Plug-in gradient coil design method based on curved surface implication substrate

Abstract

The invention relates to the technical field of gradient coil manufacturing, in particular to an inserted gradient coil design method based on a curved surface implication substrate. Comprises: establishing an optimization model; constructing a target function, and carrying out sensitivity analysis and derivation; obtaining a linear equation set related to an intrinsic substrate corresponding coefficient through sensitivity derivation; obtaining a basis coefficient corresponding to the optimal flow function solution by solving the linear equation set; and a final stream function optimization result is solved through definition of a stream function by an intrinsic substrate, and a gradient coil configuration is obtained. The method has the advantages that the flow function is defined by using a smooth intrinsic orthogonal substrate; when the method is applied to coil design, the obtained coil has good smoothness, and extra discussion on the smoothness problem of the coil in a traditional method is avoided; the method has a good application effect on a traditional cylindrical curved surface and a complex common curved surface.

Description

Technical Field

[0001] The invention relates to the technical field of gradient coil manufacturing, and in particular to a design method for an inserted gradient coil based on a curved surface intrinsic substrate. Background Art

[0002] Magnetic resonance imaging (MRI) is an advanced imaging technology widely used in clinical medicine, biology, polymer chemistry and other fields. The gradient coil is an important component of the MRI system. Its function is to generate a gradient magnetic field to provide spatial encoding of the imaging area. Traditional coil structures mostly use regular curved surfaces such as cylinders as current-carrying surfaces. In recent years, various types of coil structures with anisotropic current-carrying surfaces that fit the imaging object have been proposed. However, complex current-carrying surfaces also bring new challenges to coil design. The smoothness of the designed coil is also more difficult to ensure on non-developable surfaces. Therefore, it is necessary to develop new gradient coil design schemes to meet the increasingly complex needs of coil structures in the future.

[0003] In the prior art, there is a problem of difficult-to-control coil smoothness caused by numerical oscillation in the traditional stream function method. Therefore, during the design process, designers need to make trade-offs between various coil parameters, resulting in poor robustness of the final coil. Summary of the invention

[0004] In order to solve the above problems, the present invention provides a design method of an inserted gradient coil based on a curved surface intrinsic basis.

[0005] The present invention aims to provide a method for designing an inserted gradient coil based on a curved surface intrinsic basis, which specifically comprises the following steps: S1. Determine the current-carrying surface and imaging area of ​​the coil and establish an optimization model; S2. construct an objective function based on the optimization model, where the objective function includes a main objective function and an auxiliary objective function; S3. Set the sensitivity of the objective function to the design variables to zero, and after discretizing and calculating the objective function, obtain the corresponding linear equations; and obtain the stream function result by solving the linear equations; S4. Obtain a set of orthogonal and complete basis functions by calculating and solving the eigenvalue problem of the current-carrying surface; S5. Perform preliminary optimization calculations with different numbers of bases, compare various coil parameters of the optimization results, and select the optimal number of bases that can obtain a stable coil structure; S6. according to the determined optimal number of bases, obtaining the optimal auxiliary target weight by L-curve method; S7. Perform final optimization calculations on various coil parameters based on the optimization results to obtain the optimal stream function distribution and the final configuration of the gradient coil; obtain the final gradient coil loop based on the definition of the stream function.

[0006] Preferably, the current density on the current-carrying surface is defined by the following formula: ; in, is the tangent gradient operator on the current-carrying surface, is the stream function defined on the current-carrying surface, n is the external normal vector on the current-carrying surface; Stream Function The expression is as follows:

[0007] in, Nodes on the current-carrying surface The stream function value at is the intrinsic basis number, is the number of intrinsic bases used, is the coefficient corresponding to the basis, is the basis function at the node The value at .

[0008] Preferably, the expression of the objective function is: ; In the formula, f 0 and f 1 Represent the main objective function and auxiliary objective function respectively; The expression of the main goal is as follows: ; In the formula, represents the number of sampling points in the imaging area, Represents discrete node number; Represents the target gradient field, through the gradient strength Multiply by the position along the gradient direction , or calculate; is about the basis coefficient Function, indicating the node Where Towards the actual magnetic field; The expression of the auxiliary objective is as follows: ; In the formula, is the material conductivity, is the thickness of the conductive layer, represents the integral over the coil design surface.

[0009] Preferably, Calculated by Biot-Savart law: ; In the formula, , , represents the position along the gradient direction, c represents the basis coefficient, n x Representation Surface The x-component of the normal vector, n y Representation Surface The y component of the normal vector, n z Representation Surface The z-component of the normal vector.

[0010] Preferably, the linear equations in step S3 are expressed as follows: ; In the formula, Represents the sensitivity matrix of the magnetic field at the target position to the coefficients to be solved , express The transposed matrix of represents the energy consumption matrix of coil optimization, Represents a matrix composed of basis functions arranged in rows , represents the column vector consisting of the target magnetic field .

[0011] Preferably, in step S4, the stream function on the current-carrying surface is expressed as: ; in, is the stream function scalar field on the current-carrying surface, is the intrinsic basis number, is the number of intrinsic bases used, is the coefficient corresponding to the basis, are basis functions defined on the current-carrying surface.

[0012] Preferably, step S6 specifically includes: selecting a series of different auxiliary target weights for calculation, constructing a relationship curve using the main target value and the auxiliary target value of the corresponding calculation results, and selecting the auxiliary target weight at the inflection point from the relationship curve for calculation.

[0013] Preferably, the number of substrates is greater than 20 and not more than 100.

[0014] Compared with the prior art, the present invention can achieve the following beneficial effects: The present invention provides a gradient coil design method, which uses a smooth intrinsic orthogonal basis to define the stream function; constructs an objective function based on this definition, and performs sensitivity analysis and derivation; obtains a linear equation group related to the coefficients corresponding to the intrinsic basis through sensitivity derivation; obtains the basis coefficients corresponding to the optimal stream function solution by solving the linear equation group; and obtains the final stream function optimization result through the definition of the stream function by the intrinsic basis. The method has a good application effect on both traditional cylindrical surfaces and complex general surfaces, and when the method is applied to coil design, since the function as the basis itself is smooth, the obtained coil also has good smoothness, which can avoid additional discussion on the coil smoothness problem in the traditional method, that is, avoids the difficult-to-control coil smoothness problem caused by numerical oscillation in the traditional stream function method, and also avoids the designer's choice between various coil parameters, enriches the coil configuration, and makes the coil design more robust. By applying the method to the coil design of cylindrical surfaces and human head surfaces, the obtained calculation results and simulations show that the method is practical and effective. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of a method for designing an inserted gradient coil based on a curved surface intrinsic basis provided in accordance with an embodiment of the present invention.

[0016] Figure 2 Schematic diagram of the gradient coil optimization model provided according to Example 1 of the present invention.

[0017] Figure 3 Schematic diagram of a gradient coil optimization model provided according to Example 2 of the present invention.

[0018] Figure 4 It is a schematic diagram of the definition of a convection function provided according to an embodiment of the present invention.

[0019] Figure 5 It is a schematic diagram of a 40-order intrinsic basis of a cylindrical surface provided according to an embodiment of the present invention.

[0020] Figure 6 40-order intrinsic basis diagram of a human head curve provided by an embodiment of the present invention.

[0021] Figure 7 1 is a coil parameter curve under different substrate numbers provided according to an embodiment of the present invention.

[0022] Figure 8 Schematic diagram of an L-curve of a main target with respect to an auxiliary target provided according to an embodiment of the present invention.

[0023] Reference numerals: 101.Cylindrical current-carrying surface; 102. Current-carrying surface of human head; 2. Imaging area. DETAILED DESCRIPTION

[0024] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same modules are represented by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, the detailed description thereof will not be repeated.

[0025] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0026] The present invention provides a method for designing an inserted gradient coil based on a curved surface intrinsic basis (see flowchart). Figure 1 ), the gradient coil designed by this method can generate a magnetic field with a gradient distribution along a certain direction after being energized; specifically comprising the following steps: S1. Determine the current-carrying surface and imaging area of ​​the coil and establish an optimization model; the current-carrying surface is used to carry the current density, and the imaging area is used to calculate the magnetic field; The current density on a current-carrying surface is defined by: ; in, is the tangent gradient operator on the current-carrying surface, is the stream function defined on the current-carrying surface, n is the external normal vector on the current-carrying surface; Stream Function By defining the intrinsic basis, the expression is as follows:

[0027] in, Nodes on the current-carrying surface The stream function value at is the intrinsic basis number, is the number of intrinsic bases used, is the coefficient corresponding to the basis, is the basis function at the node The value at .

[0028] S2. Construct an objective function based on the optimization model. The objective function includes a main objective function and an auxiliary objective function. The main objective is to control the gradient linearity of the entire coil structure, and the auxiliary objective is to control the energy consumption of the coil (the main objective function is usually selected as the linearity of the magnetic field generated by the coil, and the auxiliary objective function is usually selected as the energy consumption of the coil); The expression of the objective function is: ; In the formula, f 0 and f 1 Represent the main objective function and auxiliary objective function respectively; The expression of the main goal is as follows: ; In the formula, represents the number of sampling points in the imaging area, Represents discrete node number; Represents the target gradient field, which can be expressed by the gradient strength Multiply by the position along the gradient direction (or , )calculate; is a coefficient about the basis Function, indicating the node Where The actual magnetic field can be calculated using the Biot-Savart law: ; In the formula, , , represents the position along the gradient direction, c represents the basis coefficient, n x Representation Surface The x-component of the normal vector, n y Representation Surface The y component of the normal vector, n z Representation Surface The z-component of the normal vector; The expression of the auxiliary objective is as follows: ; In the formula, is the material conductivity, is the thickness of the conductive layer, represents the integral over the coil design surface.

[0029] S3. Calculate the sensitivity of the main objective and the auxiliary objective with respect to the design variables respectively; set the sum of the sensitivities of the main objective and the auxiliary objective with respect to the design variables to zero, discretize and calculate the linear equations corresponding to solving the optimization problem; obtain the stream function result by solving the linear equations; The linear system of equations is expressed as follows: ; In the formula, express , that is, the sensitivity matrix of the magnetic field at the target position to the coefficients to be solved; express The transposed matrix of represents the energy consumption matrix of coil optimization; express , that is, the matrix composed of basis functions arranged in rows; express , which is a column vector consisting of the target magnetic field.

[0030] S4. By calculating and solving the eigenvalue problem of the current-carrying surface, a set of orthogonal and complete basis functions is obtained. The basis functions can linearly represent any second-order smooth function on the current-carrying surface; thus, the stream function on the current-carrying surface can be linearly represented as: ; in, is the stream function scalar field on the current-carrying surface, is the intrinsic basis number, is the number of intrinsic bases used, is the coefficient corresponding to the basis, are basis functions defined on the current-carrying surface.

[0031] S5. Perform preliminary optimization calculations with different numbers of substrates, compare the various parameters of the coils obtained from the optimization results, and select the best number of substrates that can obtain a stable coil structure; usually the number of substrates should be greater than 20 and not more than 100.

[0032] S6. According to the determined optimal number of bases, the optimal auxiliary target weight is obtained by the L-curve method; the specific method is as follows: a series of different auxiliary target weights are selected for calculation, and a relationship curve (the curve is usually L-shaped) is constructed using the main target value and the auxiliary target value of the corresponding calculation results, and the auxiliary target weight at the inflection point is selected from the relationship curve for calculation.

[0033] S7. Perform final optimization calculations on various coil parameters based on the optimization results to obtain the optimal stream function distribution and the final configuration of the gradient coil; obtain the final gradient coil loop based on the definition of the stream function.

[0034] Example 1 This embodiment provides a method for designing an inserted gradient coil based on a curved surface intrinsic basis, which specifically includes the following steps: S1. Establishing an optimization model: Determine the cylindrical current-carrying surface 101 and imaging area 2 of the coil and establish an optimization model; the cylindrical current-carrying surface 101 is used to carry the current density, and the imaging area 2 is used to calculate the magnetic field (see Figure 2 ); The current density on the cylindrical current-carrying curved surface 101 is defined by the following formula: ; in, is the tangent gradient operator on the current-carrying surface, is the stream function defined on the current-carrying surface, n is the external normal vector on the current-carrying surface; Different from the prior art, the stream function By defining the intrinsic basis, the expression is as follows:

[0035] in, Nodes on the current-carrying surface The stream function value at is the intrinsic basis number, is the number of intrinsic bases used, is the coefficient corresponding to the basis, is the basis function at the node The value at Figure 4 ).

[0036] S2. Construct objective function: Construct objective function based on optimization model, which includes main objective function and auxiliary objective function. The main objective is to control the overall gradient linearity of coil structure, and the auxiliary objective is to control the energy consumption of coil (the main objective function is usually selected as the linearity of magnetic field generated by coil, and the auxiliary objective function is usually selected as the energy consumption of coil).

[0037] S3. Sensitivity analysis: Calculate the sensitivity of the main objective and the auxiliary objective with respect to the design variables respectively; set the sum of the sensitivities of the main objective and the auxiliary objective with respect to the design variables to zero, discretize and calculate the linear equations corresponding to solving the optimization problem; obtain the stream function result by solving the linear equations.

[0038] S4. By calculating and solving the eigenvalue problem of the cylindrical current-carrying surface 101, a set of orthogonal and complete basis functions is obtained. The basis functions can linearly represent any second-order smooth function on the current-carrying surface. The first 40-order intrinsic basis of the cylindrical current-carrying surface 101 is as follows: Figure 5 shown.

[0039] S5. Perform preliminary optimization calculations with different numbers of substrates, compare the various parameters of the coils obtained from the optimization results, and select the best number of substrates that can obtain a stable coil structure. The coil parameter curves under different numbers of substrates are shown in Figure 1. Figure 6 shown.

[0040] S6. According to the determined optimal number of bases, the optimal auxiliary target weight is obtained by the L-curve method; the specific method is as follows: a series of different auxiliary target weights are selected for calculation, and a relationship curve is constructed using the main target value and the auxiliary target value of the corresponding calculation results ( Figure 7 ), the auxiliary target weight at the inflection point is selected from the relationship curve for calculation.

[0041] S7. Perform the final optimization calculation based on the coil parameters of the optimization results to obtain the optimal stream function distribution and the final configuration of the gradient coil; obtain the final gradient coil loop based on the definition of the stream function. Figure 8 shown.

[0042] Example 2 This embodiment provides a method for designing an inserted gradient coil based on a curved surface intrinsic basis, which specifically includes the following steps: S1. Establishing an optimization model: Determine the current-carrying curved surface 102 of the coil and the imaging area 2, and establish an optimization model; the current-carrying curved surface 102 of the coil is used to carry the current density, and the imaging area 2 is used to calculate the magnetic field (see Figure 3 ); The current density on the cylindrical current-carrying surface 1 is defined by the following formula: ; in, is the tangent gradient operator on the current-carrying surface, is the stream function defined on the current-carrying surface, n is the external normal vector on the current-carrying surface; Different from the prior art, the stream function By defining the intrinsic basis, the expression is as follows:

[0043] in, Nodes on the current-carrying surface The stream function value at is the intrinsic basis number, is the number of intrinsic bases used, is the coefficient corresponding to the basis, is the basis function at the node The value at Figure 4 ).

[0044] S2. Construct objective function: Construct objective function based on optimization model, which includes main objective function and auxiliary objective function. The main objective is to control the overall gradient linearity of coil structure, and the auxiliary objective is to control the energy consumption of coil (the main objective function is usually selected as the linearity of magnetic field generated by coil, and the auxiliary objective function is usually selected as the energy consumption of coil).

[0045] S3. Sensitivity analysis: Calculate the sensitivity of the main objective and the auxiliary objective with respect to the design variables respectively; set the sum of the sensitivities of the main objective and the auxiliary objective with respect to the design variables to zero, discretize and calculate the linear equations corresponding to solving the optimization problem; obtain the stream function result by solving the linear equations.

[0046] S4. By calculating and solving the eigenvalue problem of the head current-carrying surface 102, a set of orthogonal and complete basis functions is obtained. The basis functions can linearly represent any second-order smooth function on the current-carrying surface. The first 40-order intrinsic basis corresponding to the cylindrical current-carrying surface 1 is as follows: Figure 6 shown.

[0047] S5. Perform preliminary optimization calculations with different numbers of substrates, compare various coil parameters of the optimization results, and select the best number of substrates that can obtain a stable coil structure.

[0048] S6. According to the determined optimal number of bases, the optimal auxiliary target weight is obtained by the L-curve method; the specific method is as follows: a series of different auxiliary target weights are selected for calculation, a relationship curve is constructed using the main target value and the auxiliary target value of the corresponding calculation results, and the auxiliary target weight at the inflection point is selected from the relationship curve for calculation.

[0049] S7. Perform the final optimization calculation based on the coil parameters of the optimization results to obtain the optimal stream function distribution and the final configuration of the gradient coil; obtain the final gradient coil loop based on the definition of the stream function. Figure 8 shown.

[0050] Brief description of the present invention: The optimization model includes the current-carrying surface and imaging area of ​​the coil design. The objective function should include the main objective function and the auxiliary objective function, wherein the main objective function is usually selected as the linearity of the magnetic field generated by the coil, and the auxiliary objective function is usually selected as the energy consumption of the coil. Sensitivity analysis requires calculating the sensitivity of the main objective and the auxiliary objective relative to the design variables respectively. Then, by setting the sum of their sensitivities to zero, a linear equation system for solving the optimization problem is obtained. To obtain the intrinsic basis of the surface, it is necessary to calculate the eigenvalue problem of the surface and then obtain a series of linearly independent and complete basis functions. Determining the number of bases is to obtain the minimum number of bases required to ensure the convergence of the coil structure by calculation. Determining the auxiliary objective weight is to obtain the best auxiliary objective weight that can balance the two design objectives through numerical methods. Finally, based on the parameters obtained in the above steps, the optimal stream function distribution is calculated.

[0051] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0052] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for designing an inserted gradient coil based on a curved surface intrinsic basis, characterized in that: The specific steps include: S1. Determine the current-carrying surface and imaging area of ​​the coil and establish an optimization model; S2. construct an objective function based on the optimization model, where the objective function includes a main objective function and an auxiliary objective function; S3. Set the sensitivity of the objective function to the design variables to zero, and after discretizing and calculating the objective function, obtain the corresponding linear equations; and obtain the stream function result by solving the linear equations; S4. Obtain a set of orthogonal and complete basis functions by calculating and solving the eigenvalue problem of the current-carrying surface; S5. Perform preliminary optimization calculations with different numbers of bases, compare various coil parameters of the optimization results, and select the optimal number of bases that can obtain a stable coil structure; S6. according to the determined optimal number of bases, obtaining the optimal auxiliary target weight by L-curve method; S7. Perform final optimization calculations on various coil parameters based on the optimization results to obtain the optimal stream function distribution and the final configuration of the gradient coil; obtain the final gradient coil loop based on the definition of the stream function.

2. The method for designing an inserted gradient coil based on a curved surface intrinsic basis according to claim 1, characterized in that: The current density on the current-carrying surface is defined by the following formula: ； in, is the tangent gradient operator on the current-carrying surface, is the stream function defined on the current-carrying surface, n is the external normal vector on the current-carrying surface; Stream Function The expression is as follows: in, Nodes on the current-carrying surface The stream function value at is the intrinsic basis number, is the number of intrinsic bases used, is the coefficient corresponding to the basis, is the basis function at the node The value at .

3. The method for designing an inserted gradient coil based on a curved surface intrinsic basis according to claim 1, characterized in that: The expression of the objective function is: ； In the formula, f 0 and f 1 represents the main objective function and the auxiliary objective function respectively; The expression of the main goal is as follows: ； In the formula, represents the number of sampling points in the imaging area, Represents discrete node number; Represents the target gradient field, through the gradient strength Multiply by the position along the gradient direction , or calculate; is about the basis coefficient Function, indicating the node Where Towards the actual magnetic field; The expression of the auxiliary objective is as follows: ； In the formula, is the material conductivity, is the thickness of the conductive layer, represents the integral over the coil design surface.

4. The method for designing an inserted gradient coil based on a curved surface intrinsic basis according to claim 3, characterized in that: Calculated by Biot-Savart law: ； In the formula, , , represents the position along the gradient direction, c represents the basis coefficient, n x Representation Surface The x-component of the normal vector, n y Representation Surface The y component of the normal vector, n z Representation Surface The z-component of the normal vector.

5. The method for designing an inserted gradient coil based on a curved surface intrinsic basis according to claim 1, characterized in that: The linear equation system in step S3 is expressed as follows: ； In the formula, Represents the sensitivity matrix of the magnetic field at the target position to the coefficients to be solved , express The transposed matrix of represents the energy consumption matrix of coil optimization, Represents a matrix composed of basis functions arranged in rows , represents the column vector consisting of the target magnetic field .

6. The method for designing an inserted gradient coil based on a curved surface intrinsic basis according to claim 1, characterized in that: In step S4, the stream function on the current-carrying surface is expressed as follows using the basis function: ； in, is the stream function scalar field on the current-carrying surface, is the intrinsic basis number, is the number of intrinsic bases used, is the coefficient corresponding to the basis, are basis functions defined on the current-carrying surface.

7. The method for designing an inserted gradient coil based on a curved surface intrinsic basis according to claim 1, characterized in that: The step S6 specifically includes: selecting a series of different auxiliary target weights for calculation, constructing a relationship curve using the main target value and the auxiliary target value of the corresponding calculation results, and selecting the auxiliary target weight at the inflection point from the relationship curve for calculation.

8. The method for designing an inserted gradient coil based on a curved surface intrinsic basis according to any one of claims 1 to 7, characterized in that: The number of bases is greater than 20 and less than 100.

Images