RF Pulse Design for Parallel Excitation

1. Introduction Parallel excitation has been introduced as a means of accelerating multi-dimensional, spatially-selective excitation using multiple transmit coils, each driven by a unique RF pulse (1,2). In a manner analogous to parallel imaging, parallel excitation allows the use of a reduced excitation k-space trajectory (7) to achieve a desired excitation pattern, by exploiting the blurring effect of coil sensitivity patterns in the excitation k-space domain to deposit RF energy in regions not traversed by the trajectory. Proposed applications include the shortening of multi-dimensional RF pulses for B 1 and B 0 inhomogeneity compensation (8-11), and Specific Absorption Rate (SAR) management (2). The feasibility of parallel excitation has also recently been verified experimentally in (12,13). In this paper we present a review of RF pulse design methods for parallel excitation and demonstrate their application. The pioneering methods were introduced by Katscher, et al. (1) and by Zhu (2). The method by Katscher, et al. (1) is characterized by the explicit use of transmit sensitivity patterns in the pulse design process, and its formulation is based on a convolution in excitation k-space. It allows usage of arbitrary k-space trajectories. Grissom, et al. (3) proposed an RF pulse design technique that is closely related to Katscher's method, but is formulated in the spatial domain. It is a multi-coil generalization of the iterative pulse design method proposed by Yip, et al. (14). The method introduced by Zhu also makes explicit use of transmit sensitivity patterns and is formulated as an optimization problem in the spatial domain, and, as presently described, is restricted to Cartesian (e.g. echo-planar) k-space trajectories. Griswold, et al. (4) proposed a k-space domain method that is analogous to GRAPPA imaging (6). It is unique in that it does not require prior determination of sensitivity patterns. Instead, it involves an extra calibration step in the pulse design process. It also appears to be restricted to Cartesian k-space trajectories. All of the aforementioned design approaches are based on the assumption of small-tip-angle excitation. In the following section we review the formulations of the four RF pulse design approaches in detail. We then present a discussion of applications of parallel excitation, including the acceleration of multi-dimensional selective excitation pulses, B 1 inhomogeneity compensation, and SAR management.