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Assessments of risk to a specific 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 coefficients used as a radiation protection device for the specified exposure pathway. An estimate of the uncertainty on the associated risk is important for informing judgments on reliability; a derived uncertainty factor, UF, is an estimate of the 95% probable geometric difference between the best risk estimate and the nominal risk and is a useful tool for making this assessment. This paper describes the application of parameter uncertainty analysis to quantify uncertainties resulting from internal exposures to radioiodine by members of the public, specifically 1, 10 and 20-year old females from the population of England and Wales. Best estimates of thyroid cancer incidence risk (lifetime attributable risk) are calculated for ingestion or inhalation of 129I and 131I, accounting for uncertainties in biokinetic model and cancer risk model parameter values. These estimates are compared with the equivalent ICRP derived nominal age-, sex- and population-averaged estimates of excess thyroid cancer incidence to obtain UFs. Derived UF values for ingestion or inhalation of 131I for 1 year, 10-year and 20-year olds are around 28, 12 and 6, respectively, when compared with ICRP Publication 103 nominal values, and 9, 7 and 14, respectively, when compared with ICRP Publication 60 values. Broadly similar results were obtained for 129I. The uncertainties on risk estimates are largely determined by uncertainties on risk model parameters rather than uncertainties on biokinetic model parameters. An examination of the sensitivity of the results to the risk models and populations used in the calculations show variations in the central estimates of risk of a factor of around 2–3. It is assumed that the direct proportionality of excess thyroid cancer risk and dose observed at low to moderate acute doses and incorporated in the risk models also applies to very small doses received at very low dose rates; the uncertainty in this assumption is considerable, but largely unquantifiable. The UF values illustrate the need for an informed approach to the use of ICRP dose and risk coefficients. [ABSTRACT FROM AUTHOR]

The joint Russian (Mayak Production Association) and British (Sellafield) plutonium worker epidemiological analysis, undertaken as part of the European Union Framework Programme 7 (FP7) SOLO project, aims to investigate potential associations between cancer incidence and occupational exposures to plutonium using estimates of organ/tissue doses. The dose reconstruction protocol derived for the study makes best use of the most recent biokinetic models derived by the International Commission on Radiological Protection (ICRP) including a recent update to the human respiratory tract model (HRTM). This protocol was used to derive the final point estimates of absorbed doses for the study. Although uncertainties on the dose estimates were not included in the final epidemiological analysis, a separate Bayesian analysis has been performed for each of the 11 808 Sellafield plutonium workers included in the study in order to assess: A. The reliability of the point estimates provided to the epidemiologists and B. The magnitude of the uncertainty on dose estimates. This analysis, which accounts for uncertainties in biokinetic model parameters, intakes and measurement uncertainties, is described in the present paper. The results show that there is excellent agreement between the point estimates of dose and posterior mean values of dose. However, it is also evident that there are significant uncertainties associated with these dose estimates: the geometric range of the 97.5%:2.5% posterior values are a factor of 100 for lung dose, 30 for doses to liver and red bone marrow, and 40 for intakes: these uncertainties are not reflected in estimates of risk when point doses are used to assess them. It is also shown that better estimates of certain key HRTM absorption parameters could significantly reduce the uncertainties on lung dose in future studies. [ABSTRACT FROM AUTHOR]

This paper summarises work undertaken on behalf of the Environment Agency for England to quantify uncertainties resulting from internal exposures to a number of radionuclides considered significant because of their anthropogenic origin, namely: 238U, 226Ra, 239Pu, 241Am, 137Cs, 90Sr, 131I, 129I and 3H. Uncertainties in the biokinetic models that are used to calculate the retention and excretion of radionuclides are derived in order to calculate distributions of effective dose per unit intake following their inhalation or ingestion by members of the UK public. The central values and ranges of the distributions are used to inform the derivation of uncertainty factors (UFs) for the different dose coefficients, which can be used to assess reliability. These represent uncertainties inherent in the structures of the biokinetic models and their parameter values. The inferred UF values are typically around 2–3 for ingestion and 2–6 for inhalation for all age groups, and are comparable to UF values inferred from published studies. It is instructive to consider these ranges alongside the likely levels of exposure that are expected from the radionuclides considered (the microsievert range) and the dose limit of planned exposures for members of the public (1000 μSv). [ABSTRACT FROM AUTHOR]

The slow dissolution rate of material deposited in the lung plays a key role in determining the eventual radiation dose received by the lung. It is therefore of great importance to establish a reliable value for this parameter, to incorporate into the latest Mayak Worker Dosimetry System (MWDS-2016). Disparate values have been obtained for the slow dissolution rate of plutonium nitrate. A volunteer study performed by Public Health England (PHE) and an analysis of United States Transuranium and Uranium Registries (USTUR) case 0269 have yielded slow dissolution rates in the region of 10-40 × 10-4 d-1. However, autopsies performed on 20 Mayak workers, exposed predominantly to nitrates, have resulted in estimates of slow dissolution rates of around 2.4 × 10-4 d-1. Three hypotheses have been proposed to explain this discrepancy: (1) a slower dissolution rate in the interstitium, (2) a third exponential component in the dissolution function and (3) a small component of oxide in the aerosol to which Mayak 'nitrate' workers were exposed. This paper describes tests of these competing hypotheses. Bayesian methods have been applied to the following datasets: PHE volunteer data; Beagle dog data; USTUR cases and Mayak worker data. It is concluded that a mixture of oxide and nitrate material, with the oxide forming ~14% of the intake, best describes the Mayak dissolution rate, without introducing values for other parameters which conflict with other studies., (© The Author(s) 2019. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

Epidemiological studies have shown that the main risk arising from exposure to plutonium aerosols is lung cancer, with other detrimental effects in the bone and liver. A realistic assessment of these risks, in turn, depends on the accuracy of the dosimetric models used to calculate doses in such studies. A state-of-the-art biokinetic model for plutonium, based on the current International Commission on Radiological Protection biokinetic model, has been developed for this purpose in an epidemiological study involving the plutonium exposure of Mayak workers in Ozersk, Russia. One important consequence of this model is that the lung dose is extremely sensitive to the fraction (fb) of plutonium, which becomes bound to lung tissue after it dissolves. It has been shown that if just 1% of the material becomes bound in the bronchial region, this will double the lung dose. Furthermore, fb is very difficult to quantify from experimental measurements. This paper summarizes the work carried out thus far to quantify fb. Bayesian techniques have been used to analyze data from different sources, including both humans and dogs, and the results suggest a small, but nonzero, fraction of < 1%. A Bayesian analysis of 20 Mayak workers exposed to plutonium nitrate suggests an fb between 0 and 0.3%. Based on this work, the International Commission on Radiological Protection is currently considering the adoption of a value of 0.2% for the default bound fraction for all actinides in its forthcoming recommendations on internal dosimetry. In an attempt to corroborate these findings, further experimental work has been carried out by the US Transuranium and Uranium Registries. This work has involved direct measurements of plutonium in the respiratory tract tissues of workers who have been exposed to soluble plutonium nitrate. Without binding, one would not expect to see any activity remaining in the lungs at long times after exposure since it would have been cleared by the natural process of mucociliary clearance. Further supportive study of workers exposed to plutonium oxide is planned. This paper ascertains the extent to which these results corroborate previous inferences concerning the bound fraction.

Two important aspects in which the MWDS-2013 output (absorbed dose to organs calculated in each calendar year) differs from previous data bases (MWDS-2008 and DOSES-2005) are that they have been designed to (a) deal explicitly with uncertainties in model parameters, and (b) differentiate parameters that are considered to be shared (unknown, but having the same value for all workers) and unshared (unknown, but having different values between workers). A multiple-realisation approach is used to preserve information on the effects of shared and unshared parameters both for internal and external doses. Previously, a single realisation (a set of organ doses: one for each worker in the cohort) was calculated using the best estimates of parameter values only. In MWDS-2013, a set of 1000 realisations is produced, to reflect the uncertainty in assumed model parameters: each realisation using a different set of parameter values. Within each realisation, shared parameter values are fixed throughout the cohort, while unshared parameters are allowed to vary between workers. One problem is that because the calculation of organ dose is Bayesian, the estimate for each organ dose is not just a single value, but is itself a distribution (hyper-dose). Technically, it is the probability density of dose given the sampled set of parameter values and given the data for that worker. Thus, in our case, the realisations consist not of single doses, but distributions of doses. The term hyper-realisation is used to differentiate this from the more conventional realisation. Although the multiple hyper-realisation in principle contains all of the necessary information on parameter uncertainty, including shared and unshared parameters, in order to make preliminary epidemiological analyses tractable, and also for consistency with the external doses, it was required to convert the hyper-realisations to realisations. The aim of this paper is to discuss the different approaches that were considered to do this, and to define the method that was eventually chosen. Single spot (point) estimates of dose (for each worker) were also calculated to support the epidemiological analysis. The different methods for obtaining these and the implications are also discussed., (© The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

For the first time, plutonium retention in human upper airways was investigated based on the dosimetric structure of the human respiratory tract proposed by the International Commission on Radiological Protection (ICRP). This paper describes analytical work methodology, case selection criteria, and summarizes findings on soluble (ICRP 68 Type M material) plutonium distribution in the lungs of a former nuclear worker occupationally exposed to plutonium nitrate [239Pu(NO3)4]. Thirty-eight years post-intake, plutonium was found to be uniformly distributed between bronchial (BB), bronchiolar (bb) and alveolar-interstitial (AI) dosimetric compartments as well as between the left and right lungs. 239+240Pu and 238Pu total body activity was estimated to be 2333 ± 23 and 42.1 ± 0.7 Bq, respectively. The results of this work provide key information on the extent of plutonium binding in the upper airways of the human respiratory tract., (© Published by Oxford University Press 2016.)

Different dose estimates have been produced for the Mayak PA workforce over recent years (DOSES-2000, DOSES-2005, MWDS-2008). The dosimetry system MWDS-2013 described here differs from previous analyses, in that it deals directly with uncertainty in the assumed model parameters. This paper details the way in which uncertainty is dealt with within MWDS-2013 to produce the final output represented by a multiple hyper-realisation of organ doses. More specifically, the paper describes: Application of the WeLMoS method to calculate Bayesian posterior probability distributions of organ doses.Extension of the WeLMoS method for dealing with multiple intake regimes.How shared and unshared parameters are dealt with using a multiple realisation method.A practical algorithm for the generation of multiple hyper-realisations.How to deal with uncertainty in the intake and the intake regime. The resulting multiple hyper-realisation contains all of the information required to take account of model parameter uncertainty and the effects of shared and unshared parameters in any epidemiological analysis, which uses this information, although it is acknowledged that in practice, certain data simplifications may be required to make such analyses tractable, and comparable to previous analyses. Such simplifications are outside the scope of this paper., (© Crown copyright 2016.)

Estimates of plutonium lung doses from urine bioassay are highly dependent on the rate of absorption from the lungs to blood assumed for the inhaled aerosol. Absorption occurs by dissolution of particles in lung fluid followed by uptake to blood. The latter may occur either rapidly or dissolved ions may first become temporarily bound within airway tissue. The presence of long-term binding can greatly increase lung doses, particularly if it occurs in the bronchial and bronchiolar regions. Analyses of autopsy data from Beagle dogs and USTUR Case 0269, obtained following exposure to plutonium nitrate, suggest that a small fraction of 0.2-1.1 and 0.4-0.7%, respectively, of plutonium becomes permanently bound within the lungs. The present work performs a further analysis using autopsy data of former plutonium workers of the Mayak Production Association to determine values of the bound fraction that are supported by these data. The results suggest a bound fraction value of 0-0.3%. The results also indicate that the Mayak worker population median values of the particle transport clearance parameters from the alveolar-interstitial region are largely consistent with expected values, but suggest the rate from the alveolar region to the interstitium may be lower than initially thought., (© The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

Radionuclides in ionic form can become chemically bound in the airways of the lungs following dissolution of inhaled particulates in lung fluid. The presence of long-term binding can greatly increase lung doses from inhaled plutonium, particularly if it occurs in the bronchial and bronchiolar regions. However, the only published evidence that plutonium binding occurs in humans comes from an analysis of the autopsy and bioassay data of United States Transuranium and Uranium Registries Case 0269, a plutonium worker who experienced a very high (58 kBq) acute inhalation of plutonium nitrate. This analysis suggested a bound fraction of around 8 %, inferred from an unexpectedly low ratio of estimated total thoracic lymph node activity:total lung activity, at the time of death. However, there are some limitations with this study, the most significant being that measurements of the regional distribution of plutonium activity in the lungs, which provide more direct evidence of binding, were not available when the analysis was performed. The present work describes the analysis of new data, which includes measurements of plutonium activity in the alveolar-interstitial (AI) region, bronchial (BB) and bronchiolar (bb) regions, and extra-thoracic (ET) regions, at the time of death. A Bayesian approach is used that accounts for uncertainties in model parameter values, including particle transport clearance, which were not considered in the original analysis. The results indicate that a long-term bound fraction between 0.4 and 0.7 % is required to explain this data, largely because plutonium activity is present in the extra-thoracic (ET2), bronchial and bronchiolar airways at the time of death., (© The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

In order to check developed software tools, it was necessary to compare estimates of statistical characteristics of annual absorbed plutonium internal doses obtained by PANDORA and IMBA software with the same original data. The results were compared from dose calculations of five cases with different initial data on plutonium inhalation intake, lifetime measurements of plutonium activity in daily urine and post-mortem measurements in lungs, lung lymph nodes, liver and skeleton. Estimates of geometric mean and geometric standard deviation of annual regionally weighted lung dose and bone surface dose were compared. Satisfactory agreements of the estimates of statistical characteristics of annual doses to two critical organs for the selected cases were shown. One hundred individual hyper-realizations (forward model evaluations) are sufficient to calculate MWDS-2013 if only measurements of plutonium activity in daily urine are used, and 2000 individual hyper-realizations if both urine and autopsy measurement results are used., (© The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

The Mayak Worker Dosimetry System (MWDS-2013) is a system for interpreting measurement data from Mayak workers from both internal and external sources. This paper is concerned with the calculation of annual organ doses for Mayak workers exposed to plutonium aerosols, where the measurement data consists mainly of activity of plutonium in urine samples. The system utilises the latest biokinetic and dosimetric models, and unlike its predecessors, takes explicit account of uncertainties in both the measurement data and model parameters. The aim of this paper is to describe the complete MWDS-2013 system (including model parameter values and their uncertainties) and the methodology used (including all the relevant equations) and the assumptions made. Where necessary, Supplementary papers which justify specific assumptions are cited., (© The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

The revised human respiratory tract model, published in Part 1 of the International Commission on Radiological Protection's (ICRP) report on Occupational Intakes of Radionuclides (OIR), includes a bound fraction, fb, to represent radionuclides that have become chemically bound in the lungs following dissolution of particulates in lung fluid. Bound radionuclides are not subject to particle transport clearance but can be absorbed to blood at a rate, sb. The occurrence of long-term binding of plutonium can greatly increase lung doses, particularly if it occurs in the bronchial and bronchiolar regions. However, there has been little evidence that currently supports the existence of a long-term bound state for plutonium. The present work describes the analysis of measurements of lung data obtained from a life span study of Beagle dogs that were exposed by inhalation to different concentrations of plutonium-239 (239Pu) nitrate aerosol at Pacific Northwest Laboratories, USA. The data have been analysed to assess whether a bound state was required to explain the data. A Bayesian approach was adopted for the analysis that accounts for uncertainties in model parameter values, including uncertainties in the rates of particle transport clearance. Furthermore, it performs the analysis using two different modelling hypotheses: a model based on the current ICRP human respiratory tract model and its treatment of alveolar particle transport clearance; and a model of particle transport clearance that is based on the updated model developed by ICRP to calculate dose coefficients for the OIR. The current model better represents clearance in dogs at early times (up to 1 year following intake) and the latter better represents retention at greater times (>5 years following intake). The results indicate that a long-term bound fraction of between 0.16 and 1.1%, with a mean value of between 0.24 and 0.8% (depending on the model) is required to explain the data., (© The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

The calculation of internal doses for the Mayak Worker Dosimetry System (MWDS-2013) involved extensive computational resources due to the complexity and sheer number of calculations required. The required output consisted of a set of 1000 hyper-realizations: each hyper-realization consists of a set (1 for each worker) of probability distributions of organ doses. This report describes the hardware components and computational approaches required to make the calculation tractable. Together with the software, this system is referred to here as the 'PANDORA system'. It is based on a commercial SQL server database in a series of six work stations. A complete run of the entire Mayak worker cohort entailed a huge amount of calculations in PANDORA and due to the relatively slow speed of writing the data into the SQL server, each run took about 47 days. Quality control was monitored by comparing doses calculated in PANDORA with those in a specially modified version of the commercial software 'IMBA Professional Plus'. Suggestions are also made for increasing calculation and storage efficiency for future dosimetry calculations using PANDORA., (© The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

The distribution of calculated internal doses has been determined for 8043 Mayak Production Associate (Mayak PA) workers. This is a subset of the entire cohort of 25 757 workers, for whom monitoring data are available. Statistical characteristics of point estimates of accumulated doses to 17 different tissues and organs and the uncertainty ranges were calculated. Under the MWDS-2013 dosimetry system, the mean accumulated lung dose was 185 ± 594 mGy (geometric mean = 28 mGy; geometric standard deviation = 9.32; median value = 31 mGy; maximum value = 8980 mGy). The ranges of relative standard uncertainty were from 40 to 2200% for accumulated lung dose, from 25-90% to 2600-3000% for accumulated dose to different regions of respiratory tract, from 13-22% to 2300-2500% for systemic organs and tissues. The Mayak PA workers accumulated internal plutonium lung dose is shown to be close to log normal. The accumulated internal plutonium dose to systemic organs was close to a log triangle. The dependency of uncertainty of accumulated absorbed lung and liver doses on the dose estimates itself is also shown. The accumulated absorbed doses to lung, alveolar-interstitial region, liver, bone surface cells and red bone marrow calculated both with MWDS-2013 and MWDS-2008 have been compared. In general, the accumulated lung doses increased by a factor of 1.8 in median value, while the accumulated doses to systemic organs decreased by factor of 1.3-1.4 in median value. For the cases with identical initial data, accumulated lung doses increased by a factor of 2.1 in median value, while accumulated doses to systemic organs decreased by 8-13% in median value. For the cases with both identical initial data and all of plutonium activity in urine measurements above the decision threshold, accumulated lung doses increased by a factor of 2.7 in median value, while accumulated doses to systemic organs increased by 6-12% in median value., (© The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

Lung doses resulting from inhalation of plutonium aerosols are highly dependent on the assumed rate of particle clearance, which occurs by two competing processes: (1) particle transport clearance to the alimentary tract and to the thoracic lymph nodes and (2) clearance to systemic tissues, which occurs by dissolution of particles in lung fluid followed by uptake to blood, which is a process collectively known as absorption. Unbiased and accurate estimates of the values of lung absorption parameters are required to obtain reliable estimates of lung dose, particularly those inferred from urine bioassay. Parameter values governing the rate of absorption are best estimated from data, such as autopsy measurements of plutonium in the lungs and systemic tissues, which directly relate to the exposed workers of interest. However, because the mathematical models that determine clearance from the lungs and systemic tissues are complex and consist of many parameters, estimates of model parameter values are subject to significant uncertainties. With this in mind, this paper uses a Bayesian approach to estimate one of the most important dissolution parameters: the slow rate of dissolution. This is estimated for both plutonium nitrate and plutonium oxide bearing aerosols in the lungs of former workers of the Mayak Production Association. A value of 2.6 × 10-4 d-1 is estimated for plutonium nitrates, and 4.7 × 10-5 d-1 for plutonium oxides., (© The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

Background: Carcinogenic risks of internal exposures to alpha-emitters (except radon) are poorly understood. Since exposure to alpha particles-particularly through inhalation-occurs in a range of settings, understanding consequent risks is a public health priority. We aimed to quantify dose-response relationships between lung dose from alpha-emitters and lung cancer in nuclear workers., Methods: We conducted a case-control study, nested within Belgian, French, and UK cohorts of uranium and plutonium workers. Cases were workers who died from lung cancer; one to three controls were matched to each. Lung doses from alpha-emitters were assessed using bioassay data. We estimated excess odds ratio (OR) of lung cancer per gray (Gy) of lung dose., Results: The study comprised 553 cases and 1,333 controls. Median positive total alpha lung dose was 2.42 mGy (mean: 8.13 mGy; maximum: 316 mGy); for plutonium the median was 1.27 mGy and for uranium 2.17 mGy. Excess OR/Gy (90% confidence interval)-adjusted for external radiation, socioeconomic status, and smoking-was 11 (2.6, 24) for total alpha dose, 50 (17, 106) for plutonium, and 5.3 (-1.9, 18) for uranium., Conclusions: We found strong evidence for associations between low doses from alpha-emitters and lung cancer risk. The excess OR/Gy was greater for plutonium than uranium, though confidence intervals overlap. Risk estimates were similar to those estimated previously in plutonium workers, and in uranium miners exposed to radon and its progeny. Expressed as risk/equivalent dose in sieverts (Sv), our estimates are somewhat larger than but consistent with those for atomic bomb survivors.See video abstract at, http://links.lww.com/EDE/B232.

Assessments of risk to a specific 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 coefficients used as a radiation protection device for the specified exposure pathway. An estimate of the uncertainty on the associated risk is important for informing judgments on reliability; a derived uncertainty factor, UF, is an estimate of the 95% probable geometric difference between the best risk estimate and the nominal risk and is a useful tool for making this assessment. This paper describes the application of parameter uncertainty analysis to quantify uncertainties resulting from internal exposures to radioiodine by members of the public, specifically 1, 10 and 20-year old females from the population of England and Wales. Best estimates of thyroid cancer incidence risk (lifetime attributable risk) are calculated for ingestion or inhalation of 129 I and 131 I, accounting for uncertainties in biokinetic model and cancer risk model parameter values. These estimates are compared with the equivalent ICRP derived nominal age-, sex- and population-averaged estimates of excess thyroid cancer incidence to obtain UFs. Derived UF values for ingestion or inhalation of 131 I for 1 year, 10-year and 20-year olds are around 28, 12 and 6, respectively, when compared with ICRP Publication 103 nominal values, and 9, 7 and 14, respectively, when compared with ICRP Publication 60 values. Broadly similar results were obtained for 129 I. The uncertainties on risk estimates are largely determined by uncertainties on risk model parameters rather than uncertainties on biokinetic model parameters. An examination of the sensitivity of the results to the risk models and populations used in the calculations show variations in the central estimates of risk of a factor of around 2-3. It is assumed that the direct proportionality of excess thyroid cancer risk and dose observed at low to moderate acute doses and incorporated in the risk models also applies to very small doses received at very low dose rates; the uncertainty in this assumption is considerable, but largely unquantifiable. The UF values illustrate the need for an informed approach to the use of ICRP dose and risk coefficients.

The Alpha-Risk study required the reconstruction of doses to lung and red bone marrow for lung cancer and leukaemia cases and their matched controls from cohorts of nuclear workers in the UK, France and Belgium. The dosimetrists and epidemiologists agreed requirements regarding the bioassay data, biokinetic and dosimetric models and dose assessment software to be used and doses to be reported. The best values to use for uncertainties on the monitoring data, setting of exposure regimes and characteristics of the exposure material, including lung solubility, were the responsibility of the dosimetrist responsible for each cohort. Among 1721 subjects, the median absorbed dose to the lung from alpha radiations was 2.1 mGy, with a maximum dose of 316 mGy. The lung doses calculated reflect the higher levels of exposure seen among workers in the early years of the nuclear industry compared to today., (© Crown copyright 2016.)

Mr Litvinenko died on 23 November 2006 after having been poisoned with polonium-210 on 1 November. Measurements of the polonium-210 content of post-mortem tissue samples and samples of urine and blood showed the presence of large amounts of 210 Po. Autoradiography of hair samples showed two regions of 210 Po activity, providing evidence of an earlier poisoning attempt during October 2006, resulting in absorption to blood of about one-hundredth of that estimated for 1 November. Intake by ingestion on 1 November was estimated to be around 4 GBq, assuming 10% absorption to blood, and the resulting organ doses reached estimated values that were generally in a range from about 20 Gy to over 100 Gy. Comparison with estimates of protracted alpha particle doses required to cause irreversible organ damage supported the conclusion that death was the inevitable consequence of multiple organ failure, with destruction of the haemopoietic bone marrow, as well as damage to kidneys and liver, being important contributors. If the earlier poisoning during October 2006 had not been followed by a second major intake on 1 November, it is possible that the earlier intake of around 40 MBq, with absorption of 4 MBq to blood, might have caused irreversible kidney damage over a prolonged period of months or years, with doses of approaching 3 Gy.

The potential health impacts of chronic exposures to uranium, as they occur in occupational settings, are not well characterized. Most epidemiological studies have been limited by small sample sizes, and a lack of harmonization of methods used to quantify radiation doses resulting from uranium exposure. Experimental studies have shown that uranium has biological effects, but their implications for human health are not clear. New studies that would combine the strengths of large, well-designed epidemiological datasets with those of state-of-the-art biological methods would help improve the characterization of the biological and health effects of occupational uranium exposure. The aim of the European Commission concerted action CURE (Concerted Uranium Research in Europe) was to develop protocols for such a future collaborative research project, in which dosimetry, epidemiology and biology would be integrated to better characterize the effects of occupational uranium exposure. These protocols were developed from existing European cohorts of workers exposed to uranium together with expertise in epidemiology, biology and dosimetry of CURE partner institutions. The preparatory work of CURE should allow a large scale collaborative project to be launched, in order to better characterize the effects of uranium exposure and more generally of alpha particles and low doses of ionizing radiation.

The joint Russian (Mayak Production Association) and British (Sellafield) plutonium worker epidemiological analysis, undertaken as part of the European Union Framework Programme 7 (FP7) SOLO project, aims to investigate potential associations between cancer incidence and occupational exposures to plutonium using estimates of organ/tissue doses. The dose reconstruction protocol derived for the study makes best use of the most recent biokinetic models derived by the International Commission on Radiological Protection (ICRP) including a recent update to the human respiratory tract model (HRTM). This protocol was used to derive the final point estimates of absorbed doses for the study. Although uncertainties on the dose estimates were not included in the final epidemiological analysis, a separate Bayesian analysis has been performed for each of the 11 808 Sellafield plutonium workers included in the study in order to assess: A. The reliability of the point estimates provided to the epidemiologists and B. The magnitude of the uncertainty on dose estimates. This analysis, which accounts for uncertainties in biokinetic model parameters, intakes and measurement uncertainties, is described in the present paper. The results show that there is excellent agreement between the point estimates of dose and posterior mean values of dose. However, it is also evident that there are significant uncertainties associated with these dose estimates: the geometric range of the 97.5%:2.5% posterior values are a factor of 100 for lung dose, 30 for doses to liver and red bone marrow, and 40 for intakes: these uncertainties are not reflected in estimates of risk when point doses are used to assess them. It is also shown that better estimates of certain key HRTM absorption parameters could significantly reduce the uncertainties on lung dose in future studies.

The United States Transuranium and Uranium Registries' (USTUR) whole-body donor (Case 1031) was exposed to an acute inhalation of uranium hexafluoride (UF6) produced from an explosion at a uranium processing plant 65 years prior to his death. The USTUR measurements of tissue samples collected at the autopsy indicated long-term retention of inhaled slightly enriched uranium material (0.85% (235)U) in the deep lungs and thoracic lymph nodes. In the present study, the authors combined the tissue measurement results with historical bioassay data, and analysed them with International Commission on Radiological Protection (ICRP) respiratory tract models and the ICRP Publication 69 systemic model for uranium using maximum likelihood and Bayesian statistical methods. The purpose of the analysis was to estimate intakes and model parameter values that best describe the data, and evaluate their effect on dose assessment. The maximum likelihood analysis, which used the ICRP Publication 66 human respiratory tract model, resulted in a point estimate of 79 mg of uranium for the occupational intake composed of 86% soluble, type F material and 14% insoluble, type S material. For the Bayesian approach, the authors applied the Markov Chain Monte Carlo method, but this time used the revised human respiratory tract model, which is currently being used by ICRP to calculate new dose coefficients for workers. The Bayesian analysis estimated that the mean uranium intake was 160 mg, and calculated the case-specific lung dissolution parameters with their associated uncertainties. The parameters were consistent with the inhaled uranium material being predominantly soluble with a small but significant insoluble component. The 95% posterior range of the rapid dissolution fraction (the fraction of deposited material that is absorbed to blood rapidly) was 0.12 to 0.91 with a median of 0.37. The remaining fraction was absorbed slowly, with a 95% range of 0.000 22 d(-1) to 0.000 36 d(-1) and a median of 0.000 31 d(-1). The effective dose per unit intake calculated using the dissolution parameters derived from the maximum likelihood and the Bayesian analyses was higher than the current ICRP dose coefficient for type F uranium by a factor of 2 or 7, respectively; the higher value of the latter was due to use of the revised respiratory tract model. The dissolution parameter values obtained here may be more appropriate to use for radiation protection purposes when individuals are exposed to a UF6 mixture that contains an insoluble uranium component.

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., (© The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

In Bayesian inference, the initial knowledge regarding the value of a parameter, before additional data are considered, is represented as a prior probability distribution. This paper describes the derivation of a prior distribution of intake that was used for the Bayesian analysis of plutonium and uranium worker doses in a recent epidemiology study. The chosen distribution is log-normal with a geometric standard deviation of 6 and a median value that is derived for each worker based on the duration of the work history and the number of reported acute intakes. The median value is a function of the work history and a constant related to activity in air concentration, M, which is derived separately for uranium and plutonium. The value of M is based primarily on measurements of plutonium and uranium in air derived from historical personal air sampler (PAS) data. However, there is significant uncertainty on the value of M that results from paucity of PAS data and from extrapolating these measurements to actual intakes. This paper compares posterior and prior distributions of intake and investigates the sensitivity of the Bayesian analyses to the assumed value of M. It is found that varying M by a factor of 10 results in a much smaller factor of 2 variation in mean intake and lung dose for both plutonium and uranium. It is concluded that if a log-normal distribution is considered to adequately represent worker intakes, then the Bayesian posterior distribution of dose is relatively insensitive to the value assumed of M., (© The Author 2013. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

This paper summarises work undertaken on behalf of the Environment Agency for England to quantify uncertainties resulting from internal exposures to a number of radionuclides considered significant because of their anthropogenic origin, namely: (238)U, (226)Ra, (239)Pu, (241)Am, (137)Cs, (90)Sr, (131)I, (129)I and (3)H. Uncertainties in the biokinetic models that are used to calculate the retention and excretion of radionuclides are derived in order to calculate distributions of effective dose per unit intake following their inhalation or ingestion by members of the UK public. The central values and ranges of the distributions are used to inform the derivation of uncertainty factors (UFs) for the different dose coefficients, which can be used to assess reliability. These represent uncertainties inherent in the structures of the biokinetic models and their parameter values. The inferred UF values are typically around 2-3 for ingestion and 2-6 for inhalation for all age groups, and are comparable to UF values inferred from published studies. It is instructive to consider these ranges alongside the likely levels of exposure that are expected from the radionuclides considered (the microsievert range) and the dose limit of planned exposures for members of the public (1000 μSv).

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.

The best estimate 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 (E⁵⁰) for the specified exposure pathway. An estimate of the uncertainty on the risk is important for reliability decisions. This paper describes the application of parameter uncertainty analysis to quantify uncertainties resulting from internal exposures to uranium (as (²³⁸U) by members of the 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 central values and ranges of 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 dose coefficients. Here, a UF is a conditional probability statement that the value of the best estimate of risk per unit intake has a 95 % probability of being within a factor, UF, of the nominal risk associated with the appropriate ICRP dose coefficient, E⁵⁰, with respect to uncertainties in the biokinetic model parameter values. Ingestion: it is assumed that exposure occurs through the ingestion of uranium present in food and water. The results 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 uranium occurs via inhalation of a mixture of chemical forms. The results suggest a UF of around 2 for inhalation of uranium by members of the public, with median values close to the ICRP values.

In a recent epidemiological study, Bayesian estimates of lung doses were calculated in order to determine a possible association between lung dose and lung cancer incidence resulting from occupational exposures to uranium. These calculations, which produce probability distributions of doses, used the human respiratory tract model (HRTM) published by the International Commission on Radiological Protection (ICRP) with a revised particle transport clearance model. In addition to the Bayesian analyses, point estimates (PEs) of doses were also provided for that study using the existing HRTM as it is described in ICRP Publication 66. The PEs are to be used in a preliminary analysis of risk. To explain the differences between the PEs and Bayesian analysis, in this paper the methodology was applied to former UK nuclear workers who constituted a subset of the study cohort. The resulting probability distributions of lung doses calculated using the Bayesian methodology were compared with the PEs obtained for each worker. Mean posterior lung doses were on average 8-fold higher than PEs and the uncertainties on doses varied over a wide range, being greater than two orders of magnitude for some lung tissues. It is shown that it is the prior distributions of the parameters describing absorption from the lungs to blood that are responsible for the large difference between posterior mean doses and PEs. Furthermore, it is the large prior uncertainties on these parameters that are mainly responsible for the large uncertainties on lung doses. It is concluded that accurate determination of the chemical form of inhaled uranium, as well as the absorption parameter values for these materials, is important for obtaining unbiased estimates of lung doses from occupational exposures to uranium for epidemiological studies. Finally, it should be noted that the inferences regarding the PEs described here apply only to the assessments of cases provided for the epidemiological study, where central estimates of dose were sought. Approved dosimetry service assessments of exposures are unlikely to yield significant underestimates, as pessimistic assumptions of lung solubility would almost always be used.

Consideration of uncertainties on doses can provide numerical estimates of the reliability of the protection quantities (dose coefficients) used in radiation protection to assess exposures to radionuclides that enter the body by ingestion or inhalation ('internal emitters'). Uncertainty analysis methods have been widely applied to quantify uncertainties on doses, including effective dose. However, it is not always clear how the distributions of effective dose per unit intake that result from such analyses should be interpreted with respect to the intended use of effective dose in radiation protection and the use of dose coefficients as reference values. The ICRP system of radiological protection is reviewed briefly and it is argued that the reliability of an effective dose coefficient as a protection device can best be determined by comparing the nominal detriment adjusted cancer risk associated with the dose coefficient, with a best estimate of risk for the exposure pathway and exposed population group, considering uncertainties in biokinetic, dosimetric and risk parameters. Because it is the uncertainty on the population mean of this quantity that is required, the effect of parameter variability should be distinguished from the effect of parameter uncertainty when performing uncertainty analyses. A methodology for performing the uncertainty analysis is discussed and studies that quantify uncertainty on doses and risk from intakes of radionuclides are reviewed.

Estimating uncertainties on doses from bioassay data is of interest in epidemiology studies that estimate cancer risk from occupational exposures to radionuclides. Bayesian methods provide a logical framework to calculate these uncertainties. However, occupational exposures often consist of many intakes, and this can make the Bayesian calculation computationally intractable. This paper describes a novel strategy for increasing the computational speed of the calculation by simplifying the intake pattern to a single composite intake, termed as complex intake regime (CIR). In order to assess whether this approximation is accurate and fast enough for practical purposes, the method is implemented by the Weighted Likelihood Monte Carlo Sampling (WeLMoS) method and evaluated by comparing its performance with a Markov Chain Monte Carlo (MCMC) method. The MCMC method gives the full solution (all intakes are independent), but is very computationally intensive to apply routinely. Posterior distributions of model parameter values, intakes and doses are calculated for a representative sample of plutonium workers from the United Kingdom Atomic Energy cohort using the WeLMoS method with the CIR and the MCMC method. The distributions are in good agreement: posterior means and Q(0.025) and Q(0.975) quantiles are typically within 20 %. Furthermore, the WeLMoS method using the CIR converges quickly: a typical case history takes around 10-20 min on a fast workstation, whereas the MCMC method took around 12-72 hr. The advantages and disadvantages of the method are discussed.

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.

In a recent epidemiological study, Bayesian uncertainties on lung doses have been calculated to determine lung cancer risk from occupational exposures to plutonium. These calculations used a revised version of the Human Respiratory Tract Model (HRTM) published by the ICRP. In addition to the Bayesian analyses, which give probability distributions of doses, point estimates of doses (single estimates without uncertainty) were also provided for that study using the existing HRTM as it is described in ICRP Publication 66; these are to be used in a preliminary analysis of risk. To infer the differences between the point estimates and Bayesian uncertainty analyses, this paper applies the methodology to former workers of the United Kingdom Atomic Energy Authority (UKAEA), who constituted a subset of the study cohort. The resulting probability distributions of lung doses are compared with the point estimates obtained for each worker. It is shown that mean posterior lung doses are around two- to fourfold higher than point estimates and that uncertainties on doses vary over a wide range, greater than two orders of magnitude for some lung tissues. In addition, we demonstrate that uncertainties on the parameter values, rather than the model structure, are largely responsible for these effects. Of these it appears to be the parameters describing absorption from the lungs to blood that have the greatest impact on estimates of lung doses from urine bioassay. Therefore, accurate determination of the chemical form of inhaled plutonium and the absorption parameter values for these materials is important for obtaining reliable estimates of lung doses and hence risk from occupational exposures to plutonium.

EURADOS working group on 'Internal Dosimetry (WG7)' represents a frame to develop activities in the field of internal exposures as coordinated actions on quality assurance (QA), research and training. The main tasks to carry out are the update of the IDEAS Guidelines as a reference document for the internal dosimetry community, the implementation and QA of new ICRP biokinetic models, the assessment of uncertainties related to internal dosimetry models and their application, the development of physiology-based models for biokinetics of radionuclides, stable isotope studies, biokinetic modelling of diethylene triamine pentaacetic acid decorporation therapy and Monte-Carlo applications to in vivo assessment of intakes. The working group is entirely supported by EURADOS; links are established with institutions such as IAEA, US Transuranium and Uranium Registries (USA) and CEA (France) for joint collaboration actions.

Epidemiological studies of the relationship between risk and internal exposure to plutonium are clearly reliant on the dose estimates used. The International Commission on Radiological Protection (ICRP) is currently reviewing the latest scientific information available on biokinetic models and dosimetry, and it is likely that a number of changes to the existing models will be recommended. The effect of certain changes, particularly to the ICRP model of the respiratory tract, has been investigated for inhaled forms of (239)Pu and uncertainties have also been assessed. Notable effects of possible changes to respiratory tract model assumptions are (1) a reduction in the absorbed dose to target cells in the airways, if changes under consideration are made to the slow clearing fraction and (2) a doubling of absorbed dose to the alveolar region for insoluble forms, if evidence of longer retention times is taken into account. An important factor influencing doses for moderately soluble forms of (239)Pu is the extent of binding of dissolved plutonium to lung tissues and assumptions regarding the extent of binding in the airways. Uncertainty analyses have been performed with prior distributions chosen for application in epidemiological studies. The resulting distributions for dose per unit intake were lognormal with geometric standard deviations of 2.3 and 2.6 for nitrates and oxides, respectively. The wide ranges were due largely to consideration of results for a range of experimental data for the solubility of different forms of nitrate and oxides. The medians of these distributions were a factor of three times higher than calculated using current default ICRP parameter values. For nitrates, this was due to the assumption of a bound fraction, and for oxides due mainly to the assumption of slower alveolar clearance. This study highlights areas where more research is needed to reduce biokinetic uncertainties, including more accurate determination of particle transport rates and long-term dissolution for plutonium compounds, a re-evaluation of long-term binding of dissolved plutonium, and further consideration of modeling for plutonium absorbed to blood from the lungs.

Measurements of uranium excreted in urine have been widely used to monitor possible exposures to depleted uranium (DU). This paper describes a comprehensive probabilistic uncertainty analysis of doses determined retrospectively from measurements of DU in urine. Parametric uncertainties in the International Commission on Radiological Protection (ICRP) Human Respiratory Tract Model (HRTM) and ICRP systemic model for uranium were considered in the analysis, together with uncertainties in an alternative model for particle removal from the lungs. Probability distributions were assigned to HRTM parameters based on uncertainties documented in ICRP Publication 66 and elsewhere, including the Capstone study of aerosols produced after DU penetrator impacts. Uncertainties in the uranium systemic model were restricted to transfer rates having the greatest effect on urinary excretion, and hence retrospective dose assessments, over the measurement times considered (10-10(4) d). The overall uncertainty on dose (the ratio of the upper and lower quantiles, q0.975/q0.025) was estimated to be about a factor of 50 at 10 days after intake and about a factor of 10 at 10(3)-10(4) d. The dose to the lung dominated the committed effective dose, with the lung absorption parameters, particularly the slow dissolution rate, ss, dominating the overall uncertainty. The median dose determined from a measurement of 1 ng DU, collected in urine in a 24-h period, varied from 0.1 microSv at 10 d to about 1 mSv at 10(4) d. Despite the large uncertainties, the upper q0.975 quantile for the assessed dose was below 1 mSv up to 5,000 d.

The work of Task Group 5.1 (uncertainty studies and revision of IDEAS guidelines) and Task Group 5.5 (update of IDEAS databases) of the CONRAD project is described. Scattering factor (SF) values (i.e. measurement uncertainties) have been calculated for different radionuclides and types of monitoring data using real data contained in the IDEAS Internal Contamination Database. Based upon this work and other published values, default SF values are suggested. Uncertainty studies have been carried out using both a Bayesian approach as well as a frequentist (classical) approach. The IDEAS guidelines have been revised in areas relating to the evaluation of an effective AMAD, guidance is given on evaluating wound cases with the NCRP wound model and suggestions made on the number and type of measurements required for dose assessment.

The CONRAD Project is a Coordinated Network for Radiation Dosimetry funded by the European Commission 6th Framework Programme. The activities developed within CONRAD Work Package 5 ('Coordination of Research on Internal Dosimetry') have contributed to improve the harmonisation and reliability in the assessment of internal doses. The tasks carried out included a study of uncertainties and the refinement of the IDEAS Guidelines associated with the evaluation of doses after intakes of radionuclides. The implementation and quality assurance of new biokinetic models for dose assessment and the first attempt to develop a generic dosimetric model for DTPA therapy are important WP5 achievements. Applications of voxel phantoms and Monte Carlo simulations for the assessment of intakes from in vivo measurements were also considered. A Nuclear Emergency Monitoring Network (EUREMON) has been established for the interpretation of monitoring data after accidental or deliberate releases of radionuclides. Finally, WP5 group has worked on the update of the existing IDEAS bibliographic, internal contamination and case evaluation databases. A summary of CONRAD WP5 objectives and results is presented here.

This paper presents a novel Monte Carlo method (WeLMoS, Weighted Likelihood Monte-Carlo sampling method) that has been developed to perform Bayesian analyses of monitoring data. The WeLMoS method randomly samples parameters from continuous prior probability distributions and then weights each vector by its likelihood (i.e. its goodness of fit to the measurement data). Furthermore, in order to quality assure the method, and assess its strengths and weaknesses, a second method (MCMC, Markov chain Monte Carlo) has also been developed. The MCMC method uses the Metropolis algorithm to sample directly from the posterior distribution of parameters. The methods are evaluated and compared using an artificially generated case involving an exposure to a plutonium nitrate aerosol. In addition to calculating the uncertainty on internal dose, the methods can also calculate the probability distribution of model parameter values given the observed data. In other words, the techniques provide a powerful tool to obtain the estimates of parameter values that best fit the data and the associated uncertainty on these estimates. Current applications of the methodology, including the determination of lung solubility parameters, from volunteer and cohort data, are also discussed.