Selective RF excitation designs enabled by time‐varying spatially non‐linear ΔB₀ fields with applications in fetal MRI

Abstract

Purpose: To demonstrate, through numerical simulations, novel designs of spatially selective radiofrequency (RF) excitations of the fetal brain by both a restricted 2D slice and 3D inner-volume selection. These designs exploit a singlechannel RF pulse, conventional gradient fields, and the spatially non-linear ΔB 0 fields of a multi-coil shim array, using an auto-differentiation optimization algorithm. Methods:The design algorithm jointly optimizes the RF pulse and the timevarying ΔB 0 fields, which is produced by a 64-channel multi-coil ΔB 0 body array to augment the RF and the linear gradient fields, using an auto-differentiation approach. Two design targets were specified, one a 4-mm thick slice with a limited in-slice extent in one dimension ("restricted slice"), and the other a 3D inner-volume selection encompassing the fetal brain ("inner volume"). The RF duration was limited to 2 ms for the restricted slice excitation and 6 ms for the inner-volume excitation.Results: Excitation profiles were achieved for both the restricted slice excitation task (one-minus-minimum magnitude, 8%) within the region of interest (ROI) and (maximum-minus-zero magnitude, 8%) in the suppressed regions and the fetal brain volume excitation task (13% and 9%, respectively). Conclusions:The proposed joint design of RF and time-varying, spatially nonlinear ΔB 0 fields achieves the target excitation profiles with short RF pulse durations and demonstrates the potential to enhance fetal MRI with multi-channel body shim arrays.

Stochastic‐offset‐enhanced restricted slice excitation and 180° refocusing designs with spatially non‐linear ΔB0 shim array fields

“…Our approach extends prior work on selective fetal brain excitation 31 by incorporating the decomposition property of the time-discrete Bloch simulator into auto-differentiation optimization to enable restricted slice excitation and refocusing with arbitrary initial magnetizations. To capture the effect of idealized crusher gradients in refocusing designs, we use magnetization requirements for the optimization derived from the extended phase graph (EPG) approach, 32 which avoids costly sub-voxel isochromatic simulations.…”

“…The previous auto‐differentiation framework 26,31 required specification of the exact initial and final magnetizations for optimization. However, refocusing pulse design requires consideration of undetermined initial magnetization because of factors such as $$$ {\mathrm{B}}_0 $$$ inhomogeneity, etc.…”

“…The previous auto‐differentiation pulse designs 26,31 used fixed and equally spaced points, $$$ \left\{{r}_{i,j,k}\right\} $$$, based on the resolution and FOV, for the computation of the voxelwise loss function during optimization. However, even when the resultant slice profiles achieve high performance on the selected, fixed points of evaluation, there are no performance guarantees on locations in‐between these fixed points, which can yield undesired features of the design.…”

“…Recent developments in independently driven multi-coil shim arrays 27,28 provide additional design flexibility for selective excitations, which has been demonstrated in mouse brains 29 and in the visual cortex and peripheral cerebrum. 30 In particular, Zhang et al 31 incorporated the time-varying spatially non-linear ΔB 0 shim fields into the voxelwise auto-differentiation design of 2D and 3D spatially selective excitations with short RF duration in the imaging application of pregnancy. Compared with the Cayley-Klein polynomial framework, which assumes a static and linear gradient field, the time-discrete Bloch simulator offers an approach to incorporate a more general set of ΔB 0 fields into the excitation and refocusing design, including spatially varying non-linear, and time-varying multi-coil shim fields.…”

“…The previous designs 31 suffer from two key issues. First, the design is formulated as a voxelwise optimization problem with fixed spatial points for evaluating the loss function.…”