Designing multichannel, multidimensional, arbitrary flip angle RF pulses using an optimal control approach

The vast majority of parallel transmission RF pulse designs so far are based on small-tip-angle (STA) approximation of the Bloch equation. These methods can design only excitation pulses with small flip angles (e.g., 30 degrees ). The linear class large-tip-angle (LCLTA) method is able to design large-tip-angle parallel transmission pulses through concatenating a sequence of small-excitation pulses when certain k-space trajectories are used. However, both STA and LCLTA are linear approximations of the nonlinear Bloch equation. Therefore, distortions from the ideal magnetization profiles due to the higher order terms can appear in the final magnetization profiles. This issue is addressed in this work by formulating the multidimensional multichannel RF pulse design as an optimal control problem with multiple controls based directly on the Bloch equation. Necessary conditions for the optimal solution are derived and a first-order gradient optimization algorithm is used to iteratively solve the optimal control problem, where an existing pulse is used as an initial "guess." A systematic design procedure is also presented. Bloch simulation and phantom experimental results using various parallel transmission pulses (excitation, inversion, and refocusing) are shown to illustrate the effectiveness of the optimal control method in improving the spatial localization or homogeneity of the magnetization profiles.