Joint Design of Excitation k-Space Trajectory and RF Pulse for Small-Tip 3D Tailored Excitation in MRI

Abstract

We propose a new method for the joint design of k-space trajectory and RF pulse in 3D small-tip tailored excitation. Designing time-varying RF and gradient waveforms for a desired 3D target excitation pattern in MRI poses a non-linear, non-convex, constrained optimization problem with relatively large problem size that is difficult to solve directly. Existing joint pulse design approaches are therefore typically restricted to predefined trajectory types such as EPI or stack-of-spirals that intrinsically satisfy the gradient maximum and slew rate constraints and reduce the problem size (dimensionality) dramatically, but lead to suboptimal excitation accuracy for a given pulse duration. Here we use a 2nd-order B-spline basis that can be fitted to an arbitrary k-space trajectory, and allows the gradient constraints to be implemented efficiently. We show that this allows the joint optimization problem to be solved with quite general k-space trajectories. Starting from an arbitrary initial trajectory, we first approximate the trajectory using B-spline basis, and then optimize the corresponding coefficients. We evaluate our method in simulation using four different k-space initializations: stack-of-spirals, SPINS, KT-points, and a new method based on KT-points. In all cases, our approach leads to substantial improvement in excitation accuracy for a given pulse duration. We also validated our method for inner-volume excitation using phantom experiments. The computation is fast enough for online applications.

Fast three‐dimensional inner volume excitations using parallel transmission and optimized k‐space trajectories

“…This process resulted in highly convoluted trajectories with many turns that are not efficient from a k-space sampling and gradient performance perspective. Deniz et al (15) and Sun et al (16) extended this approach to 3D selection. As in the 2D work of Chen et al, the highly convoluted nature of the resulting gradient waveforms limited the quality of the excitations (15% normalized root-mean-square-error [NRMSE]) achievable in a short time [3.8 ms]).…”

“…In the present study, we propose a joint optimization of the pTx gradient and RF waveforms that yields fast (less than 5 ms) and smooth 3D k-space trajectories with few turns that, together with the RF waveforms, are tailored to the B þ 1 /B 0 maps at hand as well as the 3D target excitation pattern (17,18). In contrast with trajectories computed using greedy approaches (14)(15)(16), the gradient trajectories optimized by our algorithm are not highly convoluted and are efficient from a k-space sampling and gradient performance perspective. This is achieved by optimizing a small number of shape parameters that control the overall structure and shape of the trajectory instead of the position of the individual control points.…”

Rapid inner‐volume imaging in the steady‐state with 3D selective excitation and small‐tip fast recovery imaging

“…In , we proposed a method for the joint design of RF waveform and excitation k‐space trajectory that improved accuracy over several existing 3D selective excitation designs . In particular, we excited a cube with <15% relative OV excitation using a 4‐ms RF pulse and single‐coil transmission.…”

“… Summary of the 3D RF pulse design algorithm, first described in and more recently in . We first obtain a KT‐points trajectory (discrete “phase‐encoding” locations in kx‐ky‐kz; blue “+” marks) using a modified orthogonal matching pursuit approach .…”

“…Here, we propose a novel implementation of IV imaging, based on (i) 3D selective excitation using a recently proposed joint RF/gradient pulse design approach and (ii) the small‐tip fast recovery (STFR) steady‐state imaging sequence . The advantage of 3D IV excitation (over 2D) is that it allows arbitrary non‐Cartesian 3D readouts and hence rapid imaging.…”