Magnetic Resonance Imaging Gradient Coils Research Articles

Designing gradient coils with the shape derivative and the closed B-spline curves

This study proposes a versatile and efficient optimisation method for discrete coils that induce a magnetic field by their steady currents. The prime target is gradient coils for MRI (Magnetic Resonance Imaging). The derivative (gradient) of the z-component the magnetic field, which is calculated by the Biot–Savart's law, with respect to the z-coordinate in the Cartesian xyz coordinate system is considered as the objective function. Then, the derivative of the objective function with respect to a change of coils in shape is formulated according to the concept of shape optimisation. The resulting shape derivative (as well as the Biot–Savart's law) is smoothly discretised with the closed B-spline curves. In this case, the control points (CPs) of the curves are naturally selected as the design variables. As a consequence, the shape derivative is discretised to the sensitivities of the objective function with respect to the CPs. Those sensitivities are available to solve the present shape-optimisation problem with a certain gradient-based nonlinear-programming solver. The numerical examples exhibit the mathematical reliability, computational efficiency, and engineering applicability of the proposed methodology based on the shape derivative/sensitivities and the closed B-spline curves.

Overview of Methods for Noise and Heat Reduction in MRI Gradient Coils.

Magnetic resonance imaging (MRI) gradient coils produce acoustic noise due to coil conductor vibrations caused by large Lorentz forces. Accurate sound pressure levels and modeling of heating are essential for the assessment of gradient coil safety. This work reviews the state-of-the-art numerical methods used in accurate gradient coil modeling and prediction of sound pressure levels (SPLs) and temperature rise. We review several approaches proposed for noise level reduction of high-performance gradient coils, with a maximum noise reduction of 20 decibels (dB) demonstrated. An efficient gradient cooling technique is also presented.

A Comparative Study for Evaluating Passive Shielding of MRI Longitudinal Gradient Coil.

Gradient coils are vital for Magnetic Resonance Imaging (MRI). Their rapid switching generates eddy currents in the surrounding metallic structures of the MRI scanner causing undesirable thermal, acoustic, and field distortion effects. The use of actively shielded gradient coils does not eliminate such undesirable effects totally. Use of passive shielding was proposed lately to particularly help in mitigating eddy currents and loud acoustic noise. Numerical computations are necessary for calculating eddy currents and evaluating the efficacy of passive shielding. Harmonic and temporal eddy current analysis caused by gradient coil(s) using network analysis (NA) can be faster and more flexible than the traditional FDTD and FEM methods. NA was used more than a decade ago but was limited to analyzing eddy currents resulting from z-gradient coils of separated turns. NA with stream function was recently modified resulting in the more general Multilayer Integral Method (MIM) for simulation of eddy currents in thin structures of arbitrary geometries. In this work, we compared the performance of the NA method and an adapted MIM method to analyze eddy current in both the passive shielding and cryostat to the Ansys Maxwell 3D analysis thus evaluating the performance of gradient configurations with and without passive shielding. Both an unconnected and a connected z-gradient coil configuration were used. Our analysis showed high agreement in the profiles of eddy ohmic losses in metallic structures using the three methods. The NA method is the most computationally efficient however, it is limited to specific symmetries unlike the more general MIM and Ansys methods. Our implementation of the adapted MIM method showed computational efficiency relative to Ansys with comparable values. We have developed a computationally efficient eddy current analysis framework that can be used to evaluate more designs for passive shielding using different configurations of MRI gradient coils.

Design of a high-performance non-linear gradient coil for diffusion weighted MRI of the breast

Diffusion-weighted imaging (DWI) in the female breast is a magnetic resonance imaging (MRI) technique that complements clinical routine protocols, and that might provide an independent diagnostic value for specific clinical tasks in breast imaging. To further improve specificity of DWI in the breast, stronger and faster diffusion weighting is advantageous. Here, a dedicated gradient coil is designed, targeted at diffusion weighting in the female breast, with the peak gradient magnitude exceeding that of the current clinical MR scanners by an order of a magnitude.Design of application-tailored gradient coils in MRI has recently attracted increased attention. With the target application in mind, the gradient coil is designed on an irregularly shaped semi-open current-carrying surface. Due to the coil former closely fitting the non-spherical target region, non-linear encoding fields become particularly advantageous for achieving locally exceptionally high gradient strengths. As breast tissue has a predominantly isotropic cellular microstructure, the direction of the diffusion-weighting gradient may be allowed to vary within the target volume. However, due to the quadratic dependency of the b-factor on the gradient strength, variation of the gradient magnitude should be carefully controlled.To achieve the above design goals the corresponding multi-objective optimization problem is reformulated as a constrained optimization, allowing for flexible and precise control of the coil properties. A novel constraint is proposed, limiting gradient magnitude variation within every slice while allowing for variations in both the direction of the gradient within the slice and the magnitude across the slices. These innovations enable the design of a unilateral coil for diffusion weighting in the female breast with local gradient strengths exceeding 1 T/m with highly homogeneous diffusion weighting for imaging in the coronal slice orientation.

Metamaterial Magnetic Sheet at 3.7-T MRI for Animal Imaging

Animal models have been utilized for many decades to examine human diseases and symptoms via magnetic resonance imaging (MRI) techniques. To avoid the fatal effects of the strong static magnetic field (B0) when imaging the mouse brain at higher Tesla values in MRI, i.e., 7-T, we propose a compact metamaterial magnetic sheet which can improve the image resolution for simulation of the mouse brain even at lower Tesla values in MRI systems. The magnetic sheet operates at 3.7-T MRI working frequency and provides a passband within its interfaces to restore the formation of scattering of an evanescent radio-frequency (RF) field radiating from the MRI gradient coils towards the sheet. We show in the optimized simulated test bed setup that the magnetic sheet localizes and adjusts the response of the evanescent RF field and improves the transient transverse magnetic field B1 and signal-to-noise ratio at the designated region of interest, i.e., mouse brain (Mb), where B1 at the mouse brain is the response of the static magnetic field B0 generated by the magnetic resonance gradient coils. The unique concept proposed here is that negative permeability (−μ) controls the metamaterial magnetic sheet to improve image resolution inside the human brain without increasing B0 intensity at the brain, in order to avoid thermal heating of the brain tissues.

Elevation and Azimuth Rotational Actuation of an Untethered Millirobot by MRI Gradient Coils

Magnetic resonance imaging (MRI) devices provide magnetic field gradients, which can be used to remotely actuate magnetic robots that may one day carry out medical tasks, such as diagnosis, drug delivery, or therapeutic-laser-based procedures, in addition to the high-resolution tissue images for diagnosis. However, in comparison with magnetic systems that are custom designed solely for magnetic actuation, the magnetic environment of an MRI device is constrained by the requirements for imaging, which reduces the number of active degrees of freedom available for magnetic actuation. Moreover, the current MRI-powered untethered robots are limited to translational magnetic pulling in three dimensions only. In this article, we propose a design for an untethered magnetic robot that can rotate in a three-dimensional liquid volume in magnetic environments, like those in MRI devices. We demonstrate rotational actuation of our robot inside a commercially available MRI gradient coil. Two kinds of near-neutrally buoyant robot designs are proposed, where each design has particular advantages. Design methodologies, analysis of rotational performance, closed-loop orientation control of up to 2.51 rad of orientation change with maximum net displacement of 18.4 mm, and angular velocity control (0.2-0.63 rad/s) of these robot designs are presented.

Oval gradient coils for an open magnetic resonance imaging system with a vertical magnetic field

Existing open magnetic resonance imaging (MRI) systems use biplanar gradient coils for the spatial encoding of signals. We propose using novel oval gradient coils for an open vertical-field MRI. We designed oval gradients for a 0.3T open MRI system and showed that such a system could outperform a traditional biplanar gradient system while maintaining adequate gradient homogeneity and subject accessibility. Such oval gradient coils would exhibit high efficiency, low inductance and resistance, and high switching capability. Although the designed oval Y and Z coils showed more heat dissipation and less cooling capability than biplanar coils with the same gap, they showed an efficient heat-dissipation path to the surrounding air, which would alleviate the heat problem. The performance of the designed oval-coil system was demonstrated experimentally by imaging a human hand.

A simulation study on the design of gradient coils in MRI for the imaging area above the patient bed

A novel method is proposed for the simulation study the design of gradient coils in a magnetic resonance imaging (MRI) system which generate linear magnetic field gradients only in the region above the patient’s bed. In MRI, the gradient coils are usually designed to create linear-varying magnetic gradient fields in a region that is typically described as a diameter of spherical volume (DSV). In practice, the space under the patient’s bed is not used for imaging, but is still treated as part of the design target in conventional approaches. This work proposes a new design scheme in which only the DSV space above the patient’s bed is considered. In the simulation study, the coil patterns have been obtained using a boundary element method (BEM). Compared to conventional gradient coil design methods, the new scheme produces similar fields above the patient’s bed with much sparser wire spacing (for the case tested: the primary layer and shielding layer have 36%/10% and 6%/17% larger wire spacing for X- and Y-gradient coils, respectively). The new design therefore has reduced inductance compared to conventional coils; a reduction of approximately 23% and 11% for the X- and Y-gradient coils, respectively. The resistances of the coils are also reduced. Based on an acoustic analysis, the new gradient coils are slightly quieter (3 dB for the typical operating frequency) than conventional gradient systems.

Intra-coil interactions in split gradient coils in a hybrid MRI–LINAC system

An MRI–LINAC system combines a magnetic resonance imaging (MRI) system with a medical linear accelerator (LINAC) to provide image-guided radiotherapy for targeting tumors in real-time. In an MRI–LINAC system, a set of split gradient coils is employed to produce orthogonal gradient fields for spatial signal encoding. Owing to this unconventional gradient configuration, eddy currents induced by switching gradient coils on and off may be of particular concern. It is expected that strong intra-coil interactions in the set will be present due to the constrained return paths, leading to potential degradation of the gradient field linearity and image distortion. In this study, a series of gradient coils with different track widths have been designed and analyzed to investigate the electromagnetic interactions between coils in a split gradient set. A driving current, with frequencies from 100Hz to 10kHz, was applied to study the inductive coupling effects with respect to conductor geometry and operating frequency. It was found that the eddy currents induced in the un-energized coils (hereby-referred to as passive coils) positively correlated with track width and frequency. The magnetic field induced by the eddy currents in the passive coils with wide tracks was several times larger than that induced by eddy currents in the cold shield of cryostat. The power loss in the passive coils increased with the track width. Therefore, intra-coil interactions should be included in the coil design and analysis process.

Simulated Design Strategies for SPECT Collimators to Reduce the Eddy Currents Induced by MRI Gradient Fields

Combining single photon emission computed tomography (SPECT) with magnetic resonance imaging (MRI) requires the insertion of highly conductive SPECT collimators inside the MRI scanner, resulting in an induced eddy current disturbing the combined system. We reduced the eddy currents due to the insert of a novel tungsten collimator inside transverse and longitudinal gradient coils. The collimator was produced with metal additive manufacturing, that is part of a microSPECT insert for a preclinical SPECT/MRI scanner. We characterized the induced magnetic field due to the gradient field and adapted the collimators to reduce the induced eddy currents. We modeled the x-, y-, and z-gradient coil and the different collimator designs and simulated them with FEKO, a three-dimensional method of moments / finite element methods (MoM/FEM) full-wave simulation tool. We used a time analysis approach to generate the pulsed magnetic field gradient. Simulation results show that the maximum induced field can be reduced by 50.82% in the final design bringing the maximum induced magnetic field to less than 2% of the applied gradient for all the gradient coils. The numerical model was validated with measurements and was proposed as a tool for studying the effect of a SPECT collimator within the MRI gradient coils.

Modal Analysis of Currents Induced by Magnetic Resonance Imaging Gradient Coils

In magnetic resonance imaging (MRI), gradient coils are switched during fast current pulse sequences. These time-varying fields interact with the conducting structures of the scanner, producing deleterious effects such as image distortions and Joule heating. Using a multi-layer integral method, the spatiotemporal nature of the eddy currents induced by the gradient coils is investigated. The existence of the eigenmode is experimentally demonstrated by measuring the magnetic field and the time decay constant of a typical unshielded z-gradient coil and its interaction with a conductive cylinder. An effective current tailoring is achieved using the characteristic eigenvalues of the conducting domain-exciting coil system. The method can be used to understand and mitigate undesired effects of eddy currents in MRI.

A design tool for magnetic resonance imaging gradient coils using DUCAS with weighted nodes and initial current potentials

DUCAS is a computer code using an arbitrary magnetic field distribution as input and producing a sheet current distribution as output. The code was improved for application to the magnetic resonance imaging (MRI) gradient coil (GC) design. DUCAS computes the current potential (CP) distribution, and the coil conductors are placed along the contours, which are current flow lines. An improved algorithm with weights on node CPs and input initial CPs is described for use with DUCAS. The algorithm obtains the CP distribution by summing singular value decomposition (SVD) eigendistributions with the initial CP distribution. The weights modify the eigendistributions. The initial CP distribution is used to get smooth flow lines and then coil patterns. The improved DUCAS is suitable for avoiding a complex current distribution and to obtain coil patterns that are easy to manufacture. The initial CP distribution is assumed first, then DUCAS compensates the CPs for the given magnetic field distribution with the weights. This paper describes the computational algorithm and shows a GC design obtained with it.

A Novel Target-Field Method Using LASSO Algorithm for Shim and Gradient Coil Design

Target field (TF) method is very important for design of shim and gradient coils which have been used in magnetic resonance imaging (MRI) and other applications. Many works based on TF have been proposed. To restrict the current distribution on cylindrical coils with a given finite length, the current density is expanded by trigonometric series and the unknown coefficients are estimated based on the standard Least Square (LS) with L2 norm regularization (LS-L2). In this paper, we propose to estimate the coefficients using LS with L1 norm regularization (LS-L1), also named Least Absolute Shrinkage and Selection Operator (LASSO), which is solved via Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The proposed method can obtain sparse solutions and better approximations, which can be used to design cylindrical shim and gradient coils for MRI. Simulation results show that the proposed LS-L1 method performs better than the LS-L2 TF method.

Tikhonov regularization approach for acoustic noise reduction in an asymmetric, self‐shielded MRI gradient coil

AbstractWe consider a mathematical method for minimizing the acoustic noise of self‐shielded magnetic resonance imaging gradient coils designed to produce an asymmetrically located target field within a cylindrical chamber. During imaging, the gradient coils are being constantly switched on and off, subjecting the coil to large Lorentz forces. These forces cause the chamber to buckle, creating a pressure wave in the bore which manifests as acoustic noise at sound pressure levels up to about 130 dB. In this model, the linearized coil deflection, the pressure wave, and the acoustic noise level inside the chamber are all solved for in closed form. The closed‐form nature of the solutions permits simple insights into the behavior of the system. Although reductions of only 0.6 dB were achieved, the method allows some flexibility if other design sacrifices are made. The gradient coil switching frequency plays a major role in the magnitude of the acoustic noise and is studied here. Results are presented for two basic switching functions for shielded gradient coils. Unshielded gradient coils, other switching functions, and other penalty functions can be easily accommodated using the method presented. © 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 37B: 167–179, 2010

Theory of gradient coil design methods for magnetic resonance imaging

AbstractThe process to produce an MR image includes nuclear alignment, RF excitation, spatial encoding, and image formation. In simple terms, an magnetic resonance imaging (MRI) system consists of five major components: a magnet, gradient systems, an RF coil system, a receiver, and a computer system. To form an image, it is necessary to perform spatial localization of the MR signals, which is achieved using gradient coils. In modern MRI, gradient coils able to generate high gradient strengths and slew rates are required to produce high imaging speeds and improved image quality. MRI also requires the use of gradient coils that generate magnetic fields, which vary linearly with position over the imaging volume. Gradient coils for MRI must therefore have high current efficiency (defined as the ratio of gradient generated to current drawn), short switching time (i.e., low inductance), gradient linearity over a large volume, low power consumption, and minimal interaction with any other equipment, which would otherwise result in eddy currents. Over the last two decades new methods of gradient coil design have been developed, and a combination of these methods can be a mixture of them trying to avoid discomforts to patients that at the end is the center of all the technological efforts in the art of MRI. © 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part A 36A: 223–242, 2010.

MRI Coil Design Using Boundary-Element Method With Regularization Technique: A Numerical Calculation Study

A new boundary element method (BEM) based method is described for the design of coils for magnetic resonance imaging (MRI) systems. BEM is an effective approach for solving the electromagnetic forward problem and has been used in the design of MRI gradient coils. However, BEM-based gradient coil design faces an ill-posed mathematical problem, which is conventionally handled by means of a Lagrange multiplication method. This work attempts to improve the BEM method for MRI coil designs by applying the Tikhonov regularization scheme to solve the ill-posed matrix system formulated by the BEM forward model. The objective of the study is not to design some specific gradient or radio-frequency (RF) coils for MRI system, but to discuss the design scheme with practical regularization and constraints. The proposed approach was explained in the design of MRI coils including biplanar transverse gradient coils and RF phased array coils. With the consideration of the practical engineering requirements, physical constraints such as wire intervals are transformed into mathematical constraints and formulated into BEM equations. The examples demonstrate that the proposed method is efficient and flexible for the design of MRI coils with arbitrary geometries and engineering constraints.

Inversion Reconstruction of Signals Measured by the NMR Techniques

The paper describes the magnetic resonance imaging method applicable mainly in MRI and MRS in vivo studies. There is discussed and solved the efiect of changes of magnetic flelds in MR tomography. This article deals with the reverse reconstruction results obtained from the numerical simulation of MR signals by various techniques, which will be usable for the experimental results veriflcation. Nuclear Magnet Resonance (NMR) is well known diagnostic non-destructive and non-invasive method (2{6). It is used to investigation of the materials properties. One of the often use of NMR is medical application (8,11). The magnetic resonance imaging (MRI) is used to the propel a ferromagnetic core. The concept was studied for future development of microdevices designed to perform minimally invasive interventions in remote sites accessible through the human cardiovascu- lar system. A mathematical model is described (3) taking into account various parameters such as the size of blood vessels, the velocities and viscous properties of blood, the magnetic properties of the materials, the characteristics of MRI gradient coils, as well as the ratio between the diameter of a spherical core and the diameter of the blood vessels. Other paper (4) present a MRI-compatible micromanipulator, which can be employed to provide medical and biological scientists with the ability to concurrently manipulate and observe micron-scale objects inside an MRI gantry. The micromanipulator formed a two-flnger micro hand, and it could handle a micron-scale object using a chopstick motion. The material engineering use the NMR too. For example NMR logging is an advanced method in formation evaluation and oil fleld production. It can provide the porosity, permeability, bound water volume, free ∞uid volume and oil viscosity. NMR logging is playing more and more important roles in oil and gas exploitation.

Method of Propulsion of a Ferromagnetic Core in the Cardiovascular System Through Magnetic Gradients Generated by an MRI System

This paper reports the use of a magnetic resonance imaging (MRI) system to propel a ferromagnetic core. The concept was studied for future development of microdevices designed to perform minimally invasive interventions in remote sites accessible through the human cardiovascular system. A mathematical model is described taking into account various parameters such as the size of blood vessels, the velocities and viscous properties of blood, the magnetic properties of the materials, the characteristics of MRI gradient coils, as well as the ratio between the diameter of a spherical core and the diameter of the blood vessels. The concept of magnetic propulsion by MRI is validated experimentally by measuring the flow velocities that magnetized spheres (carbon steel 1010/1020) can withstand inside cylindrical tubes under the different magnetic forces created with a Siemens Magnetom Vision 1.5 T MRI system. The differences between the velocities predicted by the theoretical model and the experiments are approximately 10%. The results indicate that with the technology available today for gradient coils used in clinical MRI systems, it is possible to generate sufficient gradients to propel a ferromagnetic sphere in the larger sections of the arterial system. In other words, the results show that in the larger blood vessels where the diameter of the microdevices could be as large as a couple a millimeters, the few tens of mT/m of gradients required for displacement against the relatively high blood flow rate is well within the limits of clinical MRI systems. On the other hand, although propulsion of a ferromagnetic core with diameter of approximately 600 microm may be possible with existing clinical MRI systems, gradient amplitudes of several T/m would be required to propel a much smaller ferromagnetic core in small vessels such as capillaries and additional gradient coils would be required to upgrade existing MRI systems for operations at such a scale.

Modal analysis and acoustic noise characterization of a 4T MRI gradient coil insert

AbstractHigh magnetic field strength and high‐speed gradient coil current switching are combining to yield high acoustic sound pressure levels (SPL) in and around magnetic resonance imaging (MRI) scanners. Studies have already been conducted that partially characterize this sound field, and various methods have been investigated in an attempt to attenuate the noise generated. To more fully characterize and predict the vibration and acoustic response of a gradient coil inside a scanner, a series of finite element analysis (FEA), vibro‐acoustic analysis, and experimental measurements were carried out. The FEA and vibro‐acoustic model used was based on specific internal and external structural dimensions and the material physical properties of a gradient coil insert. The model‐based results were verified through experimental vibration and acoustic testing of the same gradient coil. It was found that the experimental analysis results were in good agreement with the model‐based results in all cases. The numerical methods developed in this study could provide a basis for the virtual testing of gradient coil designs that will allow the prediction of vibration and acoustic behavior. © 2004 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 22B: 37–49, 2004

Simple anatomical measurements do not correlate significantly to individual peripheral nerve stimulation thresholds as measured in MRI gradient coils.

To examine peripheral nerve stimulation (PNS) thresholds for normal human subjects in magnetic resonance imaging (MRI) gradient coils, and determine if observed thresholds could be predicted based on gross physiologic measurements. PNS thresholds for 21 healthy normal subjects were measured using a whole-body gradient coil. Subjects were exposed to a trapezoidal echo-planar imaging (EPI) gradient waveform and the total change in gradient strength (DeltaG) required to cause PNS as a function of the duration of the gradient switching time (tau) were measured. Correlation coefficients and corresponding P values were calculated for the PNS threshold measurements against simple physiologic measurements taken of the subjects, including weight, height, girth, and average body fat percentage, in order to determine if there were any easily observable dependencies. No convincing correlations between threshold parameters and gross physiologic measurements were observed. These results suggest it is unlikely that a simple physiologic measurement of subject anatomy can be used to guide the operation of MRI scanners in a subject-specific manner in order to increase gradient system performance while avoiding PNS.