A method for multiparametric statistical quantification of the heterogeneity of free Na + concentration by 19 F MR spectroscopy: Proof of principle in silico and in vitro

: Sodium(I) (Na+ ) is one of the most important cations in mammalian tissues. Since Na+ plays a key role in basic cell function, noninvasive methods for measuring intracellular concentrations of free sodium ions in biological tissue have been developed on the basis of 19 F NMR spectroscopy. However, intracellular Na+ levels are often not uniform throughout a tissue volume (or voxel) being measured. In such cases, [Na+ ] heterogeneity is not reflected in results obtained by the classical technique, and may even result in biased average values. For this reason, we have designed an approach for quantifying [Na+ ] heterogeneity. First, the 19 F MRS resonance from FCrown-1 serving as a "Na+ probe" is transformed into a [Na+ ] curve. Then the digital points of the resulting [Na+ ] profile are used to construct a histogram with specially developed algorithms. From each [Na+ ] histogram, at least eight quantitative parameters describing the underlying statistical [Na+ ] distribution were computed: weighted median, weighted mean, standard deviation, range, mode(s), kurtosis, skewness, and entropy. In addition to our new paradigm, we present a first validation based on (i) computer simulations and (ii) experimentally obtained 19 F MR spectra of model solutions. This basic proof of principle warrants future in vivo experiments, in particular because of its ability to provide quantitative information complementary to that made available by commonly used 23 Na MRI: (i) multiparametric statistical characterization of [Na+ ] distributions; (ii) total [Na+ ] heterogeneity analysis not intrinsically limited by the size of any MRI voxels; and (iii) analysis of unequivocally intracellular [Na+ ], as opposed to measurement of a combination of intra- and extracellular [Na+ ].