ABSTRACT:A new design approach for the construction of gradient coils for magnetic resonance imaging is presented. The theoretical formulation involves a constraint cost function between the desired field in a particular region of interest in space and an almost arbitrarily defined surface that carries the current configuration based on Biot-Savart's integral equation. An appropriate weight function in conjunction with linear approximation functions permits the transformation of the problem formulation into a linear matrix equation whose solution yields discrete current elements in terms of magnitude and direction within a specified coil surface. Numerical predictions and comparisons with practical measurements for the G x , G y , G z gradient coils underscore the success of this approach in terms of achieving highly linear fields while maintaining low parasitic fields and low inductances.
ABSTRACT:The design and construction of radio frequency (RF) coils for applicationspecific magnetic resonance imaging purposes are generally extensive, iterative engineering endeavors that involve multiple electromagnetic simulations followed by tuning and matching on the bench. Computational models of RF coil structures typically take into account the conductor topology; however, they do not address the deployment of lumped circuit elements for tuning, matching, and decoupling. As a result, the design engineer must frequently resort to exhaustive trial-and-error attempts to ensure that the coil, or coil array, is functional at the target resonance frequency. Because coil losses are often not easily predictable in simulations, the final result can be an inferior prototype construction. In this article, a general numerical procedure is outlined that enables the effective simulation and performance comparison of RF coils. The procedure relies on an integrated modeling approach, which combines full-wave electromagnetic simulations with a scattering parameter network representation of all relevant tuning, matching, and decoupling elements. With this combined distributed-lumped simulation approach, detailed comparative studies can be conducted on the basis of a figure of merit parameter that is proportional to the signal-to-noise ratio. Furthermore, major loss mechanisms affecting coil performance can readily be identified and quantified.
Purpose To implement solid state 31P MRI (31P SMRI) in a clinical scanner to visualize bone mineral. Materials and Methods Wrists of seven healthy volunteers were scanned. A quadrature wrist 31P transmit/receive coil provided strong B1 and good signal-to-noise ratio (SNR). A 1H-31P frequency converter was constructed to enable detection of the 31P signal via the 1H channel. Data points lost in the receiver dead time were recovered by a second acquisition with longer dwell time and lower gradient strength. Results Three dimensional 31P images, showing only bone mineral of the wrist, were obtained with a clinical 3T scanner. In the best overall case an image with isotropic resolution of ~5.1 mm and SNR of 30 was obtained in 37 min. 31P NMR properties (resonance line width 2 kHz and T1 17–19 s) of in vivo human bone mineral were measured. Conclusion In vivo 31P SMRI visualization of human wrist bone mineral with a clinical MR scanner is feasible with suitable modifications to circumvent the scanners’ limitations in reception of short-T2 signals. Frequency conversion methodology is useful for implementing 31P SMRI measurements on scanners which do not have multinuclear capability or for which the multinuclear receiver dead time is excessive.
A convergence study is made for the two types of low-order basis functions for the volume integral equation. Both functions impose the continuity of the normal component of the electric flux through the faces. The one basis function is that of Schaubert, Wilton, and Glisson and is face-based. Another basis function was first introduced by de Carvalho and de Souza Mendes and is edge-based. The exact number of unknowns for the edge-based functions is determined in this study. The study demonstrates a better performance of the edge-based basis functions compared to the facebased bases. First, the edge-based basis functions have nearly the same or a faster convergence rate for equal tetrahedral meshes. They also show a high numerical stability. Second, for the same tetrahedral mesh, the number of unknowns for the edge-based functions is considerably smaller. The ratio of unknowns (edge-based versus face-based) ranges from 0.6 for rough plate meshes to approximately 0.5 for large volumetric meshes. Third, the edgebased functions are piecewise constant and are easily implemented into the method of moments. Their disadvantage is a preliminary condition "operation," which implies the elimination of the nullspace of the basis set.Index Terms-Edge basis functions, method of moments (MoM), scattering, volume integral equation.
A Helmholtz-pair local transmit RF coil with an integrated four-element receive array RF coil and foot immobilization platform was designed and constructed for imaging the distal tibia in a whole-body 7 T MRI scanner. Simulations and measurements of the B1 field distribution of the transmit coil are described, along with SAR considerations for operation at 7 T. Results of imaging the trabecular bone of three volunteers at 1.5 T, 3 T and 7 T are presented, using identical 1.5 T and 3 T versions of the 7 T four-element receive array. The spatially registered images reveal improved visibility for individual trabeculae and show average gains in SNR of 2.8x and 4.9x for imaging at 7 T compared to 3 T and 1.5 T, respectively. The results thus display an approximately linear dependence of SNR with field strength and enable the practical utility of 7 T scanners for micro-MRI of trabecular bone.
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