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超椭圆柱设计表面能够减小线圈与目标的距离, 提高空间利用率, 扩大成像区域的有效范围. 提出利用流函数法及柱面的可展性在超椭圆柱面上设计核磁共振成像系统中的梯度线圈. 根据Biot-Savart定律建立磁场强度与流函数的表达式, 采用最小二乘法和Tikhonov正则化方法构造了双目标设计函数. 利用柱面的可展性提高了基于分片离散流函数计算电磁场的数值精度, 通过L-曲线方法实现了正则参数的合理选取. 通过引入适当的流函数边界约束条件, 把梯度线圈的优化问题转化为适定线性方程组的直接求解问题. 通过数值算例验证了超椭圆柱面展开求解方法的正确性. 优化结果显示, 在满足线性度误差小于5 %的设计约束下, 该方法在设计超椭圆柱面线圈驱动电流分布的同时有效控制了梯度线圈的能耗.
[1] Xu Y, Liang B L 2009 Medical Imaging Equipment (Beijing: People's Medical Publishing House) pp162-195 (in Chinese) [徐跃, 梁碧玲 2009 医学影像设备学(北京: 人民卫生出版社)第162–195 页]
[2] Wang H Z, Zhang X L, Wu J 2008 Experiment Study of Magnetic Resonance Imaging (Beijing: Science Press) pp3-29 (in Chinese) [汪红志, 张学龙, 武杰2008核磁共振成像技术试验教程(北京: 科学出版社)第3–29页]
[3] Turner R 1986 J. Phys. D: Appl. Phys. 19 L147
[4] Alsop D C, Connick T J 1996 Magn. Reson. Med. 35 875
[5] Liu Z Y, Jia F, Hennig J, Korvink J G 2012 IEEE Trans. Magn. 48 1179
[6] Liu W T, Zu D L, Tang X 2010 Chin. Phys. B 19 018701
[7] Poole M, Bowtell R 2007 Concepts Magn. Reson. B: Magn. Reson. Eng. 31B 162
[8] Peeren G N 2003 J. Comput. Phys. 191 305
[9] Tomasi D 2001 Magn. Reson. Med. 45 505
[10] Jia F, Liu Z Y, Zaitsev M, Hennig J, Korvink J 2014 Struct. Multidis. Optim. 49 523
[11] Pissanetzky S 1992 Meas. Sci. Technol. 3 667
[12] Liu H Y 1998 IEEE Trans. Magn. 34 2162
[13] Tomasi D, Caparelli E C, Panepucci H, Foerster B 1999 J. Magn. Reson. 140 325
[14] Liu W T, Zu D L, Tang X, Guo H 2007 J. Phys. D: Appl. Phys. 40 4418
[15] Zhu M H, Xia L, Liu F, Crozier S 2008 IEEE Trans. Magn. 44 2035
[16] Feng Z K, Hu G L, Xu Y, Zhu G, Zhou F, Dai Y M, Wang Q L 2013 Acta Phys. Sin. 62 230701 (in Chinese) [冯忠奎, 胡格丽, 许莹, 朱光, 周峰, 戴银明, 王秋良 2013 物理学报 62 230701]
[17] Forbes L K, Brideson M A, Crozier S 2005 IEEE Trans. Magn. 41 2134
[18] Wang L Q, Wang W M 2014 Chin. Phys. B 23 028703
[19] Moon S M, Goodrich K C, Hadley J R, Parker D L 2009 Concepts Magn. Reson. B: Magn. Reson. Eng. 35B 23
[20] Moon S M, Goodrich K C, Hadley J R, Kim S, Zeng G L, Morrell G R, McAlpine M A, Chronik B A, Parker D L 2011 Magn. Reson. Med. 65 863
[21] Brideson M A, Forbes L K, Crozier S 2002 Concepts Magn. Reson. 14 9
[22] Barr A H 1981 IEEE Comput. Graph. Appl. 1 11
[23] Franklin W R, Barr A H 1981 IEEE Comput. Graph. Appl. 1 41
[24] Pilu M, Fisher R 1995 Proceedings of the British Machine Vision Conference Birmingham, British, September 11-14, 1995 p257
[25] Jackson J D 1998 Classical Electrodynamics (New York: Wiley) pp174-224
[26] Ungersma S E, Xu H, Chronik B A, Scott G C, Macovski A, Conolly S M 2004 Magn. Reson. Med. 52 619
[27] Shi F, Ludwig R 1998 IEEE Trans. Magn. 34 671
[28] Cheng Y P, Zhang K Y, Xu Z 1989 The Theory of Matrices (Xi'an: Northwestern Polytechnical University Press) pp360-370 (in Chinese) [程云鹏, 张凯院, 徐仲1989矩阵论(西安: 西北工业大学出版社)第360–370页]
[29] Hu G L, Ni Z P, Wang Q L 2014 Acta Phys. Sin. 63 018301 (in Chinese) [胡格丽, 倪志鹏, 王秋良 2014 物理学报 63 018301]
[30] Xu W L, Zhang J C, Li X, Xu B Q, Tao G S 2013 Chin. Phys. B 22 010203
[31] Li Q Y, Wang N C, Yi D Y 2008 Numerical Analysis (Beijing: TsingHua University Press) pp202-208 (in Chinese) [李庆阳, 王能超, 易大义2008数值分析(北京: 清华大学出版社)第202–208页]
[32] Hansen P C, Nagy J G, O'Leary D P 2006 Deblurring Images: Matrices, Spectra, and Filtering (Philadelphia: Society for Industrial and Applied Mathematics) pp71-100
[33] Hansen P C 1994 Numer. Algorithms. 6 1
-
[1] Xu Y, Liang B L 2009 Medical Imaging Equipment (Beijing: People's Medical Publishing House) pp162-195 (in Chinese) [徐跃, 梁碧玲 2009 医学影像设备学(北京: 人民卫生出版社)第162–195 页]
[2] Wang H Z, Zhang X L, Wu J 2008 Experiment Study of Magnetic Resonance Imaging (Beijing: Science Press) pp3-29 (in Chinese) [汪红志, 张学龙, 武杰2008核磁共振成像技术试验教程(北京: 科学出版社)第3–29页]
[3] Turner R 1986 J. Phys. D: Appl. Phys. 19 L147
[4] Alsop D C, Connick T J 1996 Magn. Reson. Med. 35 875
[5] Liu Z Y, Jia F, Hennig J, Korvink J G 2012 IEEE Trans. Magn. 48 1179
[6] Liu W T, Zu D L, Tang X 2010 Chin. Phys. B 19 018701
[7] Poole M, Bowtell R 2007 Concepts Magn. Reson. B: Magn. Reson. Eng. 31B 162
[8] Peeren G N 2003 J. Comput. Phys. 191 305
[9] Tomasi D 2001 Magn. Reson. Med. 45 505
[10] Jia F, Liu Z Y, Zaitsev M, Hennig J, Korvink J 2014 Struct. Multidis. Optim. 49 523
[11] Pissanetzky S 1992 Meas. Sci. Technol. 3 667
[12] Liu H Y 1998 IEEE Trans. Magn. 34 2162
[13] Tomasi D, Caparelli E C, Panepucci H, Foerster B 1999 J. Magn. Reson. 140 325
[14] Liu W T, Zu D L, Tang X, Guo H 2007 J. Phys. D: Appl. Phys. 40 4418
[15] Zhu M H, Xia L, Liu F, Crozier S 2008 IEEE Trans. Magn. 44 2035
[16] Feng Z K, Hu G L, Xu Y, Zhu G, Zhou F, Dai Y M, Wang Q L 2013 Acta Phys. Sin. 62 230701 (in Chinese) [冯忠奎, 胡格丽, 许莹, 朱光, 周峰, 戴银明, 王秋良 2013 物理学报 62 230701]
[17] Forbes L K, Brideson M A, Crozier S 2005 IEEE Trans. Magn. 41 2134
[18] Wang L Q, Wang W M 2014 Chin. Phys. B 23 028703
[19] Moon S M, Goodrich K C, Hadley J R, Parker D L 2009 Concepts Magn. Reson. B: Magn. Reson. Eng. 35B 23
[20] Moon S M, Goodrich K C, Hadley J R, Kim S, Zeng G L, Morrell G R, McAlpine M A, Chronik B A, Parker D L 2011 Magn. Reson. Med. 65 863
[21] Brideson M A, Forbes L K, Crozier S 2002 Concepts Magn. Reson. 14 9
[22] Barr A H 1981 IEEE Comput. Graph. Appl. 1 11
[23] Franklin W R, Barr A H 1981 IEEE Comput. Graph. Appl. 1 41
[24] Pilu M, Fisher R 1995 Proceedings of the British Machine Vision Conference Birmingham, British, September 11-14, 1995 p257
[25] Jackson J D 1998 Classical Electrodynamics (New York: Wiley) pp174-224
[26] Ungersma S E, Xu H, Chronik B A, Scott G C, Macovski A, Conolly S M 2004 Magn. Reson. Med. 52 619
[27] Shi F, Ludwig R 1998 IEEE Trans. Magn. 34 671
[28] Cheng Y P, Zhang K Y, Xu Z 1989 The Theory of Matrices (Xi'an: Northwestern Polytechnical University Press) pp360-370 (in Chinese) [程云鹏, 张凯院, 徐仲1989矩阵论(西安: 西北工业大学出版社)第360–370页]
[29] Hu G L, Ni Z P, Wang Q L 2014 Acta Phys. Sin. 63 018301 (in Chinese) [胡格丽, 倪志鹏, 王秋良 2014 物理学报 63 018301]
[30] Xu W L, Zhang J C, Li X, Xu B Q, Tao G S 2013 Chin. Phys. B 22 010203
[31] Li Q Y, Wang N C, Yi D Y 2008 Numerical Analysis (Beijing: TsingHua University Press) pp202-208 (in Chinese) [李庆阳, 王能超, 易大义2008数值分析(北京: 清华大学出版社)第202–208页]
[32] Hansen P C, Nagy J G, O'Leary D P 2006 Deblurring Images: Matrices, Spectra, and Filtering (Philadelphia: Society for Industrial and Applied Mathematics) pp71-100
[33] Hansen P C 1994 Numer. Algorithms. 6 1
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