Nmr resonators optimized for high q factor

#This invention relates to NMR resonators. More particularly, this invention relates to a method of optimizing birdcage and related resonators for high Q factor, as well as birdcage resonators thus optimized.

#It has been known to structure a radio-frequency resonator coil in a birdcage form in order to obtain a highly homogeneous magnetic field as described, for example, in U.S. Pat. No. 4,694,255 issued Sep. 15, 1987 to C. Hayes and “Experimental Design and Fabrication of Birdcage Resonators for Magnetic Resonance Imaging” (T. Vullo, et al., Magnetic Resonance in Medicine, 24, 243 (1992)). Birdcage resonators are so called because of their general structure having a pair of generally circular conductive elements (the “rings”) separated in a longitudinal direction to define the axis of the resonator and a plurality of conductive segments (the “rungs”) evenly spaced about the circumference of and interconnecting these two ring elements. The nomenclature, “rungs”, derives from the topology of birdcage coils: when mapped to a plane, the birdcage coil is recognized as a ladder type of LC network.

#Birdcage resonators of different types have been produced, depending on the desired features. Capacitors are inserted either in the rungs for a low-pass coil, or in the rings for a high-pass coil. In the present work, “coil” and “resonator” will generally be used interchangeably, reflecting a typically integral LC structure of the object.

#FIG. 1 is perspective view of a birdcage resonator coil embodying this invention.

#FIG. 2 is a sectional view of the birdcage coil of FIG. 1 and a radio frequency shield surrounding it, as seen along its axial direction.

#FIG. 3 is a two-dimensional contour diagram showing the value of a function related to the Q factor of the coil of FIGS. 1 and 2 as a function of two selected parameters.

#The invention is described next by way of a typical example of birdcage resonator coil geometry of a type having a plurality (N=8) of rungs. FIG. 1 is its external view, showing eight rungs 10 extending axially (in the z-direction) between two conductive rings 15 and 15′ separated from each other along the z-direction. The width, thickness and general cross-sectional shape of the rungs 10 in this figure are meant to illustrate a feature of the invention. FIG. 2 is a sectional view of the resonator of FIG. 1 taken along the z-direction, showing the rungs 10 disposed circularly about the rings 15 at equal azimuthal intervals. In practice, the coil of FIG. 1 is disposed inside a radio frequency shield 20 (not shown in FIG. 1) with inner radius indicated by symbol R2. Each rung 10 has an internally facing surface 11, an externally facing surface 12 and two side surfaces 13 and 14 such that its cross-sectional shape as shown in FIG. 1 is a geometrical figure surrounded by two side edges of length t representing the (radial) thickness of the rung 10, a shorter circular arc of width w with a radius of curvature RI representing the aforementioned internally facing surface 11 and a longer circular arc representing the externally facing surface 12.

#It will be assumed that the wavelength is long compared to the geometrical size of the coil, that the length of the coil is large compared to R1, and that the radio frequency skin depth δ in the metal of the rung material is small compared to the cross-sectional dimensions of the rung. Under these assumptions, solution of Maxwell's equations may reduce to solving the Laplace equation in 2 dimensions for the z-component of the magnetic vector potential Az. The boundary conditions for the solution, appropriate for the coil cross-section shown in FIG. 1, are that Az=0 at the shield radius and that Az=A0 cos(2πn/N) on the surface of the nth rung where n=1, 2, . . . , N and A0 is an arbitrary constant. Once Az is found, the transverse magnetic field B(r, θ) can be calculated from B=V×Az.

#It is further assumed that the resistive loss of the rungs 10 dominate the coil Q factor (Qcoil). It can then be shown that resistive dependencies for Qcoil may be determined geometrically as follows: