Image brightening in samples of high dielectric constant

Abstract

An analytic solution is given for the electromagnetic problem of a lossy dielectric cylinder of infinite length, irradiated by a circularly polarized radiofrequency (RF) magnetic field; the NMR-active components of the field inside the cylinder are projected out by transforming the RF Hamiltonian to the rotating frame and retaining only those terms independent of time; it is noted that the resulting cartesian field components are required to be real. The squared magnitude of the NMR-active fields are then used to calculate the gradient-recalled images of the cylinder, for small tip angles of the magnetization; and the result is shown to predict almost quantitatively the intensity patterns of experimental proton images at 3.0 and 4.0 T, in a cylindrical phantom of radius 9.25 cm, filled with 0.05 M aqueous NaCl. In particular, the artifactual brightening at the center of the recorded image is convincingly reproduced in a simulation, whose underlying model excludes wave propagation along the direction of the cylinder axis. Formation of the artifact is explained in terms of the focussing of the RF magnetic field at the center of the cylinder, as illustrated by contour plots showing the time evolution of the rotating flux. An extended electromagnetic model—having the dielectric cylinder enclosed in a long, shielded volume resonator (e.g., of bird cage type)—is then sketched. The mathematical details appear in Appendix A; and the simulated images are shown to be virtually indistinguishable from those of the simpler original model. The theory of the Q, or quality factor, of the dielectric cylinder—considered itself as a resonant object—is developed for the enclosed cylinder model, where flux containment by the shield permits an unambiguous treatment of both the stored energy and the radiative losses. This is extended to treat the Q of a lossy dielectric sphere without shielding. Further plots of flux contours are given for the sphere, excited at 208 MHz with a uniform circularly polarized field, as well as by a surface coil, and for the enclosed cylinder in the range 140–160 MHz. It is then argued that the center brightening artifacts in magnetic resonance images are due to the underdamped dielectric resonance of the sample, i.e., at Q>0.5, while the overdamped condition, Q<0.5, leads to exclusion of flux from the center, i.e., to the classic skin effect. The term ‘dielectric resonance’ is shown to require careful interpretation for mixed-mode excitation, such as occurs with a surface coil. An extended reciprocity formula for NMR reception, valid for an arbitrary electromagnetic Green’s function, is also given in Appendix B.