Passive shimming method based on shimming sheet displacement

Abstract

The invention discloses a passive shimming method based on shimming sheet displacement, and the method comprises the following steps: determining a group of shimming sheet distribution information which comprises the initial installation position of a shimming sheet, the space size of the shimming sheet, and the shimming sheet; after the shimming sheet is installed, magnetic field distribution information, including a magnetic field value of a main magnetic field direction component and spatial position information of a measurement point, of the surface of the target area is measured; based on the shimming piece distribution information and the magnetic field distribution information, an optimization problem is established, and the optimization problem comprises a weighted objective function about magnetic field deviation and total shimming piece displacement and constraint conditions determined based on the magnetic field uniformity and the maximum shimming piece displacement; and solving the optimization problem to obtain the displacement of the shimming sheet, and operating the target shimming sheet based on the displacement. Shimming errors are effectively made up through the displacement of the shimming sheets, and excessive use of the shimming sheets in the shimming iteration process is avoided.

Description

Technical Field

[0001] The invention relates to the field of magnetic resonance technology, and in particular to a passive shimming method based on shim piece displacement. Background Art

[0002] Passive shimming technology is mainly used to optimize the magnetic field uniformity of magnetic resonance imaging (MRI) equipment. The magnet is the core of the MRI system and is used to generate a highly uniform main magnetic field. However, due to the structure of the magnet itself, manufacturing errors and magnetic interference in the environment, the main magnetic field usually has inhomogeneities, which affects the imaging quality. Passive shimming is to adjust and compensate for the inhomogeneity of the main magnetic field by placing shimming pieces such as magnetic sheets or iron sheets of specific shapes and positions around the magnet. Compared with active shimming, passive shimming does not require additional power supplies or complex control systems, and has the advantages of low cost, simple structure and less maintenance requirements. Therefore, in many portable MRI systems, passive shimming is usually relied on to improve the uniformity of the magnetic field, and in some MRI systems with high stability requirements, passive shimming is also an important supplementary technology.

[0003] Passive shimming based on shim sheets is usually calculated based on the magnetic dipole hypothesis or Biot-Savart theorem to generate the magnetic field. In practical applications, equivalent variables such as the volume, thickness, quantity, and area of ​​the shim sheets are usually used for optimization calculations. However, the change in magnetic field caused by the position of the magnetic sheet is usually ignored. Chinese invention patent CN114636958A discloses a method for shimming iron sheets, which uses the thickness of the shim iron sheet as the optimization variable and does not consider displacement as a supplementary means of shimming. Chinese invention patent CN110308411A discloses a high-precision and fast passive shimming method for Halbach magnets. The method realizes shimming adjustment without using additional iron sheets, but is only applicable to Halbach configuration magnets and requires radial adjustability, which has certain limitations and is difficult to achieve in conventional shimming.

[0004] For conventional passive shimming methods, the manufacturing specifications and manufacturing accuracy of the shims determine the discontinuity and manufacturing errors in the magnetized volume of the shims. There are also installation errors in the installation process of the shims. The existence of these errors will reduce the shimming effect and cannot be avoided in the conventional shimming process. In addition, the pre-setting of shim slots or grid points may limit the spatial freedom of passive shimming. And through continuous iteration of passive shimming, the amount of shims used will be further increased. Summary of the invention

[0005] The purpose of the present invention is to provide a passive shimming method based on shim plate displacement to solve the problems of discontinuity and manufacturing error in the magnetization volume of shims and installation error in the shim plate installation process in the prior art.

[0006] To achieve the above object, the present invention adopts the following technical solution:

[0007] A passive shimming method based on shim plate displacement comprises the following steps:

[0008] Step S1, determining a set of shim distribution information by a passive shimming method, wherein the shim distribution information includes an initial installation position of the shim, a spatial size of the shim, and the shim;

[0009] Step S2, after installing the shims, measuring the magnetic field distribution information on the surface of the target area, wherein the magnetic field distribution information includes the magnetic field value of the main magnetic field direction component and the spatial position information of the measuring point;

[0010] Step S3, establishing an optimization problem based on the shim distribution information obtained in step S1 and the magnetic field distribution information obtained in step S2, wherein the optimization problem includes a weighted objective function regarding the magnetic field deviation and the total displacement of the shims, and a constraint condition determined based on the magnetic field uniformity and the maximum displacement of the shims;

[0011] Step S4, solving the optimization problem established in step S3, obtaining the displacement of the shim, and operating the target shim based on the displacement.

[0012] Furthermore, in step S1, the shims need to determine the initial installation distribution. Before implementing the passive shimming method, the shims should be detachably fixed and movable and adjustable; displacement adjustment during shimming can be achieved by one or more methods such as magnetic adsorption, debonding, and movable mechanical structure.

[0013] Furthermore, in step S3, the optimization problem is achieved by minimizing a norm of the objective function, and the optimization problem is expressed as follows:

[0014]

[0015] -d max ≤X≤d max (3)

[0016] -d max ≤Y≤d max (4)

[0017] Among them, A x , A y Represents the coefficient matrix for displacement calculation in the x-direction and y-direction, d max is the constraint limit on the displacement of the magnetic disk; ε is the allowable uniformity error; B z1 is the test magnetic field data after the initial shimming based on the shim film; X and Y are the displacements of the shim film; w is the weight coefficient used to control the proportion of the minimized total movement in the optimization function.

[0018] Furthermore, in step S4, when solving the optimization problem, the optimization problem is simplified as follows:

[0019] Let A=[A x A y ], And further let |D|=u, The problem is transformed into the following linear programming problem:

[0020] MinimizeΣv+wΣu(5)

[0021] Du≤0 (6)

[0022] -Du≤0 (7)

[0023]

[0024]

[0025] u≥0 (12)

[0026] v≥0 (13)

[0027] D≥-d max (14)

[0028] D≤d max (15)

[0029] in, It is obtained by taking the mean value of matrix A along dimension 1; is the magnetic field data B z1 The mean of .

[0030] Furthermore, the optimization matrix of the optimization problem is calculated by the following formula:

[0031]

[0032] f=2(Δz) 2 -(Δx) 2 -(Δy) 2 (18)

[0033]

[0034] Δx=x i -x j (twenty one)

[0035] Δy=y i -y j (twenty two)

[0036] Δz=z i -zj (twenty three)

[0037] Among them, A x_ij , A y_ij Represents the matrix A x , A y The element of x i ,y i 、z i represents the coordinates of the i-th magnetic field test point; x j ,y j 、z j represents the initial position of the jth shim; V j represents the volume of the jth shim; B rzj represents the remanent magnetization of the jth shim; M zj represents the magnetization intensity of the jth shim; μ0 represents the magnetic permeability of vacuum.

[0038] Furthermore, the optimization matrix is ​​not limited to the displacements in the x and y directions in the Cartesian coordinate system, but can also be the displacements of different components in the Cartesian coordinate system, or the displacements of different components in the cylindrical coordinate system;

[0039] For the coefficient matrices in different coordinate systems, the first-order partial derivatives of the following formula and the corresponding coordinate system components are obtained:

[0040]

[0041] In the cylindrical coordinate system, the optimization matrix elements are determined by the following formula:

[0042]

[0043] Among them, A ρ_ij , Represents the matrix A ρ , The elements of the matrix A ρ , is the radial displacement coefficient matrix and circumferential displacement coefficient matrix in the cylindrical coordinate system; ρ j , Represents the jth shim at its initial position in the cylindrical coordinate system.

[0044] Furthermore, the volume variable V of the shim is j It can be replaced by a variable indicating the amount of shims used, and the variables include shim thickness, shim quantity, and shim quality.

[0045] Furthermore, in step S4, the displacement of the shim is not limited to optimizing the displacement variables in two orthogonal directions at the same time, or optimizing any one of the optimization variables or optimizing in any order, or optimizing the displacement variables in other coordinate systems.

[0046] Furthermore, the steps of the passive shimming method based on shim plate displacement are iterated, or combined with the steps of other shim methods or the combined iterative steps, or the steps of the passive shim method based on shim plate displacement are used to reduce the inhomogeneity caused by long-term static magnetic field or temperature change.

[0047] Beneficial effects: The present invention allows the installed shim plates to form a small displacement on the original position during the shim process by supplementing the displacement shim means, which can compensate for the above errors to a certain extent, and is conducive to reducing the number of shim iterations and the increase in the amount of shim plates caused by multiple iterations. In addition, a composite optimization function consisting of the magnetic plate field deviation and the total displacement of the magnetic plate is established, and the optimal solution is obtained by solving the linear programming problem. The present invention uses the shim plate displacement to achieve secondary compensation of shim, which allows the current shim error to be compensated without adding additional shims, so that the non-uniformity caused by the specification restrictions of the shim plates, manufacturing errors, and installation errors can be compensated. The shim method can also be used as compensation for the uniformity changes caused by the long-term use of magnetic resonance equipment. And by converting it into a linear programming problem to solve the original problem, the method has an extremely high solution speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 A flowchart of the steps of a passive shimming method based on shim plate displacement according to the present invention;

[0049] Figure 2 is a distribution diagram of a set of initial magnetic field data;

[0050] Figure 3 This is the magnetic field distribution result after the initial arrangement of shims;

[0051] Figure 4 The magnetic field distribution result of superimposing a random position error on the shim film;

[0052] Figure 5 This is the magnetic field distribution result after adjusting the position of the magnetic sheet using the method of the present invention. DETAILED DESCRIPTION

[0053] In order to better understand the present invention, the specific implementation of the present invention is now described in detail with reference to the accompanying drawings. The implementation of the present invention includes but is not limited to the following implementation steps, and those skilled in the relevant art can make appropriate adjustments or substitutions according to the core technical ideas of the invention.

[0054] like Figure 1 As shown, a passive shimming method based on shim plate displacement of the present invention comprises the following steps:

[0055] Step S1, determining a set of shim distribution information by a passive shimming method, the shim distribution information including the initial installation position of the shim, the spatial size of the shim, and the shim;

[0056] Among them, the shim pieces need to determine the initial installation distribution. Before implementing the passive shim method, the shim pieces should be detachably fixed and support movable adjustment; displacement adjustment during shim is achieved through magnetic adsorption, debonding, and movable mechanical structures.

[0057] Step S2, after installing the shims, measuring the magnetic field distribution information on the surface of the target area, the magnetic field distribution information includes the magnetic field value of the main magnetic field direction component and the spatial position information of the measuring point.

[0058] Step S3, establishing an optimization problem based on the shim distribution information obtained in step S1 and the magnetic field distribution information obtained in step S2, wherein the optimization problem includes a weighted objective function regarding the magnetic field deviation and the total displacement of the shims, and a constraint condition determined based on the magnetic field uniformity and the maximum displacement of the shims;

[0059] Among them, the optimization problem is realized by minimizing the norm of the objective function, and the optimization problem is expressed as follows:

[0060]

[0061] -d max ≤X≤d max (3)

[0062] -d max ≤Y≤d max (4)

[0063] Among them, A x , A y Represents the coefficient matrix for displacement calculation in the x-direction and y-direction, d max is the constraint limit on the displacement of the magnetic disk; ε is the allowable uniformity error; B z1 is the test magnetic field data after the initial shimming based on the shim film; X and Y are the displacements of the shim film; w is the weight coefficient used to control the proportion of the minimized total movement in the optimization function.

[0064] Step S4, solving the optimization problem established in step S3, obtaining the displacement of the shim, and operating the target shim based on the displacement;

[0065] When solving the optimization problem, the optimization problem is simplified as follows:

[0066] Let A=[Ax A y ],

[0067] And further let |D|=u, The problem is transformed into the following linear programming problem:

[0068] Minimize∑v+w∑u (5)

[0069] Du≤0 (6)

[0070] -Du≤0 (7)

[0071]

[0072] u≥0 (12)

[0073] v≥0 (13)

[0074] D≥-d max (14)

[0075] D≤d max (15)

[0076] in, It is obtained by taking the mean value of matrix A along dimension 1; is the magnetic field data B z1 The mean of .

[0077] Furthermore, the optimization matrix of the optimization problem is calculated by the following formula:

[0078]

[0079] f=2(Δz) 2 -(Δx) 2 -(Δy) 2 (18)

[0080]

[0081] Δx=x i -x j (twenty one)

[0082] Δy=y i -y j (twenty two)

[0083] Δz=z i -z j (twenty three)

[0084] Among them, A x_ij , A y_ij Represents the matrix A x , Ay The element of x i ,y i 、z i represents the coordinates of the i-th magnetic field test point; x j ,y j 、z j represents the initial position of the jth shim; V j represents the volume of the jth shim; B rzj represents the remanent magnetization of the jth shim; M zj represents the magnetization intensity of the jth shim; μ0 represents the magnetic permeability of vacuum.

[0085] It should be noted that the above embodiments are based on the x and y directions of the Cartesian coordinate system. The method proposed in the present invention is also applicable to the displacement of different components in the Cartesian coordinate system, or the displacement of different components in the cylindrical coordinate system or other equivalent substitutions or deformations. These transformations should be deemed to fall within the protection scope of the present invention.

[0086] The optimization matrix is ​​not limited to displacements in the x and y directions in a Cartesian coordinate system, but is also applicable to displacements of different components in a Cartesian coordinate system, or displacements of different components in a cylindrical coordinate system, or other equivalent substitutions or deformations.

[0087] For the coefficient matrices in different coordinate systems, the first-order partial derivatives of the following formula and the corresponding coordinate system components are obtained:

[0088]

[0089] In the cylindrical coordinate system, the optimization matrix elements are determined by the following formula:

[0090]

[0091] Among them, A ρ_ij , Represents the matrix A ρ , The elements of the matrix A ρ , is the radial displacement coefficient matrix and circumferential displacement coefficient matrix in the cylindrical coordinate system; ρ j , Represents the jth shim at its initial position in the cylindrical coordinate system.

[0092] Volume variable V of shim j The variable is not limited to the volume of the shims, but may be replaced by a variable representing the amount of shims used, such as shim thickness, number of shims, shim mass or other equivalent alternatives or variations.

[0093] The displacement of the shim is not limited to optimizing the displacement variables in two orthogonal directions at the same time, but can also be optimizing any one of the optimization variables or optimizing in any order, or optimizing the displacement variables in other coordinate systems.

[0094] The steps of the passive shimming method based on shim plate displacement of the present invention are iteratively implemented, or combined with the steps of other shim methods or the combined iterative implementation, or the steps of the passive shim method based on shim plate displacement of the present invention are used to reduce the inhomogeneity caused by long-term static magnetic field or temperature change.

[0095] A passive shimming method based on shim plate displacement of the present invention is applied to a group of magnetic field data of a bipolar plate magnet for illustration. Figure 2 The original distribution of magnetic field data is given. The uniformity of the original magnetic field distribution is 1074.6ppm. Figure 3 The initial shimming result based on the conventional passive shimming method is given, and its uniformity is 234.25ppm. Only one specification of shimming piece is used for illustration here. The shimming piece used is N42 small magnetic piece with a diameter of 6mm and a thickness of 0.5mm. It is distributed as a simple grid uniformly distributed in the axial and radial directions. Figure 4 The calculated magnetic field distribution after superimposing the random installation error and thickness manufacturing error of the superimposed shim is given, and its uniformity is 245.43ppm. The generated random installation error is less than 0.5mm, and the thickness error is less than 0.1mm. Figure 5 The magnetic field distribution after applying the passive shimming method based on shim plate displacement proposed by the present invention is given. The uniformity of the magnetic field is 159.78ppm, which can effectively improve the uniformity of the magnetic field without increasing the amount of shims used. Table 1 shows the movement of the shims in the X and Y directions.

[0096] Table 1

[0097]

[0098] In summary, the present invention adjusts the local displacement of the shim sheet, and after the initial shimming, uses the known magnetic sheet installation information and test magnetic field data as a secondary shimming means. Without adding additional shims, compensation for the shim sheet manufacturing specifications, manufacturing errors, installation errors and shim slot grid accuracy limitations can be achieved, thereby reducing the inhomogeneity of the magnetic field. The present invention proposes an optimization function based on the total displacement of the shim sheet and the magnetic field deviation, and by converting the absolute value function into a linear function, the original problem is simplified to a linear programming solution, thereby improving the calculation efficiency.

[0099] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A passive shimming method based on shim plate displacement, characterized in that: The following steps are involved: Step S1, determining a set of shim distribution information by a passive shimming method, wherein the shim distribution information includes an initial installation position of the shim, a spatial size of the shim, and the shim; Step S2, after installing the shims, measuring the magnetic field distribution information on the surface of the target area, wherein the magnetic field distribution information includes the magnetic field value of the main magnetic field direction component and the spatial position information of the measuring point; Step S3, establishing an optimization problem based on the shim distribution information obtained in step S1 and the magnetic field distribution information obtained in step S2, wherein the optimization problem includes a weighted objective function regarding the magnetic field deviation and the total displacement of the shims, and a constraint condition determined based on the magnetic field uniformity and the maximum displacement of the shims; Step S4, solving the optimization problem established in step S3, obtaining the displacement of the shim, and operating the target shim based on the displacement.

2. The passive shimming method based on shim plate displacement according to claim 1, characterized in that: In step S1, the shims need to determine the initial installation distribution. Before implementing the passive shimming method, the shims should be detachably fixed and movable and adjustable; displacement adjustment during shimming is achieved by one or more methods such as magnetic adsorption, debonding, and movable mechanical structure.

3. The passive shimming method based on shim plate displacement according to claim 1, characterized in that: In step S3, the optimization problem is achieved by minimizing a norm of the objective function. The optimization problem is expressed as follows: -d max ≤X≤d max (3) -d max ≤Y≤d max (4) Among them, A x , A y Represents the coefficient matrix for displacement calculation in the x-direction and y-direction, d max is the constraint limit on the displacement of the magnetic disk; ε is the allowable uniformity error; B z1 is the test magnetic field data after the initial shimming based on the shim film; X and Y are the displacements of the shim film; w is the weight coefficient used to control the proportion of the minimized total movement in the optimization function.

4. The passive shimming method based on shim plate displacement according to claim 2, characterized in that: In step S4, when solving the optimization problem, the optimization problem is simplified as follows: ReiA=[A x A y ], And further let |D|=u, The problem is transformed into the following linear programming problem: Minimize∑v+w∑u(5) Du≤0(6) -Du≤0(7) u≥0(12) v≥0(13) D≥-d max (14) D≤d max (15) in, It is obtained by taking the mean value of matrix A along dimension 1; is the magnetic field data B z1 The mean of .

5. The passive shimming method based on shim plate displacement according to claim 3, characterized in that: The optimization matrix of the optimization problem is calculated by the following formula: f=2(Δz) 2 -(Δx) 2 -(Δy) 2 (18) Δx=x i -x j (21) Δy=y i -y j (22) Δz=z i -with j (23) Among them, A x_ij , A y_ij Represents the matrix A x , A y The element of x j ,y i 、z i represents the coordinates of the i-th magnetic field test point; x j ,y j 、z j represents the initial position of the jth shim; V j represents the volume of the jth shim; B rzj represents the remanent magnetization of the jth shim; M zj represents the magnetization intensity of the jth shim; μ0 represents the magnetic permeability of vacuum.

6. The passive shimming method based on shim plate displacement according to claim 5, characterized in that: The optimization matrix is ​​applied to displacements in the x and y directions in a Cartesian coordinate system, or displacements of different components in a Cartesian coordinate system, or displacements of different components in a cylindrical coordinate system; For the coefficient matrices in different coordinate systems, the first-order partial derivatives of the following formula and the corresponding coordinate system components are obtained: In the cylindrical coordinate system, the optimization matrix elements are determined by the following formula: Among them, A ρ_ij , Represents the matrix A ρ , The elements of the matrix A ρ , is the radial displacement coefficient matrix and circumferential displacement coefficient matrix in the cylindrical coordinate system; ρ j , Represents the jth shim at its initial position in the cylindrical coordinate system.

7. The passive shimming method based on shim plate displacement according to claim 5, characterized in that: The volume variable V of the shim j It can be replaced by a variable indicating the amount of shims used, and the variables include shim thickness, shim quantity, and shim quality.

8. The passive shimming method based on shim plate displacement according to claim 1 or 3, characterized in that: In step S4, the displacement of the shim is optimized in two orthogonal directions at the same time, or any one of the optimization variables is optimized or optimized in any order, or the displacement variables in other coordinate systems are optimized.

9. The passive shimming method based on shim plate displacement according to claim 1, characterized in that: The steps of the passive shimming method based on shim plate displacement are iterated, or combined with the steps of other shimming methods or the combined iterations, or the steps of the passive shimming method based on shim plate displacement are used to reduce the inhomogeneity caused by long-term static magnetic field or temperature change.

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