A degeneracy study in the circulant and bordered-circulant approach to birdcage and planar coils.

A method for finding closed-form solutions for the normal mode frequencies of systems with circulant 2pi/2 symmetry was investigated. This method is particularly good for questions of degeneracy that arise when one considers parallel imaging techniques like SENSE and SMASH in MRI. It is applicable to systems that include birdcage coils as well as planar coils with the appropriate rotational symmetry. A proof is given that complete degeneracy of all normal mode frequencies is impossible when all mutual inductive couplings are included. We tested the method against measurements made on a planar coil array and on an 8-element birdcage coil. The inclusion of the co-rotating end-ring mode changes the fundamental symmetry of the system from circulant to "bordered circulant". Closed-form solutions for the normal mode frequencies of a bordered circulant system are also given.

Application of the SUSHI method to the design of gradient coils.

An approach to potential improvements in magnetic field shielding for a gradient coil system with cylindrical geometry is presented, utilizing "supershielding" conditions for the currents on both the primary and the secondary coils. It is demonstrated that the field can be strongly suppressed everywhere outside a cylindrical shield coil radius, even though the finite-length active shield only partially surrounds a primary coil. The supershielding method, which is aimed at controlling eddy currents, still has sufficient freedom to maintain the desired magnetic field behavior inside the imaging volume. The trade-off is an additional primary current oscillation and increased current peaks and field energy. This method has been applied to design short transverse and axial gradient coils, giving substantially improved shielding compared to an apodization method. Magn Reson Med 45:147-155, 2001.

A degeneracy study in the circulant and bordered-circulant approach to birdcage and planar coils.

A method for finding closed-form solutions for the normal mode frequencies of systems with circulant (2 pi/n) symmetry was investigated. This method is particularly useful for questions of degeneracy that arise when one considers parallel imaging techniques like SENSE and SMASH in MRI. It is applicable to systems that include birdcage coils as well as planar coils with the appropriate rotational symmetry. A proof is given that complete degeneracy of all normal mode frequencies is impossible when all mutual inductive couplings are included. We tested the method against measurements made on a planar coil array and on an 8-element birdcage coil. The inclusion of the co-rotating end-ring mode changes the fundamental symmetry of the system from circulant to 'bordered circulant.' Closed-form solutions for the normal mode frequencies of a bordered circulant system are also given.

Toward shielding improvements in MRI gradients and other systems.

A new method is described for reducing the shielding-error function in the 'supershielding' approach to designing MRI systems. The method is thus shown to lead to significantly better shielding and better control of eddy current effects associated with gradient coils. To illustrate this technique, a set of results for a z-gradient coil is presented. A generalization to non-standard geometries can be made in a straightforward manner with the new method. The usefulness of the relationship of all fringe-field quantities to the shielding-error function is emphasized. The formal limit of perfect shielding in a 'least-squares' sense is shown for a simple strip-shield model along with a numerical eigenvalue study for comparison with the theoretical limit.