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基于Pareto优化理论的多目标超椭梯度线圈设计

潘辉 王亮 王强龙 陈利民 贾峰 刘震宇

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基于Pareto优化理论的多目标超椭梯度线圈设计

潘辉, 王亮, 王强龙, 陈利民, 贾峰, 刘震宇

Design of super-elliptical gradient coils based on multiple objective Pareto optimization method

Pan Hui, Wang Liang, Wang Qiang-Long, Chen Li-Min, Jia Feng, Liu Zhen-Yu
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  • 磁共振系统梯度线圈设计是一个多目标优化问题,在设计时需要综合考虑能耗、磁场能、线性度等设计要求.这些设计要求通常难以同时获得极小解,因此在设计梯度线圈时需要权衡线圈的各方面的设计需求.本文基于柱面可展性和流函数设计方法,结合Pareto优化方法实现了在超椭圆柱设计表面上梯度线圈的多目标设计.分别分析了磁场能、能耗目标对梯度线圈线性度、线圈构型的影响;并在Pareto解空间中分析各目标的相互变化关系,通过数值算例验证了该方法在超椭梯度线圈设计时的有效性与灵活性.优化结果显示,在满足线性度误差小于5%,能耗与磁场能分别小于用户设定值的设计约束下,梯度线圈的多目标设计存在多个局部优化解.该方法可以直观地比较相同目标函数值的情况下各单目标的具体表现,有利于实现不同的设计要求下梯度线圈的最终定型设计.
    The design of gradient coils for a magnetic resonance imaging (MRI) system is a multiple objective optimization problem, which usually needs to deal with a couple of conflicting design objectives, such as the stored magnetic energy, power consumption, and target linear gradient distribution. These design requirements usually conflict with each other, and there is no unique optimal solution which is capable of minimizing all objectives simultaneously. Therefore, the design of gradient coils needs to be optimized reasonably with the tradeoff among different design objectives. Based on the developable property of the super-elliptical cylindrical surface and the stream function design method, the multiple objective optimization problem is analyzed by using the Pareto optimization method in this paper. The effect of proposed approach is illustrated by using the stream function method and three aforementioned coil design objectives are analyzed. The influences of the stored magnetic energy and power consumption target on linearity of gradient coil and the configuration of coils are analyzed respectively. The suitable sizes of gradient coils are discussed by analyzing the change of the stored magnetic energy. A weighted sum method is employed to produce the optimal Pareto solutions, in which the multiple objective problem reduces into a single objective function through a weighted sum of all objectives. The quantitative relationship of each design requirement is analyzed in the Pareto solution space, where Pareto optimal solutions can be intuitively found by dealing efficiently with the tradeoff among different coil properties. Numerical examples of super-elliptical gradient coil solutions are provided to demonstrate the effectiveness and versatility of the proposed method to design super-elliptical gradient coils with different coil requirements. The optimization results show that there are multiple available solutions in the convex Pareto solution space under the constraints that the linear gradient deviation is less than 5% and the magnetic stored energy and power dissipated are both no more than user-preset values. In the case that the values of summed objective functions are the same, the proposed method can intuitively see the performance of each individual target, thereby conducting to realizing the final design of gradient coils under the different design requirements. With the proposed approach, coil designers can have a reasonable overview of gradient coil design about the achievable performances of some specific properties and the competing or compatible relationships among coils properties. Therefore, a suitable design of the gradient coils for a given requirement of MRI application can be chosen reasonably.
      通信作者: 刘震宇, liuzy@ciomp.ac.cn
    • 基金项目: 国家自然科学基金(批准号:51675506,51275504)、吉林省科技发展计划(批准号:20140519007JH)和欧洲研究理事会ERC启动基金RANGEmri282345项目资助的课题.
      Corresponding author: Liu Zhen-Yu, liuzy@ciomp.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51675506, 51275504), the Science and Technology Development Plan of Jilin Province, China (Grant No. 20140519007JH), and an European Research Council Starting Grant RANGEmri(Grant Agreement 282345).
    [1]

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    [2]

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    [3]

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    Forbes L K, Crozier S 2002 J. Phys. D: Appl. Phys. 35 839

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    Liu W T, Zu D L, Tang X 2010 Chin. Phys. B 19 018701

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    Forbes L K, Brideson M A, Crozier S 2005 IEEE Trans. Magn. 41 2134

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    Liu W T, Zu D L, Tang X, Guo H 2007 J. Phys. D: Appl. Phys. 40 4418

    [9]

    Li X, Xie D X, Wang J M 2009 IEEE Trans. Magn. 45 1804

    [10]

    Tomasi D 2001 Magn. Reson. Med. 45 505

    [11]

    Peeren G N 2003 J. Comput. Phys. 191 305

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    Lemdiasov R A, Ludwig R 2005 Concepts Magn. Reson. B: Magn. Reson. Eng. 26B 67

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    Liu Z Y, Jia F, Hennig J, Korvink J G 2012 IEEE Trans. Magn. 48 1179

    [14]

    Wang Q L 2013 Practical Design of Magnetostatic Structure Using Numerical Simulation (Singapore: John Wiley Sons) pp39-142

    [15]

    Hu G L, Ni Z P, Wang Q L 2012 IEEE Trans. Appl. Supercond. 22 4900604

    [16]

    Zhu X C, Wang Q L, Wang H S 2016 Adv. Technol. Electral. Eng. Energ. 35 43 (in Chinese) [朱旭晨, 王秋良, 王厚生 2016 电工电能技术 35 43]

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    Li X, Xia L, Chen W F, Liu F, Crozier S, Xie D X 2011 J. Magn. Reson. 208 148

    [18]

    Hu Y, Wang Q L, Li Y, Zhu X C, Niu C Q 2016 Acta Phys. Sin. 65 218301 (in Chinese) [胡洋, 王秋良, 李毅, 朱旭晨, 牛超群 2016 物理学报 65 218301]

    [19]

    Turner R 1993 Magn. Reson. Imag. 11 903

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    Abduljalil A M, Aletras A H, Robilaille P M L 1994 Magn. Reson. Med. 31 450

    [21]

    Alsop D C, Connick T J 1996 Magn. Reson. Med. 35 875

    [22]

    Pissanetzky S 1992 Meas. Sci. Technol. 3 667

    [23]

    Bowtell R, Robyr P 1998 J. Magn. Reson. 131 286

    [24]

    Wang L Q, Wang W M 2014 Chin. Phys. B 23 028703

    [25]

    Sanchez C C, Pantoja M F, Poole M, Bretones A R 2012 IEEE Trans. Magn. 48 1967

    [26]

    Marler R T, Arora J S 2004 Struct. Multid. Optim. 26 369

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    Marler R T, Arora J S 2005 Eng. Optim. 37 551

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    Xie D X, Sun X W, Bai B D, Yang S Y 2008 IEEE Trans. Magn. 44 1006

  • [1]

    Zu D L 2004 Magnetic Resonance Imaging (Beijing: Higher Education Press) pp53-82 (in Chinese) [俎栋林 2004 核磁共振成像学(北京: 高等教育出版社)第5382页]

    [2]

    Wang L, Cao Y H, Jia F, Liu Z Y 2014 Acta Phys. Sin. 63 238301 (in Chinese) [王亮, 曹英晖, 贾峰, 刘震宇 2014 物理学报 63 238301]

    [3]

    Turner R 1986 J. Phys. D: Appl. Phys. 19 147

    [4]

    Turner R 1988 J. Phys. E: Sci. Instrum. 21 948

    [5]

    Forbes L K, Crozier S 2002 J. Phys. D: Appl. Phys. 35 839

    [6]

    Liu W T, Zu D L, Tang X 2010 Chin. Phys. B 19 018701

    [7]

    Forbes L K, Brideson M A, Crozier S 2005 IEEE Trans. Magn. 41 2134

    [8]

    Liu W T, Zu D L, Tang X, Guo H 2007 J. Phys. D: Appl. Phys. 40 4418

    [9]

    Li X, Xie D X, Wang J M 2009 IEEE Trans. Magn. 45 1804

    [10]

    Tomasi D 2001 Magn. Reson. Med. 45 505

    [11]

    Peeren G N 2003 J. Comput. Phys. 191 305

    [12]

    Lemdiasov R A, Ludwig R 2005 Concepts Magn. Reson. B: Magn. Reson. Eng. 26B 67

    [13]

    Liu Z Y, Jia F, Hennig J, Korvink J G 2012 IEEE Trans. Magn. 48 1179

    [14]

    Wang Q L 2013 Practical Design of Magnetostatic Structure Using Numerical Simulation (Singapore: John Wiley Sons) pp39-142

    [15]

    Hu G L, Ni Z P, Wang Q L 2012 IEEE Trans. Appl. Supercond. 22 4900604

    [16]

    Zhu X C, Wang Q L, Wang H S 2016 Adv. Technol. Electral. Eng. Energ. 35 43 (in Chinese) [朱旭晨, 王秋良, 王厚生 2016 电工电能技术 35 43]

    [17]

    Li X, Xia L, Chen W F, Liu F, Crozier S, Xie D X 2011 J. Magn. Reson. 208 148

    [18]

    Hu Y, Wang Q L, Li Y, Zhu X C, Niu C Q 2016 Acta Phys. Sin. 65 218301 (in Chinese) [胡洋, 王秋良, 李毅, 朱旭晨, 牛超群 2016 物理学报 65 218301]

    [19]

    Turner R 1993 Magn. Reson. Imag. 11 903

    [20]

    Abduljalil A M, Aletras A H, Robilaille P M L 1994 Magn. Reson. Med. 31 450

    [21]

    Alsop D C, Connick T J 1996 Magn. Reson. Med. 35 875

    [22]

    Pissanetzky S 1992 Meas. Sci. Technol. 3 667

    [23]

    Bowtell R, Robyr P 1998 J. Magn. Reson. 131 286

    [24]

    Wang L Q, Wang W M 2014 Chin. Phys. B 23 028703

    [25]

    Sanchez C C, Pantoja M F, Poole M, Bretones A R 2012 IEEE Trans. Magn. 48 1967

    [26]

    Marler R T, Arora J S 2004 Struct. Multid. Optim. 26 369

    [27]

    Marler R T, Arora J S 2005 Eng. Optim. 37 551

    [28]

    Xie D X, Sun X W, Bai B D, Yang S Y 2008 IEEE Trans. Magn. 44 1006

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出版历程
  • 收稿日期:  2016-12-21
  • 修回日期:  2017-02-06
  • 刊出日期:  2017-05-05

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