Fast and Accurate Large-Tip-Angle RF Pulse Design for Parallel Excitation Using a Perturbation Analysis of the Bloch Equation

Introduction: Designing RF pulses in parallel excitation (PTX) using the linear small-tip-angle approximation [1-3] produces distorted excitation patterns at large tip angles due to the nonlinear nature of the Bloch equation. Grissom et al [4] proposed the ‘Additive Angle’ (AA) method for large-tip-angle RF pulse as a means to improve upon the small-tip-angle approximation (STA). This iterative method produces an improved profile by applying a STA to the error in the magnetization profile. In this work, we demonstrate that through a perturbation analysis to the STA, it is possible to develop an exact formula that relates the error in the magnetization profile to the required B1 field. This formula is then used as the basis for a fast and accurate method for large-tip-angle RF pulse design. Method: The proposed method is analogous in concept to the ‘Additive Angle’ method [4], however, it is derived from a perturbation analysis to the Bloch equation. Given a desired transverse excitation pattern, MD(x), we design initial RF pulses, B1(t), via the small-tip-angle parallel pulse design method of [3]. If we denote by M(x) the transverse magnetization at spatial position (x) created by B1(t), then by inverting the Bloch equation,