Human biokinetics of strontium. Part I: intestinal absorption rate and its impact on the dose coefficient of 90Sr after ingestion

Analyzing lognormal data: A nonmathematical practical guide

Lognormal distributions are pervasive in pharmacology and elsewhere in biomedical science, arising naturally when biological effects multiply rather than add. Despite their ubiquity in pharmacological parameters (eg, EC50, IC50, Kd, and Km), lognormal distributions are often overlooked or misunderstood, leading to flawed data analysis. This largely nonmathematical review explains why lognormal distributions are common, how to recognize them, and how to analyze them appropriately. We show that many measured variables are lognormal. So are many derived parameters, particularly those defined as ratios of lognormal variables. Through examples and simulations accessible to working scientists, we demonstrate how misidentifying lognormal distributions as normal leads to reduced statistical power, unnecessarily large sample sizes, false identification of outliers, and inappropriate reporting of effects as differences rather than ratios. We challenge the common practice of using normality tests to decide how to analyze data, showing that many data sets pass both normality and lognormality tests, especially with small sample sizes. Instead, we advocate for assuming lognormality based on the nature of the variable. This review provides practical guidance on recognizing and presenting lognormal data, and comparing data sets sampled from lognormal distributions. Based on Monte Carlo simulations, we recommend the lognormal Welch's t test or nonparametric Brunner-Munzel test for comparing 2 unpaired groups, the lognormal ratio paired t test for paired comparisons, and lognormal ANOVA for ≥3 groups. By recognizing and properly handling lognormal distributions, pharmacologists can design more efficient experiments, obtain more reliable statistical inferences, and communicate their results more effectively. SIGNIFICANCE STATEMENT: Lognormal distributions are common in pharmacology and many scientific fields, but they are often misunderstood or overlooked. This review provides a detailed guide to recognizing and analyzing lognormal data, aiming to help pharmacologists perform more appropriate and more powerful statistical analyses, draw more meaningful conclusions from their data, and communicate their results more effectively.

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.

Age and gender specific biokinetic model for strontium in humans

A biokinetic model for strontium in humans is necessary for quantification of internal doses due to strontium radioisotopes. The ICRP-recommended biokinetic model for strontium has limitations for use in a population study, because it is not gender specific and does not cover all age ranges. The extensive Techa River data set on (90)Sr in humans (tens of thousands of measurements) is a unique source of data on long-term strontium retention for men and women of all ages at intake. These, as well as published data, were used for evaluation of age- and gender-specific parameters for a new compartment biokinetic model for strontium (Sr-AGe model). The Sr-AGe model has a similar structure to the ICRP model for the alkaline earth elements. The following parameters were mainly re-evaluated: gastrointestinal absorption and parameters related to the processes of bone formation and resorption defining calcium and strontium transfers in skeletal compartments. The Sr-AGe model satisfactorily describes available data sets on strontium retention for different kinds of intake (dietary and intravenous) at different ages (0-80 years old) and demonstrates good agreement with data sets for different ethnic groups. The Sr-AGe model can be used for dose assessment in epidemiological studies of general populations exposed to ingested strontium radioisotopes.

Assessing the reliability of dose coefficients for ingestion and inhalation of 226Ra and 90Sr by members of the public

Assessments of risk to a population group resulting from internal exposure to a particular radionuclide can be used to assess the reliability of the appropriate International Commission on Radiological Protection (ICRP) dose coefficient, E(50), used as a radiation protection device for the specified exposure pathway. An estimate of the uncertainty on the risk is important for informing judgements on reliability. This paper describes the application of parameter uncertainty analysis to quantify uncertainties resulting from internal exposures to radioisotopes of the alkaline earth metals, (90)Sr and (226)Ra, by members of the UK public. The study derives uncertainties in biokinetic model parameter values to calculate the distributions of the effective dose per unit intake using the ICRP Publication 60 formalism. The distributions are used to infer the uncertainty on the mean effective dose per unit intake to inform the derivation of uncertainty factors (UF) for the appropriate ICRP Publication 72 dose coefficients. Here, a UF indicates a 95 % probability that the best estimate of risk per unit intake is within a factor, UF, of the nominal risk associated with the appropriate ICRP dose coefficient, E(50), with respect to uncertainties in the biokinetic model parameter values. Ingestion: it is assumed that exposure occurs through the ingestion of radionuclides present in food and water. The results for both radionuclides suggest a UF of within 3 for all age groups, with median values close to the ICRP values. Inhalation: it is assumed that environmental exposure to radium occurs primarily due to insoluble forms present in fly ash discharged from coal-fired power stations; for strontium, exposure is assumed to occur due to residual aerosols produced as a result of atmospheric nuclear testing and nuclear reactor accidents. The results suggest a UF of around 3 and 6 for inhalation of (90)Sr and (226)Ra, respectively, by members of the public.

Uncertainty analysis of doses from ingestion of plutonium and americium

Uncertainty analyses have been performed on the biokinetic model for americium currently used by the International Commission on Radiological Protection (ICRP), and the model for plutonium recently derived by Leggett, considering acute intakes by ingestion by adult members of the public. The analyses calculated distributions of doses per unit intake. Those parameters having the greatest impact on prospective doses were identified by sensitivity analysis; the most important were the fraction absorbed from the alimentary tract, f(1), and rates of uptake from blood to bone surfaces. Probability distributions were selected based on the observed distribution of plutonium and americium in human subjects where possible; the distributions for f(1) reflected uncertainty on the average value of this parameter for non-specified plutonium and americium compounds ingested by adult members of the public. The calculated distributions of effective doses for ingested (239)Pu and (241)Am were well described by log-normal distributions, with doses varying by around a factor of 3 above and below the central values; the distributions contain the current ICRP Publication 67 dose coefficients for ingestion of (239)Pu and (241)Am by adult members of the public. Uncertainty on f(1) values had the greatest impact on doses, particularly effective dose. It is concluded that: (1) more precise data on f(1) values would have a greater effect in reducing uncertainties on doses from ingested (239)Pu and (241)Am, than reducing uncertainty on other model parameter values and (2) the results support the dose coefficients (Sv Bq(-1) intake) derived by ICRP for ingestion of (239)Pu and (241)Am by adult members of the public.

Reliability of a new biokinetic model of zirconium in internal dosimetry: part I, parameter uncertainty analysis

The reliability of biokinetic models is essential in internal dose assessments and radiation risk analysis for the public, occupational workers, and patients exposed to radionuclides. In this paper, a method for assessing the reliability of biokinetic models by means of uncertainty and sensitivity analysis was developed. The paper is divided into two parts. In the first part of the study published here, the uncertainty sources of the model parameters for zirconium (Zr), developed by the International Commission on Radiological Protection (ICRP), were identified and analyzed. Furthermore, the uncertainty of the biokinetic experimental measurement performed at the Helmholtz Zentrum München-German Research Center for Environmental Health (HMGU) for developing a new biokinetic model of Zr was analyzed according to the Guide to the Expression of Uncertainty in Measurement, published by the International Organization for Standardization. The confidence interval and distribution of model parameters of the ICRP and HMGU Zr biokinetic models were evaluated. As a result of computer biokinetic modelings, the mean, standard uncertainty, and confidence interval of model prediction calculated based on the model parameter uncertainty were presented and compared to the plasma clearance and urinary excretion measured after intravenous administration. It was shown that for the most important compartment, the plasma, the uncertainty evaluated for the HMGU model was much smaller than that for the ICRP model; that phenomenon was observed for other organs and tissues as well. The uncertainty of the integral of the radioactivity of Zr up to 50 y calculated by the HMGU model after ingestion by adult members of the public was shown to be smaller by a factor of two than that of the ICRP model. It was also shown that the distribution type of the model parameter strongly influences the model prediction, and the correlation of the model input parameters affects the model prediction to a certain extent depending on the strength of the correlation. In the case of model prediction, the qualitative comparison of the model predictions with the measured plasma and urinary data showed the HMGU model to be more reliable than the ICRP model; quantitatively, the uncertainty model prediction by the HMGU systemic biokinetic model is smaller than that of the ICRP model. The uncertainty information on the model parameters analyzed in this study was used in the second part of the paper regarding a sensitivity analysis of the Zr biokinetic models.

Influence of human biokinetics of strontium on internal ingestion dose of 90Sr and absorbed dose of 89Sr to organs and metastases

The objective of the present work is to apply the plasma clearance parameters to strontium, previously determined in our laboratory, to improve the biokinetic and dosimetric models of strontium-90 ((90)Sr) used in radiological protection; and also to apply this data for the estimation of the radiation doses from strontium-89 ((89)Sr) after administration to patients for the treatment of the painful bone metastases. Plasma clearance and urinary excretion of stable strontium tracers of strontium-84 ((84)Sr) and strontium-86 ((86)Sr) were measured in GSF-National Research Center for Environment and Health (GSF) in 13 healthy German adult subjects after intravenous injection and oral administration. The biological half-life of strontium in plasma was evaluated from 49 plasma concentration data sets following intravenous injections. This value was used to determine the transfer rates from plasma to other organs and tissues. At the same time, the long-term retention of strontium in soft tissue and whole body was constrained to be consistent with measured values available. A physiological urinary path was integrated into the biokinetic model of strontium. Parameters were estimated using our own measured urinary excretion values. Retention and excretion of strontium were modeled using compartmental transfer rates published by the International Commission on Radiological Protection (ICRP), the SENES Oak Ridge Inc. (SENES), and the Urals Research Center for Radiation Medicine (TBM). The results were compared with values calculated by applying our GSF parameters (GSF). For the dose estimation of (89)Sr, a bone metastases model (GSF-M) was developed by adding a compartment, representing the metastases, into the strontium biokinetic model. The related parameters were evaluated based on measured data available in the literature. A set of biokinetic parameters was optimized to represent not only the early plasma kinetics of strontium but also the long-term retention measured in soft tissue and whole body. The ingestion dose coefficients of (90)Sr were computed and compared with different biokinetic model parameters. The ingestion dose coefficients were calculated as 2.8 x 10(-8), 2.1 x 10(-8), 2.5 x 10(-8) and 3.8 x 10(-8) Sv Bq(-1) for ICRP, SENES, TBM and GSF model parameters, respectively. Moreover, organ absorbed dose for the radiopharmaceutical of (89)Sr in bone metastases therapy was estimated based on the GSF and ICRP biokinetic model parameters. The effective doses were 3.3, 1.8 and 1.2 mSv MBq(-1) by GSF, GSF-M, and ICRP Publication 67 model parameters, respectively, compared to the value of 3.1 mSv MBq(-1) reported by ICRP Publication 80. The absorbed doses of red bone marrow and bone surface, 17 and 21 mGy MBq(-1) calculated by GSF parameters, and 7.1 and 8.8 mGy MBq(-1) by GSF-M parameters, are comparable to the clinical results of 3-19 mGy MBq(-1) for bone marrow and 16 mGy MBq(-1) for bone surface. Based on the GSF-M model, the absorbed dose of (89)Sr to metastases was estimated to be 434 mGy MBq(-1). The strontium clearance half-life of 0.25 h from the plasma obtained in the present study is obviously faster than the value of 1.1 h recommended by ICRP. There are no significant changes for ingestion dose coefficients of (90)Sr using different model parameters. A model including the metastases was particularly developed for dose estimation of (89)Sr treatment for the pain of bone metastases.

Human biokinetics of strontium--part II: Final data evaluation of intestinal absorption and urinary excretion of strontium in human subjects after stable tracer administration

Fractional intestinal absorption (f1 value) and urinary excretion of strontium in healthy human volunteers has been measured by simultaneous oral and intravenous administration of the stable isotopes 86Sr and 84Sr using the double-isotope method. Final evaluation of the complete data set confirmed that ingestion of different foodstuff and nutritional factors could influence the fractional gut uptake of strontium. In some cases, significant deviations from the f1 value adopted by the International Commission on Radiological Protection (ICRP) were found. The arithmetic mean (+/- standard deviation) of the f1 values of all experiments performed was determined to be 0.46 (+/- 0.24). The probability distribution function of the f1 values is represented by a lognormal curve with a geometric mean of 0.38 and a geometric standard deviation of 2.06. Urinary excretion in all subjects varied depending on the administered foodstuff in a wide range and differs from the ICRP model, up to 2 days after tracer administration. No age or gender dependence of the absorbed strontium fraction and of the urinary excretion of strontium after an oral load was found.