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.     

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.     

L波段三维ESR成像系统的研制(Ⅳ)--系统组成与各部分性能指标

报道了自行研制的L波段三维电子自旋共振成像（3D-ESRI）系统的整机结构及各部分性能指标. 该系统主要由L波段ESR谱仪、三维梯度磁场装置、数据处理及图像重建软件组成. 系统的微波频率为1.05 GHz;最大微波功率500 mW. 采用3-环2-缝再进入式谐振腔,无载Q值>1 000;最大测量体积为φ 20 mm, 高30 mm柱状水溶液样品. 接收系统采用100 kHz锁相放大电路,最大增益可达1×10⁶;时间常数0.02 ms～1 s;磁场调制幅度>0.5 mT. 最大梯度磁场2 mT/cm;三维梯度线性度均优于5 ％;稳定度可达10^-5;主磁场可在1.6～96 mT范围内任意点选择扫场起始点;在0.2～16 mT范围选择磁场扫描宽度. 数据系统为12位A/D实现数据采集,三路8位D/A控制梯度磁场. 采用滤波反投影法实现图像重建, 成像功能包括：二维、三维自旋浓度成像;等浓度线2D图像显示;3D立体和断层图像显示等. 对水溶液和固体模型样品进行ESR成像的结果表明：本系统可以开展较大体积生物样品的ESRI研究.     

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.     

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.     

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.     

Biochemical EPR imaging of skin

EPR Imaging (EPRI) of spin labels is a powerful method for investigating skin and can give information about biochemical processes which are involved in numerous skin diseases. Furthermore it enables the non invasive investigation of the liberation, penetration and distribution of spin labelled drugs. The basis of these measurements is spectral spatial EPR imaging employing modulated field gradients and simultaneous field scans (MOSS). A skin region (?=6 mm) was treated with a 10 μl spin label solution (1 mM). EPR spectra of 128 points were recorded in 128 spatial planes resulting in a 128×128 image matrix. A spatial resolution of better than 10 μm can be obtained for a spectral line width of 0.1 mT and a gradient of 4 Tm^?1.In vivo imaging on mammalian skin can be performed by employing surface coils at S-band frequencies, 3 GHz.     

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.     

Investigation of Bi-2223 high temperature superconducting tape as the material for gradient coil in MRI

The use of Bi-2223 high temperature superconducting (HTS) tape as a material for gradient coils in MRI is evaluated in this paper. Bi-2223 tapes have a very high critical current and a very low power loss. A HTS tape gradient coil is expected to provide much higher gradient strength and generate much lower heating than a copper coil. Measurements of the AC power loss of Bi-2223 tapes at typical operating frequencies for gradient coils are presented. The degradation of the critical current and its effect on the increase of AC power loss is analyzed. Practical technical issues such as resistance, gradient strength and mechanical performance are also discussed. A prototype Bi-2223 HTS tape gradient coil is evaluated to verify the concept.     

L波段三维ESR成像系统的研制（Ⅱ）——L波段三维ESR成像系统

叙述了一个L波段（1.05 GHz）用于ESR和ESR成像的装置，用这套自制装置实现了3D ESR成像. 该装置由L波段ESR谱仪、三组梯度场线圈及控制单元和PC机数据采集系统组成. 样品腔是一个3-环2-缝再进入式谐振腔，可放入直径为20 mm、 长30 mm的H₂O样品，空谐振腔的频率是1.05 GHz. 微波振荡频率用自动频率控制（AFC）的方法自动锁在有载腔的频率上. 梯度场线圈沿X-，Y-和Z-轴产生线性梯度场，在中心40 mm球形范围内梯度场强度为2 mT/cm. 依照Lauterbur's方法进行3D ESR 图像重建. 用该系统检测了样品中TEMPO氮氧自由基的3D空间分布. 得到了TEMPO的2D、3D ESR图像、用像素灰度表示的自旋密度分布图及3D ESR-CT图像.     

Quantitative density profiling with pure phase encoding and a dedicated 1D gradient

A new centric scan imaging methodology for density profiling of materials with short transverse relaxation times is presented. This method is shown to be more robust than our previously reported centric scan pure phase encode methodologies. The method is particularly well suited to density imaging of low gyro-magnetic ratio non-proton nuclei through the use of a novel dedicated one-dimensional magnetic field gradient coil. The design and construction of this multi-layer, water cooled, gradient coil is presented. Although of large diameter (7.62 cm) to maximize sample cross section, the gradient coil has an efficiency of several times that offered by conventional designs (6 mT/m/A). The application of these ideas is illustrated with high resolution density-weighted proton (1H) images of hazelnut oil penetration into chocolate, and lithium ion (7Li) penetration into cement paste. The methods described in this paper provide a straightforward and reliable means for imaging a class of samples that, until now, have been very difficult to image.     

波段三维ESR成像系统的研制（Ⅴ）——灵敏度与分辨率实验及系统总性能指标

实验确定了自行研制的L波段三维电子自旋共振成像（3D-ESRI）系统的检测灵敏度及成像分辨率指标. 用Tempo水溶液模型测量灵敏度结果表明： 样品体积为10 mm, 高30 mm，测量浓度1×10^-4 mol/L水溶液的信噪比为S/N=4∶1；加梯度磁场后，样品浓度需>5×10^-4 mol/L，样品体积为19 mm, 高30 mm时，获得的投影谱的信噪比可满足图像重建的需要. 用DPPH固体样品确定的成像分辨率结果<1 mm. 文中还对ESRI系统的
各项总体性能做了归纳总结.     

一种用于开放式MRI的射频发射线圈设计

介绍了一种用于开放式MRI系统的射频发射线圈. 此发射线圈为上下2个相同的线圈,分别安装在磁体的2极,两线圈采用非对称的正交方式放置. 线圈为矩形螺线管结构,通过电磁场数值计算的方法对线圈的匝间距进行了优化,使线圈在300 mm的球形区域内达到偏差不超过3 dB的均匀性要求. 根据优化结果制作了一套用于0.23 T开放式MRI系统的发射线圈,并对线圈的均匀性及射频发射的效率进行了测试. 测试结果表明,线圈具有较高的发射效率和较好的均匀性,由此验证了设计方案的可行性.     

Finite size disc gradient coil set for open vertical field magnets

A new analytical approach is used in the design of disc-like gradient coils suitable for magnet geometries with main field direction perpendicular to the surface of the disc. An inverse procedure is used to optimize the coil's characteristics, subject to the restrictions imposed by the desired field behavior over a certain set of constraint points inside a predetermined imaging volume. Excellent agreement between the expected values of the gradient magnetic field and the numerical values generated by applying the Biot-Savart law to a discrete current pattern of the perspective disc coil was found. A Finite Element Analysis package was used to predict the fringe gradient field levels for a non-shielded axial disc coil and for a self-shielded transverse disc coil in the vicinity of the magnet poles. The numerical results indicate that for the self-shielded design the gradient fringe field is 1000 times smaller than the corresponding fringe field for the non-shielded disc case. Also no significant spatial dependence was noticed for the shielded coil's fringe field.     

Design of a capacitively decoupled transmit/receive NMR phased array for high field microscopy at 14.1T

A design is presented for a "phased array" of four transmit/receive saddle-geometry volume coils for microimaging at 600 MHz within a 45 mm clear-bore vertical magnet. The small size of the coils, approximately 10 mm in length, and high frequency of operation both present considerable challenges for the design of a phased array. The particular design consists of four saddle coils, stacked vertically, in order to produce an array suitable for imaging samples, typical of many microimaging studies, with a large length:diameter ratio. Optimal coil overlap is used to reduce the mutual inductance between adjacent coils, and capacitive networks are used to maximize the isolation between all of the coils. Standard 50 Omega input impedance preamplifiers are used so that the preamplifiers do not have to be integrated directly into the probe. Isolation between coils was better than 20 dB for all coil pairs. An increase in signal-to-noise of 70 +/- 3% was achieved, averaged over the whole array, compared to a single coil of the same dimensions. High resolution phased array images are shown for ex vivo tissue samples.     

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.     

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.     

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 uniplanar three-axis gradient set for in vivo magnetic resonance microscopy

We present an optimized uniplanar magnetic resonance gradient design specifically tailored for MR imaging applications in developmental biology and histology. Uniplanar gradient designs sacrifice gradient uniformity for high gradient efficiency and slew rate, and are attractive for surface imaging applications where open access from one side of the sample is required. However, decreasing the size of the uniplanar gradient set presents several unique engineering challenges, particularly for heat dissipation and thermal insulation of the sample from gradient heating. We demonstrate a new three-axis, target-field optimized uniplanar gradient coil design that combines efficient cooling and insulation to significantly reduce sample heating at sample-gradient distances of less than 5 mm. The instrument is designed for microscopy in horizontal bore magnets. Empirical gradient current efficiencies in the prototype coils lie between 3.75 G/cm/A and 4.5 G/cm/A with current and heating-limited maximum gradient strengths between 235 G/cm and 450 G/cm at a 2% duty cycle. The uniplanar gradient prototype is demonstrated with non-linearity corrections for both high-resolution structural imaging of tissue slices and for long time-course imaging of live, developing amphibian embryos in a horizontal bore 7 T magnet.     

Longitudinally detected ESR magnetometer for wide-range measurements of low fields

A new magnetometer utilizing a longitudinally detected ESR (LODESR) method was developed. The probe head of the LODESR magnetometer is equipped with a single-turn coil (8 mm in diameter) which has a very wide bandwidth because the reactance of the coil is always smaller than the resistance of the transmission line (50 ohm) at frequencies less than 700 MHz. Thus, an absolute magnetic field could be measured over a wide range (2 to 9 mT) using this magnetometer without changing the probe head.