Gaussian spatter-based nuclear magnetic resonance passive shimming module design method and device

Abstract

The application discloses a kind of passive field uniformity module design method and device based on gauss splash of nuclear magnetic resonance, it is related to the field of precise electromagnetic field optimization, including: initialization is carried out in the design domain of passive field uniformity module, obtains the initial parameter set of all gauss splash particles;The mapping relationship between the equivalent magnetic moment of each gauss splash particle and magnetization weight factor, intrinsic magnetization intensity of magnetic material and scaling vector is constructed and magnetic field strength calculation model is constructed;The initial parameter set of all gauss splash particles and real magnetic field strength are input into gauss splash particle parameter set iterative optimization algorithm, and the predicted magnetic field strength is calculated by magnetic field strength calculation model;Based on predicted magnetic field strength, real magnetic field strength, magnetization weight factor vector and center position vector, construct multi-objective loss function and iterative optimization, obtain the optimized parameter set and make passive field uniformity module.The application solves the problem of low accuracy and efficiency of compensating complex topography magnetic field.

Description

Technical Field

[0001] This invention relates to the field of precision electromagnetic field optimization technology, specifically to a design method and device for a nuclear magnetic resonance passive shimming module based on Gaussian splashing. Background Technology

[0002] In nuclear magnetic resonance (NMR) detection systems, the spatial uniformity of the main magnetic field directly determines the signal-to-noise ratio, spatial resolution, and spectral quality of the detection signal. To compensate for magnetic field inhomogeneities caused by inherent errors in the main magnet, manufacturing and assembly errors, and environmental disturbances, a passive shimming module is typically designed to generate a compensating magnetic field within the target detection area.

[0003] Most existing passive shimming module design methods are based on spherical harmonic function expansion, target field methods, or topology optimization methods based on regular grids. Patents CN114636958B and CN119780810B disclose the use of linear target optimization methods to determine the thickness distribution of the sheet matrix. A paper titled "A passive shimming method for Halbach magnet based on magnetic sheet arrays" utilizes spherical harmonic function decomposition to perform multi-order compensation of the magnetic field. A paper titled "An Improved Passive Shimming Design Method" uses an improved target field method to quickly obtain the minimum sheet arrangement scheme with the lowest magnetic field inhomogeneity, while significantly reducing iteration time. However, the above methods require fixing the number of shimming trays and optimizing the sheet size and spacing within the trays, which limits their design freedom, ability to compensate for localized magnetic field distortion, and modeling of complex structures. Although the paper titled "Additive Manufactured and Topology Optimized Passive Shimming Elements for Permanent Magnetic Systems" provides a new approach to shimming element design by improving the magnetic field uniformity of permanent magnets through topology optimization and additive manufacturing, traditional topology optimization methods heavily rely on high-frequency finite element analysis. In high-dimensional parameter spaces, these methods suffer from technical bottlenecks such as exponentially increasing computational cost, slow convergence speed, gradient vanishing, and susceptibility to local optima, making it difficult to meet the requirements for real-time, efficient, and precise shimming. Furthermore, due to its inherent spatial discretization error, it is difficult to achieve high spatial resolution magnetic field compensation. Summary of the Invention

[0004] This invention proposes a design method and device for a passive shimming module for nuclear magnetic resonance based on Gaussian splashing. Its purpose is to make up for the shortcomings of existing passive shimming design methods and to solve the problem of low accuracy and efficiency of passive shimming modules in current nuclear magnetic resonance examination instruments in compensating for complex morphological magnetic fields.

[0005] In a first aspect, the present invention provides a design method for a passive shimming module for nuclear magnetic resonance based on Gaussian splashing, comprising the following steps:

[0006] Within the design domain of the passive shimming module, several Gaussian splash particles are randomly initialized and generated, and an initial parameter set for all Gaussian splash particles is constructed. The parameter set includes a magnetization weight factor vector, a center position vector, a rotation quaternion matrix, and a scaling matrix.

[0007] For each type of magnetic material filling the design domain of the passive shimming module, a mapping relationship is constructed between the equivalent magnetic moment of each Gaussian splash particle and the magnetization weight factor, the intrinsic magnetization intensity of the magnetic material, and the scaling vector; a magnetic field strength calculation model is constructed based on the differentiable form of the Biot-Savart law.

[0008] The magnetic material to be filled within the design domain of the passive shimming module is selected. The initial parameter set and the actual magnetic field strength of all Gaussian splash particles are input into the Gaussian splash particle parameter set iterative optimization algorithm and participate in the first iteration optimization process. Based on the magnetization weight factor vector, scaling matrix, intrinsic magnetization intensity corresponding to the magnetic material, and mapping relationship obtained in the previous iteration optimization process, the equivalent magnetic moment vector of all Gaussian splash particles is determined. The equivalent magnetic moment vector, magnetization weight factor vector, center position vector, and rotation quaternion matrix are input into the magnetic field strength calculation model to obtain the predicted magnetic field strength of each sampling point in the target magnetic field region. Based on the predicted magnetic field strength, actual magnetic field strength, magnetization weight factor vector, and center position vector of each sampling point in the target magnetic field region, a multi-objective loss function is constructed. The parameter set obtained in the previous iteration optimization process is updated based on the multi-objective loss function to obtain the parameter set obtained in the current iteration optimization process. The above iterative optimization process is repeated until the maximum number of iterations is reached to obtain the optimized parameter set.

[0009] Based on the optimized parameter set and the magnetic material to be filled, a corresponding passive shimming module is fabricated.

[0010] Preferably, the rotation quaternion matrix is ​​composed of the rotation quaternions of all Gaussian splash particles; the scaling matrix is ​​composed of the scaling vectors of all Gaussian splash particles, where each scaling vector represents the scaling of a single Gaussian splash particle along the x, y, and z axes; the magnetization weight factor vector is composed of the magnetization weight factors of all Gaussian splash particles; and the center position vector is composed of the center positions of all Gaussian splash particles.

[0011] As a preferred method, the process of constructing the mapping relationship is as follows:

[0012] Within the design domain, the relative displacement of each sampling point in the target magnetic field region with respect to the center position of each Gaussian splash particle is calculated, and the spatial proportion is obtained by combining the scaling vector of each Gaussian splash particle, as shown in the following formula:

[0013] ;

[0014] in, This indicates the location of a sampling point of one of the Gaussian splash particles in the target magnetic field region. The space ratio of the location This indicates the location of any sampling point within the target magnetic field region. and These represent the locations of sampling points within the target magnetic field region. The relative positions of the center of one of the Gaussian splash particles on the x, y, and z axes. , and These represent the scaling of one Gaussian splash particle along the x, y, and z axes, respectively.

[0015] The magnetization contributions of N Gaussian splash particles are linearly superimposed within the design domain to construct the magnetization intensity of one sampling point in the target magnetic field region, as shown in the following equation:

[0016] ;

[0017] in, Indicates the location of the sampling point in the target magnetic field region. magnetization intensity, represents the peak magnetization of the i-th Gaussian splash particle, and N represents the total number of Gaussian splash particles;

[0018] By utilizing the analytical properties of the Gaussian function, the equivalent magnetic moment of each Gaussian splash particle is discretized by integrating the continuously distributed magnetization over the volume, as shown in the following equation:

[0019] ;

[0020] in, Let V represent the equivalent magnetic moment of the i-th Gaussian splash particle, and let V represent the volume. This represents the magnetization intensity of the i-th Gaussian splash particle in the target magnetic field region;

[0021] The peak magnetization of the i-th Gaussian splash particle is decomposed into the product of the magnetization weighting factor of the i-th Gaussian splash particle and the intrinsic magnetization of the material. The mapping relationship is then defined as follows:

[0022] ;

[0023] in, This represents the magnetization weighting factor of the i-th Gaussian splash particle. It represents the intrinsic magnetization intensity associated with magnetic materials.

[0024] As a preferred method, the magnetic field strength calculation model is as follows:

[0025] ;

[0026] in, This indicates the location of all Gaussian splash particles in the target magnetic field region. The predicted magnetic field strength at that location This represents the equivalent magnetic moment vector formed by the equivalent magnetic moments of all Gaussian splash particles. This indicates the location of the sampling point in the index magnetic field region, representing the center position of all Gaussian splashed particles. The displacement vector, Represents the magnetization weight factor vector. Represents the center position vector. The covariance matrix of all Gaussian splash particles is expressed as follows: , This represents the rotation matrix obtained by mapping the rotation quaternion matrix using Rodrigues transform logic. Represents the scaling matrix. This represents the transpose of a matrix.

[0027] As a preferred option, the expression for the multi-objective loss function is as follows:

[0028] ;

[0029] in, Represents a multi-objective loss function. This represents the magnetic field deviation loss function. Represents the sparsity loss function. Represents the spatial overlap loss function; and These are the weight coefficients for the sparse loss function and the spatial overlap loss function, respectively.

[0030] The expression for the magnetic field deviation loss function is as follows:

[0031] ;

[0032] in, Indicates the location of the sampling point in the target magnetic field region. The actual magnetic field strength at the location, where N represents the total number of Gaussian splash particles. Represents the L2 norm;

[0033] The expression for the sparsity loss function is as follows:

[0034] ;

[0035] in, Indicates L1 regularization;

[0036] The expression for the spatial overlap loss function is as follows:

[0037] ;

[0038] Where i and j represent the i-th Gaussian splash particle and the j-th Gaussian splash particle, respectively. Let be the distance between the center positions of the i-th Gaussian splash particle and the j-th Gaussian splash particle. For minimum safe distance, This indicates taking the maximum of the two values;

[0039] In the current iteration of optimization, the goal is to minimize the multi-objective loss function. The Gaussian splash particles are moved, split, or aggregated using an adaptive moment estimation algorithm to update the parameter set obtained in the previous iteration.

[0040] As a preferred option, a corresponding passive shimming module is fabricated based on the optimized parameter set and the magnetic material to be filled, specifically including:

[0041] Within the design domain, a spatial voxel mesh is created. The magnetization weighting factors of each Gaussian splash particle in the optimized parameter set are linearly superimposed with the spatial occupancy to obtain the location of the sampling point in the target magnetic field region. The density field at that location is shown in the following equation:

[0042] ;

[0043] Among all Gaussian splash particles, Gaussian splash particles with a density field higher than a preset density threshold are searched and transformed into the topological structure model corresponding to the passive shimming module. Based on the topological structure model corresponding to the passive shimming module, the passive shimming module is fabricated using additive manufacturing process.

[0044] Secondly, the present invention provides a design device for a passive shimming module for nuclear magnetic resonance based on Gaussian splashing, comprising:

[0045] The initialization module is configured to randomly generate several Gaussian splash particles within the design domain of the passive shimming module, and construct an initial parameter set for all Gaussian splash particles, including a magnetization weight factor vector, a center position vector, a rotation quaternion matrix, and a scaling matrix.

[0046] The model building module is configured to construct the mapping relationship between the equivalent magnetic moment of each Gaussian splash particle and the magnetization weight factor, the intrinsic magnetization intensity and scaling vector of the magnetic material, for each magnetic material filled in the design domain of the passive shimming module; and to construct a magnetic field strength calculation model based on the differentiable form of the Biot-Savart law.

[0047] The parameter optimization module is configured to select the magnetic material to be filled within the design domain of the passive shimming module. It inputs the initial parameter set and actual magnetic field strength of all Gaussian splash particles into the Gaussian splash particle parameter set iterative optimization algorithm and participates in the first iteration. Based on the magnetization weight factor vector, scaling matrix, intrinsic magnetization of the magnetic material, and mapping relationship obtained in the previous iteration, it determines the equivalent magnetic moment vector of all Gaussian splash particles. The equivalent magnetic moment vector, magnetization weight factor vector, center position vector, and rotation quaternion matrix are then input into the magnetic field strength calculation model to obtain the predicted magnetic field strength at each sampling point in the target magnetic field region. A multi-objective loss function is constructed based on the predicted magnetic field strength, actual magnetic field strength, magnetization weight factor vector, and center position vector at each sampling point in the target magnetic field region. This multi-objective loss function updates the parameter set obtained in the previous iteration, resulting in the parameter set for the current iteration. This iterative optimization process is repeated until the maximum number of iterations is reached, yielding the optimized parameter set.

[0048] The solidification module is configured to perform solidification based on the optimized parameter set and the magnetic material to be filled, thereby creating the corresponding passive shimming module.

[0049] Thirdly, the present invention provides an electronic device including one or more processors; and a storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any implementation of the first aspect.

[0050] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method as described in any of the implementations of the first aspect.

[0051] Fifthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the method as described in any of the implementations in the first aspect.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] (1) The design method of passive shimming module for nuclear magnetic resonance based on Gaussian splashing proposed in this invention utilizes the explicit anisotropy of three-dimensional Gaussian splashed particles to give the passive shimming module extremely high design freedom. It can break through the shape limitations of traditional regular geometric bodies and realize non-uniform and asymmetric complex layouts for complex irregular shapes and limited detection spaces, which significantly enhances the compensation efficiency and spatial adaptability of the passive shimming module in the compact environment of nuclear magnetic resonance instruments.

[0054] (2) The proposed design method for passive shimming modules for nuclear magnetic resonance based on Gaussian splashing transforms the traditional discrete topology optimization into a differentiable continuous gradient descent process based on the parameter set of three-dimensional Gaussian splashed particles, thus making the topology generation of the passive shimming module no longer dependent on finite element mesh generation. This adaptive evolution mechanism can grow free-form magnetic compensation blocks that highly fit the characteristics of non-uniform distorted magnetic fields, significantly improving the accuracy of magnetic field compensation while optimizing the conversion efficiency from magnetic field to geometric entity.

[0055] (3) The design method of the nuclear magnetic resonance passive shimming module based on Gaussian splashing proposed in this invention utilizes the unique splitting and pruning dynamic control technology of three-dimensional Gaussian splashing particles to automatically capture and fit the subtle physical structure at complex boundaries or electromagnetic singularities, effectively eliminating magnetic field strays in the target area. At the same time, the topological structure model constructed by the optimized parameter set has natural compatibility with the additive manufacturing process, eliminating the error of secondary modeling and greatly shortening the R&D cycle of high-precision passive shimming modules from design and simulation to finished product manufacturing. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 This is a flowchart illustrating the design method of a passive shimming module for nuclear magnetic resonance based on Gaussian splashing, as an embodiment of this application.

[0058] Figure 2 The overall design flowchart of the design method of the passive shimming module of nuclear magnetic resonance based on Gaussian splashing is shown in the embodiment of this application.

[0059] Figure 3 This is a schematic diagram of the geometric and physical properties of each Gaussian sputtered ion in the design method of the passive shimming module for nuclear magnetic resonance based on Gaussian sputtering, which is an embodiment of this application.

[0060] Figure 4 This is a schematic diagram of the passive shimming module and the target magnetic field region in the design method of the passive shimming module for nuclear magnetic resonance based on Gaussian splashing, which is an embodiment of this application.

[0061] Figure 5 The diagram illustrates the evolution of Gaussian splash particles splitting, pruning, and coalescence in the Gaussian splash-based nuclear magnetic resonance passive shimming module design method according to an embodiment of this application. Figure 5 (a) in the diagram represents the initial Gaussian splash particles. Figure 5 (b) in the diagram represents a schematic of Gaussian splashed particles after splitting and pruning. Figure 5 (c) in the diagram represents the Gaussian splash particles after aggregation;

[0062] Figure 6 This is a schematic diagram illustrating the conversion of a topological model of Gaussian splashed particles with an optimized parameter set into a solid model in the design method of a passive shimming module for nuclear magnetic resonance based on Gaussian splashing, as described in an embodiment of this application.

[0063] Figure 7 This is a comparison diagram of the magnetic field intensity distribution with initial distortion and the magnetic field intensity distribution after 3DGS compensation using the passive shimming module, based on the Gaussian splashing-based nuclear magnetic resonance passive shimming module design method of this application, as shown in the figure. Figure 7 (a) in the diagram represents the magnetic field strength distribution of the initial distortion. Figure 7 (b) in the figure represents the magnetic field intensity distribution after 3DGS compensation using the passive shimming module;

[0064] Figure 8 This is a schematic diagram of a design device for a passive shimming module of nuclear magnetic resonance based on Gaussian splashing, according to an embodiment of this application.

[0065] Figure 9 This is a schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0067] Figure 1 This application illustrates an embodiment of a passive shimming module design method for nuclear magnetic resonance based on Gaussian splashing, comprising the following steps:

[0068] S1, randomly initialize and generate several Gaussian splash particles within the design domain of the passive shimming module, and construct the initial parameter set of all Gaussian splash particles. The parameter set includes the magnetization weight factor vector, the center position vector, the rotation quaternion matrix, and the scaling matrix.

[0069] In a specific embodiment, the rotation quaternion matrix is ​​composed of the rotation quaternions of all Gaussian splash particles; the scaling matrix is ​​composed of the scaling vectors of all Gaussian splash particles, where each scaling vector represents the scaling of a single Gaussian splash particle along the x, y, and z axes; the magnetization weight factor vector is composed of the magnetization weight factors of all Gaussian splash particles; and the center position vector is composed of the center positions of all Gaussian splash particles.

[0070] For details, please refer to Figure 2 In this embodiment, a set of three-dimensional Gaussian splash particles with geometric and physical properties is first randomly initialized and generated within a preset space of the passive shimming module. The set of three-dimensional Gaussian splash particles contains several Gaussian splash particles. The randomly generated set of three-dimensional Gaussian splash particles with geometric and physical properties is constructed in the following way: each Gaussian splash particle carries a magnetization weighting factor w, which is used to quantify the magnetic field compensation strength and polarity of the Gaussian splash particle on the target magnetic field region, and serves as the core variable for optimizing magnetic inhomogeneity; such as Figure 3 As shown, each Gaussian splash particle also includes a central location. The rotation quaternion q and the three-axis scaling vector s, representing the shape and orientation of the Gaussian splash particles, are denoted as: The magnetization weighting factors of all Gaussian splash particles are used to construct the magnetization weighting factor vector w, and the center position vector of all Gaussian splash particles is constructed from their center positions. The rotation quaternion matrix is ​​obtained by constructing the rotation quaternion of all Gaussian splash particles, and the scaling matrix is ​​obtained by constructing the scaling vector of all Gaussian splash particles. The embodiments of this application employ Rodriguez transform logic to map the rotation quaternion matrices of all Gaussian splash particles into rotation matrices in three-dimensional space. Further through rotation matrix and scaling matrix Constructing the covariance matrix The spatial occupancy and directionality of magnetic materials in the Gaussian splash particles are defined; the parameter set corresponding to the Gaussian splash particle set is {w, μ, q, S}. The preset space is used as the design domain, and the adaptive growth or pruning of the topology model of the passive shimming module is achieved by dynamically adjusting the parameter set.

[0071] refer to Figure 4 In the embodiments of this application, taking the preset space of the passive shimming module as a cylindrical shell as an example, the magnetization weight factor w of each Gaussian splash particle is set to a small random value during the initialization stage, which follows a normal distribution with a mean of 0 and a standard deviation of 0.01; the center position μ of each Gaussian splash particle is uniformly and randomly distributed within the preset space of the cylindrical shell, ranging from 70 mm to 100 mm in the radial direction of the cylindrical shell, and the height is between ±150 mm; the rotation quaternion q of each Gaussian splash particle has no rotation in the initial state, and the initial q = [1, 0, 0, 0]; the initial size of the three-axis scaling vector s is 15 mm × 10 mm × 10 mm, slightly longer along the x-axis direction of the main magnetic field, and is set to exhibit weak anisotropy.

[0072] S2, for each magnetic material filled in the design domain of the passive shimming module, construct the mapping relationship between the equivalent magnetic moment of each Gaussian splash particle and the magnetization weight factor, the intrinsic magnetization intensity and scaling vector of the magnetic material; construct a magnetic field strength calculation model based on the differentiable form of the Biot-Savart law.

[0073] In a specific embodiment, the process of constructing the mapping relationship is as follows:

[0074] Within the design domain, the relative displacement of each sampling point in the target magnetic field region with respect to the center position of each Gaussian splash particle is calculated, and the spatial proportion is obtained by combining the scaling vector of each Gaussian splash particle, as shown in the following formula:

[0075] ;

[0076] in, This indicates the location of a sampling point of one of the Gaussian splash particles in the target magnetic field region. The space ratio of the location This indicates the location of any sampling point within the target magnetic field region. and These represent the locations of sampling points within the target magnetic field region. The relative positions of the center of one of the Gaussian splash particles on the x, y, and z axes. , and These represent the scaling of one Gaussian splash particle along the x, y, and z axes, respectively.

[0077] The magnetization contributions of N Gaussian splash particles are linearly superimposed within the design domain to construct the magnetization intensity of one sampling point in the target magnetic field region, as shown in the following equation:

[0078] ;

[0079] in, Indicates the location of the sampling point in the target magnetic field region. magnetization intensity, represents the peak magnetization of the i-th Gaussian splash particle, and N represents the total number of Gaussian splash particles;

[0080] By utilizing the analytical properties of the Gaussian function, the equivalent magnetic moment of each Gaussian splash particle is discretized by integrating the continuously distributed magnetization over the volume, as shown in the following equation:

[0081] ;

[0082] in, Let V represent the equivalent magnetic moment of the i-th Gaussian splash particle, and let V represent the volume. This represents the magnetization intensity of the i-th Gaussian splash particle in the target magnetic field region;

[0083] The peak magnetization of the i-th Gaussian splash particle is decomposed into the product of the magnetization weighting factor of the i-th Gaussian splash particle and the intrinsic magnetization of the material. The mapping relationship is then defined as follows:

[0084] ;

[0085] in, This represents the magnetization weighting factor of the i-th Gaussian splash particle. It represents the intrinsic magnetization intensity associated with magnetic materials.

[0086] In a specific embodiment, the magnetic field strength calculation model is as follows:

[0087] ;

[0088] in, This indicates the location of all Gaussian splash particles in the target magnetic field region. The predicted magnetic field strength at that location This represents the equivalent magnetic moment vector formed by the equivalent magnetic moments of all Gaussian splash particles. This indicates the location of the sampling point in the index magnetic field region, representing the center position of all Gaussian splashed particles. The displacement vector, Represents the magnetization weight factor vector. Represents the center position vector. The covariance matrix of all Gaussian splash particles is expressed as follows: , This represents the rotation matrix obtained by mapping the rotation quaternion matrix using Rodrigues transform logic. Represents the scaling matrix. This represents the transpose of a matrix.

[0089] Specifically, embodiments of this application also establish a mapping relationship between the equivalent magnetic moment of each Gaussian splash particle and the magnetization weighting factor, the intrinsic magnetization intensity and scaling vector of the magnetic material for each magnetic material filled in the design domain. This mapping relationship can be used to further describe the relationship between the geometric parameters of the Gaussian splash particle and the magnetization properties of the material.

[0090] In constructing the mapping relationship, the relative displacement of each sampling point in the target magnetic field region relative to the center position of each Gaussian splash particle is first calculated within the design domain. This relative displacement indicates the distance between each sampling point in the target magnetic field region and the center position of each Gaussian splash particle; the greater the relative displacement, the sparser the material. This is then combined with the scaling vector that determines the morphology of the magnetic material. , and Calculate the space ratio To characterize the continuous material distribution within the design domain, the contributions of all N Gaussian splash particles are linearly superimposed on a spatial grid to construct a global magnetization. The magnetization at each sampling point in the target magnetic field region is used to characterize the magnetic superposition effect jointly produced by all Gaussian splash particles at that sampling point. The calculation of this magnetization utilizes the smoothness of the Gaussian function to achieve a deterministic transformation from discrete geometric parameters to a continuous spatial material distribution, thus providing a continuous differentiable space. To achieve efficient forward computation, the analytic properties of the Gaussian function are used to map the continuous magnetization distribution field to discrete physical source terms. The equivalent magnetic moment of a single Gaussian splash particle... The magnetization intensity is obtained by integrating the volume of the entire space. Therefore, the discrete formula for the equivalent magnetic moment of the Gaussian splash particle can be derived using the three-dimensional Gaussian integral formula. Furthermore, the peak magnetization intensity in the discrete formula for the equivalent magnetic moment of the Gaussian splash particle can be further analyzed. Decomposed into magnetization weighting factors With intrinsic magnetization By multiplying these factors, the mapping relationship between the equivalent magnetic moment of each Gaussian splash particle and the magnetization weighting factor, the intrinsic magnetization of the magnetic material, and the scaling vector can be derived. The equivalent magnetic moment of a Gaussian splash particle determines its ability to compensate for external magnetic field interference; the magnetization weighting factor determines whether the magnetization ability of the Gaussian splash particle is enhanced or weakened; and the scaling vector reflects the amount of magnetic material contained in the Gaussian splash particle—the larger the size, the stronger the magnetic moment. Therefore, after selecting the magnetic material to fill the design domain, the corresponding mapping relationship can be determined, and the equivalent magnetic moment of each Gaussian splash particle can be analyzed using this mapping relationship, the magnetization weighting factor of each Gaussian splash particle, the intrinsic magnetization of the magnetic material, and the scaling vector.

[0091] After determining the equivalent magnetic moment of each Gaussian splash particle, a magnetic field strength calculation model can be constructed. In the process of constructing the magnetic field strength calculation model, the embodiments of this application first construct the covariance matrix of all Gaussian splash particles, use the covariance matrix of Gaussian splash particles to characterize the anisotropic distribution of local magnetization, and construct a magnetic field strength calculation model based on the differentiable Biot-Savart law to characterize the predicted magnetic field strength jointly generated by all Gaussian splash particles at each sampling point in the target magnetic field region. Specifically, the target magnetic field region is used as the reference domain for magnetic field calculation. A differentiable magnetostatic forward operator is constructed. The principle is as follows: combining the Gaussian function with the laws of electromagnetism, the contribution of the magnetic field strength induced by Gaussian splash particles at a sampling point within the target magnetic field region can be calculated using geometric and physical operators. The geometric operator (i.e., the Gaussian function) serves as the shape representation of the physical operator, and the physical operator (i.e., the magnetic dipole operator) serves as the magnetic dipole field model, following the far-field approximation of the Biot-Savart law, defining the attenuation characteristics of the magnetic field strength with distance and its directional distribution in space. Therefore, the magnetic field strength within the target magnetic field region can be calculated based on the center position, volume, and magnetization of each Gaussian splash particle. In the formula of the constructed magnetic field strength calculation model, the influence of the simulated Gaussian splash particle distribution on the predicted magnetic field strength is determined by calculating the relative distance and orientation between each sampling point and each Gaussian splash particle in the target magnetic field region. This indicates that the predicted magnetic field strength decreases with increasing distance. This term is the magnetic dipole model, which treats each Gaussian splash particle as an anisotropic magnetic dipole unit and describes the directional distribution of the magnetic field strength in space. This reflects the spatial envelope, indicating that the magnetic field strength distribution can be finely adjusted according to the major and minor axis dimensions of the Gaussian splash particles.

[0092] Because the Gaussian function is continuously differentiable throughout space, it is possible to compute smooth gradients using the Adam optimizer, allowing Gaussian splash particles to smoothly merge when they are close together. When two Gaussian splash particles approach each other, the magnetic field strengths they generate will naturally superimpose to form a continuous entity, realizing the transformation from discrete Gaussian splash particles to a continuous topological structure model.

[0093] This application's embodiments introduce Gaussian splashing technology into the design of passive shimming units. Gaussian splashing technology can be used for continuous representation and rapid rendering of 3D scenes. It efficiently approximates complex field distributions through a set of Gaussian splashed particle elements with spatial position, scale, and weight parameters. Introducing this idea into the design of passive shimming modules can provide a continuous, differentiable, and locally expressive parameterization method for the distribution of magnetic materials within the passive shimming module, thus providing a new technical path for the design of high-precision and high-efficiency shimming modules.

[0094] S3. Select the magnetic material to be filled within the design domain of the passive shimming module. Input the initial parameter set and the actual magnetic field strength of all Gaussian splash particles into the Gaussian splash particle parameter set iterative optimization algorithm and participate in the first iteration optimization process. Based on the magnetization weight factor vector, scaling matrix, intrinsic magnetization of the magnetic material, and mapping relationship obtained in the previous iteration optimization process, determine the equivalent magnetic moment vector of all Gaussian splash particles. Input the equivalent magnetic moment vector, magnetization weight factor vector, center position vector, and rotation quaternion matrix into the magnetic field strength calculation model to obtain the predicted magnetic field strength of each sampling point in the target magnetic field region. Based on the predicted magnetic field strength, actual magnetic field strength, magnetization weight factor vector, and center position vector of each sampling point in the target magnetic field region, construct a multi-objective loss function. Update the parameter set obtained in the previous iteration optimization process based on the multi-objective loss function to obtain the parameter set obtained in the current iteration optimization process. Repeat the above iterative optimization process until the maximum number of iterations is reached to obtain the optimized parameter set.

[0095] In a specific embodiment, the expression for the multi-objective loss function is as follows:

[0096] ;

[0097] in, Represents a multi-objective loss function. This represents the magnetic field deviation loss function. Represents the sparsity loss function. Represents the spatial overlap loss function; and These are the weight coefficients for the sparse loss function and the spatial overlap loss function, respectively.

[0098] The expression for the magnetic field deviation loss function is as follows:

[0099] ;

[0100] in, Indicates the location of the sampling point in the target magnetic field region. The actual magnetic field strength at the location, where N represents the total number of Gaussian splash particles. Represents the L2 norm;

[0101] The expression for the sparsity loss function is as follows:

[0102] ;

[0103] in, Indicates L1 regularization;

[0104] The expression for the spatial overlap loss function is as follows:

[0105] ;

[0106] Where i and j represent the i-th Gaussian splash particle and the j-th Gaussian splash particle, respectively. Let be the distance between the center positions of the i-th Gaussian splash particle and the j-th Gaussian splash particle. For minimum safe distance, This indicates taking the maximum of the two values;

[0107] In the current iteration of optimization, the goal is to minimize the multi-objective loss function. The Gaussian splash particles are moved, split, or aggregated using an adaptive moment estimation algorithm to update the parameter set obtained in the previous iteration.

[0108] Specifically, the embodiments of this application propose an iterative optimization algorithm for Gaussian splash particle parameter set. In this algorithm, a multi-objective loss function containing the true value of magnetic field strength is constructed, and the parameter set of each Gaussian splash particle is iteratively updated through the backpropagation algorithm, so that the Gaussian splash particles can adaptively cluster and grow in the design domain space to form a topological structure model of the passive shimming module.

[0109] The specific process of the iterative optimization algorithm for the Gaussian splash particle parameter set in the embodiments of this application is to use the gradient descent algorithm to perform variational evolution on the explicitly parameterized Gaussian model: its input is the initial parameter set of all Gaussian splash particles, and the target compensation field requirement (i.e., the actual magnetic field strength) determined by the magnetic environment; its output is the optimized parameter set of all Gaussian particles. This optimized parameter set not only defines the magnetization contribution weight of each Gaussian splash particle at the physical level, but also constructs the topological geometry of the passive shimming module through its anisotropic spatial occupancy characteristics (the covariance matrix defined by the center position vector, rotation quaternion matrix, and scaling matrix). Therefore, the embodiments of this application construct a multi-objective loss function to drive the Gaussian splash particles to adaptively cluster, grow under constraints, and prune in the design domain space. This multi-objective loss function consists of three coupled parts: a magnetic field deviation loss function... To ensure consistency between the compensation field and the target field, it is evaluated by calculating the difference between the predicted and actual magnetic field strengths within the target magnetic field region. Specifically, it uses a mean squared error loss function for calculation. This forces the magnetic field generated by Gaussian splashed particles to counteract the original inhomogeneous magnetic field, driving the Gaussian splashed particles to move towards the region with the greatest magnetic field distortion and increasing their weight; sparsity loss function. It utilizes L1 regularization to compress the magnetization weighting factor of Gaussian splashed particles, and through topological pruning of the magnetic material distribution, achieves optimal results with minimal magnetic material, forming a clear blocky topology rather than fine powder particles; spatial overlap loss function. The repulsive field constraint is established based on the Euclidean distance between Gaussian splash particles. When the distance between the Gaussian splash particles is less than... hour, The sharp increase ensures sufficient gaps between the magnetic compensation blocks in the final passive shimming module, guaranteeing that the topology of the magnetic compensation blocks meets the minimum processing size requirements for industrial applications, facilitating processing and installation.

[0110] In the embodiments of this application, the Adaptive Moment Estimation (Adam) algorithm is used as the core engine for parameter set updating. In the Adaptive Moment Estimation (Adam) algorithm, the expression for the total gradient of the multi-objective loss function is:

[0111] ;

[0112] in, This represents the total gradient of the multi-objective loss function. The gradient of the magnetic field deviation loss function is represented. The gradient of the sparse loss function is represented. This represents the gradient of the spatial overlap loss function.

[0113] By backpropagating the multi-objective loss function, the total gradient is obtained synchronously. Based on the first and second moment vectors of the total gradient, the learning rate of each parameter in the parameter set is adaptively adjusted to achieve global optimization under complex magnetic field constraints. Adjusting the learning rate enables the capture of Gaussian splash particles in complex magnetic field distortion regions and fine-tuning in smooth regions. Simultaneously, the three-dimensional coordinates of the Gaussian splash particles are updated according to the repulsion gradient, allowing the Gaussian particle ensemble to adaptively split (increase), prune, and aggregate in space. A schematic diagram of the splitting (increase), pruning, and aggregation growth of Gaussian particles is shown below. Figure 5 As shown.

[0114] When the number of iterations exceeds a preset threshold (e.g., 1000 generations), the Gaussian splash particle parameter set iterative optimization algorithm will initiate a dynamic pruning mechanism. It automatically detects the absolute value of the magnetization weight factor for each Gaussian splash particle; if... If the contribution of the Gaussian splash particle to the improvement of the magnetic field is determined to be lower than the physical manufacturing threshold, the magnetization weight factor of the Gaussian splash particle is forcibly set to zero and removed from the calculation chain.

[0115] As the iterative optimization process proceeds, the originally discrete Gaussian splash particles, driven by the Adam algorithm, gradually split, prune, and aggregate in the design domain space according to the total gradient, gradually evolving into a topological structure model of a passive shimming module with magnetic field compensation characteristics.

[0116] S4, based on the optimized parameter set and the magnetic material to be filled, is materialized to create the corresponding passive shimming module.

[0117] In a specific embodiment, step S4 specifically includes:

[0118] Within the design domain, a spatial voxel mesh is created. The magnetization weighting factors of each Gaussian splash particle in the optimized parameter set are linearly superimposed with the spatial occupancy to obtain the location of the sampling point in the target magnetic field region. The density field at that location is shown in the following equation:

[0119] ;

[0120] Among all Gaussian splash particles, Gaussian splash particles with a density field higher than a preset density threshold are searched and transformed into the topological structure model corresponding to the passive shimming module. Based on the topological structure model corresponding to the passive shimming module, the passive shimming module is fabricated using additive manufacturing process.

[0121] Specifically, in the embodiments of this application, the optimized parameter set is materialized to generate a three-dimensional solid geometric model of a manufacturable passive shimming module. A spatial voxel mesh is divided within the design domain, and the optimized magnetization weights of each Gaussian splash particle are linearly superimposed with the spatial occupancy to generate a continuous density field characterizing the probability of material distribution.

[0122] In one example, by introducing 15% of the maximum density as a preset density threshold, the continuous density field is... Binarization is performed: regions with a density higher than a preset density threshold are identified as solid magnetic materials, while regions with a density lower than the preset density threshold are considered air. This process extracts isosurfaces with well-defined geometric boundaries, thus transforming a mathematical model into a manufacturable entity. Figure 6 As shown.

[0123] Finally, the actual machining file conversion of the topology model of the passive shimming module was completed. The model data extracted from the isosurface was converted to standard STL format using an isosurface algorithm. Then, G-code was generated using slicing software to control 3D printing, or converted to STEP format to generate toolpaths for cutting the magnetic material. Based on the topology model, 3D printing technology was used to process the iron powder and polymer mixture into shape, ultimately obtaining the solidified passive shimming module.

[0124] The magnetic field strength within the target magnetic field region was measured without a passive shimming module to determine the initial distortion. The magnetic field strength within the target magnetic field region was then measured with and without a passive shimming module. The results were compared for reference. Figure 7 ,through Figure 7 Comparative verification shows that the compensation field generated by the passive shimming module effectively cancels out the higher-order non-uniform components of the original magnetic field strength, resulting in a significant reduction in the magnetic field variance within the target magnetic field region. This verifies the effectiveness of the embodiments of this application in achieving high-precision shimming. Simultaneously, a solid structure is manufactured based on the fixed geometric parameters.

[0125] Therefore, this invention provides a design method for a passive shimming module for nuclear magnetic resonance (NMR) based on Gaussian splashing. By synergistically optimizing the sparsity constraints of material distribution and the magnetic field deviation threshold of the target region, electromagnetic strays in complex topological environments can be accurately eliminated. This not only provides key technical support for the customized design of high-precision passive shimming modules, but also provides a path for real-time magnetic field compensation in complex unshielded environments for open and mobile NMR devices. The application of this invention significantly broadens the application scope and technical depth of Gaussian splashing technology in fields such as precision instrument-aided design, complex electromagnetic field fitting, and real-time dynamic control.

[0126] Further reference Figure 8As an implementation of the methods shown in the above figures, this application provides an embodiment of a design device for a passive shimming module of nuclear magnetic resonance based on Gaussian splashing. This device embodiment is similar to... Figure 1 Corresponding to the method embodiments shown, this device can be specifically applied to various electronic devices.

[0127] This application provides a design device for a passive shimming module for nuclear magnetic resonance based on Gaussian splashing, comprising:

[0128] Initialization module 1 is configured to randomly generate several Gaussian splash particles within the design domain of the passive shimming module, and construct an initial parameter set for all Gaussian splash particles. The parameter set includes a magnetization weight factor vector, a center position vector, a rotation quaternion matrix, and a scaling matrix.

[0129] Model building module 2 is configured to construct the mapping relationship between the equivalent magnetic moment of each Gaussian splash particle and the magnetization weight factor, the intrinsic magnetization intensity and scaling vector of the magnetic material, for each magnetic material filled in the design domain of the passive shimming module; and to construct a magnetic field strength calculation model based on the differentiable form of the Biot-Savart law.

[0130] Parameter optimization module 3 is configured to select the magnetic material to be filled within the design domain of the passive shimming module. It inputs the initial parameter set and true magnetic field strength of all Gaussian splash particles into the Gaussian splash particle parameter set iterative optimization algorithm and participates in the first iteration. Based on the magnetization weight factor vector, scaling matrix, intrinsic magnetization of the magnetic material, and mapping relationship obtained in the previous iteration, it determines the equivalent magnetic moment vector of all Gaussian splash particles. The equivalent magnetic moment vector, magnetization weight factor vector, center position vector, and rotation quaternion matrix are input into the magnetic field strength calculation model to obtain the predicted magnetic field strength of each sampling point in the target magnetic field region. A multi-objective loss function is constructed based on the predicted magnetic field strength, true magnetic field strength, magnetization weight factor vector, and center position vector of each sampling point in the target magnetic field region. The parameter set obtained in the previous iteration is updated based on the multi-objective loss function to obtain the parameter set obtained in the current iteration. This iterative optimization process is repeated until the maximum number of iterations is reached, resulting in the optimized parameter set.

[0131] The solidification module 4 is configured to perform solidification processing based on the optimized parameter set and the magnetic material to be filled, and to create the corresponding passive shimming module.

[0132] Figure 9 This is a schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present invention. For example... Figure 9As shown, the electronic device in this embodiment includes a processor 901 and a memory 902; wherein the memory 902 is used to store computer execution instructions; and the processor 901 is used to execute the computer execution instructions stored in the memory to implement the various steps performed by the electronic device in the above embodiment. For details, please refer to the relevant descriptions in the foregoing method embodiments.

[0133] Alternatively, the memory 902 can be either standalone or integrated with the processor 901.

[0134] When the memory 902 is set up independently, the electronic device also includes a bus 903 for connecting the memory 902 and the processor 901.

[0135] This invention also provides a computer storage medium storing computer execution instructions, which, when executed by processor 901, implement the above method.

[0136] This invention also provides a computer program product, including a computer program that, when executed by a processor 901, implements the above-described method.

[0137] In the embodiments provided by this invention, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or modules, and may be electrical, mechanical, or other forms.

[0138] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0139] Furthermore, the functional modules in the various embodiments of this invention can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit formed by the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0140] The integrated modules described above, implemented as software functional modules, can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor 901 to execute some steps of the methods of the various embodiments of this application.

[0141] It should be understood that the processor 901 described above can be a Central Processing Unit (CPU), or a Graphics Processing Unit (GPU), Digital Signal Processor (DSP), Application Specific Integrated Circuit (ASIC), etc., specifically designed for handling high-concurrency computing tasks. The general-purpose processor can be a microprocessor, or the processor 901 can be any conventional processor 901. The steps of the method disclosed in this invention can be directly manifested as execution by the hardware processor 901, or execution by a combination of hardware and software modules within the processor 901.

[0142] The memory 902 may include high-speed RAM memory, and may also include non-volatile memory NVM, such as at least one disk storage device, and may also be a USB flash drive, portable hard drive, read-only memory, disk or optical disc, etc.

[0143] Bus 903 can be an Industry Standard Architecture (ISA), a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Bus 903 can be divided into address bus, data bus, control bus, etc. For ease of illustration, the bus 903 in the accompanying drawings of this application is not limited to only one bus 903 or one type of bus 903.

[0144] The aforementioned storage medium can be implemented from any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium accessible to general-purpose or special-purpose computers.

[0145] An exemplary storage medium is coupled to a processor 901, enabling the processor 901 to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor 901. The processor 901 and the storage medium can reside in an application-specific integrated circuit (ASIC). Alternatively, the processor 901 and the storage medium can exist as discrete components in an electronic device or a host device.

[0146] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0147] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A design method for a passive shimming module for nuclear magnetic resonance based on Gaussian splashing, characterized in that, Includes the following steps: Within the design domain of the passive shimming module, several Gaussian splash particles are randomly initialized and generated, and an initial parameter set for all Gaussian splash particles is constructed. The parameter set includes a magnetization weight factor vector, a center position vector, a rotation quaternion matrix, and a scaling matrix. For each magnetic material filling the design domain of the passive shimming module, a mapping relationship is constructed between the equivalent magnetic moment of each Gaussian splash particle and the magnetization weighting factor, the intrinsic magnetization intensity of the magnetic material, and the scaling vector. The construction process of the mapping relationship is as follows: In the design domain, the relative displacement of each sampling point in the target magnetic field region with respect to the center position of each Gaussian splash particle is calculated, and the spatial proportion is calculated by combining the scaling vector of each Gaussian splash particle, as shown in the following formula: ； in, This indicates the location of a sampling point of one of the Gaussian splash particles in the target magnetic field region. The space ratio of the location This indicates the location of any sampling point within the target magnetic field region. and These represent the locations of sampling points within the target magnetic field region. The relative positions of the center of one of the Gaussian splash particles on the x, y, and z axes. , and These represent the scaling of one Gaussian splash particle along the x, y, and z axes, respectively. The magnetization contributions of N Gaussian splashed particles are linearly superimposed within the design domain to construct the magnetization intensity of one sampling point in the target magnetic field region, as shown in the following equation: ； in, Indicates the location of the sampling point in the target magnetic field region. magnetization intensity, represents the peak magnetization of the i-th Gaussian splash particle, and N represents the total number of Gaussian splash particles; By utilizing the analytical properties of the Gaussian function, the equivalent magnetic moment of each Gaussian splash particle is discretized by integrating the continuously distributed magnetization over the volume, as shown in the following equation: ； in, Let V represent the equivalent magnetic moment of the i-th Gaussian splash particle, and let V represent the volume. This represents the magnetization intensity of the i-th Gaussian splash particle in the target magnetic field region; The peak magnetization of the i-th Gaussian splash particle is decomposed into the product of the magnetization weighting factor of the i-th Gaussian splash particle and the intrinsic magnetization of the material. The mapping relationship is then defined as follows: ； in, This represents the magnetization weighting factor of the i-th Gaussian splash particle. The intrinsic magnetization associated with magnetic materials is represented; a magnetic field strength calculation model is constructed based on the differentiable form of the Biot-Savart law; Select the magnetic material to be filled within the design domain of the passive shimming module. Input the initial parameter set and the actual magnetic field strength of all Gaussian splash particles into the Gaussian splash particle parameter set iterative optimization algorithm and participate in the first iteration optimization process. Based on the magnetization weight factor vector, scaling matrix, intrinsic magnetization of the magnetic material, and the mapping relationship obtained in the previous iteration optimization process, determine the equivalent magnetic moment vector of all Gaussian splash particles. Input the equivalent magnetic moment vector, magnetization weight factor vector, center position vector, and rotation quaternion matrix into the magnetic field strength calculation model to obtain the predicted magnetic field strength of each sampling point in the target magnetic field region. Construct a multi-objective loss function based on the predicted magnetic field strength, actual magnetic field strength, magnetization weight factor vector, and center position vector of each sampling point in the target magnetic field region. Update the parameter set obtained in the previous iteration optimization process based on the multi-objective loss function to obtain the parameter set obtained in the current iteration optimization process. Repeat the above iterative optimization process until the maximum number of iterations is reached to obtain the optimized parameter set. Based on the optimized parameter set and the magnetic material to be filled, a corresponding passive shimming module is fabricated.

2. The design method for a passive shimming module of nuclear magnetic resonance based on Gaussian splashing according to claim 1, characterized in that, The rotation quaternion matrix is ​​composed of the rotation quaternions of all Gaussian splash particles; the scaling matrix is ​​composed of the scaling vectors of all Gaussian splash particles, where each scaling vector represents the scaling of a single Gaussian splash particle along the x, y, and z axes; the magnetization weight factor vector is composed of the magnetization weight factors of all Gaussian splash particles; and the center position vector is composed of the center positions of all Gaussian splash particles.

3. The design method for a passive shimming module of nuclear magnetic resonance based on Gaussian splashing according to claim 2, characterized in that, The magnetic field strength calculation model is as follows: ； in, This indicates the location of all Gaussian splashed particles in the target magnetic field region. The predicted magnetic field strength at that location This represents the equivalent magnetic moment vector formed by the equivalent magnetic moments of all Gaussian splash particles. This indicates the location of the sampling point in the index magnetic field region, representing the center position of all Gaussian splash particles. The displacement vector, Represents the magnetization weight factor vector. Represents the center position vector. The covariance matrix of all Gaussian splash particles is expressed as follows: , This represents the rotation matrix obtained by mapping the rotation quaternion matrix using Rodrigues transform logic. Represents the scaling matrix. This represents the transpose of a matrix.

4. The design method for a passive shimming module of nuclear magnetic resonance based on Gaussian splashing according to claim 3, characterized in that, The expression for the multi-objective loss function is as follows: ； in, Represents a multi-objective loss function. This represents the magnetic field deviation loss function. Represents the sparsity loss function. Represents the spatial overlap loss function; and These are the weight coefficients for the sparse loss function and the spatial overlap loss function, respectively. The expression for the magnetic field deviation loss function is as follows: ； in, Indicates the location of the sampling point in the target magnetic field region. The actual magnetic field strength at the location, where N represents the total number of Gaussian splash particles. Represents the L2 norm; The expression for the sparsity loss function is as follows: ； in, Indicates L1 regularization; The expression for the spatial overlap loss function is as follows: ； Where i and j represent the i-th Gaussian splash particle and the j-th Gaussian splash particle, respectively. Let be the distance between the center positions of the i-th Gaussian splash particle and the j-th Gaussian splash particle. For minimum safe distance, This indicates taking the maximum of the two values; In the current iteration of optimization, the goal is to minimize the multi-objective loss function. An adaptive moment estimation algorithm is used to move, split, or aggregate the Gaussian splash particles to update the parameter set obtained in the previous iteration of optimization.

5. The design method for a passive shimming module of nuclear magnetic resonance based on Gaussian splashing according to claim 1, characterized in that, Based on the optimized parameter set and the magnetic material to be filled, a corresponding passive shimming module is fabricated, specifically including: Within the design domain, a spatial voxel grid is divided. The magnetization weighting factors of each Gaussian splash particle in the optimized parameter set are linearly superimposed with the spatial occupancy to obtain the positions of sampling points in the target magnetic field region. The density field at that location is shown in the following equation: ； Among all Gaussian splash particles, Gaussian splash particles with a density field higher than a preset density threshold are searched and transformed into the topological structure model corresponding to the passive shimming module. Based on the topological structure model corresponding to the passive shimming module, the passive shimming module is fabricated by additive manufacturing process.

6. A design device for a passive shimming module of nuclear magnetic resonance based on Gaussian splashing, characterized in that, include: The initialization module is configured to randomly generate several Gaussian splash particles within the design domain of the passive shimming module, and construct an initial parameter set for all Gaussian splash particles, the parameter set including a magnetization weight factor vector, a center position vector, a rotation quaternion matrix, and a scaling matrix. The model building module is configured to construct a mapping relationship between the equivalent magnetic moment of each Gaussian splash particle and the magnetization weighting factor, the intrinsic magnetization intensity of the magnetic material, and the scaling vector for each magnetic material filling the design domain of the passive shimming module. The construction process of the mapping relationship is as follows: In the design domain, the relative displacement of each sampling point in the target magnetic field region with respect to the center position of each Gaussian splash particle is calculated, and the spatial proportion is calculated by combining the scaling vector of each Gaussian splash particle, as shown in the following formula: ； in, This indicates the location of a sampling point of one of the Gaussian splash particles in the target magnetic field region. The space ratio of the location This indicates the location of any sampling point within the target magnetic field region. and These represent the locations of sampling points within the target magnetic field region. The relative positions of the center of one of the Gaussian splash particles on the x, y, and z axes. , and These represent the scaling of one Gaussian splash particle along the x, y, and z axes, respectively. The magnetization contributions of N Gaussian splashed particles are linearly superimposed within the design domain to construct the magnetization intensity of one sampling point in the target magnetic field region, as shown in the following equation: ； in, Indicates the location of the sampling point in the target magnetic field region. magnetization intensity, represents the peak magnetization of the i-th Gaussian splash particle, and N represents the total number of Gaussian splash particles; By utilizing the analytical properties of the Gaussian function, the equivalent magnetic moment of each Gaussian splash particle is discretized by integrating the continuously distributed magnetization over the volume, as shown in the following equation: ； in, Let V represent the equivalent magnetic moment of the i-th Gaussian splash particle, and let V represent the volume. This represents the magnetization intensity of the i-th Gaussian splash particle in the target magnetic field region; The peak magnetization of the i-th Gaussian splash particle is decomposed into the product of the magnetization weighting factor of the i-th Gaussian splash particle and the intrinsic magnetization of the material. The mapping relationship is then defined as follows: ； in, This represents the magnetization weighting factor of the i-th Gaussian splash particle. The intrinsic magnetization associated with magnetic materials is represented; a magnetic field strength calculation model is constructed based on the differentiable form of the Biot-Savart law; The parameter optimization module is configured to select the magnetic material to be filled within the design domain of the passive shimming module. It inputs the initial parameter set and actual magnetic field strength of all Gaussian splash particles into the Gaussian splash particle parameter set iterative optimization algorithm and participates in the first iteration. Based on the magnetization weight factor vector, scaling matrix, intrinsic magnetization of the magnetic material, and the mapping relationship obtained in the previous iteration, it determines the equivalent magnetic moment vector of all Gaussian splash particles. The equivalent magnetic moment vector, magnetization weight factor vector, center position vector, and rotation quaternion matrix are input into the magnetic field strength calculation model to obtain the predicted magnetic field strength of each sampling point in the target magnetic field region. A multi-objective loss function is constructed based on the predicted magnetic field strength, actual magnetic field strength, magnetization weight factor vector, and center position vector of each sampling point in the target magnetic field region. The parameter set obtained in the previous iteration is updated based on the multi-objective loss function to obtain the parameter set obtained in the current iteration. This iterative optimization process is repeated until the maximum number of iterations is reached, resulting in the optimized parameter set. The solidification module is configured to perform solidification processing based on the optimized parameter set and the magnetic material to be filled, thereby creating a corresponding passive shimming module.

7. An electronic device, comprising: One or more processors; Storage device for storing one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1-5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-5.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-5.

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