- 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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