采用三阶贝塞尔径向参数化与双材料架构的双极型超低场磁共振磁体优化设计

Optimal Design of a Bipolar Ultra-Low-Field Magnetic Resonance Imaging Magnet Using Third-Order Bézier Radial Parameterization and a Dual-Material Architecture

摘要

针对超低场磁共振成像系统中双极型永磁体磁场均匀性受限且材料成本较高的问题，提出一种采用三阶贝塞尔径向参数化的磁体几何优化方法。该方法将传统圆盘磁体的单一半径参数拓展为4个径向自由度，在保持轮廓平滑性与制造可行性的同时显著扩大结构优化空间。基于遗传算法与有限元方法耦合计算，对磁体、极靴及铁轭等关键部件的几何参数进行联合仿真优化，获得磁场强度均值为59.2 mT、磁场不均匀度为1 272×10^-6的钐钴永磁体系统，相较传统圆盘结构不均匀度降低了21%。在此基础上，引入钐钴-钕铁硼（SmCo-NdFeB）双材料复合磁体架构，并在新几何范式下开展整数-贝塞尔复合优化，最终得到磁场强度均值为58.5 mT、不均匀度为556×10^-6的双材料磁体系统，不均匀度较传统方案降低66%。研究结果表明，基于三阶贝塞尔径向参数化的几何范式能够有效提升双极型超低场永磁体的磁场均匀性，并为双材料磁体的协同优化提供可行路径。

Abstract

To address the limited magnetic field homogeneity and high material cost of bipolar permanent magnet systems for ultra-low-field magnetic resonance imaging,a geometric optimization method using third-order Bézier radial parameterization is proposed.The single radius parameter of a conventional disk-shaped magnet is extended to four radial degrees of freedom,thereby significantly expanding the structural optimization space while maintaining profile smoothness and manufacturing feasibility.Coupled calculations using a genetic algorithm and the finite element method are performed to jointly optimize the geometric parameters of key components,including the magnets,pole pieces,and yoke.A SmCo permanent magnet system with an average magnetic field of 59.2 mT and a field inhomogeneity of 1 272×10^-6 is obtained,with the inhomogeneity reduced by 21% compared with that of the conventional disk structure.On this basis,an SmCo-NdFeB dual-material composite magnet architecture is introduced,and integer-Bézier composite optimization is performed under the new geometric framework.A dual-material magnet system with an average magnetic field of 58.5 mT and an inhomogeneity of 556×10^-6 is finally obtained,with the inhomogeneity reduced by 66% compared with that of the conventional design.It is shown that the geometric framework based on third-order Bézier radial parameterization effectively improves the magnetic field homogeneity of bipolar ultra-low-field permanent magnets and provides a feasible approach for the coordinated optimization of dual-material magnets.

关键词

超低场磁共振成像 / 贝塞尔径向参数化 / 双极型永磁体 / 磁场均匀性

Key words

ultra-low-field magnetic resonance imaging / Bézier radial parameterization / bipolar permanent magnet / magnetic field homogeneity

参考文献

[1] He Luyang,Yu Hao,Shi Lizheng,et al. Equity assessment of the distribution of CT and MRI scanners in China：a panel data analysis[J]. International Journal for Equity in Health, 2018,17（1）：157.

[2] 田洪君,陈思平,汪天富,等. 一种有效的低场磁共振系统的水脂分离成像方法[J]. 西安交通大学学报, 2009,43（6）：52-56.

[3] Tian Hongjun,Chen Siping,Wang Tianfu,et al. Efficient water fat separation algorithm for low field magnetic resonance imaging system[J]. Journal of Xi’an Jiaotong University, 2009,43（6）：52-56.

[4] Samardzija A,Selvaganesan K,Zhang H Z,et al. Low—field,low—cost,point—of—care magnetic resonance imaging[J]. Annual Review of Biomedical Engineering, 2024,26：67-91.

[5] 万裁,何为,沈晟,等. 超低场磁共振膝关节正交接收线圈设计[J]. 电工技术学报, 2024,39（7）：1923-1931.

[6] Wan Cai,He Wei,Shen Sheng,et al. Design of a quadrature receive coil for ultra—low—field knee magnetic resonance imaging[J]. Transactions of China Electrotechnical Society, 2024,39（7）：1923-1931.

[7] 张宇翔,何为,孔晓涵,等. 基于硅钢片均一化的超低场磁共振抗涡流Z梯度线圈设计方法[J]. 电工技术学报, 2025,40（4）：987-996.

[8] Zhang Yuxiang,He Wei,Kong Xiaohan,et al. A design method for eddy current—resistant Z—gradient coil in ultra—low field magnetic resonance imaging systems based on homogeneous of silicon steel sheets[J]. Transactions of China Electrotechnical Society, 2025,40（4）：987-996.

[9] 孟凡钦,郭轶,何为,等. 基于边界元逆问题法的超低场磁共振大鼠脑部成像双通道射频线圈优化设计[J]. 电工技术学报, 2025,40（1）：25-35.

[10] Meng Fanqin,Guo Yi,He Wei,et al. Optimal design of rat brain dual—channel RF coils for ultra—low—field magnetic resonance imaging based on boundary element inverse problem method[J]. Transactions of China Electrotechnical Society, 2025,40（1）：25-35.

[11] 杨磊,何为,贺玉成,等. 开放式超低场移动磁共振系统的电磁干扰抑制方法[J]. 电工技术学报, 2024,39（15）：4708-4717.

[12] Yang Lei,He Wei,He Yucheng,et al. Electromagnetic interference suppression method for an unshielded portable ultra—low field magnetic resonance imaging scanner[J]. Transactions of China Electrotechnical Society, 2024,39（15）：4708-4717.

[13] Liu Yilong,Leong A T L,Zhao Yujiao,et al. A low—cost and shielding—free ultra—low—field brain MRI scanner[J]. Nature Communications, 2021,12（1）：7238.

[14] 陈顺中,王秋良,孙万硕,等. 3T动物磁共振成像传导冷却超导磁体研究[J]. 电工技术学报, 2023,38（4）：879-888.

[15] Chen Shunzhong,Wang Qiuliang,Sun Wanshuo,et al. The study of a 3T conduction—cooled superconducting magnet for animal magnetic resonance imaging[J]. Transactions of China Electrotechnical Society, 2023,38（4）：879-888.

[16] Cooley C Z,Haskell M W,Cauley S F,et al. Design of sparse Halbach magnet arrays for portable MRI using a genetic algorithm[J]. IEEE Transactions on Magnetics, 2018,54（1）：5100112.

[17] O’reilly T,Teeuwisse W M,Webb A G. Three—dimensional MRI in a homogenous 27 cm diameter bore Halbach array magnet[J]. Journal of Magnetic Resonance, 2019,307：106578.

[18] O’eilly T,Teeuwisse W M,De Gans D,et al. In vivo 3D brain and extremity MRI at 50 mT using a permanent magnet Halbach array[J]. Magnetic Resonance in Medicine, 2020,85（1）：495-505.

[19] Galve F,Pallás E,Guallart—Naval T,et al. Elliptical Halbach magnet and gradient modules for low—field portable magnetic resonance imaging[J]. NMR in Biomedicine, 2024,37（12）：e5258.

[20] Algarín J M,Díaz—Caballero E,Borreguero J,et al. Simultaneous imaging of hard and soft biological tissues in a low—field dental MRI scanner[J]. Scientific Reports, 2020,10（1）：21470.

[21] Mazurek M H,Cahn B A,Yuen M M,et al. Portable,bedside,low—field magnetic resonance imaging for evaluation of intracerebral hemorrhage[J]. Nature Communications, 2021,12（1）：5119.

[22] Krupinski E A,Harris D,Arlinghaus L R,et al. Image quality assessment of advanced reconstruction algorithm for point—of—care MRI scanner[J]. Journal of Medical Imaging, 2023,10（S1）：S11913.

[23] Ljungberg E,Padormo F,Poorman M,et al. Characterization of portable ultra—low Field MRI scanners for multi—center structural neuroimaging[J]. Human Brain Mapping, 2025,46（8）：e70217.

[24] Zhao Yujiao,Ding Ye,Lau V,et al. Whole—body magnetic resonance imaging at 0.05 Tesla[J]. Science, 2024,384（6696）：eadm7168.

[25] Su Shi,Zhao Yujiao,Ding Ye,et al. Ultra—low—field magnetization transfer imaging at 0.055T with low specific absorption rate[J]. Magnetic Resonance in Medicine, 2024,92（6）：2420-2432.

[26] He Yucheng,He Wei,Tan Liang,et al. Use of 2.1 MHz MRI scanner for brain imaging and its preliminary results in stroke[J]. Journal of Magnetic Resonance, 2020,319：106829.

[27] Xuan Liang,Zhang Yuxiang,Wu Jiamin,et al. Geometry—based shim coil design applied on an ultralow—field MRI system[J]. IEEE Transactions on Instrumentation and Measurement, 2023,72：1-11.

[28] 曲洪一,刘鑫,王晖,等. 磁共振成像磁体无源匀场改进策略及实验研究[J]. 电工技术学报, 2022,37（24）：6284-6293.

[29] Qu Hongyi,Liu Xin,Wang Hui,et al. Improved strategy and experimental research on passive shimming in magnetic resonance imaging magnet[J]. Transactions of China Electrotechnical Society, 2022,37（24）：6284-6293.

[30] Wang Ya,Xu Yajie,Wang Feng,et al. A passive shimming method for Halbach magnet based on magnetic sheet arrays[J]. Journal of Magnetic Resonance, 2022,339：107210.

[31] Shang Yun,Lamesgin S G,Kelly G,et al. Advancements in MR hardware systems and magnetic field control：B0 shimming,RF coils,and gradient techniques for enhancing magnetic resonance imaging and spectroscopy[J]. Psychoradiology, 2024,4：kkae013.

[32] Miyasaka T,Kajiwara M,Kawasaki A,et al. Development of a car—mounted mobile MR imaging system for diagnosis of sports—related wrist injury[J]. Magnetic Resonance in Medical Sciences, 2023,22（3）：379-387.

[33] Wei Shufeng,Wei Zhao,Wang Zheng,et al. Optimization design of a permanent magnet used for a low field （0.2 T）movable MRI system[J]. Magnetic Resonance Materials in Physics,Biology and Medicine, 2023,36（3）：409-418.

[34] 朱文亮,王志鹏. 基于改进A*算法和三阶贝塞尔曲线融合的路径规划分析[J]. 电子技术, 2025,54（3）：56-58.

[35] Zhu Wenliang,Wang Zhipeng. Analysis of path planning based on improved A* algorithm and third—order Bézier curve fusion[J]. Electronic Technology, 2025,54（3）：56-58.

[36] 张宇彤,牛立群,荆兆龙,等. 基于贝塞尔曲线的油浸倒立式电流互感器主绝缘频域介电谱建模[J]. 高电压技术, 2026,52（2）：859-867.

[37] Zhang Yutong,Niu Liqun,Jing Zhaolong,et al. FDS modeling of main insulation in oil—immersed inverted current transformers using Bézier curves[J]. High Voltage Engineering, 2026,52（2）：859-867.

[38] An Shizhong,Ma Zhenhui,Li Wuhui,et al. Magnetic properties of anisotropic bonded NdFeB/SmCo permanent magnets[J]. AIP Advances, 2019,9（12）：125146.

[39] Zhou Jiannan,Xiao Xia,Wang Zhenchang,et al. A novel magnetic thermal stability index system for evaluating the temperature effects on magnetic fields in high—homogeneity portable whole—body MRI[J]. IEEE Transactions on Instrumentation and Measurement, 2025,74：1-8.

基金资助

国家自然科学基金资助项目(52507273)

2024年陕西省博士后科研资助项目(2024BSHSDZZ132)

陕西省自然科学基础研究计划资助项目(2023-JC-QN-0437)