Magnetic resonance passive shimming optimization method based on GA-SQP hybrid algorithm

Abstract

The invention discloses a magnetic resonance passive shimming optimization method based on a GA-SQP hybrid algorithm, and the method comprises the steps: firstly operating a GA algorithm, operating a GA number generation (the generation is far smaller than the generation which is operated when the GA is independently used), and then switching to the SQP algorithm. And the SQP algorithm can quickly find a globally optimal solution or a final solution close to the globally optimal solution. According to the method, the uniformity of the main magnetic field can be greatly improved, the requirement of high-quality imaging can be met, meanwhile, the limitation of the total amount of shimming iron sheets can be met, the weight of the iron sheets required for magnetic field uniformity is reduced by adopting a regularization method, and sparse shimming iron sheet distribution is obtained.

Description

Technical Field

[0001] The invention belongs to the field of magnetic resonance imaging, and in particular relates to a magnetic resonance passive shimming optimization method based on a GA-SQP hybrid algorithm. Background Art

[0002] In the Magnetic Resonance Imaging (MRI) system, the high uniformity main magnetic field (B0) plays a vital role in the imaging process. In engineering practice, the inhomogeneity of the main magnetic field of the MRI magnet will lead to several problems: including a large loss of image information, geometric deformation and distortion of the image, incomplete fat suppression, and poor spectral imaging line width. Therefore, MRI magnets have strict design requirements and standards during the design stage. However, due to factors such as the hardware design, manufacturing tolerances, and installation environment of the MRI system, the magnetic field uniformity of the target imaging area is bound to be difficult to meet the increasingly high image quality requirements of today's MRI systems. In order to achieve the high uniformity requirements of the MRI main magnetic field, two shimming methods, active shimming (AS) and passive shimming (PS), are generally used.

[0003] The principle of active shimming technology is to use an energized coil to generate an additional magnetic field in the target imaging area to compensate for the inhomogeneity of the main magnetic field, while the principle of passive shimming technology is to use a shimming iron sheet to generate a compensating magnetic field to optimize the main magnetic field in the target imaging area. However, the coils used in active shimming will occupy a certain space and compete with gradient coils and superconducting coils for space. At the same time, different-order shimming systems will occupy their own important space, and it is difficult to shim high-order harmonics, and the subsequent maintenance price is relatively expensive. On the other hand, passive shimming technology does not require additional current sources, nor does it compete with superconducting magnet components for space. It completes shimming optimization for high-order magnetic fields that are difficult to compensate, and its own cost is low. However, passive shimming technology is usually slow, and it is difficult to balance the magnetic field quality and the total amount of shimming iron sheets. Passive shimming technology is difficult to further improve the uniformity of the main magnetic field in the target imaging area, and produces imaging artifacts based on image-based active shimming or image post-processing. Summary of the invention

[0004] The purpose of the present invention is to provide a magnetic resonance passive shimming optimization method based on a GA-SQP hybrid algorithm. In view of the defects in the prior art, a magnetic resonance passive shimming optimization method based on a hybrid algorithm of a genetic algorithm and a sequential quadratic programming (GA-SQP) is proposed, which can greatly improve the uniformity of the main magnetic field and meet the limitation of the total amount of shimming iron sheets at the same time. A regularization method is used to reduce the weight of the iron sheets required for a uniform magnetic field, thereby obtaining a sparse distribution of shimming iron sheets.

[0005] In order to solve the above technical problems, the following technical solutions are adopted:

[0006] A magnetic resonance passive shimming optimization method based on a GA-SQP hybrid algorithm, characterized by comprising the following steps:

[0007] (1) MRI passive shimming: In the MRI system, shimming iron sheets are placed in the passive shimming layer, and the sensitivity coefficient matrix A of the MRI system is established;

[0008] (3) Optimization based on GA algorithm;

[0009] (3) Optimization based on SQP algorithm.

[0010] After optimization, the step (1) evaluates the inhomogeneity of the bare magnetic field Bm at the sampling point in the imaging area before passive shimming of MRI: using a magnetic field probe / camera to record the initial magnetic field data of a specified measuring point on the spherical surface diameter DSV of the imaging space; the measured magnetic field Bm is expressed as [B 1 ,B 2 ,B 3 …B N ], where N is the number of sample points; the average magnetic field strength B avr and the peak value of the magnetic field H p-p Inhomogeneity is used to assess the quality of the magnetic field B m , measured in parts per million (PPM), the calculation formulas for both are as follows;

[0011]

[0012]

[0013] Among them, Max(B m ) is the maximum magnetic field strength, Min(B m ) is the minimum magnetic field strength.

[0014] After optimization, in the step (1), the shim tray is inserted into the passive shim layer in the gradient coil assembly, and the shim tray is composed of a shim pocket, and the shim pocket is used to accommodate shim iron sheets of a specific size.

[0015] After optimization, the sensitivity coefficient matrix A of step (1) represents the magnetic field effect generated by the unit shim iron sheet located in the shim drawer on the inner wall of the superconducting MRI system magnet on the sampling points on the surface of the imaging area.

[0016] After optimization, the sensitivity coefficient matrix A is constructed by numerically calculating the magnetic field contribution of each unit thickness shim iron sheet to each measurement point on the DSV surface, or by experimental testing.

[0017] After optimization, the dimension of the sensitivity coefficient matrix A is N×M, where N is the total number of magnetic field sample points and M is the total number of shim drawers.

[0018] After optimization, the calculation of each element in the sensitivity coefficient matrix A is obtained by the following formula, with coordinates The magnetic field at any point is generated by a unit shim iron piece dV magnetized at coordinates Q(u,θ,α), Where R and t are the radius of the shim drawer and the thickness of the unit shim, respectively;

[0019]

[0020] M z is the magnetization intensity of the shim iron sheet, is the Legendre coefficient of order n and degree m, the Newman coefficient ∈ m as follows:

[0021]

[0022] After optimization, the step (2) comprises:

[0023] a. The GA algorithm parameters are set as follows: the population size P is 100, and the maximum evolutionary generation Gt is set to 25;

[0024] b. Set the replication probability Pr to 80%, and calculate that the parameters m and n of the optimal preservation strategy used in the selection operation are 20 and 80 respectively;

[0025] c. Set the mutation probability Pm to 10%;

[0026] e. Set the standard deviation coefficient α in the mutation operation to 0.2;

[0027] e. Under the above parameter conditions, the passive shimming of magnetic resonance is optimized for the first time, and the optimal solution is obtained as the initial solution of the SQP algorithm.

[0028] After optimization, the step (3): in order to solve the magnetic field uniformity model using the SQP algorithm, the magnetic field uniformity model of the passive shimming system is converted into a nonlinear constraint form; the nonlinear constraint optimization problem can be expressed as:

[0029] minf(X)

[0030]

[0031] Where f(X) is the nonlinear objective function, X represents the parameter to be optimized, h(X) function and g(X) describe the equation and inequality constraints respectively, and l and u are the upper bounds of the variables;

[0032] The Lagrangian function L(X,λ,μ) of this problem can be expressed as

[0033] L(X,λ,μ)=f(X)+λ*h(X)+μ*g(X)

[0034] The optimization problem of the equation based on the quadratic approximation of the Lagrangian function can be transformed into a QP subproblem:

[0035]

[0036]

[0037] The subscript k represents the kth iteration, and d represents the search direction. Solving equation d yields the solution vector and multiplier vectors λ and μ, defined as d=XX, respectively. k , Δλ=λ-λ k and Δμ=μ-μ k ; This quadratic result creates a search direction and calculates the Karush-Kuhn-Tucker (KKT) multiplier and H k An acceptable estimate of; in the above equation, H k is the positive definite Hessian matrix of the Lagrangian function, which is used to update the Broyden-Fletcher-Goldfarb-Shanno method, which involves calculating the second-order derivatives of the objective function and the constraint function; when the vector d is less than the relative tolerance and satisfies the KKT condition, a converged solution is obtained; the step size α is selected to ensure that the objective function decreases; the above process is repeated until the optimal solution is obtained;

[0038] SQP uses the gradient and constraints of the nonlinear optimization problem to construct a quadratic programming (QP) subproblem, and gradually solves a series of QP subproblems to obtain the minimum value of the objective function; this subproblem is a QP subproblem, and its solution is used to form the search direction d of the line search process. k :

[0039] xk+1 =x k +α k d k

[0040] Step size parameter α k is determined by a line search procedure to obtain a sufficient reduction in the merit function; the merit function is as follows:

[0041]

[0042] where v i is the penalty parameter, initially set to

[0043]

[0044] After optimization, the method further includes: adding an L1-Norm regularization term to the GA-SQP algorithm, re-running the optimization program, and obtaining a second uniform magnetic field.

[0045] The above technical solution has the following beneficial effects:

[0046] 1. The present invention proposes a 7T magnetic resonance magnet passive shimming method based on GA-SQP hybrid optimization algorithm. Through the comparison of multiple algorithm simulations, the algorithm can achieve the best balance between magnetic field uniformity and shimming iron sheet weight consumption. Under the GA-SQP hybrid optimization algorithm, the magnetic field uniformity is improved, which can meet the requirements of high-quality imaging, and the algorithm has good robustness.

[0047] 2. The present invention realizes the sparse distribution requirement of the shim iron sheets through L1-Norm regularization, and can obtain good sparsity in the thickness distribution of the shim iron sheets, meeting the needs of actual engineering.

[0048] 3. The present invention can bring the following engineering benefits: First, the main magnetic field of the magnetic resonance magnet is more uniform, so that high-quality MRI images can be generated, which is conducive to the subsequent accurate segmentation of human or animal tissue images. Secondly, the iron sheets of the magnetic resonance passive shimming are more sparse, reducing the use of shimming iron sheets, which can improve thermal stability and reduce eddy current effects. In addition, the excellent performance demonstrated by the algorithm proposed in the present invention does not require any modification to the standard shimming hardware system. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The present invention will be further described below in conjunction with the accompanying drawings:

[0050] Figure 1 It is the flow chart of GA-SQP algorithm;

[0051] Figure 2 Trajectory diagrams of different optimization methods towards the optimal point;

[0052] Figure 3 is the DSV magnetic field distribution map obtained by using the GA-SQP algorithm;

[0053] Figure 4 The thickness distribution diagram of the uniform field iron sheet obtained by using the GA-SQP algorithm;

[0054] Figure 5 Obtain the uniform field iron distribution map for the GA-SQP algorithm. DETAILED DESCRIPTION

[0055] The present invention aims to provide a magnetic resonance passive shimming optimization method based on a GA-SQP hybrid algorithm, first running a GA algorithm, and then switching to an SQP algorithm. The SQP algorithm can quickly find a global optimal solution or a final solution close to the global optimal solution. The uniformity of the main magnetic field can be greatly improved, and at the same time, the limitation of the total amount of shimming iron sheets can be met. At the same time, a regularization method is used to reduce the weight of the iron sheets required for a uniform magnetic field, and a sparse shimming iron sheet distribution is obtained.

[0056] The technical solution of the present invention is described in detail below through a specific embodiment, taking the optimization of the passive shimming of the magnetic field of a 7T superconducting magnetic resonance magnet as an example, comprising the following steps:

[0057] (1) MRI passive shimming:

[0058] Use a magnetic field probe / camera to record initial magnetic field data of a specified measurement point on the spherical surface diameter DSV of the imaging space;

[0059] Before passive shimming of MRI, it is very important to evaluate the inhomogeneity of the bare magnetic field Bm at the sampling points in the imaging area. The imaging space is usually spherical, so it is called the volume spherical diameter (DSV), also known as the volume of interest (VOI). The magnetic field probe / camera is used to record the initial magnetic field data of the specified measurement points on the DSV surface diameter, also known as magnetic field mapping. This measured magnetic field Bm is expressed as [B 1 ,B 2 ,B 3 …B N ], where N is the number of sample points; the average magnetic field strength B avr and the peak value of the magnetic field H p-p Inhomogeneity is used to assess the quality of the magnetic field B m , measured in parts per million (PPM), the calculation formulas for both are as follows;

[0060]

[0061]

[0062] Among them, Max(B m) is the maximum magnetic field strength, Min(B m ) is the minimum magnetic field strength.

[0063] In a typical cylindrical MRI system, dozens of shim trays are inserted into the passive shim layer within the gradient coil assembly. Each shim tray consists of dozens of shim drawers to accommodate shim iron sheets of a specific size. Since the magnetic field strength of superconducting MRI is very high, it can be assumed that the shim iron sheets are in a magnetic saturation state. Then it is necessary to establish the sensitivity matrix of the system, that is, the magnetic field influence of the unit shim iron sheet located in the drawer of the inner wall of the superconducting MRI system magnet on the sampling point on the surface of the imaging area. The sensitivity coefficient matrix can be obtained by both numerical calculation and experimental testing. The dimension of the system matrix A is N×M, where N is the total number of sampling points and M is the total number of shim bags. This system matrix, also called the sensitivity matrix, can be constructed by numerically calculating the field contribution of each shim iron sheet of unit thickness to each measurement point on the DSV surface.

[0064] The calculation of each element in the sensitivity coefficient matrix A is obtained by the following formula, with coordinates The magnetic field at any point is generated by a unit shim iron piece dV magnetized at coordinates Q(u,θ,α), Where R and t are the radius of the shim drawer and the thickness of the unit shim, respectively;

[0065]

[0066] M z is the magnetization intensity of the shim iron sheet, is the Legendre coefficient of order n and degree m, the Newman coefficient ∈ m as follows:

[0067]

[0068] Based on the above method, there are 576 shimming iron positions and 576 magnetic field sampling points in the superconducting magnetic resonance passive shimming research of this embodiment. The initial peak-to-peak non-uniformity of the magnetic field measured by a standard magnetic field camera is 462ppm within a 40cm spherical surface diameter.

[0069] (2) Optimization based on GA algorithm;

[0070] a. The GA algorithm parameters are set as follows: the population size P is 100, and the maximum evolutionary generation Gt is set to 25;

[0071] b. Set the replication probability Pr to 80%, and calculate that the parameters m and n of the optimal preservation strategy used in the selection operation are 20 and 80 respectively;

[0072] c. In order to give full play to the role of mutation operation, the mutation probability Pm is set to 10%;

[0073] d. Set the standard deviation coefficient α in the mutation operation to 0.2; while ensuring that the algorithm has a faster convergence speed, it effectively prevents it from falling into the local optimal solution.

[0074] e. Under the above parameter conditions, the passive shimming of 7T MRI was optimized for the first time, and the optimal solution was obtained as the initial solution of the SQP algorithm.

[0075] (3) Optimization based on SQP algorithm

[0076] The passive shimming experiment was carried out under the condition of magnetic resonance magnetic field strength of 7 Tesla and initial magnetic field B0 = 462ppm. The SQP algorithm was used alone to solve the problem of passive shimming optimization of magnetic resonance. This method sets different initial points to study the performance of SQP in passive shimming optimization. Among them, the initial value is within the setting range of the thickness of the shimming iron sheet, including the maximum value, minimum value, intermediate value and arbitrary value, etc.

[0077] In order to solve the magnetic field uniformity model using the SQP algorithm, the magnetic field uniformity model of the passive shimming system is transformed into a nonlinear constraint form; the nonlinear constraint optimization problem can be expressed as:

[0078] minf(X)

[0079]

[0080] Where f(X) is the nonlinear objective function, X represents the parameter to be optimized, h(X) function and g(X) describe the equation and inequality constraints respectively, and l and u are the upper bounds of the variables;

[0081] The Lagrangian function L(X,λ,μ) of this problem can be expressed as

[0082] L(X,λ,μ)=f(X)+λ*h(X)+μ*g(X)

[0083] The optimization problem of the equation based on the quadratic approximation of the Lagrangian function can be transformed into a QP subproblem:

[0084]

[0085]

[0086] The subscript k represents the kth iteration, and d represents the search direction. Solving equation d yields the solution vector and multiplier vectors λ and μ, defined as d=XX, respectively. k , Δλ=λ-λ k and Δμ=μ-μ k; This quadratic result creates a search direction and calculates the Karush-Kuhn-Tucker (KKT) multiplier and H k An acceptable estimate of; in the above equation, H k is the positive definite Hessian matrix of the Lagrangian function, which is used to update the Broyden-Fletcher-Goldfarb-Shanno method, which involves calculating the second-order derivatives of the objective function and the constraint function; when the vector d is less than the relative tolerance and satisfies the KKT condition, a converged solution is obtained; the step size α is selected to ensure that the objective function decreases; the above process is repeated until the optimal solution is obtained;

[0087] The main principle of SQP is to construct a quadratic programming (QP) subproblem using the gradient and constraints of the nonlinear optimization problem, and obtain the minimum value of the objective function by gradually solving a series of QP subproblems; this subproblem is a QP subproblem, and its solution is used to form the search direction d of the line search process. k :

[0088] x k+1 =x k +α k d k

[0089] Step size parameter α k is determined by a line search procedure to obtain a sufficient reduction in the merit function; the merit function is as follows:

[0090]

[0091] where v i is the penalty parameter, initially set to

[0092]

[0093] For active constraints at the solution point, this ensures that constraints with smaller gradients contribute more to the penalty parameter.

[0094] The passive shimming experiment was carried out under the condition of magnetic resonance magnetic field strength of 7 Tesla and initial magnetic field B0 = 462 ppm. The present invention proposes to perform SQP algorithm on the basis of GA algorithm, namely GA-SQP hybrid algorithm. The convergence speed of GA-SQP hybrid algorithm and single GA algorithm is shown in Figure 2 As shown in the figure, the number of objective function evaluations required for GA-SQP to reach the optimal solution is greatly reduced, from 170,000 iterations of the GA algorithm to more than 80,000.

[0095] (4) L1-Norm regularization term

[0096] In order to find a sparse solution, the L1-Norm regularization term is added to the GA-SQP algorithm. The optimization procedure is re-run to obtain the second shim magnetic field. After rounding the shim iron sheet, the uniformity of the main magnetic field is about 4.5ppm (peak-to-peak), and the corresponding magnetic field uniform distribution is as follows Figure 3 The total mass consumed by the shim iron sheet is 0.8 kg, and the thickness distribution of the shim iron sheet is as follows: Figure 4 shown. Figure 5 The corresponding plane distribution diagram of iron sheet thickness is shown. It can be seen from the figure that the GA-SQP algorithm has achieved the best optimization effect in terms of magnetic field uniformity. At the same time, the distribution pattern of shimming iron sheets is relatively sparse, and the consumption of shimming iron sheets has been greatly improved.

[0097] The above are only specific embodiments of the present invention, but the technical features of the present invention are not limited thereto. Any simple changes, equivalent replacements or modifications made based on the present invention to solve basically the same technical problems and achieve basically the same technical effects are all included in the protection scope of the present invention.

Claims

1. A magnetic resonance passive shimming optimization method based on GA-SQP hybrid algorithm, characterized in that The steps include: (1) MRI passive shimming: In the MRI system, shimming iron sheets are placed in the passive shimming layer, and the sensitivity coefficient matrix A of the MRI system is established; (2) Optimization based on GA algorithm; (3) Optimization based on SQP algorithm.

2. The method for optimizing passive shimming of magnetic resonance based on the GA-SQP hybrid algorithm according to claim 1, characterized in that: The step (1) is to evaluate the inhomogeneity of the bare magnetic field Bm at the sampling point in the imaging area before the MRI passive field shimming: use a magnetic field probe / camera to record the initial magnetic field data of the specified measuring point on the spherical surface diameter DSV of the imaging space; this measured magnetic field Bm is represented by [B1, B2, B3 ... B N ], where N is the number of sample points; the average magnetic field strength B avr and the peak value of the magnetic field H p-p Inhomogeneity is used to evaluate the quality of the magnetic field and is measured in parts per million (PPM). The calculation formulas for both are as follows: Among them, Max(B m ) is the maximum magnetic field strength, Min(B m ) is the minimum magnetic field strength.

3. The method for optimizing passive shimming of magnetic resonance based on the GA-SQP hybrid algorithm according to claim 1, characterized in that: In the step (1), a shim tray is inserted into a passive shim layer in the gradient coil assembly. The shim tray is composed of a shim pocket, and the shim pocket is used to accommodate shim iron sheets of a specific size.

4. The method for optimizing passive shimming of magnetic resonance based on the GA-SQP hybrid algorithm according to claim 2, characterized in that: The sensitivity coefficient matrix A of step (1) represents the magnetic field effect generated by the unit shim iron sheet located in the shim drawer on the inner wall of the superconducting MRI system magnet on the sampling points on the surface of the imaging area.

5. The method for optimizing passive shimming of magnetic resonance based on GA-SQP hybrid algorithm according to claim 2, characterized in that: The sensitivity coefficient matrix A is constructed by numerically calculating the magnetic field contribution of each unit thickness shim iron sheet to each measurement point on the DSV surface, or by experimental testing.

6. The method for optimizing passive shimming of magnetic resonance based on GA-SQP hybrid algorithm according to claim 4, characterized in that: The dimension of the sensitivity coefficient matrix A is N×M, where N is the total number of magnetic field sample points and M is the total number of shim drawers.

7. The method for optimizing passive shimming of magnetic resonance based on GA-SQP hybrid algorithm according to claim 4, characterized in that: The calculation of each element in the sensitivity coefficient matrix A is obtained by the following formula, with coordinates The magnetic field at any point is generated by a unit shim iron piece dV magnetized at coordinates Q(u,θ,α), Where R and t are the radius of the shim drawer and the thickness of the unit shim, respectively; M z is the magnetization intensity of the shim iron sheet, is the Legendre coefficient of order n and degree m, the Newman coefficient ∈ m as follows:

8. The method for optimizing passive shimming of magnetic resonance based on GA-SQP hybrid algorithm according to claim 1, characterized in that: The step (2) comprises: a. The GA algorithm parameters are set as follows: the population size P is 100, and the maximum evolutionary generation Gt is set to 25; b. Set the replication probability Pr to 80%, and calculate that the parameters m and n of the optimal preservation strategy used in the selection operation are 20 and 80 respectively; c. Set the mutation probability Pm to 10%; d. Set the standard deviation coefficient α in the mutation operation to 0.2; e. Under the above parameter conditions, the passive shimming of magnetic resonance is optimized for the first time, and the optimal solution is obtained as the initial solution of the SQP algorithm.

9. The method for optimizing passive shimming of magnetic resonance based on GA-SQP hybrid algorithm according to claim 1, characterized in that: The step (3): in order to solve the magnetic field uniformity model using the SQP algorithm, the magnetic field uniformity model of the passive shimming system is converted into a nonlinear constraint form; the nonlinear constraint optimization problem can be expressed as: min f(X) Where f(X) is the nonlinear objective function, X represents the parameter to be optimized, h(X) function and g(X) describe the equation and inequality constraints respectively, and l and u are the upper bounds of the variables; The Lagrangian function L(X,λ,μ) of this problem can be expressed as L(X,λ,μ)=f(X)+λ*h(X)+μ*g(X) The optimization problem of the equation based on the quadratic approximation of the Lagrangian function can be transformed into a QP subproblem: The subscript k represents the kth iteration, and d represents the search direction. Solving equation d yields the solution vector and multiplier vectors λ and μ, defined as d=XX, respectively. k , Δλ=λ-λ k and Δμ=μ-μ k ; This quadratic result creates a search direction and calculates the Karush-Kuhn-Tucker (KKT) multiplier and H k An acceptable estimate of; in the above equation, H k is the positive definite Hessian matrix of the Lagrangian function, which is used to update the Broyden-Fletcher-Goldfarb-Shanno method, which involves calculating the second-order derivatives of the objective function and the constraint function; when the vector d is less than the relative tolerance and satisfies the KKT condition, a converged solution is obtained; the step size α is selected to ensure that the objective function decreases; the above process is repeated until the optimal solution is obtained; SQP uses the gradient and constraints of the nonlinear optimization problem to construct a quadratic programming (QP) subproblem, and gradually solves a series of QP subproblems to obtain the minimum value of the objective function; this subproblem is a QP subproblem, and its solution is used to form the search direction d of the line search process. k : x k+1 =x k +a k d k Step size parameter α k is determined by a line search procedure to obtain a sufficient reduction in the merit function; the merit function is as follows: where v i is the penalty parameter, initially set to 10. The magnetic resonance passive shimming optimization method based on GA-SQP hybrid algorithm according to claim 1, characterized in that: The method also includes: adding an L1-Norm regularization term to the GA-SQP algorithm, re-running the optimization program, and obtaining a second uniform magnetic field.

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