Spatially tailored radio frequency (RF) excitations accelerated with parallel transmit systems provide the opportunity to create shaped volume excitations or mitigate inhomogeneous B 1 excitation profiles with clinically relevant pulse lengths. While such excitations are often designed as a least-squares optimized approximation to a target magnitude and phase profile, adherence to the target phase profile is usually not important as long as the excitation phase is slowly varying compared with the voxel dimension. In this work, we demonstrate a method for a magnitude least squares optimization of the target magnetization profile for multichannel parallel excitation to improve the magnitude profile and reduce the RF power at the cost of a less uniform phase profile. The method enables the designer to trade off the allowed spatial phase variation for the improvement in magnitude profile and reduction in RF power. We validate the method with simulation studies and demonstrate its performance in fourfold accelerated two-dimensional spiral ex- 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 threedimensional [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,...

Slice-selective RF waveforms that mitigate severe B 1 ؉ inhomogeneity at 7 Tesla using parallel excitation were designed and validated in a water phantom and human studies on six subjects using a 16-element degenerate stripline array coil driven with a butler matrix to utilize the eight most favorable birdcage modes. The parallel RF waveform design applied magnitude least-squares (MLS) criteria with an optimized k-space excitation trajectory to significantly improve profile uniformity compared to conventional least-squares (LS) designs. Parallel excitation RF pulses designed to excite a uniform in-plane flip angle (FA) with slice selection in the z-direction were demonstrated and compared with conventional sinc-pulse excitation and RF shimming. In all cases, the parallel RF excitation significantly mitigated the effects of inhomogeneous B 1 ؉ on the excitation FA. The optimized parallel RF pulses for human B 1 ؉ mitigation were only 67% longer than a conventional sinc-based excitation, but significantly outperformed RF shimming. Key words: parallel excitation; slice-selective excitation; RF inhomogeneity mitigation; multidimensional RF pulse; RF coil array Slice-selective excitation plays a crucial role in MRI. With the push toward higher magnetic field strength, dramatic B 1 ϩ inhomogeneity for human imaging has become a serious issue, causing inhomogeneous flip-angle (FA) distribution in-plane for slice-selective excitations and detrimental nonuniformity for both signal-to-noise ratio (SNR) and image contrast. Several RF design approaches have been suggested to compensate for this inhomogeneity, including adiabatic pulses (1,2), RF-shimming (3-6), and spatially tailored excitation designs (7-11).For relatively mild B 1 ϩ inhomogeneity, using the low-FA approximation (12) with appropriate echo-volumnar k-space trajectories (9 -11), termed either "fast-k z " or "spokes" excitation trajectories, the within-slice FA inhomogeneity can be corrected. With these pulses, slice selection is achieved with a conventional sinc-like RF pulse during each k z traversal (a spoke), and in-plane FA inhomogeneity is mitigated by the appropriate choice of the complex-valued amplitude that modulates the RF waveform of each spoke. Nonetheless, if the transmit (Tx) B 1 ϩ field is rapidly varying with position, a large number of spokes will be required at correspondingly high k x and k y locations, rendering the RF pulse too lengthy for practical use.With the introduction of parallel excitation systems (13-16), the k-space trajectory can be undersampled significantly to accelerate the RF pulse and reduce its duration. A number of successful demonstrations of this concept have been reported (e.g., . For example, it has been demonstrated at 3T (18,21) and 4.7T (17) that a parallel RF design method using low-FA approximation with spokebased excitation trajectories can produce highly uniform slice-selective excitation with reasonable excitation durations.In this work we use spoke-based excitation in combination with magnitude least-squar...