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

Uncertainty analysis in internal dose calculations for cerium considering the uncertainties of biokinetic parameters and S values

Radioactive cerium and other lanthanides can be transported through the aquatic system into foodstuffs and then be incorporated by humans. Information on the uncertainty of reported dose coefficients for exposed members of the public is then needed for risk analysis. In this study, uncertainties of dose coefficients due to the ingestion of the radionuclides 141Ce and 144Ce were estimated. According to the schema of internal dose calculation, a general statistical method based on the propagation of uncertainty was developed. The method takes into account the uncertainties contributed by the biokinetic models and by the so-called S values. These S-values were derived by using Monte Carlo radiation transport simulations with five adult non-reference voxel computational phantoms that have been developed at Helmholtz Zentrum München, Germany. Random and Latin hypercube sampling techniques were applied to sample parameters of biokinetic models and S values. The uncertainty factors, expressed as the square root of the 97.5th and 2.5th percentile ratios, for organ equivalent dose coefficients of 141Ce were found to be in the range of 1.2-5.1 and for 144Ce in the range of 1.2-7.4. The uncertainty factor of the detriment-weighted dose coefficient for 141Ce is 2.5 and for 144Ce 3.9. It is concluded that a general statistical method for calculating the uncertainty of dose coefficients was developed and applied to the lanthanide cerium. The dose uncertainties obtained provide improved dose coefficients for radiation risk analysis of humans. Furthermore, these uncertainties can be used to identify those parameters most important in internal dose calculations by applying sensitivity analyses.

Measurement, model prediction and uncertainty quantification of plasma clearance of cerium citrate in humans

Double tracer studies in healthy human volunteers with stable isotopes of cerium citrate were performed with the aim of investigating the gastro-intestinal absorption of cerium (Ce), its plasma clearance and urinary excretion. In the present work, results of the clearance of Ce in blood plasma are shown after simultaneous intravenous and oral administration of a Ce tracer. Inductively coupled plasma mass spectrometry was used to determine the tracer concentrations in plasma. The results show that about 80% of the injected Ce citrate cleared from the plasma within the 5 mins post-administration. The data obtained are compared to a revised biokinetic model of Ce, which was initially developed by the International Commission on Radiological Protection (ICRP). The measured plasma clearance of Ce citrate was mostly consistent with that predicted by the ICRP biokinetic model. Furthermore, in an effort to quantify the uncertainty of the model prediction, the laboratory animal data on which the ICRP biokinetic Ce model is based, was analyzed. The measured plasma clearance and its uncertainty was also compared to the plasma clearance uncertainty predicted by the model. It was found that the measured plasma clearance during the first 15 min after administration is in a good agreement with the modelled plasma clearance. In general, the measured clearance falls inside the 95% confidence interval predicted by the biokinetic model.

Parameter uncertainty analysis of a biokinetic model of caesium

Parameter uncertainties for the biokinetic model of caesium (Cs) developed by Leggett et al. were inventoried and evaluated. The methods of parameter uncertainty analysis were used to assess the uncertainties of model predictions with the assumptions of model parameter uncertainties and distributions. Furthermore, the importance of individual model parameters was assessed by means of sensitivity analysis. The calculated uncertainties of model predictions were compared with human data of Cs measured in blood and in the whole body. It was found that propagating the derived uncertainties in model parameter values reproduced the range of bioassay data observed in human subjects at different times after intake. The maximum ranges, expressed as uncertainty factors (UFs) (defined as a square root of ratio between 97.5th and 2.5th percentiles) of blood clearance, whole-body retention and urinary excretion of Cs predicted at earlier time after intake were, respectively: 1.5, 1.0 and 2.5 at the first day; 1.8, 1.1 and 2.4 at Day 10 and 1.8, 2.0 and 1.8 at Day 100; for the late times (1000 d) after intake, the UFs were increased to 43, 24 and 31, respectively. The model parameters of transfer rates between kidneys and blood, muscle and blood and the rate of transfer from kidneys to urinary bladder content are most influential to the blood clearance and to the whole-body retention of Cs. For the urinary excretion, the parameters of transfer rates from urinary bladder content to urine and from kidneys to urinary bladder content impact mostly. The implication and effect on the estimated equivalent and effective doses of the larger uncertainty of 43 in whole-body retention in the later time, say, after Day 500 will be explored in a successive work in the framework of EURADOS.

Age-dependent inhalation doses to members of the public from indoor short-lived radon progeny

The main contribution of radiation dose to the human lungs from natural exposure originates from short-lived radon progeny. In the present work, the inhalation doses from indoor short-lived radon progeny, i.e., (218)Po, (214)Pb, (214)Bi, and (214)Po, to different age groups of members of the public were calculated. In the calculations, the age-dependent systemic biokinetic models of polonium, bismuth, and lead published by the International Commission on Radiological Protection (ICRP) were adopted. In addition, the ICRP human respiratory tract and gastrointestinal tract models were applied to determine the deposition fractions in different regions of the lungs during inhalation and exhalation, and the absorption fractions of radon progeny in the alimentary tract. Based on the calculated contribution of each progeny to equivalent dose and effective dose, the dose conversion factor was estimated, taking into account the unattached fraction of aerosols, attached aerosols in the nucleation, accumulation and coarse modes, and the potential alpha energy concentration fraction in indoor air. It turned out that for each progeny, the equivalent doses to extrathoracic airways and the lungs are greater than those to other organs. The contribution of (214)Po to effective dose is much smaller compared to that of the other short-lived radon progeny and can thus be neglected in the dose assessment. In fact, 90 % of the effective dose from short-lived radon progeny arises from (214)Pb and (214)Bi, while the rest is from (218)Po. The dose conversion factors obtained in the present study are 17 and 18 mSv per working level month (WLM) for adult female and male, respectively. This compares to values ranging from 6 to 20 mSv WLM(-1) calculated by other investigators. The dose coefficients of each radon progeny calculated in the present study can be used to estimate the radiation doses for the population, especially for small children and women, in specific regions of the world exposed to radon progeny by measuring their concentrations, aerosol sizes, and unattached fractions.

Bayesian model selection validates a biokinetic model for zirconium processing in humans

BACKGROUND

In radiation protection, biokinetic models for zirconium processing are of crucial importance in dose estimation and further risk analysis for humans exposed to this radioactive substance. They provide limiting values of detrimental effects and build the basis for applications in internal dosimetry, the prediction for radioactive zirconium retention in various organs as well as retrospective dosimetry. Multi-compartmental models are the tool of choice for simulating the processing of zirconium. Although easily interpretable, determining the exact compartment structure and interaction mechanisms is generally daunting. In the context of observing the dynamics of multiple compartments, Bayesian methods provide efficient tools for model inference and selection.

RESULTS

We are the first to apply a Markov chain Monte Carlo approach to compute Bayes factors for the evaluation of two competing models for zirconium processing in the human body after ingestion. Based on in vivo measurements of human plasma and urine levels we were able to show that a recently published model is superior to the standard model of the International Commission on Radiological Protection. The Bayes factors were estimated by means of the numerically stable thermodynamic integration in combination with a recently developed copula-based Metropolis-Hastings sampler.

CONCLUSIONS

In contrast to the standard model the novel model predicts lower accretion of zirconium in bones. This results in lower levels of noxious doses for exposed individuals. Moreover, the Bayesian approach allows for retrospective dose assessment, including credible intervals for the initially ingested zirconium, in a significantly more reliable fashion than previously possible. All methods presented here are readily applicable to many modeling tasks in systems biology.

Bayesian model selection validates a biokinetic model for zirconium processing in humans

BACKGROUND

In radiation protection, biokinetic models for zirconium processing are of crucial importance in dose estimation and further risk analysis for humans exposed to this radioactive substance. They provide limiting values of detrimental effects and build the basis for applications in internal dosimetry, the prediction for radioactive zirconium retention in various organs as well as retrospective dosimetry. Multi-compartmental models are the tool of choice for simulating the processing of zirconium. Although easily interpretable, determining the exact compartment structure and interaction mechanisms is generally daunting. In the context of observing the dynamics of multiple compartments, Bayesian methods provide efficient tools for model inference and selection.

RESULTS

We are the first to apply a Markov chain Monte Carlo approach to compute Bayes factors for the evaluation of two competing models for zirconium processing in the human body after ingestion. Based on in vivo measurements of human plasma and urine levels we were able to show that a recently published model is superior to the standard model of the International Commission on Radiological Protection. The Bayes factors were estimated by means of the numerically stable thermodynamic integration in combination with a recently developed copula-based Metropolis-Hastings sampler.

CONCLUSIONS

In contrast to the standard model the novel model predicts lower accretion of zirconium in bones. This results in lower levels of noxious doses for exposed individuals. Moreover, the Bayesian approach allows for retrospective dose assessment, including credible intervals for the initially ingested zirconium, in a significantly more reliable fashion than previously possible. All methods presented here are readily applicable to many modeling tasks in systems biology.

Reliability of a new biokinetic model of zirconium in internal dosimetry: part II, parameter sensitivity analysis

The reliability of biokinetic models is essential for the assessment of internal doses and a radiation risk analysis for the public and occupational workers exposed to radionuclides. In the present study, a method for assessing the reliability of biokinetic models by means of uncertainty and sensitivity analysis was developed. In the first part of the paper, the parameter uncertainty was analyzed for two biokinetic models of zirconium (Zr); one was reported by the International Commission on Radiological Protection (ICRP), and one was developed at the Helmholtz Zentrum München-German Research Center for Environmental Health (HMGU). In the second part of the paper, the parameter uncertainties and distributions of the Zr biokinetic models evaluated in Part I are used as the model inputs for identifying the most influential parameters in the models. Furthermore, the most influential model parameter on the integral of the radioactivity of Zr over 50 y in source organs after ingestion was identified. The results of the systemic HMGU Zr model showed that over the first 10 d, the parameters of transfer rates between blood and other soft tissues have the largest influence on the content of Zr in the blood and the daily urinary excretion; however, after day 1,000, the transfer rate from bone to blood becomes dominant. For the retention in bone, the transfer rate from blood to bone surfaces has the most influence out to the endpoint of the simulation; the transfer rate from blood to the upper larger intestine contributes a lot in the later days; i.e., after day 300. The alimentary tract absorption factor (fA) influences mostly the integral of radioactivity of Zr in most source organs after ingestion.

Human biokinetic data and a new compartmental model of zirconium--a tracer study with enriched stable isotopes

Biokinetic models describing the uptake, distribution and excretion of trace elements are an essential tool in nutrition, toxicology, or internal dosimetry of radionuclides. Zirconium, especially its radioisotope (95)Zr, is relevant to radiation protection due to its production in uranium fission and neutron activation of nuclear fuel cladding material. We present a comprehensive set of human data from a tracer study with stable isotopes of zirconium. The data are used to refine a biokinetic model of zirconium. Six female and seven male healthy adult volunteers participated in the study. It includes 16 complete double tracer investigations with oral ingestion and intravenous injection, and seven supplemental investigations. Tracer concentrations were measured in blood plasma and urine collected up to 100 d after tracer administration. The four data sets (two chemical tracer forms in plasma and urine) each encompass 105-240 measured concentration values above detection limits. Total fractional absorption of ingested zirconium was found to be 0.001 for zirconium in citrate-buffered drinking solution and 0.007 for zirconium oxalate solution. Biokinetic models were developed based on the linear first-order kinetic compartmental model approach used by the International Commission on Radiological Protection (ICRP). The main differences of the optimized systemic model of zirconium to the current ICRP model are (1) recycling into the transfer compartment made necessary by the observed tracer clearance from plasma, (2) different parameters related to fractional absorption for each form of the ingested tracer, and (3) a physiologically based excretion pathway to urine. The study considerably expands the knowledge on the biokinetics of zirconium, which was until now dominated by data from animal studies. The proposed systemic model improves the existing ICRP model, yet is based on the same principles and fits well into the ICRP radiation protection approach.