基于硅钢片均一化的超低场磁共振抗涡流<em>Z</em>梯度线圈设计方法

doi:10.19595/j.cnki.1000-6753.tces.240166

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摘要在超低场磁共振成像设备中,铁磁材料（抗涡流板、铁轭等）会对成像目标区域梯度磁场产生影响,并且在梯度线圈,特别是Z方向线圈工作时,这些金属部件中感应的涡流会导致成像伪影。为解决上述问题,该文提出一种针对永磁型超低场磁共振设备的平面抗涡流Z梯度线圈设计方法。首先,对线圈外侧的铁磁材料进行等效简化,将高磁导率的复杂抗涡流板结构（硅钢片压叠而成）简化为均质磁性板结构以减少计算复杂度。然后,提出一种梯度线圈的参数化设计方法,通过对线圈结构进行参数化表达,直接对Z方向梯度线圈的最终绕线结构进行多目标快速优化,同时在线圈外侧设置反向电流绕线控制系统涡流效应。在保证线圈效率（200 μT/(m·A)）、最大非线性度（小于5%）的前提下,线圈外侧目标平面最大杂散磁场降低了52%。最后,通过有限元仿真与实验验证了模型简化的准确性与所设计Z梯度线圈的抗涡流性能。

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关键词 ：磁共振成像, 梯度线圈, 电磁场逆问题, 铁磁结构简化

Abstract：In ultra-low field magnet magnetic resonance imaging (MRI) devices, ferromagnetic materials such as anti-eddy current plates and yokes can affect the gradient magnetic field in the imaging target area. Meanwhile, during the operation of gradient coils, especially the Z-direction gradient coil, induced eddy currents can lead to imaging artifacts. This paper proposes a design method for a planar eddy current-resistant Z-gradient coil for permanent magnet ultra-low field MRI devices.
Firstly, the ferromagnetic materials on the outer side of the coil are equivalently simplified. The complex eddy current shield structure (formed by stacking silicon steel sheets) with high magnetic permeability is simplified into a homogeneous magnetic plate structure. In general, conducting structures with high permeability closed to gradient coils can affect the magnetic field, and laminated structures can cause large computations. An analytical solution for the effective permeability of an anti-eddy current plate is introduced, and the laminated structure is reduced to the homogeneous magnetic plate. Thus, the simplified structure combined with the mirror current method introduces the influence of ferromagnetic materials on the gradient coil design process. Subsequently, a parameterized design method for a planar eddy current-resistant Z gradient coil is proposed. By parameterizing the coil structure, direct multi-objective rapid optimization of the final winding structure of the Z-direction gradient coil is achieved. At the same time, additional reverse current windings are implemented on the outer side of the coil to mitigate the eddy current effects. In detail, the structure of the proposed planar Z gradient coils is pre-defined as two groups of clockwise and anticlockwise spiral lines, which are parameterized to a set of points in the x-axis. Then, a multi-objective optimization is performed to obtain the point’s position considering the gradient coil’s maximum nonlinearity, efficiency, and stray magnetic field.
While ensuring coil efficiency (200 μT/(m·A)) and maximum nonlinearity (less than 5%), the maximum stray magnetic field on the outer side of the coil target plane is reduced by 52%. Finite element simulations and gradient field measurements are performed. By simulations, the errors between complete and simplified system models in coil efficiency and maximum nonlinearity are less than 4% and 0.1%, respectively. Also, the differences between simulation and measurement results for the complete model are less than 3% for efficiency and 1% for nonlinearity. Finally, the eddy current-resistant performance of the designed Z-gradient coil is verified through finite element simulations. Moreover, imaging experiments are implemented, and fewer image artifacts can be found.
Compared to conventional design methods, the proposed one considers the influence of high-permeability materials and eddy-current effects. The model simplification is also suitable for gradient coil design for other directions, which can be utilized for system eddy current characterizations. Future works may focus on quantitively evaluating the coils’ anti-eddy current effects and the impact of reverse current on coil efficiency in the design process.

Key words： Magnetic resonance imaging active shielded gradient coil electromagnetic field inverse problem ferromagnetic structure simplification

收稿日期: 2024-01-24

PACS:

TM12

基金资助:国家自然科学基金（52077023）和重庆科卫联合基金（2023MSXM016）资助项目

通讯作者: 徐征男,1980年生,教授,博士生导师,研究方向为电磁成像、电磁计算、磁共振系统设计及开发等。E-mail: xuzheng@cqu.edu.cn

作者简介: 张宇翔男,1994年生,博士研究生,研究方向为电磁成像、磁共振系统设计及优化等。E-mail: zhangyuxiang@cqu.edu.cn

引用本文:

张宇翔, 何为, 孔晓涵, 宣亮, 徐征. 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. Zhang Yuxiang, He Wei, Kong Xiaohan, Xuan Liang, Xu Zheng. 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. Transactions of China Electrotechnical Society, 2025, 40(4): 987-996.

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