D 44 (1990) p. 92-98 | MR 1069673 | Zbl 0703.58053
[GH] & , An exploration of the invertibility of the Bloch transform, Inverse Problems 2 (1986) p. 75-81 | MR 839981 | Zbl 0612.44005
[Ha] , , & , Magnetic Resonance Imaging, Wiley-Liss, 1999
[Ho1] , The principle of reciprocity in signal strength calculations - A mathematical guide, Concepts Magn. Res. 12 (2000) p. 173-187
[Ho2] , Sensitivity and power deposition in a high field imaging experiment, JMRI 12 (2000) p. 46-67
[Ma] , Discrete Inverse Scattering Theory and NMR pulse design, PhD. Thesis, University of Pennsylvania, 2004
[Me] , Quantum Mechanics, 2nd ed., John Wiler \& Sons, 1970 | MR 260284 | Zbl 0102.42701
[PRNM] , , & , Parameter relations for the Shinnar-Le Roux selective excitation pulse design algorithm, IEEE Trans. Med. Imaging 10 (1991) p. 53-65
[MR] & , The inverse scattering transform and its use in the exact inversion of the Bloch equation for noninteracting spins, J. Magn. Res. 99 (1992) p. 118-138
[SL1] & , The application of spinors to pulse synthesis and analysis, Magn. Res. in Med. 12 (1989) p. 93-98
[SL2] & , Inversion of the Bloch equation, J. Chem. Phys. 98 (1993) p. 6121-6128
[To] , Bloch equations with diffusion terms, Phys. Review 104 (1956) p. 563-565