基于Pareto优化理论的多目标超椭梯度线圈设计

磁共振系统梯度线圈设计是一个多目标优化问题,在设计时需要综合考虑能耗、磁场能、线性度等设计要求.这些设计要求通常难以同时获得极小解,因此在设计梯度线圈时需要权衡线圈的各方面的设计需求.本文基于柱面可展性和流函数设计方法,结合Pareto优化方法实现了在超椭圆柱设计表面上梯度线圈的多目标设计.分别分析了磁场能、能耗目标对梯度线圈线性度、线圈构型的影响;并在Pareto解空间中分析各目标的相互变化关系,通过数值算例验证了该方法在超椭梯度线圈设计时的有效性与灵活性.优化结果显示,在满足线性度误差小于5%,能耗与磁场能分别小于用户设定值的设计约束下,梯度线圈的多目标设计存在多个局部优化解.该方法可以直观地比较相同目标函数值的情况下各单目标的具体表现,有利于实现不同的设计要求下梯度线圈的最终定型设计.     

超椭圆柱面梯度线圈设计

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.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.     

结合振动控制的柱面纵向梯度线圈目标场设计方法

在磁共振成像系统的工作过程中,噪声主要是由梯度线圈系统产生的.梯度线圈置于高均匀度超导磁体的室温孔内,并工作于脉冲状态,频繁的开启和关闭会使线圈中电流急剧随时间变化,变化的电流导致线圈受到变化的洛伦兹力作用,从而产生振动,这种高频振动所发出的噪声会对病人产生刺激,严重时甚至会对病人的听觉神经产生损伤.梯度场的场强越强、切换速度越快,所产生的噪声就越大.降低噪声的最根本方法是通过有效的梯度线圈设计,降低洛伦兹力的空间分布.本文针对纵向梯度线圈,在原经典目标场设计方法基础上,加入对振动参量,从而能够有效地降低线圈工作时所产生的噪声.其具体方法是将振动控制函数作为约束条件,通过目标场法建立数学模型,利用MATLAB进行电磁验算.计算结果表明,所提数学模型可有效地降低线圈振动的最大振幅.     

矩阵梯度线圈研究现状与发展趋势

梯度和匀场线圈性能的好坏直接影响磁共振成像质量．常规线圈在成像过程中存在一些固有的不足,如产生的磁场形态单一、不灵活,需要的线圈种类较多,结构较复杂等．而新型矩阵梯度线圈可以较好地弥补这些缺点．本文首先介绍了矩阵梯度线圈的概念及其特性,然后根据结构和功能对其研究现状进行分类汇总,在此基础上对矩阵线圈未来的发展趋势进行分析．此外,本文还对矩阵梯度线圈的前期研究基础进行了介绍．     

Equivalent magnetic dipole method used to design gradient coil for unilateral magnetic resonance imaging

The conventional magnetic resonance imaging(MRI) equipment cannot measure large volume samples nondestructively in the engineering site for its heavy weight and closed structure. In order to realize the mobile MRI, this study focuses on the design of gradient coil of unilateral magnet. The unilateral MRI system is used to image the local area above the magnet. The current density distribution of the gradient coil cannot be used as a series of superconducting nuclear magnetic resonance gradient coils, because the region of interest(ROI) and the wiring area of the unilateral magnet are both cylindrical side arc surfaces. Therefore, the equivalent magnetic dipole method is used to design the gradient coil, and the algorithm is improved for the special case of the wiring area and the ROI, so the X and Y gradient coils are designed.Finally, a flexible printed circuit board(PCB) is used to fabricate the gradient coil, and the magnetic field distribution of the ROI is measured by a Gauss meter, and the measured results match with the simulation results. The gradient linearities of x and y coils are 2.82% and 3.56%, respectively, less than 5% of the commercial gradient coil requirement.     

Designing shielded radio-frequency phased-array coils for magnetic resonance imaging

In this paper, an approach to the design of shielded radio-frequency (RF) phased-array coils for magnetic resonance imaging (MRI) is proposed. The target field method is used to find current densities distributed on primary and shield coils. The stream function technique is used to discretize current densities and to obtain the winding patterns of the coils. The corresponding highly ill-conditioned integral equation is solved by the Tikhonov regularization with a penalty function related to the minimum curvature. To balance the simplicity and smoothness with the homogeneity of the magnetic field of the coil’s winding pattern, the selection of a penalty factor is discussed in detail.     

Shim coil design for Halbach magnet by equivalent magnetic dipole method

Low-field nuclear magnetic resonance magnet(2 MHz) is required for rock core analysis. However, due to its low field strength, it is hard to achieve a high uniform B_0 field only by using the passive shimming. Therefore, active shimming is necessarily used to further improve uniformity for Halbach magnet. In this work, an equivalent magnetic dipole method is presented for designing shim coils. The minimization of the coil power dissipation is considered as an optimal object to minimize coil heating effect, and the deviation from the target field is selected as a penalty function term. The lsqnonlin optimization toolbox of MATLAB is used to solve the optimization problem. Eight shim coils are obtained in accordance with the contour of the stream function. We simulate each shim coil by ANSYS Maxwell software to verify the validity of the designed coils. Measurement results of the field distribution of these coils are consistent with those of the target fields.The uniformity of the B_0 field is improved from 114.2 ppm to 26.9 ppm after using these shim coils.     

A novel approach to designing cylindrical-surface shimcoils for a superconducting magnet of magnetic resonance imaging

For a superconducting magnet of magnetic resonance imaging (MRI), the novel approach presented in this paper allows the design of cylindrical gradient and shim coils of finite length. The method is based on identification of the weighting of harmonic components in the current distribution that will generate a magnetic field whose z-component follows a chosen spherical harmonic function. Mathematical expressions which relate the harmonic terms in the cylindrical current distribution to spherical harmonic terms in the field expansion are established. Thus a simple matrix inversion approach can be used to design a shim coil of any order pure harmonic. The expressions providing a spherical harmonic decomposition of the field components produced by a particular cylindrical current distribution are novel. A stream function was applied to obtain the discrete wire distribution on the cylindrical-surface. This method does not require the setting of the target-field points. The discussion referring to matrix equations in terms of condition numbers proves that this novel approach has no ill-conditioned problems. The results also indicate that it can be used to design cylindrical-surface shim coils of finite length that will generate a field variation which follows a particular spherical harmonic over a reasonably large-sized volume.     

基于边界元方法的超导核磁共振成像设备高阶轴向匀场线圈优化算法

在磁共振成像设备中,为了消除目标区域内的高阶谐波磁场分量,传统方法采用无源匀场,但该方法匀场精度较低,针对性较差,适用于全局匀场,而有源匀场则可以通过优化线圈分布来产生所需要的特定的磁场分布.但是,由于匀场线圈线型的复杂度会随着线圈阶数的增加而增加,难以满足设计需要,因此本文提出了一种用于磁共振成像超导匀场线圈系统的多变量非线性优化设计方法.该方法基于边界元方法,将匀场线圈所产生的磁场与目标磁场之间的偏差作为目标函数,线匝间距、线圈半径等作为约束条件,通过非线性优化算法,得到满足设计要求的线圈分布.通过一个中心磁场为0.5 T的开放式双平面磁共振成像超导轴向匀场线圈的设计案例,说明本方法具有计算效率高、灵活性好的特点.     

An Efficacious Target-Field Approach to Design Shim Coils for Halbach Magnet of Mobile NMR Sensors

The main magnetic fields of mobile nuclear magnetic resonance (NMR) magnets differ from those of conventional NMR and magnetic resonance imaging (MRI) magnets. In the Halbach magnet, the main field B ₀ is perpendicular to the longitudinal axis, the symmetry of the current distribution with respect to the symmetry of the magnetic field differs from that in conventional target-field applications, and the current distribution on the coil surface cannot be expressed in terms of periodic basis functions. To obtain the winding pattern of the coil, an efficacious target-field approach. The surface of a coil is divided into small discrete elements, where each element is represented by a magnetic dipole. From the stream function of the elements, the resultant magnetic field is calculated. The optimization strategy follows an objective function defined by the power dissipation or efficiency of the coil. This leads to the optimum stream function on the coil surface, whose contour lines define the winding patterns of the coil. This paper shows winding patterns designed of shim coils for Halbach magnet and illustrates the craft of a shim coil using flexible printed circuit board. The performance of the coils is verified by simulating the fields they produce over the sensitive volume.     

Modeling the static fringe field of superconducting magnets

The resonance frequency-space and the frequency gradient-space relations are evaluated analytically for the static fringe magnetic field of superconducting magnets used in the NMR diffusion measurements. The model takes into account the actual design of the high-homogeneity magnet coil system that consists of the main coil and the cryoshim coils and enables a precise calibration of the on-axis magnetic field gradient and the resonance frequency inside and outside of the superconducting coil.     

Multi-objective optimization of gradient coil for benchtop magnetic resonance imaging system with high-resolution

Significant high magnetic gradient field strength is essential to obtaining high-resolution images in a benchtop mag- netic resonance imaging （BT-MRI） system with permanent magnet. Extending minimum wire spacing and maximum wire width of gradient coils is one of the key solutions to minimize the maximum current density so as to reduce the local heating and generate higher magnetic field gradient strength. However, maximum current density is hard to optimize together with field linearity, stored magnetic energy, and power dissipation by the traditional target field method. In this paper, a new multi-objective method is proposed to optimize the maximum current density, field linearity, stored magnetic energy, and power dissipation in MRI gradient coils. The simulation and experimental results show that the minimum wire spacings are improved by 159% and 62% for the transverse and longitudinal gradient coil respectively. The maximum wire width increases from 0.5 mm to 1.5 mm. Maximum gradient field strengths of 157 mT/m and 405 mT/m for transverse and lon- gitudinal coil are achieved, respectively. The experimental results in BT-MRI instrument demonstrate that the MRI images with in-plane resolution of 50 ~tm can be obtained by using the designed coils.     

Planar Gradient Coil Design Using L1 and L2 Norms

We present a novel and general formulation for the optimisation of gradient coils, wherein the minimization of the conductor length and the simplicity of construction are two of the main design parameters. The bi-planar gradient coils are intended to be part of a new compact neonatal magnetic resonance imaging (MRI) scanner based on a 0.35 T permanent magnet. It is shown that minimizing the current density vector is equivalent to minimizing the wire length. The gradient coil design involves a convex optimization method where the Euclidian and Manhattan norms of the current density vector are minimized under the field linearity, wire width, force and shielding constraints. The design problem is solved iteratively in order to include the influence of the magnetization of the pole and iron ring over the gradient field linearity. A suite of gradient coils using both norms and resistance minimization are designed and their performances are compared. Gradient coils designed using Euclidian norm show shorter wire length and slightly better performance than that designed using Manhattan norms; however, the presence of straight wires in the current pattern is very convenient for manufacturing purpose.     

Short planar gradient coils for MR microscopy using concentric return paths

The aim of this work is to design a set of gradient coils with an optimal geometry for magnetic resonance microscopy studies. Designs for a three-axis gradient coil system particularly suited for studies with small radiofrequency coils are presented. The novel geometry involves a planar section with concentric return paths to keep the coil short. Reduction of the external field has been attempted by varying the positions of the return paths using a simulated annealing algorithm. A biplanar version of x- and z-directed prototype gradients was built and tested. A 2D-MR image of a grid phantom has been obtained on a 7-T MR instrument to demonstrate the theory. A three-axis set used as a surface gradient set has also been built and used to obtain high-resolution MR images.     

短腔、自屏蔽磁共振成像超导磁体系统的混合优化设计方法

本文提出一种用于短腔、自屏蔽磁共振成像超导磁体系统的混合优化设计方法,通过结合线性规划和非线性优化算法,设计出的磁体系统具有建造成本低、结构简单、以及线圈中最高磁场、电流安全裕度和电磁应力可控等优点.首先,通过线性规划算法在欲布置线圈空间范围内建立二维连续网格划分,搜索满足磁场约束条件的网格电流分布图;其次,将电流分布图中的非零电流簇离散成螺线管线圈,通过非线性优化算法计算出满足成像区域磁场均匀度要求、5 Gs杂散场限制、线圈中最高磁场限制、电流安全裕度以及线圈间尺寸间隔等约束条件的线圈结构参数.文中给出一个中心磁场为1.5T自屏蔽磁共振成像超导磁体系统的设计案例,在50 cm球形成像区域所产生的磁场峰峰值不均匀度为10 ppm,线圈最大长度为1.32 m.该设计方法可用于对称、非对称螺线管线圈系统以及开放式双平面线圈系统的磁共振成像磁体系统设计.     

An optimized solenoidal head radiofrequency coil for low-field magnetic resonance imaging

Applications of low-field magnetic resonance imaging (MRI) systems (<0.3 T) are limited due to the signal-to-noise ratio (SNR) being lower than that provided by systems based on superconductive magnets (≥1.5 T). Therefore, the design of radiofrequency (RF) coils for low-field MRI requires careful consideration as significant gains in SNR can be achieved with the proper design of the RF coil. This article describes an analytical method for the optimization of solenoidal coils. Coil and sample losses are analyzed to provide maximum SNR and optimum B₁ field homogeneity. The calculations are performed for solenoidal coils optimized for the human head at 0.2 T, but the method could also be applied to any solenoidal coil for imaging other anatomical regions at low field. Several coils were constructed to compare experimental and theoretical results. A head magnetic resonance image obtained at 0.2 T with the optimum design is presented.     

Fast Optimization of a Biplanar Gradient Coil Set

This work presents an approach for fast optimization of gradient coils, using the simulated annealing method. The shielding condition derived from a target field method and the analytical evaluation of the fields produced by simple geometries were used to reduce the computing time. This method is applied to the optimization of a shielded biplanar gradient coil set. Efficiency, inductance, and homogeneity of the gradient fields produced by the optimized geometries were studied as a function of the number of wires, for the longitudinal and transverse gradient coils. A prototype of the gradient set was made to test the proposed design method. The resulting experimental values of coil efficiency, inductance, field linearity, and shielding performance exhibit good agreement between theory and experiment.     

Actively shielded multi-layer gradient coil designs with improved cooling properties

In standard cylindrical gradient coils consisting of a single layer of wires, a limiting factor in achieving very large magnetic field gradients is the rapid increase in coil resistance with efficiency. This is a particular problem in small-bore scanners, such as those used for MR microscopy. By adopting a multi-layer design in which the coil wires are allowed to spread out into multiple layers wound at increasing radii, a more favourable scaling of resistance with efficiency is achieved, thus allowing the design of more powerful gradient coils with acceptable resistance values. Previously this approach has been applied to the design of unshielded, longitudinal, and transverse gradient coils. Here, the multi-layer approach has been extended to allow the design of actively shielded multi-layer gradient coils, and also to produce coils exhibiting enhanced cooling characteristics. An iterative approach to modelling the steady-state temperature distribution within the coil has also been developed. Results indicate that a good level of screening can be achieved in multi-layer coils, that small versions of such coils can yield higher efficiencies at fixed resistance than conventional two-layer (primary and screen) coils, and that performance improves as the number of layers of increases. Simulations show that by optimising multi-layer coils for cooling it is possible to achieve significantly higher gradient strengths at a fixed maximum operating temperature. A four-layer coil of 8 mm inner diameter has been constructed and used to test the steady-state temperature model.     

A practical multinuclear transceiver volume coil for in vivo MRI/MRS at 7 T

A practical multinuclear transceiver RF volume coil with improved efficiency for in vivo small animal ¹H/¹³C/²³Na MR applications at the ultrahigh magnetic field of 7 T is reported. In the proposed design, the coil's resonance frequencies for ¹H and ¹³C are realized by using a traditional double-tuned approach, while the resonant frequency for ²³Na, which is only some 4 MHz away from the ¹³C frequency, is tuned based upon ¹³C channel by easy-operating capacitive “frequency switches”. In contrast to the traditional triple-tuned volume coil, the volume coil with the proposed design possesses less number of resonances, which helps improve the coil efficiency and alleviate the design and operation difficulties. This coil design strategy is advantageous and well suitable for multinuclear MR imaging and spectroscopy studies, particularly in the case where Larmor frequencies of nuclei in question are not separate enough. The prototype multinuclear coil was demonstrated in the desired unshielded design for easy construction and experiment implementation at 7 T. The design method may provide a practical and robust solution to designing multinuclear RF volume coils for in vivo MR imaging and spectroscopy at ultrahigh fields. Finite difference time domain method simulations for evaluating the design and 7-T MR experiment results acquired using the prototype coil are presented.     

Multilayer Gradient Coil Design

In standard cylindrical gradient coils consisting of wires wound in a single layer, the rapid increase in coil resistance with efficiency is the limiting factor in achieving very large magnetic field gradients. This behavior results from the decrease in the maximum usable wire diameter as the number of turns is increased. By adopting a multilayer design in which the coil wires are allowed to spread out into multiple layers wound at increasing radii, a more favorable scaling of resistance with efficiency is achieved, thus allowing the design of more powerful gradient coils with acceptable resistance values. By extending the theory used to design standard cylindrical gradient coils, we have developed mathematical expressions which allow the design of multilayer coils, and the evaluation of their performance. These expressions have been used to design a four-layer,z-gradient coil of 8 mm inner diameter, which has an efficiency of 1.73 Tm⁻¹A⁻¹, a resistance of 1.8 Ω, and an inductance of 50 μH. This coil produces a gradient which deviates from linearity by less than 5% within a central cylindrical region of 4.5 mm length and 4.5 mm diameter. A coil has been constructed from this design and tested in simple imaging and pulsed gradient spin echo experiments. The resulting data verify the predicted coil performance, thus demonstrating the advantages of using multilayer coils for experiments requiring very large magnetic field gradients.