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浙江大学学报(工学版)
浙江大学学报(工学版)  2024, Vol. 58 Issue (6): 1305-1314    DOI: 10.3785/j.issn.1008-973X.2024.06.020
生物医学工程     
基于遗传算法-序列二次规划的磁共振被动匀场优化方法
赵杰1(),刘锋2,夏灵3,范一峰1,*()
1. 杭州医学院 医学影像学院，浙江 杭州 310053
2. 昆士兰大学 信息技术与电气工程学院，昆士兰 布里斯班 4072
3. 浙江大学 生物医学工程教育部重点实验室，浙江 杭州 310027
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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摘要：

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    
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
收稿日期: 2023-07-06 出版日期: 2024-05-25
CLC:  TP 3  
基金资助: 浙江省基础公益研究计划资助项目(LTGY23H180019).
通讯作者: 范一峰     E-mail: zjuzhaojie@zju.edu.cn;fanyifeng@hmc.edu.cn
作者简介: 赵杰（1987—），男，博士，从事磁共振匀场技术研究. orcid.org/0000-0002-0485-2759. E-mail：zjuzhaojie@zju.edu.cn
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引用本文:

赵杰,刘锋,夏灵,范一峰. 基于遗传算法-序列二次规划的磁共振被动匀场优化方法[J]. 浙江大学学报(工学版), 2024, 58(6): 1305-1314.

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.

链接本文:

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

图 1  磁共振系统和内部匀场系统
图 2  单元匀场铁片磁场效果示意图
图 3  GA-SQP算法流程图
物理量/单位数值
磁场强度/ T7
球形区域直径/ mm400
匀场托盘半径/ mm360
匀场托盘数量24
每个托盘匀场抽屉数量24
匀场片尺寸/ mm40$ \times $50
每个匀场片厚度/ mm0.1
匀场抽屉最大厚度/ mm12
表 1  7 T磁共振系统被动匀场的系统参数
图 4  7 T磁共振原始磁场图
图 5  GA算法磁场分布和匀场铁片厚度仿真结果
图 6  GA算法获得的匀场铁片平面分布
初始点算法tFo/10?6
Upper boundSQP3 2567.9
Lower boundSQP3675.5
Middle pointSQP7246.8
RandomGA170 345145.0
GA solutionGA-SQP80 3674.5
表 2  不同初始点的SQP算法结果
图 7  SQP算法磁场分布和匀场铁片厚度仿真结果
图 8  SQP算法获得的匀场铁片厚度平面分布
图 9  不同优化方法的优化轨迹
图 10  GA-SQP 算法磁场分布和匀场铁片厚度仿真结果
图 11  GA-SQP 混合算法获得的匀场铁片平面分布
算法F/10?6M/kg
GA145.05.6
GA-SQP4.50.8
SQP5.51.5
LS6.89.6
LP12.09.5
表 3  多种优化算法的仿真结果
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