An oblate ring-to-magnet system design method for magnetic particle concentration magnetoacoustic tomography

Abstract

This invention discloses a design method for an Obert ring-to-magnet system for magnetoacoustic-electromagnetic imaging (MAET-ED) of magnetic particle concentration. MAET-ED is a novel method for imaging the concentration of magnetic nanoparticles (MNPs), offering advantages such as low electromagnetic excitation, high resolution, and MNP concentration reconstruction. Currently, MAET-ED uses a rectangular permanent magnet as its magnetic field excitation unit. To improve magnetic field quality and reduce system weight, this invention discloses a design method for an Obert ring-to-magnet system for MAET-ED, replacing the static magnetic field excitation unit with an Obert ring-to-magnet system. The method first sets the basic parameters of the permanent magnet and coil based on the imaging area size. Then, it sets relevant indices based on the required magnetic field uniformity and magnetic flux density for MAET-ED imaging. Finally, a non-dominated sorting genetic algorithm is used to optimize the structural parameters of the permanent magnet, and the coil excitation current is obtained using relevant calculation formulas. This method can design an Obert ring-to-magnet system specifically for MAET-ED, laying the foundation for its experimental system construction and clinical application.

Description

Technical Field

[0001] This invention belongs to the field of medical imaging technology, and particularly relates to an Obert ring-to-magnet system design method for magnetic particle concentration magnetoacoustic imaging. Background Technology

[0002] In recent years, the application of magnetic particle sensors (MNPs) in the medical field has attracted much attention from scholars both domestically and internationally. In targeted therapy, they have enabled precise drug delivery, effectively improving treatment outcomes. Traditional magnetic particle imaging (MPI) technology suffers from problems such as high-power electromagnetic excitation and low resolution. Electrode-detection magnetic particle concentration magnetoacoustic-electroelectric imaging (MAET-ED), through multi-physics coupling of magneto-acoustic-electric fields, provides a new approach to solving these problems. However, existing MAET-ED magnet systems exhibit poor magnetic field quality within the imaging region, failing to meet imaging requirements.

[0003] Regarding the design of permanent magnets in the field of medical imaging, Pang Yanwei et al. of Tianjin Tianda Tuzhi Technology Co., Ltd. disclosed a method, system, equipment, and medium for designing permanent magnets for magnetic resonance imaging in 2023. First, a target magnetic field map of the target magnetic block set is obtained. Then, the target magnetic field map is input into a parameter model to obtain a parameterized matrix. Finally, the three-dimensional spatial structure and material distribution of the permanent magnet are determined based on the parameterized matrix. However, the input parameter model, including the number of target magnetic blocks and the coordinates of the center position, needs to be constructed based on a neural network. The complexity of the permanent magnet system structure leads to many drawbacks in practical engineering. Therefore, to simplify the magnet system design and improve the magnetic field quality in the imaging region, this invention proposes an Obert ring pair magnet system design method for magnetic particle concentration magnetoacoustic-electromagnetic imaging, providing a new solution and method for addressing the current challenges faced by MAET-ED. Summary of the Invention

[0004] The purpose of this invention is to solve the problems of low magnetic field strength and poor magnetic field uniformity in magnetic particle concentration magnetoacoustic imaging systems. It proposes an Obert ring pair magnet system design method for magnetic particle concentration magnetoacoustic imaging. This magnet system can improve the magnetic field strength and magnetic field uniformity in the imaging area, thereby improving the level of magnetic particle concentration magnetoacoustic imaging systems. Figure 5 The improved Obert ring pair MAET-ED magnet system shown introduces axially magnetized Obert ring pairs into the MAET-ED system. The Obert ring pairs are divided into upper and lower groups with the z-axis as the axis and the origin as the center. Two layers of coils are added at the ends of the imaging region to improve the uniformity of the magnetic field at the ends. This ensures that the magnetic flux density and magnetic field uniformity in the imaging region meet the requirements of MAET-ED imaging.

[0005] Electrode-detection magnetic particle concentration magnetoacoustic imaging system, such as Figure 1 As shown, it includes: 1) Static magnetic field excitation unit: composed of Oberthian ring pairs and second-order Z-gradient shimming coils, the purpose of which is to generate a static magnetic field and act on biological tissue containing MNPs; 2) Magnetoacoustic and electrical signal acquisition and display unit: It consists of an ultrasonic transducer, an ultrasonic probe, a power amplifier, a lock-in amplifier, electrode plates, an oscilloscope, and a PC. Its purpose is to acquire magnetoacoustic and electrical signals and to condition and display the acquired signals. 3) Mechanical drive scanning unit: It consists of a drive circuit, a stepper motor group and a three-axis controller. Its purpose is to move the ultrasonic probe to a designated position and then send an excitation signal from the ultrasonic excitation device to make the magnetic particles in the sample vibrate after being excited by the ultrasonic.

[0006] This invention employs an improved Oberthian ring pair magnet system as the magnetic field excitation unit of a magnetoacoustic-electromagnetic imaging device for magnetic particle concentration. This magnet system consists of Oberthian ring pairs and two sets of second-order Z-gradient shimming coils. The invention uses N50 neodymium iron boron permanent magnets as the basic components of the MAET-ED magnet system. The remanence of the permanent magnets is set to 1.4 T, the intrinsic coercivity to 1353 kA / m, and the relative permeability to 0.9. To facilitate numerical calculations and define the magnetization direction, each layer of magnetic rings is split into eight parts, with a magnetization direction step angle of 45°. The outer radius of the magnetic rings is... Inner radius is This ensures that the magnetic field covers the entire imaging area. A second-order Z-gradient shimming coil is a device used to generate a small-scale uniform magnetic field. It consists of two sets of parallel and coaxial circular coils. The currents in the coils are in the same direction and equal in magnitude. When the distance d between the two coils is equal to their radius R, the coils generate a relatively wide uniform magnetic field near the midpoint of their common axis. The theoretical basis for generating this magnetic field is the Biot-Savart law. Therefore, second-order Z-gradient shimming coils can be used to counteract the Earth's magnetic field and design a uniform magnetic field region.

[0007] By altering the structure or parameters of various parts of the Oberthian ring-magnet system, a static magnetic field required for imaging is generated in the imaging region. The second-order Z-gradient shimming coil in this invention can output compensation magnetic fields of varying magnitudes in the imaging region by changing the coil's radius, current magnitude, and direction. The magnetic field generated by the MAET-ED magnet system magnetizes the microparticles (MNPs). The magnetized MNPs then undergo magnetostrictive vibration under ultrasonic excitation, resulting in the separation of positive and negative charges in the magnetic particles within the imaging region. Electrodes attached to the surface of biological tissue detect the magnetoacoustic signal, thereby reconstructing the conductivity distribution image of the imaging region and achieving magnetoacoustic imaging of magnetic particle concentration.

[0008] The improved Obert ring-magnet system described in this invention is specifically designed for MAET-ED. Currently, the imaging region of MAET-ED is a spherical region with a radius of 25 mm. Therefore, the spacing between the upper and lower Obert ring pairs is set to 130 mm, the magnet thickness to 10 mm, the outer radius to 90 mm, and the inner radius to 60 mm. Two sets of opposing second-order Z-gradient shimming coils are each supplied with an equal current in the same direction. The outer coil has a radius of 30 mm, a distance of 50 mm from the origin, 100 turns, a cross-sectional radius of 4 mm, and an excitation current of 1.4 A; the inner coil also has a radius of 30 mm, a distance of 30 mm from the origin, 100 turns, a cross-sectional radius of 4 mm, and an excitation current of 0.8 A. Since MAET-ED only requires a static magnetic field in the z-axis direction, the improved Obert ring-magnet system of this invention is only used to generate a static magnetic field in the z-axis direction.

[0009] In the improved Obert ring pair magnet system described in this invention, the positions of each permanent magnet and each set of coils are fixed. Under the condition that the required static magnetic field is known, the non-dominated sorting genetic algorithm NSGA-III can be used to optimize the Obert ring pair according to its structural and positional parameters. With magnetic flux density and magnetic field uniformity as objective functions, the parameters of the Obert ring pair that meet the requirements of MAET-ED imaging are calculated, thereby constructing a complete MAET-ED magnet system.

[0010] The improved Oberth ring magnet system described in this invention includes the following steps in its structural optimization design: 1) Set the basic parameters of the study area and Oberth ring according to the imaging area; 2) Determine the imaging area and the required static magnetic field size based on the relationship between magnetoacoustic and electrical signals and magnetic flux density in magnetoacoustic-electric imaging of magnetic particle concentration; 3) According to the superposition theorem of magnetic fields, the magnetic fields generated by the Obert ring pair and the second-order Z-gradient shimming coil are superimposed to obtain the magnetic field generated by the MAET-ED magnet system in the imaging region, and the magnetic flux density value of the magnetic field is calculated from this. 4) The non-dominated sorting genetic algorithm NSGA-III was used for optimization, with magnetic flux density and magnetic field uniformity as objective functions, to calculate the parameters of the Oberthian ring pair that meet the requirements of MAET-ED imaging. 5) Use the F1 score as an evaluation index to verify the effectiveness of the design scheme.

[0011] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the purpose, features and advantages of the present invention more obvious and understandable, the present invention will be described in detail below with reference to the accompanying drawings. Attached Figure Description

[0012] Figure 1This is a schematic diagram illustrating the principle of the improved magnetic particle concentration magnetoacoustic-electric imaging device of the present invention.

[0013] Figure 2 This is a schematic diagram of the physical process of magnetoacoustic-electromagnetic imaging of magnetic particle concentration according to the present invention;

[0014] Figure 3 This is a diagram of the improved Oberth ring-permanent magnet structure for the magnetic particle concentration magnetoacoustic imaging device of the present invention;

[0015] Figure 4 This is a structural diagram of the second-order z-gradient shimming coil of the magnetoacoustic-electromagnetic imaging device for magnetic particle concentration according to the present invention;

[0016] Figure 5 This is a schematic diagram of the background magnetic field excitation unit structure of the improved magnetoacoustic-electromagnetic imaging device for magnetic particle concentration according to the present invention.

[0017] Figure 6 This is a schematic diagram of the NSGA-Ⅲ optimization method for improving the magnetic particle concentration magnetoacoustic imaging device according to the present invention.

[0018] Figure 7 This is a graph showing the trend of the Langevin function value in this invention. Detailed Implementation

[0019] To make the purpose, technical solution, and advantages of the improved static magnetic field excitation unit clearer, a detailed description is provided below with reference to the accompanying drawings. Furthermore, for the sake of simplicity and ease of understanding, only the relevant parts of the invention are schematically shown in each figure.

[0020] like Figure 1 As shown, the electrode-detection type magnetic particle concentration magnetoacoustic imaging device includes: 1) Static magnetic field excitation unit: composed of Oberthian ring pairs and second-order Z-gradient shimming coils, the purpose of which is to generate a static magnetic field and act on biological tissue containing MNPs; 2) Magnetoacoustic and electrical signal acquisition and display unit: It consists of an ultrasonic transducer, an ultrasonic probe, a power amplifier, a lock-in amplifier, electrode plates, an oscilloscope, and a PC. Its purpose is to acquire magnetoacoustic and electrical signals and to condition and display the acquired signals. 3) Mechanical drive scanning unit: It consists of a drive circuit, a stepper motor group and a three-axis controller. Its purpose is to move the ultrasonic probe to a designated position and then send an excitation signal from the ultrasonic excitation device to make the magnetic particles in the sample vibrate after being excited by the ultrasonic.

[0021] Improved Oberth ring structure for magnet systems, such as Figure 5As shown, the device consists of a signal generator, a power amplifier, an Obert loop pair, and a second-order Z-gradient shimming coil. In this invention, the second-order Z-gradient shimming coil is a device used to improve the uniformity of the magnetic field, consisting of two sets of parallel and coaxial circular coils. The currents within the coils are in the same direction and equal in magnitude. The theoretical basis for generating the magnetic field is the Biot-Savart law. Therefore, the second-order Z-gradient shimming coil can be used to counteract the Earth's magnetic field and design a uniform magnetic field region.

[0022] This invention proposes a magnet system design method for magnetoacoustic-electromagnetic imaging of magnetic particle concentration. Besides its simple magnet structure and convenient system construction, this magnet system can achieve lightweight design and reduce the excitation current value of the second-order Z-gradient shimming coil while meeting the requirements of MAET-ED imaging. The uniform static magnetic field generated acts on the MNPs region, realizing the principle of magnetoacoustic-electromagnetic imaging of magnetic particle concentration as follows: Figure 2 As shown in the figure. The uniform static magnetic field generated by the MAET-ED magnet system designed in this paper magnetizes MNPs. The magnetized MNPs then undergo magnetostrictive vibrations under ultrasonic signal excitation. Due to the Lorentz force, the positive and negative charges of the magnetic particles separate within the imaging region. Electrodes attached to the surface of biological tissue detect magnetoacoustic signals. By processing the acquired magnetoacoustic signal data using image reconstruction algorithms, the concentration distribution image of MNPs can be reconstructed, achieving magnetoacoustic imaging of magnetic particle concentration. Therefore, different MNP concentrations lead to different magnetic forces, which in turn result in different magnetoacoustic signals.

[0023] The improved design method of the Oberth ring pair MAET-ED magnet system of this invention includes the following steps:

[0024] 1) Set the basic parameters of the study area and Oberth ring according to the imaging area; In this invention, the MAET-ED imaging region is a spherical region with a radius of 25 mm. Therefore, the research region is set as a spherical region with a radius of 25 mm centered at the origin (0, 0, 0). The Oberth ring pair uses N50 neodymium iron boron permanent magnets as the permanent magnet material, with a remanence of 1.4 T, intrinsic coercivity of 1353 kA / m, and relative permeability of 0.9.

[0025] 2) Determine the imaging area and the required static magnetic field size based on the relationship between magnetoacoustic and electrical signals and magnetic flux density in magnetoacoustic-electric imaging of magnetic particle concentration; The improved Oberth ring-magnet system described in this invention is specifically designed for MAET-ED. Based on the theory of electrode-detection magnetic particle concentration magnetoacoustic-electroelectric imaging, the type of magnetic nanoparticles, and the Langevin function, the magnitude of the static magnetic field required for MAET-ED imaging is calculated. The specific calculation process is as follows: MAET-ED magnetoacoustic-electroelectric signal expression:

[0026] Depend on , It can be seen that when When changing, The trend of change is as follows Figure 7 As shown.

[0027] Using Langevin functions From the changing trend, we can see that when... hour, Rapidly increase; when hour, The growth rate is slow and approaches 1 infinitely. To meet the requirements of magnetoacoustic-electric imaging based on magnetic particle concentration, and to save on magnet usage, this paper sets... =0.97( When the magnetic particles are approximately saturated, the magnetic field strength is... 0.05T. That is, when At time T, the magnetic particles can be considered to have reached saturation.

[0028] Substituting the Langevin function into the above equation, we obtain the following: The expression for the magnetoacoustic signal:

[0029] when When the value is much greater than 1, the expression for the magnetoacoustic signal simplifies to:

[0030] 3) According to the superposition theorem of magnetic fields, the magnetic fields generated by the Obert ring pair and the second-order Z-gradient shimming coil are superimposed to obtain the magnetic field generated by the MAET-ED magnet system in the imaging region, and the magnetic flux density value of the magnetic field is calculated from this. This paper uses the equivalent magnetic charge method to optimize the design of the Oberth ring pair. It assumes that magnetic charges exist both inside and outside the magnet, and that the magnet is filled with magnetic charges at a density of . The internal magnetic charge, with a density of distributed outside the magnet. Surface magnetic charge, introducing a magnetic scalar potential Magnetic field strength is expressed as:

[0031] Substituting the above equation into Maxwell's fourth equation, we get:

[0032] Considering the boundary conditions and using the Green's function, we get:

[0033] Magnetic charge density: areal density: , The magnet is in free space The magnetic field strength at point x is:

[0034] For an Oberth ring with its magnetization direction radially outward, the bulk magnetic charge density of the magnet is: The surface magnetic charge is inside the magnet. On the outside of the magnet To calculate the magnetic scalar potential at a point on the axis, we need to differentiate it with respect to z: We will get two terms: one is the contribution from the end face magnetic charge (inverse square root term), and the other is the contribution from the side face magnetic charge (logarithmic term).

[0035] If a magnetic scalar potential is used The expression at the end face, after integration, yields a form containing logarithmic terms. The complete expression for a uniformly radially magnetized finite-length cylinder is shown below:

[0036] in: , , ,

[0037] The remanence of a permanent magnet is , Let z be the z-coordinate of the field point. This represents the distance from the origin to the inner surface of the upper and lower magnetic rings. Where is the magnet thickness, and the inner diameter of the Oberth ring is... The outer diameter of the Obert ring is The non-dominated sorting genetic algorithm NSGA-III was used for optimization, with magnetic flux density and magnetic field uniformity as objective functions, to calculate various parameters of the Oberthian ring pair that meet the requirements of MAET-ED imaging, thereby constructing a complete MAET-ED magnet system.

[0038] A second-order Z-gradient shimming coil is a device used to generate a small-scale uniform magnetic field. This magnetic system consists of two sets of parallel and coaxial circular coils. The currents within the coils are in the same direction and of equal magnitude. The theoretical basis for generating the magnetic field is the Biot-Savart law. Therefore, second-order Z-gradient shimming coils can be used to counteract the Earth's magnetic field and design uniform magnetic field regions.

[0039] Biot-Savart law expression:

[0040] Magnetic flux density at any point on the central axis (z-axis) of a second-order Z-gradient uniform field coil:

[0041] in The permeability of free space, The average radius of the coil, For the number of coil turns, For the current passing through the coil, It is the distance from a point on the axis to the center of the circle.

[0042] This paper addresses the "high center, low edge" distribution characteristic of the existing magnetic field region B by proposing an active shimming scheme using second-order Z-gradient shimming coils. This coil assembly generates a second-order gradient magnetic field, with the strongest magnetic field strength at the center point, which decreases symmetrically with increasing distance from the center (radial and axial). This weakens the central field strength and strengthens the edge field strength, thus achieving the goal of active shimming. The coil assembly structure is as follows: Figure 4 As shown.

[0043] According to the superposition theorem of magnetic fields, the magnetic fields generated by the Obert ring pair and the second-order Z-gradient uniform field coil are superimposed to obtain the final magnetic field generated by the MAET-ED magnet system. The magnetic field at any field point after superposition is:

[0044] 4) The non-dominated sorting genetic algorithm NSGA-III was used for optimization, with magnetic flux density and magnetic field uniformity as objective functions, to calculate the parameters of the Oberthian ring pair that meet the requirements of MAET-ED imaging.

[0045] in, Let U be the magnetic field generated by the Oberthian rings, and U be the magnetic field uniformity of the imaging region. The distance from the inner surface of the upper and lower magnetic rings to the origin is... The value range is 50~100mm, and the magnet thickness is... The value ranges from 10 to 20 mm, and the inner diameter of the Oberth ring is... The value ranges from 10 to 50 mm, and the outer diameter of the Oberth ring is... The value range is 50~100mm.

[0046] The process of the optimization algorithm is as follows: Figure 6As shown, the population is first initialized in the imaging region, with the number of decision variables (nVar) set to 4, the number of objective functions (nObj) set to 2, the number of partitions (nDivision) set to 10, the maximum number of iterations set to 200, and the population size set to 200. To ensure that the solution found by the algorithm is optimal, the crossover mutation rate (nCrossover) of NSGA-III is set to 0.8, the mutation probability (pMutation) to 0.3, and the mutation rate (mu) to 0.02. The algorithm iterates continuously to update its Pareto optimal solution until the maximum number of iterations is reached. The top 10 optimal solutions are then selected and imported into the COMSOL magnetic field simulation to find the optimal combination of magnet parameters.

[0047] 5) Use the F1 score as an evaluation index to verify the effectiveness of the design scheme.

[0048] The absolute distance between the magnetic flux density and the standard value:

[0049] in: .

[0050] The absolute distance between the magnetic field homogeneity and the standard value:

[0051] in: .

[0052] Comprehensive evaluation index F1:

[0053] in: The weight of magnetic flux density in relation to the comprehensive evaluation index F1; This represents the weight of the magnetic field uniformity. This paper will... , All values ​​are set to 0.5. The smaller the F1 value, the closer the sample point is to the target reference point, which is the optimal solution of the non-dominated sorting genetic algorithm NSGA-III.

[0054] The MAET-ED magnet system was designed using the above method. The parameters of the Oberth ring pair are as follows: h = 65 mm, d = 10 mm, R1 = 60 mm, R2 = 90 mm. The parameters of the second-order Z-gradient shimming coils are as follows: coil radius r = 30 mm, distance d from the origin of outer coil group 1 = 50 mm, distance d from the origin of inner coil group 2 = 30 mm, number of turns of outer coil group 1 = 100, number of turns of inner coil group 2 = 100, and excitation currents of 1.4 A and 0.8 A, respectively. This magnet system can generate a uniform static magnetic field with a magnetic flux density of 0.05 T and a magnetic field uniformity of less than 5% within a spherical region with a radius of 25 mm.

[0055] The main innovation of this invention lies in using an improved Obert ring pair magnet system to replace the original rectangular permanent magnet as the magnetic field excitation unit of the electrode detection type magnetic particle concentration magnetoacoustic-electromagnetic imaging device. In addition to the simple magnet structure and convenient system construction, the improved Obert ring pair magnetic field excitation unit can achieve a lightweight magnet system and reduce the excitation current value of the second-order Z-gradient shimming coil while meeting the requirements of MAET-ED imaging, thus realizing MAET-ED imaging research.

[0056] The above description is merely a specific embodiment of the present invention and should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for designing an Oersted loop pair magnet system for magnetic particle concentration magnetoacoustic-electric imaging, characterized in that: Oberth rings are used as the main magnetic field excitation unit for magnetoacoustic-electric imaging of magnetic particle concentration. The structural parameters of the Oberth rings are optimized by the non-dominated sorting genetic algorithm NSGA-III. By changing the structure or parameters of each part of the Oberth ring magnet system, the static magnetic field required for imaging is generated in the imaging area. The second-order Z-gradient shimming coil in this invention can output a compensation magnetic field of different magnitudes in the imaging area by changing the radius, current magnitude and direction of the coil. The magnetic field generated by the MAET-ED magnet system will cause MNPs to reach a saturated magnetization state. The magnetized MNPs will undergo magnetostrictive vibration under the action of ultrasonic excitation. The positive and negative charges of magnetic particles are separated in the imaging area. The electrode plates attached to the surface of biological tissue detect the magnetoacoustic-electric signal. Then, the image reconstruction algorithm is used to process the acquired magnetoacoustic-electric signal data to reconstruct the concentration distribution image of MNPs, thereby realizing magnetoacoustic-electric imaging of magnetic particle concentration.

2. The method of claim 1, wherein: The magnetic field excitation unit in the magnetic particle concentration magnetoacoustic imaging platform was changed from a single rectangular permanent magnet to a combination of an Obert ring-permanent magnet and a second-order Z-gradient shimming coil. The Obert ring-permanent magnet and the shimming coil are divided into upper and lower parts, and each part is arranged along the same axis and symmetrical about the xoy plane.

3. The method of claim 1, wherein: The upper and lower Oberthian rings are split into eight segments relative to the permanent magnet, with a magnetization step angle of 45°. This simplifies the finite element simulation. The Oberthian rings are 130mm apart from the permanent magnet to ensure that their magnetic field covers the entire imaging area.

4. The method of claim 1, wherein: The imaging area of ​​magnetic particle concentration magnetoacoustic imaging is a spherical region with a radius not exceeding 25 mm. The thickness and inner and outer radii of the Oberth ring pair (2) are set according to the imaging area.

5. The method for designing an Oberthian ring-magnet system for magnetoacoustic imaging of magnetic particle concentration according to claim 1, characterized in that: The second-order Z-gradient shimming coil is made of copper enameled wire with a diameter of 8mm. The inner and outer coils are wound with 1 layer and 100 turns. The outer radius of the coil is 32mm and the inner radius is 30mm. The inner and outer coil groups are 60mm and 100mm apart, respectively, and the coils in the same coil group are carried by the same current in the same direction.

6. The method for designing an Obert ring-to-magnet system for magnetoacoustic imaging of magnetic particle concentration according to claim 1, characterized in that: The steps for optimizing the structural parameters of the Oberth ring pair are as follows: 1) Set the relevant parameters of the research area and permanent magnet material according to the imaging area; 2) Based on the derived relationship between magnetoacoustic and electrical signals and magnetic flux density in magnetoacoustic-electric imaging of magnetic particle concentration, as well as the Langevin function, determine the required background magnetic field size for the imaging area. 3) According to the superposition theorem of magnetic fields, the magnetic field generated by the second-order Z-gradient shimming coil is superimposed with the magnetic field generated by the Obert ring pair to obtain the magnetic field generated by the improved Obert ring pair magnet system in the imaging region, and the magnetic flux density and uniformity of the magnetic field are calculated from this. 4) The non-dominated sorting genetic algorithm NSGA-III is used to optimize the structure or parameters of the Oberth ring pair permanent magnet. The magnetic flux density and magnetic field uniformity are used as objective functions to calculate the parameters of the Oberth ring pair that meet the requirements of MAET-ED imaging. 5) Use the F1 score as an evaluation index to verify the effectiveness of the design scheme.

Images