Passive shimming optimization method of MRI based on genetic algorithm-sequential quadratic programming

doi:10.3785/j.issn.1008-973X.2024.06.020

Journal of ZheJiang University (Engineering Science)

2024, Vol. 58

Issue (6): 1305-1314 DOI: 10.3785/j.issn.1008-973X.2024.06.020

Passive shimming optimization method of MRI based on genetic algorithm-sequential quadratic programming

Jie ZHAO1(

),Feng LIU2,Ling XIA3,Yifeng FAN1,*(

)

1. School of Medical Imaging, Hangzhou Medical College, Hangzhou 310053, China
2. School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane 4072, Australia
3. Key Laboratory of Biomedical Engineering, Ministry of Education, Zhejiang University, Hangzhou 310027, China

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Abstract

A genetic algorithm-sequential quadratic programming (GA-SQP) was proposed to improve the uniformity performance of main magnetic field (B₀) in 7 T magnetic resonance imaging (MRI), in order to solve the inherent problem of uneven B₀ field in MRI system. From the perspective of the mathematical model of passive shimming, a stable initial solution was obtained with the GA algorithm to achieve the first optimization of B₀ field, and then the second optimization of the main magnetic field was realized in less time through the rapid solution of the SQP algorithm, and the uniformity of B₀ of MRI was significantly improved. Additionally, L1-Norm regularization method was utilized to reduce the weight of the iron sheets and obtain a sparse iron distribution. Through simulation-based case studies, a bare magnetic field successfully shimmed with an uniformity of 462$ \times $10^?6 to 4.5$ \times $10^?6, using only 0.8 kg of iron pieces on shimming space. The magnetic field uniformity of the new solution was improved by 96.7% and the total iron sheet consumption weight was reduced by 85.7%, compared with those of the traditional GA optimization method. Experimental results show that the GA-SQP algorithm is more robust and competitive than other optimization algorithms.

Key words： magnetic resonance imaging passive shimming genetic algorithm-sequential quadratic programming (GA-SQP) regularization method nonlinear programming

Received: 06 July 2023 Published: 25 May 2024

CLC:

TP 3

Fund: 浙江省基础公益研究计划资助项目(LTGY23H180019).

Corresponding Authors: Yifeng FAN E-mail: zjuzhaojie@zju.edu.cn;fanyifeng@hmc.edu.cn

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Cite this article:

Jie ZHAO,Feng LIU,Ling XIA,Yifeng FAN. Passive shimming optimization method of MRI based on genetic algorithm-sequential quadratic programming. Journal of ZheJiang University (Engineering Science), 2024, 58(6): 1305-1314.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2024.06.020 OR https://www.zjujournals.com/eng/Y2024/V58/I6/1305

基于遗传算法-序列二次规划的磁共振被动匀场优化方法

为了解决磁共振成像（MRI）系统中固有的主磁场(B₀)不均匀的问题，提出遗传算法-序列二次规划(GA-SQP)算法，以提高7 T磁共振的主磁场均匀性. 从被动匀场数学模型的角度出发，该混合算法利用GA算法获得稳定的初始解，实现主磁场的第1次优化，再通过SQP算法的快速求解，在较少的时间内实现主磁场的第2次优化，同时提高磁共振主磁场的均匀性. 采用正则化方法减少磁场均匀所需的铁片质量，并且获得稀疏的铁片分布. 在仿真建模的案例研究中，7 T磁共振裸磁场均匀度可以从462$ \times $10^?6 优化到4.5$ \times $10^?6，并且在匀场空间上仅消耗0.8 kg的铁片. 相比于传统的GA优化方法，新方案的磁场均匀性提高了96.7%，总铁片消耗质量减少了85.7%. 实验结果表明，GA-SQP算法比其他优化算法具有更强的鲁棒性和竞争力.

关键词： 磁共振成像, 被动匀场, 遗传算法-序列二次规划（GA-SQP）, 正则化方法, 非线性优化

Fig.1 MRI system and internal shim system

Fig.2 Schematic diagram of magnetic field effect of unit shim iron sheet

Fig.3 Flow chart of GA-SQP algorithm

Tab.1 Passive shimming system parameters of 7 T MRI

Fig.4 Diagram of bare magnetic field at 7 T MRI

Fig.5 Simulation results of magnetic field distribution and shim iron sheet thickness of GA algorithm

Fig.6 Planar distribution of iron sheets obtained by GA algorithm

Tab.2 Results of SQP algorithm with different initial points

Fig.7 Simulation results of magnetic field distribution and shim iron sheet thickness of SQP algorithm

Fig.8 Planar distribution of iron sheet obtained by SQP algorithm

Fig.9 Optimization trajectory of different optimization methods

Fig.10 Simulation results of magnetic field distribution and shim iron sheet thickness of GA-SQP algorithm

Fig.11 Planar distribution of iron sheet obtained by GA-SQP hybrid algorithm

Tab.3 Simulation results of different optimization algorithms


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