Hybrid nonlinear programming method for optimizing MRI passive shimming

Abstract

The invention discloses a hybrid nonlinear programming method for optimizing MRI passive shimming. The hybrid nonlinear programming method comprises two steps of a shimming method and a hybrid optimization algorithm. Before passive shimming, non-uniformity of a naked magnetic field of sampling points in an imaging area is evaluated, a sensitivity coefficient matrix of an MRI system is established, and a hybrid PSO-SQP algorithm is adopted to optimize the passive shimming technology of the MRI. According to the method, the PSO-SQP hybrid algorithm is established to optimize magnetic resonance passive shimming, so that the global search capability of the PSO algorithm is reserved, the rapid convergence of the SQP algorithm is utilized, the magnetic field quality, iron use and harmonic waves can be balanced in an optimal mode, and a smoother magnetic field contour is obtained.

Description

Technical Field

[0001] The invention belongs to the field of magnetic resonance imaging, and in particular relates to a hybrid nonlinear programming method for optimizing MRI passive shimming. Background Art

[0002] In magnetic resonance imaging (MRI) systems, a high uniformity main magnetic field (B0) is crucial in the imaging process. In imaging practice, the non-uniformity of the B0 magnetic field in MRI can lead to 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 must follow strict design requirements and standards during the design phase. However, due to factors such as hardware system design, manufacturing tolerances, and installation environment, the magnetic field uniformity of the target imaging area is difficult to meet the increasingly high image quality requirements of today's MRI systems.

[0003] In order to achieve the required B0 uniformity level, two shimming methods, active shimming (AS) and passive shimming (PS), are generally used. AS uses energized coils to generate additional magnetic fields in the target imaging area to compensate for the inhomogeneity of the main magnetic field, while PS uses shimming iron sheets to generate compensation magnetic fields to optimize the main magnetic field in the target imaging area. However, the coils used in AS 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. In contrast, PS does not require additional current sources, nor does it compete with superconducting magnet components for space. It can optimize the shimming of high-order magnetic fields that are difficult to compensate, and it has low cost itself. 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, resulting in imaging artifacts such as image-based active shimming or image post-processing. Summary of the invention

[0004] The purpose of the present invention is to provide a hybrid nonlinear programming method for optimizing MRI passive shimming. In view of the defects in the prior art, a hybrid optimization algorithm (PSO-SQP) combining particle swarm optimization (PSO) and SQP algorithm is proposed, which can improve the efficiency of passive vibration reduction, balance the magnetic field quality, iron usage and harmonics in an optimal way, and obtain a smoother magnetic field profile.

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

[0006] A hybrid nonlinear programming method for optimizing MRI passive shimming, 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] (2) Hybrid optimization: The robust global search capability of the PSO algorithm is used to solve the given mathematical model problem. The search results are then used as the starting point of the SQP algorithm, and the SQP algorithm is used to explore the original optimization problem. The hybrid PSO-SQP algorithm is used to optimize the passive field of the MRI system.

[0009] 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: the spherical surface diameter (DSV) of the imaging space, also called the volume of interest (VOI)

[0010] Use a magnetic field probe / camera to record the initial magnetic field data at a specified measurement point on the DSV; 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 evaluate the quality of the magnetic field and is 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), dozens of shim trays are inserted into the passive shim layer in the gradient coil assembly, and each shim tray is composed of dozens of shim pockets, which are used to accommodate shim iron sheets of a specific size.

[0015] After optimization, in step (1), due to the high magnetic field strength of the superconducting magnetic resonance magnet, it can be assumed that the shimming iron pieces are all magnetically saturated. Then, it is necessary to establish a sensitivity coefficient matrix A of the system, which represents the magnetic field effect generated by the unit shimming iron piece located in the shimming drawer on the inner wall of the superconducting MRI system magnet on the sampling point 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.

[0017] After optimization, the sensitivity coefficient matrix A can also be constructed through experimental testing.

[0018] 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.

[0019] 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 sheet 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;

[0020]

[0021] 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:

[0022]

[0023] After optimization, the step (2) comprises:

[0024] 1) Determine the basic parameters of the PSO algorithm and collect relevant system data;

[0025] 2) Evaluate the fitness level of each particle to determine the best particle pbest and the global best particle gbest;

[0026] 3) The PSO operator updates particles according to a specific equation to form a new population data set;

[0027] 4) The algorithm iterates to find the optimal particle until a satisfactory stopping condition is met;

[0028] 5) The PSO algorithm defines a set of discrete variables in the feasible domain to provide initial values ​​for the SQP algorithm processing;

[0029] 6) The SQP algorithm optimizes the discrete variables to find the optimal value set of passive shimming;

[0030] 7) The process ends when the solution does not improve significantly within the specified number of iterations.

[0031] The above technical solution has the following beneficial effects:

[0032] The present invention optimizes MRI passive shimming by using a hybrid optimization algorithm (PSO-SQP) combining particle swarm optimization PSO and SQP algorithm, which can improve the efficiency of passive vibration reduction, balance the magnetic field quality, iron usage and harmonics in an optimal way, and obtain a smoother magnetic field profile.

[0033] The hybrid optimization algorithm PSO-SQP not only retains the global search capability of the PSO algorithm, but also utilizes the fast convergence of the SQP algorithm, ultimately enhancing the homogeneity of B0. The simulation results verify that the algorithm can quickly and effectively obtain the optimal solution. The proposed PSO-SQP hybrid optimization algorithm has multiple engineering advantages.

[0034] The B0 magnetic field of MRI is more uniform, which can produce high-quality MRI images;

[0035] The distribution density of shim iron in the MRI magnet system is significantly reduced, resulting in a reduction in the total mass of the shim iron. This reduction can enhance thermal stability and reduce eddy current effects.

[0036] The proposed algorithm does not require any modification to the standard shimming hardware system and has superior performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The present invention will be further described below in conjunction with the accompanying drawings:

[0038] Figure 1 It is the flow chart of PSO-SQP algorithm;

[0039] Figure 2 It is a schematic diagram of the magnetic field of the uniform field iron sheet at the coordinate Q (u, θ, α) to the point P (w, γ, β);

[0040] Figure 3 The DSV surface magnetic field distribution map obtained by using the PSO-SQP algorithm;

[0041] Figure 4 The thickness distribution diagram of the uniform field iron sheet obtained by using the PSO-SQP algorithm;

[0042] Figure 5 This is the iron piece distribution map obtained by the PSO-SQP algorithm;

[0043] Figure 6 This is the convergence characteristic diagram of PSO-SQP and PSO algorithms. DETAILED DESCRIPTION

[0044] The following is a technical solution of a hybrid nonlinear programming method for optimizing MRI passive shimming according to the present invention, which is further described in conjunction with specific embodiments:

[0045] Example 1

[0046] 1. Initial magnetic field measurement

[0047] The magnetic field of 576 sampling points on the 40 cm DSV surface was measured using a standard magnetic field camera. On the DSV surface, the positions of 24 points were measured at 15 degree intervals. The average magnetic field intensity was 7.04 T, and the peak-to-peak magnetic field inhomogeneity was Hp-p = 462 ppm.

[0048] Various shim iron sheets with a minimum thickness of 0.1 mm are used in the designed PS system. The size of the shim iron sheet is 40 mm × 50 mm, and the maximum thickness is 12 mm. A plastic sheet with a thickness of 0.5 mm is used to encapsulate the shim iron sheets. The shims are contained in 24 shim trays installed along the circumference of the thermal magnetic hole, and each shim tray contains 24 shim pockets. The number of circumferential shims is 1 to 24.

[0049] 2. Optimization Algorithm

[0050] The proposed mathematical model was solved using the PSO-SQP algorithm, and the number of population particles was 1000. The PSO algorithm was executed using the fmincon function in Matlab, with a total of 1000 iterations. The algorithm was executed on a personal computer using an Intel CoreTM i7 1.70GHz processor and Windows 11 operating system.

[0051] Example 2

[0052] 1. Initial magnetic field measurement

[0053] The magnetic field of 576 sampling points on the 40 cm DSV surface was measured using a standard magnetic field camera. On the DSV surface, the positions of 24 points were measured at 15 degree intervals. The average magnetic field intensity was 7.04 T, and the peak-to-peak magnetic field inhomogeneity was Hp-p = 462 ppm.

[0054] Various shim iron sheets with a minimum thickness of 0.1 mm are used in the designed PS system. The size of the shim iron sheet is 40 mm × 50 mm, and the maximum thickness is 12 mm. A plastic sheet with a thickness of 0.5 mm is used to encapsulate the shim iron sheets. The shims are contained in 24 shim trays installed along the circumference of the thermal magnetic hole, and each shim tray contains 24 shim pockets. The number of circumferential shims is 1 to 24.

[0055] 2. Optimization Algorithm

[0056] The proposed mathematical model was solved using the PSO algorithm with a population of 1000 particles. It was implemented in Matlab using a population of 1000 particles. The algorithm was executed on a personal computer using an Intel CoreTM i7 1.70GHz processor and Windows 11 operating system.

[0057] Example 3

[0058] 1. Initial magnetic field measurement

[0059] The magnetic field of 576 sampling points on the 40 cm DSV surface was measured using a standard magnetic field camera. On the DSV surface, the positions of 24 points were measured at 15 degree intervals. The average magnetic field intensity was 7.04 T, and the peak-to-peak magnetic field inhomogeneity was Hp-p = 462 ppm.

[0060] Various shim iron sheets with a minimum thickness of 0.1 mm are used in the designed PS system. The size of the shim iron sheet is 40 mm × 50 mm, and the maximum thickness is 12 mm. A plastic sheet with a thickness of 0.5 mm is used to encapsulate the shim iron sheets. The shims are contained in 24 shim trays installed along the circumference of the thermal magnetic hole, and each shim tray contains 24 shim pockets. The number of circumferential shims is 1 to 24.

[0061] 2. Optimization Algorithm

[0062] The proposed mathematical model is solved using the SQP algorithm, which uses the built-in fmincon function of Matlab to solve nonlinear programming (NP) problems. The SQP algorithm uses different initial values ​​to converge to a solution. The algorithm is executed on a personal computer using an Intel CoreTM i7 1.70GHz processor and Windows 11 operating system.

[0063] In the embodiment 1, the PSO-SQP hybrid algorithm first uses the PSO algorithm to obtain the initial solution of the iron thickness, and then applies the SQP method to improve the B0 uniformity. The l1 norm regularization term is added to obtain a sparse solution; after the shim iron sheet is rounded, the B0 uniformity is 3.6ppm (peak-to-peak value), and the obtained B0 magnetic field distribution is as follows: Figure 3 The total mass of the uniform field iron sheet is 1.2 kg, and the thickness distribution of the uniform field iron sheet is as follows: Figure 4 shown. Figure 5 is the two-dimensional distribution of the shim iron sheets. From the figure, we can see the sparse distribution pattern of the shim iron sheets, which indicates that the workload of putting the shim iron sheets into the iron sheet pockets will be greatly reduced.

[0064] Compared with the PSO algorithm, the magnetic field uniformity reaches 96.7% at (105~3.6) / 105. In contrast, the PSO-SQP method only uses 1.2kg of shimmed iron sheets with pads, which increases the total mass of the iron sheets by (2.6-1.2) / 2.6=53.9%. Simulation experiments show that the PSO-SQP algorithm is superior to the PSO algorithm in terms of magnetic field uniformity and total mass of shimmed iron sheets. In addition, the PSO-SQP algorithm can also generate a sparser shimmed iron sheet configuration through regularization.

[0065] In order to evaluate the effectiveness of the proposed algorithm, additional experiments were conducted and the convergence characteristics of the proposed PSO-SQP algorithm and PSO algorithm were obtained as follows Figure 6 As shown in Figure 2. The PSO-SQP algorithm starts with 1000 particles and after 1000 iterations, the initial solution obtained is not as good as PSO. However, as the algorithm develops, the PSO-SQP algorithm shows improvement and produces a more superior solution.

[0066] Subsequently, the effect of different numbers of iterations of the PSO-SQP algorithm on the solution quality was studied. The PSO algorithm used 20 particles for a single iteration. The experimental results show that when the number of SQP iterations is large, the PSO-SQP algorithm obtains the best results. However, when the number of iterations exceeds 1000, this relative improvement decreases, which may be because the SQP algorithm has reached a local optimal solution. When the number of iterations exceeds 2000, the PSO-SQP algorithm fails to produce meaningful results.

[0067] Simulation studies have shown that using only 1.2 kg of shimming iron in a 7T MRI magnet with a 40 cm diameter spherical surface diameter (DSV) can improve the magnetic field from 462 ppm to 3.6 ppm. Compared with traditional optimization techniques, this method improves magnetic field uniformity by 96.7% and reduces iron requirements by 81.8%.

[0068] 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 hybrid nonlinear programming method for optimizing MRI passive shimming, 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) Hybrid optimization: The robust global search capability of the PSO algorithm is used to solve the given mathematical model problem. The search results are then used as the starting point of the SQP algorithm, and the SQP algorithm is used to explore the original optimization problem. The hybrid PSO-SQP algorithm is used to optimize the passive field of the MRI system.

2. A hybrid nonlinear programming method for optimizing MRI passive shimming 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. A hybrid nonlinear programming method for optimizing MRI passive shimming 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. A hybrid nonlinear programming method for optimizing MRI passive shimming according to claim 2, characterized in that: The sensitivity coefficient matrix A in 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. A hybrid nonlinear programming method for optimizing MRI passive shimming 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.

6. A hybrid nonlinear programming method for optimizing MRI passive shimming according to claim 2, characterized in that: The sensitivity coefficient matrix A is constructed through experimental tests.

7. A hybrid nonlinear programming method for optimizing MRI passive shimming 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. M is the total number of shim drawers.

8. The hybrid nonlinear programming method for optimizing MRI passive shimming 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:

9. The hybrid nonlinear programming method for optimizing MRI passive shimming according to claim 1, characterized in that: The step (2) comprises: 1) Determine the basic parameters of the PSO algorithm and collect relevant system data; 2) Evaluate the fitness level of each particle to determine the best particle pbest and the global best particle gbest; 3) The PSO operator updates particles according to a specific equation to form a new population data set; 4) The algorithm iterates to find the optimal particle until a satisfactory stopping condition is met; 5) The PSO algorithm defines a set of discrete variables in the feasible domain to provide initial values ​​for the SQP algorithm processing; 6) The SQP algorithm optimizes the discrete variables to find the optimal value set of passive shimming; 7) The process ends when the solution does not improve significantly within the specified number of iterations.

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