Forward and inverse analysis of electromagnetic fields for MRI using computational techniques

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