Theory of gradient coil design methods for magnetic resonance imaging

Concepts in Magnetic Resonance Part A: Bridging Education and Research

Volumn 36, Issue 4, 2010, Pages 223-242

  Hidalgo Tobon, S S ^a  

^a DEPARTAMENTO DE QUÍMICA   (Mexico)

Author keywords

Acoustic noise; Gradient coil design; Magnetic resonance imaging; Review; Target field method

Indexed keywords

EID: 77955778890     PISSN: 15466086     EISSN: 15525023     Source Type: Journal    
DOI: 10.1002/cmr.a.20163     Document Type: Article

References (114)

1. Mansfield P, Grannell PK. 1973. NMR difraction in solids. J Phys C: Solid State Phys 6:L422-L427.
2. Lauterbur PC. 1973. Image formation by induced local interactions: examples employing nuclear magnetic resonance. Nature 242:190-191.
3. Jackson JD. 1998. Classical Electrodynamics. Wiley: New York.
4. Turner R. 1988. Minimum inductance coils. Phys E Sci Instrum 21:948-952.
5. Turner R. 1993. Gradient coil design: a review of methods. Magn Reson Imaging 11:903-920.
6. Turner R, Bowley RM. 1986. Passive screening of switched magnetic field gradients. J Phys E: Sci Instrum 19:876-879.
7. Schmitt F, Irnich W, Fischer H. 1998. Physiological Side Effects of Fast Gradient Switching in Echo Planar Imaging. Springer-Verlag: Berlin, Chapter 3.
8. Turner R. 1986. A target field approach to optimal coil design. J Phys D: Appl Phys 19:L147-L151.
9. Carlson JW, Derby KA, Hawryszko KC, Weideman M. 1992. Design and evaluation of shielded gradient coils. Magn Reson Med 26:191-206.
10. Xu H, Conolly SM, Scott GC, Macovski A. 1999. Fundamental scaling relations for homogeneous magnets. In: Proceedings of the ISMRM 7th Scientific Meeting, Philadelphia, PA, p 475.
11. Silva AC, Merkle H. 2003. Hardware considerations for functional magnetic resonance imaging. Concepts Magn Reson A 16:35-49.
12. Sabate J, Garces LJ, Szczesny PM, Qiming L, Wirth WF. 2004. High-power high-fidelity switching amplifier driving gradient coils for MRI systems. In: Proceedings of the 35th Annual IEEE Power Electronics Specialists Conference, Germany.
13. While PT, Forbes LK, Crozier S. 2010. Designing gradient coils with reduced hot spot temperatures. J Magn Reson 203:91-99.
14. Poole M, Weiss P, Sanchez-Lopez H, Ng M, Crozier S. 2010. Minimax current density coil design. J Phys D: Appl Phys 43:095001.
15. Lopez HS, Liu F, Poole M, Crozier S. 2009. Equivalent magnetization current method applied to the design of gradient coils for magnetic resonance imaging. IEEE Trans Magn 45:767-775.
16. Andrew ER, Szcesniak E. 1995. Low inductance transverse gradient system of restricted length. Magn Reson Med 13:607-613.
17. Mansfield P, Chapman BLW, Bowtell R, Glover P, Coxon R, Harvey PR. 1995. Active acoustic screening: reduction of noise in gradient coils by Lorentz force balancing. Magn Reson Med 33:276-281.
18. Wang F, Mechefske C. 2008. Vibration analysis and testing of a thin-walled gradient coil model. J Sound Vib 311:554-566.
19. Wang F, Mechefske C. 2007. Dynamic analysis of a multi-layered gradient coil insert in a 4T MRI scanner. Concepts in Magn Reson B 31:237-254.
20. Demas V, Prado PJ. 2009. Compact magnets for magnetic resonance. Concepts Magn Reson A 34:48-59.
21. Glover P. 2009. Interaction of MRI field gradients with the human body. Phys Med Biol 54:R99-R115.
22. Schenck JF, Edelstein WA, Hart HR, Williams CS, Bean CP, Bottomley PA, et al. 1983. Switched gradients and rapidly changing magnetic-field hazards in NMR imaging. Med Phys 10:133-133.
23. Hidalgo-Tobon SS, Bencsik M, Bowtell R. 2004. Reduction of peripheral nerve stimulation via the use of combined gradient and uniform field coils. In: ISMRM, Kyoto, Japan; Abstract No. 659.
24. Hidalgo-Tobon SS. 2005. Novel Gradient Coils. PhD Thesis, The University of Nottingham.
25. International Commission on Non-Ionizing Radiation Protection. 1998. ICNIRP Guidelines for Limiting Exposure to Time-Varying Electric, Magnetic, and Electromagnetic Fields International Commission on Non-Ionizing Radiation Protection. Health Physics 74:494-522.
26. Harvey PR, Katznelson E. 1999. Modular gradient coil: a new concept in high-performance whole-body gradient coil design. Magn Reson Med 42:561-570.
27. Kimmlingen R, Gebhardt M, Schuster J, Brand M, Schmitt F, Haase A. 2002. Gradient system providing continuously variable field characteristics. J Magn Reson Med 47:800-808.
28. Chronik B, Rutt B. 2001. A simple linear formulation for magnetostimulation specific to MRI gradient coils. Magn Reson Med 45:916-919.
29. Zhang B, Yen Y, Chronik B, McKinnon G, Schaefer D, Rutt B. 2003. Peripheral nerve stimulation properties of head and body gradient of various sizes. Magn Reson Med 50:50-58.
30. Faber S, Hoffmann A, Ruedig Ch, Reiser M. 2003. MRI-induced stimulation of peripheral nerves: dependency of stimulation threshold on patient positioning. Magn Reson Imaging 21:715-724.
31. Bencsik M, Bowtell R, Bowley R. 2007. Electric fields induced in the human body by time-varying magnetic field gradients in MRI: numerical calculations and correlation análisis. Phys Med Biol 52:2337-2353.
32. Schaefer D, Bourland J, Nyenhuis J. 2000. Review of patient safety in time-varying gradient fields. J Magn Reson Imaging 12:20-29.
33. Roméo F, Hould DI. 1984. Magnet field profiling: analysis and correcting coil design. Magn Reson Med 1:44-65.
34. Golay MJE. Magnetic Field Control Apparatus. US Patent 3,515,979. November 4, 1957.
35. Purcell EM. 1989. Helmholtz coils revisited. Am J Phys 57:18-22.
36. Frenkiel TA, Jasinski A, Morris PG. 1988. Apparatus for generation of magnetic field gradient waveforms for NMR imaging. J Phys E: Sci Instrum 21:374-377.
37. Suits BH, Wilken DE. 1989. Improving magnetic field gradient coils for NMR imaging. J Phys E: Sci Instrum 22:565-573.
38. Siebold H. 1990. Gradient field coils for MR imaging with high spectral purity. IEEE Trans Magn 26:897-900.
39. Vegh V, Zhao H, Brereton IM, Galloway GJ, Doddrell DM. 2006. A wave equation technique for designing compact gradient coils. Concepts Magn Reson B 29:62-64.
40. Lu H, Jesmanowicz A, Li Sh, Hyde J. 2004. Momentum-weighted conjugate gradient descent algorithm for gradient coil optimization. Magn Reson Med 51:158-164.
41. Crozier S, Doddrell D. 1993. Gradient-coil design by simulated annealing. J Magn Reson Ser A 103:354-357.
42. Crozier S, Forbes LK, Doddrell DM. 1994. The design of transverse gradient coils of restricted length by simulated annealing. J Magn Reson Ser A 107:126-128.
43. Peters A, Bowtell R. 1994. Biplanar gradient coil design by simulated annealing. MAGMA 2:387-389.
44. Hoult DI. 1973. The application of high field nuclear magnetic resonance. PhD Thesis, Oxford University.
45. Compton RC. 1982. Gradient coil apparatus for a magnetic resonance system. US Patent 4,456,881.
46. Schweikert KH, Krieg R, Noack F. 1988. A highfield air-cored magnet coil design for fast-field-cycling NMR. J Magn Reson 78:77-96.
47. Wong EC, Jesmanowicz A, Hyde JS. 1991. Coil optimization for MRI by conjugate gradient descent. Magn Reson Med 21:39-48.
48. Chronik B, Rutt B. 1998. Constrained length minimum inductance gradient coil design. Magn Reson Med 39:270-278.
49. Abramowitz M, Stegun IA. 1965. Handbook of Mathematical Functions. Dover, New York.
50. Mansfield P, Chapman B, Turner R, Roger M.1990. Magnetic Field Screens. US Patent 4,978,920.
51. Vavrek R, Schaefer D, Myers Ch, McFarland T, Turner R. 1993. Local Gradient Coil. US Patent 5,185,576.
52. Hidalgo S, Gadzinski C, Rutt B. 2009. Comparison between CCMI and CAHM for design shielded gradient coils for MRI. In: Proceedings of the ISMRM, Honolulu, HI; Abstract No 3057.
53. Lemdiasov A, Reinhold L. 2005. A stream function method for gradient coil design. Concepts Magn Reson B Mag Reson Eng 26:67-80.
54. Poole M, Bowtell R. 2007. Novel gradient coils designed using a boundary element method. Concepts Magn Reson B 31:162-175.
55. Poole M, Sanchez Lopez, Crozier S. 2009. Adaptively regularised gradient coils for reduced local heating. Concepts Magn Reson B 33:220-227.
56. Poole M. 2007. Improved Equipment and Techniques for Dynamic Shimming in High Field MRI. PhD Thesis, The University of Nottingham.
57. Pissanetzky S. 1992. Minimum energy MRI gradient coils of general geometry. Meas Sci Technol 3:667-673.
58. Peeren GN. 2003. Stream function approach for determining optimal surface currents. J Comput Phys 191:305-321.
59. Poole M, Bowtell R, Green D, Pittard S, Lucas A, Hawkes R, Carpenter A. 2009. Split gradient coils for simultaneous PET-MRI. Magn Reson Med 62:1106-1111.
60. Shou G, Xia L, Liu F, Zhu M, Li Y, Crozier S. 2010. MRI coil design using boundary-element method with regularization technique: a numerical calculation study. IEEE Trans Magn 46:1052-1059.
61. Krawczyk-Stando D, Rudnicki M. 2007, Regularization parameter selection in discrete ill-posed problems- the use of U-Curve. Int J Appl Math Comput Sci 17:157-164.
62. Tikhonov AN. 1963. Solution of incorrectly formulated problem and the regularization method. Soviet Math Dokl 4:1035-1038.
63. Tikhonov AN. 1963. Regularization of incorrectly posed problems. Soviet Math Dokl 4:1624-1627.
64. Bowtell R, Bencsik M, Bowley R. 2003. Reducing peripheral nerve stimulation due to switched transverse field gradients using an additional concomitant field coil. In: International Society for Magnetic Resonance in Medicine International Meeting, Toronto, Canada; Abstract No 2424.
65. Sánchez H, Liu F, Trakic A, Crozier S. 2007. A simple relationship for high efficiency-gradient uniformity tradeoff in multilayer asymmetric gradient coils for magnetic resonance imaging. IEEE Trans Magn 43:523-533.
66. Liu Q, Mantone A, McKinnon G, Sellers M. 2007. An efficient multiple field of view gradient coil set. Proc Int Soc Magn Reson Med 15:994.
67. Goodrich KC, Hadley JR, Moon S, Chronik BA, Scholl TJ, Debever JT, et al. 2009. Design, fabrication, and testing of an insertable double-imaging-region gradient coil. Concepts Magn Reson B 35:98-105.
68. Labros S. Petropoulos M, Morich A. 1995. Novel gradient coil set with canceled net thrust force for nuclear magnetic resonance applications. IEEE Trans Magn 31:3536-3539.
69. Alsop D, Connick T. 1996. Optimization of torquebalanced asvmmetric head j gradient coils. Magn Reson Med 35:875-888.
70. Liu H, Petropoulos L. 1997. Spherical gradient coil for ultrafast imaging. J Appl Phys 81:3853-3855.
71. Liu H, Petropoulos LS. 1997. Spherical gradient coil for ultrafast imaging. J Appl Phys 81:3853-3856.
72. Green D, Legget J, Bowtell R. 2005. Hemispherical gradient coils for magnetic resonance imaging. Magn Reson Med 54:656-668.
73. Mansfield P, Chapman BJ. 1986. Active magnetic screening coils in NMR imaging. Magn Reson 66:573-576.
74. Mansfield P, Chapman BJ. 1986. Active magnetic screening of coils for static and time-dependent magnetic field generation in NMR imaging. Phys E: Sci Instrum 19:541-546.
75. Mansfield P, Chapman B. 1987. Multishield active magnetic screening of coil structures in NMR. J Magn Reson 72:211-223.
76. Roemer PB, Hickey. 1986. Self-shielded gradient coils for unclear magnetic resonance imaging. European Patent Application 87,101,198.
77. Bowtell R, Mansfield P. 1991. Gradient coil design using active magnetic screening. Magn Reson Med 17:15-21.
78. Chapman BLW, Mansfield P. 1995. Quiet gradient coils-active acoustically and magnetically screened distributed transverse gradient designs. Meas Sci Technol 6:349-354.
79. Crozier S, Doddrell DM. 1995. A design methodology for short, whole-body, shielded gradient coils for MRI. Magn Reson Imaging 13:615-620.
80. Forbes L, Crozier S. 2004. Novel target-field method for designing shielded bi-planar shim and gradient coils. IEEE Trans Magn 40:1929-1938.
81. Leggett J, Crozier S, Bowtell R. 2003. Actively shielded multi-layer gradient coil designs with improved cooling properties. J Magn Reson 165:196-207.
82. Brown R, Shvartsman S. 1999. Supershielding: confinement of magnetic fields. Phys Rev Lett 83:1946-1949.
83. Shvartsman Sh, Morich M, Demeester G, Zhai Z. 2005. Ultrashort shielded gradient coil design with 3D geometry. Concepts Magn Reson B 26:1-15.
84. Martens MA, Petropoulos LS, Brown RW, Andrews JH, Morich MA, Patrick JL. 1991. Insertable biplanar gradient coil for MR imaging. Rev Sci Instrum 62:2639-2645.
85. Van Vaals JJ, Bergman AH. 1990. New high frequency resonator for NMR imaging and spectroscopy. J Magn Reson 89:331-342.
86. Mansfield P, Morris PG. NMR Imaging in Biomedicine. Academic Press: New York, 1982.
87. Martens MA, Petropoulos LS, Brown RW, Andrews JH, Morich MA, Patrick JL. 1991. Insertable biplanar gradient coils for magnetic resonance imaging. Rev Sci Instrum 62:2639-2645.
88. Bowtell R, Robyr P. 1998. Multilayer gradient coil design. J Magn Reson 131:286-294.
89. Tomasi D, Caparelli EC, Panepucci H, Foerster B. 1999. Fast optimization of a biplanar gradient coil set. J Magn Reson 140:325-339.
90. Moon CH, Park HW, Lee WY. 1999. A design method of minimum-inductance planar MRI gradient coils considering pole piece effect. J Sci Technol 10:136-141.
91. Dodd SJ, Ho C. 2002. Short planar gradient coils for MR microscopy using concentric return paths. J Magn Reson 156:1-9.
92. Lemdiasov R, Ludwig R, Brevard ME, Ferris CF. 2004. Design and implementation of a uniplanar gradient field coil for magnetic resonance imaging. J Magn Reson Eng B 20:17-29.
93. Vegh V, Zhao H, Doddrell DM, Brereton IM, Galloway GJ. 2005. The design of planar gradient coils. Part II: a weighted superposition method. Concepts Magn Reson B 27:25-33.
94. Vegh V, Zhao H, Galloway GJ, Doddrell DM, Brereton IM. 2005. The design of planar gradient coils. Part I: a winding path correction method. Concepts Magn Reson B 27:17-24.
95. Bowtell R, Mansfield P. 1989. Minimum power, flat gradient pairs for NMR microsopy. Proceedings of the 8th Annual Meeting International Society of Magnetic Resonance Imaging. Amsterdam, p 977.
96. Tomasi D. 2006. Optimization of biplanar gradient coils for magnetic resonance imaging. Braz J Phys 36:23-27.
97. Forbes LK, Brideson MA, Crozier SA. 2005. Target-field method to design circular biplanar coils for asymmetric shim and gradient fields. IEEE Trans Magn 41:2134-2144.
98. Liu W, Zu D, Tang X, Guo H. 2007. Target-field method for MRI biplanar gradient coil design. J Phys D 40:4418-4424.
99. Liu W, Zu D. 2007. Research on target-field method for designing gradient coil in permanent-magnet MRI system. In: Progress in Electromagnetics Research Symposium, Beijing, China, pp 1894-1897.
100. Liu H. 2000. An efficient geometric image distortion correction method for a biplanar planar gradient coil. Magn Reson Mater Phys Biol Med 10:75-79.
101. Plewes DB, Silver S, Starkoski P, Walker C. 2000. Magnetic resonance imaging of ultrasound fields: gradient characteristics J Magn Reson Imaging 11: 452-457.
102. Pichler BJ, Wehrl HF, Kolb A, Judenhofer MS. 2008. PET/MRI: the next generation of multi-modality imaging? Semin Nucl Med 38:199-208.
103. Pichler B, Judenhofer M, Catana C, Walton J, Kneilling M, Nutt R, et al. 2006. Performance test of an LSO-APD detector in a 7-T MRI scanner for simultaneous PET/MRI. J Nucl Med 47:639-647.
104. Poole M, Bowtell R, Green D, Pittard S, Lucas A, Hawkes R, et al. 2009. Split gradient coils for simultaneous PET-MRI. Magn Reson Med 62:1106-1111.
105. Andrew ER, Kempka M. 1998. Transverse gradient coil with circle current paths. Magn Reson Mater Phys Biol Med 7:55-60.
106. While PT, Forbes LK, Crozier S. 2009. 3D gradient coil design-initial theoretical framework. IEEE Trans Biomed Eng 56:1169-1183.
107. Moon H, Park H, Cho M, Lee Y. 2000. Design of convex-surface gradient coils for a vertical-field open MRI system. Meas Sci Technol 11:N89-N94.
108. Tomasi D. 2001. Stream function optimization for gradient coil design. Magn Reson Med 45:505-512.
109. Ruset I, Tsai L, Mair R, Patz S, Hrovat M, Rosen M, et al. 2006. A system for open-access 3He human lung imaging at very low field. Concepts Magn Reson B 29:210-221.
110. Leggett J, Crozier S, Blackband S, Beck B, Bowtell RW. 2003. Multilayer transverse gradient coil design. Concepts Magn Reson B 16:38-46.
111. Crozier S, Doddrell DMA. 1998. Simple design methodology for elliptical cross-section, transverse, asymmetric, head gradient coils for MRI. IEEE Trans Biomed Eng 45:945-948.
112. Forbes LK, Brideson MA, Crozier S, While PT. 2007. An analytical approach to the design of quiet cylindrical asymmetric gradient coils in MRI. Concepts Magn Reson B 31:218-236.
113. Zhang B, Gazdzinski C, Chronik BA, Xu H, Conolly S, Rutt B. 2005. Simple design guidelines for short MRI systems. Concepts Magn Reson B Magn Reson Eng 25:53-59.
114. While P, Forbes L, Crozier S. 2009. 3D gradient coil design-toroidal surfaces. J Magn Reson 198: 31-40.