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.     

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.     

Experimental evaluation of nonlinearities of small-sized insertable gradient coils

A phase imaging technique is proposed to map out and quantify gradient nonlinearities of small-sized insertable gradient coils, assuming the whole-body system gradients are highly linear in the domain of interest. The theory is developed and simple equations are derived to allow quantification. It is applied to a 4-loop 18-cm diameter cylindrical gradient coil of optimal design. Experimental gradient nonlinearity maps are obtained for different fields of view. Gradient non-linearities are quantified locally and in regions of interest, showing close agreement with model data.     

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.     

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.     

High-sensitivity,fiber-optic,flexural disk hydrophone with reduced acceleration response

Abstract

A hydrophone consisting of a hollow cylinder whose flexible, circular end plates are bonded to pairs of pat, spiral wound coils of optical fiber is described. When the end plate/disk is deformed due to a pressure difference, the outer and inner fiber coils experience opposite strains resulting in a “push—pull” optical path length difference which is detected in an all-fiber Michelson interferometer. The close proximity of the interferometric fiber coils, separated by the thin thermally conducting end plate, rejects thermal gradient-induced signals. The addition of a second identical end plate and fiber coil pair at the opposite end of the cylinder will double the acoustic sensitivity while canceling acceleration induced signals. The calculated and measured optical strain of a single simply supported plate, single-coil sensor (8.0 cm diameter, 3.0 mm thickness) using static pressure, acoustic pressure, and acceleration are in good agreement and yield a sensitivity of 0.21 rad/Pa (ΔΦ/ΦΔP = -301 dB re I μPa-1) below its resonance frequency of 3 kHz. The calculated and measured strain for a dual clamped disk (4.5 cm diameter, 1.0 mm thickness) acceleration-canceling sensor with four 8-m coils are in good agreement also and yield a sensitivity of 1.0 rad/Pa (ΔΦ/ΦpΔP = -291 dB re 1 μPa^?1) below the disk resonance frequency of 4.5 kHz. These are the highest fiber-optic, omnidirectional hydrophone sensitivities reported to date.     

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.     

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.     

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.     

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.     

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.     

CCT型超导组合磁体样机结构设计

基于斜螺线管型(Canted-Cosine-Theta,简称CCT)线圈结构,研制了一台四极与六极组合的超导磁体样机,它的四极和六极梯度场分别为22 T/m和120 T/m²。该组合型磁体的好场区范围为Φ0.16 m×1.3 m,有效长度为1.3 m。其中四极与六极磁体均采用两层骨架结构,每层骨架的线槽内并排放置多层多根超导线。本文根据导体轨迹,以约束电磁力为结构设计目标,设计了磁体关键部件线圈支撑骨架和磁体内外支撑结构,并介绍了磁体制造过程中的关键环节。     

Eddy current simulation in thick cylinders of finite length induced by coils of arbitrary geometry

Eddy currents are inevitably induced when time-varying magnetic field gradients interact with the metallic structures of a magnetic resonance imaging (MRI) scanner. The secondary magnetic field produced by this induced current degrades the spatial and temporal performance of the primary field generated by the gradient coils. Although this undesired effect can be minimized by using actively and/or passively shielded gradient coils and current pre-emphasis techniques, a residual eddy current still remains in the MRI scanner structure. Accurate simulation of these eddy currents is important in the successful design of gradient coils and magnet cryostat vessels. Efficient methods for simulating eddy currents are currently restricted to cylindrical-symmetry. The approach presented in this paper divides thick conducting cylinders into thin layers (thinner than the skin depth) and expresses the current density on each as a Fourier series. The coupling between each mode of the Fourier series with every other is modeled with an inductive network method. In this way, the eddy currents induced in realistic cryostat surfaces by coils of arbitrary geometry can be simulated. The new method was validated by simulating a canonical problem and comparing the results against a commercially available software package. An accurate skin depth of 2.76 mm was calculated in 6 min with the new method. The currents induced by an actively shielded x-gradient coil were simulated assuming a finite length cylindrical cryostat consisting of three different conducting materials. Details of the temporal-spatial induced current diffusion process were simulated through all cryostat layers, which could not be efficiently simulated with any other method. With this data, all quantities that depend on the current density, such as the secondary magnetic field, are simply evaluated.     

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.     

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.     

Combining a Magnetic Field Modulation Coil with a Surface-Coil-Type EPR Resonator

It is thought that the design of magnetic field modulation coils is one of the factors limiting enlargement of the sample size in electron paramagnetic resonance (EPR) measurements. In this study, we miniaturized the magnetic field modulation coil and combined it with a surface-coil-type resonator (SCR). The inductor of the SCR was a circular single-turn one-loop coil (diameter, 1 mm), and the magnetic field modulation coil was a twin-loop coil consisting of two solenoid coils each made of 15 turns of copper wire on a cylindrical bobbin with an axial length of 3 mm and an elliptical cross section (major axis, 7 mm; minor axis, 3 mm). The former was located on the latter via a spacer (thickness, 3 mm) in such a way that the directions of their axes coincided. Their combined size was about 10 mm wide, 10 mm deep, and 6 mm high. The transmission lines of the SCR were set on resonance at about 700 MHz. EPR measurements of a phantom (comprising agar that included a nitroxide radical and physiological saline solution), made with a miniaturized modulation coil combined with the SCR, exhibited a sensitivity similar to that for the conventional method. Authors' address: Hidekatsu Yokoyama, Department of Pharmaceutical Sciences, International University of Health and Welfare, 2600-1 Kitakanemaru, Ohtawara 324-8501, Japan     

High-sensitivity, fiber-optic, flexural disk hydrophone with reduced acceleration response

A hydrophone consisting of a hollow cylinder whose flexible, circular end plates are bonded to pairs of pat, spiral wound coils of optical fiber is described. When the end plate/disk is deformed due to a pressure difference, the outer and inner fiber coils experience opposite strains resulting in a “push—pull” optical path length difference which is detected in an all-fiber Michelson interferometer. The close proximity of the interferometric fiber coils, separated by the thin thermally conducting end plate, rejects thermal gradient-induced signals. The addition of a second identical end plate and fiber coil pair at the opposite end of the cylinder will double the acoustic sensitivity while canceling acceleration induced signals. The calculated and measured optical strain of a single simply supported plate, single-coil sensor (8.0 cm diameter, 3.0 mm thickness) using static pressure, acoustic pressure, and acceleration are in good agreement and yield a sensitivity of 0.21 rad/Pa (ΔΦ/ΦΔP = -301 dB re I μPa-1) below its resonance frequency of 3 kHz. The calculated and measured strain for a dual clamped disk (4.5 cm diameter, 1.0 mm thickness) acceleration-canceling sensor with four 8-m coils are in good agreement also and yield a sensitivity of 1.0 rad/Pa (ΔΦ/ΦpΔP = -291 dB re 1 μPa^-1) below the disk resonance frequency of 4.5 kHz. These are the highest fiber-optic, omnidirectional hydrophone sensitivities reported to date.     

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.     

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.