Method of designing magnetic resonance active shimming coil based on target field point method and flow function

Qing-Ming Huang; Shan-Shan Chen; Jian-Qing Zhang; Yang Yang; Gang Zheng

doi:10.7498/aps.68.20190612

Journals >Acta Physica Sinica >Volume 68 >Issue 19 >Page 198301-1 > Article

Acta Physica Sinica
Vol. 68, Issue 19, 198301-1 (2019)

Method of designing magnetic resonance active shimming coil based on target field point method and flow function

Qing-Ming Huang^{1、2、3、4}, Shan-Shan Chen^2、3, Jian-Qing Zhang^2、3, Yang Yang², and Gang Zheng^1、4、*

Author Affiliations

¹School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

²School of Medical Imaging, Shanghai University of Medicine and Health Sciences, Shanghai 201318, China

³Shanghai Key Laboratory of Molecular Imaging, Shanghai University of Medicine and Health Sciences, Shanghai 201318, China

⁴Laboratory of Medical Imaging Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

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DOI: 10.7498/aps.68.20190612 Cite this Article

Qing-Ming Huang, Shan-Shan Chen, Jian-Qing Zhang, Yang Yang, Gang Zheng. Method of designing magnetic resonance active shimming coil based on target field point method and flow function[J]. Acta Physica Sinica, 2019, 68(19): 198301-1 Copy Citation Text

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Fig. 1. Design algorithm flow of active shimming coil based on target field and flow function.目标场及流函数结合的有源匀场线圈设计算法流程

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Flow function distribution and coil winding of each order coils: (a) Flow function distribution and coil winding of X and Y coil; (b) flow function distribution and coil winding of Z coil; (c) flow function distribution and coil winding of XY coil; (d) flow function distribution and coil winding of XZ and YZ coil; (e) flow function distribution and coil winding of Z2 coil各阶次线圈的流函数和绕线分布 (a) X, Y线圈的流函数和绕线分布; (b) Z线圈的流函数和绕线分布; (c) XY线圈的流函数和绕线分布; (d) XZ, YZ线圈的流函数和绕线分布; (e) Z2线圈的流函数和绕线分布

Fig. 2. Flow function distribution and coil winding of each order coils: (a) Flow function distribution and coil winding of X and Y coil; (b) flow function distribution and coil winding of Z coil; (c) flow function distribution and coil winding of XY coil; (d) flow function distribution and coil winding of XZ and YZ coil; (e) flow function distribution and coil winding of Z² coil 各阶次线圈的流函数和绕线分布　(a) X, Y线圈的流函数和绕线分布; (b) Z线圈的流函数和绕线分布; (c) XY线圈的流函数和绕线分布; (d) XZ, YZ线圈的流函数和绕线分布; (e) Z²线圈的流函数和绕线分布

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Fig. 3. FID signal detected by magnetic resonance before and after shimming with active shimming coil: (a) Experimental platform of active shimming coil applied to magnetic resonance system; (b) FID signal before shimming; (c) FWHM of the pre-shimming spectrum; (d) FID signal after the second-order shimming coil shimming; (e) FWHM of after the second-order shimming coil shimming采用有源匀场线圈匀场前后磁共振检测的FID信号和频谱的FWHM　(a)有源匀场线圈应用于磁共振系统的实验平台; (b)匀场前FID信号; (c)匀场前频谱的FWHM; (d)二阶匀场线圈匀场后的FID信号; (e)二阶匀场线圈匀场后频谱的FWHM

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阶次	次序	分量	系数	球坐标系	直角坐标系
阶次	次序	分量	系数	( $r,\;\,\theta,\;\,\phi $)	( $x,\;\,y,\;\,z$)
0	0	Z⁰	A⁰₁	1	1
1	0	Z	2A⁰₂	rcos⁡θ	z
1	1	X	3A¹₂	rsin⁡θ cosϕ	x
1	1	Y	3B¹₂	rsin⁡θ sinϕ	y
2	0	Z²	3A⁰₃	r² (3cos²⁡θ–1)/2	z²–(x²+y²)/2
2	1	XZ	12A¹₃	r² cos ⁡θ sinθcosϕ	xz
2	1	YZ	12B¹₃	${r^2}\cos \theta {\rm{sin}}\theta {\rm{sin}}\phi $	yz
2	2	X²–Y²	15A²₃	${r^2}{\rm{si}}{{\rm{n}}^2}\theta {\rm{cos}}2\phi $	x²–y²
2	2	2XY	15B²₃	${r^2}{\rm{si}}{{\rm{n}}^2}\theta {\rm{sin}}2\phi $	2xy
3	0	Z³	4A⁰₄	${r^3}\cos \theta (5{\cos ^2}\theta - 3)/2$	$z[{z^2} - 3\left( {{x^2} + {y^2}} \right)/2]$
3	1	XZ²	15A¹₄	${r^3}\sin \theta \cos \phi (5{\cos ^2}\theta - 1)/2$	$x[4{z^2} - \left( {{x^2} + {y^2}} \right)]$
3	1	YZ²	15B¹₄	${r^3}\sin \theta \sin \phi (5{\cos ^2}\theta - 1)/2$	$y[4{z^2} - \left( {{x^2} + {y^2}} \right)]$
3	2	Z(X²–Y²)	90A²₄	${r^3}{\rm{cos}}\theta {\rm{si}}{{\rm{n}}^2}\theta {\rm{cos}}2\phi $	z(x²–y²)
3	2	XYZ	90B²₄	${r^3}{\rm{cos}}\theta {\rm{si}}{{\rm{n}}^2}\theta {\rm{sin}}2\phi $	2xyz
3	3	X³	105A³₄	${r^3}{\rm{si}}{{\rm{n}}^3}\theta {\rm{cos}}3\phi $	${x^3} - 3x{y^2}$
3	3	Y³	105B³₄	${r^3}{\rm{si}}{{\rm{n}}^3}\theta {\rm{sin}}3\phi $	$3{x^2}y - {y^3}$
4	0	Z⁴	5A⁰₅/8	${r^4}(35{\cos ^4}\theta - 30{\rm{co}}{{\rm{s}}^2}\theta + 3)$	$8{z^4} - 24{z^2}\left( {{x^2} + {y^2}} \right) + 3{\left( {{x^2} + {y^2}} \right)^2}$
… …

Table 1. Component representation of in Cartesian and spherical coordinates. 在直角坐标系和球坐标系下的分量表示

有源匀场线圈	FID信号(积分区域)	频谱半高宽/Hz	磁场均匀性/ppm
匀场前	1270683	338	19.17
一阶线圈匀场	3937325	98	18.23
二阶线圈匀场	4866520	48	1.98

Table 2. Comparison of technical indicators for evaluating shimming effect of active shimming coil.

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