Modeling the effects of RF penetration in magnetic resonance (MR) imaging requires a knowledge of the local values of conductivity and permittivity. The inverse problem of determining the electlic properties of the materid under investigation using the M R images themselves has not previously been addressed.W e review such an approach for the heterogeneous layer model and examine the parsmeter sensitivity l o geometry and signal-to-noise ratio. For a few-layer system, it is within the realm of present day M a systems to extract the electric properties 10 within 10% or better. Knowledge of the electrical propertis will then allow a better prediction of the R F penetration and power deposition at high fields.

Insertable planar gradient coils offer the potential for significant performance increases in magnetic resonance imaging through higher gradient strength and shorter rise times. Using variational methods to minimize inductance, and thereby to optimize switching speeds, we have analyzed and constructed a biplanar y-gradient coil for insertion into a solenoidal magnet system where z is the magnet axis. We have also analyzed biplanar x-gradient and z-gradient coil designs using the same methods. These biplanar coils offer an advantage over a cylindrical coil of comparable diameter in that they achieve high gradient strengths with relatively short rise times while maintaining patient access. Although the requirement that the currents for the x gradient lie in the same plane as for the y and z gradients increases the stored energy by a factor of 3 with respect to the other two gradients, this stored energy is still smaller by a factor of 2 than that of a comparably constrained x-gradient cylindrical coil. The biplanar coil design offers improved linearity over its single planar coil alternative. The particular designs we have investigated are generally limited to small-volume imaging.

We present preliminary results for a 3D finite element calculation to evaluate RF penetration in conducting dielectric materials at high field strengths. A tetrahedral mesh is used along with a Coulomb gauge constraint in a finite element method that yields excellent numerical stability at high frequencies. Accuracy is verified by comparisons with analytic solutions for single-layer and multiple-layer heterogeneous systems and for a 3D spherical model. We have also compared the finite element model with experimental results presented by Foo et al., Magn. Reson. Med. 23, (1992). Agreement is very good and argues for the usefulness of the method in the calculation of RF penetration and RF power deposition effects in heterogeneous objects.

High performance magnetic field gradient coils have always been desirable in today’s ultrafast magnetic resonance imaging (MRI) applications, such as single-shot echo-planar imaging and fast spin echo imaging, as well as MR diffusion imaging and microscopy. We present a Lagrange multiplier technique of a minimum inductance gradient coil with spherical geometry. Based on this minimization approach, we construct a functional F in terms of the stored magnetic energy, the magnetic field and a set of field constraint points which are chosen over the desired imaging volume. Minimizing F, we obtain the continuous current density distribution for the spherical gradient coil. Applying the stream function technique to the continuous current distribution, the discrete current pattern can then be generated. Employing the Biot–Savart law to the discrete current loops, the gradient magnetic field has been re-evaluated in order to validate the theory. Using this approach, we have been able to design a spherical z-gradient coil which is capable of generating a gradient field of 176 mT/m with slew rate of 3422 T/m/s over a 30-cm-diam spherical volume if driven by a 350 V–220 A current amplifier. A prototype of the spherical z-gradient coil has been built. The agreement between the analytical and experimental results is excellent. Initial imaging experiments have been conducted. The results indicate the potential use of such a coil for in vivo and in vitro fast NMR applications.

We present an application to elliptical coordinates of Turner's target field method. Coils are designed with their inductance minimized subject to constraints on the magnetic field. This is of value, for example, in magnetic resonance imaging (MRI) where it is desired that high-strengfh gradient coils be rapidly switched on and off Green functions and associated computational toois in elliptic coordinates are developed, We also discuss the advantages d elliptically cylindrical coils compared with circularly cylindrical coils for whole-body MRI applications