Magnetic Particle Imaging Using Moving Halbach Cuboid and Frequency Mixing Magnetic Detection


 We present a magnetic particle imaging (MPI) device using a Halbach cuboid magnet and frequency mixing magnetic detection (FMMD) technology. A Field Free Line was formed in the center of a two-piece Halbach cuboid. Then, the cuboid was moved in the sample volume in a T-shaped and circular shape. The sample was exposed to a magnetic excitation field of two different frequencies. Due to the nonlinearity of the superparamagnetic iron oxide nanoparticles (SPIONs), harmonic frequencies and intermodulation products of the excitation frequencies are generated. This characteristic response signal from the particles was acquired by a coil system and demodulated by a FMMD electronics. Images were created by a backprojection method based on Radon and inverse Radon transformation. Using the Halbach cuboid, we were able to generate a stronger magnetic field compared to the previously reported equipment using large permanent magnets.. The results of the experiment showed that the combination of the Halbach cuboid and FMMD can acquire images similar to those of other existing MPI systems, suggesting that it is a method that has advantages in manufacturing and operation of MPI.


[Introduction]
Magnetic Particle Imaging (MPI) technology is one of the technologies of medical imaging equipment that has recently received considerable attention 1-4 . Much work has been done since Gleich and Weizenecker published the first paper on MPI in 2005 5 . MPI is a method of measuring the spatial distribution of magnetic nanoparticles and a field in which various kinds of clinical applications are being studied due to the advantage of being able to identify the location of various kinds of diseases because antibodies or antigens can be immobilized on the surface of Nano Magnetic Particles (NMP) 1, [6][7][8] . Since MPI is a non-ionizing method, it has the other advantage of higher safety than radiation-based methods such as Positron Emission Tomography. In relation to the instrumentation of MPI, fabrication can be largely divided into two parts. The first concerns how to obtain the signal from the magnetic nanoparticles.
The second is to find out where the signal is generated. The signal of MPI developed so far is based on the nonlinear magnetic properties of NMPs. The core material of magnetic particles used in MPI is mostly iron oxide. Magnetite and maghemite are the most commonly used NMPs among iron oxides. Although the basic magnetic properties of these two iron oxides are ferrimagnetic, when the size of the particles is less than 100 nm, they have superparamagnetic properties, which are good properties as signal materials. So, while the core material is iron oxide, NMPs, which have superparamagnetic properties (SPIOs), are mainly used in many applications including MPI 6 . SPIOs reacts sensitively to changes in the external magnetic field due to its very high magnetic susceptibility, but has a characteristic that it does not exhibit magnetic force when the external magnetic field is removed because remnant magnetization is very small. The magnetic properties of SPIOs can be described by the Langevin function. The selection field is made by a permanent magnet and the drive field by a solenoid coil (https://www.magneticinsight.com/). Another method is to create an FFL using a permanent magnet and move it mechanically. This method can be divided into a method using a large magnet and a method using a Halbach magnet array according to the method using a permanent magnet. In the case of large magnets, there is an advantage that the amount of calculation required when designing MPI is very small and can be made in an intuitive form. However, in order to increase the size, it is very difficult to obtain a large magnet with a constant magnetic force on the surface, and safety issues arise during manufacture. In a previous study, we presented a study on a device that can image the spatial distribution of SPIOs by permanent magnets and FMMD technology 14,15 . In this research, instead of using large magnets, an MPI system using Halbach cuboid and detection coils based on FMMD technology was fabricated.
A Halbach array is a way to control the direction and intensity of magnetic force by spatially arranging several permanent magnets. A Halbach cylinder is a magnet array in a ring shape.
The biggest feature of the Halbach cylinder is that the strength of the magnetic field outside the ring is theoretically almost zero, and the strength of the magnetic field inside and the distribution of the magnetic field can be controlled. FFL generation systems using Halbach cylinders are currently being used frequently in MPI research 16,17 . The method of making the Halbach cylinder proposed so far is to harden a small magnet with epoxy resin while adjusting the angle in a circular frame, or to make a frame using nonferrous metal (mainly aluminum) to fix the positions [17][18][19][20] . In reality, it is difficult and dangerous to arrange strong magnets at an angle. Instead, we fabricated a Halbach cuboid that can produce an FFL by arranging magnets only vertically or horizontally. In addition, by using a stage that permits translational "T" and "Round" mechanical movements, the equipment could be manufactured without additionally required components such as drive coil, cooling parts and power supply.    Therefore, in order to obtain a three-dimensional image, the specimen is moved to pass the FFL using the Z-axis stage. Table 1 gives detailed information on this coil system. The bobbin is fabricated from Polyetheretherketone material. The control box (UML-SNAS-100, UMLogics, Daejeon, Korea) used in this study includes a function to apply two frequencies to the FMMD coil and automatically acquire a non-linear signal. In addition, it includes a function to simultaneously acquire location information generated in the used stage. In order to supply sufficient power to the currently used FMMD coil, the low frequency and high frequency channels were connected to an AC amplifier (7224, AE TECHRON, IN, USA) and amplified 20 times.

[Operation and performance verification for MPI system]
The SPIO solution was purchased from Micromod (Synomag®, Rostock, Germany). The nominal hydrodynamic size of the particle was 50 nm. In this experiment, the pure NMP solution was used as the stock solution and the concentration was 25 mg/ml. The experimental data was obtained by performing a few procedures before acquiring image data.
For all experiments, 3 sets of samples were prepared, measured at least 3 times, and the average value and standard deviation of the FMMD signal 1 f +2 2 f were recorded. In order to get the negative reference data, the MPI system was operated without a sample, and the signal of 1 f +2 2 f was measured. Then, the sample was placed exactly at the center position of the detection coil, which gives the strongest signal. The detection limit for the SPIOs was measured The generated volume data was imaged using a voluemeviewer function of Matlab® (Mathworks, Natick, MA, USA). In order to prepare Figure 5, the parameters of the rendering editor were set to the maximum intensity projection, the alpha power was set to Mri-Mpi, and the color power was set to hot.
[Results and Discussion] In this study, we designed and fabricated an MPI system using a Halbach array consisting of relatively small magnets available on the market, replacing the large magnets that were used in our previous work 14  for an area such as this. Therefore, it is optimal to finally go to the cuboid shape by performing simulation on shapes other than the traditional cylinder method. In the case of the cuboid structure, the total area is 9,800 square mm (smaller than 36% compared to the cylinder structure). To fabricate an FFL-generating Halbach cuboid, a study on the optimal magnet placement was conducted using electromagnetic field simulation software (Faraday V10.2 Enginia Research Inc, MB, Canada) in advance. Figure 3 and 4 (top) shows that a FFL (Field Free Line) is generated in the center of the structure and the magnetic field gradient within 2.7 mm from the center of the FFL is +/-10 mT.. Based on this simulation, the following structures were fabricated ( Figure 3). All of the spherical objects surrounding the magnet were made of aluminum, and then anodizing treatment was performed. In this study, by using a Halbach cuboid instead of the plate-shaped magnet used in our previously published paper 14 , the weight could be reduced to about 1/3 (from 33.0 kg to 11.0 kg), and the strength of the magnetic force was higher than in the MPI using a plate-shaped magnet. It could be increased from 2.9 T/m on average to 3.7 T/m. The magnet shape proposed by other research teams is that many small magnets are solidified with epoxy resin 16,17 , or a Halbach cuboid shape is made by adjusting the angle of a square magnet.
This form is typical according to Halbach's theory. However, there are the following problems to be applied in an actual laboratory or commercialization. Even a small magnet has a slight difference in the strength of the magnetic field for each magnet, so even if a theoretically perfect calculation is performed, there are many cases that differ from the calculation in the process of hardening with resin. In reality, it is very difficult to determine the relative and absolute angles of each magnet. However, we were able to minimize various problems required to control the angle and position by placing all magnets vertically or horizontally through simulation.   Figure 4 shows that the actual FFL was created in the center of the Halbach cuboid.. The MPI system using the Halbach cuboid proposed so far uses the method of rotating the cuboid. However, since only rotation can obtain information on angle change, which is one of two sets of information necessary (degree and moving distance), an additional drive coil is installed in most cases 17,20 . In addition, the drive coil installation requires a separate design for the coil and ancillary equipment for power supply and cooling. Therefore, in the method proposed in this study, the function of the drive coil was replaced with a mechanical stage that moves in a "T" shape, as used in our previous setup 14 . The difference from the equipment we presented previously was that a coil was used on one side to provide an aperture for inserting the sample, while the two overlapping Halbach cuboids were used to make even this unnecessary. The left figure of Figure 5 shows the imaging results of samples filled with SPIO solution placed side by side with a width of 5.0~2.0 mm. This result shows that at least 5.0 mm can be separated and imaged using the currently developed MPI system. The figure on the right shows the test result of whether it is possible to image a sample of a spiral structure, which is a 3D sample. The results of this experiment show that it is possible to fully image the distribution of three-dimensional samples. and Silicone tube filled with SPIOs wound on an acryl rod. [Conclusion] In this paper, we introduced a novel approach for manufacturing of MPI equipment, an emerging technology in the medical imaging field, by combining Halbach cuboid, FMMD technology, and stages moving in the "T" and "Round" shapes. When removing the Halbach cuboid, the difficulty in manufacturing was solved by placing the magnet vertically and horizontally, which is not a typical method. Finally, by replacing the production and operation of the drive coil with a stage, it was possible to control the position of the FFL and reduce the need for an additional current supply system. Therefore, this study showed a clear possibility for a new MPI method different from the existing MPI system. [Acknowledgement]

[Competing Interests]
The authors declare no competing interests. [References]