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.

Determination of crystal orientation from micrographs using a MATLAB program

Crys.m is a MATLAB routine that combines a micrograph of a crystal with a scaleable, rotatable three-dimensional cage structure to determine the orientation of the crystal axes. The example presented here uses the morphology of tetragonal lysozyme. Rotation of the cage until it aligns with the crystal in the image yields the orientation of the c axis of the crystal relative to the image normal. This analysis can be used for quantitative determination of crystal orientation effects induced by electric, magnetic and/or gravitational fields.

Synthesis of gadolinium-labeled shell-crosslinked nanoparticles for magnetic resonance imaging applications

Shell-crosslinked knedel-like nanoparticles (SCKs; knedel is a Polish term for dumplings) were derivatized with gadolinium Shell chelates and studied as robust magnetic-resonance-imaging-active structures with hydrodynamic diameters of 40 +/- 3 nm. SCKs possessing an amphiphilic core-shell morphology were produced from the aqueous assembly of diblock copolymers of poly(acrylic acid) (PAA) and poly(methyl acrylate) (PMA), PAA(52)-b-PMA(128), and subsequent covalent crosslinking by amidation upon reaction with 2,2'-(ethylenedioxy)bis(ethylamine) throughout the shell layer. The properties of these materials, including non-toxicity towards mammalian cells, non-immunogenicity within mice, and capability for polyvalent targeting, make them ideal candidates for utilization within biological systems. The synthesis of SCKs derivatized with Gd-III and designed for potential use as a unique nanometer-scale contrast agent for MRI applications is described herein. Utilization of an amino-functionalized diethylenetriaminepentaacetic acid-Gd analogue allowed for direct covalent conjugation throughout the hydrophilic shell layer of the SCKs and served to increase the rotational correlation lifetime of the Gd. In addition, the highly hydrated nature of the shell layer in which the Gd was located allowed for rapid water exchange; thus, the resulting material demonstrated large ionic relaxivities (39 s(-1) mM(-1)) in an applied magnetic field of 0.47 T at 40 degrees C and, as a result of the large loading capacity of the material, also demonstrated high molecular relaxivities (20 000 s(-1) mM(-1)).

A target-field method to design circular biplanar coils for asymmetric shim and gradient fields

The paper presents a method for designing circular, shielded biplanar coils that can generate any desired field. A particular feature of these coils is that the target field may be located asymmetrically within the coil. A transverse component of the magnetic field produced by the coil is made to match a prescribed target field over the surfaces of two concentric spheres (the diameter of spherical volume) that define the target field location. The paper shows winding patterns and fields for several gradient and shim coils. It examines the effect that the finite coil size has on the winding patterns, using a Fourier-transform calculation for comparison.

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

Time-harmonic methods are required in the accurate design of RF coils as operating frequency increases. This paper presents such a method to find a current density solution on the coil that will induce some desired magnetic field upon an asymmetrically located target region within. This inverse method appropriately considers the geometry of the coil via a Fourier series expansion, and incorporates some new regularization penalty functions in the solution process. A new technique is introduced by which the complex, time-dependent current density solution is approximated by a static coil winding pattern. Several winding pattern solutions are given, with more complex winding patterns corresponding to more desirable induced magnetic fields.

Magnetic susceptibility measurement applied to the minerals industry

The efficiency of numerous mineral processing operations can be determined by measuring the magnetic properties of the process streams. This measurement, if done at all, is currently performed by laboratory testing of spot samples. This is an inherently slow process and, where feed grades are variable, optimum performance is generally not achieved. This paper describes the rapid measurement of the magnetic properties of minerals. AC measurement techniques, including the analysis of the phase component of the magnetic vector; frequency dependent magnetic susceptibility and the effect of applied magnetic field strength will be discussed. Industrial applications in mineral sands, copper smelting, ferrosilicon testing and drill core scanning will be reported. (C) 2006 Elsevier Ltd. All rights reserved.

Analysis of transient eddy currents in MRI using a cylindrical FDTD method

Most magnetic resonance imaging (MRI) spatial encoding techniques employ low-frequency pulsed magnetic field gradients that undesirably induce multiexponentially decaying eddy currents in nearby conducting structures of the MRI system. The eddy currents degrade the switching performance of the gradient system, distort the MRI image, and introduce thermal loads in the cryostat vessel and superconducting MRI components. Heating of superconducting magnets due to induced eddy currents is particularly problematic as it offsets the superconducting operating point, which can cause a system quench. A numerical characterization of transient eddy current effects is vital for their compensation/control and further advancement of the MRI technology as a whole. However, transient eddy current calculations are particularly computationally intensive. In large-scale problems, such as gradient switching in MRI, conventional finite-element method (FEM)-based routines impose very large computational loads during generation/solving of the system equations. Therefore, other computational alternatives need to be explored. This paper outlines a three-dimensional finite-difference time-domain (FDTD) method in cylindrical coordinates for the modeling of low-frequency transient eddy currents in MRI, as an extension to the recently proposed time-harmonic scheme. The weakly coupled Maxwell's equations are adapted to the low-frequency regime by downscaling the speed of light constant, which permits the use of larger FDTD time steps while maintaining the validity of the Courant-Friedrich-Levy stability condition. The principal hypothesis of this work is that the modified FDTD routine can be employed to analyze pulsed-gradient-induced, transient eddy currents in superconducting MRI system models. The hypothesis is supported through a verification of the numerical scheme on a canonical problem and by analyzing undesired temporal eddy current effects such as the B-0-shift caused by actively shielded symmetric/asymmetric transverse x-gradient head and unshielded z-gradient whole-body coils operating in proximity to a superconducting MRI magnet.

Numerical method for determination of the NMR frequency of the single-qubit operation in a silicon-based solid-state quantum computer

A numerical method is introduced to determine the nuclear magnetic resonance frequency of a donor (P-31) doped inside a silicon substrate under the influence of an applied electric field. This phosphorus donor has been suggested for operation as a qubit for the realization of a solid-state scalable quantum computer. The operation of the qubit is achieved by a combination of the rotation of the phosphorus nuclear spin through a globally applied magnetic field and the selection of the phosphorus nucleus through a locally applied electric field. To realize the selection function, it is required to know the relationship between the applied electric field and the change of the nuclear magnetic resonance frequency of phosphorus. In this study, based on the wave functions obtained by the effective-mass theory, we introduce an empirical correction factor to the wave functions at the donor nucleus. Using the corrected wave functions, we formulate a first-order perturbation theory for the perturbed system under the influence of an electric field. In order to calculate the potential distributions inside the silicon and the silicon dioxide layers due to the applied electric field, we use the multilayered Green's functions and solve an integral equation by the moment method. This enables us to consider more realistic, arbitrary shape, and three-dimensional qubit structures. With the calculation of the potential distributions, we have investigated the effects of the thicknesses of silicon and silicon dioxide layers, the relative position of the donor, and the applied electric field on the nuclear magnetic resonance frequency of the donor.

An inverse methodology for high frequency RF head coil design with pre-emphasized B1 field in MRI

An inverse methodology to assist in the design of radio-frequency (RF) head coils for high field MRI application is described in this work. Free space time-harmonic electromagnetic Green's functions and preemphasized B1 field are used to calculate the current density on the coil cylinder. With B1 field preemphasized and lowered in the middle of the RF transverse plane, the calculated current distribution can generate an internal magnetic field that can reduce the EM field/tissue interactions at high frequencies. The current distribution of a head coil operating at 4 T is calculated using inverse methodology with preemphasized B1 fields. FDTD is employed to calculate B1 field and signal intensity inside a homogenous cylindrical phantom and human head. A comparison with conventional RF birdcage coil is reported here and demonstrated that inverse-method designed coil with preemphasized B1 field can help in decreasing the notorious bright region caused by EM field/tissue interactions in the human head images at 4 T.

An equivalent distributed magnetic current based FDTD method for the calculation of e-fields induced by gradient coils in MRI

This paper evaluates a low-frequency FDTD 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 (DEMC) 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 discretizing of complicated gradient coil geometries into a mesh of Yee cells, and thereby enables any type of gradient coil modeling 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 multilayered spherical phantom model and a complete body model.

Attentional modulation of oscillatory activity in human visual cortex

The effects of attentional modulation on activity within the human visual cortex were investigated using magnetoencephalography. Chromatic sinusoidal stimuli were used to evoke activity from the occipital cortex, with attention directed either toward or away from the stimulus using a bar-orientation judgment task. For five observers, global magnetic field power was plotted as a function of time from stimulus onset. The major peak of each function occurred at about 120 ms latency and was well modeled by a current dipole near the calcarine sulcus. Independent component analysis (ICA) on the non-averaged data for each observer also revealed one component of calcarine origin, the location of which matched that of the dipolar source determined from the averaged data. For two observers, ICA revealed a second component near the parieto-occipital sulcus. Although no effects of attention were evident using standard averaging procedures, time-varying spectral analyses of single trials revealed that the main effect of attention was to alter the level of oscillatory activity. Most notably, a sustained increase in alpha-band (7-12 Hz) activity of both calcarine and parieto-occipital origin was evident. In addition, calcarine activity in the range of 13-21 Hz was enhanced, while calcarine activity in the range of 5-6 Hz was reduced. Our results are consistent with the hypothesis that attentional modulation affects neural processing within the calcarine and parieto-occipital cortex by altering the amplitude of alpha-band activity and other natural brain rhythms. © 2003 Elsevier Inc. All rights reserved.

The influence of age on the pattern and flash visual evoked magnetic response (VEMR)

The visual evoked magnetic response (VEMR) was measured over the occipital cortex to pattern and flash stimuli in 86 normal subjects aged 15-86 years. The latency of the major positive component (outgoing magnetic field) to the pattern reversal stimulus (P100M) increased with age, particularly after 55 years, while the amplitude of the P100M decreased more gradually over the lifespan. By contrast, the latency of the major positive component to the flash stimulus (P2M) increased more slowly with age after about 50 years, while its amplitude may have decreased in only a proportion of the elderly subjects. The changes in the P100M with age may reflect senile changes in the eye and optic nerve, e.g. senile miosis, degenerative changes in the retina or geniculostriate deficits. The P2M may be more susceptible to senile changes in the visual cortex. The data suggest that the contrast channels of visual information processing deteriorate more rapidly with age than the luminance channels.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

A critical assessment of the finite element method for calculating electric and magnetic fields

The present dissertation is concerned with the determination of the magnetic field distribution in ma[.rnetic electron lenses by means of the finite element method. In the differential form of this method a Poisson type equation is solved by numerical methods over a finite boundary. Previous methods of adapting this procedure to the requirements of digital computers have restricted its use to computers of extremely large core size. It is shown that by reformulating the boundary conditions, a considerable reduction in core store can be achieved for a given accuracy of field distribution. The magnetic field distribution of a lens may also be calculated by the integral form of the finite element rnethod. This eliminates boundary problems mentioned but introduces other difficulties. After a careful analysis of both methods it has proved possible to combine the advantages of both in a .new approach to the problem which may be called the 'differential-integral' finite element method. The application of this method to the determination of the magnetic field distribution of some new types of magnetic lenses is described. In the course of the work considerable re-programming of standard programs was necessary in order to reduce the core store requirements to a minimum.

The electron optical limits of performance of single-polepiece magnetic electron lenses

The thesis is concerned with the electron properties of single-polepiece magnetic electron lenses especially under conditions of extreme polepiece saturation. The electron optical properties are first analysed under conditions of high polepiece permeability. From this analysis, a general idea can be obtained of the important parameters that affect ultimate lens performance. In addition, useful information is obtained concerning the design of improved lenses operating under conditions of extreme polepiece saturation, for example at flux densities of the order of 10 Tesla. It is shown that in a single-polepiece lens , the position and shape of the lens exciting coil plays an important role. In particular, the maximum permissible current density in the windings,rather than the properties of the iron, can set a limit to lens performance. This factor was therefore investigated in some detail. The axial field distribution of a single-polepiece lens, unlike that of a conventional lens, is highly asymmetrical. There are therefore two possible physical arrangements of the lens with respect to the incoming electron beam. In general these two orientations will result in different aberration coefficients. This feature has also been investigated in some detail. Single-pole piece lenses are thus considerably more complicated electron- optically than conventional double polepiece lenses. In particular, the absence of the usual second polepiece causes most of the axial magnetic flux density distribution to lie outside the body of the lens. This can have many advantages in electron microscopy but it creates problems in calculating the magnetic field distribution. In particular, presently available computer programs are liable to be considerably in error when applied to such structures. It was therefore necessary to find independent ways of checking the field calculations. Furthermore, if the polepiece is allowed to saturate, much more calculation is involved since the field distribution becomes a non-linear function of the lens excitation. In searching for optimum lens designs, care was therefore taken to ensure that the coil was placed in the optimum position. If this condition is satisfied there seems to be no theoretical limit to the maximum flux density that can be attained at the polepiece tip. However , under iron saturation condition, some broadening of the axial field distribution will take place, thereby changing the lens aberrations . Extensive calculations were therefore made to find the minimum spherical and chromatic aberration coefficients . The focal properties of such lens designs are presented and compared with the best conventional double-polepiece lenses presently available.