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An Aubert Ring Aggregate Magnet Helmet for 3D Head Imaging in a Low-field Portable MRI
Zhi Hua Ren1 and Shao Ying Huang1,2

1Engineering Product Development, Singapore University of Technology and Design, Singapore, Singapore, 2Department of Surgery, National University of Singapore, Singapore, Singapore

### Synopsis

A permanent magnet helmet based on an Aubert ring aggregate is proposed to have a linear gradient along the axial direction for 3D head imaging in a low-field portable MRI system. It is a magnet array that consists of a series of asymmetric Aubert ring pairs, forming a Helmet shape. The inner radii of each ring are successfully optimized for a linear gradient along the axial direction, a comparably strong field strength (67.06mT), and a controlled homogeneity. Genetic Algorithm (GA) was used for the optimization. This design can be used to supply B0 in a miniaturized low-field portable MRI system.

### INTRODUCTION

Recently, a permanent magnet array, Halbach array, was used to supply both the main field ($\mathbf{B_0}$) and gradient fields in the transverse direction for 2D head imaging in an MRI system, so that the MRI system can be miniaturized and gradient coils are omitted, paving a way towards portability[1]. 3D imaging, Transmit Array Spatial Encoding (TRASE), was further developed by applying $B_1^+$ encoding along the third dimension[2]. Meanwhile, an Aubert ring aggregate was proposed based on a permanent magnet Aubert ring pair, showing a longitudinal field with a concentric field pattern and a relatively high field strength and homogeneity for 2D imaging[3]. The Aubert ring aggregate in [3] provides a field strength that is more than twice of that in a Halbach array in[1]. It is in the longitudinal direction thus the advancement in MRI coils can be applied directly. In this abstract, we propose a further design where a linear gradient is obtained on top of a high field strength and a small homogeneity of an Aubert ring aggregate for 3D head imaging.

### METHOD

The proposed design as shown in Fig.1(a) is based on an Aubert ring pair (shown in Fig. 1 (b)) [4]. It consists of $N$ ring pairs where the $i_{th}$ ring pair has an inner and outer radii of $r_\textrm{in}^\textrm{i-T}$ and $r_\textrm{out}^\textrm{i-T}$ for the ring on the top, and those of $r_\textrm{in}^\textrm{i-B}$ and $r_\textrm{out}^\textrm{i-B}$ for the ring at the bottom. Each ring has a thickness of $t$. The magnet rings on the top are radially polarized inwards, and those at the bottom are radially polarized outwards.

In the optimization, the two rings in a pair are allowed to have different dimensions. The distance between the two innermost edges of the rings was fixed to be 120mm. The outer radii of the rings are fixed at 250mm. The field of view (FOV) is a cylindrical (200mm in diameter, and 50mm in length) for head imaging. The volume center of the FOV is 50mm below the central plane of the proposed magnet array. The variables, $r_\textrm{in}^\textrm{i-T}$ and $r_\textrm{in}^\textrm{i-B}$ ($i = 1, ...., N$), were optimized to get a field strength over 65 mT, a field inhomogeneity less than 10000 ppm, and at the same time, a linear gradient field along the axial direction. The optimization tool is the Genetic algorithm (GA). To further accelerate the optimization, a current model for a single magnet ring [3] was used for a fast forward calculation.

### RESULTS

Fig.2(a) show the cross-sectional profile of the optimized Aubert ring aggregate. COMSOL Multiphysics was used to simulate the optimized array. Fig.2(b) shows the field distribution on the central plane in the FOV. It is a concentric pattern. Fig.2(c) shows the field distribution on the $rz$-plane and Fig. 2 (d) shows the field plots along the $z$-direction at different values of $r$. As shown clearly in Fig. 2 (d), linear gradients are obtained at different values of $r$. For now, the average field strength in the FOV is 67.06mT and the homogeneity is 380000ppm. The field strength is comparable to that of a Halbach-array[1]. For the field homogeneity, further shimming needs to be done next.

### DISCUSSION & CONCLUSION

In this abstract, we propose to further optimize an Auber ring aggregate permanent magnet array to obtain a linear gradient field along the axial direction. The optimization successfully leads to a linear gradient field along the axial direction. It results in a Helmet shape for the array. The average field strength in a FOV (a cylinder with a diameter of 200mm and a length of 50mm) is 67.06mT, which is comparable to the field a Halbach-array can generate. It is for 3D head imaging in a low-field portable MRI system. The homogeneity of the current version is still relatively large, further shimming will be done. Alternatively, to work with the inhomogeneity, a wideband radiofrequency(RF) excitation and reception can be applied to a system using the optimized magnet.

### Acknowledgements

Singapore MIT Alliance Research and Technology (SMART) innovation grant (ING137068-BIO)

### References

[1] C. Z. Cooley, J. P. Stockmann, B. D. Armstrong, M. Sarracanie, M. H. Lev, M. S. Rosen, and L. L. Wald, “Two-dimensional imaging in a lightweight portable MRI scanner without gradient coils,” Magnetic resonance in medicine, vol. 73, no. 2, pp. 872–883, 2015.

[2] Clarissa Zimmerman Cooley, Jason P Stockmann, Mathieu with, Matthew S Rosen, and Lawrence L Wald, 3D Imaging in a Portable MRI Scanner using Rotating Spatial Encoding Magnetic Fields and Transmit Array Spatial Encoding (TRASE), ISMRM 2015

[3] Z. H. Ren, W. C. Mu, and S.Y.Huang, “Design and Optimization of a Ring-Pair Permanent Magnet Array for Head Imaging in a Low-field Portable MRI System”, IEEE Transactions on Magnetics, 2018, in press

[4] G. Aubert, “Permanent magnet for nuclear magnetic resonance imaging equipment,” July 26 1994. US Patent 5,332,971

### Figures

Fig. 1 Cutaway view of (a) the proposed magnet array. The magnet rings on the top are radially polarized inwards, and those at the bottom are radially polarized outwards. (b) an Auber ring pair [4].

Fig. 2 (a) The optimized profile of the Aubert ring aggregate, (b) the simulated field pattern on the center plane of the FOV, (c) the field distribution on the $rz$-plane, (d) the field plots along the $z$-direction at different values of $r$.

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