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The design of a homogenous large-bore Halbach array for low field MRI
Thomas O'Reilly1, Wouter Teeuwisse1, Lukas Winter2, and Andrew Webb1

1C.J. Gorter Center for High Field MRI, Radiology, Leiden University Medical Center, Leiden, Netherlands, 2Physikalisch-Technische Bundesanstalt (PTB), Braunschweig and Berlin, Germany

Synopsis

The homogeneity of cylindrical Halbach arrays for low-field MRI is compromised by the finite length and discretisation into individual magnets. In this work we design and construct a large-bore Halbach array intended for imaging hydrocephalus in young children. The magnet is constructed using 23 double-layer Halbach rings with layer radii optimised for homogeneity. Simulated magnetic field strength and homogeneity over a 20cm spherical volume are 50.64mT and 433ppm, respectively. The homogeneity of the realised Halbach array is slightly degraded compared to simulations, but is sufficiently high to allow the use of conventional spatial encoding methods on such a system.

Introduction

The use of permanent magnets for generating the B0 field in low-cost, low-field MRI is attractive due to the very low stray field and the lack of power requirements. Cylindrical Halbach arrays are a common implementation for both NMR and MRI systems, but the theoretical high field homogeneity is severely compromised by the practical requirement of finite length1, as well as magnetic field perturbations due to the discretised elements of the Halbach array and variations in the magnetisation direction and magnitude of the individual magnets2. Previous work has shown that significant improvements in the magnetic field homogeneity are possible by optimising the positioning of the individual magnets of the Halbach array3. Most magnets produced so far have relatively small diameters, which prevent, for example, imaging of young children with hydrocephalus, which is the end goal of our research.

In this work we design and construct a new large-diameter Halbach array configuration that uses stacked rings of small magnets consisting of two concentric Halbach layers. The radii of the layers in each ring are varied to optimise the homogeneity of the Halbach array. We propose the use of smaller magnets for several reasons: (i) more rings can be stacked in a given length of magnet enabling finer optimisation, (ii) a larger total number of magnets is used which helps average out the variations in the flux of individual magnets, and (iii) the smaller forces associated with smaller magnets increases safety during filling and reduces physical demands on the magnet housing.

Methods

The Halbach array consists of 23 rings spaced 22mm apart, each ring contains two layers of 12mm cubic N48 magnets positioned in a k=1 Halbach configuration. Ring sizes of 148 mm radius (50 magnets) to 221mm radius (75 magnets) were simulated in CST Microwave Studio (Darmstadt, Germany). The field variation over a 25cm diameter spherical region was minimised by varying the ring radii in each layer using a genetic algorithm in python. Mirror symmetry of the ring sizes was enforced in order to maximise homogeneity. The outer layer of each ring has a 20/21mm larger radius than the inner layer to facilitate manufacturing. Each ring was assembled individually using a 12mm thick ring of PMMA to holdthe magnets and 3mm rings of PMMA were used as lids. The spacing between rings was fixed using M5 threaded rods.

B0 field measurements were acquired using the frequency of the proton peak of a small sample. Data were acquired using a solenoid RF coil (diameter: 15mm, length: 25mm, f0: 2.151MHz, bandwidth: 41kHz) controlled by a Kea2 Spectrometer (Magritek, Germany) with a 0.1ml sunflower oil phantom placed in the coil centre. Spectra were acquired using block pulse excitation (pulse length: 50µs, acquisition delay: 200µs, dwell time: 100µs, points: 1024, repetition time: 300ms, averages: 25).

Results

The optimised Halbach array is shown in Figure 1, the details on ring configurations and number of magnets are shown in Figure 2. Simulated and experimentally measured B0 maps are compared in Figure 3. Simulations give a mean field strength of 50.64mT over a 20cm diameter of spherical volume (DSV) and a field variation of 433ppm over the same volume. Figure 3c shows that the most significant variation occurs in the axis perpendicular to the direction of the magnetic field. The experimental results show a slightly lower central field (50.45mT), with larger field variations than in simulations: however the overall homogeneity is still very high. Figure 4 shows an experimentally-measured FID from the phantom, with a full-width-half-maximum linewidth of 120Hz.

Discussion

The Halbach array represents the largest one yet constructed for low-field MR, with the clear diameter of 27cm designed for imaging paediatrics with hydrocephalus. The use of a large number of small closely-spaced magnets not only enables rapid and safe assembly, but also helps to average out the effects of non-equivalent magnets, as evidenced by the relatively close agreement between the simulated and measured fields. Manufacturing tolerances and flexing of the final structure as well as variation in the properties of individual magnets are the likely cause of the small differences. Nevertheless, this degree of inhomogeneity should be relatively easy to improve by shimming using additional ferrous material. The high magnet homogeneity removes many of the problems of limited bandwidth of RF coils, and means that relatively low strength gradients can be incorporated to obtain 3-dimensional images: this is the next step in this project.

Acknowledgements

This work was funded by the following grant: ERC Advanced NOMA-MRI 670629

References

1. Turek K, Liszkowski P. Magnetic field homogeneity perturbations in finite Halbach dipole magnets. J. Magn. Reson. 2014;238:52–62

2. Soltner H, Blümler P. Dipolar Halbach magnet stacks made from identically shaped permanent magnets for magnetic resonance. Concepts Magn. Reson. Part A 2010;36A:211–222

3. Cooley CZ, Haskell MW, Cauley SF, et al. Design of Sparse Halbach Magnet Arrays for Portable MRI Using a Genetic Algorithm. IEEE Trans. Magn. 2018;54:1–12

Figures

Figure 1.a) Overview of a single ring of the Halbach array consisting of two layers of 12mm cubic N48 neodymium magnets, the magnetisation direction is indicated by the arrows. b) Side view of the final design of the magnet consisting of 23 rings with a total of 2948 12mm cubic N48 magnets. c) Photo of the constructed Halbach array. The magnetic field strength in the centre of the Halbach array is 50.45mT. The material cost of the Halbach array was 4000 euros.

Figure 2. The most homogenous ring configuration as suggested by a genetic algorithm for a Halbach array consisting of 23 rings of double Halbach layers using 12mm cube N48 magnets.

Figure 3. a & b) Simulated B0 field maps of the optimised Halbach array configuration. The magnetic field is oriented along the x axis, the bore of the magnet is oriented along the z-axis (see also figure 1). The mean field in a DSV at the centre of the magnet is 50.64mT with a field variation of 433 ppm. The constructed magnet shows a very similar magnetic field strength at the centre and larger field variations than simulations, as is expected, but overall homogeneity remains very high.

Figure 4. The time domain (left) and frequency spectrum (right) of an FID measurement (B1 frequency = 2.15 MHz, pulse length = 50 µs, repetition time = 300 ms, averages = 25) of a 0.1 ml oil phantom placed in the centre of a large-bore (27 cm diameter) Halbach array. The full-width-half-maximum linewidth of the spectra is 120 Hz.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
0272