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fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Cobos Sanchez, Clemente
Languages: English
Types: Unknown
Subjects:
MRI has become an invaluable tool for diagnostic medicine. Its operation is based on the principles of electromagnetism that are dictated by Maxwell's equations. MRI relies on the existence of well defined, spatially and temporally controlled magnetic fields, which are usually generated by coils of wire. Human exposure to these fields has become a safety concern, especially with the increase in the strength of the magnetic fields used. In this thesis, problems in electromagnetism relevant to different areas in MRI and involving the calculation of solutions to both forward and inverse problems are investigated using techniques derived for computational mechanics. The first section of the work focuses on the development of an accurate technique for the solution of magnetostatic inverse problems using boundary element methods (BEM) with the aim of designing optimised gradient coils. This approach was found to be an extremely effective method which can be applied to a wide range of coil geometries and is particularly valuable for designs where the coil surface has low symmetry. BEM-based approaches to designing gradient coils that reduce the likelihood of peripheral nerve stimulation due to rapidly switched magnetic fields are also considered. In the second section of the work, a novel BEM tool to allow the calculation of solutions to quasi-static forward problems has been developed, and used for the evaluation of the electric fields induced in the human body by temporally varying magnetic fields, due to either gradient switching or body movements in strong static magnetic fields. This approach has been tested by comparison with analytic solutions for simply shaped objects, exposed to switched gradients or moving in large static fields, showing good agreement between the results of numerical and analytical approaches. The BEM approach has also been applied to the evaluation of the electric fields induced in human body models. This work involved the development of an appropriate theoretical framework for the study of conducting systems moving in magnetic fields. This involved correcting some misconceptions that had propagated in the literature and allowed the development of an effcient implementation of a BEM suited to this problem.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 1 Introduction 1 1.1 Scope of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
    • 2 Coil Design 4 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Magneto-statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Requirements and performance parameters . . . . . . . . . . . . . . . . . . 7 2.4 Coil design methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.1 Coils with discrete windings . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.2 Coils with distributed windings . . . . . . . . . . . . . . . . . . . . . 17 2.4.3 New methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
    • 3 Boundary Element Stream Function Method 30 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 Divergence-free BEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2.1 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2.2 Shape functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5 E-¯elds generated by magnetic ¯elds used in MRI 69 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2 Electric ¯eld induced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.3 Faraday's Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.4 Quasi-Static Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
    • 1 L. Marin, H. Power, R.W. Bowtell, C. Cobos Sanchez, A.A. Becker, P. Glover and I.A. Jones, Numerical solution for an inverse MRI problem using a regularized boundary element method, (Special Issue) Engineering Analysis with Boundary Elements 2007.
    • 2 L. Marin, H. Power, R.W. Bowtell, C. Cobos Sanchez, A.A. Becker, P. Glover and I.A. Jones, Boundary element method for an inverse problem in magnetic resonance imaging gradient coils, Computer Methods in Engineering & Sciences, CMES 2007.
    • 3 C. Cobos Sanchez, P. Glover, H. Power, L. Marin, A.A. Becker, I.A. Jones and R.W. Bowtell, Forward electric ¯eld calculation using BEM for time-varying magnetic ¯eld gradients and motion in strong static ¯elds, submitted (Engineering Analysis with Boundary Elements).
    • 4 C. Cobos Sanchez, H. Power, P. Glover, L. Marin, A.A. Becker, I.A. Jones and R.W. Bowtell, Electromagnetic formalism for calculation of electric ¯elds generated by magnetic ¯elds used in MRI., in progress.
    • 5 C. Cobos Sanchez, H. Power, P. Glover, L. Marin, A.A. Becker, I.A. Jones and R.W. Bowtell, Coil design using a quasi-static IBEM, in progress.
    • 1 C. Cobos Sanchez, L. Marin, H. Power, R.W. Bowtell, A.A. Becker, P. Glover and I.A. Jones, Application of higher-order boundary element method to gradient coil design, British Chapter of the International Society for Magnetic Resonance in Medicine (ISMRM 2006), 12th Annual Meeting, University of Surrey, Guildford, UK, 23-25 August 2006. (Poster)
    • 2 C. Cobos Sanchez, L. Marin, H. Power, R.W. Bowtell, A.A. Becker, P. Glover and I.A. Jones, Application of high-order boundary element method to gradient coil design, Paper 737, 23rd Annual Scienti¯c Meeting of the European Society for Magnetic Resonance in Medicine and Biology (ESMRMB 2006), Warsaw, Poland, 21-23 September 2006. (Talk)
    • 3 C. Cobos Sanchez, P. Glover, H. Power, L. Marin, A.A. Becker, I.A. Jones and R.W. Bowtell, Boundary element method for calculation of induced electric ¯elds in quasistatic regime , ISMRM Workshop on Advances in High Field MR, 25-28 March 2007 at Asilomar in Paci¯c Grove, California, USA. (Poster)
    • 4 C. Cobos Sanchez, P. Glover, H. Power, L. Marin, A.A. Becker, I.A. Jones and R.W. Bowtell, Boundary element method for induced electric ¯elds due to switched magnetic ¯eld gradients and movement in strong static ¯elds, International Society for Magnetic Resonance in Medicine (ISMRM 2007), 16th Annual Meeting, Berlin, Germany, 19-25 May 2007. (Poster)
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