Two-spoke placement optimization under explicit specific absorption rate and power constraints in parallel transmission at ultra-high field

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

“…One should be cautious in overinterpreting the meaning of the results from these spokes optimization parameters and extrapolating them to other experimental settings, because the simulations were conducted specifically for this particular field strength, coil design, anatomical region, and slice arrangement. For instance, another study with a different head coil geometry at 7T found that a 3‐spoke pulse brings only marginal benefit over a 2‐spoke pulse 60 [for a more general approach in joint optimization of complex RF scaling factors and k‐space trajectory, see Cao et al 61 and Dupas et al 62]. A recent study has shown that by using a more advanced twisted spokes trajectory, the subpulse duration can be further shortened while achieving better slice profile, homogenization, and robustness against off‐resonance 63.…”

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

“…In [10], it was demonstrated that as far as the RF variables were concerned, the returned solution seemed robust with respect to the initialization when using the A-S algorithm. In [15], likewise it was shown that a few random k-space trajectories trials were enough to obtain convergence toward the possibly globally optimal blipped k-space trajectory with high probability, also via an A-S algorithm implementation. The latter, however, was performed for 2 spokes and in the small tip angle regime.…”

“…(1) thus correspond to values which leave room for the train of small flip angle pulses used in that particular sequence [10]. To solve this optimization problem, we use the active-set (A-S) algorithm implementation of Matlab (Mathworks, Natick, MA, USA) because of its speed and robustness as demonstrated in [10,15,29], with initialization obtained via the variable-exchange method [23] with initial target phase taken as the one of the circularly-polarized (CP) mode. The A-S algorithm is a (Quasi-)Newton approach which iteratively approximates the problem as a quadratic programming problem.…”

“…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.…”

“…For k T -points pulses however, either the blipped k-space trajectory was not optimized [10,20,21] or the constraints were not taken into account [22]. In this work, we build on the previous work of Dupas et al [15] to investigate the simultaneous optimization of non-selective k T -points RF pulses and the blipped k-space trajectories at 7T, under explicit SAR and power constraints, using the Magnitude Least Squares (MLS) cost function [23] and in the large flip angle regime, which can be used for instance for inversion [6] and refocusing [24] purposes. Convergence and robustness of the method with respect to initialization are studied for 5, 7 and 9 k T -points trajectories.…”