Usefulness of continuous probability distributions of rates for modelling radionuclide biokinetics in humans and animals

Modelling the biokinetics of radionuclide excretion or retention is important in nuclear medicine and following accidental/malicious radioactivity releases. Sums of discrete exponential decay rates are often used, but we hypothesized that continuous probability distributions (CPD) of decay rates can describe the data more parsimoniously and robustly. We tested this hypothesis on diverse human and animal data sets involving various radionuclides (including plutonium, strontium, caesium) measured in the laboratory and in regions contaminated by the Fukushima and Chernobyl nuclear accidents. We used four models on each data set: mono-exponential (ME) with one discrete decay rate, bi-exponential (BE) with two rates, gamma-exponential (GE) with a Gamma distribution of stretched-exponential rates, and power-decay (PD) with a Gamma distribution of power-decay rates. Information-theoretic model selection suggested that radionuclide biokinetics, e.g. for plutonium in humans, are often better described by CPD models like GE and PD, than by discrete rates (ME and BE). Extrapolation of models fitted to data at short times to longer times was frequently more robust for CPD formalisms. We suggest that using a set of several CPD and discrete-rate models, and comparing them by information-theoretic methods, is a promising strategy to enhance the analysis of radionuclide excretion and retention kinetics.