An approach to evaluation of the point-spread function for ²³ Na magnetic resonance imaging

Despite the technical challenges that require lengthy acquisitions to overcome poor signal-to-noise ratio (SNR), sodium (²³ Na) magnetic resonance imaging (MRI) is an intriguing area of research due to its essential role in human metabolism. Low SNR images can impact the measurement of the point-spread function (PSF) by adding uncertainty into the resulting quantities. Here, we present methods to calculate the PSF by using the modulation transfer function (MTF), and a 3D-printed line-pair phantom in the context of ²³ Na MRI. A simulation study investigated the effect of noise on the resulting MTF curves, which were derived by direct modulation (DM) and a method utilizing Fourier harmonics (FHs). Experimental data utilized a line-pair phantom with nine spatial frequencies, filled with different concentrations (15, 30, and 60 mM) of sodium in 3% agar. MTF curves were calculated using both methods from data acquired from density-adapted 3D radial projections (DA-3DRP) and Fermat looped orthogonally encoded trajectories (FLORET). Simulations indicated that the DM method increased variability in the MTF curves at all tested noise levels over the FH method. For the experimental data, the FH method resulted in PSFs with a narrower full width half maximum with reduced variability, although the improvement in variability was not as pronounced as predicted by simulations. The DA-3DRP data indicated an improvement in the PSF over FLORET. It was concluded that a 3D-printed line-pair phantom represents a convenient method to measure the PSF experimentally. The MTFs from the noisy images in ²³ Na MRI have reduced variability from a FH method over DM.