Ideal current patterns yielding optimal signal-to-noise ratio and specific absorption rate in magnetic resonance imaging: Computational methods and physical insights

At high and ultra-high magnetic field strengths, understanding interactions between tissues and the electromagnetic fields generated by radiofrequency coils becomes crucial for safe and effective coil design as well as for insight into limits of performance. In this work, we present a rigorous electrodynamic modeling framework, using dyadic Green's functions, to derive the electromagnetic field in homogeneous spherical and cylindrical samples resulting from arbitrary surface currents in the presence or absence of a surrounding radiofrequency shield. We show how to calculate ideal current patterns that result in the highest possible signal-to-noise ratio (ultimate intrinsic signal-to-noise ratio) or the lowest possible radiofrequency power deposition (ultimate intrinsic specific absorption rate) compatible with electrodynamic principles. We identify familiar coil designs within optimal current patterns at low to moderate field strength, thereby establishing and explaining graphically the near-optimality of traditional surface and volume quadrature designs. We also document the emergence of less familiar patterns, e.g., involving substantial electric- as well as magnetic-dipole contributions, at high field strength. Performance comparisons with particular coil array configurations demonstrate that optimal performance may be approached with finite arrays if ideal current patterns are used as a guide for coil design.