Joint Design of Continuous Excitation k-space Trajectory and RF pulse for 3D Tailored Excitation

In 3D tailored RF pulse design, one typically predetermines a k-space (gradient) trajectory and then designs the corresponding RF waveforms for a target excitation pattern. Recently, the KT-points method was proposed as an approach for jointly designing the trajectory and RF pulses for 3D flip-angle homogenization (B1 shimming). KT-points models the 3D pulse design as a sparse approximation problem and selects sparse phase encoding locations by either a greedy approach or a simple inverse Fourier transform ignoring transmit coil sensitivity and field inhomogeneity. However, with only a few discrete phase encoding locations, it is difficult to approximate a non-smooth target excitation pattern in 3D. Also, it is relatively inefficient to traverse 3D k-space by discrete gradient blips with no RF transmission along those blips. In this work, we extend the KT-points method to a joint optimization of the continuous k-space trajectory and the RF waveform by: (1) applying local minimization to further optimize those KT points, and (2) efficiently ordering those points and generating a fast gradient waveform to traverse those points. We evaluate our proposed joint design with and without local minimization, and compare them with a recently proposed continuous nonselective spiral (SPINS) trajectory for 3D cubic excitation.

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