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A New Yokeless Permanent Magnet Array with High Field Strength and High Field Homogeneity for Low-field Portable MRI System
Zhi Hua Ren1, Wen Chuan Mu1, and Shao Ying Huang1

1Engineering Product Development, Singapore University of Technology and Design, Singapore, Singapore

Synopsis

Permanent magnet array is a good candidate for providing the main magnetic field for a low-field portable MRI system. In this abstract, we present the design of a new yokeless permanent magnet array that generates a longitudinal magnetic field with a significant increase in field strength and in homogeneity compared to a traditional two-ring structure. It is compatible with existing RF coils thus the advancement in coil designs can be applied. The optimization was done based on genetic algorithm and a current model which shows much higher calculation efficiency than finite element method. The effectiveness of the optimization is validated by realistic simulations using COMSOL.

Introduction

Permanent magnet array is a good candidate for providing the main magnetic field for a low-field portable MRI system. Halbach array is popular in such a system. However, it provides magnetic fields that are transverse to the bore and therefore, RF coils have to be re-engineered to fit in [1,2]. A yokeless magnet array with a pair of rings that provides longitudinal field has intrinsic compatibility to existing RF coils [3]. However, the homogeneities of the magnetic field generated are not enough for MRI imaging in a large volume, for example, human head. In this abstract, we present the design of a new yokeless permanent magnet array that generates a longitudinal $$$\bf{B_0}$$$ field with significant improvement in field strength and in homogeneity compared to the traditional two-ring structure. The design and optimization was done for a portable MRI system using a current model and genetic algorithm (GA).

Methods

The design is an assembly of $$$n$$$ pairs of symmetric magnet rings with the axis of the rings aligned with the $$$z$$$-axis, as shown in Fig.$$$\,1$$$. Each pair of rings is the magnet assembly proposed by G. Aubert in $$$1991$$$ which generates a longitudinal field to the bore [3]. In the proposed design, as shown in Fig.$$$\,1$$$, each pair has an inner radius of $$$R_{in}^i$$$, an outer radius of $$$R_{out}^i$$$, a thickness of $$$t_i$$$, and a distance between the innermost rings of $$$d$$$. The above parameters can be optimized for field homogeneity and field strength using the GA. In order to accelerate the forward calculation of the magnetic field for optimization, a current model is applied. $$$\bf{Current}$$$ $$$\bf{Model}$$$ $$$\bf{for}$$$ $$$\bf{the}$$$ $$$\bf{Calculation}$$$ $$$\bf{of}$$$ $$$\bf{Magnetic}$$$ $$$\bf{Field:}$$$ In the current model for a single magnet ring as shown in Fig.$$$\,2(d)$$$, the magnet is reduced to the equivalent distribution of currents. Therefore, the generated magnetic field can be calculated by (1) (shown in Fig.$$$\,1$$$(b))[4], where $$$\bf{X}$$$ is the observation point, $$$\bf{X}^{\prime}$$$ is the current source point, and $$$S$$$ is the surface of the magnet. For a single magnet ring with outwards radial magnetization (shown in Fig.$$$\,2(c)$$$), the equivalent current source is shown in Eq.$$$\,(2)$$$, where $$$M_0$$$ is the magnitude of the remanent magnetization. The equivalent currents for the magnet ring in Fig.$$$\,2(d)$$$ are surface currents circulating on the front and the back surfaces of the ring.Since a magnet ring is symmetrical with respect to its radial axis, $$$\bf{B}(\bf{X})$$$ is $$$\theta$$$-independent. Therefore, the observation point is defined as $$$(r,0,z)$$$ to simplify the derivation and the calculation is reduced to a two-dimensional problem. Substitute (2) into (1) and take the integration, we get (3). It is validated by comparing with simulation results using COMSOL [5]. Fig.$$$\,$$$ 3 shows the results calculated using (3) (in MATLAB) and COMSOL. As shown, they agree with each other well. The calculation time by using (3) is about $$$1$$$ s in comparison to about $$$10$$$ s in COMSOL. The proposed approach takes much less time, thus it is ready for the forward model in optimization. $$$\bf{Genetic}$$$ $$$\bf{Algorithm:}$$$ Fig.$$$\,4$$$ shows the flowchart of GA. The parameters that are under optimization are $$$R_{in}^i$$$ $$$(i=2,...10)$$$ and the distance $$$d$$$ between the two innermost rings. The rest are preset as shown in Fig.$$$\,4$$$. The optimization criteria are field homogeneity and field strength.

Optimization Results

The optimization results are shown in Fig.$$$\,5$$$. A two-ring G. Aubert's configuration with a constant inner radius of 200 mm as shown in Fig.$$$\,5(d)$$$ is used as a reference. Fig.$$$\,5$$$(a) shows that the fitness value (field inhomogeneities) decreases as the number of iterations increases. Fig.$$$\,5$$$(b) shows the best $$$R_{in}^i$$$ after $$$100$$$ iterations which determines the inner profile of the optimized magnet array. The optimized array is shown in Fig$$$\,5$$$(c). Fig$$$\,5$$$(e)-(g) and (f)-(i) shows the z-components of $$$B_0$$$ on the central plane in the FOV of the optimized magnet array and that of the reference magnet, respectively, using both the current model and COMSOL. After optimization, the field inhomogeneity is greatly reduced by over $$$93\%$$$ from $$$374100$$$ ppm to $$$24687$$$ ppm in the FOV. In the meanwhile, the average field strength is increased by over $$$39\%$$$ from $$$125.9$$$ mT to $$$175.5$$$ mT in the FOV.

Conclusion

We proposed the design of a new yokeless permanent magnet array that generates a longitudinal $$$B_0$$$ field whose inhomogeneities are significantly reduced by $$$93\%$$$ and field strength is increased by $$$39\%$$$, compared to a conventional two-ring configuration [3]. The optimization was done based on a current model and GA. The effectiveness of the optimization is validated by realistic simulations using COMSOL. The optimized magnet array will be built for low-field portable MRI system in the near future.

Acknowledgements

No acknowledgement found.

References

[1] Cooley, C. Z., Stockmann, J. P., Armstrong, B. D., et al. Two‐dimensional imaging in a lightweight portable MRI scanner without gradient coils. Magnetic resonance in medicine, 73(2) (2015): 872-883.

[2] Ren, Z. H., Zhou, W., Huang, S. Y., A Convertible Magnet Array and Solenoid Coil for a Portable Magnetic Resonance Imaging (MRI) System, 24th International Society for Magnetic Resonance in Medicine Annual Meeting $\&$ Exhibition, 2017.

[3] Aubert G. US Patent 5,014,032.

[4] Furlani EP. 2001. Permanent Magnet and Electromechanical Devices: Materials, Analysis, and Applications. San Diego, CA: Academic.

[5] COMSOL Inc., Burlington, USA

Figures

(a) Side view of the proposed yokeless magnet array. It consists of $$$n$$$ pairs of rings. Each pair has an inner radius of $$$R_{in}^i$$$, an outer radius of $$$R_{out}^i$$$, a thickness of $$$t_i$$$, and the distance between two innermost rings of $$$d$$$. The above parameters can be optimized to increase field homogeneity and increase field strength using the genetic algorithm (GA). (b) Equations for forward current model calculation.

(a) Side view. (b) Front view. (c) Back view of a yokeless magnet array ring pair proposed by G. Aubert. It consists of two magnet rings with opposite radial magnetization direction, one inwards and the other outwards. The combination of these rings generates a confined longitudinal field in the central volume of the structure. (d) A single-layer magnet ring with the axis aligned with the z-axis in a cylindrical coordinate system. The magnet ring is radially magnetized in the outward direction.

(a) Model of magnet array in COMSOL. (b-d) Z-components of the magnetic field on the cylindrical surfaces with $$$r$$$ = 0, 10, 20 mm, respectively, using both the current model and COMSOL. The test magnet array consists of two magnet rings with the same inner radius of 40 mm and a thickness of 20 mm. The outer radii are 60 mm and 50 mm from right to left. As it is shown in (b-d), the results from the current model and COMSOL show good agreement with each other at different observation points.

Flow chart of the genetic algorithm. $$$R_{out}^i$$$ is set to be 250 mm. The number of layers is set to be $$$10$$$, and the thicknesses for each layer is set to be 10 mm. The field of view (FOV) is a cylindrical region with a diameter of 200 mm and a length of 50 mm in the center of the magnet bore. There are 11 variables for each candidate solution in the population (ten for $$$R_{in}^i$$$, and one for $$$d$$$). The population size is set to be 50.

(a) The decrease of field inhomogeneities with the iteration is observed, and the stronger field strength is guaranteed by defining another nonlinear constraint. (b) The best candidate solution is shown. In (c) and (d), the part sectioned views of optimized and reference magnet array are shown, respectively. (e-i) The z-components of $$$\bf{B_0}$$$ in the central plane of FOV for optimized and reference magnet array. They are calculated by the current model and COMSOL. The calculation results by the current model and COMSOL show close agreement. Better field inhomogeneities and stronger field strength are shown in (e) and (g) compared with those in (f) and (i).

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)
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