Dynamically Updated B0 Shimming for Multi-band Imaging with High Order Spherical Harmonics
Hoby Hetherington1, Chan Moon1, and Jullie Pan1

1Radiology, University of Pittsburgh, Pittsburgh, PA, United States


High order spherical harmonic shims (SH) and multi-coil approaches have demonstrated that the best B0 homogeneity for 2D human brain imaging is achieved by dynamic updating and single slice-by-slice (SBS) shimming. However, the use of multi-band (MB) imaging with its superior data collection efficiency has overshadowed the benefits of single SBS updating. In this abstract we demonstrate that MB=2 B0 shimming (MBB0) can be achieved with equivalent homogeneity as single SBS imaging for SH shimming with a 4th+ high order/degree shim insert. For MBB0 =3 or 4, significant gains over static 4th order shimming are predicted.


Recent work with both high order spherical harmonic shims (SH) (1) and multi-coil approaches (MC) (2,3) have demonstrated that the best B0 homogeneity in the human brain for 2D imaging studies can be achieved by use of dynamic updating and single slice-by-slice (SBS) shimming. However, the development of multi-band (MB) imaging and the advantages in efficiency in data collection for fMRI and DTI have overshadowed the benefits of single SBS updating. Thus to make a significant impact for fMRI and DTI, dynamic updating needs to expand to provide enhanced shimming simultaneously (i.e., MBB0>1) over multiple spatially distinct slices. This work addresses the theoretical basis for achieving this goal and demonstrates experimentally (MBB0=2) and theoretically (MBB0=3,4) that significant advantages for dynamic updating can be achieved using a high degree shim insert based on spherical harmonics.


All data were collected at 7T in 5 subjects (3 men, 2 women) using an 8x2 transceiver array with a very high order/degree shim insert and 2nd degree shims from the gradient set; providing all 1st, 2nd, 3rd, 4th (except Z4), and ZC4, ZS4. All B0 maps were collected at 3x3x2 mm resolution spanning 112 to 116mm (56 to 58 slices) in the z direction. The ROIs for shimming were selected to include all brain within each slice. Eddy-current limitations associated with dynamically updating the shims were eliminated by using 2ms ramps to change the shims and the maximum aggregate amplitude for all shims (other than linear terms) was constrained to 15amps.


For thin single slices in predominantly axial orientations, the achieved B0 homogeneity is dominated by SH shims with pure in-plane dependencies, i.e. X,Y,C2,S2,...Cn,Sn, denoted here as {Cn,Sn}. With no z dependence, the in-plane variation of these shims is described by B0(r)=f(x,y). To achieve identical B0 homogeneity across multiple spatially distinct slices simultaneously (i.e. MBB0 shimming) in comparison to single SBS shimming, the simultaneous optimal values for {Cn,Sn} within each slice will need to vary as a function of z position. This is achieved theoretically (Fig 1, representative subject) and experimentally (Table 2, n=5 subjects) by the inclusion of the SH shim terms {ZCn,ZSn}, that modulate in-plane terms as a function of axial position. These terms are included in our 4th degree/order shim insert. Thus for {Cn,Sn,ZCn,ZSn} B0(r) = (a0n + a1nz){Cn,Sn}, provides the needed spatial dependence for MBB0 =2 imaging and as shown in Table 1, performs identically to SBS shimming. Notably for approximately 1⁄2 of the slices, the measured remaining B0 inhomogeneity is dominated by the intrinsic difference in gray and white matter susceptibility, i.e. an intrinsic limitation to achievable performance (Fig 2). For MBB0 =3, three distinct sets of {Cn,Sn} values need to be achieved simultaneously depending upon z position. To fit 3 simultaneous arbitrary values in z, a quadratic dependence in z is needed, such that shim symmetries approximating B0(r) = (a0n + a1nz + a2nz2){Cn, Sn}, are needed. With the current high order shim insert, these terms are not present (highest degree shims available are ZC4, ZS4), such that the achieved homogeneity is predicted to decrease in comparison to single SBS shimming. Nonetheless, the MBB0 =3 shim still provides significant improvements in comparison to static shimming as shown in Fig. 1.


In summary, MBB0 =2 imaging can be achieved with equivalent homogeneity as single SBS imaging both theoretically and experimentally for SH shimming with a 4th+ high order/degree shim insert. For MBB0 =3,4, some performance decline occurs in comparison to single SBS imaging, however significant gains over static 4th order/degree SH shimming are predicted. Further, we have established the spatial dependencies necessary to enable additional improvements to optimize MBB0=3,4 shimming. The pertinence of the multi-band shimming is evident for integration with multi-band imaging in whole brain echo-planar acquisitions.


This work was supported by NIH R01-EB011639, R01-EB024408, R01-NS090417, R01-NS081772


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2. Boer VO, Klomp DW, Juchem C, Luijten PR, de Graaf RA. Multislice (1)H MRSI of the human brain at 7 T using dynamic B(0) and B(1) shimming. Magnetic resonance in medicine 2012;68(3):662-670.

3. Stockmann JP, Wald LL. In vivo B0 field shimming methods for MRI at 7T. NeuroImage 2018;168:71-87.


Fig 1. Predicted B0 homgeneity (SD) as a function of slice position using 1st-4th+ shims and static shimming, dynamic SBS shimming and MB=2 and MB=3 shimming.

Table 1: Summary data for B0 homogeneity (SD) from the all slices measured from n=5 subjects using static shimming (1st&2nd, 1st-4th+) and dynamic updating SBS and MB=2.

Fig 2. B0 maps from all slices. The contrast has been reversed such that gray matter reflects positive B0 offsets.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)