Multiparametric quantification of the heterogeneity of free Ca²⁺ concentration by ¹⁹F MR spectroscopy

For biological tissue that is heterogeneous with respect to free intracellular Ca²⁺ concentration ([Ca²⁺]_i), the lineshape of the ¹⁹F MRS resonance of injected [Ca²⁺]-sensitive 4-FBAPTA or BAPTA-FF reflects the statistical distribution of [Ca²⁺]_i values. While conventional ¹⁹F MRS of these fluorinated Ca²⁺ reporter molecules only provides one [Ca²⁺]_i value per spectrum, our specially designed lineshape analysis reveals at least eight quantitative statistical parameters (descriptors) characterizing the [Ca²⁺]_i distribution within the observed tissue volume. To this end, the [Ca²⁺]-sensitive ¹⁹F MRS resonance is transformed into a [Ca²⁺]_i curve. Subsequently, the digital points of this [Ca²⁺]_i profile are used to build a histogram using dedicated algorithms. The following statistical descriptors are computed from this histogram: weighted mean and median, standard deviation, range, mode(s), kurtosis, skewness, and entropy. Our new method is thoroughly validated through in silico and experimental models. The potential of combining statistical [Ca²⁺] information with spatial resolution is demonstrated by simulated statistical CSI maps. This proof of principle should form the basis of future in vivo studies in physiology and medicine, notably in heart and muscle research.