Ultimate intrinsic signal-to-noise ratio for parallel MRI: electromagnetic field considerations

A method is described for establishing an upper bound on the spatial encoding capabilities of coil arrays in parallel MRI. Ultimate intrinsic signal-to-noise ratio (SNR), independent of any particular conductor arrangement, is calculated by expressing arbitrary coil sensitivities in terms of a complete set of basis functions that satisfy Maxwell's equations within the sample and performing parallel imaging reconstructions using these basis functions. The dependence of the ultimate intrinsic SNR on a variety of experimental conditions is explored and a physically intuitive explanation for the observed behavior is provided based on a comparison between the electromagnetic wavelength and the distance between aliasing points. Imaging at high field strength, with correspondingly short wavelength, is shown to offer advantages for parallel imaging beyond those already expected due to the larger available spin polarization. One-dimensional undersampling of k-space yields a steep drop in attainable SNR for more than a 5-fold reduction of scan time, while 2D undersampling permits access to much higher degrees of acceleration. Increased tissue conductivity decreases baseline SNR, but improves parallel imaging performance. A procedure is also provided for generating the optimal coil sensitivity pattern for a given acceleration, which will serve as a useful guide for future coil designs.