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1、I 摘 要 本课题为国家自然科学基金资助项目 “反传统医用核磁共振成像磁体系统关键问题研究” (项目编号：50377027)的一部分。 目前的医用磁共振成像(Magnetic Resonance Imaging, MRI)装置大多为传统的 “磁体包围样品”结构。这种结构的主磁体体积庞大，整套设备价格昂贵，不利于 MRI系统在中小医院的普及。而且，其成像区域位于磁体内部，限制了 MRI 装置在介入式治疗和手术中的使用。全开放薄片型磁场永磁 MRI 系统是一种新型设备，其成像区位于主磁体外的一侧，具有完全的开放性。这种结构的磁体体积小、重量轻而且价格低，有利于 MRI 系统在基层医疗机构的普及。梯
2、度线圈是 MRI 系统重要的组成部分，其设计属于电磁场逆问题的范畴，近年来受到研究者的关注。对于上述新型永磁MRI 系统，梯度线圈的设计更是一个特殊的电磁场逆问题。 能够在灵敏区内产生沿 x(或 z)方向线性变化， 方向与主磁场方向一致的梯度磁场的线圈称为 x(或 z)方向的梯度线圈。本论文研究了新型全开放薄片型磁场永磁 MRI设备中梯度线圈的设计方法， 提出一种新型的目标场方法来实现 x 方向和 z 方向单平面梯度线圈的设计。根据 R.Turner 目标场方法的思想，提出了单平面梯度线圈的目标场方法的数学模型，并得出了线圈磁场能量和功率损耗的解析表达方式。在方法的实现中，将线圈平面的等值面电
3、流密度展开成二维傅立叶级数，得到灵敏区中磁场 z分量表达式。以磁场能量和功率损耗为惩罚函数，建立目标函数，把直接求解电流密度的问题转化为求解其傅立叶系数的问题。得到电流密度的分布以后，采用流函数方法离散化得到实际的绕线形式，并用 Biot-Savart 定律再验证计算结果。最终得到的线圈设计方案的非线性度、电感和电阻均满足设计要求。 梯度线圈中的脉冲电流具有很高的切换速度， 这必然会在周围导电部件中引起涡流。这种涡流将抑制梯度磁场的快速变换，从而防碍正常的成像过程。为了尽可能地减小涡流的影响，本文研究了自屏蔽线圈的设计方法，并完成了一种涡流自屏蔽单平面梯度线圈的设计。 沈阳工业大学博士学位论文
4、 II 由于主磁体静磁场的存在，载流梯度线圈会受到洛伦兹力的作用，在 MRI 系统工作扫描时，梯度线圈会产生震动和噪声。这种噪声会对病人产生刺激，严重的会对病人造成损伤。为了解决这一问题，本文研究了减少噪声的力平衡梯度线圈的设计方法，并完成了洛伦兹力近似为零的线圈设计。 为了验证理论与方法的正确性，制作了一个 x 方向平面指纹式梯度线圈的模型，并对该模型在成像区产生的磁场进行了测量。 计算结果与实验结果的对比验证了本文提出的设计方法的有效性。 关键词：全开放永磁磁体系统，梯度线圈，目标场方法，流函数技术关键词：全开放永磁磁体系统，梯度线圈，目标场方法，流函数技术III Study on the
5、 Design of Gradient Coils for Fully Open Permanent MRI System Abstract This work is a part of the National Natural Science Foundation of China “key issues on magnet system of Anti-traditional medical magnetic resonance imaging device”under Grant 50377027. In present medicine applications, most magne
6、tic resonace imaging (MRI) devices are traditional systems in which imaging regions are surrounded by main magnets. The main magnet of this kind of MRI system has huge volume, so that the whole equipment is very expensive, which makes small hospitals not able to afford it. Besides, the imaging regio
7、n is located inside the magnet, which is not suitable for the use in intervention therapy and operation. Fully open permanent MRI system is a newly proposed device of which the imaging region has a slice shape and is located outside the magnet structure. The weight of permanent main magnet for the n
8、ew type of MRI system is much less than that of magnet for the traditional MRI system. Thereore, the new MRI devide is not so expensive, and is fit to use more extensively. Gradient coils are important part of MRI system, the design of which is categorized as an inverse problem of electromagnetic fi
9、eld and has attracted many attentions recently. Furthermore, the gradient coils design for the newly proposed permanent MRI system is a special inverse problem of electromagnetic field. The x(or z) gradient coil is designed to generate gradient magnetic fields which are parallel to the magnets main
10、field and vary linearly in region of interest along the x(or z) axe of a Cartesian coordinates system. In this paper, the design methods of gradient coils for fully open permanent MRI device with slice imaging region are studied, and a novel target field method is proposed to design x and z uniplana
11、r gradient coils. The theoretical optimal design of uniplanar gradient coil has been formulated based on R.Turners target field method, the expression of coil energy and power dissipation can be acquired. The surface current density of the coil is represented by a two-dimensional Fourier series expa
12、nsions, and the z component of magnetic field in region of interest can be obtained. A target function is constructed in terms of gradient coils energy and power dissipation. The Abstract IV problem of solving current density is converted into that of Fourier coefficients. Appling stream function te
13、chnique, the coil patterns are acquired. Employing the Biot-Savart law to the discrete current loops, the gradient magnetic field has been re-evaluated in order to validate the method proposed. The nonlinearity, inductance and resistance of the gradient coils designed with the methods roposed satisf
14、y the design requirement. Eddy currents will be caused in ambient conducting parts because of the rapid switch speed of current pulse in gradient coils. The desired fast rise of the gradient magnetic filed is suppressed by the eddy currents so that the imaging process is affected. To diminish the in
15、fluence of the eddy currents, the design method of self-shielded gradient coils is studied and the self-shielded uniplanar gradient coils are designed in this paper. The interaction between the current of the gradient coil and spatially static magnetic field components of main magnet generates a net
16、 Lorentz force, which causes problems of vibration and excess acoustic noise. The noise will make patients uneasy and does harm to patients sometimes.To avoid the generation of the noise, the design method of balanced Lorentz force gradient coils is studied and the gradient coils with cacelled net thrust force are designed. To revalidate the theory and method presented in this paper, an x planar finger gradient coil model is made and the z component of magnetic field in imaging region
