Permanent magnet system and method of forming the same

Abstract

A method for forming a permanent magnet system is provided, the method comprising: determining one or more types of geometric parameters for forming a magnetic ring pair array, the magnetic ring pair array comprising a first subarray of a first magnetic ring and a second subarray of a second magnetic ring spaced apart from the first subarray of the first magnetic ring along a longitudinal axis; forming the magnetic ring pair array based on the determined one or more types of geometric parameters, wherein the above-mentioned determination of the one or more types of geometric parameters for forming the magnetic ring pair array is based on a genetic algorithm. A corresponding permanent magnet system such as formed by the method is also provided.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of priority to Singapore Patent Application No. 10201807522U filed on September 3, 2018, the contents of which are incorporated herein by reference in their entirety for all purposes. Technical Field

[0003] The present invention relates generally to a permanent magnet system and method of forming the same, and more particularly to a portable magnetic resonance imaging (MRI) system. Background Art

[0004] Most clinical magnetic resonance imaging (MRI) scanners are based on superconducting magnets. They are large, bulky, and have high purchase, site selection and maintenance costs. The various shortcomings of conventional MRI systems have led to an increasing interest in the development of portable MRI scanners. Compared with conventional MRI scanners based on superconducting magnets, portable MRI scanners have low cost, portability and compatibility with patients with metal implants, so they can provide complementary medical imaging solutions for mobile environments (e.g., ambulances and field hospitals), rural areas or underdeveloped regions / countries. In order to make MRI scanners portable, it may be inevitable to replace the superconducting magnets that occupy most of the space of the MRI system with other mechanisms to provide the B0 field. In addition, building an MRI scanner around the imaged part of the human body rather than covering the entire human body helps to achieve the compactness of the MRI system. On this basis, a portable MRI imaging system has been proposed, which builds a magnet or a magnet array and a radio frequency (RF) coil around the scanned object (e.g., head and limbs). The magnet array in this MRI system is configured to be compact so that the MRI system is compact. In this scheme, electromagnets and permanent magnet arrays may be good or suitable options for providing B0 fields. However, conventional portable MRI systems have not been found to be able to generate sufficient or expected magnetic fields for imaging (MRI imaging) within the intended field of view, for example, the field of view can accommodate a portion of the human body (e.g., a person's head).

[0005] In addition, the idea of ​​using a permanent magnet array as a source of a static main magnetic field (B0 field) for a portable MRI scanner may be attractive if zero power consumption and low cost are considered. However, when using conventional imaging methods using Fourier transform and linear gradient fields, a uniform B0 field may be required in an MRI scanner, which results in a bulky magnet array; or, if the magnet array is reduced to a portable size, the imaging capacity becomes too small to image organs such as the human body.

[0006] Therefore, it is desirable to provide a permanent magnet system and a method of forming the same in an attempt to overcome or at least improve one or more defects or problems associated with conventional permanent magnet systems, such as, but not limited to, being able to generate a sufficient or expected magnetic field within an expected field of view (e.g., a field of view that can accommodate a portion of a human body, such as a human head) for imaging in a portable MRI system. The above is the development background of the present invention. Summary of the invention

[0007] A first aspect of the present invention provides a method of forming a permanent magnet system, the method comprising:

[0008] determining one or more types of geometric parameters for forming an array of magnetic ring pairs, the array of magnetic ring pairs comprising a first subarray of a first magnetic ring and a second subarray of a second magnetic ring, the second subarray of the second magnetic ring being spaced apart from the first subarray of the first magnetic ring along a longitudinal axis; and

[0009] forming the magnetic ring pair array based on the determined one or more types of geometric parameters,

[0010] The above-mentioned determination of one or more types of geometric parameters for forming the magnetic ring pair array is based on a genetic algorithm.

[0011] In various first embodiments, based on the genetic algorithm, determining one or more types of geometric parameters for forming the magnetic ring pair array includes:

[0012] The one or more types of geometric parameters used to form the magnetic ring pair array are optimized with respect to the field strength and field uniformity in the longitudinal direction of the magnetic field in the field of view within the magnetic ring pair array, which are generated when the magnetic ring pair array is formed based on the determined one or more types of geometric parameters.

[0013] In various second embodiments, the first subarray of the first magnetic rings is divided into a first subarray of first ring segments around the longitudinal axis, and the second subarray of the second magnetic rings is divided into a second subarray of second ring segments around the longitudinal axis, each first ring segment extends through all first magnetic rings in the first subarray, and each second ring segment extends through all second magnetic rings in the second subarray.

[0014] In various second embodiments, based on the genetic algorithm, the above-mentioned determination of one or more types of geometric parameters for forming the magnetic ring pair array includes:

[0015] The one or more types of geometric parameters used to form the magnetic ring pair array are optimized with respect to the field strength and field uniformity of the magnetic field in the longitudinal direction and the field monotonicity of the magnetic field in the transverse direction in the field of view within the magnetic ring pair array, which are generated when the magnetic ring pair array is formed based on the determined one or more types of geometric parameters.

[0016] According to a second aspect of the present invention, there is provided a permanent magnet system, comprising:

[0017] Magnetic ring pair array, including:

[0018] a first sub-array of first magnetic rings; and

[0019] A second subarray of second magnetic rings, the second subarray of the second magnetic rings being spaced apart from the first subarray of the first magnetic rings along the longitudinal axis.

[0020] In various first embodiments, the magnetic ring pair array is configured based on one or more types of geometric parameters, and the one or more types of geometric parameters are determined to generate a magnetic field with an average field strength in the longitudinal direction equal to or greater than 150mT and a field uniformity equal to or less than 50000ppm in the field of view within the magnetic ring pair array.

[0021] In various first embodiments, the permanent magnet system is formed by a method of forming a permanent magnet system according to the various first embodiments described herein.

[0022] In various second embodiments, the first subarray of the first magnetic rings is divided into a first subarray of first ring segments around the longitudinal axis, and the second subarray of the second magnetic rings is divided into a second subarray of second ring segments around the longitudinal axis, each first ring segment extends through all first magnetic rings in the first subarray, and each second ring segment extends through all second magnetic rings in the second subarray.

[0023] In various second embodiments, the magnetic ring pair array is configured based on one or more types of geometric parameters to generate a magnetic field in the field of view within the magnetic ring pair array having an average field strength in the longitudinal direction equal to or greater than 100 mT and a field uniformity equal to or less than 200,000 ppm and a field gradient of field monotonicity equal to or less than 0.40 T / m in the transverse direction.

[0024] In various second embodiments, the permanent magnet system is formed by a method of forming a permanent magnet system according to various second embodiments described herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Embodiments of the present invention will be more easily understood and more apparent to those skilled in the art through the following written description which is merely an example and is combined with the accompanying drawings, in which:

[0026] Figures 1A to 1D Various types of conventional magnets are shown;

[0027] Figure 2 A schematic flow chart showing a method of forming a permanent magnet system according to various first embodiments of the present invention;

[0028] Figure 3 A schematic diagram showing a perspective view of a permanent magnet system according to various first embodiments of the present invention;

[0029] Figure 4 A schematic flow chart showing a method of forming a permanent magnet system according to various second embodiments of the present invention;

[0030] Figure 5 A schematic diagram showing a perspective view of a permanent magnet system according to various second embodiments of the present invention;

[0031] Figure 6 shows a schematic diagram of an MRI system according to various embodiments of the present invention;

[0032] Figure 7 A system for determining geometric parameters for forming an array of magnetic ring pairs according to various embodiments is shown;

[0033] Figure 8 shows a method for implementing or implementing Figure 7 A schematic block diagram of an example computer system of the system shown in;

[0034] Fig. 9 The first exemplary embodiment of the present invention is shown as follows Figure 3 A side cross-sectional view of a permanent magnet system shown in FIG.

[0035] Fig.10 A schematic flow chart showing the application of a genetic algorithm to design or configure a ring pair permanent magnet array according to various first exemplary embodiments of the present invention;

[0036] Fig.11 The first exemplary embodiment of the present invention is shown as follows Figure 3 A schematic diagram of a single magnetic ring of the magnetic ring pair array shown in FIG.

[0037] Fig. 12A A perspective view of an example magnetic ring aggregate showing two magnetic rings according to various first example embodiments of the present invention;

[0038] FIG. 12B to FIG. 12D The following table shows the relationship between (a)r=0mm( Fig. 12B )、(b)r=10mm( Fig. 12C ) and (c)r=20mm( Fig.12D ) using both the current model (indicated by asterisks) and COMSOL Multiphysics (indicated by a solid black line) to calculate the z-component of the magnetic field on the cylindrical surface of

[0039] Fig.13A shows a graph of fitness value variation versus iteration step for both the average fitness value and the best fitness value for candidate configurations according to various first exemplary embodiments of the present invention;

[0040] Fig. 13B A three-dimensional cross-sectional view of a ring-pair magnet array with an inner radius parameter ranging from 150 mm to 220 mm based on an optimized configuration according to various first exemplary embodiments of the present invention is shown;

[0041] Fig.14A and Fig. 14B The first exemplary embodiment of the present invention is respectively shown. Fig. 13B The optimized ring pair structure uses a simplified current model in FoV in (a) rz plane ( Fig.14A ) and (b) rz plane ( Fig. 14B ) on the magnetic field generated;

[0042] Fig.15A and Fig. 15B The reference Aubert ring pairs according to various first exemplary embodiments of the present invention are shown in FIG. Fig.15A ) and (b) rz plane ( Fig. 15B ) on the magnetic field generated;

[0043] Fig.16 The first exemplary embodiment of the present invention is shown. Fig. 13B The optimized ring pair design uses the r component of the magnetic field generated on the θ = 0 plane in the FoV using a simplified current model;

[0044] Fig.17A shows a schematic diagram of a segmented optimized magnet array according to various first exemplary embodiments of the present invention;

[0045] Fig. 17B and Fig. 17C An example of a piecewise optimized magnet array in the COMSOL Multiphysics simulation FoV is shown in the (a) r-θ plane ( Fig. 17B ) and (b) rz plane ( Fig. 17C ) on the magnetic field generated;

[0046] Fig.18 shows a concentric circle pattern provided by a ring-pair magnet array according to various first exemplary embodiments of the present invention;

[0047] Fig.19A and Fig.19B A front view and a side cross-sectional view respectively show a magnet array according to various second exemplary embodiments of the present invention;

[0048] Fig.19C Ring segments (segmented magnet elements) according to various second example embodiments are shown;

[0049] Fig. 20A shows a three-dimensional view of a pair of sector magnet segments according to various second example embodiments;

[0050] Fig. 20B The following are shown in Figure 1 based on MATLAB and based on COMSOL Multiphysics according to various second exemplary embodiments of the present invention. Fig. 20A The calculated B of the magnet segment pair on the y-axis observation point is shown in z ;

[0051] Fig.21A shows a graph of fitness value variation versus iteration step for both the average fitness value and the best fitness value for candidate configurations according to various second exemplary embodiments of the present invention;

[0052] Fig. 21B and Fig. 21C Shows perspective and front views of an optimized magnet array according to various second example embodiments of the present invention;

[0053] FIG. 22A to FIG. 22C The second exemplary embodiment of the present invention is shown. Fig. 21B and Fig. 21C The optimized magnet array shown in FIG is in the center xy plane (z = 0 mm) of the FoV calculated by MATLAB ( Fig.22A )、lateral xy plane (z=25mm) ( Fig. 22B ) and xz plane (y=0mm)( Fig. 22C ) z ;

[0054] Fig.22D and Fig.22E The second exemplary embodiment of the present invention is shown. Fig. 21B and Fig. 21C The optimized magnet array shown in FIG. is in the center xy plane (z = 0 mm) ( Fig.22D ) and the lateral xy plane in FoV (z = 25 mm) ( Fig.22E )B generated along the x direction z ;

[0055] FIG. 23A to FIG. 23CFIG. 4 shows a simulation performed in COMSOL Multiphysics to verify the optimized magnet array design according to various second exemplary embodiments of the present invention, namely, the simulated B0 field ( Fig.23A ), |B on the center plane of FoV xy / B0|(Unit: %) Fig. 23B ) and the simulated B0 field on the xz plane (y=0mm) ( Fig.23C );

[0056] Fig.24A and Fig. 24B The three-dimensional model of the short sparse Halbach array and the associated simulated field distribution on the central xy plane are shown respectively;

[0057] Fig.25A The Shepp-Logan two-dimensional phantom is shown;

[0058] Fig.25B Shows the use of Fig.24A The reconstructed image obtained by using the reference magnetic field generated by the Halbach array in;

[0059] Fig.25C The use of various second exemplary embodiments according to the present invention is shown Fig. 21B Reconstructed image obtained by the B0 field generated by the optimized magnet array in;

[0060] Fig.25D The use of various second exemplary embodiments according to the present invention is shown FIG. 26A to FIG. 26E A reconstructed image obtained by further optimizing the reference magnetic field generated by the array with improved monotonicity;

[0061] FIG. 26A to FIG. 26C The further optimized design with higher field monotonicity according to various second exemplary embodiments of the present invention is shown in the central xy plane (z=0 mm) of the FoV calculated by MATLAB ( Fig.26A )、lateral xy plane (z=25mm) ( Fig.26B ) and xz plane (y=0mm)( Fig.26C ) generated on z ;

[0062] Fig.26D and Fig.26E The center xy plane of the FoV (z=0 mm) ( Fig.26D ) and lateral xy plane (z=25mm) ( Fig.26E )B along the x direction z ;

[0063] Fig. 27 A circle around the FoV with its center in the xy plane (z=0 mm) offset by 25 mm from the center of the array in the negative x direction is shown according to various second exemplary embodiments of the present invention;

[0064] FIG. 28A to FIG. 28F 26 are divided into 4, 8, 12, 18, 24 and 36 sector magnets according to various second exemplary embodiments of the present invention; and

[0065] Figure 28G and Fig.28H The average B0 field strength (B 0-avg ) and field inhomogeneity as the number of segments increases. DETAILED DESCRIPTION

[0066] Various embodiments of the present invention provide a permanent magnet system and a method for forming the same, and more specifically, provide a permanent magnet system for a portable magnetic resonance imaging (MRI) system. For example, as described in the background art, it has not been found that a conventional portable MRI system can generate a sufficient or expected magnetic field within a desired field of view for imaging (MRI imaging), for example, the field of view can accommodate a portion of the human body (e.g., a person's head). To this end, various embodiments provide a permanent magnet system and a method for forming the same, which attempts to overcome or at least improve one or more defects or problems associated with conventional permanent magnet systems, such as but not limited to: being able to generate a sufficient or expected magnetic field within an expected field of view (e.g., the field of view can accommodate a portion of the human body, such as a person's head), thereby imaging in a portable MRI system.

[0067] According to various first embodiments, as described in the background technology, most clinical MRI scanners are based on superconducting magnets. These scanners are large, bulky, and have high purchase, site selection and maintenance costs. The various shortcomings of conventional MRI systems have led to an increasing interest in the development of portable MRI scanners. Compared with conventional MRI scanners based on superconducting magnets, portable MRI scanners have low cost, portability and compatibility with patients with metal implants, so they can provide complementary medical imaging solutions for mobile environments (e.g., ambulances and field hospitals), rural areas or underdeveloped regions / countries. In order to make MRI scanners portable, it may be inevitable to replace the superconducting magnets that occupy most of the space of the MRI system with other mechanisms to provide a B0 field. In addition, building an MRI scanner around the imaged part of the human body rather than covering the entire human body to build an MRI scanner helps to achieve the compactness of the MRI system. On this basis, a portable MRI imaging system has been proposed, which builds a magnet or a magnet array and a radio frequency (RF) coil around the scanned object (e.g., head and limbs). The magnet array in this MRI system is configured to be compact so that the MRI system is compact. In this scheme, electromagnets and permanent magnet arrays may be a better or more suitable choice for providing the B0 field. However, various first embodiments of the present invention note that providing such a magnet system is challenging, and therefore such a magnet system may need to have high field strength and high field uniformity within an expected field of view that can accommodate a portion of the human body (e.g., a human head). For example, various first embodiments of the present invention note that high field strength leads to a high signal-to-noise ratio, thereby bringing high spatial resolution in imaging, while high uniformity leads to a narrow operating bandwidth, which may bring possible high quality factors (Q values) to the radio frequency coils and spectrometer consoles. In addition, high uniformity may be necessary for the use of conventional gradient coils and the application of many conventional MRI sequences.

[0068] As for electromagnets, they use direct current to generate a static magnetic field. Electromagnets can be relatively easy to install and can be turned off at any time. However, the limitations of electromagnetic fields are that the output magnetic field is small and the size is large. Electromagnets dissipate a lot of heat, which limits the input power and therefore the field strength they can generate. Moreover, such electromagnets must be much larger in size than the field of view (FoV). In 2015, a low-cost MRI system using electromagnets became available. The custom-made biplanar electromagnet has a cross-sectional outer diameter of 220 cm, a width of 90 cm, and weighs about 340 kg. It is used to generate a magnetic field with an average field strength of 6.5 mT and a uniformity of about 100 ppm in a FoV with a diameter of 40 cm (e.g., the size of a head).

[0069] Permanent magnet systems can also be used as an option to generate B0 fields. They are compact in size, consume no power, and have no heat dissipation, so no cooling system is required, while the cost is relatively low. There are mainly two types of systems that have been used in portable MRI systems. One type is a magnetic circuit that includes two magnetic poles (with a converging magnet) and an iron yoke. In this system, the space between the two magnetic poles is used for imaging. Figure 1A and Figure 1B The H-shaped and C-shaped yokes shown are two examples of this type of system. The poles consist of small magnets that are stacked. A disadvantage of this system is that the size and weight of the system is proportional to the FoV. The iron yoke guides and focuses the magnetic flux, greatly reducing the fringe fields. However, it also significantly increases the weight and size of the magnet assembly. Typically, the FoV is much smaller than the size of the poles. For a head-sized FoV, the system can occupy up to the size of a room (>30m 2 ), weighing more than 10 tons. A mobile MRI system for imaging outdoor trees based on a C-shaped magnet was developed. The total weight of the magnet assembly is 57 kg, with a gap of 80 mm. It produces a B0 field with an average field strength of 0.3 T and a field uniformity of 60 ppm in a spherical space with a diameter of 30 mm.

[0070] Another type of permanent magnet system is a permanent magnet array. Two representatives of this type are the Halbach array proposed by Halbach (such as, see K. Halbach, "Design of permanent multipole magnets with oriented rare Earth cobalt material", Nucl. Instrum. Methods, 1980, Vol. 169, No. 1, pp. 1-10) and the unyoke magnetic ring pair proposed by Aubert on July 26, 1994 in U.S. Patent No. 5,332,971, inventor G. Aubert, "Permanent magnet for nuclear magnetic resonance imaging equipment" (for all purposes, the entire contents of which are incorporated herein by reference). (It may also be referred to as the Aubert ring pair in this article). Figure 1C and Figure 1D Representatives of these two categories are shown separately.

[0071] An ideal Halbach cylinder is a cylindrical magnet of infinite length whose polarization varies continuously in the azimuthal direction. These polarizations are Figure 1C As shown by the outer arrow in the figure. The Halbach cylinder has a Figure 1CA unidirectional uniform transverse field is generated inside the Halbach array (as shown by the inner arrow in the figure), while a negligible fringe field is generated outside. The Halbach array is an implementation of the Halbach cylinder, in which the cylinder is discretized in the azimuthal direction and constructed using permanent magnet strips, permanent magnet cubes, and permanent magnet cylinders. Compared with other permanent magnet systems, the discretization makes the Halbach array lighter. But on the other hand, sparse discretization reduces the field strength and uniformity. The use of small magnetic cubes for field shimming has been proposed to compensate for the degradation caused by discretization. In recent years, the Halbach array has been used to provide the B0 field in portable MRI systems. In the Halbach array, since the direction of the B0 field is transverse, the existing design of the RF coil of a conventional MRI scanner needs to be redesigned for a system using the Halbach array.

[0072] like Figure 1D The Aubert ring pair shown includes two magnetic rings with opposite radial polarizations (as shown by the outer arrows), one magnetic ring with polarization pointing inward and the other magnetic ring with polarization pointing outward. The combination of the two rings produces a confined longitudinal field in the central space of the structure (as shown by the inner arrows). When it is applied to MRI imaging, since the direction of the magnetic field is the same as the direction of the magnetic field in the superconducting magnet-based MRI system, the existing design and improvement of the RF coil of the conventional MRI scanner can be directly applied. However, various embodiments have noted that the uniformity and field strength of the magnetic field in the existing designs are insufficient, for example, insufficient for MRI imaging in a head-sized FoV. For example, the development of the Aubert ring pair has been reported. In particular, the ring pair includes 48 identical NdFeB magnetic cubes with dimensions of 12×12×12 mm and at 5 mm 3 The Aubert ring pair produces a magnetic field with an average field strength of 100 mT and a field uniformity of 40 ppm in space. The inner diameter of the magnet assembly is 52 mm. Therefore, for MRI imaging in a FoV such as the size of the head, the Aubert ring pair cannot produce a magnetic field with sufficient uniformity and field strength.

[0073] Thus, in various first embodiments, a design and optimization of a ring pair permanent magnet array for imaging (e.g., head imaging) in a portable MRI system is disclosed. The design may be based on an Aubert ring pair. In various embodiments, the design process applies a genetic algorithm (GA) to optimize the magnetic intensity and uniformity in a cylindrical FoV of, for example, 200 mm in diameter and 50 mm in length, located at the center of the magnet's inner cavity. According to various first embodiments, a simplified current model (which may also be referred to as a current density model in this application) is provided in the optimization loop to increase the speed at which the magnetic field is accurately calculated or determined.

[0074] Figure 2A schematic flow chart of a method 200 for forming a permanent magnet system according to various first embodiments of the present invention is shown. The method 200 includes: (at 202) determining one or more types of geometric parameters for forming a magnetic ring pair array, the magnetic ring pair array including a first sub-array of a first magnetic ring and a second sub-array of a second magnetic ring, the second sub-array of the second magnetic ring being spaced apart from the first sub-array of the first magnetic ring along a longitudinal axis; and (at 204) forming the magnetic ring pair array based on the determined one or more types of geometric parameters, wherein the above-mentioned determination of the one or more types of geometric parameters for forming the magnetic ring pair array is based on a genetic algorithm.

[0075] In various first embodiments, the longitudinal axis may be the longitudinal axis of the magnetic ring pair array and may be referred to as the z-axis of a three-dimensional (3D) Cartesian coordinate system (having an x-axis, a y-axis, and a z-axis).

[0076] In various first embodiments, with respect to 204, the first magnetic rings in the first sub-array are formed in series or arranged in series, and the adjacent (immediately adjacent) first magnetic rings are in contact with each other (through the cross-sections or planes facing each other). Similarly, the second magnetic rings in the second sub-array are formed in series or arranged in series, and the adjacent (immediately adjacent) second magnetic rings are in contact with each other (through the cross-sections or planes facing each other).

[0077] It has been advantageously found that a permanent magnet system including a magnetic ring pair array (the magnetic ring pair array includes a first subarray of a first magnetic ring and a second subarray of a second magnetic ring, and the second subarray of the second magnetic ring is spaced apart from the first subarray of the first magnetic ring along the longitudinal axis) formed in the manner described herein according to various first embodiments of the present application (based on one or more types of geometric parameters determined) can generate a sufficient or expected magnetic field (such as a magnetic field with a field strength (or average field strength) equal to or greater than 150 mT and a field uniformity equal to or less than 50000 ppm (million parts) in the longitudinal direction within the expected field of view) in an expected field of view (for example, the field of view can accommodate a part of the human body, such as a human head), thereby enabling imaging in a portable MRI system. As a non-limiting example, as described in various first exemplary embodiments later, the example permanent magnet system is advantageously found to be able to generate a longitudinal main static magnetic field with an average field strength of 169.7 mT and a uniformity of 24786 ppm in a field of view (cylindrical field of view) with a diameter of 200 mm and a thickness of 50 mm. For example, compared to a conventional ring pair structure of the same or similar size and mass, this significantly improves the field uniformity by about 80% while maintaining similar field strength.

[0078] In various first embodiments, based on a genetic algorithm, the above-mentioned determination of one or more types of geometric parameters for forming a magnetic ring pair array includes: optimizing the one or more types of geometric parameters for forming the magnetic ring pair array according to the field strength and field uniformity in the longitudinal direction of the magnetic field in the field of view within the magnetic ring pair array generated when the magnetic ring pair array is formed based on the determined one or more types of geometric parameters.

[0079] In various first embodiments, based on a genetic algorithm, the above-mentioned optimization of one or more types of geometric parameters for forming a magnetic ring pair array includes: obtaining a plurality of test configurations for forming the magnetic ring pair array, each test configuration including a geometric parameter test set, the geometric parameter test set being related to the one or more types of geometric parameters optimized to form the magnetic ring pair array; and determining, for each test configuration in the plurality of test configurations, a field strength and a field uniformity of the magnetic field in the longitudinal direction in the field of view within the magnetic ring pair array having the test configuration.

[0080] In various first embodiments, the above-mentioned determination of the field strength and field uniformity of the magnetic field for each test configuration in the multiple test configurations includes: for each test configuration in the multiple test configurations, determining the magnetic field of the magnetic ring pair array having the test configuration based on the current density model of each magnetic ring in the magnetic ring pair array having the test configuration.

[0081] In various first embodiments, the current density model is based on a first equivalent surface current source associated with a first surface of the magnetic ring facing a first direction and a second equivalent surface current source associated with a second surface of the magnetic ring facing a second direction, wherein the first direction is substantially parallel to the longitudinal axis, and the second direction is substantially parallel to the longitudinal axis and opposite to the first direction.

[0082] In various first embodiments, the current density model is simplified by configuring the current density model to determine that the magnetic field of each magnetic loop in the array of magnetic loop pairs having the test configuration is symmetric about the longitudinal axis.

[0083] In various first embodiments, the above-mentioned optimization of one or more types of geometric parameters for forming the magnetic ring pair array further includes: for each of the multiple test configurations, determining a fitness metric (e.g., a metric indicating the degree of fitness) of the field strength and field uniformity of the magnetic field, which is determined based on the current density model for the magnetic ring pair array having the test configuration; and determining whether the fitness metric determined for the multiple test configurations meets a predetermined condition. In this regard, if these fitness metrics meet the predetermined condition, the above-mentioned optimization of one or more types of geometric parameters for forming the magnetic ring pair array further includes: selecting one of the multiple test configurations as the one or more types of geometric parameters determined for the magnetic ring pair array. On the other hand, if these fitness metrics do not meet the predetermined condition, the above-mentioned optimization of one or more types of geometric parameters for forming the magnetic ring pair array further includes: generating multiple offspring configurations based on the selected number of test configurations in the multiple test configurations; performing mutation and crossover on the generated multiple offspring configurations; and for each of the multiple offspring configurations, determining the field strength and field uniformity of the magnetic field in the field of view within the magnetic ring pair array having the offspring configuration in the longitudinal direction.

[0084] Therefore, based on the genetic algorithm, the above optimization of one or more types of geometric parameters may be an iterative process, and is continuously performed until the predetermined condition is met.

[0085] In various first embodiments, the forming of the magnetic ring pair array includes: forming the magnetic ring pair array based on the determined one or more types of geometric parameters to generate a magnetic field having an average field strength in the longitudinal direction equal to or greater than 150 mT and a field uniformity equal to or less than 50,000 ppm in the field of view within the magnetic ring pair array. In various first embodiments, the average field strength may be equal to or greater than 160 mT, equal to or greater than 180 mT, equal to or greater than 200 mT, or within a range of 150 mT to 500 mT. In various embodiments, the field uniformity may be equal to or less than 40,000 ppm, equal to or less than 35,000 ppm, equal to or less than 30,000 ppm, equal to or less than 25,000 ppm, equal to or less than 20,000 ppm, equal to or less than 15,000 ppm, equal to or less than 10,000 ppm, or within a range of 5,000 ppm to 50,000 ppm.

[0086] In various first embodiments, the one or more types of geometric parameters for the array of magnetic ring pairs include one or more types of geometric parameters for each magnetic ring pair in the array of magnetic ring pairs.

[0087] In various first embodiments, each magnetic ring in the first sub-array and the second sub-array is in the shape of a hollow cylinder and is thus substantially annular. In various first embodiments, the hollow cylinder may be defined by a plurality of geometric parameters, the plurality of geometric parameters comprising: an inner radius parameter associated with an inner radius of the hollow cylinder, an outer radius parameter associated with an outer radius of the hollow cylinder, and a thickness (or height) parameter associated with a thickness (or height) of the hollow cylinder.

[0088] In various first embodiments, the one or more types of geometric parameters for each magnetic ring pair are selected from the group consisting of: an inner radius parameter related to the inner radius of the magnetic ring pair, an outer radius parameter related to the inner radius of the magnetic ring pair, and a thickness parameter related to the thickness of each magnetic ring in the magnetic ring pair.

[0089] In various first embodiments, the one or more types of geometric parameters for the magnetic ring pair array also include a quantity parameter related to the number of ring pairs in the magnetic ring pair array, and a distance parameter related to the distance between the first sub-array and the second sub-array along the longitudinal axis.

[0090] In various first embodiments, the one or more types of geometric parameters are at least multiple types of geometric parameters, ie, 2 or more types of geometric parameters.

[0091] In various first embodiments, the one or more types of geometric parameters consist of the inner radius parameter and the distance parameter.

[0092] In various embodiments, each magnetic ring pair in the array of magnetic ring pairs is an Aubert ring pair. In various first embodiments, each first magnetic ring in the first sub-array has a radial polarization in a first direction, and each second magnetic ring in the second sub-array has a radial polarization in a second direction, wherein the first direction and the second direction are opposite in direction (e.g., inward radial polarization and outward radial polarization).

[0093] Figure 3 A permanent magnet system 300 according to various first embodiments of the present invention is shown (such as corresponding to the permanent magnet system 300 described above with reference to FIG. Figure 2 Schematic diagram of a perspective view of a permanent magnet system formed by the method 200 for forming a permanent magnet system as described above. The permanent magnet system 300 includes: an array 302 of magnetic ring pairs 304 (304-1, 304-2, ..., 304-i, ..., 304-n), the array 302 including a first sub-array 308 of first magnetic rings and a second sub-array 309 of second magnetic rings, the second sub-array 309 of the second magnetic rings and the first sub-array 308 of the first magnetic rings are spaced apart along a longitudinal axis 312.

[0094] In various first embodiments, the array 302 of magnetic ring pairs 304 is configured based on one or more types of geometric parameters, wherein the one or more types of geometric parameters are determined to produce a magnetic field with an average field strength in the longitudinal direction 312 equal to or greater than 150mT and a field uniformity equal to or less than 50000ppm in the field of view within the array 302 of magnetic ring pairs 304.

[0095] In various first embodiments, according to the above reference Figure 2 The method 200 for forming a permanent magnet system as described above is used to form the permanent magnet system 300. Therefore, various features of the permanent magnet system 300 may correspond to (e.g., be the same as) features of the permanent magnet system formed by the method 200 as described above according to the various first embodiments, and therefore, for the sake of clarity and brevity, there is no need to specifically describe them. Figure 3 The permanent magnet system 300 shown repeats these features. Figure 2 The various first embodiments described in the method 200 are analogously applicable to Figure 3 300 shown, and vice versa.

[0096] As previously described, it has been advantageously discovered that such a permanent magnet system comprising an array of magnetic ring pairs according to various first embodiments (the magnetic ring pair array comprising a first subarray of first magnetic rings and a second subarray of second magnetic rings, the second subarray of the second magnetic rings being spaced apart from the first subarray of the first magnetic rings along a longitudinal axis) is capable of generating a sufficient or expected magnetic field within an intended field of view (e.g., a field of view that can accommodate a portion of a human body, such as a human head) for imaging in a portable MRI system.

[0097] According to various second embodiments, as also described in the background technology, if zero power consumption and low cost are considered, the idea of ​​using a permanent magnet array as a source of a static main magnetic field (B0 field) for a portable MRI scanner may be more attractive. However, when using a traditional imaging method using Fourier transform and linear gradient fields, a uniform B0 field may be required in the MRI scanner, which leads to a bulky magnet array; or, if the magnet array is reduced to a portable size, the imaging area becomes too small to image organs such as human bodies. In recent years, it has been proposed to use a nonlinear gradient field as a spatial encoding magnetic field (SEM) for MRI image reconstruction to overcome the physiological limitations of conventional spatial linear gradient settings, such as reducing peripheral nerve stimulation. Some examples are parallel imaging techniques using local gradient (PatLoc) imaging and O space imaging. In these methods, because a static field pattern without spatial linearity can be used to encode MRI signals for imaging, the requirements for the uniformity of the static field can be reduced. When a permanent magnet array is used to provide a B0 field, the array can have a smaller size and lighter weight to increase the imaging area that can accommodate a part of the human body (such as the head). This provides the opportunity to build a truly portable and low-cost MRI scanner.

[0098] The disclosed sparse dipole Halbach array (also referred to as "NMR mandala") is used to provide a SEM with a quadrupole field pattern in the transverse direction (main field plus gradient field) for portable head imaging. The SEM produced by the sparse Halbach array is a non-bijective curved field, thereby utilizing sensitivity encoding (SENSE) using multiple receiver coils to resolve spatial ambiguity. In addition, the change of the B0 field relative to the sample is obtained by rotating the magnet array to provide additional spatial encoding information to focus the MR signal. Although the ambiguity is reduced by utilizing multiple receiving coils and by rotating the magnet, there is still significant blurring in the central area of ​​the imaging space due to the relatively uniform central area of ​​the quadrupole SEM. In addition, the image quality is greatly reduced in areas with low or zero gradients. It is reported that shorter sparse Halbach arrays can be implemented for MR imaging. However, similar imaging problems caused by non-bijective encoded B0 fields still exist. In such an MRI system using a permanent magnet array, various second embodiments note that a monotonic SEM with a stronger gradient linearity can be preferred to obtain higher image quality.

[0099] Other magnet designs that produce linear SEMs have been reported in the literature. This is commonly seen in single-sided or single-sided NMR / MRI systems with one-dimensional profiles near the magnet surface. Examples in this category are horseshoe magnets, magnet arrays consisting of many small magnet blocks that are optimally arranged, single-bar magnets, single magnets with shaped iron pole caps on top, and Halbach cylinders when using stray fields outside the cylinder. For the magnets reported for single-sided or single-sided NMR / MRI systems, although the SEM is linear, the field of view (FoV) is usually limited to the area near the magnet surface, which is not large enough to accommodate and image large samples (e.g., a human head). Halbach arrays can have larger FoVs when using internal fields. In addition to the optimization of the reported monotonic fields, concentrically nested dipole and quadrupole Halbach cylinders have been previously proposed to obtain constant gradients for MRI imaging. For example, theoretically, the proposed nested Halbach cylinder has an average field strength of 0.45 T in a circular area with a diameter of 20 mm, and the gradient in the FoV can be varied in the range of 44.5 to 53.0 mT / m.

[0100] For the Halbach array, the magnetic field it provides is located in the transverse plane of the array cylinder, where the design of the conventional radio frequency (RF) coil cannot be directly applied. A ring pair magnet array 302 is provided as described according to various first embodiments, which shows a longitudinal field with relatively high field strength and uniformity in a cylindrical FoV (e.g., a diameter of 20 cm and a length of 5 cm). According to various first embodiments, the ring pair magnet array 302 may include a plurality of ring pairs 304 with different inner and / or outer radii. A single ring pair may have one ring with magnetization radially inward and another ring with magnetization radially outward. In G. Aubert's U.S. Patent "Cylindrical permanent magnet with longitudinal induced field" (May 7, 1991, Patent No. 5,014,032A, the entire contents of which are incorporated herein by reference for all purposes), a single ring pair is extended to a double ring pair structure to obtain a uniform field for MRI. As described according to various first embodiments, the design is further extended to an array of magnetic ring pairs (e.g., 10 ring pairs) to produce a stronger SEM with lower uniformity, thereby performing nonlinear imaging of MRI. According to various first embodiments, to indicate its characteristics, such a ring pair may be referred to as an inner and outer ring pair (IO ring pair). The field pattern generated by the IO ring pair magnet array 302 according to various first embodiments may be concentric, which is essentially to spatially encode the NMR / MRI signal in the radial direction. For this design or configuration according to various first embodiments, the encoding along the θ direction may be discarded or omitted. In order to achieve two-dimensional spatial encoding, according to various first embodiments, one method is to apply coil sensitivity encoding provided by a rotating receiving coil to obtain additional information in the θ direction. In various other embodiments, a rotating encoding magnet block (or multiple rotating encoding magnet blocks) may be introduced to break the axial symmetry of the magnetic field, thereby bringing additional information in the θ direction for two-dimensional imaging.

[0101] Therefore, in various second embodiments, in addition to having a higher field strength and acceptable field uniformity in the longitudinal direction, the IO ring pair magnet array 302 according to various first embodiments can be further optimized to obtain a one-dimensional monotonic field pattern that is conducive to image reconstruction. To achieve this purpose, according to various second embodiments, the ring pair can be discretized into ring segment pairs for optimization to obtain irregularly shaped rings. The IO ring pair magnet array design or configuration obtained in this way may be referred to as an irregularly shaped IO ring pair magnet array in this article. According to various second embodiments, a genetic algorithm is applied (for example, in the same or similar manner as the various first embodiments), and a current model (which may also be referred to as a current density model) for ring segment pairs (which may also be referred to as fan-shaped pairs) is derived and utilized to perform fast forward calculations of the magnetic field in the optimization.

[0102] Figure 4 A schematic flow chart of a method 400 for forming a permanent magnet system according to various second embodiments is shown. The method 400 includes: (at 402) determining one or more types of geometric parameters for forming an array of magnetic ring pairs, the array of magnetic ring pairs including a first subarray of first magnetic rings and a second subarray of second magnetic rings, the second subarray of the second magnetic rings being spaced apart from the first subarray of the first magnetic rings along a longitudinal axis, wherein the first subarray of the first magnetic rings is divided around the longitudinal axis into a first subarray of first ring segments, and the second subarray of the second magnetic rings is divided around the longitudinal axis into a second subarray of second ring segments, each first ring segment extending through all first magnetic rings in the first subarray, and each second ring segment extending through all second magnetic rings in the second subarray; and (at 404) forming the array of magnetic ring pairs based on the determined one or more types of geometric parameters, wherein the determining of the one or more types of geometric parameters for forming the array of magnetic ring pairs is based on a genetic algorithm.

[0103] In various second embodiments, as in various first embodiments, the longitudinal axis may be the longitudinal axis of the magnetic ring pair array and may be referred to as the z-axis of a three-dimensional (3D) Cartesian coordinate system (having an x-axis, a y-axis, and a z-axis).

[0104] In various second embodiments, regarding step 404, similar to various first embodiments, the first magnetic rings in the first sub-array are formed in series or arranged in series, and the adjacent (immediately adjacent) first magnetic rings are in contact with each other (through the cross-sections or planes facing each other). Similarly, the second magnetic rings in the second sub-array are formed in series or arranged in series, and the adjacent (immediately adjacent) second magnetic rings are in contact with each other (through the cross-sections or planes facing each other).

[0105] It has been advantageously found that a permanent magnet system including an array of magnetic ring pairs (the magnetic ring pair array includes a first subarray of first magnetic rings and a second subarray of second magnetic rings, the second subarray of the second magnetic rings being spaced apart from the first subarray of the first magnetic rings along the longitudinal axis, wherein the first subarray of the first magnetic rings is divided into a first subarray of first ring segments around the longitudinal axis, and the second subarray of the second magnetic rings is divided into a second subarray of second ring segments around the longitudinal axis) formed in the manner described in the second embodiment of the present application (based on the determined one or more types of geometric parameters) can generate a sufficient or expected magnetic field (such as a magnetic field with a field strength (or average field strength) equal to or greater than 100 mT and a field uniformity equal to or less than 200,000 ppm (million parts per million) in the longitudinal direction within the expected field of view) and a field monotonicity with a field gradient equal to or less than 0.40 T / m in the transverse direction (for example, along the x-axis) within the expected field of view, thereby performing imaging in a portable MRI system. As a non-limiting example, as will be subsequently described with respect to various example second embodiments, the example permanent magnet system is advantageously found to be capable of producing a longitudinal main static magnetic field having an average field strength of 132.98 mT and a field uniformity of 151840 ppm in a field of view (cylindrical field of view) having a diameter of 200 mm and a thickness (or length) of 50 mm.

[0106] In various second embodiments, based on the genetic algorithm, the above-mentioned determination of one or more types of geometric parameters for forming the magnetic ring pair array includes: optimizing the one or more types of geometric parameters for forming the magnetic ring pair array, with respect to the field strength and field uniformity in the longitudinal direction of the magnetic field in the field of view within the magnetic ring pair array and the field monotonicity in the transverse direction of the magnetic field, which are generated when the magnetic ring pair array is formed based on the determined one or more types of geometric parameters.

[0107] In various second embodiments, generally speaking, the genetic algorithm performs or functions in a manner similar or identical to the various first embodiments described herein, except that one or more types of geometric parameters are additionally optimized for field monotonicity in the transverse direction of the magnetic field in the field of view within the magnetic ring pair array.

[0108] In various second embodiments, based on the genetic algorithm, the above-mentioned optimization of one or more types of geometric parameters for forming the magnetic ring pair array includes: obtaining multiple test configurations for forming the magnetic ring pair array, each test configuration including a geometric parameter test set, and the geometric parameter test set is related to the one or more types of geometric parameters optimized to form the magnetic ring pair array; and for each test configuration in the multiple test configurations, determining the field strength and field uniformity of the magnetic field in the longitudinal direction and the field monotonicity of the magnetic field in the transverse direction in the field of view within the magnetic ring pair array having the test configuration.

[0109] In various second embodiments, the above-mentioned determination of the field strength, field uniformity and field monotonicity of the magnetic field for each test configuration in the multiple test configurations includes: for each test configuration in the multiple test configurations, determining the magnetic field of the magnetic ring pair array having the test configuration based on the current density model of each ring segment of each magnetic ring in the magnetic ring pair array having the test configuration.

[0110] In various second embodiments, the current density model is based on a first equivalent surface current source associated with a first surface of the ring segment facing a first direction, a second equivalent surface current source associated with a second surface of the ring segment facing a second direction, and a third equivalent surface current source associated with a third surface of the ring segment and a fourth surface of the ring segment, wherein the first direction is substantially parallel to the longitudinal axis, the second direction is substantially parallel to the longitudinal axis and opposite to the first direction, the third surface is between the first surface and the second surface, and the fourth surface is between the first surface and the second surface and facing the third surface.

[0111] In various second embodiments, the current density model is simplified by configuring the current density model so that each ring segment of each magnetic ring in the array of magnetic ring pairs having the test configuration generates a magnetic field, wherein configuring the current density model includes setting each magnetic ring pair in the array of magnetic ring pairs to have an inner radius parameter associated with an inner radius of the magnetic ring pair that tapers (e.g., increases incrementally) from an outermost magnetic ring pair in the array of magnetic ring pairs to an innermost magnetic ring pair in the array of magnetic ring pairs.

[0112] In various second embodiments, the current density model is further simplified by configuring the current density model to determine that the magnetic field of each ring segment of each magnetic ring in the array of magnetic ring pairs having the test configuration is symmetric relative to a plane perpendicular to the longitudinal axis and symmetric about the transverse axis.

[0113] In various second embodiments, the above-mentioned optimization of one or more types of geometric parameters for forming the magnetic ring pair array further includes: determining, for each test configuration in the plurality of test configurations, a fitness metric (e.g., a metric indicating the degree of fitness) of field strength, field uniformity, and field monotonicity of a magnetic field, the magnetic field being determined for the magnetic ring pair array having the test configuration based on the current density model; and determining whether the fitness metric determined for the plurality of test configurations satisfies a predetermined condition. In this regard, if the fitness metric satisfies the predetermined condition, the above-mentioned optimization of the one or more types of geometric parameters for forming the magnetic ring pair array further includes: selecting one of the plurality of test configurations as the one or more types of geometric parameters determined for the magnetic ring pair array. On the other hand, if the fitness metric does not satisfy the predetermined condition, the above-mentioned optimization of the one or more types of geometric parameters used to form the magnetic ring pair array also includes: generating multiple offspring configurations based on a selected number of test configurations among the multiple test configurations; mutating and crossing the generated multiple offspring configurations; and for each offspring configuration among the multiple offspring configurations, determining the field strength and field uniformity of the magnetic field in the longitudinal direction and the field monotonicity of the magnetic field in the transverse direction in the field of view within the magnetic ring pair array having the offspring configuration.

[0114] Therefore, based on the genetic algorithm, similar to or the same as the various first embodiments, the above optimization of one or more types of geometric parameters may be an iterative process, and is continuously performed until the predetermined condition is met.

[0115] In various second embodiments, the forming of the magnetic ring pair array includes: forming the magnetic ring pair array based on the determined one or more types of geometric parameters to generate a magnetic field in the field of view within the magnetic ring pair array with an average field strength in the longitudinal direction equal to or greater than 100 mT and a field uniformity equal to or less than 200,000 ppm and a field gradient of field monotonicity equal to or less than 0.40 T / m. In various second embodiments, the average field strength may be equal to or greater than 120 mT, equal to or greater than 140 mT, equal to or greater than 160 mT, equal to or greater than 180 mT, or within a range of 100 mT to 300 mT. In various embodiments, the field uniformity may be equal to or less than 180,000 ppm, equal to or less than 150,000 ppm, equal to or less than 120,000 ppm, equal to or less than 100,000 ppm, or within a range of 50,000 ppm to 200,000 ppm. In various embodiments, the field gradient may be equal to or less than 0.36 T / m, equal to or less than 0.30 T / m, equal to or less than 0.26 T / m, equal to or less than 0.23 T / m, equal to or less than 0.20 T / m, or within a range of 0.10 T / m to 0.40 T / m.

[0116] In various second embodiments, the one or more types of geometric parameters for the array of magnetic ring pairs include one or more types of geometric parameters for each ring segment of each magnetic ring pair in the array of magnetic ring pairs.

[0117] In various second embodiments, one or more types of geometric parameters for each ring segment are selected from the group consisting of: an inner radius parameter associated with the inner radius of the ring segment, an outer radius parameter associated with the outer radius of the ring segment, a step reduction parameter associated with the step reduction of the outer radius of the ring segment, and a gradient series parameter associated with the series of the gradient function associated with the ring segment.

[0118] In various second embodiments, the one or more types of geometric parameters for the array of magnetic ring pairs also include a quantity parameter related to the number of ring segments in each of the first sub-array of the first magnetic ring and the second sub-array of the second magnetic ring, and a distance parameter related to the distance between the first sub-array of the first magnetic ring and the second sub-array of the second magnetic ring along the longitudinal axis.

[0119] In various first embodiments, the one or more types of geometric parameters are at least multiple types of geometric parameters, ie, two or more types of geometric parameters.

[0120] In various second embodiments, the one or more types of geometric parameters consist of an outer radius parameter, a step reduction parameter, and a gradient level parameter.

[0121] In various second embodiments, each magnetic ring pair in the array of magnetic ring pairs is an Aubert ring pair. In various second embodiments, each first magnetic ring in the first sub-array has a radial polarization in a first direction, and each second magnetic ring in the second sub-array has a radial polarization in a second direction, wherein the first direction and the second direction are opposite in direction (e.g., inward radial polarization and outward radial polarization).

[0122] Figure 5 A permanent magnet system 500 according to various second embodiments of the present invention (such as corresponding to the permanent magnet system 500 described above) is shown. Figure 4Schematic diagram of a perspective view of a permanent magnet system formed by the method 400 for forming a permanent magnet system as described above. The permanent magnet system 500 includes: an array 502 of magnetic ring pairs, the array including a first sub-array 508 of first magnetic rings and a second sub-array 509 of second magnetic rings, the second sub-array 509 of the second magnetic rings and the first sub-array 508 of the first magnetic rings being spaced apart along a longitudinal axis 512. In addition, the first sub-array 508 of the first magnetic rings is divided into a first sub-array 522 of first ring segments 524 around the longitudinal axis 512, and the second sub-array 509 of the second magnetic rings is divided into a second sub-array 526 of second ring segments 528 around the longitudinal axis 512. Figure 5 As can be seen in FIG. 5 , each first ring segment 524 extends through all first magnetic rings in the first sub-array 508 , and each second ring segment 528 extends through all second magnetic rings in the second sub-array 509 .

[0123] In various second embodiments, each magnetic ring pair in the magnetic ring pair array is configured to have an inner radius parameter associated with an inner radius of the magnetic ring pair that gradually changes (e.g., incrementally increases) from an outermost magnetic ring pair in the magnetic ring pair array to an innermost magnetic ring pair in the magnetic ring pair array.

[0124] In various second embodiments, the magnetic ring pair array is configured based on one or more types of geometric parameters to generate a magnetic field having an average field strength equal to or greater than 100 mT and a field uniformity equal to or less than 200,000 ppm in the longitudinal direction (e.g., parallel to the longitudinal axis 512 (or z-axis)) and a field gradient equal to or less than 0.40 T / m in the transverse direction (e.g., parallel to the transverse axis 513 (or x-axis)) in the field of view within the magnetic ring pair array.

[0125] In various second embodiments, by referring to Figure 4 The method 400 for forming a permanent magnet system described above is used to form the permanent magnet system 500. Therefore, various features of the permanent magnet system 500 may correspond to (e.g., be the same as) the features of the permanent magnet system formed by the method 400 described above according to various second embodiments. Therefore, for the sake of clarity and brevity, there is no need to specifically Figure 5 The permanent magnet system 500 shown repeats these features. Figure 4 The various second embodiments described in the method 400 are analogously applicable to Figure 5 The permanent magnet system 400 shown is also vice versa.

[0126] Figure 6 Schematic diagram of an MRI system 600 according to various embodiments of the present invention is shown. In various embodiments, the MRI system 600 is a portable MRI system. The MRI system 600 includes a first embodiment of the present invention. Figure 3The permanent magnet system 300 described herein or according to various second embodiments referred to herein Figure 5 The described permanent magnet system 500, the permanent magnet system 300 or 500 is configured to generate or generate a magnetic field for MRI. Those skilled in the art will recognize that the various components of the MRI system are known in the art, so for the sake of clarity and brevity, there is no need to describe the various components known in the art for the system 200. For example, those skilled in the art will recognize that the MRI system 600 can be based on a desired or suitable existing MRI system, but its permanent magnet system is replaced with a permanent magnet system 300 or 500 according to various first or second embodiments of the present invention. Those skilled in the art will also recognize that various modifications can be made to such an MRI system as needed or appropriate without exceeding the scope of the present invention, such as reducing the size of the MRI system by the permanent magnet system 300 or 500 of various first or second embodiments of the present invention.

[0127] Figure 7 A schematic block diagram of a system 700 for determining one or more types of geometric parameters for forming a magnetic ring pair array (or simply, for determining geometric parameters) according to various embodiments, such as the above referenced system 700 according to various first embodiments. Figure 3 The magnetic ring pair array 302 described above or according to various second embodiments Figure 5 The magnetic ring pair array 502 described. The system 700 includes a memory 702 and at least one processor 704, the processor 704 is connected to the memory 702 in communication and is configured to: determine the above reference for forming the various first embodiments Figure 3 One or more types of geometric parameters of the magnetic ring pair array 302 described, the magnetic ring pair array 302 includes a first sub-array of a first magnetic ring and a second sub-array of a second magnetic ring, the second sub-array of the second magnetic ring and the first sub-array of the first magnetic ring are spaced apart along the longitudinal axis; or, determining the above reference for forming the various second embodiments according to the present invention. Figure 5 One or more types of geometric parameters of the described magnetic ring pair array 502, the magnetic ring pair array 502 includes a first sub-array of first magnetic rings and a second sub-array of second magnetic rings, the second sub-array of the second magnetic rings and the first sub-array of the first magnetic rings are spaced apart along a longitudinal axis, wherein the first sub-array of the first magnetic rings is divided into a first sub-array of first ring segments around the longitudinal axis, and the second sub-array of the second magnetic rings is divided into a second sub-array of second ring segments around the longitudinal axis, each first ring segment extends through all first magnetic rings in the first sub-array, and each second ring segment extends through all second magnetic rings in the second sub-array.

[0128] Those skilled in the art will appreciate that the at least one processor may be configured to perform the desired functions or operations through one or more sets of instructions (e.g., software modules) that may be executed by the at least one processor 704 to perform the desired functions or operations. Figure 7 As shown, the system 700 may include a geometric parameter determination module (or a geometric parameter determination circuit) 706, which is configured to: determine the geometric parameter determination circuit for forming the geometric parameter determination circuit according to the various first embodiments. Figure 3 One or more types of geometric parameters of the magnetic ring pair array 302 described, the magnetic ring pair array 302 includes a first sub-array of a first magnetic ring and a second sub-array of a second magnetic ring, the second sub-array of the second magnetic ring and the first sub-array of the first magnetic ring are spaced apart along the longitudinal axis; or, determining the above reference for forming the various second embodiments according to the present invention. Figure 5 One or more types of geometric parameters of the described magnetic ring pair array 502, the magnetic ring pair array 502 includes a first sub-array of first magnetic rings and a second sub-array of second magnetic rings, the second sub-array of the second magnetic rings and the first sub-array of the first magnetic rings are spaced apart along a longitudinal axis, wherein the first sub-array of the first magnetic rings is divided into a first sub-array of first ring segments around the longitudinal axis, and the second sub-array of the second magnetic rings is divided into a second sub-array of second ring segments around the longitudinal axis, each first ring segment extends through all first magnetic rings in the first sub-array, and each second ring segment extends through all second magnetic rings in the second sub-array.

[0129] Those skilled in the art will recognize that the above modules may be implemented by or as a functional module (e.g., a circuit or a software program) as needed or appropriate. For example, the geometric parameter determination module 706 may be implemented as an executable software program (e.g., a software application or simply referred to as an "app"), which may be stored in the memory 702 and executed by the at least one processor 704 to perform the functions / operations described herein according to various embodiments.

[0130] In various embodiments, system 700 corresponds to the above reference Figure 2 Step 202 of determining one or more types of geometric parameters for forming an array of magnetic ring pairs in the method 200 described above, or corresponds to the above reference Figure 4The step 402 of determining one or more types of geometric parameters for forming a magnetic ring pair array in the method 400 described above, therefore, the various functions or operations configured to be executed by at least one processor 704 may correspond to the step 202 in the method 200 described above according to various first embodiments or to the step 402 in the method 400 described above according to various second embodiments, so for the sake of clarity and brevity, there is no need to repeat these functions or operations for the system 200. In other words, the various embodiments described in the context of step 202 of the method 200 or step 402 of the method 400 of the present application are applicable to the corresponding system (e.g., system 700) by analogy, and vice versa.

[0131] For example, in various embodiments, the memory 702 may have stored therein a geometric parameter determination module 706 as described above according to various embodiments, which can be executed by at least one processor 704 to perform the corresponding functions / operations described above in this application.

[0132] According to various embodiments of the present disclosure, a computing system, a controller, a microcontroller, or any other system providing processing capabilities may be provided. Such a system may be considered to include one or more processors and one or more computer-readable storage media. For example, the aforementioned system 700 may include a processor (or controller) 704 and a computer-readable storage medium (or memory) 702, for example, these processors 704 and computer-readable storage medium 702 are used to perform various processes as described in the present application therein. The memory or computer-readable storage medium used in various embodiments may be: a volatile memory, such as a dynamic random access memory (DRAM); or a non-volatile memory, such as a programmable read-only memory (PROM), an erasable PROM (EPROM), an electrically erasable PROM (EEPROM); or a flash memory, such as a floating gate memory, a charge trap memory, a magnetoresistive random access memory (MRAM), or a phase change random access memory (PCRAM).

[0133] In various embodiments, a "circuit" may be understood as any kind of logical implementation entity, which may be a dedicated circuit or a processor that executes software stored in a memory, firmware, or any combination thereof. Thus, in one embodiment, a "circuit" may be a hard-wired logic circuit or a programmable logic circuit, such as a programmable processor, for example, a microprocessor (e.g., a complex instruction set computer (CISC) processor or a reduced instruction set computer (RISC) processor). A "circuit" may also be a processor that runs software, such as any kind of computer program, such as a computer program using a virtual machine code such as Java. According to a number of alternative embodiments, any other kind of implementation of the corresponding functions described in further detail below may also be understood as a "circuit". Similarly, a "module" may be part of a system according to various embodiments of the present invention, and may encompass the aforementioned "circuit", or may be understood as any kind of logical implementation entity therein.

[0134] Some portions of the present disclosure are presented explicitly or implicitly using algorithms and functional or symbolic representations of operations on data in a computer memory. These algorithmic descriptions and functional or symbolic representations are the means used by those skilled in the art of data processing to most effectively communicate the substance of their work to others skilled in the art. An algorithm herein is generally considered to be a self-consistent sequence of steps leading to a desired result. These steps require physical manipulations of physical quantities, such as electrical, magnetic, or optical signals that can be stored, transmitted, combined, compared, and otherwise manipulated.

[0135] It should be understood that, unless otherwise specifically stated and as will become apparent from the following, throughout the specification of this application, discussions using terms such as "determine," "optimize," "obtain," "generate," "mutate," "perform crossover," etc. refer to the actions and processes of a computer system or similar electronic device that processes data represented by physical quantities within the computer system and converts it into other data similar to physical quantities within the computer system, other information storage, transmission device, or display device.

[0136] The specification of the application also discloses a system (for example, it can also be embodied as equipment or devices) for performing the operation / function of each step of the method described in the application. Such a system can be specially constructed for the desired purpose, or can include a general-purpose computer or other devices selectively activated or reconfigured by a computer program stored in a computer. The algorithm presented in the application is not inherently associated with any specific computer or other device. Various general-purpose machines can be used together with computer programs according to the teachings of the application. Alternatively, it may also be appropriate to construct a more specialized device for performing the required method steps.

[0137] In addition, it is obvious to those skilled in the art that the various steps of the method described in this application can be made effective by computer code, so this specification also discloses at least implicitly a computer program or software / functional module. The computer program is not intended to be limited by any specific programming language and its implementation method. It should be understood that various programming languages ​​and their encodings can be used to implement the teachings disclosed in this application. Moreover, the computer program is not intended to be limited by any specific control flow. There are many other variants of the computer program, and these variants can use different control flows without departing from the spirit or scope of the present invention. For example, those skilled in the art will recognize that the geometric parameter determination module 706 can be a software module implemented by a computer program or instruction set executable by a computer processor for performing the desired function, or it can be a hardware module as a functional hardware unit designed to perform the desired function. It should also be recognized that a combination of hardware modules and software modules can be implemented.

[0138] In addition, one or more steps of the computer program / module or method described in the present application can be performed in parallel rather than in sequence. Such a computer program can be stored on any computer-readable medium. The computer-readable medium may include a storage device, such as a disk or optical disk, a memory chip, or other storage devices that are suitable for being connected to a general-purpose computer. When loaded and executed on such a general-purpose computer, the computer program effectively realizes a device for realizing one or more steps of the method described in the present application.

[0139] In various embodiments, a computer program product is provided, which is embodied in one or more computer-readable storage media (non-transitory computer-readable storage media) and includes instructions (e.g., a geometric parameter determination module 706) that can be executed by one or more computer processors to perform the above referenced method according to various first embodiments. Figure 2 The step 202 of determining one or more types of geometric parameters for forming the magnetic ring pair array described above, or performing the above reference according to various second embodiments Figure 4 The step 402 of determining one or more types of geometric parameters for forming a magnetic ring pair array is described. Therefore, various computer programs or modules described in this application can be stored in a system (such as a computer program) that can be used in this application. Figure 7 The computer program product received by the system 700 shown in the figure is used to implement the required or expected functions through the execution of at least one processor 704 of the system 700.

[0140] The software or functional modules described in this application may also be implemented as hardware modules. More particularly, in a hardware sense, a module is a functional hardware unit designed to be used together with other components or modules. For example, a module may be implemented using discrete electronic components, or a module may form a part of an entire electronic circuit such as an application specific integrated circuit (ASIC). Many other possibilities also exist. Those skilled in the art will recognize that the software or functional modules described in this application may also be implemented as a combination of hardware modules and software modules.

[0141] In various embodiments, system 700 may be implemented by any computer system (e.g., a desktop or portable computer system) including at least one processor and memory, such as in Figure 8 800 is schematically shown as a non-limiting example in FIG. 800. Multiple steps or functional modules (e.g., geometric parameter determination module 706) can be implemented as software, such as a computer program that is executed within the computer system 800 and instructs the computer system 800 (particularly one or more processors therein) to perform one or more steps of the method / function of various embodiments described in the present application. The computer system 800 may include a computer module 802, input modules such as a keyboard 804 and a mouse 806, and multiple output devices such as a display 808 and a printer 810. The computer module 802 can be connected to a computer network 812 via a suitable transceiver device 814 to enable access to other network systems such as the Internet or a local area network (LAN) or a wide area network (WAN). The computer module 802 in this example may include a processor 818, a random access memory (RAM) 820, and a read-only memory (ROM) 822 for executing various instructions. The computer module 802 may also include a number of input / output (I / O) interfaces, such as an I / O interface 824 to the display 808 and an I / O interface 826 to the keyboard 804. In general, the components of the computer module 802 communicate via an interconnect bus 828 in a manner known to those skilled in the relevant art.

[0142] Those skilled in the art will recognize that the terms used in this application are only used to describe various embodiments and are not intended to limit the present invention. As used in this application, unless other meanings are clearly shown in the context, the singular forms "one", "an" and "the" are also intended to cover plural forms. It is further recognized that when the specification of the application uses the terms "include" and / or "comprising", the terms specify the presence of the described features, integers, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or combinations thereof.

[0143] Those skilled in the art will recognize that the terms used in this application are only used to describe various embodiments and are not intended to limit the present invention. As used in this application, unless other meanings are clearly shown in the context, the singular forms "one", "an" and "the" are also intended to cover plural forms. It is further recognized that when the specification of the application uses the terms "include" and / or "comprising", the terms specify the presence of the described features, integers, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or combinations thereof.

[0144] In order to make the present invention easy to understand and put into practice, various exemplary embodiments of the present invention will be described below by way of example only and not limitation. However, those skilled in the art will recognize that the present invention can be implemented in a variety of different forms, and the present invention should not be construed as being limited to the exemplary embodiments set forth below. On the contrary, these exemplary embodiments are provided so that this disclosure is comprehensive and complete, and fully convey the scope of the present invention to those skilled in the art.

[0145] In particular, for a better understanding of the present invention and without limitation or loss of generality, various example embodiments of the present invention will now be described with respect to an example permanent magnet array for head imaging in a low-field portable MRI system.

[0146] According to various first exemplary embodiments, a design and optimization (e.g., configuration) of a ring pair permanent magnet array is disclosed, which is used for head imaging in a portable MRI system. The design can be based on an Aubert ring pair. During the design process, according to various first exemplary embodiments, a genetic algorithm (GA) is applied to optimize the field strength and uniformity, for example, to optimize the field strength and uniformity in a cylindrical FoV with a diameter of 200 mm and a length of 50 mm at the center of the magnet inner cavity. In the optimization cycle, according to various first exemplary embodiments, a simplified current model is provided to accelerate the accurate calculation of the magnetic field. In the "I. Design and Optimization" section described below, a design and optimization process including the application of an example genetic algorithm and a simplified current model is described according to various first exemplary embodiments. In the "II. Results" section described below, simulation results of the optimized magnet array are shown according to various first exemplary embodiments, which show that the optimized magnetic field uniformity is significantly improved compared to the Aubert ring pair of magnetic materials of similar size and the same mass after optimization. Subsequently, the "III. Discussion" section shows a discussion of the design and optimization, and the "IV. Conclusion" section provides a conclusion.

[0147] I. Design and Optimization

[0148] According to various first exemplary embodiments, an exemplary ring pair permanent magnet array (eg, corresponding to the permanent magnet system 300 described according to various first embodiments) is an Aubert ring pair (eg, Figure 1D In various first example embodiments, the example permanent magnet system 300 may be a component of these Aubert ring pairs, where Figure 3 and Fig. 9 As shown, the axis of the ring 304 is aligned with the z-axis 312 . Figure 3 and Fig. 9 A three-dimensional view and a two-dimensional side view of an example permanent magnet system 300 are shown, respectively. In particular, Figure 3 and Fig. 9 An example ring-pair permanent magnet array 302 is shown, wherein: Figure 3 The polarization of each ring is indicated by the corresponding arrow and labeled and A three-dimensional view of Fig. 9 Shows the mark t i and side view of d.

[0149] For illustrative purposes only, Figure 3 and Fig. 9 In both, the example Aubert ring pair is indicated by a white border. In the example permanent magnet system 300, as Fig. 9 As shown, the inner radius of each ring pair 304 (304-1, 304-2, ..., 304-i, ..., 304-n) is The outer radius is Thickness t i , and are the coordinates of the outer surface and the inner surface of the magnetic ring 304-i along the z-axis 312, respectively, which define the position of the ring 304-i along the z-axis 312, where j=1 and j=2 indicate the left ring and the right ring, respectively. d represents the distance between the two inner surfaces of the two innermost rings, and i is the index of the ring pair when the ring pair is indexed from the outside to the inside (i.e., from the outermost ring pair to the innermost ring pair). In the example permanent magnet system 300, the size of the magnet array 302 can be optimized towards achieving high field uniformity and high field strength. and t i and the number of ring pairs. By way of example, for two-dimensional head imaging, the FoV can be set to a cylindrical region with a diameter of 200 mm and a length of 50 mm at the center of the magnet cavity. For optimization, a genetic algorithm is applied, and an efficient current model is provided and used for fast forward calculation. Details are shown below according to various first exemplary embodiments of the present invention.

[0150] IA. Genetic Algorithm

[0151] Genetic algorithms are random search algorithms based on the theory of natural selection in biological evolution. Genetic algorithms provide potential solutions with a high diversity. Typically, genetic algorithms include an improvement iteration in which offspring are generated, crossover, and mutated. In various first example embodiments, the optimization goals are high field strength (e.g., greater than 160 mT) and high field uniformity (e.g., less than 50,000 ppm) within a cylindrical FoV (diameter = 200 mm and length = 50 mm) at the center of a magnet lumen for head imaging.

[0152] For ease of implementation, each layer (magnetic ring) The total number of layers on each side (for each sub-array 308, 309) is set to 10, and the thickness of each layer is set to 10 mm. The remanence of all magnetic rings after magnetization is set to 1.4 T. Fig.10 1 shows a schematic flow chart of applying a genetic algorithm 1000 to design or configure a ring pair permanent magnet array 302 according to various first exemplary embodiments of the present invention. The first step is to randomly initialize a population including N individuals (which may also be referred to as individual configurations, or simply configurations). In various first exemplary embodiments, there are 11 parameters in an individual (configuration), namely and the distance d between the two innermost rings. The population size may be set to 100 to provide sufficient diversity for the scheme. After initialization, the magnetic field may be calculated (determined) for N configurations of the parameters of the N individuals in the preset FoV (e.g., corresponding to the "multiple test configurations" described above according to various first embodiments). Fitness values ​​(e.g., corresponding to the "fitness metric" described above according to various first embodiments) are calculated based on the calculated field. These fitness values ​​are checked based on a stopping criterion (e.g., corresponding to the "predetermined condition" described above according to various first embodiments), which is the field strength and field uniformity in the FoV. If the stopping criterion is not met, a population with high field strength and field uniformity is selected based on the calculated fitness value to generate offspring. As a non-limiting example only, an example fitness function will be described below with reference to equation (7). Then, mutation and crossover are applied to the generated offspring to bring diversity to the population. Thereafter, the magnetic field and fitness values ​​are calculated again for the N configurations in the population (e.g., corresponding to the "multiple offspring configurations" described above according to various first embodiments). When the stop condition is not satisfied, another iteration is started again, and when the condition is satisfied, the optimization is ended.

[0153] exist Fig.10In the schematic flow chart of , the time spent on each step is marked for illustrative purposes, and the time is expressed as a percentage of the total optimization time. It can be seen that when using COMSOL Multiphysics, the optimization takes less than 10% of the time, but the forward calculation of the magnetic field of the magnet array being optimized takes more than 90% of the time. Therefore, various first exemplary embodiments note that the speed of the forward calculation dominates or determines the speed of the optimization. Therefore, it may be crucial or desirable to perform accurate calculations quickly to be able to complete the optimization in practical time. In this regard, various first exemplary embodiments determine that the current model used for magnetic field calculations provides both high calculation speed and high accuracy. Therefore, in various first exemplary embodiments, the current model is simplified and accelerated for field calculations used for optimization. The derivation and verification are shown below in the section "IB. Simplified current model for accelerating forward field calculations". In various first exemplary embodiments, based on the genetic algorithm, the field inhomogeneity is significantly reduced by 95%.

[0154] IB. Simplified current model for accelerating forward field calculations

[0155] As mentioned above, various first example embodiments note that fast calculation may be crucial or desirable for the acceleration of optimization. In the literature, different calculation methods for magnet systems are used. For systems with both magnets and iron (such as C-shaped systems and H-shaped systems), numerical methods such as boundary integral methods and finite element methods (FEM) can handle the calculation of magnetic fields. The forward model can be accelerated for optimization. An example is "Design of sparse Halbach magnetarrays for portable MRI using a genetic algorith" published by Cooley et al. in IEEE Trans. Magn. Vol. 54, No. 1, Article No. 5100112 in January 2018, which uses finite element simulation for the forward calculation of magnetic fields. Before optimizing the combination of material selection (no magnet, or N42 or N52 grade material) assigned to each space, the calculation is simplified by fixing the total magnet size and range. For systems having only magnets, such as the Halbach array, Aubert ring pair, and ring pair permanent magnet array 302 according to various first embodiments of the present invention, various first exemplary embodiments determine that physical models such as the current model (which may also be referred to as the current density model) are much simpler than numerical methods, as described in "Permanent Magnet and Electromechanical Devices: Material, Analysis, and Applications" by EP Furlani, published by Academic, New York, USA, in 2001, the contents of which are hereby incorporated by reference in their entirety for all purposes. Therefore, various first exemplary embodiments determine that the physical model can improve computational efficiency due to simplicity. Therefore, for the ring pair magnet array 302, because it includes magnets and is axisymmetric, various first exemplary embodiments select the current model and simplify it for optimized fast forward calculations.

[0156] Fig.11 A schematic diagram of a single magnetic ring 304 in a magnetic ring pair array 302 according to various first example embodiments of the present invention is shown, with its axis aligned with the z-axis 312 in a cylindrical coordinate system. The magnetic ring 304 is polarized radially outward.

[0157] For magnetic fields generated by permanent magnets, the superposition principle is valid. Therefore, the calculation of the total magnetic field generated by the example magnet array 302 can be completed by adding the fields generated by each magnetic ring 304. Next, the application and simplification of the current model are described in more detail according to various first example embodiments of the present invention to calculate or determine the magnetic field generated by the magnetic ring 304.

[0158] In the current model according to various first exemplary embodiments, the permanent magnet can be converted into the distribution of equivalent current. Fig.11 The permanent magnet 304 shown has only equivalent surface currents. The magnetic field generated by these equivalent currents can be calculated by the following formula:

[0159]

[0160] Where r =<r′,θ′,z′> is the observation point, r′=<r′,θ′,z′> is the point of the current source, and S is the surface of the magnet. In various first exemplary embodiments, a cylindrical coordinate system is used. For a single magnetic ring with radially outward polarization, the equivalent surface current source can be expressed as follows:

[0161]

[0162] Wherein, M0 is the magnitude of the residual magnetization, z1 and z2 are the positions of the front surface and the rear surface of the ring along the z-axis, respectively. As shown in equation (2), the equivalent surface current circulating on the front surface (e.g., corresponding to the "first equivalent surface current source" and the "second equivalent surface current source" described above according to various first embodiments) is clockwise, while the equivalent surface current circulating on the rear surface is counterclockwise. There is no surface current on the inner and outer walls of the ring.

[0163] Since the magnetic ring 304 with continuously changing radial polarization is symmetrical with respect to its radial axis, B(r) is independent with respect to θ, or B(r) is axisymmetric. Therefore, for the field in three-dimensional space, only the field at a specific θ needs to be calculated. The calculation at θ = 0 is completed, so the observation point is defined as r =<r,0,z> The derivation is simplified. The calculation is thus simplified to a two-dimensional problem.<r,0,z> Substituting equation (2) into equation (1) and integrating it, we can obtain the following equation (3):

[0164]

[0165] Among them, R in and R out are the inner and outer radii of the ring, respectively. As shown in equation (3), the θ component of B(r) is zero. Equation (3) is applied to calculate the magnetic field generated by the ring and the ring aggregate. The calculation results are compared with those obtained using COMSOL Multiphysics based on FEM to verify the calculation results.

[0166] Use equation (3) and COMSOL Multiphysics to calculate Fig. 12A In particular, Fig. 12AA three-dimensional view of an example magnetic ring aggregate of two magnetic rings is shown. The dual ring aggregate consists of two magnetic rings having the same inner radius of 40 mm and the same thickness of 20 mm, and outer radii of 60 mm and 50 mm respectively. As indicated by the arrows, the two magnetic rings are polarized radially outward.

[0167] FIG. 12B to FIG. 12D The results calculated using equation (3) (in MATLAB) and the results calculated using COMSOL Multiphysics on different observation lines along the z-axis direction are shown. In particular, the z component of the magnetic field is calculated using both the current model (indicated by an asterisk) and COMSOL Multiphysics (indicated by a black solid line) on the cylindrical surface at (b) r = 0 mm, (c) r = 10 mm, and (d) r = 20 mm. As shown in the figure, the results obtained using the simplified current model and COMSOL Multiphysics according to various first example embodiments have a high consistency with each other at different observation points. The time consumed by the calculation using equation (3) is only 1 / 10 of the time consumed by using COMSOL Multiphysics. It has been verified that the magnetic field generated by the magnet array 302 can be calculated (determined) in the optimization process according to various first example embodiments using equation (3) combined with the superposition principle. In the calculation, the ring is at r =<r,0,z> The field B generated at depends on the position and size of the ring and can be written as Therefore, in the genetic algorithm 1000 according to various first example embodiments, the field generated by the example ring-pair magnet array 302 may be calculated using the following equation (4):

[0168]

[0169] Wherein, the superscript i indicates that the first ring pair is the outermost ring and the nth ring pair is the innermost ring (for example, Figure 3 and 9 , n is the total number of ring pairs, and j represents the ring on the left (j=1) and the ring on the right (j=2). In the example magnet array 302, B total The z component of is used as the main magnetic field (B0) for MRI imaging. Therefore, the average B0 in the FoV can be calculated using the following formula:

[0170]

[0171] Where k is the index of the observation point in the FoV and M is the total number of these points. In the genetic algorithm 1000, a high B0 field strength can be enforced by applying the following constraints:

[0172] B 0-avg >160mT. (6)

[0174] Because B 0-avg The relationship with the parameter to be optimized is not linear, so the constraint is nonlinear. For field uniformity, a fitness function in ppm can be applied as follows:

[0175]

[0176] II. Results

[0177] According to various first example embodiments, the optimization is performed multiple times in MATLAB and the optimization converges to a set of non-identical results. From the results, better candidates are selected based not only on field uniformity and field strength, but also on the geometry of the magnet array when examining the feasibility of manufacturing and assembling the array. Fig.13A and Fig. 13B The selected candidate is shown in . Fig.13A It is shown that both the mean and the best fit value (which indicates field inhomogeneity) decrease as the number of iterations increases. In particular, Fig.13A The variation of fitness value with respect to iteration step is shown. The optimization stops at iteration 335 when the difference between two consecutive best individuals remains at 10 for 50 iterations. -12 Within. Fig. 13B Shows the best 3D view of a ring-pair magnet array between 150mm and 220mm. is [214 223 210 209 151 150 150 150 150 150] (unit: mm). It can be seen that The inner contour of the optimized magnet array was determined, and the optimal spacing d was 200 mm.

[0178] Fig.14A and Fig. 14B They are shown respectively by Fig. 13B The optimized ring pair design in Fig. Magnetic field generated in FoV in (a) rz plane and (b) rz plane using simplified current model. In particular, Fig.14A and Fig. 14B The z component of B (B) generated by the optimized design in the plane when z = 0 (r-θ plane) and the plane when θ = 0 (rz plane) in the FoV calculated by equations (3) and (4) are plotted respectively. z ). z The field is symmetric with respect to the z-axis, so that the graph when θ = 0 is symmetric with the graph when θ = π about the z-axis. Figure 1DThe Aubert ring pairs shown were calculated. For a fair comparison, the outer radius and thickness of the Aubert rings were set to 250 mm and 100 mm, respectively, which are the same as those of the proposed optimized ring pair array. The spacing between the two Aubert rings was set to 200 mm, the same as the spacing of the innermost ring pair of the optimized array. In addition, the inner radius of the Aubert ring pair was set to 178.5 mm to ensure the same mass of magnetic material in the two magnet arrays being compared. Fig.15A and Fig. 15B They are shown respectively by Figure 1D Magnetic field generated by the reference Aubert ring pair shown in FIG. 1 in the FoV in (a) the r-θ plane and (b) the rz plane using a simplified current model. Fig.15A and Fig. 15B The calculated B generated by the reference Aubert ring pair on the z = 0 plane and the θ = 0 plane in the FoV are shown respectively. z The calculation is done using equations (3) and (4).

[0179] Compare Fig.14A and Fig. 14B The magnetic field generated by the optimized array and Fig.15A and Fig. 15B The magnetic field generated by the Aubert array with the same mass and similar size in the same FoV, the field uniformity of the optimized magnet array is 24786ppm, the average field strength is 169.7mT, while the field uniformity of the reference magnet array is 122150ppm, the average field strength is 178.5mT. It can be seen that the optimization reduces the non-uniformity by more than 79.7% at the expense of less than 5% of the field strength (from 178.5 to 169.7mT). Therefore, the optimization according to various first example embodiments significantly improves the field uniformity while still maintaining similar field strength. The optimization results meet the preset optimization goals, namely, the average field strength is greater than 160mT and the field uniformity is less than 50000ppm (24786ppm in this example).

[0180] Fig.16 The r component of the optimized magnet array in the θ=0 plane is shown. In particular, Fig.16 Shown by Fig. 13B The optimized ring pair design shown in Figure 1 generates the r component of the magnetic field in the θ = 0 plane using a simplified current model in the FoV. Fig.14AThe r component of the magnetic field generated by the magnet array according to the first example embodiment is much smaller than the z component compared to the z component shown in . The z component dominates the magnetic field in the magnet array, so the field is in the longitudinal direction. When it is used to provide a B0 field for imaging, its relative orientation is the same as that of a conventional superconducting magnet-based MRI scanner, allowing the system using the proposed magnet array to be applied to the available technology for building RF coils. The optimized magnet array is suitable for providing a B0 field to a portable MRI system that works with spatial encoding.

[0181] According to various first exemplary embodiments, the design or configuration of the magnetic ring pair array may be segmented into multiple ring segments (eg, 12 identical sector magnets) having uniform polarization. Fig.17A A three-dimensional view of a magnet assembly 1700 according to various first example embodiments is shown. In particular, Fig.17A FIG. 1 shows a three-dimensional view of a segmented optimized magnet array 1700 composed of sector magnets. The segmented optimized magnet array is in the COMSOL Multiphysics simulation FoV on the (a) r-θ plane ( Fig. 17B ) and (b) on the rz plane ( Fig. 17C ) generates a magnetic field. Fig. 17B and Fig. 17C The simulation results are shown in Figure 2. The field uniformity of the segmented magnet array is 32511ppm and the average field strength is 167.6mT. Fig.14A and Fig. 14B Compared to the results for an array with continuously varying polarization in , the field uniformity is reduced by 31.2% and the field strength is reduced by 1.24% due to the discretization. Fig.15A and Fig. 15B Compared to the results of the ideal reference Aubert ring pair in , the inhomogeneity is still improved by 73.4%. In addition, the reference Aubert ring pair was segmented and simulated using COMSOL Multiphysics. A field uniformity of 133430ppm and an average intensity of 174.5mT were shown. Compared to the segmented reference Aubert ring, the segmented design or configuration 1700 according to various first example embodiments still shows a 75.6% improvement in field inhomogeneity and a 4% reduction in average field intensity. This result shows that discretization does not degrade the performance of the magnet array according to various first example embodiments.

[0182] III. Discussion

[0183] In various first exemplary embodiments, the design and optimization framework is flexible and effective. The genetic algorithm has a flexible definition of the fitness function. Those skilled in the art will recognize that the various first exemplary embodiments of the present invention are not limited to field uniformity and field strength, and that the optimization allows for more design goals, which may be preferred or important goals for the design of magnet arrays for portable MRI, such as but not limited to lighter weight, more compact size, and specific magnetic field patterns. Those skilled in the art will also recognize that the various first exemplary embodiments of the present invention are not limited to applications in portable MRI systems, and that the design or configuration method can be used to design magnet arrays for other applications (such as but not limited to accelerators or motors).

[0184] According to various first exemplary embodiments, a portable MRI system may require a specific B0 field pattern to encode a signal with information about the location that can obviate the need for a gradient coil. However, this field pattern should be generated within a certain field non-uniformity ΔB0. The uniformity corresponds to the RF bandwidth Δω, which can be expressed as follows:

[0185] Δω=γΔB0 (8)

[0187] Where γ is the gyromagnetic ratio in MHz / T. To excite all magnetic dipoles in the FoV, the bandwidth of the RF coil must be greater than or equal to Δω, Δω coil ≥Δω. On the other hand, Δω coil Must be small to maintain high efficiency and high Q factor. Therefore, when applied to the magnet array of a portable MRI system where the magnetic field generated by the magnet array is used to encode imaging, B0 needs to have a certain amount of non-uniformity (with a pattern) for imaging, but the non-uniformity cannot be so large that it cannot be operated using an RF coil with a reasonable Q factor. In this application, the FoV for two-dimensional head imaging is a cylinder with a diameter of 200mm and a length of 50mm. In various first example embodiments, the length can be extended for three-dimensional imaging.

[0188] In terms of the B0 field pattern, the ring pair magnet array according to various first exemplary embodiments provides the following Fig.18 In particular, Fig.18 A non-uniform pattern of concentric circles is shown.

[0189] This pattern is essentially able to spatially encode the signal in the r direction, which is equivalent to always applying a gradient field in the radial direction. In order to apply this pattern to signal encoding in imaging, one approach is to apply coil sensitivity encoding provided by rotating the receiving coils to obtain additional information for image reconstruction in the θ direction. Another possible solution is to introduce one (or more) rotating encoding magnets to break the radial symmetry of the magnetic field, thereby bringing additional information for image reconstruction in the θ direction. The gradient coils can be removed in the above scenario.

[0190] Compared to the Halbach magnet array, in addition to being compatible with existing radio frequency coils, the ring pair design according to various first exemplary embodiments is easier to manufacture and assemble, thereby achieving performance close to that of an ideal magnet polarization. In various first exemplary embodiments, the magnetic ring array can be formed using various manufacturing techniques or processes known in the art (such as using a computer numerical control device) based on the geometric parameters determined according to the various first embodiments of the present invention, so it is not necessary to describe it here for the sake of clarity and brevity. As a non-limiting example only, the magnetic rings in the magnetic ring pair array can be made of NdFeB. In addition, the outer shell structure of the magnetic ring array can be a nylon ring with a manufacturable designed groove, for example, which can be made using a standard manufacturing program on a computer numerical control device, which is relatively easy compared to using a sparse Halbach cylinder. Compared with the corresponding ideal design (for example, using a full filling factor), the magnetic ring array design or configuration according to various first exemplary embodiments brings a more compact size and a higher filling factor, which helps to obtain high field strength and similar performance. The filling factor can be defined as the ratio of the total mass of the magnet when the array is established to the mass of the magnet in the ideal model. For example, Fig.17A The filling factor in the Halbach magnet array is almost 100%. However, for the Halbach magnet array, the Halbach cylinder is often divided into magnetic rods and cylindrical magnets, which leads to a relatively low filling factor. For the example Halbach array, the filling factor is only 32.5%. Although the sparse segmentation makes the structure lighter and cheaper, the field strength and uniformity are significantly deteriorated. With regard to the fringe field of the magnetic ring array, the design or configuration according to various first example embodiments produces a stronger fringe field outside the magnet assembly compared to Halbach. One possible solution is to cover the magnet assembly with a high permeability screen. High permeability materials can guide and concentrate magnetic flux, thereby significantly reducing the strength of the fringe field and enhancing the internal magnetic field.

[0191] Due to the inevitable defects in magnet materials and manufacturing, there may be non-negligible differences between magnets in terms of residual magnetization strength and even polarization direction. In various first exemplary embodiments, the impact of defective materials and manufacturing can be identified and minimized. One way to minimize the impact of material defects is to mark, measure and classify the magnets before assembly, so that those magnets with serious defects can be discarded and the arrangement of the magnets can be optimized. For magnet assemblies, there may be differences between the defined position of the magnet and its actual position. If the housing is properly designed and manufactured to have a groove suitable for the size of the magnet, the accuracy of the magnet position can be improved. Another potential problem with permanent magnets is that the residual magnetism will slowly decrease over time and is sensitive to temperature. In this regard, according to various first exemplary embodiments, a relatively constant temperature environment can be used, and tracking of field drift can be used during MRI scanning for temperature compensation. The solution to this problem according to various first exemplary embodiments is to add an NMR probe to the system to track the field strength drift caused by both temperature changes and demagnetization effects.

[0192] IV. Conclusion

[0193] Therefore, in various first example embodiments, the design and optimization of a ring pair permanent magnet array for head imaging in a low-field portable MRI system is described. For example, the example magnet array produces a longitudinal B0 field with a magnetic field strength of 169.7mT and a uniformity of 24786ppm in a FoV with a diameter of 200mm and a thickness of 50mm. Compared with a conventional ring pair structure of similar size and mass, the inhomogeneity is reduced by 79.7%, while the field strength is reduced by less than 5%. In various first example embodiments, optimization is achieved by applying a genetic algorithm and providing an efficient current model for forward calculation. The efficient current model is a simplification of the traditional current model based on the unique arrangement of the magnets in the design of various first embodiments. The effectiveness of the optimization has been verified by actual simulations performed using COMSOL Multiphysics. Using the longitudinal B0 field, the prior art related to the RF coil of an MRI scanner based on a superconducting magnet can be directly applied to an imaging system using a magnet array according to various first embodiments. Also provided are example 12 segmented magnet assemblies based on optimized designs according to various first example embodiments, which show similar field strength and uniformity as unsegmented corresponding magnets.

[0194] In various second embodiments, in addition to having a high field strength and acceptable field uniformity in the longitudinal direction, the IO ring pair magnet array 302 according to various first embodiments can be further optimized to obtain a one-dimensional monotonic field pattern that is conducive to image reconstruction. To achieve this purpose, according to various second embodiments, the ring pair can be discretized into ring segment pairs for optimization to obtain irregularly shaped rings. The IO ring pair magnet array design or configuration obtained in this way can be referred to as an irregularly shaped IO ring pair magnet array in this article. According to various second embodiments, a genetic algorithm is applied, and a current model (also referred to as a current density model) for ring segment pairs (also referred to as fan-shaped pairs) is derived and utilized to perform a fast forward calculation of the magnetic field in the optimization. The design and optimization (e.g., configuration) according to various second example embodiments are described in detail in the "V. Method" section below. The optimization results are described in the "VI. Results" section, and by using simulation, the magnet array according to various second example embodiments and the Halbach array are compared when the magnetic field of the Halbach array is used for MR imaging encoding to show that the design or configuration according to various second example embodiments is conducive to image reconstruction. Below, a discussion on the design and optimization is given in Section “VII. Discussion” and a conclusion is then given in Section “VIII. Conclusion”.

[0195] V. Methods

[0196] Figure 5 An example design or configuration of a magnet array 500 according to various second example embodiments is shown in , which includes a plurality of segmented IO ring pairs with inner radius varying from one pair to another and outer radius varying from one segment to another. Figure 1D The basic IO ring pair is shown in Figure 1. Figure 1D As shown in FIG. 1 , the ring pair includes two annular magnets of the same size, whose central axes are aligned and spaced a certain distance apart, forming a cylindrical space. In the magnetic ring pair, the magnetization of one magnetic ring is radially inward (left magnetic ring), and the magnetization of the other magnetic ring is radially outward (right magnetic ring). The ring pair provides a dipole magnetic field along the axial direction of the cylinder (from left to right). Figure 5As shown, the example magnetic array 500 has M IO ring pairs and is symmetrical about a central plane (xy plane, z=0). The magnetic rings in a pair are identical. In various second example embodiments, all magnetic rings have the same thickness t. Therefore, on each side (e.g., corresponding to the "first subarray of annular magnets" and the "second subarray of annular magnets" described above according to various second embodiments), the aggregate includes M magnetic rings. The distance between the two inner edges of the two innermost rings is represented as d. The polarization of all magnetic rings on the left side (z>0) can be radially outward, while the polarization of all magnetic rings on the right side (z<0) can be radially inward, thereby generating a longitudinal magnetic field (along the z-axis 512). In various second example embodiments, as Figure 5 As shown, for each magnetic ring, they are divided into N sector segments (eg, corresponding to the “ring segments” described above according to various second embodiments). Fig.19A and Fig.19B A front view and a side cross-sectional view of the magnet array 500 are shown, respectively, and the FoV 1905 is also shown. Fig.19C Ring segments according to various second example embodiments are shown. In particular, Fig.19C A segmented sector magnet element with radially outward polarization is shown. Each ring segment can be indexed using j and i, where j is the index of the jth ring pair and i is the index of the i-th ring segment. The inner radius and outer radius of each segment are denoted by and

[0197] For optimization, according to various second exemplary embodiments, the same inner radius is set for segments from the same ring pair (e.g., the jth ring pair). On the other hand, the outer radius varies from one segment to another along the ring, while the outer radius of segments with the same index between different rings is the same. Can be set to In optimization, (j=1, ..., M and i=1, ..., N) are the geometric parameters to be optimized for producing a target SEM with a desired field pattern, field strength, and uniformity. The distance d between the two inner edges of the two innermost rings can be fixed to 240 mm. For two-dimensional head imaging, the optimized FoV can be set to a cylinder with a diameter of 200 mm and a length of 50 mm in the magnetic cavity. In various second exemplary embodiments, as Fig.19A and Fig.19B As shown, the FoV can be offset from the origin by 25 mm in the -x direction. For optimization, a genetic algorithm is applied, and a current model for calculating the magnetic field of the magnet ring segment is derived and used for fast forward calculation. Various second exemplary embodiments of the present invention will be described in detail below.

[0198] VA. Optimization using genetic algorithms

[0199] According to various second example embodiments, a genetic algorithm is used to optimize the magnet array. In various second example embodiments, the genetic algorithm is performed or operated in the same or similar manner as described in the various first embodiments, except that one or more geometric parameters are additionally optimized for field monotonicity of the magnetic field in the transverse direction in the field of view within the magnetic ring array. Therefore, for the sake of clarity and brevity, the genetic algorithm need not be repeated in detail for the various second example embodiments.

[0200] Genetic algorithms provide highly diverse candidate solutions. Typically, they include improved iterations in which offspring are generated and crossover and mutation are performed on the offspring. The key to applying genetic algorithms is to define an effective fitness function that rewards better offspring and penalizes poorer offspring. Various second example embodiments may include three optimization goals: high average field strength (>100mT), controlled field inhomogeneity (<10mT), and a monotone field pattern that is as linear as possible. In various second example embodiments, all three goals can be combined in a single fitness function to accelerate optimization rather than using a multi-objective genetic algorithm. Example fitness functions according to various second example embodiments are shown below:

[0201]

[0202] Where k is the index of the observation point r in the FoV, N1 is the total number of points, N2 is the total number of observation lines in the FoV parallel to the x-axis with a spatial step of 10 mm, and h is the index of the observation line in the FoV. is the lth point along the hth observation line. The total number of points along the hth line is expressed as Represented. The first term in equation (9) may correspond to field inhomogeneity, with units of parts per million (ppm). The second term in equation (9) may reward offspring with field strengths above 100 mT and penalize offspring with field strengths below 100 mT. The third term in equation (9) may handle the monotonicity of the field pattern by checking the field gradient along the x direction. In various second example embodiments, the function issorted may be used to verify the monotonicity of the field along the observation line, and requires less computation than calculating the number of voxels with unexpected gradients. In order to balance these three objectives, according to various second example embodiments, weighting coefficients α and β may be applied to the second and third terms in equation (9), respectively. In various second example embodiments, the weighting coefficients α and β may be empirically set to 5×10 3 and 2.5×10 4 .

[0203] VB. Forward Computation: Current Model

[0204] The current model can be applied to calculate the magnetic field of the yokeless magnet system without segmenting the magnet. Compared with the finite element method (FEM) or the boundary integral method (BIM), the calculation using the current model can be more efficient. For the magnet array according to various second exemplary embodiments, for the sector ring segment (such as Fig.19C A current model of φ(R) is derived and implemented for fast forward calculation for optimization. The details of the derivation are described below. In the derivation, a cylindrical coordinate system is used.

[0205] In the current model, according to various second exemplary embodiments, an equivalent current source can be used to model the permanent magnet. The magnetic field generated by these equivalent current sources can be calculated by the following equation (10):

[0206]

[0207] Where μ0 is the magnetic permeability of free space, r =<r,φ,z> is the observation point, r′=<r′,φ′,z′> is the current source point, j m is the equivalent surface current source, J m is the equivalent current source, S and V are the surface and volume of the magnet respectively. Fig.19C For the sector magnet shown in the figure, the equivalent current density can be determined by the following formula:

[0208]

[0209] Where M0 is the residual magnetization of the permanent magnet. Since the residual magnetization is constant along different polarizations, its curl is zero. Therefore, based on equation (11), the equivalent body current is zero. Therefore, in equation (10), only the equivalent surface current can be retained. Equation (10) can be rewritten as:

[0210]

[0211] The equivalent surface current can be expressed as:

[0212]

[0213] in, represents the unit normal vector of the magnet surface. Substituting (13) into (12) yields the expression for B(r). The z component of B(r) dominates the magnetic field generated by the magnet array according to various second exemplary embodiments, and B generated by the sector magnet ring segment z (r) can be expressed as:

[0214]

[0215] C1=-r cos(φ-φ′)+φsin(φ-φ′)+r′=0

[0216] C2=(r 2 +r′ 2 -2rr′cos(φ-φ′)+(z1-z′) 2 ) (3 / 2)

[0217] C3=(r 2 +r′ 2 -2rr′cos(φ-φ′)+(z2-z′) 2 ) (3 / 2) (15)

[0219] The superposition principle holds true in the yokeless magnet system, so that Figure 5 The total composite magnetic field B generated by the entire magnet array 502 according to various second exemplary embodiments is shown. total (r) can be calculated by the following formula:

[0220]

[0221] In order to verify this derivation, we use Equation (16) and COMSOL Multiphysics to Fig. 20A The fan-shaped segments shown in are calculated. In particular, Fig. 20A A three-dimensional view of a sector-shaped magnetic segment pair is shown, with the polarization of the magnets also shown. Fig. 20B Two results along the radial direction are shown. In particular, Fig. 20B The B calculated using MATLAB based on equation (14) and using COMSOL Multiphysics at multiple observation points along the y-axis (from 0 to 70 mm, with a step size of 5 mm) is shown. z .like Fig. 20B As shown, the results using the derived current model and the results using COMSOL Multiphysics (based on FEM) show good agreement with each other.

[0222] In the GA optimization, according to various second exemplary embodiments, the number of ring pairs M can be set to 9, the thickness t of each ring can be set to 12 mm, and the distance d between the two innermost rings can be set to 240 mm. The remanence of all magnets can be set to 1.4 T. In various second exemplary embodiments, when the inner radius of the ring pair gradually changes from the outside to the inside, a relatively high field strength and low inhomogeneity can be obtained. In order to speed up the optimization, in the current optimization according to various second exemplary embodiments, the inner radius of the ring pair in the initial candidate solution is set to 1.4 T. In addition, each magnetic ring is divided into 24 sectors, thus obtaining 24 for optimization.

[0223] In order to further accelerate the optimization efficiency, according to various second exemplary embodiments, symmetry is set relative to the central rθ plane (xy plane) and relative to the x-axis, which has the following advantages: the parameters to be optimized in one individual (configuration) can be reduced to 12, namely

[0224] In order to have a monotonic field in the FoV along the x-direction, various second exemplary embodiments determine that a gradual outer radius along the half-ring is beneficial. Therefore, according to various second exemplary embodiments, Can be set to be gradual and can further reduce the number of optimization parameters. May be subject to the following restrictions:

[0225]

[0226] where ρ is the step-wise decrease in the outer radius as index i increases, σ is the order of the gradient function, and Indicates optimized The maximum radius in . Using the gradient function in equation (17), the number of parameters in an individual (configuration) can be advantageously reduced from 12 to only 3. In the GA optimization according to various second exemplary embodiments, ρ∈[0.1 4], σ∈[0.1 5], The population size is set to 50, which provides enough diversity for the candidate solutions. The forward calculation of one iteration is greatly accelerated due to the use of the current model (whose calculation time is 1 / 10 of that using FEM) and the reduced number of optimization parameters.

[0227] VI. Results

[0228] During the optimization process, the optimization may be repeated multiple times since the genetic algorithm may not always converge to the same result. Fig.21A A plot showing the change in fitness value with respect to the iteration step is shown. In particular, Fig.21A It is shown that both the average value and the best fitness value decrease as the number of iterations increases in one optimization cycle. By making a trade-off between field strength, field inhomogeneity and monotonicity of the field pattern along the x-direction, a good result with a fitness value of 61584 is shown here. is [276.0 267.6 256.8 243.6 228.0 212.4 199.2 188.4 180.0] (unit: mm), and the optimized ρ, σ and The values ​​of are 2.3, 1.05 and 320 mm respectively. Based on formula (17), the optimized It is [320.0 317.7 315.2 312.7 310.1 307.5 304.9 302.3 299.6 296.9 294.2 291.5] (unit: mm). According to the optimized parameters, the optimized array is modeled in SolidWorks, and the results are shown in Fig. 21B and Fig. 21C . In particular, Fig. 21B shows the three-dimensional model of the optimal design, and Fig. 21C shows the front view of the optimal magnet array according to various second exemplary embodiments. In Fig. 21C , the dashed circle is a reference circle with a radius of 320 mm.

[0229] For evaluation, Equation (14) is used to calculate the field pattern of the optimal structure. The optimized magnet array provides a B0 field with an average field strength of 132.98 mT and a field uniformity of 151840 ppm in the FoV (the z-component of the magnetic field generated by the magnet array according to various second exemplary embodiments). FIG. 22A to FIG. 22C Shows the B z distributions in the xy plane at z = 0 and z = 25 mm, respectively. In particular, FIG. 22A to FIG. 22C shows the central xy plane (z = 0 mm) of the FoV calculated in MATLAB by the optimized magnet array ( Fig.22A ), the side xy plane (z = 25 mm) ( Fig. 22B ), and the xz plane (y = 0 mm) ( Fig. 22C ) generated by B z . Fig.22D and Fig.22E show the Fig.22A and Fig. 22B in the FoV, respectively. The B z at y = 0, 20, 40, 60, and 80 mm along the x direction in the plane shown in Fig.22D and Fig.22E show the central xy plane (z = 0 mm) of the FoV ( Fig.22D ) and the side xy plane (z = 25 mm) ( Fig.22E ) at y = 0, 20, 40, 60, and 80 mm along the x direction. The B z .

[0230] As shown in FIG. 22A to FIG. 22C , B z decreases monotonically from left to right, especially when -125 mm < x < 25 mm. From Fig.22D and Fig.22EThe monotonicity of the field can be clearly seen in the one-dimensional plots along different straight lines. When -125 mm < x < 50 mm and -20 mm < y < 20 mm, the gradients in the xy plane at z = 0 and 25 mm are approximately 122.5 mT / m and 140 mT / m, respectively. Outside the region of -20 mm < y < 20 mm, the region with a linear field is smaller and the gradient is also smaller. For example, when y = 60 mm, the field shows linearity from -105 mm to 0 mm, with gradients of approximately 105.7 mT / m and 121 mT / m in the xy plane at z = 0 and 25 mm, respectively. From FIG. 22A to FIG. 22E It can be seen that through the optimization when the inner radius of the ring gradually changes from outside to inside and the outer radius of each ring segment gradually changes along the x direction and is optimized, the field monotonicity along the x-axis for imaging is successfully obtained.

[0231] Actual simulations are carried out in COMSOL Multiphysics to verify the optimal design. Fig.23A and Fig.23C respectively show the B z field simulated on the central xy plane (z = 0 mm) and the xz plane (y = 0 mm). In particular, Fig.23A shows the B0 field simulated on the central xy plane (z = 0 mm), Fig.23C shows the B0 field simulated on the xz plane (y = 0 mm). Compared with the B0 fields shown in Fig.22A and Fig. 22C , the current model and COMSOL Multiphysics show almost the same field pattern in the FoV of the optimal design. The average field strength and field inhomogeneity obtained by COMSOL Multiphysics are 134.69 mT and 145680 ppm, respectively, and the differences compared with the current model are within 1.3% and 4.1% respectively. They show good agreement with each other and verify the effectiveness of the optimization. The x and y components of the magnetic field in the FoV are also studied here, and |B xy / B0| (unit: %) is calculated and shown in Fig. 23B . In particular, Fig. 23B shows |B xy / B0| (unit: %) on the central plane of the FoV. As can be seen, |B xy / B0| is less than 0.05% on the central plane of the FoV, and the z component dominates the generated B0 field.

[0232] The optimized magnet array is compared with the field generated by the sparse Halbach array and when the fields they generate are used as SEMs for imaging. Fig.24A and Fig. 24BThe 3D model of the short sparse Halbach array and the simulated field distribution on the central xy plane (with a diameter of 200 mm) are shown respectively. In particular, Fig.24A A three-dimensional model of a reference short sparse Halbach array is shown, where the outer diameter of the Halbach cylinder is 380 mm and includes 20 1′×1′×6.5′ N52 NdFeB magnetic rods and 40 1′×1′×1′ N52 NdFeB magnetic cubes. Fig. 24B The field distribution obtained by simulation on the central xy plane (z = 0 mm) of the Halbach array using COMSOL Multiphysics is shown. Fig. 24B As can be seen in Figure 2, there are considerable areas where the gradient is low or zero, especially in the central region. FIG. 22A to FIG. 22C The field pattern of the proposed magnet array is similar to Fig. 24B By comparing the field patterns of the Halbach array in Figure 2, it can be seen that most of the areas with low or zero gradients are successfully eliminated.

[0233] By using simulation, the magnet arrays and Halbach arrays (such as Fig.22A and Fig. 24B The magnetic field shown in Figure 1 is used as a SEM to Fig.25A The quality of the reconstructed image obtained when encoding the signal of the Shepp-Logan phantom shown in the figure is used to evaluate the magnetic field from both the magnet array and the Halbach array according to various second exemplary embodiments. For encoding, all SEMs are rotated 180° with a step size of 2.8125° (a total of 64 steps). Eight surface coils with a diameter of 50 mm are located around the side walls of the cylindrical FoV and are used for signal reception. In the simulation, the spin echo signals are collected by orthogonal demodulation using a CPMG pulse sequence. For each angle, 256 readings with a duration of 25us are collected for image reconstruction. For two SEMs with relatively low field strength, the signal-to-noise ratio of the NMR signal is set to 20dB, and the field strength and field inhomogeneity are normalized to the same level (mean(B0)=100mT, ΔB0=1mT) to eliminate the influence of field strength and inhomogeneity on the quality of the reconstructed image. Iterative time domain reconstruction (iTDR) based on conjugate gradient (CG) is used for image reconstruction. Fig.25B and Fig.25C The fields ( Fig. 24B ) and the reconstructed image obtained using the magnetic field center portion ( Fig.22A ) to obtain the reconstructed image. In particular, Fig.25B Shows the use of Fig.24AThe reconstructed image is obtained by using the reference magnetic field generated by the Halbach array in Fig.25C shows a reconstructed image obtained using the B0 field produced by the optimized magnet array, Fig.25D Shows the use of FIG. 26A to FIG. 26E Reconstructed image obtained with reference magnetic field generated by further optimized array with improved monotonicity.

[0234] For example, compare Fig.25B and Fig.25C In the image in Figure 1, clearer features can be seen in the image obtained using the magnetic field from the proposed array with improved monotonicity. Compared with the image obtained using the reference Halbach array, the normalized root mean square error (NRMSE) of the image obtained using the proposed array is reduced from 10.03% to 8.02%, a reduction of about 22.73%. As shown in Fig.25B and Fig.25C As can be seen in Figure 1, the blur of the image obtained using the proposed array is greatly reduced, especially in the center, compared with the reference Halbach array. Fig.25A The structural similarity index (SSIM) of the proposed array is 0.296, which is about 54.94% higher than the image obtained using the Halbach array (SSIM is 0.191). The magnetic field of the proposed array can reconstruct a clearer image, which is attributed to the fact that the field pattern of the proposed array removes the central zero gradient area and the low gradient area relative to the field image of the Halbach array.

[0235] VII. Discussion

[0236] Thus, it has been shown that the irregularly shaped IO ring pair magnet array according to various second exemplary embodiments provides a monotonic field in a single direction in the center plane of a cylindrical FoV for head imaging. By using a genetic algorithm for optimization, the field strength within the FoV can be maintained above 130 mT while controlling the inhomogeneity to 151840 ppm. Due to the linearity of the gradient, it is better used as a SEM than the Halbach array and the IO magnetic ring pair aggregate according to various first embodiments, thereby producing better image quality in the MRI system. For the Halbach array with a quadrupole B0 field pattern, there are areas where the gradient is low or zero, while for the IO magnetic ring pair aggregate according to various first exemplary embodiments, although it can be compensated by adding additional structure of the magnet or additional mechanical movement when encoding, it still lacks a gradient in the θ direction. Compared to the optimized sparse Halbach array, the magnet array according to the second example embodiment has a similar length (45.6 cm vs. 45.7 cm in length), but a 21.9% increase in diameter (64 cm vs. 52.5 cm in diameter), and both are designed and optimized to obtain a monotonic SEM for imaging in a FoV of 20 cm in diameter. The magnet array according to various second example embodiments produces a B0 field with an average field strength of 132.98 mT, which is a 64% increase compared to 81.1 mT for the sparse array. However, the field inhomogeneity of the sparse Halbach array may be only about 10% of that of the magnet array according to various second example embodiments. The larger inhomogeneity requires the RF system to have a larger bandwidth, which will be discussed in the next paragraph. In general, in addition to the sparse Halbach array, the irregularly shaped IO ring pair magnet array according to various second example embodiments can also be a good candidate for providing SEM in a low-field portable MRI system.

[0237] Compared to the IO ring pair aggregate according to various first exemplary embodiments, the field uniformity from the optimized array is reduced from 24786ppm to 151840ppm, which can be understood as balancing the field monotonicity for the purpose of spatial encoding. The low uniformity results from the fact that radio frequency (RF) excitation and signal reception require a large bandwidth, which may require the RF coil and CONSOLE to have a wide operating frequency band. Therefore, as a result, the RF hardware may need to be redesigned to obtain a corresponding wide operating bandwidth. Ultra-wideband technology for RF systems has been previously proposed for NMR / MRI systems. For example, a broadband RF system can be achieved using a transformer-based non-resonant transmitter and receiver covering a wide frequency range, or using a receiver with a binary switch array to switch resonant frequencies across a fairly wide bandwidth.

[0238] If the requirement for uniformity can be further relaxed by implementing ultra-wideband technology, a more linear field can be obtained from the genetic algorithm optimization. FIG. 26A to FIG. 26E A designed B0 field is shown, which has a loose field uniformity but has a much more uniform monotonic gradient pattern than the design presented in the section "VI. Results". In particular, FIG. 26A to FIG. 26C shows the central xy plane (z = 0 mm) in the FoV calculated by MATLAB through a further optimized design with more field monotonicity ( Fig.26A ), the side xy plane (z = 25 mm) ( Fig.26B ), and the xz plane (y = 0 mm) ( Fig.26C ) where the B z is generated. Fig.26D And Fig.26E show the B Fig.26D at y = 0, 20, 40, 60, and 80 mm along the x direction in the central xy plane (z = 0 mm) and the side xy plane (z = 25 mm) in the FoV z .

[0239] Preset is the same as that shown in the section "VI. Results", and the optimized is [300 297.6 295.2 292.8 290.4 288.0 285.6 283.2 280.8 278.4 276.0 273.6] (unit: mm). This further optimized design provides a B0 field with an average field strength of 103.04 mT and a field non-uniformity of 178960 ppm in the FoV, and the gradient field has a range of 82.1 mT / m to 85.2 mT / m in the region of -100 mm < x < 50 mm along the x direction on the central xy plane (z = 0 mm) of the FoV. Compared with the FIG. 22A to FIG. 22E results presented, after balancing the field strength and field uniformity, the monotonic region is wider in the x direction, and the gradients are closer to each other at different values of y. The uniformity of the gradient along the y direction helps to improve the uniformity of the resolution when reconstructing the image. Fig.25D shows the reconstructed image obtained by using the magnetic field in Fig.26A through simulation, and it shows that the NRMSE is 7.67%, and compared with Fig.25C , the NRMSE is improved by 4.36%. At the same time, compared with the enlarged region shown in Fig.25C , through a more linear SEM, Fig.25DGibbs (truncation) artifacts at the magnified region shown in . However, it is noted that the improved monotonicity is obtained at the expense of lower field strength and lower field uniformity, which may lead to lower SNR and consequently lower spatial resolution and wide operating band for the RF system, respectively.

[0240] The FoV was offset 25 mm from the center of the magnet array to obtain more areas with monotonic gradients and avoid areas with low gradients (e.g. Fig. 27 ). The magnet array will rotate around the center of the FoV rather than the center of the magnet array to facilitate non-Fourier transform image reconstruction. The rotation mechanism can be designed accordingly to achieve this eccentric rotation. In particular, Fig. 27 In FIG. 5 , there is a circle around the FoV centered 25 mm off the center of the array in the negative x direction on the xy plane (z=0 mm), and there is a white dashed circle around the FoV with no offset.

[0241] A smaller number of segments helps reduce the cost of the entire magnet array. Here, the effect of the number of segments on the field pattern is explored. Each optimized ring magnet is divided into 4, 8, 12, 18, 24, and 36 sector elements, and calculated using equations (7) and (8) respectively. In all six cases, According to formula (17), it gradually changes from 300 mm to 273.6 mm (such as Fig.26B and Fig.26C design shown). FIG. 28A to FIG. 28F The B0 field calculated based on different segmentations is shown in the xy plane (z=0 mm) in the FoV. In particular, FIG. 28A to FIG. 28F The B0 fields generated by the irregular shaped 10 ring-pair magnet array shown in FIG. 26 are shown when each ring magnet is divided into 4, 8, 12, 18, 24 and 36 sector magnets, respectively. Figure 28G and Fig.28H The average B0 field strength (B 0-avg ) and field inhomogeneity (in ppm) as the number of segments increases. It can be seen that segmentations with different numbers of elements show similar field patterns and average field strengths. However, Fig.28H As shown, field non-uniformity is greatly affected by the number of segments. In general, in various second exemplary embodiments, the number of segments of the ring magnets in the proposed irregular-shaped IO ring-pair magnet array may be in a suitable range of 20 to 24, which can provide both good magnetic field uniformity and fewer segments to be calculated.

[0242] In various second exemplary embodiments, similar to the various first exemplary embodiments, a magnetic ring array may be formed based on the geometric parameters determined according to the various first exemplary embodiments of the present invention using a variety of manufacturing techniques or processes known in the art (such as using computer numerical control equipment), and therefore, for the sake of clarity and brevity, there is no need to describe them here.

[0243] VIII. Conclusion

[0244] Therefore, various second exemplary embodiments provide the design and optimization of irregularly shaped IO ring pair magnet arrays, which produce a one-dimensional monotonic field pattern for two-dimensional head imaging. A genetic algorithm is applied for optimization, and a current model of the sector ring segment pair is derived for fast forward calculation of optimization. In the example simulation described above, the optimized magnet array according to various second exemplary embodiments presents an average B0 field of 132.98mT and a field uniformity of 151840ppm in a cylindrical FoV with a diameter of 200mm and a length of 50mm. In addition, the obtained magnetic field is used as a SEM for signal encoding in imaging to further evaluate the magnet array according to various second exemplary embodiments. Due to the highly monotonic gradient, the magnet array according to various second exemplary embodiments successfully removes the blur at the central area of ​​the image encoded by the Halbach array. In addition to the sparse Halbach array and IO ring pair aggregate according to various first exemplary embodiments, providing a SEM for imaging in a low-field portable MRI system based on a permanent magnet is a promising alternative.

[0245] Although the embodiments of the present invention have been particularly shown and described with reference to specific embodiments, it will be understood by those skilled in the art that various changes may be made in form and detail without departing from the scope of the present invention as defined in the appended claims. Therefore, the scope of the present invention is indicated by the appended claims, and it is therefore intended to cover all changes that fall within the equivalent meanings and equivalent ranges of the claims.

Claims

1. A method of forming a permanent magnet system, the method comprising: determining one or more types of geometric parameters for forming an array of magnetic ring pairs, the array of magnetic ring pairs comprising a first subarray of a first permanent magnetic ring and a second subarray of a second permanent magnetic ring, the second subarray of the second permanent magnetic ring being spaced apart from the first subarray of the first permanent magnetic ring along a longitudinal axis; as well as The magnetic ring pair array is formed based on the determined one or more types of geometric parameters, wherein: The determining of one or more types of geometric parameters for forming the magnetic ring pair array is based on a genetic algorithm, wherein the one or more types of geometric parameters for the magnetic ring pair array include one or more types of geometric parameters for each magnetic ring pair in the magnetic ring pair array; wherein the one or more types of geometric parameters include an inner radius parameter associated with an inner radius of the magnetic ring pair, and the magnetic ring pair array includes a plurality of ring pairs having different inner radii; The first permanent magnetic rings in the first sub-array are arranged in series along the longitudinal axis, wherein the first permanent magnetic rings in adjacent first sub-arrays are in contact with each other through their planes facing each other; The second permanent magnetic rings in the second sub-array are arranged in series along the longitudinal axis, wherein the second permanent magnetic rings in adjacent second sub-arrays are in contact with each other through their planes facing each other.

2. The method according to claim 1, wherein: Based on the genetic algorithm, determining one or more types of geometric parameters for forming the magnetic ring pair array includes: The one or more types of geometric parameters used to form the magnetic ring pair array are optimized with respect to the field strength and field uniformity in the longitudinal direction of the magnetic field in the field of view within the magnetic ring pair array, which are generated when the magnetic ring pair array is formed based on the determined one or more types of geometric parameters.

3. The method according to claim 2, wherein: Based on the genetic algorithm, the one or more types of geometric parameters for optimizing the array of magnetic ring pairs include: obtaining a plurality of test configurations for forming the array of magnetic ring pairs, each test configuration comprising a geometric parameter test set associated with the one or more types of geometric parameters optimized to form the array of magnetic ring pairs; and For each test configuration in the plurality of test configurations, a field strength and a field uniformity of a magnetic field in the longitudinal direction in the field of view within the magnetic ring pair array having the test configuration are determined.

4. The method according to claim 3, wherein: For each test configuration in the multiple test configurations, determining the field strength and field uniformity of the magnetic field includes: for each test configuration in the multiple test configurations, determining the magnetic field of the magnetic ring pair array having the test configuration based on a current density model of each magnetic ring in the magnetic ring pair array having the test configuration.

5. The method according to claim 4, wherein: The current density model is based on a first equivalent surface current source associated with a first surface of the magnetic ring facing a first direction and a second equivalent surface current source associated with a second surface of the magnetic ring facing a second direction, wherein the first direction is substantially parallel to the longitudinal axis, and the second direction is substantially parallel to the longitudinal axis and opposite to the first direction.

6. The method according to claim 4 or 5, wherein: The current density model is simplified by configuring the current density model to determine that the magnetic field of each magnetic loop in the array of magnetic loop pairs having the test configuration is symmetric about the longitudinal axis.

7. The method according to claim 4, wherein: The optimizing the one or more types of geometric parameters for forming the magnetic ring pair array further comprises: determining, for each test configuration of the plurality of test configurations, a fitness metric of field strength and field uniformity of a magnetic field determined based on the current density model for the array of magnetic loop pairs having the test configuration; and determining whether the fitness metrics determined for the plurality of test configurations satisfy a predetermined condition; Wherein, if the fitness metric satisfies the predetermined condition, the optimizing the one or more types of geometric parameters used to form the magnetic ring pair array further comprises: selecting one of the multiple test configurations as the one or more types of geometric parameters determined for the magnetic ring pair array; and Wherein, if the fitness metric does not satisfy the predetermined condition, the optimizing the one or more types of geometric parameters used to form the magnetic ring pair array further includes: generating a plurality of descendant configurations based on a selected number of test configurations from the plurality of test configurations; performing mutation and crossover on the resulting multiple offspring configurations; and For each of the plurality of subsequent configurations, the field strength and field uniformity of the magnetic field in the longitudinal direction in the field of view within the magnetic ring pair array having the subsequent configuration are determined.

8. The method according to claim 2, wherein: The forming of the magnetic ring pair array includes: forming the magnetic ring pair array based on the determined one or more types of geometric parameters to generate a magnetic field with an average field strength in the longitudinal direction equal to or greater than 150mT and a field uniformity equal to or less than 50000ppm in the field of view within the magnetic ring pair array.

9. The method according to claim 1, wherein: The one or more types of geometric parameters for each magnetic ring pair further include the following parameters: an outer radius parameter related to the outer radius of the magnetic ring pair, and a thickness parameter related to the thickness of each magnetic ring in the magnetic ring pair.

10. The method according to claim 1, wherein: The one or more types of geometric parameters for the magnetic ring pair array also include a quantity parameter related to the number of ring pairs in the magnetic ring pair array and a distance parameter related to the distance separating the first sub-array and the second sub-array along the longitudinal axis.

11. The method according to claim 1, wherein: The one or more types of geometric parameters are composed of the inner radius parameter and the distance parameter.

12. The method according to claim 1, wherein: Each magnetic ring pair in the magnetic ring pair array is an Aubert ring pair.

13. The method according to claim 1, wherein: The first subarray of the first permanent magnetic rings is divided into a first subarray of first ring segments around the longitudinal axis, and the second subarray of the second permanent magnetic rings is divided into a second subarray of second ring segments around the longitudinal axis, each first ring segment extends through all the first permanent magnetic rings in the first subarray, and each second ring segment extends through all the second permanent magnetic rings in the second subarray.

14. The method according to claim 1, wherein: Based on the genetic algorithm, determining one or more types of geometric parameters for forming the magnetic ring pair array includes: The one or more types of geometric parameters used to form the magnetic ring pair array are optimized with respect to the field strength and field uniformity of the magnetic field in the longitudinal direction and the field monotonicity of the magnetic field in the transverse direction in the field of view within the magnetic ring pair array, which are generated when the magnetic ring pair array is formed based on the determined one or more types of geometric parameters.

15. The method according to claim 14, wherein: Based on the genetic algorithm, the one or more types of geometric parameters for optimizing the array of magnetic ring pairs include: obtaining a plurality of test configurations for forming the array of magnetic ring pairs, each test configuration comprising a geometric parameter test set associated with the one or more types of geometric parameters optimized to form the array of magnetic ring pairs; and For each test configuration in the plurality of test configurations, the field strength and field uniformity of the magnetic field in the longitudinal direction and the field monotonicity of the magnetic field in the transverse direction in the field of view within the magnetic ring pair array having the test configuration are determined.

16. The method according to claim 15, wherein: Determining the field strength, field uniformity and field monotonicity of the magnetic field for each of the multiple test configurations includes: for each of the multiple test configurations, determining the magnetic field of the magnetic ring pair array having the test configuration based on a current density model of each ring segment of each magnetic ring in the magnetic ring pair array having the test configuration.

17. The method according to claim 16, wherein: The current density model is based on a first equivalent surface current source associated with a first surface of the ring segment facing a first direction, a second equivalent surface current source associated with a second surface of the ring segment facing a second direction, and a third equivalent surface current source associated with a third surface of the ring segment and a fourth surface of the ring segment, wherein the first direction is substantially parallel to the longitudinal axis, the second direction is substantially parallel to the longitudinal axis and opposite to the first direction, the third surface is between the first surface and the second surface, and the fourth surface is between the first surface and the second surface and is opposite to the third surface.

18. The method according to claim 16 or 17, wherein: The current density model is simplified by configuring the current density model so that each ring segment of each magnetic ring in the magnetic ring pair array having the test configuration generates a magnetic field, wherein configuring the current density model includes: setting each magnetic ring pair in the magnetic ring pair array to have an inner radius parameter related to the inner radius of the magnetic ring pair that gradually changes from the outermost magnetic ring pair in the magnetic ring pair array to the innermost magnetic ring pair in the magnetic ring pair array.

19. The method according to claim 18, wherein: The current density model is further simplified by configuring the current density model to determine that the magnetic field of each ring segment of each magnetic ring in the array of magnetic ring pairs having the test configuration is symmetric with respect to a plane perpendicular to the longitudinal axis and symmetric about a transverse axis.

20. The method according to claim 16, wherein: The optimizing the one or more types of geometric parameters for forming the magnetic ring pair array further comprises: determining, for each test configuration of the plurality of test configurations, fitness metrics for field strength, field uniformity, and field monotonicity of a magnetic field determined based on the current density model for the array of magnetic loop pairs having the test configuration; and determining whether the fitness metrics determined for the plurality of test configurations satisfy a predetermined condition; Wherein, if the fitness metric satisfies the predetermined condition, the optimizing the one or more types of geometric parameters used to form the magnetic ring pair array further comprises: selecting one of the multiple test configurations as the one or more types of geometric parameters determined for the magnetic ring pair array; and Wherein, if the fitness metric does not satisfy the predetermined condition, the optimizing the one or more types of geometric parameters used to form the magnetic ring pair array further includes: generating a plurality of descendant configurations based on a selected number of test configurations from the plurality of test configurations; performing mutation and crossover on the resulting multiple offspring configurations; and For each of the plurality of subsequent configurations, the field strength and field uniformity of the magnetic field in the longitudinal direction and the field monotonicity of the magnetic field in the transverse direction in the field of view within the magnetic ring pair array having the subsequent configuration are determined.

21. The method according to claim 14, wherein: The forming of the magnetic ring pair array includes: forming the magnetic ring pair array based on one or more types of determined geometric parameters to generate a magnetic field in the field of view within the magnetic ring pair array with an average field strength in the longitudinal direction equal to or greater than 100 mT and a field uniformity equal to or less than 200,000 ppm and a field gradient of field monotonicity equal to or less than 0.40 T / m in the transverse direction.

22. The method according to claim 14, wherein: The one or more types of geometric parameters for the magnetic ring pair array include one or more types of geometric parameters for each ring segment of each magnetic ring pair in the magnetic ring pair array.

23. The method according to claim 22, wherein: The one or more types of geometric parameters for each ring segment further include the following parameters: an outer radius parameter related to the outer radius of the ring segment, a step reduction parameter related to the step reduction of the outer radius of the ring segment, and a gradient level parameter related to the level of the gradient function associated with the ring segment.

24. The method according to claim 22 or 23, wherein: The one or more types of geometric parameters for the magnetic ring pair array also include a quantity parameter related to the number of ring segments in each of the first subarray of the first permanent magnetic ring and the second subarray of the second permanent magnetic ring, and a distance parameter related to the distance between the first subarray of the first permanent magnetic ring and the second subarray of the second permanent magnetic ring along the longitudinal axis.

25. The method according to claim 23, wherein: The one or more types of geometric parameters consist of outer radius parameters, step reduction parameters and gradient series parameters.

26. The method of claim 13, wherein: Each magnetic ring pair in the magnetic ring pair array is an Aubert ring pair.

27. The method of claim 1, further comprising introducing a rotating encoded magnet block to break the axial symmetry of the magnetic field generated by the magnetic ring pair array.

28. A permanent magnet system comprising: Magnetic ring pair array, including: a first subarray of first permanent magnetic rings; and a second subarray of a second permanent magnetic ring, wherein the second subarray of the second permanent magnetic ring is spaced apart from the first subarray of the first permanent magnetic ring along the longitudinal axis, wherein The magnetic ring pair array includes a plurality of ring pairs having different inner radii; The first permanent magnetic rings in the first sub-array are arranged in series along the longitudinal axis, wherein the first permanent magnetic rings in adjacent first sub-arrays are in contact with each other through their planes facing each other; The second permanent magnetic rings in the second sub-array are arranged in series along the longitudinal axis, wherein the second permanent magnetic rings in adjacent second sub-arrays are in contact with each other through their planes facing each other.

29. The permanent magnet system according to claim 28, wherein The magnetic ring pair array is configured based on one or more types of geometric parameters, and the one or more types of geometric parameters are determined to generate a magnetic field with an average field strength in the longitudinal direction equal to or greater than 150mT and a field uniformity equal to or less than 50000ppm in the field of view within the magnetic ring pair array.

30. The permanent magnet system according to claim 28 or 29, formed on the basis of the method of forming a permanent magnet system according to claim 1.

31. The permanent magnet system of claim 29, wherein: The first subarray of the first permanent magnetic rings is divided into a first subarray of first ring segments around the longitudinal axis, and the second subarray of the second permanent magnetic rings is divided into a second subarray of second ring segments around the longitudinal axis, each first ring segment extends through all the first permanent magnetic rings in the first subarray, and each second ring segment extends through all the second permanent magnetic rings in the second subarray.

32. The permanent magnet system of claim 31, wherein: Each magnetic ring pair in the magnetic ring pair array is configured to have the inner radius parameter associated with the inner radius of the magnetic ring pair that gradually changes from an outermost magnetic ring pair in the magnetic ring pair array to an innermost magnetic ring pair in the magnetic ring pair array.

33. A permanent magnet system according to claim 31 or 32, wherein: The magnetic ring pair array is configured based on one or more types of geometric parameters to generate a magnetic field in the field of view within the magnetic ring pair array with an average field strength in the longitudinal direction equal to or greater than 100 mT and a field uniformity equal to or less than 200,000 ppm and a field gradient of field monotonicity equal to or less than 0.40 T / m in the transverse direction.

34. The permanent magnet system according to claim 31, formed based on the method of forming a permanent magnet system according to claim 13.

35. The permanent magnet system of claim 28, further comprising rotating the encoded magnet block to break the axial symmetry of the magnetic field generated by the magnetic ring pair array.

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