A simple design methodology for elliptical cross-section, transverse, asymmetric, head gradient coils for MRI

A simple design process for the design of elliptical cross-section, transverse gradient coils for use in magnetic resonance imaging (MRI) is presented. This process is based on a flexible stochastic optimization method and results in designs of high linearity and efficiency with low switching times. A design study of a shielded, transverse asymmetric elliptical coil set for use in neural imaging is presented and includes the minimization of the torques experienced by the gradient set.

Calculating current densities and fields due to shielded bi-planar radio-frequency coils

A method for the accurate computation of the current densities produced in a wide-runged bi-planar radio-frequency coil is presented. The device has applications in magnetic resonance imaging. There is a set of opposing primary rungs, symmetrically placed on parallel planes and a similar arrangement of rungs on two parallel planes surrounding the primary serves as a shield. Current densities induced in these primary and shielding rungs are calculated to a high degree of accuracy using an integral-equation approach, combined with the inverse finite Hilbert transform. Once these densities are known, accurate electrical and magnetic fields are then computed without difficulty. Some test results are shown. The method is so rapid that it can be incorporated into optimization software. Some preliminary fields produced from optimized coils are presented.

Determining complicated winding patterns for shim coils using stream functions and the target-field method

In a magnetic resonance imaging equipment, gradient and shim coils are needed to produce a spatially varying magnetic field throughout the sample being imaged. Such coils consist of turns of wire wound on the surface of a cylindrical tube. Shim coils in particular, must sometimes be designed to produce complicated magnetic fields to correct for impurities. Streamline patterns for shim coils are much more complicated than those for gradient coils, In this work we present a detailed analysis of streamline methods and their application to shim coil design, A method is presented for determining the winding patterns to generate these complicated fields. (C) 2002 John Wiley & Sons, Inc.

A time-harmonic inverse methodology for the design of RF coils in MRI

An inverse methodology is described to assist in the design of radio-frequency (RF) coils for magnetic resonance imaging (MRI) applications. The time-harmonic electromagnetic Green's functions are used to calculate current on the coil and shield cylinders that will generate a specified internal magnetic field. Stream function techniques and the method of moments are then used to implement this theoretical current density into an RF coil. A novel asymmetric coil operating for a 4.5 T MRI machine was designed and constructed using this methodology and the results are presented.

A method for the design of MRI radiofrequency coils based on triangular and pulse basis functions

This paper presents a numerical technique for the design of an RF coil for asymmetric magnetic resonance imaging (MRI) systems. The formulation is based on an inverse approach where the cylindrical surface currents are expressed in terms of a combination of sub-domain basis functions: triangular and pulse functions. With the homogeneous transverse magnetic field specified in a spherical region, a functional method is applied to obtain the unknown current coefficients. The current distribution is then transformed to a conductor pattern by use of a stream function technique. Preliminary MR images acquired using a prototype RF coil are presented and validate the design method. (C) 2002 Elsevier Science B.V. All rights reserved.

The design of planar gradient coils. Part I: A winding path correction method

In this work a new approach for designing planar gradient coils is outlined for the use in an existing MRI apparatus. A technique that allows for gradient field corrections inside the diameter-sensitive volume is deliberated. These corrections are brought about by making changes to the wire paths that constitute the coil windings, and hence, is called the path correction method. The existing well-known target held method is used to gauge the performance of a typical gradient coil. The gradient coil design methodology is demonstrated for planar openable gradient coils that can be inserted into an existing MRI apparatus. The path corrected gradient coil is compared to the coil obtained using the target field method. It is shown that using a wire path correction with optimized variables, winding patterns that can deliver high magnetic gradient field strengths and large imaging regions can be obtained.

A novel target-field method for finite-length magnetic resonance shim coils: I. Zonal shims

This paper presents a new approach for the design of genuinely finite-length shim and gradient coils, intended for use in magnetic resonance imaging equipment. A cylindrical target region is located asymmetrically, at an arbitrary position within a coil of finite length. A desired target field is specified on the surface of that region, and a method is given that enables winding patterns on the surface of the coil to be designed, to produce the desired field at the inner target region. The method uses a minimization technique combined with regularization, to find the current density on the surface of the coil. The method is illustrated for linear, quadratic and cubic magnetic target fields located asymmetrically within a finite-length coil.

Asymmetric zonal shim coils for magnetic resonance applications

A method is presented for the systematic design of asymmetric zonal shim coils for magnetic resonance applications. Fourier-series methods are used to represent the magnetic field inside and outside a circular cylinder of length 2L and radius a. The current density on the cylinder is also represented using Fourier series. Any desired field can be specified in advance on the cylinder's radius, over some nonsymmetric portion pL

Winding patterns for actively shielded shim coils with asymmetric target-fields

A method is presented for calculating the currents and winding patterns required to design independent zonal and tesseral shim coils for magnetic resonance imaging. Both actively shielded and unshielded configurations are considered, and the region of interest can be located asymmetrically with respect to the coil's length. Streamline, target-field and Fourier-series methods are utilized. The desired target-field is specified at two cylindrical radii, on and inside a circular conducting cylinder of length 2L and radius a. The specification is over some asymmetric portion pL < z < qL of the coil's length (-1 < p < q < 1). Arbitrary functions are used in the outer sections, -L < z < pL and qL < z < L, to ensure continuity of the magnetic field across the entire length of the coil. The entire field is then periodically extended as a half-range cosine Fourier series about either end of the coil. The resultant Fourier coefficients are then substituted into the Fourier-series expressions for the internal and external magnetic fields, and current densities and stream functions on both the primary coil and shield. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis and shielding analysis on field calculations from a ZX shim coil indicate that example designs and theory are well matched.

On the induced electric field gradients in the human body for magnetic stimulation by gradient coils in MRI

Prior theoretical studies indicate that the negative spatial derivative of the electric field induced by magnetic stimulation may he one of the main factors contributing to depolarization of the nerve fiber. This paper studies this parameter for peripheral nerve stimulation (PNS) induced by time.-varying gradient fields during MRI scans. The numerical calculations are based on an efficient, quasi-static, finite-difference scheme and an anatomically realistic human, full-body model. Whole-body cylindrical and planar gradient sets in MRI systems and various input signals have been explored. The spatial distributions of the induced electric field and their gradients are calculated and attempts are made to correlate these areas with reported experimental stimulation data. The induced electrical field pattern is similar for both the planar coils and cylindrical coils. This study provides some insight into the spatial characteristics of the induced field gradients for PNS in MRI, which may be used to further evaluate the sites where magnetic stimulation is likely to occur and to optimize gradient coil design.

A novel target-field method for magnetic resonance shim coils: III. Shielded zonal and tesseral coils

This paper continues the development of a new approach for the design of shim and gradient coils, used in magnetic resonance imaging (MRI) applications. A cylindrical primary coil of radius a and length 2L is placed inside a co-axial shield cylinder of radius b. An active shielding strategy is used to create a desired target field at an arbitrarily specified (cylindrical) location within the primary coil, and to annul the field at a certain radius outside the shield. The form of the interior target field may be chosen arbitrarily by the designer, although zonal and tesseral harmonics are typically used in MRI applications. The method presented here designs coil windings on both the primary and shielding cylinders, to produce fields that conform to the specified interior target field and the annulled field exterior to the shield. An additional feature of the method presented here is that the target field inside the primary coil is matched at two different radii, to improve overall accuracy. The method is illustrated by designing several shielded shim coils, for creating higher order tesseral fields located asymmetrically within the coil. The simpler case of pure zonal fields is discussed separately and applied to the design of some higher order shielded coils.

A distributed equivalent magnetic current based FDTD method for the calculation of E-fields induced by gradient coils

This paper evaluates a new, low-frequency finite-difference time-domain method applied to the problem of induced E-fields/eddy currents in the human body resulting from the pulsed magnetic field gradients in MRI. In this algorithm, a distributed equivalent magnetic current is proposed as the electromagnetic source and is obtained by quasistatic calculation of the empty coil's vector potential or measurements therein. This technique circumvents the discretization of complicated gradient coil geometries into a mesh of Yee cells, and thereby enables any type of gradient coil modelling or other complex low frequency sources. The proposed method has been verified against an example with an analytical solution. Results are presented showing the spatial distribution of gradient-induced electric fields in a multi-layered spherical phantom model and a complete body model. (C) 2004 Elsevier Inc. All rights reserved.

Electromagnetic fields inside a lossy, multilayered spherical head phantom excited by MRI coils: models and methods

The precise evaluation of electromagnetic field (EMF) distributions inside biological samples is becoming an increasingly important design requirement for high field MRI systems. In evaluating the induced fields caused by magnetic field gradients and RF transmitter coils, a multilayered dielectric spherical head model is proposed to provide a better understanding of electromagnetic interactions when compared to a traditional homogeneous head phantom. This paper presents Debye potential (DP) and Dyadic Green's function (DGF)-based solutions of the EMFs inside a head-sized, stratified sphere with similar radial conductivity and permittivity profiles as a human head. The DP approach is formulated for the symmetric case in which the source is a circular loop carrying a harmonic-formed current over a wide frequency range. The DGF method is developed for generic cases in which the source may be any kind of RF coil whose current distribution can be evaluated using the method of moments. The calculated EMFs can then be used to deduce MRI imaging parameters. The proposed methods, while not representing the full complexity of a head model, offer advantages in rapid prototyping as the computation times are much lower than a full finite difference time domain calculation using a complex head model. Test examples demonstrate the capability of the proposed models/methods. It is anticipated that this model will be of particular value for high field MRI applications, especially the rapid evaluation of RF resonator (surface and volume coils) and high performance gradient set designs.

Winding patterns for biplanar MRI shim coils with rectangular and circular target-field regions

A method is presented for calculating the winding patterns required to design independent zonal and tesseral biplanar shim coils for magnetic resonance imaging. Streamline, target-field, Fourier integral and Fourier series methods are utilized. For both Fourier-based methods, the desired target field is specified on the surface of the conducting plates. For the Fourier series method it is possible to specify the target field at additional depths interior to the two conducting plates. The conducting plates are confined symmetrically in the xy plane with dimensions 2a x 2b, and are separated by 2d in the z direction. The specification of the target field is symmetric for the Fourier integral method, but can be over some asymmetric portion pa < x < qa and sb < y < tb of the coil dimensions (-1 < p < q < 1 and -1 < s < t < 1) for the Fourier series method. Arbitrary functions are used in the outer sections to ensure continuity of the magnetic field across the entire coil face. For the Fourier series case, the entire field is periodically extended as double half-range sine or cosine series. The resultant Fourier coefficients are substituted into the Fourier series and integral expressions for the internal and external magnetic fields, and stream functions on both the conducting surfaces. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis of field calculations from a ZX shim coil indicates that example designs and theory are well matched.

Novel target-field method for designing shielded biplanar shim and gradient coils

A new method is presented here for the systematic design of biplanar shielded shim and gradient coils, for use in magnetic resonance imaging (MRI) and other applications. The desired target field interior to the coil is specified in advance, and a winding pattern is then designed to produce a field that matches the target as closely as possible. Both gradient and shim coils can be designed by this approach, and the target region can be located asymmetrically within the coil. The interior target field may be matched at two or more interior locations, to improve accuracy. When shields are present, the winding patterns are designed so that the fields exterior to the biplanar coil are made as small as possible. The method is illustrated here by the design of some transverse gradient and shim coils.