A passive shimming method based on shimming plate displacement

Abstract

This invention discloses a passive shimming method based on the displacement of a shimming plate, comprising the following steps: determining a set of shimming plate distribution information using a passive shimming method, including the initial installation position of the shimming plate, the spatial dimensions of the shimming plate, and the shimming plate itself; after installing the shimming plate, measuring the magnetic field distribution information on the surface of the target area, including the magnetic field values ​​of the main magnetic field direction components and the spatial position information of the measurement points; based on the shimming plate distribution information and the magnetic field distribution information, establishing an optimization problem, including a weighted objective function for magnetic field deviation and the total displacement of the shimming plate, and constraints determined based on magnetic field uniformity and the maximum displacement of the shimming plate; solving the optimization problem to obtain the displacement of the shimming plate, and operating the target shimming plate based on the displacement. This invention effectively compensates for shimming errors through the displacement of the shimming plate, avoiding excessive use of the shimming plate during the shimming iteration process.

Description

Technical Field

[0001] This invention relates to the field of magnetic resonance technology, and specifically to a passive shimming method based on the displacement of a shimming plate. Background Technology

[0002] Passive shimming is primarily used to optimize the magnetic field homogeneity of magnetic resonance imaging (MRI) equipment. The magnet is the core of an MRI system, responsible for generating a highly uniform main magnetic field. However, due to the magnet's structure, manufacturing errors, and environmental magnetic interference, the main magnetic field often exhibits inhomogeneities, affecting image quality. Passive shimming adjusts and compensates for these inhomogeneities by placing shimming plates of specific shapes and positions around the magnet, such as magnetic or iron sheets. Compared to active shimming, passive shimming requires no additional power supply or complex control system, offering advantages such as lower cost, simpler structure, and less maintenance. Therefore, many portable MRI systems rely on passive shimming to improve magnetic field homogeneity, and it is also an important supplementary technique in some MRI systems with high stability requirements.

[0003] Passive shimming based on shimming plates typically calculates the magnetic field generated by the shimming plate according to the magnetic dipole hypothesis or Biot-Savart theorem. In practical applications, the volume, thickness, number, area, and other effective variables of the shimming plate are usually used for optimization calculations. However, the change in magnetic field caused by the position of the magnetic plate is usually ignored. Chinese invention patent CN114636958A discloses a shimming method using iron sheet thickness as an optimization variable, without considering displacement as a supplementary shimming method. Chinese invention patent CN110308411A discloses a high-precision and fast passive shimming method for Halbach magnets, which achieves shimming adjustment without the use of additional iron sheets, but it 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 precision of the shimming plate determine the discontinuity and manufacturing errors in its magnetization volume. Installation errors also exist during the shimming plate assembly process. These errors reduce the shimming effect and cannot be avoided in conventional shimming processes. Furthermore, pre-setting shimming slots or grid points may restrict the spatial degrees of freedom of passive shimming. Moreover, continuously iterating through passive shimming further increases the amount of shimming plate required. Summary of the Invention

[0005] The purpose of this invention is to provide a passive shimming method based on the displacement of the shimming plate, so as to solve the problems of discontinuity in the magnetization volume of the shimming plate and manufacturing errors, as well as installation errors in the installation process of the shimming plate in the prior art.

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

[0007] A passive shimming method based on the displacement of shimming plates includes the following steps:

[0008] Step S1: Determine a set of shimming plate distribution information using a passive shimming method. The shimming plate distribution information includes the initial installation position of the shimming plate, the spatial dimensions of the shimming plate, and the shimming plate itself.

[0009] Step S2: After installing the shimming plate, measure 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 measurement point.

[0010] Step S3: Based on the distribution information of the shimming plate obtained in step S1 and the magnetic field distribution information obtained in step S2, an optimization problem is established. The optimization problem includes a weighted objective function for magnetic field deviation and total displacement of the shimming plate, as well as constraints determined based on magnetic field uniformity and maximum displacement of the shimming plate.

[0011] Step S4: Solve the optimization problem established in step S3 to obtain the displacement of the shimming plate, and operate on the target shimming plate based on the displacement.

[0012] Furthermore, in step S1, the initial installation distribution of the shimming sheet needs to be determined. Before implementing the passive shimming method, the shimming sheet should be detachably fixed and movable and adjustable. Displacement adjustment during shimming can be achieved through one or more methods such as magnetic adsorption, adhesive removal, and movable mechanical structures.

[0013] Furthermore, in step S3, the optimization problem is achieved by minimizing the norm of the objective function, which 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 d represents the coefficient matrix for displacement calculation in the x and y directions, respectively. max To constrain the displacement of the magnetic sheet; ε is the allowable uniformity error; B z1 The test magnetic field data is based on the initial shimming of the shimming plate; X and Y are the displacements of the shimming plate; w is a weighting coefficient used to control the proportion of the total displacement 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 can be 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, The mean value of matrix A is obtained by taking the mean along dimension one; For magnetic field data B z1 The mean.

[0030] Furthermore, the optimization matrix of the optimization problem is calculated using 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 Representing matrix A respectively x A y The element, x i y i z i x represents the coordinates of the i-th magnetic field test point; j y j z j V represents the initial position of the j-th homogenizer; j B represents the volume of the j-th homogenizer; rzj M represents the remanence of the j-th uniform plate; zj μ represents the magnetization of the j-th uniform plate; μ0 represents the free permeability.

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

[0039] For the coefficient matrix in different coordinate systems, it can be obtained by taking the first-order partial derivative with respect to the following equation and the corresponding coordinate system components:

[0040]

[0041] In cylindrical coordinates, the elements of the optimization matrix are determined by the following formula.

[0042]

[0043] Among them, A ρ_ij , Representing matrix A respectively ρ , The elements of matrix A ρ , Here are the radial and circumferential displacement coefficient matrices in cylindrical coordinates; ρ j , This represents the initial position of the j-th uniform plate in cylindrical coordinates.

[0044] Furthermore, the volume change V of the shimming plate j It can be replaced by a variable representing the amount of shimming sheet used, including shimming sheet thickness, number of shimming sheets, and shimming sheet mass.

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

[0046] Furthermore, the steps of the passive shimming method based on shimming plate displacement are implemented iteratively, or combined with the steps of other shimming methods, or combined iteratively, or the steps of the passive shimming method based on shimming plate displacement are used to reduce the non-uniformity caused by long-term static magnetic field or temperature changes.

[0047] Beneficial Effects: This invention, through supplementary displacement shimming during the shimming process, allows the installed shimming plates to undergo a small displacement in situ. This can compensate for the aforementioned errors to a certain extent, reducing the number of shimming iterations and the increased number of shimming plates required due to multiple iterations. Furthermore, a composite optimization function consisting of magnetic plate field deviation and total magnetic plate displacement is established, and the optimal solution is obtained by solving a linear programming problem. This invention uses shimming plate displacement to achieve secondary compensation for shimming, allowing compensation for current shimming errors without adding additional shimming plates. Therefore, it can compensate for non-uniformity caused by shimming plate specification limitations, manufacturing errors, and installation errors. It can also compensate for uniformity changes caused by long-term use of magnetic resonance equipment. Moreover, by converting the problem into a linear programming problem to solve the original problem, this method has extremely high solution speed. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating the steps of a passive shimming method based on the displacement of a shimming plate according to the present invention.

[0049] Figure 2 A distribution map of a set of initial magnetic field data;

[0050] Figure 3 The results show the magnetic field distribution after the initial shim plate was applied.

[0051] Figure 4 The result is the magnetic field distribution after superimposing a random position error onto a uniform field plate;

[0052] Figure 5 The magnetic field distribution is shown after adjusting the position of the magnetic sheet using the method of the present invention. Detailed Implementation

[0053] To better understand the present invention, specific embodiments are now described in detail with reference to the accompanying drawings. The embodiments of the present invention include, but are not limited to, the following implementation steps, and those skilled in the art can make appropriate adjustments or substitutions based on the core technical concept of the invention.

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

[0055] Step S1: Determine a set of shimming plate distribution information using the passive shimming method. The shimming plate distribution information includes the initial installation position of the shimming plate, the spatial dimensions of the shimming plate, and the shimming plate itself.

[0056] The initial installation distribution of the shimming plates needs to be determined. Before implementing this passive shimming method, the shimming plates should be detachably fixed and support movement adjustment. Displacement adjustment during shimming can be achieved through magnetic adsorption, adhesive removal, and movable mechanical structures.

[0057] Step S2: After installing the shimming plate, measure 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 location information of the measurement point.

[0058] Step S3: Based on the distribution information of the shimming plate obtained in step S1 and the magnetic field distribution information obtained in step S2, an optimization problem is established. The optimization problem includes a weighted objective function for magnetic field deviation and total displacement of the shimming plate, as well as constraints determined based on magnetic field uniformity and maximum displacement of the shimming plate.

[0059] The optimization problem is achieved by minimizing the 1-norm of the objective function, and it 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 d represents the coefficient matrix for displacement calculation in the x and y directions, respectively. max To constrain the displacement of the magnetic sheet; ε is the allowable uniformity error; B z1 The test magnetic field data is based on the initial shimming of the shimming plate; X and Y are the displacements of the shimming plate; w is a weighting coefficient used to control the proportion of the total displacement in the optimization function.

[0064] Step S4: Solve the optimization problem established in step S3 to obtain the displacement of the shimming plate, and operate on the target shimming plate 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 can be 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, The mean value of matrix A is obtained by taking the mean along dimension one; For magnetic field data B z1 The mean.

[0077] Furthermore, the optimization matrix of the optimization problem is calculated using 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 Representing matrix A respectively x Ay The element, x i y i z i x represents the coordinates of the i-th magnetic field test point; j y j z j V represents the initial position of the j-th homogenizer; j B represents the volume of the j-th homogenizer; rzj M represents the remanence of the j-th uniform plate; zj μ represents the magnetization of the j-th uniform plate; μ0 represents the free permeability.

[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 this invention is also applicable to displacements of different components in the Cartesian coordinate system, or displacements of different components in the cylindrical coordinate system, or other equivalent substitutions or deformations. These transformations should be considered to fall within the protection scope of this invention.

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

[0087] For the coefficient matrix in different coordinate systems, it can be obtained by taking the first-order partial derivative with respect to the following equation and the corresponding coordinate system components:

[0088]

[0089] In cylindrical coordinates, the elements of the optimization matrix are determined by the following formula.

[0090]

[0091] Among them, A ρ_ij , Representing matrix A respectively ρ , The elements of matrix A ρ , Here are the radial and circumferential displacement coefficient matrices in cylindrical coordinates; ρ j , This represents the initial position of the j-th uniform plate in cylindrical coordinates.

[0092] Volume change V of the shim j It is not limited to the volume variable of the shimming sheet; it can be replaced by a variable representing the amount of shimming sheet used, such as the thickness of the shimming sheet, the number of shimming sheets, the mass of the shimming sheet, or other equivalent substitutions or modifications.

[0093] The displacement of the shim is not limited to optimizing displacement variables in two orthogonal directions simultaneously. It can also be optimized for any single variable or in any order, or for displacement variables in other coordinate systems.

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

[0095] The passive shimming method based on the displacement of the shimming plate, according to the present invention, is applied to a set of magnetic field data of a bipolar magnet for illustration. Figure 2 The original magnetic field distribution is given. The uniformity of the original magnetic field distribution is 1074.6 ppm. Figure 3 The initial shimming results based on the conventional passive shimming method are presented, with a uniformity of 234.25 ppm. Only one type of shimming sheet is used for illustration. The shimming sheet used is an N42 small magnetic sheet with a diameter of 6 mm and a thickness of 0.5 mm, which is distributed as a simple grid that is uniformly distributed in the axial and radial directions. Figure 4 The calculated magnetic field distribution after superimposing random installation error and thickness manufacturing error on the shim is given. 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 the displacement of the shimming plate proposed in this invention is presented. The magnetic field uniformity is 159.78 ppm, which can effectively improve the magnetic field uniformity without increasing the amount of shimming plate used. Table 1 shows the displacement of the shimming plate in the X and Y directions.

[0096] Table 1

[0097]

[0098] In summary, this invention adjusts the local displacement of the shimming plate after the initial shimming, and then uses known magnetic plate installation information and test magnetic field data as a secondary shimming method. Without the need for additional shimming plates, it can compensate for limitations in shimming plate manufacturing specifications, manufacturing errors, installation errors, and shimming groove mesh accuracy, thereby reducing magnetic field inhomogeneity. This invention proposes an optimization function based on the total displacement of the shimming plate and the magnetic field deviation, and simplifies the original problem into a linear programming solution by transforming the absolute value function into a linear function, thus improving computational efficiency.

[0099] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A passive shimming method based on the displacement of a shimming plate, characterized in that: Includes the following steps: Step S1: Determine a set of shimming plate distribution information using a passive shimming method. The shimming plate distribution information includes the initial installation position of the shimming plate, the spatial dimensions of the shimming plate, and the shimming plate itself. Step S2: After installing the shimming plate, measure 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 measurement point. Step S3: Based on the distribution information of the shim plate obtained in step S1 and the magnetic field distribution information obtained in step S2, an optimization problem is established. The optimization problem includes a weighted objective function for the magnetic field deviation and the total displacement of the shim plate, as well as constraints determined based on the magnetic field uniformity and the maximum displacement of the shim plate. The optimization problem is achieved by minimizing the first norm of the objective function, and is expressed as follows: (1) (2) (3) (4) in, , These represent the coefficient matrices for displacement calculations in the x and y directions, respectively. To constrain and limit the displacement of the magnetic sheet; To allow for uniformity error; This is based on the test magnetic field data after the initial shimming of the shimming plate; and is the displacement of the uniform field plate; w is a weighting coefficient used to control the proportion of the total minimized movement in the optimization function; Step S4: Solve the optimization problem established in step S3 to obtain the displacement of the shimming plate, and operate on the target shimming plate based on the displacement.

2. The passive shimming method based on shimming plate displacement according to claim 1, characterized in that: In step S1, the initial installation distribution of the shimming sheet needs to be determined. Before implementing the passive shimming method, the shimming sheet should be detachably fixed and movable and adjustable. Displacement adjustment during shimming can be achieved through one or more methods such as magnetic adsorption, adhesive removal, and movable mechanical structure.

3. The passive shimming method based on shimming plate displacement according to claim 1, characterized in that: In step S4, when solving the optimization problem, the optimization problem is simplified as follows: make , , And further , The problem can be transformed into the following linear programming problem: (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) in, The mean value of matrix A is obtained by taking the mean along dimension one; For magnetic field data The mean.

4. The passive shimming method based on shimming plate displacement according to claim 3, characterized in that: The optimization matrix of the optimization problem is calculated using the following formula: (16) (17) (18) (19) (20) (21) (22) (23) in, , Representing matrices respectively , elements, , , The coordinates of the i-th magnetic field test point; , , This represents the initial position of the j-th uniform plate; This represents the volume of the j-th uniform plate; Represents the remanence of the j-th uniform plate; This represents the magnetization intensity of the j-th uniform plate; It represents the vacuum permeability.

5. The passive shimming method based on shimming plate displacement according to claim 4, characterized in that: The optimization matrix is ​​applied to displacements in the x and y directions in Cartesian coordinates, or displacements of different components in Cartesian coordinates, or displacements of different components in cylindrical coordinates. For the coefficient matrix in different coordinate systems, it can be obtained by taking the first-order partial derivative with respect to the following equation and the corresponding coordinate system components: (24) In cylindrical coordinates, the elements of the optimization matrix are determined by the following formula. (25) (26) in, , Representing matrices respectively , Elements of the matrix , These are the radial displacement coefficient matrix and the circumferential displacement coefficient matrix in cylindrical coordinates; , This represents the initial position of the j-th uniform plate in cylindrical coordinates.

6. The passive shimming method based on shimming plate displacement according to claim 4, characterized in that: The volume change of the shim plate It can be replaced by a variable representing the amount of shimming sheet used, including shimming sheet thickness, number of shimming sheets, and shimming sheet mass.

7. The passive shimming method based on shimming plate displacement according to claim 1, characterized in that: In step S4, the displacement of the shimming plate is optimized simultaneously in two orthogonal directions, or any one of the optimization variables is optimized or optimized in any order, or the displacement variable in other coordinate systems is optimized.

8. The passive shimming method based on shimming plate displacement according to claim 1, characterized in that: The steps of the passive shimming method based on shimming plate displacement are implemented iteratively, or combined with the steps of other shimming methods, or combined iteratively, or the steps of the passive shimming method based on shimming plate displacement are used to reduce the non-uniformity caused by long-term static magnetic field or temperature changes.

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