应用于磁共振成像系统的超椭圆柱面梯度线圈设计方法研究

	应用于磁共振成像系统的超椭圆柱面梯度线圈设计方法研究
	王亮
学位类型	硕士
导师	刘震宇
	2014-11
学位授予单位	中国科学院大学
学位专业	机械制造及其自动化
关键词	磁共振成像梯度线圈流函数超椭圆柱面可展曲面
摘要	磁共振成像(Magnetic Resonance Imaging, MRI) 是一种用于探测人体内部结构和疾病诊断的非介入式医疗影像技术。磁共振成像仪器主要由主磁体、梯度线圈系统、射频系统、以及计算机操作系统组成。对于存在空间差异性的被检测物质，线性梯度磁场的引入成功实现了被检测物质的空间定位问题。用于产生梯度磁场的梯度线圈构型由最初的麦克斯韦和鞍形线圈组合发展为目前通常采用的双平面或圆柱面线圈，梯度线圈的设计方法由最初的目标场法发展为流函数法。根据双平面、圆柱面的几何特性，本论文提出在超椭圆柱面上设计梯度线圈，并应用流函数法和柱面的可展性，在超椭圆柱面的展开平面上实现磁共振成像系统梯度线圈设计。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。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空间特定区域电磁场分布的数值精度，通过L-curve方法实现了正则参数的合理选取。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代数方程组的直接求解问题。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，在满足梯度磁场线性度误差小于5%的设计约束下，本文所提出的优化方法可以在设计超椭圆柱面线圈驱动电流分布的同时有效控制线圈的电流功耗。在实际应用中，磁共振成像的梯度线圈系统需要同时满足梯度磁场的高线性度、快速切换、涡流抑制、以及梯度磁场的自屏蔽等。根据上述实际应用需求，首先提出在满足线性度要求的基础上实现通过引入电磁场能的辅助目标控制线圈自感的设计模型。通过引入多层线圈的协同优化实现自屏蔽梯度线圈的设计。通过选取适当的设计参数，获得线性度误差小于5%，能耗、电感均得到有效控制的自屏蔽梯度线圈构型。数值算例证明对电感、电阻的优化分别等价于对磁场能、电流功耗的优化。最后总结和展望了基于流函数法和柱面的可展性，在超椭圆柱面展开平面上设计梯度线圈的优越性和进一步需要完善的研究内容。
其他摘要	Magnetic resonance imaging (MRI) is a commonly used non-invasive technique in radiology to visualize the structure and function of the body. In an MRI scanner, there are four main parts: a main magnet, the gradient coils system, the radio frequency transmitter-receiver, and the computer-aided control system. For a test substance with the spatial difference, gradient coils spatially encode the positions of protons by varying the magnetic field across the imaging volume. The layout of gradient coils evolved from discrete Maxwell pairs and saddle coils to the surface coils wound on bi-planar or cylindrical surfaces, and the design method for the gradient coils evolved from target field method to the currently widely used stream function method. Considering the geometric properties of the bi-planar and cylindrical surfaces, designing gradient coils on super-elliptical cylindrical surface is proposed in this thesis using the stream function and the developable property of the super-elliptical cylindrical surface. A super-elliptical cylindrical surface can shorten the distance between coils and target, enhance space utilization, and enlarge the homogeneous imaging volumes. Based on the Biot-Savart law, the relationship between the magnetic flux density and stream function is established firstly, and the objective is chosen as the least-square form with the additional Tikhonov regularization term. The numerical accuracy of the magnetic flux density in the region of interest is maintained through transforming the super-elliptical cylindrical surface to the corresponding flat surface and the value of regularization coefficient of the dissipated powers is chosen automatically by using the L-curve method. Via imposing specified boundary conditions for the stream function on the developed surface, the optimization of gradient coils is implemented by directly solving well-posed linear algebraic equations. Numerical examples illustrate the feasibility of the proposed design method. The designed coils on super-elliptical cylindrical surface show that the current and the dissipated powers are adequately optimized under the condition that the linear gradient deviation is less than 5%. In order to obtain a better performance in applications, the influence of linearity, switch time, inductance, and eddy current should be considered during the design process. A flexible winding pattern can be obtained by substituting magnetic energy for dissipated power, proving that magnetic energy can also be chosen as the additional Tikhonov regularization term. Self-shielded coils, which is used to decrease eddy current, are designed via the multiple-layer coil design. Numerical analysis of the designed coils demonstrates that the optimization of inductance and resistance is equivalent to the optimization of magnetic energy and dissipated power, respectively. Finally the advantages and the potential improvement of the proposed numerical optimization method are discussed for the further research on gradient coils on the super-elliptical cylindrical surfaces.
语种	中文
文献类型	学位论文
条目标识符	http://ir.ciomp.ac.cn/handle/181722/44695
专题	中科院长春光机所知识产出
推荐引用方式 GB/T 7714	王亮. 应用于磁共振成像系统的超椭圆柱面梯度线圈设计方法研究[D]. 中国科学院大学,2014.

条目包含的文件
文件名称/大小	文献类型	版本类型	开放类型	使用许可
王亮.pdf（4824KB）			开放获取	ODC PDDL	请求全文