Introduction

For the human brain, optimizing the B₀ shim corrections on a slice-by-slice basis (SBS) as opposed to a single global solution over the entire brain, is known to significantly improve B0 homogeneity [1]. However, regardless of hardware configuration used for shimming, the advantages of rapid multi-band (MB) imaging, (where multiple spatially disparate slices are excited simultaneously) has outweighed the gains in B₀ homogeneity of slower SBS shimming with dynamic shim updating (DSU). Therefore, the goal of this work was to develop a theoretical framework for MB shimming (i.e. simultaneous optimization of multiple spatially discrete slices) and demonstrate its performance using the very high order shim (VHOS) insert with echo planar imaging (EPI) at 7T.

Theory

For thin axial slices, spherical harmonic shims can be divided into two groups, i.e. those without a linear z-dependence (Cn,Sn,Z0,Z2,Z2Cn,Z2Sn…), denoted as “non-z-degenerate NzD” and with a linear z dependence “z-degenerate zD” (ZCn,ZSn,Z,Z3,Z3Cn,Z3Sn…) where
zD_i(x,y) = b₀*Z0 + b₁*z * NzD_i(x,y) [Eq. 1]
Since the zD_i shims are numerically related to their NzD_i, partners by a scaling parameter determined by their position along the Z axis, they provide no additional improvement in in-plane homogeneity for thin axial slices, such that the optimal shim is given by
B₀(r) = B₀(x,y,z) = a₀*Z0 + Σa_i*NzD_i(x,y) [Eq. 2]
Thus, DSU SBS shimming using only the NzD terms (i.e., ~ half of the available shims) should be largely identical to SBS DSU shimming using all (NzD and zD) of the available shims. However, combination of the zD_i and NzD_i shims allows for different and arbitrary sets of NzD_i shim fields to be simultaneously generated at two disparate spatial locations, such that DSU MB=2 shimming of thin axial slices using NzD_i and zD_i shims should be able to achieve nearly identical results as DSU SBS (MB=1).

Methods

Data were acquired on a Siemens 7T system using an 8x2-channel transceiver array and a VHOS insert (Resonance Research, Inc., MA) providing 3^rd, 4^th and two 5^th degree harmonic shims (ZC4 and ZS4). 1^st and 2^nd degree shims are provided by the Siemens gradient set. Each shim channel is dynamically updated for each slice (MB=1) or slice pair (MB=2) using 2ms ramp times. B₀ maps were acquired with matrix size of 64x64x58 at 3x3x2 mm³ using 5 evolution times (0,1,2,4 and 8ms) [2].
Shimming: The B₀ data were acquired using 5 strategies: (1) 1^st&2^nd static global shimming; (2) 1^st-4^th static global shimming, (3) 1^st-4^th dynamic slice-by-slice (SBS DSU MB=1), (4) NzD only shims with dynamic SBS (i.e., using half of all available channels), and (5) 1^st-4^th DSU MB=2, using 8 subjects per group. The performance for higher MB factors (MB=3,4) was also simulated using the mapping data acquired from the NzD studies.
SMS MB EPI: To focus on issues of distortion, conventional (MB=1) and MB=2 spin echo (SE) EPI were acquired with 2mm isotropic resolution, GRAPPA acceleration in the PE direction (AF=3), 1408Hz/pixel with an echo spacing of 0.9ms. The SMS MB=2 EPI image was reconstructed using full 3D kx-ky-kz GRAPPA [3].
Analysis: The standard deviation (SD) of the B₀ distribution per slice for the whole brain was measured. EPI images were compared to the B₀ map and anatomy across the 3 acquisitions: 1^st&2^nd, 1^st-4^th static shimming vs. DSU MB=2 (Fig 3).

Results

Table 1 summarizes the experimentally achieved shim results, acquired with 8 subjects per group. DSU with 1^st-4^th order spherical harmonics reduces the inhomogeneity present by 53% and 40% in comparison to static global shimming with 2^nd and 4^th order shims respectively. Consistent with theory, MB=1 shimming using only the non-degenerate shims or MB=2 shimming or with all shims gave nearly identical results to that achieved with SBS (MB=1) shimming with all shims. Fig 1 displays B₀ maps with MB=2 shimming. For the upper 40% of the brain (Fig 2), the residual inhomogeneity (<10Hz SD) is dominated by the intrinsic susceptibility difference between gray and white matter. Fig 3 show SE EPI data using the different shimming methods. As expected, DSU MB=2 EPI images were superior over entire brain in comparison data acquired with 1^st&2^nd static and 1^st-4^th static shimming. Predicted results from N=8 subjects for MB=3,4 are also provided (Table 1).

Conclusions

When using DSU shimming with 1^st-4^th degree spherical harmonics, the residual B₀ inhomogeneity over the upper 40% of the brain is largely limited by the intrinsic difference in susceptibility of gray and white matter. For more inferior brain locations substantial reductions in inhomogeneity are achieved which significantly reduce spatial distortions in EPI. Due to the intrinsic spatial symmetries for spherical harmonic shims, MB=2 shimming can be achieved without loss in homogeneity in comparison to SBS MB=1 shimming. Alternatively, for SBS (MB=1) shimming only ½ of the full set of harmonic shims are required to achieve optimal results, thereby simplifying hardware demands. At higher MB factors, (MB=3,4), the predicted improvement decreases, but still achieves 43% and 32% improvement respectively over 1^st&2^nd static global shimming. The developed MB DSU can significantly reduce in-plane geometric distortions at 7T for EPI acquisitions.

Acknowledgements

The study is supported by NIH EB011639, EB009871, NS090417, NS081772.

References

[1] Moon et al, ISMRM, #6653, 2018. [2] Hetherington et al, MRM, 56:26-33, 2006. [3] Moon et al, ISMRM, #2411, 2019.