Multiparametric quantification of thermal heterogeneity within aqueous materials by water 1H NMR spectroscopy: Paradigms and algorithms.

Processes involving heat generation and dissipation play an important role in the performance of numerous materials. The behavior of (semi-)aqueous materials such as hydrogels during production and application, but also properties of biological tissue in disease and therapy (e.g., hyperthermia) critically depend on heat regulation. However, currently available thermometry methods do not provide quantitative parameters characterizing the overall temperature distribution within a volume of soft matter. To this end, we present here a new paradigm enabling accurate, contactless quantification of thermal heterogeneity based on the line shape of a water proton nuclear magnetic resonance (1H NMR) spectrum. First, the 1H NMR resonance from water serving as a "temperature probe" is transformed into a temperature curve. Then, the digital points of this temperature profile are used to construct a histogram by way of specifically developed algorithms. We demonstrate that from this histogram, at least eight quantitative parameters describing the underlying statistical temperature distribution can be computed: weighted median, weighted mean, standard deviation, range, mode(s), kurtosis, skewness, and entropy. All mathematical transformations and calculations are performed using specifically programmed EXCEL spreadsheets. Our new paradigm is helpful in detailed investigations of thermal heterogeneity, including dynamic characteristics of heat exchange at sub-second temporal resolution.