An inverse method for designing high-frequency RF coils in MRI

In this thesis an inverse method is developed for the theoretical design of radio-frequency (RF) coils for use in magnetic resonance imaging (MRI) at high-frequency. New design techniques are required for RF coils at high-field, where the wavelength of operation becomes comparable to the dimensions of the coils. In addition, the effects of sample loading on the homogeneity of induced fields become more pronounced as the frequency of operation increases and can result in severe distortion to the acquired image. The general aim of the design method presented is to find a current density solution on the coil that will induce some desired homogeneous magnetic field upon a spherical target region within. This is an ill-conditioned inverse problem that can be solved using regularisation, in which the error between induced and target magnetic fields is minimised along with some additional constraint of the designer's choosing. This general technique is demonstrated and adapted throughout the thesis for a wide variety of RF coil types. The method is initially applied to the design of unloaded, unshielded RF volume coils, with asymmetrically located target regions. Time-harmonic methods involving retarded potential Green's functions are used to obtain field expressions, with the geometry of the coil accounted for using a Fourier series representation of the current density components. The resulting integral equation is solved using a hybrid regularisation penalty function that allows a trade-off between coil winding simplicity and field homogeneity. The important case of RF shielding is considered in a straightforward extension of the design method, to induce a null field exterior to the coils. In addition, the method is reworked to account for sample loading and its corresponding effects at high-field. This requires a three-layer model which is solved using Fourier-Bessel series expansions, along with appropriate boundary conditions on the surfaces of the load and RF coils. Finally, the inverse method is adapted further for the design of RF phased arrays, which afford a number of advantages over RF volume coils, including a high signal-to-noise ratio (SNR) over a large field of view. A robust design method is presented for this coil type, which allows complete freedom over array size, field focussing and polarisation considerations