Improvements in magnetic resonance imaging excitation pulse design

Abstract

This thesis focuses on the design of magnetic resonance imaging (MRI) radio-frequency (RF) excitation pulses, and its primary contributions are made through connections with the novel multiple-system single-output (MSSO) simultaneous sparse approximation problem. The contributions are both conceptual and algorithmic and are validated with simulations, as well as anthropogenic-object-based and in vivo trials on MRI scanners. Excitation pulses are essential to MRI: they excite nuclear spins within a subject that are detected by a resonant coil and then reconstructed into images. Pulses need to be as short as possible due to spin relaxation, tissue heating, and main field inhomogeneity limitations. When magnetic spins are tilted by only a small amount, pulse transmission may be interpreted as depositing energy in a continuous three-dimensional Fourier-like domain along a one-dimensional contour to form an excitation in the spatial domain. Pulse duration is proportional to the length of the contour and inversely proportional to the rate at which it is traversed, and the rate is limited by system gradient hardware restrictions. Joint design of the contour and a corresponding excitation pulse is a difficult and central problem, while determining near-optimal energy deposition once the contour is fixed is significantly easier. We first pose the NP-Hard MSSO problem and formulate greedy and convex relaxation-based algorithms with which to approximately solve it. We find that second-order-cone programming and iteratively-reweighted least squares approaches are practical techniques for solving the relaxed problem and prove that single-vector sparse approximation of a complex-valued vector is an MSSO problem.

(cont.) We then focus on pulse design, first comparing three algorithms for solving linear systems of multi-channel excitation design equations, presenting experimental results from a 3 Tesla scanner with eight excitation channels. Our aim then turns toward the joint design of pulses and trajectories. We take joint design in a novel direction by utilizing MSSO theory and algorithms to design short-duration sparsity-enforced pulses. These pulses are used to mitigate transmit field inhomogeneity in the human brain at 7 Tesla, a significant step towards the clinical use of high-field imaging in the study of cancer, Alzheimer's disease, and Multiple Sclerosis. Pulses generated by the sparsity-enforced method outperform those created via conventional Fourier-based techniques, e.g., when attempting to produce a uniform magnetization in the presence of severe RF inhomogeneity, a 5.7-ms 15-spoke pulse generated by the sparsity-enforced method produces an excitation with 1.28 times lower root-mean-square error than conventionally-designed 15-spoke pulses. To achieve this same level of uniformity, conventional methods must use 29-spoke pulses that are 1.4 times longer. We then confront a subset selection problem that arises when a parallel excitation system has more transmit modes available than hardware transmit channels with which to drive them. MSSO theory and algorithms are again applicable and determine surprising targetspecific mixtures of light and dark modes that yield high-quality excitations. Finally, we study the critical patient safety issue of specific absorption rate (SAR) of multi-channel excitation pulses at high field. We develop a fast SAR calculation algorithm and propose optimizing an individual pulse and time-multiplexing a set of pulses as ways to reduce SAR; the latter is capable of reducing maximum local SAR by 11% with no impact on pulse duration.