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.     

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．     

一种减小梯度线圈产生的涡流的方法

从原理上分析了减小梯度线圈的半径可以减小其在带抗涡流板磁体中引起的涡流.然后采用目标场方法设计了一组半径缩减的梯度线圈，并用Biot-Savart定理计算了这个梯度线圈的梯度线性区.最后通过磁共振成像实验证明了原理中分析得出的结论. 关键词： 梯度线圈 涡流 目标场 流函数     

Acoustic noise simulation and measurement of a gradient insert in a 4 T MRI

High speed switching of current in gradient coils within high magnetic field strength magnetic resonance imaging (MRI) scanners results in high acoustic sound pressure levels (SPL) in and around these machines. Many studies have already been conducted to characterize the sound field in and around MRIs and various methods have been investigated to attenuate the noise generated. In the work presented here a computational vibro-acoustic model was developed based on an iteratively modified and validated finite element (FE) model to characterize the acoustic noise properties of the gradient coil. The simulation results from the computational model were verified through experimental noise measurement for the gradient coil insert in a 4 T MRI scanner by using swept sinusoidal time waveform inputs. Comparisons show that the computational model predicts the noise characteristic properties extremely accurately. There are three dominant frequency bands where the SPL is much higher than those at other frequencies. The SPL in the horizontal direction is much higher than that in the vertical direction due to the excitation to the horizontally placed X coil. The SPL to the inner surface of the coil is higher than far from the inner surface, which proves that the acoustic noise is radiated from the inner surface and primarily caused by the normal vibration of the inner surface. Further verification was conducted by using two types of trapezoidal sequence inputs usually used, which is to simulate real scanning sequences for small animals. Again the accuracy of the developed model is verified. The validated acoustic computational model could be used as an effective method to predict the noise that would be produced by a coil in the design stage. Modification of the structural design or the excitation pulse could be performed to reduce the acoustic noise when the gradient coil is in scanning.     

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.     

Special designed RF-antenna with integrated non-invasive carbon electrodes for simultaneous magnetic resonance imaging and electroencephalography acquisition at 7T

The construction of a high quality MR RF-antenna with incorporated EEG electrodes for simultaneous MRI and EEG acquisition is presented. The antenna comprises an active decoupled surface coil for receiving the MR signal and a whole body coil for transmitting the excitation RF pulses. The surface coil offers a high signal-to-noise ratio required for fMRI application and the whole body coil has a good B(1) excitation profile, which enables the application of homogeneous RF pulses. Non-invasive carbon electrodes are used in order to minimise the magnetic susceptibility artefacts that occur upon application of conductive materials. This dedicated set-up is compared to a standard set-up being a linear birdcage coil and commercially available Ag/AgCl electrodes. As the acquired EEG signals are heavily disturbed by the gradient switching, intelligent filtering is applied to obtain a clean EEG signal.     

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.     

Levitation in the field of a nonsuperconducting coil with magnetic flux stabilization

A method providing the “frozen flux” conditions in a nonsuperconducting coil is suggested and demonstrated with a model. The feasibility of permanent magnet stable levitation in the field of the coil with magnetic flux stabilization and mean current control is shown. The method allows researchers to exploit permanent magnet-superconducting body interaction in physical devices, for example, to reproduce, using nonsuperconducting coils, the frozen magnetic flux conditions required for the stable levitation of the magnet over a superconducting body.     

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.     

一种超导重力仪磁悬浮力的等效计算

为实现超导重力仪磁悬浮力的精确计算,以GWR型超导重力仪为模型基础,采用有限元的思想,将超导球表面电流理想化为多个等高共轴电流环,计算出各个电流环与超导线圈的作用力,求和得到线圈与超导球间的磁悬浮力。利用MATLAB完成计算程序实现,通过改变下线圈电流和上、下线圈电流比,获得满足一定条件的磁悬浮力及其梯度。选取合适的模型参数,计算出线圈对质量为m=4.069 g超导球的磁悬浮力大小为:Ftotal=3.988×10^-2N,磁悬浮力梯度为:-9.699×10^-3N/m,此时悬浮力梯度合适,满足系统稳定性和灵敏度的要求。     

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.     

Vibration analysis and measurement of a gradient coil insert in a 4 T MRI

High speed switching of current in gradient coils within high magnetic field strength Magnetic Resonance Imaging (MRI) scanners may result in high acoustic sound pressure levels in and around these machines. Many studies have already been conducted to characterize the sound field in and around MRIs and various methods have been investigated to attenuate the noise generated. To characterize the vibration properties of the gradient coil, a modified Finite Element (FE) model was developed according to the dimensional design of an available gradient coil insert and the concentration of the copper windings in the coil. The finite element analysis results were verified through experimental modal testing of the same gradient coil in a free-free state (no boundary constraints). Comparisons show that the FE model predicts the vibration properties extremely accurately. Based on the verified FE model, boundary conditions (supports) were added to the model to simulate the operating condition when the gradient coil insert is in place in an MRI machine. Vibration analysis results from the FE model were again verified through experimental vibration testing with the gradient coil insert installed in a 4 T MRI and excited using swept sinusoidal time waveforms. Through a comparison of the vibration signals generated it was found that the vibration resonances, both from the FE model and the experimental vibration testing, shift to higher frequencies after the boundary constraints were applied, as was expected. The predicted vibration response was very close to that measured from the gradient coil insert in operation. The FE modeling procedure that has been developed could easily be used to accurately predict the vibration properties of other gradient coil designs. Furthermore, the vibration analysis results from the FE model could be used in acoustic noise analysis to predict the sound pressure level produced by different types of input current pulse sequences.     

Sample-Induced Resistance Estimation in Magnetic Resonance Experiments: Simulation and Comparison of Two Methods

Signal-to-noise ratio estimation in magnetic resonance experiments requires the knowledge of sample-induced resistance value, where the sample can be protein solutes, cell suspensions, plants, animals, portions of human body or saline solution phantoms. Many authors studied sample–coil interaction using homogeneous infinitely long cylinders, spheres or half-space as approximations of the sample geometry. However, in real magnetic resonance experiments, both sample shape and dimensions can be very different with respect to these models. This paper describes and compares two different methods developed by the authors for sample-induced resistance estimation, both useful for predicting the performance of radio-frequency coils strictly coupled to the sample, where the knowledge of a sample–coil interaction model permits to estimate the different noise contributors. The main goal of our research is testing the proposed algorithms and finding their limitations by comparing their performances for a simple case which uses a sample simplified geometry. The first method, based on the magnetostatic approach, employs vector potential calculation and can be easily implemented for simple coils and sample geometries. The second method uses finite-difference time-domain algorithm and permits to simulate systems with various geometries, without approximations in sample and coil geometries. Comparison with experimental data, performed on three homebuilt surface coils each of them successively tuned at three different frequencies, demonstrated the differences in accuracy of the developed methods.     

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.     

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.     

Inverse design of an organ-oriented RF coil for open,vertical-field,MR-guided,focused ultrasound surgery

The advantages of open, vertical-field, magnetic resonance-guided, focused ultrasound surgery (MRgFUS) are attractive. The inverse technique using the bi-boundary conditions is proposed to design a uterine-oriented intraoperative RF coil with an ultrasound aperture for the MRgFUS system. In the current proposed scheme, the desired magnetic field of the RF coil was set to completely overlap the target organ. The current density distribution on the RF coil surface, accounting for the expected magnetic field, was solved using the inverse technique. The stream function was available through the ‘discretization’ of the current density distribution on the RF coil surface. The coil windings were obtained from the contour plot of the stream function. As a modification of previous designs, the bi-boundary conditions are proposed in the inverse technique for the existence of the ultrasound aperture. Based on the obtained coil windings, a prototype coil was constructed. MR imaging of the phantom and the human body was performed to show the efficacy of the prototype coil. The results of temperature measurement using the prototype coil in a 0.4-T MR system were satisfactory. The performance of the prototype coil improved compared with the previously reported design.     

Calculations ofB 1 distribution, specific energy absorption rate, and intrinsic signal-to-noise ratio for a body-size birdcage coil loaded with different human subjects at 64 and 128 MHz

A numerical model of a female body is developed to study the effects of different body types with different coil drive methods on radio-frequency magnetic (B ₁) field distribution, specific energy absorption rate (SAR), and intrinsic signal-to-noise ratio (ISNR) for a body-size birdcage coil at 64 and 128 MHz. The coil is loaded with either a larger, more muscular male body model (subject 1) or a newly developed female body model (subject 2), and driven with-two-port (quadrature), four-port, or many (ideal) sources. Loading the coil with subject 1 results in significantly less homogeneousB ₁ field, higher SAR, and lower ISNR than those for subject 2 at both frequencies. This dependence of MR performance and safety measures on body type indicates a need for a variety of numerical models representative of a diverse population for future calculations. The different drive methods result in similarB ₁ field patterns, SAR, and ISNR in all cases.     

Design and Analysis of Microstrip-Based RF Birdcage Coil for 1.5 T Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) technique is widely used to capture the images of the liquid items inside the human body. The radio-frequency (RF) coil is one of the important modules present inside an MRI system, which plays a major role in image quality. In this work, a microstrip-based high-pass RF birdcage coil is proposed for 1.5 T MRI. The cylindrical-shaped birdcage coil consists of 12 microstrip radiating elements and tuning capacitors to achieve a resonance at 63.85 MHz. The coil is made up of 10 mm polytetrafluoroethylene substrate coated by a conducting transmission line of desired length and width. A finite difference time domain simulation is carried out to analyze the return loss (S₁₁), magnetic field homogeneity and Specific Absorption Rate (SAR) parameters of the RF coil. The SAR values of the proposed microstrip-based 1.5 T birdcage coil was compared with 3 T RF birdcage coil. The simulation results indicate the proposed birdcage coil structure gives optimal values of S₁₁, magnetic field homogeneity and SAR.     

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.