| Parallel transmission of radiofrequency (RF) pulses has shown great potential in various magnetic resonance imaging applications such as reduced field-of-view excitation and B1 inhomogeneity correction. However, designing RF pulses with specified spatial-spectral properties for parallel transmission is a challenging problem. Most of the current design methods are based on small-tip-angle (STA) approximation of the Bloch equation. These design methods suffer from two notable weaknesses: (a) the resulting RF pulses cannot be used for large-tip-angle (e.g., tip angle >90°) applications and (b) the pulses can have excessive B1 amplitude (and therefore excessive RF' power or specific absorption rate). This thesis is focused on addressing these two issues.;To address the first issue, two complementary methods are presented. The first one is a noniterative method based on the linear class large-tip-angle (LCLTA) theory, which permits the design of a wider range of RF pulses (e.g., refocusing or inversion pulses). Both STA and LCLTA are linear approximations of the Bloch equations, and errors due to the higher-order terms can appear in the final magnetization profiles. Therefore, the second method (iterative) in this thesis starts directly from the Bloch equation and addresses the above problem by formulating the parallel transmission RF pulse design as an optimal control problem with multiple controls. The necessary conditions for the optimal solution are derived using calculus of variations and a first-order gradient optimization algorithm is proposed to iteratively solve the optimal control problem. Various Bloch equation simulations and experiments are carried out to demonstrate that the proposed methods are able to generate large-tip-angle parallel transmission RF pulses which produce high quality magnetization profiles.;To address the second issue, the difficulty of directly applying the variable-rate selective excitation principle to multidimensional RF pulses (including both single-channel and parallel transmission) is first identified. Then, an alternative approach using a new class of spiral trajectories, termed the variable slew-rate spirals, is proposed to locally reduce B 1 amplitude of 2D RF pulses. The peak B1 reduction is achieved by changing the gradient slew-rate profile, and hardware constraints such as gradient amplitude and slew-rate constraints are inherently satisfied by the design of variable slew-rate spiral gradient waveforms. The governing differential equations for a variable slew-rate spiral are derived, and both numeric and analytic solutions to the equations are given. The variable slew-rate spiral design is applicable to peak B 1 amplitude reduction of both single-channel and parallel transmission RF pulses. The localized manipulation of gradient waveforms empowers variable slew-rate spirals to generate shorter RF pulses than conventional constant slew-rate spiral-based pulses under the same hardware constraints. These shorter RF pulses are in general less sensitive to resonance frequency offsets. |
