A High Order Finite Element Coupled Multi-Physics Approach To MRI Scanner Design

Magnetic Resonance Imaging (MRI) scanners are becoming increasingly popular with many clinical experts for use in both medical research and clinical imaging of patients, due to their ability to perform high-resolution non-intrusive imaging examinations. Recently, however, there has been an increasing demand for higher resolution scanners that are capable of performing quicker scans with increased patient comfort. With this demand for more advanced MRI systems, there also follows a number of challenges facing designers. Understanding the physical phenomena behind MRI is crucial in the development of scanners that are capable of producing accurate images of the patient with maximum comfort and minimal noise signatures.MRI scanners utilise strong static magnetic fields coupled with rapidly time varying gradient magnetic fields to generate images of the patient. In the presence of these time varying fields, the conducting components of MRI scanners generate eddy currents, which give rise to Lorentz forces and cause the conductors to vibrate.These vibrations cause acoustic waves to form that propagate through the air and result in audible noise which can cause significant discomfort for the patient. They also generate Lorentz currents which feedback into the electromagnetic field and this process results in a fully coupled non-linear acousto-magneto-mechanical system.The determination of the coupling mechanisms involved in such a system is a nontrivial task and so, in order to understand the behaviour of MRI systems during operation, advanced computational tools and techniques are required. Moreover, there exists certain small scale physical phenomena that arise in the coupled system which require high resolutions to obtain accurate results.In this thesis, a new computational framework for the treatment of acoustomagneto-mechanical coupling that arises in low-frequency electro-magneto-mechanical systems, such as MRI scanners, is proposed. The transient Newton-Raphson strategy involves the solution of a monolithic system, obtained from the linearisation of the coupled system of equations and two approaches are considered: (i) the linearised approach and (ii) the non-linear approach.In (i), physically motivated by the excitation from static and time varying current sources of MRI scanners, the fields may be split into a dominant static component and a much smaller dynamic component. The resulting linearised system is obtained by performing the linearisation of the fields about this dominant static component.This approach permits solutions in the frequency domain, for understanding the response of MRI systems under various excitations, and provides a computationally efficient way to solve this challenging problem, as it allows the tangent stiffness matrix to be inverted independently of time or frequency.In (ii), there is no approximation from a physical standpoint and the linearization is performed about the current solution. This approach requires that solutions are obtained in the time domain and thus the focus is then put on transient solutions to the coupled system of equations to address the following two important questions: 1) How good is the agreement between the computationally efficient linearised approach compared with the intensive non-linear approach?; and 2) Over what range of MRI operating conditions can the linearised approach be expected to provide acceptable results for MRI scanner design?Motivated by the need to solve industrial problems rapidly, solutions will be restricted to problems consisting of axisymmetric geometries and current sources. This treatment also discusses, in detail, the computational requirements for the solution of these coupled problems on unbounded domains and the accurate discretisation of the fields using hp-finite elements. A set of academic and industrially relevant examples are studied to benchmark and illustrate both approaches, in a hp- finite element context, as well as performing rigorous comparisons between the approaches