Voxel-wise partial volume correction method for accurate estimation of tissue sodium concentration in ²³ Na-MRI at 7...

Sodium is crucial for the maintenance of cell physiology, and its regulation of the sodium-potassium pump has implications for various neurological conditions. The distribution of sodium concentrations in tissue can be quantitatively evaluated by means of sodium MRI (²³ Na-MRI). Despite its usefulness in diagnosing particular disease conditions, tissue sodium concentration (TSC) estimated from ²³ Na-MRI can be strongly biased by partial volume effects (PVEs) that are induced by broad point spread functions (PSFs) as well as tissue fraction effects. In this work, we aimed to propose a robust voxel-wise partial volume correction (PVC) method for ²³ Na-MRI. The method is based on a linear regression (LR) approach to correct for tissue fraction effects, but it utilizes a 3D kernel combined with a modified least trimmed square (3D-mLTS) method in order to minimize regression-induced inherent smoothing effects. We acquired ²³ Na-MRI data with conventional Cartesian sampling at 7 T, and spill-over effects due to the PSF were considered prior to correcting for tissue fraction effects using 3D-mLTS. In the simulation, we found that the TSCs of gray matter (GM) and white matter (WM) were underestimated by 20% and 11% respectively without correcting tissue fraction effects, but the differences between ground truth and PVE-corrected data after the PVC using the 3D-mLTS method were only approximately 0.6% and 0.4% for GM and WM, respectively. The capability of the 3D-mLTS method was further demonstrated with in vivo ²³ Na-MRI data, showing significantly lower regression errors (ie root mean squared error) as compared with conventional LR methods (p < 0.001). The results of simulation and in vivo experiments revealed that 3D-mLTS is superior for determining under- or overestimated TSCs while preserving anatomical details. This suggests that the 3D-mLTS method is well suited for the accurate determination of TSC, especially in small focal lesions associated with pathological conditions.