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

Abstract

This invention discloses a design method and apparatus for nuclear magnetic resonance shimming coils based on Gaussian splashing, belonging to the field of precision electromagnetic field optimization technology. The method includes: inputting an initial parameter set of all Gaussian particles and the target magnetic field strength at each sampling point on the current-carrying surface into an iterative optimization algorithm for the Gaussian particle parameter set; obtaining the predicted magnetic field strength at each sampling point on the current-carrying surface based on the parameter set obtained in the previous iteration using a magnetic field strength calculation model; constructing a multi-objective loss function based on the deviation between the predicted and target magnetic field strengths, the stream function weighting factor vector, and the center position vector; updating the parameter set obtained in the previous iteration to obtain the parameter set for the current iteration; repeating the above iterative optimization process until the maximum number of iterations is reached; outputting the optimized parameter set and fabricating the resulting shimming coil. This invention solves the problem of low accuracy and efficiency of current shimming coils when generating magnetic fields with complex shapes.

Description

Technical Field

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

[0002] In nuclear magnetic resonance (NMR) spectrometers and imagers, the spatial linearity and homogeneity of the main magnetic field determine the signal-to-noise ratio, spatial resolution, and spectral quality of the detected signal. However, due to inherent design flaws and manufacturing tolerances, the initial magnetic field often exhibits distortion; further fine calibration is typically required after static passive shimming. Therefore, designing gradient coils and shimming coils to precisely control the input current and generate a customized magnetic field within the target detection region for spatial encoding and magnetic field compensation is crucial for achieving the high-uniformity magnetic field required for complex NMR detection.

[0003] Existing design methods for gradient coils and shim coils are mainly based on the target field method, spherical harmonic function expansion method, or topology optimization methods using regular grids. These traditional methods typically obtain a continuous surface current density distribution by solving the inverse electromagnetic field problem on a specific symmetrical structure, and then use discretization techniques such as stream functions to transform it into an actual coil layout. In 2021, patent CN110703170B disclosed the design of a breast MRI coil using the finite element method; in the same year, patent CN 113671431 B established a model of the magnetic interaction energy and energy storage between the shim coil and the original coil based on a finite element grid, and used this as an optimization objective to achieve coil decoupling design. In 2022, patent CN 115718275 B addressed the structural design of a gradient coil with an off-center conical head and the winding solution based on the finite element nodal stream function. In 2024, patent CN114741881B disclosed an equivalent magnetic dipole coil design method considering the image current effect of anti-eddy current plates. This method improves magnetic field linearity and effectively reduces magnetic resonance image distortion by pre-compensating for the anti-eddy current plate as a magnetic field source. In 2022, a paper titled "CoilGen: Open-source MR coil layout generator" demonstrated the ability to quickly generate high-precision, low-discretion-error MRI shimming coil layouts based on the boundary element method. Also in 2022, a paper titled "A SphericalHarmonics Decomposition Method (SHDM) for Irregular Matrix Coils Design" utilized a multi-objective matrix coil optimization method based on spherical harmonic function decomposition. This method achieves magnetic field compensation performance similar to the ordinary spherical harmonic method with lower power consumption and current, significantly improving the shimming efficiency of compact and conventional MRI systems. However, these methods require finite element meshing of the current surface, which limits their design freedom, local distortion magnetic field compensation capabilities, and complex structural compensation. Although the 2018 paper "Design of small-scale gradientcoils in MRI by using the topology optimization method" and the 2022 paper "Exploring Beyond the Helmholtz Coils for Uniform Magnetic Field Generation With Topology Optimization" utilize topology optimization to improve coil performance in the target region, traditional topology optimization methods still rely on high-frequency finite element analysis.In high-dimensional parameter spaces, traditional coil design methods suffer from technical bottlenecks such as exponentially increasing computational complexity, slow convergence, gradient vanishing, and susceptibility to local optima, making it difficult to meet the demands for real-time, efficient, and precise shimming. Furthermore, due to inherent spatial discretization errors, achieving high spatial resolution magnetic field compensation is challenging. However, most of these methods rely on finite element meshes, current basis functions, equivalent magnetic dipoles, or pre-defined coil structures for modeling and optimization. Their design variables are typically related to discrete mesh nodes, coil windings, or specific structural parameters, making it difficult to achieve a continuously differentiable representation of the shimming coil topology. Especially when dealing with highly irregular and complex three-dimensional curved anatomical sites such as the human brain, breast, and knee joint, traditional coil design methods are severely limited in terms of spatial wiring freedom and conformity preservation, still facing technical bottlenecks in computational accuracy and efficiency. There is an urgent need to introduce a novel three-dimensional field representation and optimization algorithm that combines high spatial freedom with high computational efficiency to achieve a breakthrough in the comprehensive design of complex coils. Summary of the Invention

[0004] This application proposes a design method and apparatus for a shimming coil based on Gaussian splashing in nuclear magnetic resonance (NMR), aiming to overcome the shortcomings of existing coil design methods and solve the problems of low accuracy and efficiency of shimming coils in current NMR detection instruments when generating complex magnetic fields.

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

[0006] The current-carrying surface of the shimming coil is initialized within the design domain, and several Gaussian ions are randomly generated on the current-carrying surface to obtain the initial parameter set of all Gaussian particles. The parameter set includes the stream function weight factor vector, the center position vector, the rotation quaternion matrix, and the scaling matrix.

[0007] A magnetic field strength calculation model is constructed based on the parameter set of all Gaussian particles and the differentiable form of the Biot-Savart law;

[0008] The initial parameter set of all Gaussian particles is used as the parameter set obtained in the first iteration. This parameter set is then combined with the target magnetic field strength at each sampling point on the current-carrying surface and input into the Gaussian particle parameter set iterative optimization algorithm. In the current iteration, the predicted magnetic field strength at each sampling point on the current-carrying surface is obtained using the magnetic field strength calculation model based on the parameter set obtained in the previous iteration. A multi-objective loss function is constructed based on the deviation between the predicted and target magnetic field strengths, the stream function weighting factor vector, and the center position vector. This multi-objective loss function is then used to update 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, outputting the optimized parameter set and its corresponding current density distribution.

[0009] Based on the current density distribution corresponding to the optimized parameter set, the conductor winding structure is generated by the contour discretization method and then materialized to obtain the corresponding uniform field coil.

[0010] Preferably, the rotation quaternion matrix is ​​composed of the rotation quaternions of all Gaussian particles; the scaling matrix is ​​composed of the scaling vectors of all Gaussian particles; the center position vector is composed of the center positions of all Gaussian particles, with the center position of each Gaussian particle constrained on the flow-carrying surface; the stream function weighting factor vector is composed of the stream function weighting factors of all Gaussian particles; and the parameters of the i-th Gaussian particle on the flow-carrying surface are expressed as... ,in This represents the center position of the i-th Gaussian particle. This represents the stream function weighting factor for the i-th Gaussian particle. Let i represent the rotation quaternion of the i-th Gaussian particle. Let represent the scaling vector of the i-th Gaussian particle. The covariance matrix of the i-th Gaussian particle is defined using its scaling vector and rotation matrix. As shown in the following formula: ; This represents the rotation quaternion of the i-th Gaussian particle using Rodrigues transform logic. The rotation matrix obtained by mapping, T represents the transpose of the matrix, i = 1, 2, ..., N, and N represents the total number of Gaussian particles.

[0011] As a preferred option, the process of constructing the magnetic field strength calculation model is as follows:

[0012] Within the design domain, the relative displacement of any sampling point on the flow-carrying surface with respect to the center position of each Gaussian particle is calculated. Combined with the covariance matrix of each Gaussian particle, the spatial proportion of each Gaussian particle at any sampling point on the flow-carrying surface is calculated, as shown in the following equation:

[0013] ;

[0014] in, This indicates the position of one of the sampling points on the current-carrying surface. This represents the position of the i-th Gaussian particle at one of the sampling points on the flow-carrying surface. The space ratio of the location;

[0015] The total stream function at any sampling point on the flow-carrying surface is represented as the superposition of the stream function components of N Gaussian particles, as shown in the following equation:

[0016] ;

[0017] in, Indicates the position of one of the sampling points on the current-carrying surface. The total flow function at that point, This represents the position of one of the sampling points on the current-carrying surface of the i-th Gaussian particle. The stream function component at that location;

[0018] Since the equivalent current density generated by each Gaussian particle on the current-carrying surface is determined by the curl of the stream function component corresponding to each Gaussian particle, the total current density at any sampling point on the current-carrying surface is obtained by superimposing the equivalent current densities generated by all Gaussian particles at the corresponding sampling point, as shown in the following equation:

[0019] ;

[0020] Where n is the unit normal vector of the current-carrying surface. The surface gradient of the current-carrying surface. Indicates the position of one of the sampling points on the current-carrying surface. Total current density at the location, This represents the position of one of the sampling points on the current-carrying surface of the i-th Gaussian particle. The equivalent current density generated at the location;

[0021] Substituting the above equation into the Biot-Savart law formula, we obtain the magnetic field strength calculation model, as shown in the following equation:

[0022] ;

[0023] in, Represents the current-carrying surface. Represents the first on the target magnetic field region The location of each observation point Represents the first on the target magnetic field region Location of each observation point The predicted magnetic field strength at that location Represents the permeability of free space. Let r be the distance from one of the sampling points on the current-carrying surface to the first point on the target magnetic field region. Location of each observation point The vector.

[0024] As a preferred option, the expression for the multi-objective loss function is as follows:

[0025] ;

[0026] in, This indicates the loss due to magnetic field deviation. Indicates power loss. Indicates smoothness loss. and These are the regularization power weights and the smoothing weights, respectively. Represents a multi-objective loss function. This represents the set of parameters for all Gaussian particles. Indicates taking When it is the minimum value ;

[0027] The expression for the magnetic field deviation loss is:

[0028] ;

[0029] in, Represents the first on the target magnetic field region Location of each observation point The target magnetic field strength at that location, Describing the L2 norm, This represents the total number of observation points in the target magnetic field region;

[0030] The expression for power loss is:

[0031] ;

[0032] Where σ is the conductivity of the material of the shimming coil. The thickness of the conductor layer of the shimming coil, and These represent the positions of the i-th Gaussian particle and the k-th Gaussian particle at one of the sampling points on the flow-carrying surface, respectively. The space ratio of the location and Let represent the stream function weighting factors of the i-th Gaussian particle and the k-th Gaussian particle, respectively, where k = 1, 2, ..., N;

[0033] The expression for smoothness loss is:

[0034] ;

[0035] in, Let N(i) be the spatial neighborhood set of the i-th Gaussian particle, and g∈N(i) represent the g-th Gaussian particle in the spatial neighborhood set of the i-th Gaussian particle. The spatial similarity weight between the i-th Gaussian particle and the g-th Gaussian particle in the spatial neighborhood set is defined as: , and Let be the center positions of the i-th Gaussian particle and the g-th Gaussian particle in the spatial neighborhood set, respectively. This is the neighborhood scale parameter.

[0036] As a preferred option, the Gaussian particle parameter set iterative optimization algorithm also includes:

[0037] When the number of iterations exceeds the threshold, it is determined whether the magnitude of the stream function weight factor of each Gaussian particle is less than the preset lower limit threshold. If so, a pruning operation is performed to force the stream function weight factor of the Gaussian particle to zero; otherwise, the pruning operation is not performed.

[0038] Determine whether the magnitude of the stream function weight factor of each Gaussian particle is greater than or equal to a preset upper limit threshold. If so, perform a split operation on the Gaussian particle as the parent Gaussian particle to generate two child Gaussian particles, which inherit the parameters of the parent Gaussian particle. Otherwise, do not perform a split operation on the Gaussian particle.

[0039] In the current iteration optimization process, with the goal of minimizing the multi-objective loss function, the parameter set obtained in the previous iteration is updated by using the adaptive moment estimation algorithm, and the Gaussian particle splitting or pruning operation is performed to complete the update of the parameter set obtained in the previous iteration.

[0040] As a preferred embodiment, the process for generating the conductor winding structure is as follows:

[0041] By performing an area integral on the current density distribution corresponding to the optimized parameter set, a continuous stream function on the current-carrying surface is obtained;

[0042] The current increment step size is determined based on the preset total number of coil turns, as shown in the following formula:

[0043] ;

[0044] in, and Let represent the maximum and minimum values ​​of the continuous stream function on the current-carrying surface, respectively. Indicates the total number of turns of the coil. Indicates the current increment step size;

[0045] Extract the continuous stream function on the current-carrying surface as follows: The contour lines serve as the center path of the nth turn of the conductor winding. The center paths of each turn of the conductor winding form a closed curve, and its winding direction is uniquely determined by the gradient direction of the continuous stream function.

[0046] By adjusting the center path of the wire winding in conjunction with the printed circuit manufacturing process, the wire winding structure is obtained.

[0047] Secondly, the present invention provides a design device for nuclear magnetic resonance shimming coils based on Gaussian splashing, comprising:

[0048] The initialization module is configured to initialize the current-carrying surface of the shimming coil within the design domain and randomly generate several Gaussian ions on the current-carrying surface to obtain the initial parameter set of all Gaussian particles. The parameter set includes the stream function weight factor vector, the center position vector, the rotation quaternion matrix, and the scaling matrix.

[0049] The model building module is configured to build a magnetic field strength calculation model based on the parameter set of all Gaussian particles and the differentiable form of the Biot-Savart law;

[0050] The iterative optimization module is configured to use the initial parameter set of all Gaussian particles as the parameter set obtained in the first iteration, and combine it with the target magnetic field strength of each sampling point in the current-carrying surface as input to the Gaussian particle parameter set iterative optimization algorithm. In the current iteration optimization process, the predicted magnetic field strength of each sampling point on the current-carrying surface is obtained through the magnetic field strength calculation model based on the parameter set obtained in the previous iteration. A multi-objective loss function is constructed based on the deviation between the predicted magnetic field strength and the target magnetic field strength, the stream function weight factor vector, and the center position vector. The parameter set obtained in the previous iteration is updated based on the multi-objective loss function to obtain the parameter set for the current iteration. The above iterative optimization process is repeated until the maximum number of iterations is reached, and the optimized parameter set and its corresponding current density distribution are output.

[0051] The solidification module is configured to generate the conductor winding structure using the contour discretization method based on the current density distribution corresponding to the optimized parameter set, and then perform solidification processing to produce the corresponding uniform field coil.

[0052] 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.

[0053] 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.

[0054] 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.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] (1) The design method of shimming coil based on Gaussian splashing mentioned in this invention uses anisotropic Gaussian particle stream functions for continuous parameterization on the current-carrying surface. Compared with traditional design methods based on regular meshes, finite element node stream functions, or pre-set winding structures, this invention can characterize the current-carrying topology using the weighting factor, center position, rotation quaternion, and scaling vector of the Gaussian particle stream function, thereby improving the spatial expression freedom of the coil structure. This method can adapt to the design requirements of shimming coils in complex irregular shapes, asymmetry, and limited installation spaces, which is conducive to forming a more flexible non-uniform current-carrying distribution and enhancing the structural adaptability and magnetic field compensation capability of shimming coils in compact nuclear magnetic resonance systems.

[0057] (2) The nuclear magnetic resonance shimming coil design method based on Gaussian splashing mentioned in this invention transforms the traditional discrete topology optimization into a differentiable continuous gradient descent process based on the Gaussian particle parameter set, thus completely eliminating the dependence on finite element mesh generation for the generation of the coil topology model. Furthermore, combined with the unique splitting and pruning dynamic control mechanism of Gaussian particles, the number and spatial distribution of particles can be adaptively adjusted according to the magnetic field error distribution and local topological complexity, thereby improving the expression accuracy of complex boundary regions and local compensation regions, and reducing invalid parameters in redundant regions. As a result, while improving the magnetic field uniformity of the target region, it can suppress local current abrupt changes, reduce redundant current distribution, and help reduce coil power consumption, inductance, and manufacturing complexity. Attached Figure Description

[0058] 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.

[0059] Figure 1 This is a schematic flowchart illustrating the design method of nuclear magnetic resonance shimming coil based on Gaussian splashing, as an embodiment of this application.

[0060] Figure 2 This is a schematic diagram illustrating the distribution characteristics of Gaussian particles within the current-carrying surface in the nuclear magnetic resonance shimming coil design method based on Gaussian splashing, as described in an embodiment of this application.

[0061] Figure 3 The overall design flowchart of the nuclear magnetic resonance shim coil design method based on Gaussian splashing is an embodiment of this application;

[0062] Figure 4 This is a schematic diagram illustrating the spatial relationship between the nuclear magnetic resonance magnet, the shimming coil, and the target magnetic field region in the nuclear magnetic resonance shimming coil design method based on Gaussian splashing, as described in an embodiment of this application.

[0063] Figure 5 This diagram illustrates the evolution of the Gaussian particle distribution into a discrete coil layout through iterative optimization in the Gaussian splash-based nuclear magnetic resonance shimming coil design method, as described in an embodiment of this application. Figure 5 (a) in the diagram is a schematic diagram of the initial distribution of Gaussian particles. Figure 5 (b) in the diagram shows the distribution of Gaussian particles after splitting and pruning operations. Figure 5 (c) in the diagram is a schematic diagram of the current density formed by the aggregation of Gaussian particles;

[0064] Figure 6 This is a schematic diagram of the cylindrical and semi-circular shimming coils in the Gaussian splash-based nuclear magnetic resonance shimming coil design method of this application, wherein... Figure 6 (a) in the diagram is a cylindrical shimming coil. Figure 6 (b) in the diagram represents a semi-circular shim coil;

[0065] Figure 7 This is a comparison diagram showing the intensity distribution of the initial magnetic field and the magnetic field after compensation by the cylindrical and semi-circular shimming coils in the nuclear magnetic resonance shimming coil design method based on Gaussian splashing, as described in an embodiment of this application; wherein, Figure 7 (a) in the figure shows the high-order compensation effect of the cylindrical shimming coil. The left figure shows the intensity distribution of the initial magnetic field, and the right figure shows the intensity distribution of the magnetic field after shimming compensation by the coil. Figure 7 (b) in the figure shows the higher-order compensation effect of the semi-circular shimming coil. The left figure shows the intensity distribution of the initial magnetic field, and the right figure shows the intensity distribution of the magnetic field after shimming compensation by the coil.

[0066] Figure 8 This is a schematic diagram of a nuclear magnetic resonance shimming coil design device based on Gaussian splashing, as an embodiment of this application.

[0067] 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

[0068] 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 only a part of the embodiments of this invention, and not all of them. 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.

[0069] Figure 1The present application illustrates an embodiment of a nuclear magnetic resonance shimming coil design method based on Gaussian splashing, comprising the following steps:

[0070] S1. Initialize the current-carrying surface of the shimming coil within the design domain and randomly generate several Gaussian ions on the current-carrying surface to obtain the initial parameter set of all Gaussian particles. The parameter set includes the stream function weight factor vector, the center position vector, the rotation quaternion matrix, and the scaling matrix.

[0071] In a specific embodiment, the rotation quaternion matrix is ​​composed of the rotation quaternions of all Gaussian particles; the scaling matrix is ​​composed of the scaling vectors of all Gaussian particles; the center position vector is composed of the center positions of all Gaussian particles, and the center position of each Gaussian particle is constrained on the flow-carrying surface; the stream function weighting factor vector is composed of the stream function weighting factors of all Gaussian particles; the parameters of the i-th Gaussian particle on the flow-carrying surface are expressed as... ,in This represents the center position of the i-th Gaussian particle. This represents the stream function weighting factor for the i-th Gaussian particle. Let i represent the rotation quaternion of the i-th Gaussian particle. Let represent the scaling vector of the i-th Gaussian particle. The covariance matrix of the i-th Gaussian particle is defined using its scaling vector and rotation matrix. As shown in the following formula: ; This represents the rotation quaternion of the i-th Gaussian particle using Rodrigues transform logic. The rotation matrix obtained by mapping, T represents the transpose of the matrix, i = 1, 2, ..., N, and N represents the total number of Gaussian particles.

[0072] For details, please refer to Figure 2 In this embodiment, a set of three-dimensional Gaussian particles is randomly initialized within the current-carrying surface of the shimming coil. This set of Gaussian particles includes several Gaussian particles, each carrying geometric and physical properties. The construction method is as follows: each Gaussian particle contains four types of parameters: the stream function weighting factor w, the center position... The rotation quaternion q and the scaling vector along the three axes are used to characterize the shape and orientation of the Gaussian particle. That is, the parameters of the i-th Gaussian particle are ; where w is used to determine the equivalent current density distribution in the space where the Gaussian particle resides through mapping, thereby quantifying the magnetic field compensation strength and polarity of the Gaussian particle on the target magnetic field region; q and The shape and spatial orientation of the Gaussian particles are collectively represented. A stream function weight factor vector is constructed from the stream function weight factors of all Gaussian particles, a center position vector is constructed from the center positions of all Gaussian particles, a rotation quaternion matrix is ​​constructed from the rotation quaternions q of all Gaussian particles, and a scaling matrix is ​​constructed from the scaling vectors of all Gaussian particles. In this embodiment, Rodrigues transform logic is used to map the rotation quaternion matrix of each Gaussian particle to a rotation matrix in three-dimensional space. Furthermore, through the rotation matrix of each Gaussian particle and scaling vector Constructing the covariance matrix This is used to define the geometric spatial distribution of each Gaussian particle in the preset current-carrying surface and the anisotropic orientation of its current vector; the preset space is used as the design domain, and the adaptive growth or pruning of the topology model of the shimming coil is achieved by dynamically adjusting the parameter set of all Gaussian particles.

[0073] refer to Figure 3 The embodiments of this application first measure the initial distorted magnetic field in the target space to obtain the non-uniform three-dimensional distribution of the target magnetic field strength, which serves as the input basis for subsequent compensation optimization. Then, Gaussian particles are randomly initialized in the current-carrying surface of the shimming coil to generate a three-dimensional Gaussian particle set carrying geometric and physical properties, which serves as the parameterized expression carrier of the current density distribution. In the optimization iteration stage, a forward mapping from the parameters of the Gaussian particles to the magnetic field distribution is established based on the differentiable Biot-Savart law. The multi-objective loss function is optimized by using a weighted combination of magnetic field deviation loss, power loss, and smoothness loss. The magnetic field distribution is calculated through forward propagation, and the gradient is calculated through backpropagation to achieve joint optimization of the parameter space. As the iteration progresses, the Gaussian particles gradually evolve through adaptive operations such as splitting and pruning to form a continuous current density distribution that matches the target magnetic field. Finally, the converged current density distribution is converted into the center path of a machinable wire winding, and the physical manufacturing of the shimming coil is completed by circuit processing equipment.

[0074] refer to Figure 4 In the embodiments of this application, a cylinder is used as an example to represent the preset space of the shimming coil. The shimming coil is located at the midpoint between the passive shimming module and the target detection area. The current-carrying surface of the shimming coil... The preset geometric surface used to carry the current distribution is specifically a cylindrical current-carrying surface in the embodiments of this application. The stream function weighting factor w of each Gaussian 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 particle is uniformly and randomly distributed within the cylindrical current-carrying surface, with a diameter of 70 cm and a height of 100 cm; the rotation quaternion q of each Gaussian particle has no rotation in the initial state, and the initial rotation quaternion q = [1, 0, 0, 0]; the initial size of the three-axis scaling vector s is 15 cm × 10 cm × 10 cm, slightly longer along the z-axis direction of the main magnetic field, and is set to exhibit weak anisotropy.

[0075] S2, a magnetic field strength calculation model is constructed based on the parameter set of all Gaussian particles and the differentiable form of the Biot-Savart law.

[0076] In a specific embodiment, the process of constructing the magnetic field strength calculation model is as follows:

[0077] Within the design domain, the relative displacement of any sampling point on the flow-carrying surface with respect to the center position of each Gaussian particle is calculated. Combined with the covariance matrix of each Gaussian particle, the spatial proportion of each Gaussian particle at any sampling point on the flow-carrying surface is calculated, as shown in the following equation:

[0078] ;

[0079] in, This represents the position of the i-th Gaussian particle at one of the sampling points on the flow-carrying surface. The space ratio of the location This indicates the position of one of the sampling points on the current-carrying surface;

[0080] The total stream function at any sampling point on the flow-carrying surface is represented as the superposition of the stream function components of N Gaussian particles, as shown in the following equation:

[0081] ;

[0082] in, Indicates the position of one of the sampling points on the current-carrying surface. The total flow function at that point, This represents the position of one of the sampling points on the current-carrying surface of the i-th Gaussian particle. The stream function component at that location;

[0083] Since the equivalent current density generated by each Gaussian particle on the current-carrying surface is determined by the curl of the stream function component corresponding to each Gaussian particle, the total current density at any sampling point on the current-carrying surface is obtained by superimposing the equivalent current densities generated by all Gaussian particles at the corresponding sampling point, as shown in the following equation:

[0084] ;

[0085] Where n is the unit normal vector of the current-carrying surface. The surface gradient of the current-carrying surface. Indicates the position of one of the sampling points on the current-carrying surface. Total current density at the location, This represents the position of one of the sampling points on the current-carrying surface of the i-th Gaussian particle. The equivalent current density generated at the location;

[0086] Substituting the above equation into the Biot-Savart law formula, we obtain the magnetic field strength calculation model, as shown in the following equation:

[0087] ;

[0088] in, Represents the current-carrying surface. Represents the first on the target magnetic field region The location of each observation point Represents the first on the target magnetic field region Location of each observation point The predicted magnetic field strength at that location Represents the permeability of free space. Let r be the distance from one of the sampling points on the current-carrying surface to the first point on the target magnetic field region. Location of each observation point The vector.

[0089] Specifically, in the process of constructing the magnetic field strength calculation model, the embodiments of this application first establish a mapping relationship between the equivalent stream function of the Gaussian particle set and the stream function weighting factor, and the geometric morphology parameters (intermediate position, rotation matrix and scaling vector) of the Gaussian particle set for the current density of each sampling point distributed on the current-carrying surface. Then, the mapping relationship is used to explicitly characterize the evolution law between the geometric morphology parameters of the Gaussian particle and the surface current density.

[0090] In constructing the mapping relationship, the relative displacement of each sampling point on the current-carrying surface relative to the center position of each Gaussian particle is first calculated within the design domain. This relative displacement describes the spatial association between the sampling point and the Gaussian particle: the larger the relative displacement, the weaker the physical contribution of the Gaussian particle to that sampling point. This is combined with the rotation matrix describing the geometry of the Gaussian particle. Scaling vectors of the three axes The spatial proportion of Gaussian particles was calculated. To characterize the continuous current distribution within the current-carrying surface, the physical contributions of N Gaussian particles were linearly superimposed in space to construct the total current function ψ. During the calculation, the infinite-order smoothness of the Gaussian function was utilized to achieve a deterministic transformation from discrete geometric parameters to a continuous spatial physical field, providing a continuously differentiable search space for subsequent gradient optimization.

[0091] When constructing the magnetic field strength calculation model, the analytical continuity of the Gaussian function is utilized to equivalently map the continuously distributed total current function into a series of discrete current contribution terms. The current contribution term of a single Gaussian particle is determined by its parameters. Determined by: Stream function weighting factor w i The scaling vector determines the intensity and polarity of the local current; the scaling vector reflects the physical distribution scale of the Gaussian element on the current-carrying surface and its equivalent current carrying capacity. The larger the size, the stronger its equivalent current carrying capacity. Through the above mapping relationship, a deterministic correlation is achieved between the geometric physical parameter space of the Gaussian particle and the magnetic field strength space of the target region, supporting end-to-end evolution calculation of the electromagnetic properties of the coil.

[0092] Once the distribution parameters of the Gaussian particles are determined, a model for calculating the magnetic field strength can be constructed. This model utilizes the anisotropic covariance matrix. i Morphological features characterizing local current distribution. A method for calculating the magnetic field strength generated by all Gaussian particles at each sampling point is constructed based on the differentiable form of the Biot-Savart law. .

[0093] The embodiments of this application deeply couple Gaussian particles with the laws of electromagnetic physics to construct a differentiable magnetic field strength calculation model. The magnetic field contribution of Gaussian particles at the sampling point is calculated jointly by geometric and physical operators. The geometric operator serves as a shape representation of the current density, while the physical operator, acting as an electromagnetic response operator, follows the Biot-Savart law, defining the attenuation characteristics of the magnetic field strength with distance and its directional distribution in space. In the magnetic field strength calculation model, the influence of the Gaussian particle distribution on the predicted magnetic field strength is determined by calculating the relative distance and orientation between the sampling point and each Gaussian particle.

[0094] Because the Gaussian function is continuously differentiable throughout space, it is possible to compute smooth gradients using the Adam optimizer, allowing Gaussian particles to smoothly merge when they are close together. When two Gaussian particles approach each other, the magnetic field strengths they generate will naturally superimpose to form a continuous entity, realizing the transformation from discrete Gaussian particles to a continuous topological structure model.

[0095] The embodiments of this application introduce Gaussian splashing technology into the design of uniform coils, using a set of Gaussian particles with spatial position, scale, and weight parameters to efficiently represent the current density distribution on the current-carrying surface. Introducing this idea into coil design provides a continuous, differentiable, and locally expressive parameterized method for coil layout, thus offering a new technical path for high-precision, high-efficiency coil design.

[0096] S3 uses the initial parameter set of all Gaussian particles as the parameter set obtained in the first iteration, and combines it with the target magnetic field strength of each sampling point in the current-carrying surface as input to the Gaussian particle parameter set iterative optimization algorithm. In the current iteration optimization process, the predicted magnetic field strength of each sampling point on the current-carrying surface is obtained through the magnetic field strength calculation model based on the parameter set obtained in the previous iteration. A multi-objective loss function is constructed based on the deviation between the predicted magnetic field strength and the target magnetic field strength, the stream function weight factor vector, and the center position vector. The parameter set obtained in the previous iteration is updated based on the multi-objective loss function to obtain the parameter set of the current iteration. The above iterative optimization process is repeated until the maximum number of iterations is reached, and the optimized parameter set and its corresponding current density distribution are output.

[0097] In a specific embodiment, the expression for the multi-objective loss function is as follows:

[0098] ;

[0099] in, This indicates the loss due to magnetic field deviation. Indicates power loss. Indicates smoothness loss. and These are the regularization power weights and the smoothing weights, respectively. Represents a multi-objective loss function. This represents the set of parameters for all Gaussian particles. Indicates taking When it is the minimum value ;

[0100] The expression for the magnetic field deviation loss is:

[0101] ;

[0102] in, Represents the first on the target magnetic field region Location of each observation point The target magnetic field strength at that location, Describing the L2 norm, This represents the total number of observation points in the target magnetic field region;

[0103] The expression for power loss is:

[0104] ;

[0105] Where σ is the conductivity of the material of the shimming coil. The thickness of the conductor layer of the shimming coil, and These represent the positions of the i-th Gaussian particle and the k-th Gaussian particle at one of the sampling points on the flow-carrying surface, respectively. The space ratio of the location and Let represent the stream function weighting factors of the i-th Gaussian particle and the k-th Gaussian particle, respectively, where k = 1, 2, ..., N;

[0106] The expression for smoothness loss is:

[0107] ;

[0108] in, Let N(i) be the spatial neighborhood set of the i-th Gaussian particle, and g∈N(i) represent the g-th Gaussian particle in the spatial neighborhood set of the i-th Gaussian particle. The spatial similarity weight between the i-th Gaussian particle and the g-th Gaussian particle in the spatial neighborhood set is defined as: , and Let be the center positions of the i-th Gaussian particle and the g-th Gaussian particle in the spatial neighborhood set, respectively. This is the neighborhood scale parameter.

[0109] Specifically, the embodiments of this application propose an iterative optimization algorithm for Gaussian particle parameter set. In this algorithm, a multi-objective loss function containing the target magnetic field strength (i.e., the true value) is constructed, and the parameter set of all Gaussian particles is iteratively updated through the backpropagation algorithm, so that the Gaussian particles can adaptively cluster and grow in the current-carrying surface to form a distribution that can represent the current density.

[0110] The specific process of the Gaussian particle parameter set iterative optimization algorithm in the embodiments of this application is to perform variational evolution on the explicitly parameterized Gaussian model using the gradient descent algorithm: its input is the initial parameter set of all Gaussian particles and the target magnetic field strength determined by the magnet and the environment; its output is the optimized parameter set of all Gaussian particles. This optimized parameter set not only defines the current excitation weights of each Gaussian particle at the physical level, but also constructs the topological structure model of the shimming coil 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 particles to adaptively split and prune in the design domain space. The multi-objective loss function consists of three coupled parts: magnetic field deviation loss, power loss, and smoothing loss. The magnetic field deviation loss constrains the consistency between the predicted and target magnetic field strengths generated by all Gaussian particles. It is evaluated by calculating the difference between the predicted and target magnetic field strengths within the target magnetic field region, specifically using the mean square error loss function. By constraining the distribution of Gaussian particles, the current density field generated by the topology model can produce an accurate magnetic field, driving Gaussian particles to move towards the region with the greatest magnetic field distortion and increasing their weight. The power loss is achieved by applying an L2 positive coefficient to the stream function weighting factor of the Gaussian particles. The regularization constraint aims to minimize the global current intensity to minimize ohmic power consumption. The smoothing loss is based on the parameter continuity constraint between Gaussian particles. By suppressing the sharp fluctuations in the gradient of the stream function between adjacent Gaussian particles, it ensures the smoothness and physical connectivity of the current distribution. The spatial similarity weight is used to characterize the proximity of the center positions of two Gaussian particles on the current-carrying surface. When the center positions of two Gaussian particles are close, the spatial similarity weight is larger; when the center positions of two Gaussian particles are far apart, the spatial similarity weight gradually approaches zero. The neighborhood scale parameter is used to control the decay range of the spatial similarity weight. The power loss and smoothing loss are weighted using regularized power weight and smoothing weight, respectively. The regularized power weight and smoothing weight are used to achieve an optimal balance between magnetic field accuracy, power consumption burden, and current distribution continuity.

[0111] In a specific embodiment, the iterative optimization process in each round also includes:

[0112] When the number of iterations exceeds the threshold, it is determined whether the magnitude of the stream function weight factor of each Gaussian particle is less than the preset lower limit threshold. If so, a pruning operation is performed to force the stream function weight factor of the Gaussian particle to zero; otherwise, the pruning operation is not performed.

[0113] Determine whether the magnitude of the stream function weight factor of each Gaussian particle is greater than or equal to a preset upper limit threshold. If so, perform a split operation on the Gaussian particle as the parent Gaussian particle to generate two child Gaussian particles, which inherit the parameters of the parent Gaussian particle. Otherwise, do not perform a split operation on the Gaussian particle.

[0114] In the current iteration optimization process, with the goal of minimizing the multi-objective loss function, the parameter set obtained in the previous iteration is updated by using the adaptive moment estimation algorithm, and the Gaussian particle splitting or pruning operation is performed to complete the update of the parameter set obtained in the previous iteration.

[0115] Specifically, in the embodiments of this application, the Adaptive Moment Estimation (Adam) algorithm is used as the core engine for parameter set updating. In the Adam algorithm, the expression for the total gradient of the multi-objective loss function is:

[0116] ;

[0117] in, This represents the total gradient of the multi-objective loss function. The gradient representing the magnetic field deviation loss, The gradient of the sparse loss function is represented. This represents the gradient of the spatial overlap loss function.

[0118] 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 particles in complex magnetic field distortion regions and fine-tuning in smooth regions. Simultaneously, the three-dimensional coordinates of the Gaussian particles are updated according to the repulsion gradient, allowing the Gaussian particle set to adaptively split (increase) and prune in space. The process of Gaussian particle splitting and pruning is as follows: Figure 5 As shown.

[0119] When the number of iterations exceeds a threshold (e.g., 1000 generations), the Gaussian particle parameter set iterative optimization algorithm will initiate a dynamic pruning and splitting mechanism. The magnitude of the stream function weight factor for each Gaussian particle is automatically detected. ,like Less than the preset lower threshold ϵ min (For example If the contribution of the Gaussian particle to the improvement of the magnetic field is below the physical manufacturing threshold, then a pruning operation can be performed. This involves forcibly setting the stream function weighting factor of the Gaussian particle to zero and removing the Gaussian particle from the Gaussian particle set; otherwise, no pruning operation is performed. Greater than or equal to the preset upper limit threshold ϵ maxThen, a splitting operation can be performed on the Gaussian particle, that is, the Gaussian particle is used as the parent Gaussian particle to generate two child Gaussian particles, and the two child Gaussian particles can inherit the parameters of the parent Gaussian particle.

[0120] As the iterative optimization process proceeds, the originally discrete Gaussian particles, driven by the Adam algorithm, gradually split and prune in the design domain space according to the total gradient, and gradually evolve into a topological model that can represent the current density in the current-carrying surface.

[0121] S4. Based on the current density distribution corresponding to the optimized parameter set, the conductor winding structure is generated by the contour discretization method and then solidified to produce the corresponding uniform field coil.

[0122] In a specific embodiment, the process of generating the conductor winding structure is as follows:

[0123] By performing an area integral on the current density distribution corresponding to the optimized parameter set, a continuous stream function on the current-carrying surface is obtained;

[0124] The current increment step size is determined based on the preset total number of coil turns, as shown in the following formula:

[0125] ;

[0126] in, and Let represent the maximum and minimum values ​​of the continuous stream function on the current-carrying surface, respectively. Indicates the total number of turns of the coil. Indicates the current increment step size;

[0127] Extract the continuous stream function on the current-carrying surface as follows: The contour lines serve as the center path of the nth turn of the conductor winding. The center paths of each turn of the conductor winding form a closed curve, and its winding direction is uniquely determined by the gradient direction of the continuous stream function.

[0128] By adjusting the center path of the wire winding in conjunction with the printed circuit manufacturing process, the wire winding structure is obtained.

[0129] Specifically, by prioritizing the optimized parameter set and its infinitely smooth basis function characteristics, a globally continuous total flow function is reconstructed on the flow-carrying surface. This ensures the non-dispersion and continuity of the current distribution from a physical structure perspective. Subsequently, a contour discretization algorithm is used to perform topological mapping on the total current function, based on the preset total number of coil turns N. c Determine a constant current increment step size And extract the equations that satisfy the analytical equations. The set of contour lines serves as the center path of the nth turn of the conductor winding, passing through discretized cylindrical and hemispherical shimming coils, as shown below. Figure 6 As shown. Based on this, the center path of the generated conductor winding is modified using printed circuit manufacturing technology. The modification parameters include wiring width and thickness. The discretized conductor winding center path is precisely manufactured into a solid shimming coil with highly conformal characteristics. The conductor winding layout of the shimming coil is finally completed. Based on the conductor winding layout of the shimming coil, the coil is fabricated using rigid or flexible PCB, and the final solid shimming coil is installed in the corresponding nuclear magnetic resonance measurement instrument.

[0130] The magnetic field strength within the target magnetic field region was measured without cylindrical and hemispherical shimming coils to determine the initial distortion. The magnetic field strength within the target magnetic field region was then measured with and without cylindrical and hemispherical shimming coils. The results were compared as follows: Figure 7 As shown, via Figure 7 Comparative verification shows that the compensating magnetic fields generated by the cylindrical and hemispherical shimming coils effectively cancel 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.

[0131] The shimming coil designed using the method provided in this embodiment of the invention, as measured by simulation software, achieves higher efficiency while reducing power consumption and inductance compared to traditional methods. The simulation results for the Z2 coil are shown in Table 1.

[0132] Table 1. Performance Comparison of Z2 Uniform Coil:

[0133] Therefore, this invention provides a design method for nuclear magnetic resonance (NMR) shimming coils based on Gaussian splashing. By synergistically optimizing the sparsity constraints of the coil conductor distribution and the magnetic field deviation threshold of the target region, it can accurately eliminate electromagnetic strays in complex topological environments. This not only provides key technical support for the customized design of high-precision shimming coils 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.

[0134] Further reference Figure 8 As an implementation of the methods shown in the above figures, this application provides an embodiment of a design device for nuclear magnetic resonance shimming coils based on Gaussian splashing. This device embodiment is similar to... Figure 1Corresponding to the method embodiments shown, this device can be specifically applied to various electronic devices.

[0135] This application provides a design device for nuclear magnetic resonance shimming coils based on Gaussian splashing, including:

[0136] Initialization module 1 is configured to initialize the current-carrying surface of the shimming coil within the design domain and randomly generate several Gaussian ions on the current-carrying surface to obtain the initial parameter set of all Gaussian particles. The parameter set includes the stream function weight factor vector, the center position vector, the rotation quaternion matrix, and the scaling matrix.

[0137] Model building module 2 is configured to build a magnetic field strength calculation model based on the parameter set of all Gaussian particles and the differentiable form of the Biot-Savart law;

[0138] Iterative optimization module 3 is configured to use the initial parameter set of all Gaussian particles as the parameter set obtained in the first iteration, and combine it with the target magnetic field strength of each sampling point in the current-carrying surface as input to the Gaussian particle parameter set iterative optimization algorithm. In the current iteration optimization process, the predicted magnetic field strength of each sampling point on the current-carrying surface is obtained through the magnetic field strength calculation model based on the parameter set obtained in the previous iteration. A multi-objective loss function is constructed based on the deviation between the predicted magnetic field strength and the target magnetic field strength, the stream function weight factor vector, and the center position vector. The parameter set obtained in the previous iteration is updated based on the multi-objective loss function to obtain the parameter set of the current iteration. The above iterative optimization process is repeated until the maximum number of iterations is reached, and the optimized parameter set and its corresponding current density distribution are output.

[0139] The solidification module 4 is configured to generate the conductor winding structure based on the current density distribution corresponding to the optimized parameter set using the contour discretization method and perform solidification processing to produce the corresponding uniform field coil.

[0140] 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 9 As 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.

[0141] Alternatively, the memory 902 can be either standalone or integrated with the processor 901.

[0142] 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.

[0143] This invention also provides a computer storage medium storing computer execution instructions, which, when executed by processor 901, implement the above method.

[0144] This invention also provides a computer program product, including a computer program that, when executed by a processor 901, implements the above-described method.

[0145] 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.

[0146] 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.

[0147] 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.

[0148] 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.

[0149] It should be understood that the processor 901 described above can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. 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.

[0150] 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.

[0151] 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.

[0152] 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.

[0153] 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.

[0154] 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.

[0155] 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 therein. Such 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 nuclear magnetic resonance shimming coils based on Gaussian splashing, characterized in that, Includes the following steps: The current-carrying surface of the shimming coil is initialized within the design domain, and several Gaussian ions are randomly generated on the current-carrying surface to obtain the initial parameter set of all Gaussian particles. The parameter set includes the stream function weight factor vector, the center position vector, the rotation quaternion matrix, and the scaling matrix. A magnetic field strength calculation model is constructed based on the parameter set of all Gaussian particles and the differentiable form of the Biot-Savart law; The initial parameter set of all Gaussian particles is used as the parameter set obtained in the first iteration. This parameter set is then combined with the target magnetic field strength at each sampling point on the current-carrying surface and input into the Gaussian particle parameter set iterative optimization algorithm. In the current iteration, the predicted magnetic field strength at each sampling point on the current-carrying surface is obtained using the magnetic field strength calculation model based on the parameter set obtained in the previous iteration. A multi-objective loss function is constructed based on the deviation between the predicted and target magnetic field strengths, the stream function weighting factor vector, and the center position vector. This multi-objective loss function is then used to update 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, and the optimized parameter set and its corresponding current density distribution are output. Based on the current density distribution corresponding to the optimized parameter set, the conductor winding structure is generated by the contour discretization method and then materialized to obtain the corresponding uniform field coil.

2. The design method for nuclear magnetic resonance shimming coils based on Gaussian splashing according to claim 1, characterized in that, The rotation quaternion matrix is ​​composed of the rotation quaternions of all Gaussian particles; the scaling matrix is ​​composed of the scaling vectors of all Gaussian particles; the center position vector is composed of the center positions of all Gaussian particles, and the center position of each Gaussian particle is constrained on the flow-carrying surface; the stream function weighting factor vector is composed of the stream function weighting factors of all Gaussian particles; the parameters of the i-th Gaussian particle on the flow-carrying surface are expressed as... ,in This represents the center position of the i-th Gaussian particle. This represents the stream function weighting factor for the i-th Gaussian particle. Let i represent the rotation quaternion of the i-th Gaussian particle. Let represent the scaling vector of the i-th Gaussian particle. The covariance matrix of the i-th Gaussian particle is defined using its scaling vector and rotation matrix. As shown in the following formula: ; This represents the rotation quaternion of the i-th Gaussian particle using Rodrigues transform logic. The rotation matrix obtained by mapping, T represents the transpose of the matrix, i = 1, 2, ..., N, and N represents the total number of Gaussian particles.

3. The design method for nuclear magnetic resonance shimming coils based on Gaussian splashing according to claim 2, characterized in that, The construction process of the magnetic field strength calculation model is as follows: Within the design domain, the relative displacement of any sampling point on the flow-carrying surface with respect to the center position of each Gaussian particle is calculated. Combined with the covariance matrix of each Gaussian particle, the spatial proportion of each Gaussian particle at any sampling point on the flow-carrying surface is calculated, as shown in the following equation: ； in, This indicates the position of one of the sampling points on the current-carrying surface. This represents the position of the i-th Gaussian particle at one of the sampling points on the flow-carrying surface. The space ratio of the location; The total stream function at any sampling point on the flow-carrying surface is represented as the superposition of the stream function components of N Gaussian particles, as shown in the following equation: ； in, Indicates the position of one of the sampling points on the current-carrying surface. The total flow function at that point, This represents the position of one of the sampling points on the current-carrying surface of the i-th Gaussian particle. The stream function component at that location; Since the equivalent current density generated by each Gaussian particle on the current-carrying surface is determined by the curl of the stream function component corresponding to each Gaussian particle, the total current density at any sampling point on the current-carrying surface is obtained by superimposing the equivalent current densities generated by all Gaussian particles at the corresponding sampling point, as shown in the following equation: ； Where n is the unit normal vector of the current-carrying surface. The surface gradient of the current-carrying surface. Indicates the position of one of the sampling points on the current-carrying surface. Total current density at the location, This represents the position of one of the sampling points on the current-carrying surface of the i-th Gaussian particle. The equivalent current density generated at the location; Substituting the above equation into the Biot-Savart law formula, we obtain the magnetic field strength calculation model, as shown in the following equation: ； in, Represents the current-carrying surface. Represents the first on the target magnetic field region The location of each observation point Represents the first on the target magnetic field region Location of each observation point The predicted magnetic field strength at that location Represents the permeability of free space. Let r be the distance from one of the sampling points on the current-carrying surface to the first point on the target magnetic field region. Location of each observation point The vector.

4. The design method for nuclear magnetic resonance shimming coils based on Gaussian splashing according to claim 3, characterized in that, The expression for the multi-objective loss function is as follows: ； in, Indicates the loss due to magnetic field deviation. Indicates power loss. Indicates smoothness loss. and These are the regularization power weights and the smoothing weights, respectively. Represents a multi-objective loss function. This represents the set of parameters for all Gaussian particles. Indicates taking When it is the minimum value ; The expression for the magnetic field deviation loss is: ； in, Represents the first on the target magnetic field region Location of each observation point The target magnetic field strength at that location, Represents the L2 norm. This represents the total number of observation points in the target magnetic field region; The expression for the power loss is: ； Where σ is the conductivity of the material of the shimming coil. The thickness of the conductor layer of the shimming coil, and These represent the positions of the i-th Gaussian particle and the k-th Gaussian particle at one of the sampling points on the flow-carrying surface, respectively. The space ratio of the location and Let represent the stream function weighting factors of the i-th Gaussian particle and the k-th Gaussian particle, respectively, where k = 1, 2, ..., N; The expression for the smoothness loss is: ； in, Let N(i) be the spatial neighborhood set of the i-th Gaussian particle, and g∈N(i) represent the g-th Gaussian particle in the spatial neighborhood set of the i-th Gaussian particle. The spatial similarity weight between the i-th Gaussian particle and the g-th Gaussian particle in the spatial neighborhood set is defined as: , and Let be the center positions of the i-th Gaussian particle and the g-th Gaussian particle in the spatial neighborhood set, respectively. This is the neighborhood scale parameter.

5. The design method for nuclear magnetic resonance shimming coils based on Gaussian splashing according to claim 2, characterized in that, The Gaussian particle parameter set iterative optimization algorithm also includes: When the number of iterations exceeds the threshold, it is determined whether the magnitude of the stream function weight factor of each Gaussian particle is less than the preset lower limit threshold. If so, a pruning operation is performed to force the stream function weight factor of the Gaussian particle to zero; otherwise, the pruning operation is not performed. Determine whether the magnitude of the stream function weight factor of each Gaussian particle is greater than or equal to a preset upper limit threshold. If so, perform a split operation on the Gaussian particle as the parent Gaussian particle to generate two child Gaussian particles, which inherit the parameters of the parent Gaussian particle. Otherwise, do not perform a split operation on the Gaussian particle. In the current iteration optimization process, with the goal of minimizing the multi-objective loss function, the parameter set obtained in the previous iteration is updated by gradient through the adaptive moment estimation algorithm, and Gaussian particle splitting or pruning operations are performed to complete the update of the parameter set obtained in the previous iteration.

6. The design method for nuclear magnetic resonance shimming coils based on Gaussian splashing according to claim 1, characterized in that, The process of generating the conductor winding structure is as follows: The current density distribution corresponding to the optimized parameter set is integrally applied to the surface to obtain the continuous flow function on the current-carrying surface; The current increment step size is determined based on the preset total number of coil turns, as shown in the following formula: ； in, and Let represent the maximum and minimum values ​​of the continuous stream function on the current-carrying surface, respectively. Indicates the total number of turns of the coil. Indicates the current increment step size; Extract the continuous stream function on the current-carrying surface as follows: The contour lines serve as the center path of the nth turn of the conductor winding. The center paths of each turn of the conductor winding form a closed curve, and its winding direction is uniquely determined by the gradient direction of the continuous stream function. By adjusting the center path of the wire winding in conjunction with the printed circuit manufacturing process, the wire winding structure is obtained.

7. A design device for nuclear magnetic resonance shimming coils based on Gaussian splashing, characterized in that, include: The initialization module is configured to initialize the current-carrying surface of the shimming coil within the design domain and randomly generate several Gaussian ions on the current-carrying surface to obtain an initial parameter set for all Gaussian particles. The parameter set includes a stream function weight factor vector, a center position vector, a rotation quaternion matrix, and a scaling matrix. The model building module is configured to build a magnetic field strength calculation model based on the parameter set of all Gaussian particles and the differentiable form of the Biot-Savart law; The iterative optimization module is configured to use the initial parameter set of all Gaussian particles as the parameter set obtained in the first iteration, and combine it with the target magnetic field strength of each sampling point in the current-carrying surface as input to the Gaussian particle parameter set iterative optimization algorithm. In the current iteration optimization process, the predicted magnetic field strength of each sampling point on the current-carrying surface is obtained through the magnetic field strength calculation model based on the parameter set obtained in the previous iteration. A multi-objective loss function is constructed based on the deviation between the predicted magnetic field strength and the target magnetic field strength, the stream function weight factor vector, and the center position vector. The parameter set obtained in the previous iteration is updated based on the multi-objective loss function to obtain the parameter set for the current iteration. The above iterative optimization process is repeated until the maximum number of iterations is reached, and the optimized parameter set and its corresponding current density distribution are output. The solidification module is configured to generate a conductor winding structure based on the current density distribution corresponding to the optimized parameter set using the contour discretization method and perform solidification processing to produce the corresponding uniform field coil.

8. An electronic device, comprising: One or more processors; A storage device for storing one or more programs, characterized in that, 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 1-6.

9. 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 1-6.

10. 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 1-6.

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