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Numerical assessment of a multi-coil shimming system in human brain MRI
Pei-Yan Li1, Yi-Tien Li1,2, and Fa-Hsuan Lin3,4

1Institute of Biomedical Engineering, National Taiwan University, Taipei, Taiwan, 2Taipei Medical University - Shuang Ho Hospital, Taipei, Taiwan, 3Department of Medical Biophysics, University of Toronto, Toronto, ON, Canada, 4Department of Neuroscience and Biomedical Engineering, Aalto University, Espoo, Finland

Synopsis

We numerically evaluated the performance of multi-coil shimming in human brain using an array of up to 1,000 coils with realistic off-resonance distributions of 37 healthy participants. The average and variation of shim current distributions were revealed. Singular Value Decomposition suggested orthogonal current modes to reduce off-resonance. The first 6 current modes accounted for about 90% of the variance of shim current distributions. They achieved shimming performance comparable to the 5th-order and 4th-order spherical harmonic in global and slice-selective shimming, respectively.

Introduction

To mitigate off-resonance artifacts, shim fields are created to reduce field inhomogeneity. The shim fields can be modeled by spherical harmonic (SH) functions1,2 or a collection of localized shim coils in multi-coil (MC) shimming3-5. Here we numerically evaluated the performance of MC shimming on the human brain using a shim coil array with up to 1,000 coils to reduce the off resonance in a group of participants (N=37). Specifically, we I) studied average and variation of shim current distributions, II) revealed important orthogonal “modes” of shim current distributions, III) evaluated how much off-resonance in human head can be reduced by different modes of shim current distributions, and IV) compared multi-coil shimming with SH shimming.

Methods

The off-resonance field maps were measured on a 3T MRI (Skyra; Siemens) using a two-echo sequence (TE1 = 2 ms, TE2 = 4.46 ms) from 37 participants, who gave written informed consents approved by the Institution Review Board of National Taiwan University Hospital. Before the measurement, the MRI was first shimmed by the 2nd-order systematic shimming. Off-resonance field maps were co-registered to the standard brain MNI 305 atlas6. Shimming was simulated using an array consisting of circular shim coils evenly distributed over either a complete sphere (Ns = 1,000, 500, 200 or 100) or a partial sphere (Ns = 891, 452, 174 or 88). Figure 1 shows the shim arrays. The partial sphere removed coils in the bottom in order to create a circular space to accommodate the neck. The shim field generated by one circular shim coil was calculated by the Biot-Savart’s law. The off-resonance field from a participant was shimmed by a given shim array using ridge regression7,8 to avoid over fitting. We pooled 36 estimated shim current distributions from 36 participantsto create a matrix,which was subsequently decomposed by Singular Value Decomposition (SVD) into orthogonal “current modes”. The shimming performance of current modes from pooled data was evaluated by calculating the root-mean-squares of the residual field after using these current modes to shim the off-resonance field of the left-out participant. The data pooling and shimming was repeated 37 times across different left-out participants. We also evaluated the performance of slice-selective shimming. The shim fields at a specified axial slice was separately estimated based on the shim current pattern optimized for global shimming. For comparison, slice-selective shimming was also calculated using the 0th to the 7th-order of spherical harmonics9.

Results

Figure 1 shows shim arrays and average as well as standard deviation of the shim current distributions across all participants. More shim coils gave more spatially smooth shim current distributions, where strong shim currents and large variations were estimated at both sides, front, and top of the head. SVD decomposed the shim currents into multiple orthogonal current modes. Figure 2 shows the average and the standard deviation of the accumulated percentage power of current modes. More than 90% of power was provided by the first 6 modes. No clear difference between shim arrays with coils distributed over a complete or a partial sphere. Figure 3 shows the first 6 current modes and the shim fields of the array with 891 circular shim coils distributed over a partial sphere. The first mode targeted bilateral temporal lobe and the orbitofrontal cortex, typical regions showing strong off resonance10,11. Higher modes targeted at other regions. Figure 4 shows the average of RMS of the residual off-resonance across 37 leave-one-out validation trials after multi-coil shimming using current modes accumulatively from different shim arrays. We noticed a transition of the shimming performance around the 6th current mode. For global shimming, using up to the 6th current mode had off-resonance about 0.13 ppm, comparable to the performance of the 5th-order SH global shimming. For slice-selective shimming, using up to the 6th current modes had the performance comparable to the 4th-order SH slice-selective shimming. Figure 5 shows the residual off-resonance distributions. The off-resonance around the frontal and bilateral temporal lobes was reduced.

Discussion

SVD can suggest mutually orthogonal current modes, which can be beneficial to avoid coupling between each other in future realization. The first 6 current modes accounted for more than 90% of the variance of shim current distributions. Using all these 6 current modes together had comparable shimming to either the 5th-order or the 4th-order SH for global and slice-selective shimming, respectively. Our calculations can be taken as the upper limit of shimming performance, since we did not account for any errors in realizing the shim array.

Acknowledgements

This work was partially supported by Ministry of Science and Technology, Taiwan (103-2628-B-002-002-MY3, 105-2221-E-002-104), the National Health Research Institutes, Taiwan (NHRI-EX107-10727EI), and the Academy of Finland (No. 298131).

References

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Figures

Figure 1: Top row: Shim coils are distributed over either a complete sphere or a partial sphere to tightly cover the whole head. Middle and bottom rows: The average and standard deviation of the magnitude of shim current were color-coded at the center of each circular shim coil, respectively. Red means counter-clockwise current with the normal vector to the surface, while blue means the opposite. Circular shim coils were distributed over either a complete sphere (C) with 100 or 1,000 circular shim coils, or a partial sphere (P) with 88 or 891 circular shim coils.

Figure 2: The average and the standard deviation of the accumulated percentage power in SVD across 37 leave-one-out validation trials. The horizontal axes indicate the number of SVD current modes used accumulatively to shim the off-resonance. The SVD current modes were estimated for shim coils distributed either over a complete or a partial sphere with 1,000 or 891 circular shim coils, respectively.

Figure 3: The current distributions and the generated magnetic fields of the first 6 SVD current modes, each of which was estimated from a shim array consisting of 891 circular shim coils distributed over the partial sphere. The top row shows the current distributions of the first 6 SVD current modes, while the second to fourth rows show the magnetic fields generated by circular shim coils with the three orthogonal slices referred to MNI305 atlas. Individual percentage powers for SVD current modes are indicated at the bottom of each column.

Figure 4: The average of RMS of the residual off-resonance after global shimming (A) or slice-selective shimming at difference slices indexed by s (B) based on SVD current modes across 37 leave-one-out validation trials. N denotes the first N (1 ≤ N ≤ 36) sets of the shim field, each of which was suggested by a current mode. The slice-selective shimming (B) was based on a shim array with 891 circular shim coils distributed over the partial sphere. C1000 corresponded to 1,000 shim coils distributed over a complete sphere. P891 corresponded to 891 shim coils distributed over a partial sphere.

Figure 5: The RMS of the residual off-resonance fields from a representative participant after shimming based on SVD current modes (the 1st, 1st– 6th and 1st– 36th modes) either globally (A) or slice-selectively (B), the generated magnetic field of each mode was created by 891 circular shim coils distributed over a partial sphere. For comparison, SH global shimming (the 1st, 5th and 7th-order) and SH slice-selective shimming (the 1st, 4th and 7th-order) are shown in (A) and (B), respectively. The off-resonance field maps and T1-weighted images of the participant are shown at two left columns.

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