Use of Exotic Coordinate Systems in the Design of RF Resonators for High-Field MRI

High field human MRI (11.7 Tesla is FDC approved for human research) renders standard RF coil design inadequate because the resonant wavelength in human soft tissue (about 8 cm at 500 MHz) is significantly smaller than the physical size of the human body. I propose optimizing the design of such RF coils using coordinate systems appropriate to human body parts, as has been done with elliptical\footnote{Crozier et al, \textit{Concepts Magn Reson} 1997; \textbf{9}:195-210.} and Cassinian oval\footnote{De Zanche et al, \textit{Magn Reson Med} 2005; \textbf{53}:201-211.} cross sections. I have computed analytically the magnetic fields produced by a device of toroidal cross section using a cascade of conformal transformations.\footnote{Butterworth {\&} Gore, J Magn Reson 2005; 175:114-123.} Building upon these efforts, I will use the eleven coordinate systems of Moon {\&} Spencer,\footnote{Moon {\&} Spencer, Field\textit{ Theory Handbook,} Berlin: Springer-Verlag; 1971.} along with other possible coordinate systems and conformal transformations, to identify a small number of configurations that have the highest probability of being useful as RF coil designs for ultrahigh-field MRI.