PhD THESIS

Magnetic susceptibility artefacts in MRI: Mathematical study and numerical simulation

Defended at University of Rennes I on November the 27th 1997.
Thesis Supervisor: Prof. Gabriel Caloz.

This work has been performed at the Institut de Recherche Mathématique de Rennes (Numerical Analysis Team) in the framework of a joint project with the Laboratoire de Résonance Magnétique en Biologie et Médecine (Université de Rennes1).

Summary of the thesis

This thesis is devoted to the mathematical modelling and to the numerical simulation of magnetic susceptibility artefacts in magnetic resonance imaging (MRI). Two distinct aspects of the problem have been considered. The first one is the calculation of the magnetic field induced by a paramagnetic implant under the conditions of a MRI experience. The second one is the determination of the way the magnetic field disrupts the imaging process giving rise to an artefact in the MRI image.

The first part of the thesis is devoted to the study of the magnetostatic problem and we present two methods for calculating the magnetic field induced by a metallic implant under the conditions of a MRI experiment. The first method uses a Finite Elements method to calculate the scalar magnetic potential. An artificial boundary on which a proper boundary condition is imposed, is introduced in order to bound the computational domain. We perform the analysis of both the truncation error and discretisation error. The second method is based on an surface integral representation formula for the magnetic field induction. For an implant having a polyhedral shape our method computes the magnetic field exactly. For a more general geometry we use numerical quadrature formulas for the calculation of the surface integral over the curved parts of the implant boundary. A detailed study of the approximation error is achieved.

The second part of the thesis is devoted to the modelling of the process giving rise to the artifacts. This model allowed us to propose a detailed analysis of the phenomena of image distortion and to present an algorithm for the numerical simulation of susceptibility artefacts in MRI.

Download the thesis manuscript

(The thesis manuscript is written in French)

PDF format (3373033 bytes).
Compressed Postscript format (2182385 bytes).

Numerical simulation softwares developed during the PhD thesis

CMAGXX: a Fortran Finite Element code for the computation of the magnetic field induced by a uniformly magnetised object (require the MODULEF software : free download from INRIA website)
ARAMIS : a Matlab program for the numerical simulation of Radio-Frequency artefacts induced by a spherical implant in MRI
SIMART : a Matlab program for the numerical simulation of Susceptibility artefacts induced by a spherical implant in MRI
ATHOS : a Matlab program for the numerical simulation of Susceptibility artefacts induced by a cylindrical implant in MRI

(Follow the links for a free download of the simulation codes)

Publications related to the PhD thesis

S. Balac and G. Caloz. Induced magnetic field computations using a boundary integral formulation. Applied Numerical Mathematics, 41(3):345-367, 2002.
S. Balac, G. Caloz, G. Cathelineau, B. Chauvel and J.D. De Certaines. An integral representation method for numerical simulation of MRI artifacts induced by metallic implants. Journal of Magnetic Resonance in Medicine, 45(4):724-727, 2001.
S. Balac and G. Caloz. Mathematical modeling and numerical simulation of magnetic susceptibility artifacts in Magnetic Resonance Imaging. Computer Methods in Biomechanics and Biomedical Engineering, 3:335-349, 2000.
S. Balac. Simulation numérique des artefacts de susceptibilité magnétique en IRM. Innovation et Technologie en Biologie et Médecine (ITBM), 19(5):369-379, 1998.
S. Balac and G. Caloz. Magnetic susceptibility artifacts in Magnetic Resonance Imaging : calculation of the magnetic field disturbances. IEEE Trans. on Magnetics, 32(3):1645-1648, 1996.
B. Chauvel, G. Cathelineau, S. Balac, J. Lecerf and J.D. De Certaines. Cancellation of metalinduced MRI artifacts with dual-component and diamagnetic material : mathematical modelization and experimental verification. Journal of Magnetic Resonance Imaging, 6(6):936-938 (1996)

Publications subsequent to the PhD thesis on similar subjects

S. Balac and L. Chupin. Fast approximate solution of Bloch equation for simulation of RF artifacts in Magnetic Resonance Imaging. Mathematical and Computer Modelling, 48 : 1901-1913 (2008)
S. Balac, H. Benoit-Cattin, T. Lamotte and C. Odet. Analytic solution to boundary integral computation of susceptibility induced magnetic field inhomogeneities. Mathematical and Computer Modelling, 39(4/5) : 437-455 (2004)