Peter T. While

Minimax current density gradient coils: Analysis of coil performance and heating

Standard gradient coils are designed by minimizing the inductance or resistance for an acceptable level of gradient field nonlinearity. Recently, a new method was proposed to minimize the maximum value of the current density in a coil additionally. The stated aim of that method was to increase the minimum wire spacing and to reduce the peak temperature in a coil for fixed efficiency. These claims are tested in this study with experimental measurements of magnetic field and temperature as well as simulations of the performance of many coils. Experimental results show a 90% increase in minimum wire spacing and 40% reduction in peak temperature for equal coil efficiency and field linearity. Simulations of many more coils indicate increase in minimum wire spacing of between 50 and 340% for the coils studied here. This method is shown to be able to increase coil efficiency when constrained by minimum wire spacing rather than switching times or total power dissipation. This increase in efficiency could be used to increase gradient strength, duty cycle, or buildability. Magn Reson Med, 2012.

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 time-harmonic target-field method for designing shielded RF coils in MRI

An inverse method for designing shielded, high-frequency RF coil systems is presented. A time-harmonic target-field approach is taken to find current densities on primary and shield RF coils. The correspondingly induced magnetic field is required to be homogeneous upon an asymmetrically located target region within the scanner and to be zero over an exterior target region. The finite length of the coil system is represented via a Fourier series expansion for the current density. Some new regularization penalty functions are considered in the solution process. A technique is given for creating coil winding patterns from complex, time-dependent current densities. To demonstrate the power of this design method, several coil windings are displayed for the primary and shield coils along with the corresponding fields.

3-D Gradient Coil Design—Initial Theoretical Framework

An analytic inverse method is presented for the theoretical design of 3-D transverse gradient coils. Existing gradient coil design methods require the basic geometry of the coil to be predetermined before optimization. Typically, coil windings are constrained to lie on cylindrical, planar, spherical, or conical surfaces. In this paper, a fully 3-D region in the solution space is explored and the precise geometry of the gradient coils is obtained as part of the optimization process. Primary interest lies in minimizing the field error between induced and target gradient fields within a spherical target region. This is achieved using regularization, in which the field error is minimized along with the total coil power, to obtain a 3-D current density solution within the coil volume. A novel priority streamline technique is used to create 3-D coil windings that approximate this current density, and a secondary optimization is performed to obtain appropriate coil currents. The 3-D coil windings display an interesting general geometric form involving sets of closed loops plus spiral-type coils, and a number of examples are presented and discussed. The corresponding induced magnetic field is found to be highly linear within the region of interest, and a shielding constraint may be implemented to minimize the field outside the coil volume.

3D Gradient coil design - toroidal surfaces

Gradient coil design typically involves optimisation of current densities or coil windings on familiar cylindrical, planar, spherical or conical surfaces. In this paper, an analytic inverse method is presented for the theoretical design of toroidal transverse gradient coils. This novel geometry is based on previous work involving a 3D current density solution, in which the precise geometry of the gradient coils was obtained as part of the optimisation process. Regularisation is used to solve for the toroidal current densities, whereby the field error is minimised in conjunction with the total power of the coil. The method is applied to the design of unshielded and shielded, whole-body and head coil gradient systems. Preliminary coil windings displaying high gradient homogeneity, low inductance, high efficiency and good force balancing are displayed and discussed. Potential benefits associated with this morphology include self-shielding gradient sets, greater access to cooling mechanisms, a reduction in acoustic noise due to force-balancing, a lessening of patient claustrophobia and greater patient access for clinicians.

An inverse method for designing RF phased array coils in MRI- : theoretical considerations

Phased array coils afford a number of advantages over RF volume coils, including a high SNR over a large field of view. In this paper, a time-harmonic inverse method is presented for the theoretical design of RF phased arrays. The method allows any array size to be considered, for which a homogeneous magnetic field is desired within some spherical target region within the coils. An ill-conditioned integral equation is solved using regularization, whereby the error between induced and target magnetic fields is minimized along with an additional constraint related to the curvature of the coil windings. The ability to focus the RF field to arbitrary locations within the coil volume is incorporated into the model and a number of examples are displayed. Attention is also given to the polarization of the induced field, with the direction of linear polarization investigated along with circular polarization. Phased arrays comprising smooth windings that are able to induce highly homogeneous magnetic fields are displayed and discussed for a range of array sizes, and for several different field focusing and polarization considerations.

A comparative simulation study of bayesian fitting approaches to intravoxel incoherent motion modeling in diffusion‐weighted MRI

To assess the performance of various least squares and Bayesian modeling approaches to parameter estimation in intravoxel incoherent motion (IVIM) modeling of diffusion‐weighted MRI data.

Minimum maximum temperature gradient coil design

Ohmic heating is a serious problem in gradient coil operation. A method is presented for redesigning cylindrical gradient coils to operate at minimum peak temperature, while maintaining field homogeneity and coil performance. To generate these minimaxT coil windings, an existing analytic method for simulating the spatial temperature distribution of single layer gradient coils is combined with a minimax optimization routine based on sequential quadratic programming. Simulations are provided for symmetric and asymmetric gradient coils that show considerable improvements in reducing maximum temperature over existing methods. The winding patterns of the minimaxT coils were found to be heavily dependent on the assumed thermal material properties and generally display an interesting “fish‐eye” spreading of windings in the dense regions of the coil. Small prototype coils were constructed and tested for experimental validation and these demonstrate that with a reasonable estimate of material properties, thermal performance can be improved considerably with negligible change to the field error or standard figures of merit. Magn Reson Med 70:584–594, 2013.

An inverse method for designing loaded RF coils in MRI

Radio-frequency (RF) coils are designed such that they induce homogeneous magnetic fields within some region of interest within a magnetic resonance imaging (MRI) scanner. Loading the scanner with a patient disrupts the homogeneity of these fields and can lead to a considerable degradation of the quality of the acquired image. In this paper, an inverse method is presented for designing RF coils, in which the presence of a load (patient) within the MRI scanner is accounted for in the model. To approximate the finite length of the coil, a Fourier series expansion is considered for the coil current density and for the induced fields. Regularization is used to solve this ill-conditioned inverse problem for the unknown Fourier coefficients. That is, the error between the induced and homogeneous target fields is minimized along with an additional constraint, chosen in this paper to represent the curvature of the coil windings. Smooth winding patterns are obtained for both unloaded and loaded coils. RF fields with a high level of homogeneity are obtained in the unloaded case and a limit to the level of homogeneity attainable is observed in the loaded case.

Designing MR Shim Arrays With Irregular Coil Geometry: Theoretical Considerations

In magnetic resonance imaging and spectroscopy, a highly uniform magnetic field is desired for minimizing image distortions and line broadening, respectively. Typically, shim coils are employed to provide correcting fields for inhomogeneities brought about by magnetic interactions with the sample under study. Flexible field modeling is possible using an array of regularly shaped conducting loops that are independently electrically driven. In this paper, a design method is presented for generating coil winding patterns for shim arrays with irregular geometry elements. These designs are compared theoretically to the use of circular loop arrays and are shown to provide considerable improvements in field accuracy and efficiency for generating low-order correcting fields.