Multiparametric quantification of heterogeneity of metal ion concentrations, as demonstrated for [Mg 2+ ] by way of 31 P MRS.

Magnesium(II) is the second most abundant intracellular cation in mammals. Non-invasive 31 P MRS is currently used to measure intracellular free Mg2+ levels in studies of magnesium deficiency disorders. However, this technique only provides one [Mg2+ ] value for a given tissue volume (or voxel), based on the chemical shift of the ATP-β (or NTP-β) resonance. We present here an approach for quantifying tissue heterogeneity in regard to [Mg2+ ], by way of multiple 31 P MRS-derived descriptors characterizing the statistical intra-volume distribution of free [Mg2+ ] values. Our novel paradigm exploits the fact that the lineshape of the ATP-β 31 P MRS resonance reflects the statistical distribution of [Mg2+ ] values within the observed volume (or voxel). Appropriate lineshape analysis reveals multiple quantitative statistical parameters (descriptors) characterizing the [Mg2+ ] distribution. First, the ATP-β 31 P MRS resonance is transformed into a [Mg2+ ] curve that is used to construct a histogram with our specially developed algorithms. From this histogram, at least eight [Mg2+ ] descriptors are computed: weighted mean concentration and median concentration, standard deviation of concentration, range of concentration, concentration mode(s), concentration kurtosis, concentration skewness, and concentration entropy. Comprehensive evaluation based on in silico and experimental models demonstrates the validity of this new method. This basic feasibility study should open new avenues for future in vivo studies in physiology and medicine.