Radiofrequency microcoils for magnetic resonance imaging and spectroscopy

A full mathematical framework for the analysis and production of localized magnetic field profiles is presented. Of primary use in the production of highly homogeneous fields for nuclear magnetic resonance studies, the paper details the analysis of fields in terms of spherical harmonics, describes how field plotting in the appropriate manner may be used to obtain a direct measure of which harmonics are present, and shows how to combine basic "building blocks" to produce the various lower-order zonal and tesseral harmonics. "Building blocks" described include coils, arcs, and sinusoids of current as well as rings and arcs of steel. The use of shaped magnets is also briefly mentioned. Attention is drawn to the presence, in high-order designs, of possibly dominant lower orders of harmonics created by errors in fabrication. The goal of the paper is to present a design philosophy, backed by the appropriate mathematics, which is applicable to the variety of situations encountered in magnet design. Practical examples of correcting coils and "shims" are also given.

The signal-to-noise ratio achieved in a nuclear magnetic-resonance microscopy experiment is directly related to the performance of the radiofrequency coil. An accurate determination of coil performance requires that the resistance of the coil be well characterized. Traditional high-frequency electric-circuit models used to describe larger NMR coils are inadequate when the diameter of the conductor is reduced to the dimensions of the electrical skin depth (delta) at the frequency of operation. A more extensive model based on a scaling parameter that includes delta is presented. This model complements other existing circuit models that represent sample losses, ground-loop and parasitic losses, and the signal induced in the RF coil. Experimental verification is accomplished using a series of solenoidal microcoils in 1H NMR microspectroscopy experiments at 4.7 T (200 MHz). This study demonstrates for the first time that a predictable performance enhancement is achieved using microcoils as small as 50 microns in diameter.