A gradient coil design simplification method and system for magnetic resonance imaging

Abstract

This invention discloses a simplified method and system for gradient coil design in magnetic resonance imaging, comprising: dividing the wiring surface into a symmetrical mesh and setting the target magnetic field distribution; calculating the magnetic field matrix and the optimization matrix; dividing nodes at symmetrical positions into the same group according to the symmetry of the mesh nodes, and arbitrarily selecting a node in each group as the representative node of the group, and calculating the mapping matrix from the representative node stream function to the complete node stream function; simplifying the magnetic field matrix and the optimization matrix through the mapping matrix to obtain the mapped magnetic field matrix and the mapped optimization matrix; solving for the representative node stream function based on the mapped magnetic field matrix, and obtaining the complete node stream function based on the mapping matrix; and discretizing the stream function into coil wiring using a stream function discretization method based on the complete node stream function. This invention, by introducing the mapping matrix, reduces the number of stream function variables that need to be solved, effectively preserves the symmetry of the gradient coil, and significantly improves the efficiency of the solution process.

Description

Technical Field

[0001] This invention belongs to the field of magnetic resonance imaging technology, specifically relating to a simplified method and system for designing gradient coils for magnetic resonance imaging, particularly suitable for longitudinal gradient coils. Background Technology

[0002] Magnetic resonance imaging (MRI) technology, with its non-invasive, radiation-free nature and high soft tissue contrast, has become an important tool in the field of medical imaging. Gradient coils, as a key physical component of the MRI system, encode signals from different spatial locations by applying a spatial gradient magnetic field, thereby generating high-resolution three-dimensional images. The application of gradient fields in the X, Y, and Z axes enables precise localization and scanning of different regions within the body, providing a foundation for the generation of high-quality image data. To reduce stray magnetic field leakage from the gradient coils and suppress eddy currents caused by gradient switching, a self-shielding structure is employed in the design. This is achieved by laying a reverse coil loop in the secondary layer of the gradient coils to significantly reduce stray field leakage and further decrease the induced eddy currents formed by the stray field within the metallic conductor.

[0003] Currently, gradient coil design methods based on boundary element method and equivalent magnetic dipole method typically require meshing the coil surface and setting multiple target field points for solving. However, the symmetry of the gradient coil is often ignored in the optimization design process. While this approach can improve the solution accuracy when using overly dense meshes and too many target field points, it significantly increases the computational load, leading to low efficiency. Conversely, overly sparse meshes and field point configurations can significantly reduce solution accuracy and may even cause local overfitting, thereby disrupting the symmetry of the computational wiring results.

[0004] Furthermore, most existing gradient coil discretization methods discretize by dividing the convection function into equally spaced contour lines. This method, under the premise of forcibly constraining the coil boundary to zero, will lead to the inability to effectively control stray field leakage in the end shielding region. Although the error caused by forcibly constraining the boundary to zero can be avoided by connecting the wiring surface of the primary coil and the secondary coil, this increases the complexity of the manufacturing process. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a simplified method for designing gradient coils for magnetic resonance imaging, in order to solve the problem of low solution efficiency caused by excessively large computation matrices in the design of gradient coils in the prior art, and to reduce the ill-conditioned nature of the solution.

[0006] Technical solution: The design simplification method described in this invention includes the following steps:

[0007] Based on the geometric structure of the wiring and the target magnetic field region, the wiring surface is divided into symmetrical grids, and the target magnetic field distribution is set; then the magnetic field matrix is ​​calculated, and an optimization matrix is ​​established, which includes one or more of the following: power consumption matrix, energy storage matrix, torque matrix, and torque matrix.

[0008] Based on the symmetry of the grid nodes, nodes at symmetrical positions are grouped together, and a node is randomly selected from each group as the representative node of that group. The mapping matrix from the representative node flow function to the complete node flow function is calculated.

[0009] The magnetic field matrix is ​​simplified by a mapping matrix to obtain a mapped magnetic field matrix; and the mapping optimization matrix corresponding to the optimized matrix is ​​calculated using the mapping matrix to obtain one or more of the following: a mapped power consumption matrix, a mapped energy storage matrix, a mapped force matrix, and a mapped torque matrix.

[0010] Based on the mapped magnetic field matrix and combined with the mapped optimization matrix, the representative node flow function is solved using regularization or constraint optimization methods, and the complete node flow function is further obtained based on the mapping matrix.

[0011] Based on the complete node flow function, the flow function is discretized into coil wiring using the flow function discretization method.

[0012] Furthermore, the elements of the mapping matrix are filled with values ​​of 1, -1, or 0 according to the symmetric relationship of the flow function of the corresponding node; represented as:

[0013] ;

[0014] in, Represents the first in the mapping matrix Line number The elements of the column.

[0015] Furthermore, the expression for the mapped magnetic field matrix is:

[0016] ;

[0017] in, To map the magnetic field matrix, For the magnetic field matrix, It is a mapping matrix.

[0018] Furthermore, the expressions for the mapped power consumption matrix and the mapped energy storage matrix are as follows:

[0019] ;

[0020] in, This represents the mapped power consumption matrix or mapped energy storage matrix. This is a power consumption matrix or energy storage matrix. for The transpose of the matrix, It is a mapping matrix;

[0021] The expressions for the mapped force matrix and the mapped moment matrix are:

[0022] ;

[0023] in, This represents the mapped force matrix or mapped moment matrix. It is the force matrix or torque matrix.

[0024] Furthermore, complete node flow functions The calculation methods include:

[0025] ;

[0026] in, Represents the optimization function. This represents the optimal solution. To map the magnetic field matrix, To represent the node flow function, This indicates the target magnetic field to be set. Indicates the allowable magnetic field error;

[0027] The optimization function is represented as a combination of several optimization objectives:

[0028] ;

[0029] in, , , , , These are weighting coefficients, representing the weight of the corresponding optimization objective in the optimization function, and at least one of these weighting coefficients is not 0; Represents the mapping power consumption matrix; Represents the mapped energy storage matrix; Represents the mapping force matrix; Represents the mapped moment matrix. for Transpose of;

[0030] Complete node stream function The calculation formula is:

[0031] ;

[0032] in, It is a mapping matrix.

[0033] Furthermore, stream function discretization methods include:

[0034] The primary and secondary laminar flow functions of the gradient coil are discretized respectively, and the following relationship is satisfied:

[0035] ;

[0036] ;

[0037] in, This represents the maximum value of the flow function in the primary layer. This represents the minimum value of the flow function in the primary layer. This represents the maximum value of the flow function in the secondary layer. This represents the minimum value of the flow function in the secondary layer; The partitioning of the stream function in the primary layer, relative to the minimum value of the stream function, represents the distance between the stream function partitions. The ratio, The partitioning of the stream function in the primary layer, relative to the side closest to the maximum value of the stream function, represents the distance between the stream functions. The ratio, The interval between stream functions in the secondary layer, representing the distance from the minimum stream function to the minimum stream function, is relative to... The ratio, The interval between stream functions in the secondary layer, representing the distance from the maximum value of the stream function to the maximum value, is relative to... The ratio; This indicates the number of discretized contour lines in the primary layer. This indicates the number of discretized contour lines in the secondary layer. The stream function interval for the primary layer. The flow function interval for the secondary layer.

[0038] Furthermore, the aforementioned ,exist and Given that the integer is an integer, it needs to be combined with... The closest approximation is calculated using the following formula:

[0039] ;

[0040] ;

[0041] in, The function is used to round variables.

[0042] Furthermore, the stream function discretization method requires determining the coil routing based on the contour lines of the stream function. The stream function values ​​corresponding to the contour lines are determined based on the following formula:

[0043] ;

[0044] ;

[0045] in, The first laminar flow function represents the... The stream function values ​​corresponding to each contour line. The second laminar flow function represents the first... The stream function values ​​corresponding to each contour line.

[0046] The present invention also provides a simplified gradient coil design system for magnetic resonance imaging, comprising:

[0047] The first unit is used to perform symmetrical meshing of the wiring surface according to the geometric structure of the wiring and the target magnetic field region, and to set the target magnetic field distribution; then, the magnetic field matrix is ​​calculated and an optimization matrix is ​​established, wherein the optimization matrix includes one or more of the following: power consumption matrix, energy storage matrix, torque matrix, and torque matrix.

[0048] The second unit is used to divide nodes at symmetrical positions into the same group based on the symmetry of the grid nodes, and arbitrarily select a node in each group as the representative node of the group, and calculate the mapping matrix from the representative node flow function to the complete node flow function.

[0049] The third unit is used to simplify the magnetic field matrix through the mapping matrix to obtain the mapped magnetic field matrix; and to use the mapping matrix to calculate the mapping optimization matrix corresponding to the optimization matrix to obtain the mapped power consumption matrix, the mapped energy storage matrix, the mapped force matrix and the mapped torque matrix.

[0050] The fourth unit is used to solve the representative node flow function based on the mapped magnetic field matrix using regularization or constraint optimization methods, and further to obtain the complete node flow function based on the mapping matrix.

[0051] The fifth unit is used to discretize the stream function into coil wiring based on the complete node stream function using the stream function discretization method.

[0052] The present invention also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the method described.

[0053] Compared with existing technologies, the significant technical advantages of this invention are as follows: By introducing a mapping matrix, the complete nodal stream function in the design of symmetric gradient coils can be represented by a representative nodal stream function, thereby significantly reducing the number of stream function variables to be solved and the size of the matrix required for optimization, while effectively preserving the symmetric structural characteristics of the coil. This method significantly improves solution efficiency and reduces computational resource consumption while ensuring magnetic field accuracy. Furthermore, the stream function discretization method proposed in this invention allows for different stream function partitioning intervals between the primary and secondary layers, improving the stream function partitioning at the coil ends and effectively reducing stray field leakage caused by forced end constraints. Attached Figure Description

[0054] Figure 1 This is a flowchart of the method involved in the present invention;

[0055] Figure 2 This is a schematic diagram illustrating the mapping from the representative node flow function to the complete node flow function in this invention;

[0056] Figure 3 This is a schematic diagram of the wiring surface mesh used in Example E1;

[0057] Figure 4 This is a schematic diagram of the target magnetic field point distribution used in Example E1;

[0058] Figure 5 The diagrams are schematic diagrams of stream function discretization methods, where (a) is a schematic diagram of a conventional stream function discretization method and (b) is a schematic diagram of the stream function discretization method proposed in this invention.

[0059] Figure 6 The diagram shows the axial stray field distribution on the shielding surface in Example E1, where (a) is the stray field distribution using the conventional stream function discretization method, and (b) is the stray field distribution using the stream function discretization method proposed in this invention.

[0060] Figure 7 The diagram shows the wiring distribution of Example E1, where (a) is a schematic diagram of the 3D wiring distribution of the coil, (b) is a schematic diagram of the wiring unfolded in the primary layer of the coil, and (c) is a schematic diagram of the wiring unfolded in the secondary layer of the coil.

[0061] Figure 8 The diagram below is a schematic diagram of Example E2, where (a) is a schematic diagram of the wiring surface mesh of Example E2, and (b) is a schematic diagram of the 3D wiring distribution of Example E2. Detailed Implementation

[0062] The present invention will be further described below with reference to specific embodiments and accompanying drawings.

[0063] This invention presents a simplified design method for gradient coils used in magnetic resonance imaging. Taking advantage of the symmetry of the target mesh nodes, a mapping matrix is ​​introduced to map the same stream function value to symmetrical mesh nodes, and the mapped magnetic field matrix and various mapping optimization matrices are further calculated. Then, the stream function distribution of the simplified nodes is solved, and the stream function distribution of the complete mesh nodes is calculated using the mapping matrix. During the stream function discretization process, the stream function partitioning interval between the primary and secondary layers is allowed to differ, improving the interval of stream function values ​​at the ends and reducing the intensity of stray fields generated by the wiring after stream function discretization. This invention reduces the number of stream function variables that need to be solved by introducing a mapping matrix, while effectively preserving the symmetry of the gradient coil. This simplified method significantly improves the efficiency of the solution process while reducing the computational resource requirements while maintaining high accuracy. The stream function discretization method used in this invention avoids the end stray field leakage problem caused by forcibly constraining the boundary stream function of the wiring surface to zero in existing methods, thereby effectively suppressing eddy currents generated by the gradient coil.

[0064] like Figure 1 As shown, the method of the present invention includes the following steps:

[0065] S1. Based on the geometric structure of the wiring and the target magnetic field region, the wiring surface is divided into symmetrical grids, and the target magnetic field distribution is set; on this basis, the magnetic field matrix is ​​calculated; further, a series of optimization matrices are established, which may include one or more of the following: power consumption matrix, energy storage matrix, force matrix, and torque matrix.

[0066] The magnetic field matrix and various optimization matrices can be obtained using mature numerical calculation methods in this field, such as the boundary element method and the equivalent magnetic dipole method, which are typical grid-based target field methods. For example, the magnetic field matrix and optimization matrices can be calculated using the boundary element method or the equivalent magnetic dipole method. The magnetic field matrix is ​​the relationship matrix between the stream function distribution and the magnetic field value at the target point. The optimization matrix is ​​the relationship matrix between the stream function distribution and the corresponding optimization objective, and the optimization matrix is ​​selected according to the optimization objective requirements of the actual coil design.

[0067] S2. Based on the symmetry of the grid nodes, divide the nodes at symmetrical positions into the same group, and determine a representative node for each group. The method for determining the representative node is to arbitrarily select one node from the group as the representative node; calculate the stream function of the representative node. to complete node flow function mapping matrix The size of the mapping matrix is ,in This represents the total number of nodes (i.e., the total number of nodes in the grid). This indicates the number of representative nodes in the mapping.

[0068] The mapping matrix is ​​used to represent the correspondence between complete nodes and representative nodes. The elements of the mapping matrix are filled with values ​​of 1, -1, or 0 according to the symmetry of the flow function of the nodes at corresponding positions. Represents the first in the mapping matrix Line number The elements of a column. The corresponding element can be determined by the following formula.

[0069] (1)

[0070] like Figure 2 This is a schematic diagram illustrating the mapping from the representative node stream function to the complete node stream function. For the transverse gradient coil, it includes both mirror symmetry and centrosymmetry, represented by the nodes in the diagram. Taking a point as an example, it is symmetrical to the other 7 nodes in the complete node. A point whose corresponding element in the mapping matrix is ​​1 indicates... and The flow function values ​​of the nodes are equal; for the example A point whose corresponding element in the mapping matrix is ​​-1 represents... and The stream function values ​​of the nodes are opposite. For the longitudinal gradient coil, its structure exhibits both axisymmetric and mirror symmetric properties. Taking a node on a generatrix in the upper half of the mesh as a representative node, the stream function of that node can be mapped to the symmetric node stream function at the same height and the corresponding node stream function in the lower half, respectively.

[0071] Based on the symmetry of the mesh structure of the target wiring surface, the present invention calculates a mapping matrix that maps the same flow function value to symmetrical mesh nodes, and the complete node flow function distribution can be calculated by representing the node flow function distribution.

[0072] In this process, the symmetry of the gradient coil can be preserved at all times, avoiding the destruction of the wiring symmetry in the final calculation due to local overfitting during the calculation process.

[0073] S3. Simplify the magnetic field matrix using the mapping matrix to obtain the mapped magnetic field matrix; and use the mapping matrix to calculate the mapping optimization matrix corresponding to the optimization matrix. The mapping optimization matrix may include one or more of the following: mapping power consumption matrix, mapping energy storage matrix, mapping force matrix, and mapping torque matrix.

[0074] The mapped magnetic field matrix satisfies the following relationship:

[0075] (2)

[0076] in, To map the magnetic field matrix, For the magnetic field matrix, It is a mapping matrix.

[0077] For quadratic power consumption or energy storage matrices, the mapping relationship can be uniformly expressed as:

[0078] (3)

[0079] in, This represents the mapped power consumption matrix or mapped energy storage matrix. This is a power consumption matrix or energy storage matrix. for The transpose of the matrix;

[0080] For linear quantities such as the force matrix and moment matrix, the mapping relationship can be expressed as:

[0081] (4)

[0082] in, This represents the mapped force matrix or mapped moment matrix. It is the force matrix or torque matrix.

[0083] S4. Based on the mapped magnetic field matrix and combined with the mapped optimization matrix, solve for the representative node flow function using regularization or constraint optimization methods. Based on this, the complete node flow function is obtained from the mapping matrix. ;

[0084] The stream function can be solved using established regularization or constraint optimization methods in this field. For example, it can be solved based on the following constraint optimization problem.

[0085] (5)

[0086] in, This represents the optimization function, which is a function defined by mapping the optimization matrix. This represents the optimal solution. This indicates the target magnetic field to be set. This indicates the permissible magnetic field error.

[0087] An optimization function can be expressed as a combination of several optimization objectives as follows.

[0088] (6)

[0089] in, , , , , The weight coefficient represents the weight of the corresponding optimization objective in the optimization function. The weight coefficient can be 0, but at least one of them is not 0. Represents the mapping power consumption matrix; Represents the mapped energy storage matrix; Represents the mapping force matrix; This represents the mapped torque matrix.

[0090] Complete node stream function The calculation formula is:

[0091] (7)

[0092] in, To represent the node flow function, The complete node flow function is represented by equation (7), which indicates the mapping matrix. It can implement the representative node flow function to complete node flow function The mapping.

[0093] S5 is based on complete node flow functions The stream function is discretized into coil wiring using the stream function discretization method.

[0094] To overcome the stray field leakage problem in the end-shielded region caused by the forced constraint of the mesh boundary to zero in the prior art, this invention provides a stream function discretization method. In this method, the primary and secondary layers of the coil are allowed to use different stream function intervals. Based on the different stream function intervals of the primary and secondary layers, the error caused by the forced constraint of the boundary to zero during the discretization process is distributed to the whole. Based on this method, the stray field leakage in the end-shielded region can be improved and the maximum value of the stray field can be reduced.

[0095] The stream function discretization method specifically involves discretizing the primary and secondary layer stream functions of the gradient coil, respectively, while satisfying the following relationship:

[0096] (8)

[0097] (9)

[0098] in, This represents the maximum value of the flow function in the primary layer. This represents the minimum value of the flow function in the primary layer. This represents the maximum value of the flow function in the secondary layer. This represents the minimum value of the flow function in the secondary layer; The partitioning of the stream function in the primary layer, relative to the minimum value of the stream function, represents the distance between the stream function partitions. The ratio, The partitioning of the stream function in the primary layer, relative to the side closest to the maximum value of the stream function, represents the distance between the stream functions. The ratio, The interval between stream functions in the secondary layer, representing the distance from the minimum stream function to the minimum stream function, is relative to... The ratio, The interval between stream functions in the secondary layer, representing the distance from the maximum value of the stream function to the maximum value, is relative to... The ratio; This indicates the number of discretized contour lines in the primary layer. This indicates the number of discretized contour lines in the secondary layer. The stream function interval for the primary layer. The flow function interval for the secondary layer.

[0099] The ,exist and Given that the integer is an integer, it needs to be combined with... The closest approximation can be calculated using the following formula:

[0100] (10)

[0101] (11)

[0102] in, The function is used to round variables.

[0103] The stream function discretization method requires determining the coil routing based on the stream function contour lines. The stream function values ​​corresponding to the contour lines can be determined based on the following formula:

[0104] (12)

[0105] (13)

[0106] in, The first laminar flow function represents the... The stream function values ​​corresponding to each contour line. The second laminar flow function represents the first... The stream function values ​​corresponding to each contour line.

[0107] Based on equations (12) and (13), a series of stream function values ​​can be determined. The corresponding stream function values ​​are then substituted into the primary and secondary layers to perform contour mapping. The resulting contour lines about the stream function are the coil wiring after stream function discretization.

[0108] The present invention provides a simplified gradient coil design system for magnetic resonance imaging, comprising:

[0109] The first unit is used to perform symmetrical meshing of the wiring surface according to the geometric structure of the wiring and the target magnetic field region, and to set the target magnetic field distribution; then, the magnetic field matrix is ​​calculated and an optimization matrix is ​​established, wherein the optimization matrix includes one or more of the following: power consumption matrix, energy storage matrix, torque matrix, and torque matrix.

[0110] The second unit is used to divide nodes at symmetrical positions into the same group based on the symmetry of the grid nodes, and arbitrarily select a node in each group as the representative node of the group, and calculate the mapping matrix from the representative node flow function to the complete node flow function.

[0111] The third unit is used to simplify the magnetic field matrix through the mapping matrix to obtain the mapped magnetic field matrix; and to use the mapping matrix to calculate the mapping optimization matrix corresponding to the optimization matrix to obtain the mapped power consumption matrix, the mapped energy storage matrix, the mapped force matrix and the mapped torque matrix.

[0112] The fourth unit is used to solve the representative node flow function based on the mapped magnetic field matrix using regularization or constraint optimization methods, and further to obtain the complete node flow function based on the mapping matrix.

[0113] The fifth unit is used to discretize the stream function into coil wiring based on the complete node stream function using the stream function discretization method.

[0114] The present invention provides a computer program product comprising a computer program / instruction that, when executed by a processor, implements the method described herein.

[0115] This embodiment E1 provides a design for a self-shielded longitudinal gradient coil on a cylindrical surface to generate a gradient magnetic field along the Z direction. The primary layer of the coil has a diameter of 254 mm and a length of 620 mm, while the secondary layer has a diameter of 298 mm and a length of 640 mm. Figure 3 The diagram shows the mesh configuration of the longitudinal gradient coil involved in embodiment E1. The mesh has a total of 4032 center nodes, 192 boundary nodes, and 8256 triangular faces. Figure 4 As shown, this embodiment E1 involves the configuration of the target magnetic field of the longitudinal gradient coil, wherein the target linear region has 1297 target magnetic field points and the target shielding surface has 1764 target magnetic field points.

[0116] The magnetic field matrix can be calculated based on the boundary element method. Furthermore, the energy storage matrix was calculated in this embodiment E1. And calculate the power consumption matrix. The magnetic field matrix The energy storage matrix has a size of 3061×4032. The power consumption matrix has a size of 4032×4032. The size is 4032×4032.

[0117] Calculate the mapping matrix based on the symmetry of the longitudinal gradient coil current function. Its size is 4032×84, which is used to map the representative node flow function vector of size 84×1 to the complete node flow function vector of size 4032×1.

[0118] The mapped magnetic field matrix can be calculated based on the mapping matrix. Size is 3061×84; Mapped energy storage matrix The size is 84×84, and the mapping power consumption matrix is... The size is 84×84.

[0119] In this embodiment E1, the following energy storage-based optimization function is used:

[0120] (14)

[0121] in, To optimize the function, for The transpose of .

[0122] The linearity constraint is 2%, and the stray field constraint is 1.4Gs, which are used as constraints.

[0123] Using the mapping power consumption matrix as a regularization term, a set of representative node flow functions is obtained based on the regularization. Let be the initial value for the optimization process. The optimization is implemented using the "fmincon" function in Matlab.

[0124] Solving vectors And further mapped to To implement the boundary constraints of the stream function, the stream function of the boundary nodes is supplemented with zeros.

[0125] Figure 5 (a) is a schematic diagram of the traditional stream function discretization method. Figure 5 Image (b) is a schematic diagram of the stream function discretization method of the present invention. In conventional stream function discretization methods, it is necessary to ensure that the overall stream function interval is consistent, that is, to uniformly adopt the stream function interval. This leads to uncontrolled intervals of the stream function values ​​at the ends of the primary and secondary layers of the cylindrical coil, making it prone to local stray field leakage. The stream function discretization method in this invention allows for deviations in the stream function intervals between the primary and secondary layers, achieving control over the end stream function intervals. Preferably, the... , , , Set it to 0.5.

[0126] For the stream function discretization process, the first step is to select the number of contour lines for the primary layer. Furthermore, based on equation (10), the number of contour lines in the secondary layer can be calculated. Based on equations (8) and (11), the stream function intervals of the primary and secondary layers can be determined. and .

[0127] Figure 6 In (a), the stray field distribution generated by the wiring on the shielding surface along the axis is obtained based on the traditional stream function discretization method. The stream function interval ratio coefficient is 0.5 and 0.5 at the maximum and minimum values ​​of the overall stream function, respectively. After discretization, the maximum value of the stray field generated by the coil is 8.8 Gauss. Figure 6 Image (b) shows the stray field distribution along the shielding surface obtained by the stream function discretization method proposed in this invention. Preferably, , , , The value is uniformly set to 0.5, and the maximum value of the stray field generated by the discretized coil is 4.3 Gauss.

[0128] Figure 7 This is a wiring diagram of the longitudinal gradient coil in embodiment E1, where (a) is a schematic diagram of the three-dimensional wiring distribution of the coil, (b) is a schematic diagram of the wiring unfolded in the primary layer of the coil, and (c) is a schematic diagram of the wiring unfolded in the secondary layer of the coil.

[0129] Based on the results of this embodiment E1, the longitudinal gradient coil design method can effectively reduce the number of optimization variables of the stream function and the size of the optimization matrix during the solution process. In addition, the discretization method can effectively reduce the maximum stray field intensity of the gradient coil.

[0130] Example E2 is a bipolar longitudinal gradient coil used to generate a gradient magnetic field along the Z direction. It is designed according to steps S1 to S5 described above.

[0131] Figure 8 In Figure (a), the wiring mesh of Example E2 is shown. Figure 8 (b) is a wiring diagram of the longitudinal gradient coil in Example E2.

[0132] For embodiment E2, a series of nodes along their respective radii on the upper surface of the primary layer and the upper surface of the secondary layer are used as representative nodes. These nodes can be mapped to nodes of equal radius on the same surface and nodes of equal radius on the symmetrical lower surface. For the same surface with the same radius, the flow function values ​​are equal, and the mapping matrix element is "1". For symmetrical surfaces, the mapped flow function values ​​are related to the normal directions of the upper and lower surfaces. If the normal directions of the upper and lower surfaces are in the same direction, the flow function mapping values ​​between the upper and lower surfaces are opposite, and the mapping matrix element is "-1". If the normal directions of the upper and lower surfaces are opposite, the flow function mapping values ​​between the upper and lower surfaces are the same, and the mapping matrix element is "1".

[0133] For Example E2, the representative node flow function is solved by regularizing the power consumption matrix. For stream function discretization , , , Set it to 0.5.

[0134] In summary, the method of this invention solves the problem of low solution efficiency caused by excessively large calculation matrices in the design of gradient coils in the prior art, and reduces the ill-conditioned nature of the solution. In addition, it can avoid the destruction of the original symmetry of the gradient coil due to local overfitting caused by insufficient or uneven setting of target field points. Furthermore, this invention provides a stream function discretization method to improve the stray field leakage problem in the end shielding region of existing gradient coils.

[0135] The implementation methods of the present invention should not be limited to the above embodiments. All modifications, substitutions or improvements within the scope of the ideas and technical solutions of the present invention should be considered within the protection scope of the present invention.

Claims

1. A simplified method for designing gradient coils for magnetic resonance imaging, characterized in that, Includes the following steps: Based on the geometry of the wiring and the target magnetic field region, the wiring surface is divided into symmetrical grids, and the target magnetic field distribution is set. Then, the magnetic field matrix is ​​calculated, and an optimization matrix is ​​established. The optimization matrix includes one or more of the following: power consumption matrix, energy storage matrix, torque matrix, and torque matrix. Based on the symmetry of the grid nodes, nodes at symmetrical positions are grouped together, and a node is randomly selected from each group as the representative node of that group. The mapping matrix from the representative node flow function to the complete node flow function is calculated. The magnetic field matrix is ​​simplified by using a mapping matrix to obtain the mapped magnetic field matrix; The mapping optimization matrix corresponding to the optimization matrix is ​​calculated using the mapping matrix, resulting in one or more of the following: mapping power consumption matrix, mapping energy storage matrix, mapping force matrix, and mapping torque matrix. Based on the mapped magnetic field matrix and combined with the mapped optimization matrix, the representative node flow function is solved using regularization or constraint optimization methods, and the complete node flow function is further obtained based on the mapping matrix. Complete node stream function The calculation methods include: ； in, Represents the optimization function. This represents the optimal solution. To map the magnetic field matrix, To represent the node flow function, This indicates the target magnetic field to be set. Indicates the allowable magnetic field error; The optimization function is represented as a combination of several optimization objectives: ； in, , , , , These are weighting coefficients, representing the weight of the corresponding optimization objective in the optimization function, and at least one of these weighting coefficients is not 0; Represents the mapping power consumption matrix; Represents the mapped energy storage matrix; Represents the mapping force matrix; Represents the mapped moment matrix. for Transpose of; Complete node stream function The calculation formula is: ； in, It is a mapping matrix; Based on the complete node flow function, the flow function is discretized into coil wiring using the flow function discretization method.

2. The simplified method according to claim 1, characterized in that, The elements of the mapping matrix are filled with values ​​of 1, -1, or 0 according to the symmetry relationship of the stream function of the corresponding node; represented as: ； in, Represents the first in the mapping matrix Line number The elements of the column.

3. The simplified method according to claim 1, characterized in that, The expression for the mapped magnetic field matrix is: ； in, To map the magnetic field matrix, For the magnetic field matrix, It is a mapping matrix.

4. The simplified method according to claim 1, characterized in that, The expressions for the mapped power consumption matrix and the mapped energy storage matrix are: ； in, This represents the mapped power consumption matrix or mapped energy storage matrix. This is a power consumption matrix or energy storage matrix. for The transpose of the matrix, It is a mapping matrix; The expressions for the mapped force matrix and the mapped moment matrix are: ； in, This represents the mapped force matrix or mapped moment matrix. It is the force matrix or torque matrix.

5. The simplified method according to claim 1, characterized in that, Stream function discretization methods include: The primary and secondary laminar flow functions of the gradient coil are discretized respectively, and the following relationship is satisfied: ； ； in, This represents the maximum value of the flow function in the primary layer. This represents the minimum value of the flow function in the primary layer. This represents the maximum value of the flow function in the secondary layer. This represents the minimum value of the flow function in the secondary layer; The partitioning of the stream function in the primary layer, relative to the minimum value of the stream function, represents the distance between the stream function partitions. The ratio, The partitioning of the stream function in the primary layer, relative to the side closest to the maximum value of the stream function, represents the distance between the stream functions. The ratio, The interval between stream functions in the secondary layer, representing the distance from the minimum stream function to the minimum stream function, is relative to... The ratio, The interval between stream functions in the secondary layer, representing the distance from the maximum value of the stream function to the maximum value, is relative to... The ratio; This indicates the number of discretized contour lines in the primary layer. This indicates the number of discretized contour lines in the secondary layer. The stream function interval for the primary layer. The flow function interval for the secondary layer.

6. The simplified method according to claim 5, characterized in that, The ,exist and Given that the integer is an integer, it needs to be combined with... The closest approximation is calculated using the following formula: ； ； in, The function is used to round variables.

7. The simplified method according to claim 5, characterized in that, The stream function discretization method requires determining the coil routing based on the contour lines of the stream function. The stream function values ​​corresponding to the contour lines are determined based on the following formula: ； ； in, The first laminar flow function represents the... The stream function values ​​corresponding to each contour line. The second laminar flow function represents the first... The stream function values ​​corresponding to each contour line.

8. A simplified gradient coil design system for magnetic resonance imaging, characterized in that, include: The first unit is used to divide the wiring surface into symmetrical grids according to the geometric structure of the wiring and the target magnetic field region, and to set the target magnetic field distribution. Then, the magnetic field matrix is ​​calculated, and an optimization matrix is ​​established. The optimization matrix includes one or more of the following: power consumption matrix, energy storage matrix, torque matrix, and torque matrix. The second unit is used to divide nodes at symmetrical positions into the same group based on the symmetry of the grid nodes, and arbitrarily select a node in each group as the representative node of the group, and calculate the mapping matrix from the representative node flow function to the complete node flow function. The third unit is used to simplify the magnetic field matrix through the mapping matrix to obtain the mapped magnetic field matrix; The mapping optimization matrix corresponding to the optimization matrix is ​​calculated using the mapping matrix, resulting in the mapping power consumption matrix, mapping energy storage matrix, mapping force matrix, and mapping torque matrix. The fourth unit is used to solve for the representative nodal flow function based on the mapped magnetic field matrix, using regularization or constrained optimization methods, and further to obtain the complete nodal flow function from the mapping matrix; the complete nodal flow function. The calculation methods include: ； in, Represents the optimization function. This represents the optimal solution. To map the magnetic field matrix, To represent the node flow function, This indicates the target magnetic field to be set. Indicates the allowable magnetic field error; The optimization function is represented as a combination of several optimization objectives: ； in, , , , , These are weighting coefficients, representing the weight of the corresponding optimization objective in the optimization function, and at least one of these weighting coefficients is not 0; Represents the mapping power consumption matrix; Represents the mapped energy storage matrix; Represents the mapping force matrix; Represents the mapped moment matrix. for Transpose of; Complete node stream function The calculation formula is: ； in, It is a mapping matrix; The fifth unit is used to discretize the stream function into coil wiring based on the complete node stream function using the stream function discretization method.

9. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the method described in any one of claims 1-7.

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