Abstract：Based on the magneto acoustic coupling effect, inductive magnetic acoustic tomography (MACT-MI) is a novel technique for imaging magnetic nano particle concentration (MNPs). However, previous research indicates that the current MACT-MI necessitates the employment of a high-amplitude excitation source device to generate magneto acoustic signals. To enable the ultrasonic probe to detect these acoustic signals, passing a pulse current of approximately 200 amperes through a Maxwell coil with a radius of 0.4 meters imposes stringent requirements on hardware configuration and hinders the advancement of experimental work. This paper introduces a device composed of a Maxwell-Helmholtz coil and a conical iron core for generating magnetic fields. Compared to traditional MACT-MI excitation units, this device incorporates an additional time-varying gradient magnetic field component induced by the conical iron core within the region of interest (ROI). The iron core's design optimization enhances the magnetic field's intensity and gradient allowing MNPs to convert magnetic energy into acoustic energy more efficiently, amplifying the magneto acoustic signals and reducing the excitation source's required amplitude. Firstly, the formula for the magnetic force acting on MNPs is derived, and the magnetic field distribution induced by the iron core in MACT-MI is analyzed. Secondly, three optimization objectives are identified: maximizing the magnetic induction intensity of the gradient magnetic field, the overall amplification intensity, and the simulated magnetic force. A multi-objective function is constructed, and the range of values for the decision variables is set. Then, the COMSOL simulation software is utilized to model and calculate all decision variables related to the iron core coil. Finally, constraint conditions are established after comprehensively considering the applicability and production cost of the iron core and coil. Two sets of optimized iron core dimensions are obtained by applying the harmony search algorithm to filter the decision variables. COMSOL software is used to generate two-dimensional distribution maps and one-dimensional graphs of magnetic flux density, magnetic force, and sound pressure for the cylindrical and conical iron core coil models. Under identical excitation current conditions, the maximum magnetic induction intensity of the gradient magnetic field within the ROI for the cylindrical and conical iron core coils has increased by approximately 0.4 times and 6.9 times compared to the air-core coil. Furthermore, the axial magnetic field gradient has expanded by 0.2 times and 3 times, and the magnetic force experienced by the MNPs at the central position has intensified by 0.6 times and 10.4 times. The single-sided conical iron core coil designed in this paper can significantly enhance the gradient magnetic field generated by the MACT-MI device, leading to a notable increase in the magnetic force experienced by MNPs and the acoustic pressure. However, although magnetic field focusing can amplify the magnetic field intensity and gradient in regions proximal to the iron core, it inevitably decreases the uniformity of the magnetic field distribution. In conclusion, this paper conducts an in-depth study on the design of MACT-MI imaging devices, marking a significant step towards the practical application of MACT-MI imaging technology in biomedicine.
闫孝姮, 王兵, 陈伟华, 侯潇涵, 王宇飞. 基于锥形铁心线圈的感应式磁声磁粒子浓度成像研究[J]. 电工技术学报, 2025, 40(16): 5204-5215.
Yan Xiaoheng, Wang Bing, Chen Weihua, Hou Xiaohan, Wang Yufei. Study on Induction Magneto-Acoustic Magnetic Particle Concentration Imaging Based on Conical Core Coils. Transactions of China Electrotechnical Society, 2025, 40(16): 5204-5215.
[1] 闫孝姮, 李政兴, 孙迪, 等. 基于矩阵式线圈的感应式磁声磁粒子浓度成像研究[J]. 电工技术学报, 2022, 37(17): 4269-4283. Yan Xiaoheng, Li Zhengxing, Sun Di, et al.Mag- netoacoustic concentration tomography of magnetic nanoparticles with magnetic induction based on matrix coil[J]. Transactions of China Electrotechnical Society, 2022, 37(17): 4269-4283. [2] Shi Xiaoyu, Liu Guoqiang, Yan Xiaoheng, et al.Simulation research on magneto-acoustic concentration tomography of magnetic nanoparticles with magnetic induction[J]. Computers in Biology and Medicine, 2020, 119: 103653. [3] 闫孝姮, 李政兴, 潘也, 等. 相同极性永磁体对感应式磁声磁粒子浓度成像过程影响的仿真[J]. 电工技术学报, 2022, 37(8): 1926-1937. Yan Xiaoheng, Li Zhengxing, Pan Ye, et al.Simu- lation of the influence of permanent magnets of the same polarity on the magneto-acoustic concentration tomography of magnetic nanoparticles with magnetic induction process[J]. Transactions of China Electro- technical Society, 2022, 37(8): 1926-1937. [4] Al-Mutawaly N, de Bruin H, Findlay D. Magnetic nerve stimulation: field focality and depth of penetration[C]//2001 Conference Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Istanbul, Turkey, 2001: 877-880. [5] Salvador R, Miranda P C, Roth Y, et al.High- permeability core coils for transcranial magnetic stimulation of deep brain regions[C]//2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Lyon, France, 2007: 6652-6655. [6] Lai Lingfeng, Gu Chen, Qu Timing, et al.Simulation of AC loss in small HTS coils with iron core[J]. IEEE Transactions on Applied Superconductivity, 2015, 25(3): 4700905. [7] Rastogi P, Tang Yalun, Zhang Bowen, et al.Quadruple butterfly coil with passive magnetic shielding for focused transcranial magnetic stimu- lation[J]. IEEE Transactions on Magnetics, 2017, 53(11): 5400305. [8] 夏思萍, 徐雅洁, 顾卫国, 等. 经颅磁刺激铁芯线圈的优化设计研究[J]. 航天医学与医学工程, 2021, 34(4): 304-313. Xia Siping, Xu Yajie, Gu Weiguo, et al.Research on optimal design of transcranial magnetic stimulation coil with iron core[J]. Space Medicine & Medical Engineering, 2021, 34(4): 304-313. [9] 孙钰婷, 逯迈. 不同铁芯材料对经颅磁刺激电磁场分布的对比研究[J]. 生物医学工程研究, 2022, 41(4): 382-390. Sun Yuting, Lu Mai.Comparative study on transcra- nical magnetic stimulation electromagnetic field distribution of different iron core materials[J]. Journal of Biomedical Engineering Research, 2022, 41(4): 382-390. [10] 闫孝姮, 淡新贤, 陈伟华, 等. 基于改进目标场法梯度线圈的感应式磁声磁粒子浓度成像研究[J]. 电工技术学报, 2024, 39(14): 4305-4316. Yan Xiaoheng, Dan Xinxian, Chen Weihua, et al.Magneto-acoustic magnetic particle concentration imaging based on improved target field method gradient coil[J]. Transactions of China Electro- technical Society, 2024, 39(14): 4305-4316. [11] 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. Wan Cai, He Wei, Shen Sheng, et al.Design of a quadrature receive coil for ultra-low-field knee mag- netic resonance imaging[J]. Transactions of China Electrotechnical Society, 2024, 39(7): 1923-1931. [12] 杨丹, 刘素羽, 张昊, 等. 基于永磁体和线圈复合结构的MPI零磁场研究[J]. 电工技术学报, 2025, 40(2): 335-345. Yang Dan, Liu Suyu, Zhang Hao, et al.Research on MPI zero magnetic field based on permanent magnet and coil composite structure[J]. Transactions of China Electrotechnical Society, 2025, 40(2): 335-345. [13] 董明, 李航辉, 马宏伟, 等. 高纯度横波蝶形线圈电磁超声换能器优化设计[J]. 电工技术学报, 2024, 39(11): 3270-3279. Dong Ming, Li Hanghui, Ma Hongwei, et al.Optimi- zation design of high-purity shear wave electro- magnetic acoustic transducer with butterfly coil[J]. Transactions of China Electrotechnical Society, 2024, 39(11): 3270-3279. [14] Zhao Zhiyuan, Torres-Díaz I, Rinaldi C.Brownian dynamics simulations of magnetic nanoparticles captured in strong magnetic field gradients[J]. The Journal of Physical Chemistry C, 2017, 121(1): 801-810. [15] 梁昆淼. 数学物理方法[M]. 4版. 北京: 高等教育出版社, 2010. [16] Tobias K, M Buzug T. Magnetic Particle Imaging[M]. New York: Springer Science, 2012. [17] Yan Xiaoheng, Li Jun, Xu Hong, et al.Numerical study on imaging of magnetic nanoparticles with ultrasound based on saturation magnetization[J]. Journal of Physics D: Applied Physics, 2022, 55(42): 425401. [18] Cao Ruijie, Huang Yang, Guo Gepu, et al.Perfor- mance improvement of magnetoacoustic harmonic imaging for magnetic nanoparticles based on the electromagnetic excitation with a conical core[J]. Applied Acoustics, 2021, 180: 108105. [19] Mirzaei M, Ripka P, Grim V.A novel position sensor with a conical iron core[J]. IEEE Transactions on Instrumentation and Measurement, 2020, 69(11): 9178-9189. [20] Binns K J, Lawrenson P J, Trowbridge C W.The Analytical and Numerical Solution of Electric and Magnetic Fields[M]. 1 ed, Wiley, 1992. [21] Mirzaei M, Ripka P, Chirtsov A, et al.Eddy current linear speed sensor[J]. IEEE Transactions on Mag- netics, 55(1): 1-4. [22] 郑涛, 何瑞, 潘志远, 等. MMC-HVDC换流变压器复杂性涌流产生机理及其影响分析[J]. 电力系统自动化, 2022, 46(23): 102-108. Zheng Tao, He Rui, Pan Zhiyuan, et al.Analysis on generation mechanism and influence of complex inrush current in MMC-HVDC converter transfor- mer[J]. Automation of Electric Power Systems, 2022, 46(23): 102-108. [23] Yan Xiaoheng, Pan Ye, Chen Weihua, et al.Simu- lation research on the forward problem of mag- netoacoustic concentration tomography for magnetic nanoparticles with magnetic induction in a saturation magnetization state[J]. Journal of Physics D: Applied Physics, 2021, 54(7): 075002. [24] Ali M, Siarry P, Pant M.An efficient differential evolution based algorithm for solving multi-objective optimization problems[J]. European Journal of Opera- tional Research, 2012, 217(2): 404-416. [25] 杨松松. 铁芯绕组结构的磁场分布与漏磁分析研究[D]. 昆明: 昆明理工大学, 2015. Yang Songsong.Study on magnetic field distribution and magnetic leakage analysis of iron core winding structure[D]. Kunming: Kunming University of Science and Technology, 2015. [26] Li Weijun, Liu Zhenyu.A method of SVM with normalization in intrusion detection[J]. Procedia Environmental Sciences, 2011, 11: 256-262. [27] Kim J H, Geem Z W, Jung D, et al.Advances in Harmony Search, Soft Computing and Applications[M]. Cham: Springer International Publishing, 2020.
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