Problèmes mathématiques et numériques issus de l'imagerie par résonance magnétique nucléaire

Abstract : Metallic implants in Magnetic Resonance Imaging induce dysfunctions which appear through artifacts, abnormal heating effects,... In the present work, we shall build up and study mathematical models to explain temperature increase.

In part one, the birdcage coil is studied. We show that the resonant frequencies are the eigenvalues of a generalized eigenvalue problem and an efficient numerical method is presented. Then the radiofrequency field properties are studied through numerical simulations : rotation at each interior point and homogeneity at the center of the coil are presented.

In the part two, we model the magnetic problem of the MRI by the Maxwell equations with the radiofrequency field as boundary condition. We show that this problem is well posed in the space and is equivalent to a series of axisymmetric bidimensional decoupled problems. Numerical tests in the axisymmetric case are given, confirming the theoretical results.
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Theses
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https://tel.archives-ouvertes.fr/tel-00011378
Contributor : Patrice Boissoles <>
Submitted on : Friday, January 13, 2006 - 4:59:23 PM
Last modification on : Friday, November 16, 2018 - 1:31:22 AM
Long-term archiving on : Saturday, April 3, 2010 - 9:23:20 PM

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  • HAL Id : tel-00011378, version 1

Citation

Patrice Boissoles. Problèmes mathématiques et numériques issus de l'imagerie par résonance magnétique nucléaire. Mathématiques [math]. Université Rennes 1, 2005. Français. ⟨tel-00011378⟩

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