Small‐tip‐angle spokes pulse design using interleaved greedy and local optimization methods

Abstract

Current spokes pulse design methods can be grouped into methods based either on sparse approximation or on iterative local (gradient descent-based) optimization of the transverse-plane spatial frequency locations visited by the spokes. These two classes of methods have complementary strengths and weaknesses: sparse approximation-based methods perform an efficient search over a large swath of candidate spatial frequency locations but most are incompatible with off-resonance compensation, multifrequency designs, and target phase relaxation, while local methods can accommodate off-resonance and target phase relaxation but are sensitive to initialization and suboptimal local cost function minima. This article introduces a method that interleaves local iterations, which optimize the radiofrequency pulses, target phase patterns, and spatial frequency locations, with a greedy method to choose new locations. Simulations and experiments at 3 and 7 T show that the method consistently produces single- and multifrequency spokes pulses with lower flip angle inhomogeneity compared to current methods.

High‐resolution gradient‐recalled echo imaging at 9.4T using 16‐channel parallel transmit simultaneous multislice spokes excitations with slice‐by‐slice flip angle homogenization

“…The elements in the system matrix for the k th spokes subpulse can be expressed as 44 $A_k{}_{ij}=S_{ij}{e}^{i{\mathrm{boldr}}_i·\mathbf{k}\left(t_k^{\text{'}}\right)}\underset{l=1}{\overset{N_{rf}}{true\sum }}{f}_l{e}^{i\gamma \Delta B_{0i}\left(t_k^{\text{'}}+N_{rf}\Delta t-l\Delta t\right)},$where S ij is complex transmit sensitivity of the j th transmit coil in the i th voxel, ${\mathrm{boldr}}_i$ is the position vector of the i th voxel relative to the gradient's isocenter, and $\mathbf{k}\left(t_k^{\text{'}}\right)$ is the excitation k‐space trajectory, which is the product of the gyromagnetic ratio, $\gamma$, and the total gradient moment from the end of the k th subpulse to the end of the pulse train (i.e., $t_k^{\text{'}}$), $N_{rf}$ is the total number of discretized samples of the slice‐selective RF waveform of which the sample at the l th time point is $f_l$, $\Delta B_{0i}$ is the frequency offset in the i th voxel and $\Delta t$ is the RF dwell time.…”

Joint design of k T -points trajectories and RF pulses under explicit SAR and power constraints in the large flip angle regime

“…a second-order optimization method (A-S). Alternatively, they could be optimized by alternating the optimizations of the RF pulses and the blipped k-space trajectories, as in [13,22]. However, the simultaneous optimization approach here was preferred in particular due to the strong dependence between the two sets of variables (k-space and RF).…”

“…The success of the method lies in the sparsity of the k-space trajectory, thereby making the calculations fast and SAR-efficient by spending a sufficient amount of time at each k-space location [10]. For its slice-selective counterpart, the spokes method [11], optimization of the k-space placement has been studied using a variety of different techniques [12][13][14][15]. Importantly, in [15] it was shown that the fitness of a given kspace trajectory in fact could heavily depend on the imposed power and SAR constraints, thus justifying the need to perform the optimizations under those specific constraints.…”

MR imaging of the temporomandibular joint: comparison between acquisitions at 7.0 T using dielectric pads and 3.0 T

“…31,32 However, several issues, including the management of the specific absorption rate levels, are still challenging and need to be solved to ensure a safe application in clinical routine. 15,33,34 Nevertheless, these approaches yield great potential for improving the image quality at 7.0 T and might make a significant contribution towards further optimization of 7.0 T TMJ imaging in the future. [33][34][35] Quantitative analysis In the current study, we applied an intricate voxelwise approach to determine SNR for different field strengths in vivo.…”

“…15,33,34 Nevertheless, these approaches yield great potential for improving the image quality at 7.0 T and might make a significant contribution towards further optimization of 7.0 T TMJ imaging in the future. [33][34][35] Quantitative analysis In the current study, we applied an intricate voxelwise approach to determine SNR for different field strengths in vivo. In contrast to other methods to assess SNR, such as calculating the ratio between the mean signal intensity and the corresponding standard deviation within a specific region of interest or the subtraction method, the current approach, which is based on a second scan without radiofrequency pulses and gradient switching, accounts for potential noise correlation among all coil channels and yields therefore robust voxelwise maps of the entire field of view.…”