Introduction to magnetic resonance imaging for mathematicians

Charles L. Epstein[1]

  • [1] University of Pennsylvania, Department of Mathematics, Philadelphia (USA)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 5, page 1697-1716
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Epstein, Charles L.. "Introduction to magnetic resonance imaging for mathematicians." Annales de l’institut Fourier 54.5 (2004): 1697-1716. <http://eudml.org/doc/116156>.

@article{Epstein2004,
abstract = {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.},
affiliation = {University of Pennsylvania, Department of Mathematics, Philadelphia (USA)},
author = {Epstein, Charles L.},
journal = {Annales de l’institut Fourier},
keywords = {nuclear magnetic resonance; imaging; selective excitation; inverse scattering},
language = {eng},
number = {5},
pages = {1697-1716},
publisher = {Association des Annales de l'Institut Fourier},
title = {Introduction to magnetic resonance imaging for mathematicians},
url = {http://eudml.org/doc/116156},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Epstein, Charles L.
TI - Introduction to magnetic resonance imaging for mathematicians
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 5
SP - 1697
EP - 1716
AB - 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.
LA - eng
KW - nuclear magnetic resonance; imaging; selective excitation; inverse scattering
UR - http://eudml.org/doc/116156
ER -

References

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  12. F. Grünbaum, Concentrating a potential and its scattering transform for a discrete version of the Schrödinger and Zakharov-Shabat operators, Physica D 44 (1990), 92-98 Zbl0703.58053MR1069673
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  14. E.M. Haacke, R.W. Brown, M.R. Thompson, R. Venkatesan, Magnetic Resonance Imaging, (1999), Wiley-Liss, New York 
  15. D. Hoult, The principle of reciprocity in signal strength calculations - A mathematical guide, Concepts Magn. Res. 12 (2000), 173-187 
  16. D. Hoult, Sensitivity and power deposition in a high field imaging experiment, JMRI 12 (2000), 46-67 
  17. J. Magland, Discrete Inverse Scattering Theory and NMR pulse design, (2004) 
  18. E. Merzbacher, Quantum Mechanics, (1970), John Wiler & Sons, New York Zbl0102.42701MR260284
  19. J. Pauly, P. Le Roux, D. Nishimura, A. Macovski, Parameter relations for the Shinnar-Le Roux selective excitation pulse design algorithm, IEEE Trans. Med. Imaging 10 (1991), 53-65 
  20. D.E. Rourke, P.G. Morris, The inverse scattering transform and its use in the exact inversion of the Bloch equation for noninteracting spins, J. Magn. Res. 99 (1992), 118-138 
  21. M. Shinnar, J. Leigh, The application of spinors to pulse synthesis and analysis, Magn. Res. in Med. 12 (1989), 93-98 
  22. M. Shinnar, J. Leigh, Inversion of the Bloch equation, J. Chem. Phys. 98 (1993), 6121-6128 
  23. H.C. Torrey, Bloch equations with diffusion terms, Phys. Review 104 (1956), 563-565 

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