Synopsis

A numerical method based on stream function Singular Value Decomposition is proposed for optimization of Multi-Coil array (MCA) design for human brain shimming. It provides geometries other than circles for shim loops and halves the amount of channels needed to achieve the same whole-brain inhomogeneity reduction as current MCA systems. Strong impacts are expected for imaging and spectroscopy at Ultra-High Field.

Introduction

Multi-coil arrays (MCA) placed as close as possible to the human head are becoming an increasingly popular choice for B0 shimming of the brain for Ultra-High Field MRI thanks to their good performance, easiness to build and versatility, compared to spherical harmonic coils. Past MCA studies feature circular loops placed regularly over a cylindrical surface¹, or more recently, choke-equipped RF loops for concomitant B0 shimming and RF reception². In such works, loop shape, size and placement were not really optimized for brain shimming.

Here we propose a numerical method for defining shimming loops location and geometry for MCA design. The method is supported by a field based coil design algorithm computing optimal stream functions³, followed by a Principal Component Analysis thereof. Unlike most existing MCA designs, our approach offers a multi-layer solution to provide enhanced degrees of freedom for shimming. Here a proof of concept is presented based on two cylindrical layers surrounding the RF head coil.

Methods

We first built a database of 55 three-dimensional ΔB₀ brain maps from informed and consenting adults. They were acquired after 2^nd-order shimming at a 3T Siemens Magnetom-Prisma imager with 1.7-mm isotropic resolution and rescaled to 7T, since a shim system is intended for UHF. FSL’s brain extraction tool was used to ignore non-brain voxels. These maps were used as target fields for the coil design algorithm.

From two cylindrical coil formers of 300-mm length and 138-mm and 144-mm concentric radii at the gradients isocenter, a set of 55 tailored coils is generated for each former, each coil addressing a target brain in the database and being a priori driven by a single current source⁴. Every tailored shim coil is designed to reduce as much as possible the global inhomogeneity of the brain fieldmap used as target, while maintaining acceptable levels of power consumption (<40W). The inhomogeneity is defined as the standard deviation of the ΔB₀ map.

As in⁴, the two resulting sets of 55 coils are independently post-processed using Singular Value Decomposition of the 55 stream functions for PCA. For each newly generated set of 55 SVD coils, the elements associated with higher singular values present higher degrees of similarity with the entire input set. Then for the 138-mm coil, only the SVD coil with the highest singular value is kept; for the 144-mm radius coil, the second highest is picked (Figure-1).

The stream-function SVD coil insert generation naturally provides a coil wiring which is denser around brain zones where inhomogeneity is worse (near frontal sinuses and temporal inner ears). Searching for “loop-like” structures, the wire pattern can be segmented to obtain optimized loop geometries and locations for an SVD-Based Multi-Coil (SBMC) Array (Figure-2).

A 22-Channel SBMC Array based on the two SVD coils was modeled in ANSYS^® Electronic Desktop (Figure-3a). The fieldmap and electric resistance of each channel were obtained from electromagnetic simulations.

These fieldmaps were adapted to represent the effect of 80 turns of wire per channel. The currents to drive each channel of the SBMC Array are calculated through minimization of the ΔB₀ inhomogeneity, while limiting the electric current per channel to 5A.

An MCA inspired by the design proposed in¹ was also modeled with 138-mm cylinder radius, 48 circular loops of 2-cm radius with 80 turns each, and regularly distributed around the cylinder at heights -10-cm, -8-cm, 1-cm and 3-cm with respect to gradients isocenter (Figure-3b). This simulation is used as a benchmark for performance comparison.

Results

The 48-channel MCA with regularly distributed coils delivers an average inhomogeneity reduction of 30% (Figure-4a), with a final average inhomogeneity of 46±8Hz. Average power consumption of the system is estimated at 2W.

The 22-channel SBMC array inhomogeneity distribution is shown in Figure-4b, across the 55 brains of our database. An average inhomogeneity reduction of 33% is achieved, from 67±12Hz to 45±8Hz. Average power consumption of the system is estimated at 25W.

Figure-5 shows residual B₀ axial slices of one subject after shimming with either one of the presented arrays.

Discussion and conclusion

The SBMC-Array presents slightly better inhomogeneity reduction than the 48-channel MCA with less than half the number of channels. Its design thus represents an important progress for global brain shimming, highlighting the usefulness of the designed windings. However, the increase in power consumption could be a limiting factor and needs to be further analyzed to guarantee limited heating.

More SVD layers can be added to increase the amount of channels, address more inter-subject variability and improve performance.

Like most MCA, the SBMC design could also be exploited for dynamic slice-by-slice shimming for improved performance.

Acknowledgements

References

1. C. Juchem, et al. Dynamic multi-coil shimming of the human brain at 7 T. Journal of Magnetic Resonance, 2011 Oct; 212(2):280-8.

2. J. Stockman, L.L. Wald. In vivo B0 field shimming methods for 7 T. Neuroimage, 2018 Mar; 168:71-87.

3. B.P. Meneses, A. Amadon. Dipole Boundary Method: a simple approach to compute stream functions for shim coil design. ISMRM 2019.

4. B.P. Meneses, A. Amadon. A novel few-channel shim coil design for the human brain based on stream function Singular Value Decomposition. ISMRM 2019.