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.     

An "openable," high-strength gradient set for orthopedic MRI.

A novel three-axis gradient set and RF resonator for orthopedic MRI has been designed and constructed. The set is openable and may be wrapped around injured joints. The design methodology used was the minimization of magnetic field spherical harmonics by simulated annealing. Splitting of the longitudinal coil presents the major design challenge to a fully openable gradient set and in order to efficiently design such coils, we have developed a new fast algorithm for determining the magnetic field spherical harmonics generated by an arc of multiturn wire. The algorithm allows a realistic impression of the effect of split longitudinal designs. A prototype set was constructed based on the new designs and tested in a 2-T clinical research system. The set generated 12 mT/m/A with a linear region of 12 cm and a switching time of 100 micros, conforming closely with theoretical predictions. Preliminary images from the set are presented.     

Plate form three-dimensional gradient coils for L-band ESR imaging experiment

A set of plate form three-dimensional magnetic gradient coils was developed and used in electron spin resonance imaging (ESRI) experiment. The coils were processed with whole copper plates instead of wound with copper wires, which made its structure so compact that it was much thinner and smaller comparing to those traditionally used in ESRI. The coil set had a pie-like appearance of which the total thickness was only 14 mm and the outer diameter was 250 mm. The efficiency of the coils could be greater than 10 mT/m/A when distance between the two side-pieces was 63 mm. A maximum gradient strength of more than 200 mT/m could be obtained with driving current of about 20 A in each dimension coil. The spatial linearity was better than 5% in all three dimensions within the available spatial linearity area of larger than a sphere of 40 mm in diameter. The stability of the gradients strength could reach the level of 10(-5). An imaging resolution of better than 1 mm could be achieved with the coil set. Some preliminary practical imaging results show that the developed gradient coil set is suitable for L-band ESRI experiment of biological samples or even in vivo small animals.     

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.     

Multiple Parallel Round Leg Design for Quadrature Birdcage Coil in Ultrahigh-Field MRI

Copper foil has been widely employed in conventional radio frequency (RF) birdcage coils for magnetic resonance imaging (MRI). However, for ultrahigh-field (UHF) MRI, current density distribution on the copper foil is concentrated on the surface and the edge due to proximity effect. This increases the effective resistance and distorts the circumferential sinusoidal current distribution on the birdcage coils, resulting in low signal-to-noise ratio (SNR) and inhomogeneous distribution of RF magnetic (B₁) field. In this context, multiple parallel round wires were proposed as legs of a birdcage coil to optimize current density distribution and to improve the SNR and the B₁ field homogeneity. The design was compared with three conventional birdcage coils with different width flat strip surface legs for a 9.4 T (T) MRI system, e.g., narrow-leg birdcage coil (NL), medium-leg birdcage coil (ML), broad-leg birdcage coil (BL) and the multiple parallel round wire-leg birdcage coil (WL). Studies were carried out in in vitro saline phantom as well as in vivo mouse brain. WL showed higher coil quality factor Q and more homogeneous B₁ field distribution compared to the other three conventional birdcage coils. Furthermore, WL showed 12, 10 and 13% SNR increase, respectively, compared to NL, ML and BL. It was proposed that conductor’s shape optimization could be an effective approach to improve RF coil performance for UHF MRI.     

Design of biplanar gradient coils for magnetic resonance imaging of the human torso and limbs.

A method is described for design of gradient coils of unconventional geometry for MRI that is based on the superpositions of magnetic fields arising from individual current elements calculated by the Biot-Savart Law. Use of an optimization method based on a genetic algorithm enables a wide diversity in the shapes of coil that can be modeled. To exemplify this a two axis, biplanar gradient set is presented; this geometry offers good access for rectangular objects whilst holding the coils closer to the region of interest than is possible for cylindrical configurations. The inner dimensions of the gradient set were 40.0 x 24.4 x 40.0 cm and the gradient efficiencies were 0.3 and 0.4 mT m(-1) A(-1) in the z- and y- directions respectively over a 15 cm diameter region. Correction of signals arising from regions for which gradient linearity was not optimized was successful for the monotonic region within the set; the largest cuboid from which the MR signal could be processed to produce an undistorted image is of dimensions 36.3 x 17.2 x 24.4 cm.     

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.     

Design of small-scale gradient coils in magnetic resonance imaging by using the topology optimization method

A topology optimization method based on the solid isotropic material with penalization interpolation scheme is utilized for designing gradient coils for use in magnetic resonance microscopy. Unlike the popular stream function method, the proposed method has design variables that are the distribution of conductive material. A voltage-driven transverse gradient coil is proposed to be used as micro-scale magnetic resonance imaging(MRI) gradient coils, thus avoiding introducing a coil-winding pattern and simplifying the coil configuration. The proposed method avoids post-processing errors that occur when the continuous current density is approximated by discrete wires in the stream function approach. The feasibility and accuracy of the method are verified through designing the z-gradient and y-gradient coils on a cylindrical surface.Numerical design results show that the proposed method can provide a new coil layout in a compact design space.     

14T MRI大口径全身自屏蔽超导磁体的一种优化设计方法

磁共振成像(MRI)的磁体设计首先是确保中心成像区的场值和均匀性, 二是尽可能减少场值耗散的距离即漏磁5Gs 线. 基于此本文提出了一种线性与非线性规划联合优化的方法. 首先将导体作为基本单元, 在预布置线圈的空间范围内构建二维连续导体网格. 通过线性规划搜索满足磁场约束条件的网格电流分布图. 再将存在电流的网格离散为一个个矩形线圈区域, 在保证场值均匀性、 杂散场5 Gs 线范围以及线圈位置间隔、 导体超导线安全裕度的前提下利用非线性规划, 具体确定各个线圈的轴向和径向位置、 线圈内导体层数和各层匝数以及通电流大小等. 采用这种联合优化方法, 不仅节省优化时间, 还可以自行设计线圈形状有利于工程实现. 文中由此方法给出了14 T MRI 磁体的一种设计方案, 依靠4 组线圈使得45 cm 中心球形成像内不均匀度降低到5 ppm, 而高场耗散的5 Gs 线通过磁体自屏蔽减小到15 m 以内. 满足了设计的要求.     

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.     

1.5 T关节磁共振成像超导磁体的设计、制作与测试

磁共振成像(magnetic resonance imaging,MRI)是当今世界上最先进的医学影像技术之一,现阶段MRI技术正朝着成像质量更清晰、功能更强大、效率更高、个体化更强的趋势发展.与全身MRI设备相比,专科型MRI设备具有体积小、重量轻、成本低、病人舒适度高、成像质量高、功能更强等优点.但是关节专用超导MRI系统需要长度方向上被严格限制的超导磁体在160 mm直径球域(diameter sphere volume,DSV)内产生高均匀度的磁场.本文综合考虑了超导线用量、中心磁感应强度和成像区磁场不均匀度等因素,使用0-1规划和遗传算法相结合的方法设计了一种非屏蔽型1.5 T关节MRI超导磁体,该磁体的室温孔径为280 mm,总长度为520 mm,液氦量为30 L,载流区最大磁场为5.48 T,5高斯线范围为径向3.2 m、轴向2.6 m,160 mm DSV的磁场不均匀度设计值为22 ppm,考虑加工误差及冷缩因素,磁体加工完成并经过被动匀场后的预估值为60 ppm.经过绕制、固化、组装、焊接等工序,该磁体已制作完成.经过3次锻炼后成功励磁到1.5 T,经过被动匀场后160 mm DSV的磁场不均匀度达到50 ppm,各项指标均达到设计目标.     

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.     

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.     

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．     

L波段三维ESR成像系统的研制(Ⅰ)——L波段ESR成像的磁场及三维梯度磁场系统

研究并实现了L波段电子自旋共振三维成像（3D-EPRI）专用的三维梯度磁场系统，主磁场及扫描磁场系统以及相应的驱动控制系统. 梯度场线圈采用在铜板上用电切割方法加工的 平板式线圈，避免了用铜导线绕制线圈体积较大的缺点，从而缩小了主磁场的体积和极间距 . 梯度场强度在三维方向上均达到200 mT/m，驱动电流为20 A. 三维空 间线性度均优于5％；线性区域大于直径42 mm的球形空间. 两磁极间距离为63 mm，可以容纳通常体积的L波段谐振腔. 主磁场和扫描场线圈固定在同一轭铁架上. 它们可分别产生1.6～ 96 mT和0.2～16 mT的线性变化磁场. 5组磁场线圈（包括主磁场， 扫描磁场和三维梯度磁场）分别由5台独立的恒流驱动电源控制驱动. 电源通过数据接口由计算机控制. 初步成像实 验证明本工作所建立的磁场和梯度磁场系统可以用于EPRI实验.     

A simple electromagnetic method of cyclic loss measurement for superconducting wires in a combined alternating transverse magnetic field and transport current

We measured cyclic losses in a superconducting wire, carrying alternating transport current, simultaneously exposed to an alternating transverse magnetic field. Samples of Bi-2223 Ag-sheathed tapes have configuration of a double-layer non-inductive coil, which itself is a pickup coil to measure the AC losses. Potential taps were attached to both terminals of the sample coil. The external field was applied along the axis of the sample coil. In this procedure, we can estimate an averaged Poynting's vector on a cylindrical surface between the two layers by means of signals from a pair of the potential taps and from pickup coils for the external magnetic field and the transport current. We can also measure a magnetization and an extended transport-current components of AC losses in addition to a total cyclic loss for a combined alternating external field and transport current. Obtained results are compared with numerical predictions of the critical state model taking into account the magnetic field dependence of critical current density.     

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.     

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.     

Globally optimal superconducting magnets part II: symmetric MSE coil arrangement

A globally optimal superconducting magnet coil design procedure based on the Minimum Stored Energy (MSE) current density map is outlined. The method has the ability to arrange coils in a manner that generates a strong and homogeneous axial magnetic field over a predefined region, and ensures the stray field external to the assembly and peak magnetic field at the wires are in acceptable ranges. The outlined strategy of allocating coils within a given domain suggests that coils should be placed around the perimeter of the domain with adjacent coils possessing alternating winding directions for optimum performance. The underlying current density maps from which the coils themselves are derived are unique, and optimized to possess minimal stored energy. Therefore, the method produces magnet designs with the lowest possible overall stored energy. Optimal coil layouts are provided for unshielded and shielded short bore symmetric superconducting magnets.