Magnitude Least Squares Optimization for Parallel RF Excitation Design Demonstrated at 7 Tesla with 8 Channels

Introduction: Parallel RF excitations (pTx) are often designed as a least-squares (LS) optimized approximation to a target magnitude and phase profile. However, adherence to the target phase profile is usually not important as long as the excitation phase is slowly varying compared to the voxel dimension. Kerr et al. [1] proposed an approach for magnitude-least-squares (MLS) optimization of the target magnetization profile and demonstrate its benefit in reducing excitation error for a spiral excitation. In this work, we outline a different method for MLS optimization to improve both the magnitude profile and reduce the RF power while maintaining a smoothly and slowly varying phase profile. We validate the method with a slice selective spoke excitation for in-plane B1 + mitigation, and a 4-fold (R=4) accelerated 2D spiral excitation using an 8-channel transmit array on a 7T human MRI scanner. The method resulted in significant improvements over LS, especially for the spoke excitation where a 34% drop in root magnitude mean square error (RMMSE) and 49% drop in integrated RF power were observed. Theory: We formulated pTx as in Grissom et al [2], where the RF is normally designed by solving, by LS: