Magnitude least squares optimization for parallel radio frequency excitation design demonstrated at 7 Tesla with eight channels.

Parallel excitation offers a means of designing multidimensional radio frequency (RF) pulses using accelerated gradient trajectories resulting in a short pulse duration compared with single-channel excitation. Accelerations of four- to sixfold have been shown using an eight-channel transmit system (1), potentially enabling several important applications, including flexibly shaped excitation volumes, and mitigation of RF field inhomogeneity at high field. Various methods have been proposed for the design of such RF and gradient waveforms (2–5), primarily in the low flip domain (6), and successfully implemented on multichannel hardware (1,7). In this work, we propose an extension to the spatial domain parallel excitation pulse design method introduced by Grissom et al. (5), where we apply magnitude least squares optimization to improve excitation magnitude profile and reduce the required RF power at a cost of increased phase variations in the excitation pattern. However, for many excitation applications, such as when magnitude images are recorded, low-order spatial phase variations do not impose a significant penalty. In fact, they can potentially decrease the dynamic range requirements of the imaging (which can be extensive for high field three-dimensional [3D] acquisitions) by reducing the amplitude at the center of k-space. We, therefore, developed a method for pulse calculation with an adjustable regularization parameter de-emphasizing the excitation phase profile and study the potential benefits in magnitude profile fidelity and SAR, which can accompany this relaxed constraint. The idea of permitting phase variation in the excitation profile has previously been exploited in several applications, including the design of quadratic-phase RF pulses (8,9), RF shimming (10–13), and frequency-sweep pulses (14), with benefits such as improved magnitude transition bands for saturation pulses, homogeneity for RF shimming, and reduced RF peak power for frequency-sweep pulses. In this work, we propose a method that allows us to take advantage of relaxed constraints on the phase profile for parallel excitation design. Our approach is based on a variant of a local optimization method used for solving general magnitude least square problems (15). We demonstrate the method using a 2D spiral excitation with R = fourfold acceleration over the Nyquist sampling and a uniform in-plane slice-selective spoke excitation (1,16) on an eight-channel excitation system at 7 Tesla (T). Recently, at the ISMRM’07 conference, Katscher el al. (17) demonstrated the significant improvement gained in RF shimming when a magnitude least square approach is used. Kerr et al. (18) also proposed an approach for magnitude least square optimization for the design of parallel RF excitation and demonstrate the method using a spiral trajectory. The approach in this work differs in that it takes into account intravoxel dephasing and enables the designer to systematically trade off the allowed spatial phase variation for the improvement in magnitude profile and reduction in RF power. Furthermore, the work provides an extensive simulation and experimental study on the possible benefit of the algorithm on both spiral and spoke k-space trajectory excitations at high magnetic field strength.