Gradient Coil Design Research Articles

Design of Gradient Coil for Magnetic Resonance Imaging Applying Particle-Swarm Optimization

Designing a gradient coil for magnetic resonance imaging (MRI) is an electromagnetic inverse problem often formulated as a constrained optimization, which has been successfully solved by inverse boundary element methods. The constant search for new coil features and improved performance has highlighted the need of employing more versatile optimization techniques capable of dealing with the new requirements. In this paper, the solution of linear and nonlinear optimization problems using particle-swarm optimization (PSO) algorithms is presented. Examples of coil designed using this heuristic method are shown, including a comparison to solutions provided by conventional optimization approaches. Numerical experiments reveal that the application of PSO for the solution of inverse boundary element problems for coil design is a computationally efficient algorithm that is capable of handling nonlinear problems and that offers fast convergence, especially for those symmetric coil geometries where the computational effort can be drastically reduced by using suitable dimensionality-reduction techniques.

An optimized target-field method for MRI transverse biplanar gradient coil design

Gradient coils are essential components of magnetic resonance imaging (MRI) systems. In this paper, we present an optimized target-field method for designing a transverse biplanar gradient coil with high linearity, low inductance and small resistance, which can well satisfy the requirements of permanent-magnet MRI systems. In this new method, the current density is expressed by trigonometric basis functions with unknown coefficients in polar coordinates. Following the standard procedures, we construct an objective function with respect to the total square errors of the magnetic field at all target-field points with the penalty items associated with the stored magnetic energy and the dissipated power. By adjusting the two penalty factors and minimizing the objective function, the appropriate coefficients of the current density are determined. Applying the stream function method to the current density, the specific winding patterns on the planes can be obtained. A novel biplanar gradient coil has been designed using this method to operate in a permanent-magnet MRI system. In order to verify the validity of the proposed approach, the gradient magnetic field generated by the resulted current density has been calculated via the Biot–Savart law. The results have demonstrated the effectiveness and advantage of this proposed method.

Minimizing Hot Spot Temperature in Asymmetric Gradient Coil Design

Heating caused by gradient coils is a considerable concern in the operation of magnetic resonance imaging (MRI) scanners. Hot spots can occur in regions where the gradient coil windings are closely spaced. These problem areas are particularly common in the design of gradient coils with asymmetrically located target regions. In this paper, an extension of an existing coil design method is described, to enable the design of asymmetric gradient coils with reduced hot spot temperatures. An improved model is presented for predicting steady-state spatial temperature distributions for gradient coils. A great amount of flexibility is afforded by this model to consider a wide range of geometries and system material properties. A feature of the temperature distribution related to the temperature gradient is used in a relaxed fixed point iteration routine for successively altering coil windings to have a lower hot spot temperature. Results show that significant reductions in peak temperature are possible at little or no cost to coil performance when compared to minimum power coils of equivalent field error.

Eddy currents in MRI gradient coils configured as rings and patches

The current distribution in a set of parallel rings and patches, called islands, positioned at the surface of a cylinder, is investigated. The current is driven by an externally applied source current. The islands are rectangular pieces of copper (patches) placed in parallel between the rings. The eddy currents in the islands induce currents in the rings that vary in the tangential direction. From the quasi-static Maxwell equations, an integral equation for the current distribution in the strips is derived. The Galerkin method, using global basis functions, is applied to solve this integral equation. It shows fast convergence. The global basis functions are Legendre polynomials in the axial direction and 2π-periodic trigonometric functions in the tangential direction. The Legendre polynomials efficiently cope with the singularity of the kernel function of the integral equation. Explicit numerical results are shown for three configurations. Apart from the current distributions, the resistance and self-inductance of the three systems of rings and islands are computed. The resulting tool can be used to qualitatively understand eddy currents in z-gradient coils, and as such enable the incorporation of eddy currents in the optimization of gradient-coil design.

Quasi-static multi-domain inverse boundary element method for MRI coil design with minimum induced E-field

Boundary element methods represent a valuable approach for designing MRI gradient coils. The temporally varying magnetic fields produced by gradient coils induce electric currents in conducting tissues and so the exposure of human subjects to these magnetic fields has become a safety concern, especially with the increase in the strength of the field gradients used in MRI. Here we extend the boundary element method presented in Cobos Sanchez et al. (2010) [4], for the design of coils that minimize the electric field induced in prescribed multi-compartment volume conductor made of different homogeneous sub-domains. The multi-domain E-coil method is illustrated with the design of cylindrical head gradient coils, whose performance is numerically compared to that produced by conventional coils and single domain E-coils.

Head gradient coil for MRI with a window

Boundary element methods have been successfully used to design gradient coils for MRI. Here the full potential of this geometry-independent technique is used to design head gradient coils, incorporating a rectangular window so as to allow visual interaction with the subject. The inclusion of the window can ameliorate significantly the claustrophobia perception in many subjects, as well as, it allows visual stimuli necessary for certain fMRI experiments to be displayed. This work details some numerical examples for the design of torque-balanced coils of minimum inductance, where the incorporation of the window is shown to improve visual interaction with the subject compared with conventional coils. © 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part A 36A: 388–393, 2010

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.

3D gradient coil design for open MRI systems

Existing gradient coil design methods typically require some predetermined surface to be specified upon which the precise locations of coil windings are optimised with respect to gradient homogeneity and other measures of coil performance. In contrast, in this paper an analytic inverse method is presented for the theoretical design of 3D gradient coils in which the precise 3D geometry of the coils is obtained as part of the optimisation process. This method has been described previously for cylindrical whole-body gradients and is extended here for open MRI systems. A 3D current density solution is obtained using Fourier series combined with Tikhonov regularisation. The examples presented involve a minimum power penalty function and an optional shielding constraint. A discretised set of 3D coil windings is obtained using an equi-flux streamline seeding method. Results for an unshielded example display a concentration of windings within the portion of the coil volume nearest the imaging region and looped return path windings taken away from this region. However, for a shielded example the coil windings are found to lie almost exclusively on biplanar surfaces, suggesting that this is the optimum geometry for a shielded minimum power open coil.

Calculating temperature distributions for gradient coils

AbstractThe operation of gradient coils typically requires large currents to be driven in resistive copper wires. A major problem in gradient coil design is therefore the correspondingly large Ohmic heating that results, which can severely impact image quality or lead to system failure. Of particular concern is the location and extent of temperature hot spots in the coil system. In this article, a model is presented for predicting the spatial temperature distribution of a gradient coil. The model includes axial and azimuthal dissipation of heat via conduction throughout a copper layer, radial conduction of heat through an insulating former, and radial convection and radiation to the environment. Two steady‐state solutions for the temperature distribution are presented, involving Green's functions and Fourier series. In addition, an approximate time‐dependent solution is sought describing the hot spot temperature as a function of time, which demonstrates that the steady‐state solutions are likely to be reached within a typical scanning scenario. The impact on the temperature distribution of a great number of coil properties may be investigated using the model and examples are given for different coil geometries, thermal material properties, and cooling mechanisms, such as convective air, forced air, and forced water cooling. © 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 37B: 146–159, 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.

E-coil: an inverse boundary element method for a quasi-static problem

Boundary element methods represent a valuable approach for designing gradient coils; these methods are based on meshing the current carrying surface into an array of boundary elements. The temporally varying magnetic fields produced by gradient coils induce electric currents in conducting tissues and so the exposure of human subjects to these magnetic fields has become a safety concern, especially with the increase in the strength of the field gradients used in magnetic resonance imaging. Here we present a boundary element method for the design of coils that minimize the electric field induced in prescribed conducting systems. This work also details some numerical examples of the application of this coil design method. The reduction of the electric field induced in a prescribed region inside the coils is also evaluated.

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.

Minimax current density coil design

‘Coil design’ is an inverse problem in which arrangements of wire are designed to generate a prescribed magnetic field when energized with electric current. The design of gradient and shim coils for magnetic resonance imaging (MRI) are important examples of coil design. The magnetic fields that these coils generate are usually required to be both strong and accurate. Other electromagnetic properties of the coils, such as inductance, may be considered in the design process, which becomes an optimization problem. The maximum current density is additionally optimized in this work and the resultant coils are investigated for performance and practicality. Coils with minimax current density were found to exhibit maximally spread wires and may help disperse localized regions of Joule heating. They also produce the highest possible magnetic field strength per unit current for any given surface and wire size. Three different flavours of boundary element method that employ different basis functions (triangular elements with uniform current, cylindrical elements with sinusoidal current and conic section elements with sinusoidal-uniform current) were used with this approach to illustrate its generality.

A novel approach to designing cylindrical-surface shim coils 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.

A DIVERGENCE-FREE BEM METHOD TO MODEL QUASI-STATIC CURRENTS: APPLICATION TO MRI COIL DESIGN

The modeling of quasi-static optimization problems often involves divergence-free surface current densities. In this paper, a novel technique to implement these currents by using the boundary element method framework is presented. A locally-based characterization of the current density is employed, to render a fully geometry-independent formulation, so that it can be applied to arbitrary shapes. To illustrate the versatility of this approach, we employ it for the design of gradient coils for MRI, providing a solid mathematical framework for this type of problem. 1. INTRODUCTION Many problems in engineering require to determine the spatial distribution of electric currents ∞owing in a conductive surface which satisfles given requirements for the flelds, electromagnetic energy, etc. they produce. The reconstruction of current distribution on the conducting surface subjected to these constraints can be seen as an inverse problem. An appropriate and realistic formulation of this type of problems is presented in this paper, by incorporating a suitable model of the current under search, in terms of the stream function, into the Boundary Element Method (BEM). The use of stream function for the characterization of surface current densities has been widely employed (1). The BEM has been proved to be an excellent tool in the solution of electromagnetic problems (2,3); and the incorporation of the stream function into a numerical computational technique, such us BEM, has also been already considered for the solution of electromagnetic inverse

Designing gradient coils with reduced hot spot temperatures

Gradient coil temperature is an important concern in the design and construction of MRI scanners. Closely spaced gradient coil windings cause temperature hot spots within the system as a result of Ohmic heating associated with large current being driven through resistive material, and can strongly affect the performance of the coils. In this paper, a model is presented for predicting the spatial temperature distribution of a gradient coil, including the location and extent of temperature hot spots. Subsequently, a method is described for designing gradient coils with improved temperature distributions and reduced hot spot temperatures. Maximum temperature represents a non-linear constraint and a relaxed fixed point iteration routine is proposed to adjust coil windings iteratively to minimise this coil feature. Several examples are considered that assume different thermal material properties and cooling mechanisms for the gradient system. Coil winding solutions are obtained for all cases considered that display a considerable drop in hot spot temperature ( > 20 % ) when compared to standard minimum power gradient coils with equivalent gradient homogeneity, efficiency and inductance. The method is semi-analytical in nature and can be adapted easily to consider other non-linear constraints in the design of gradient coils or similar systems.

A wrapped edge transverse gradient coil design for increased gradient homogeneity

AbstractA transverse gradient coil design is described for wire wound cylindrical applications. The proposed design is aimed for use as a fixed gradient coil or as an insertable gradient coil. Although we describe a transverse gradient coil for clinical MRI scanners, the principle could be applied for use in preclinical systems. The gradient coil wire wound return paths are altered to allow for the ends of the gradient coil to be wrapped into the transverse plane of the MRI system to reduce the effect of their contribution to the magnetic field within the FoV. In essence, this new configuration reduces the inductance of the coil by decreasing the primary path and return path interactions, and in addition, minimising field oscillations to reduce peripheral nerve stimulation. The proposed design produces a large FoV, low coil inductance and small high order harmonics contributing to improved gradient magnetic field linearity. The proposed concept is particularly aimed at short bore magnets, as the length of the gradient tube becomes the limiting factor in magnet system bore length. © 2009 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 35B: 139–152, 2009

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 5mm. The instrument is designed for microscopy in horizontal bore magnets. Empirical gradient current efficiencies in the prototype coils lie between 3.75G/cm/A and 4.5G/cm/A with current and heating-limited maximum gradient strengths between 235G/cm and 450G/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 7T magnet.

WE-C-210A-01: Quantitative Cardiac Motion Encoding with Magnetic Resonance Imaging

Cardiac magnetic resonance imaging (MRI) is a powerful medical imaging modality that can be safely and effectively used to quantify cardiac structure and function. Imaging the beating heart poses certain challenges that are increasingly met by advances in imaging hardware, image reconstruction, and image processing. In particular, improvements in gradient hardware and coil design have facilitated faster imaging times and real-time cardiac imaging is now routinely possible. Advances in image reconstruction have arisen from the need to robustly reconstruct sparse datasets. The increasing desire for the quantitative evaluation of image data has driven the design of more sophisticated image acquisition and quantitative image processing approaches. This talk will emphasize the latest advances in quantitative cardiac motion encoding with MRI. The outstanding capabilities of MRI include the ability to clearly contrast different soft tissues, the ability to acquire images of arbitrary orientation, the ability to acquire true three-dimensional image datasets, and the lack of ionizing radiation. Most of clinical cardiac MRI focuses on the qualitative and semi-quantitative analysis of dynamic scalar (conventional grayscale) images. Scalar images are especially well suited for appreciating gross anatomical structural relationships and global function. In particular, the measurement of right and left ventricular wall masses and volumes, cardiac output, and ejection fraction using steady-state free precession pulse sequences are routinely used to assess cardiac function. With the administration of contrast agents, additional images can be acquired that are informative about regional myocardial perfusion and infarct location and mass. Remarkably, MRI is not limited to acquiring scalar images. The MRI signal can be sensitized to each velocity vector component for moving structures using a technique termed phase contrast. In this way three-dimensional images of three-dimensional velocity-vector fields can be acquired. In particular, cardiac phase contrast techniques can be used to quantify regional blood flow patterns. This data can be used to quantify trans-valvular flow rates, intraventricular flow patterns and pressure gradients, turbulance, and more. Particle tracing and streamline generation is possible with this kind of data. Other cardiac motion encoding strategies are implemented for studying regional myocardial wall motion. Such strategies include tagged MRI, harmonic phase (HARP) imaging, and displacement encoding with stimulated echoes (DENSE). Each of these techniques has unique attributes, but each ultimately provides quantitative information about regional myocardial displacement from which regional myocardial strains can be computed. Regional strains are useful engineering measures of myocardial performance. Under these circumstances, MRI can be considered a tensor field imaging method. Finally, recent research in diffusion tensor MRI (DTMRI) provides a means for the non-destructive evaluation of microstrutural tissue organization in non-moving structures. The requirement for non-moving structures generally limits the application of DTMRI in cardiac imaging to ex vivo tissue samples. The diffusion tensor data contains a wealth of information about the regional vector orientations of the tissue's myofibers and also more sophisticated measures of tissue anisotropy and the orientation of higher-order structures. The structural organization of the myocardium is essential for understanding myocardial performance. The current goal of many research groups is to integrate the quantitative wall motion, blood flow, and microstructural information into sophisticated finite element models of healthy and diseased hearts. Learning Objectives 1. MRI can be used to acquire scalar (conventional grayscale), vector-field, and tensor-field images. 2. Conventional scalar imaging is the clinical norm and is used routinely to observe cardiac structures and quantify global cardiac function. 3. Cardiac MRI can be used to quantify three-dimensional blood velocities. This information can be used to measure flowrates and pressure gradients. 4. Cardiac MRI can be used to quantify regional cardiac wall strains. Regional strains are useful engineering measures of myocardial performance. 5. Ex vivo diffusion tensor MRI can be used to quantify the microstructural organization tissue. The structural organization of the myocardium is essential for understanding myocardial performance.

An improved equivalent magnetization current method applied to the design of local breast gradient coils

Magnetic resonance imaging (MRI) is an important tool in the diagnosis of breast cancer. Increased gradient strengths and slew rates assist in terms of the potential to image with increased spatial and/or temporal resolution. Strong gradients also facilitate diffusion studies; one well-known method of increasing gradient strength is to design local gradient coils, those with reduced diameter where the gradient conductors are closer to the region of interest. In the case of breast imaging, this necessitates the use of coil geometries that lack the symmetry (e.g. cylindrical) required by some standard coil design techniques. Therefore a symmetry-free, inverse boundary element method (BEM) was employed to design a set of local breast gradient coils which would allow simultaneous imaging of both breasts. This BEM is a modified version of a previously reported equivalent magnetisation current method that now incorporates a piecewise-linear magnetisation rather than piecewise-constant. It is demonstrated that coil geometries more closely encompassing the sample shape, hence possessing wire windings located close the sample, produce superior coil performances. The use of two regions of interest instead one that covers the two samples produces superior high performance breast gradient coils. Additionally, it was demonstrated that this inverse BEM produced standard cylindrical coils with comparable properties and that the method is robust when challenged with difficult coil design problems in two other examples.