Comparison of dose estimation from occupational exposure to 239Pu using different modelling approaches

Several approaches are available for bioassay interpretation when assigning Pu doses to Mayak workers. First, a conventional approach is to apply ICRP models per se. An alternative method involves individualised fitting of bioassay data using Bayesian statistical methods. A third approach is to develop an independent dosimetry system for Mayak workers by adapting ICRP models using a dataset of available bioassay measurements for this population. Thus, a dataset of 42 former Mayak workers, who died of non-radiation effects, with both urine bioassay and post-mortem tissue data was used to test these three approaches. All three approaches proved to be adequate for bioassay and tissue interpretation, and thus for Pu dose reconstruction purposes. However, large discrepancies are observed in the resulting quantitative dose estimates. These discrepancies can, in large part, be explained by differences in the interpretation of Pu behaviour in the lungs in the context of ICRP lung model. Thus, a careful validation of Pu lung dosimetry model is needed in Mayak worker dosimetry systems.     

Variability and uncertainty of biokinetic model parameters: the discrete empirical Bayes approximation

In the Bayesian approach to internal dosimetry, uncertainty and variability of biokinetic model parameters need to be taken into account. The discrete empirical Bayes approximation replaces integration over biokinetic model parameters by discrete summation in the evaluation of Bayesian posterior averages using Bayes theorem. The discrete choices of parameters are taken as best-fit point determinations of model parameters for a study subpopulation with extensive data. A simple heuristic model is constructed to numerically and theoretically study this approximation. The heuristic example is the measurement of heights of a group of people, say from a photograph where measurement uncertainty is significant. A comparison is made of posterior mean and standard deviation of height after a measurement, (i) using the exact prior describing the distribution of true height in the population and (ii) using the approximate discrete empirical Bayes prior obtained from measurements of some study subpopulation.     

Bayesian prior probability distributions for internal dosimetry

The problem of choosing a prior distribution for the Bayesian interpretation of measurements (specifically internal dosimetry measurements) is considered using a theoretical analysis and by examining historical tritium and plutonium urine bioassay data from Los Alamos. Two models for the prior probability distribution are proposed: (1) the log-normal distribution, when there is some additional information to determine the scale of the true result, and (2) the 'alpha' distribution (a simplified variant of the gamma distribution) when there is not. These models have been incorporated into version 3 of the Bayesian internal dosimetry code in use at Los Alamos (downloadable from our web site). Plutonium internal dosimetry at Los Alamos is now being done using prior probability distribution parameters determined self-consistently from population averages of Los Alamos data.     

Internal dosimetry verification and validation database

Simulated-data internal dosimetry cases for use in intercomparison exercises or as a software verification and validation tool have been published on the internet (www.lanl.gov/bayesian/software Bayesian software package II). A user may validate their internal dosimetry code or method using this simulated bioassay data. Or, the user may choose to try out the Los Alamos National Laboratory codes ID and UF, which are also supplied. A Poisson-lognormal model of data uncertainty is assumed. A collection of different possible models for each nuclide (e.g. solubility types and particle sizes) are used. For example, for 238Pu, 14 different biokinetic models or types (8 inhalation, 4 wound and 2 ingestion) are assumed. Simulated data are generated for all the assumed biokinetic models, both for incidents, where the time of intake is known, and for non-incidents, where it is not. For the dose calculations, the route of intake, but not the biokinetic model, is considered to be known. The object is to correctly calculate the known true dose from simulated data covering a period of time. A 'correct' result has been defined in two ways: (1) that the credible limits of the calculated dose include the correct dose and (2) that the calculated dose is within a factor of 2 of the correct dose.     

Uncertainties in doses from intakes of radionuclides assessed from monitoring measurements

The evaluation of uncertainties in doses from intakes of radionuclides is one of the most difficult problems in internal dosimetry. In this paper, the process of assessing internal doses from monitoring measurements is reviewed and the major sources of uncertainty are discussed. Methods developed independently at HPA and at IRSN for the determination of uncertainties in internal doses assessed from monitoring measurements are described. Both use a Monte Carlo simulation approach. Results are described for three illustrative examples. An alternative method developed at the Los Alamos National Laboratory that uses Bayesian statistical methods is also described briefly.     

Internal dosimetry of uranium isotopes using Bayesian inference methods

A group of personnel at Los Alamos National Laboratory is routinely monitored for the presence of uranium isotopes by urine bioassay. Samples are analysed by alpha spectroscopy, and the results are examined for evidence of an intake of uranium. Because the measurement uncertainties are often comparable to the quantities of material we wish to detect, statistical considerations are crucial for the proper interpretation of the data. The problem is further complicated by the significant, but highly non-uniform, presence of uranium in local drinking water and, in some cases, food supply. Software originally developed for internal dosimetry of plutonium has been adapted to the problem of uranium dosimetry. The software uses an unfolding algorithm to calculate an approximate Bayesian solution to the problem of characterising any intakes which may have occurred, given the history of urine bioassay results for each individual in the monitored population. The program uses biokinetic models from ICRP Publications 68 and later, and a prior probability distribution derived empirically from the body of uranium bioassay data collected at Los Alamos over the operating history of the laboratory. For each individual, the software creates a posterior probability distribution of intake quantity and solubility type as a function of time. From this distribution, estimates are made of the cumulative committed dose (CEDE) to each individual. Results of the method are compared with those obtained using an earlier classical (non-Bayesian) algorithm for uranium dosimetry. We also discuss the problem of distinguishing occupational intakes from intake of environmental uranium, within a Bayesian framework.     

A study of early Los Alamos internal exposures to plutonium

Internal dose caused by exposure to (239)Pu/(240)Pu is calculated for a group of 210 former Los Alamos workers who participated in the urine bioassay programme during the years 1944-45. An iterative Bayesian procedure is employed, where the distribution of intake amounts resulting from an initial calculation is used to define a prior probability distribution of inhalation intakes for an iterated second calculation. The urine bioassay data from this time period were not of high quality, and the more accurate intake prior tempers the effect of spurious high samples, which were probably caused by sample contamination.     

A fully Bayesian approach for combining multilevel failure information in fault tree quantification and optimal follow-on resource allocation

This paper presents a fully Bayesian approach that simultaneously combines non-overlapping (in time) basic event and higher-level event failure data in fault tree quantification. Such higher-level data often correspond to train, subsystem or system failure events. The fully Bayesian approach also automatically propagates the highest-level data to lower levels in the fault tree. A simple example illustrates our approach. The optimal allocation of resources for collecting additional data from a choice of different level events is also presented. The optimization is achieved using a genetic algorithm.     

Bayesian internal dosimetry calculations using Markov Chain Monte Carlo

A new numerical method for solving the inverse problem of internal dosimetry is described. The new method uses Markov Chain Monte Carlo and the Metropolis algorithm. Multiple intake amounts, biokinetic types, and times of intake are determined from bioassay data by integrating over the Bayesian posterior distribution. The method appears definitive, but its application requires a large amount of computing time.     

Response Surface Optimization in the Presence of Internal Noise With Application to Optimal Alignment of Carbon Nanotubes

Internal noise, which means fluctuation of input factors around their set values, is common in many experiments in the physical and engineering sciences. Existing methods for response surface optimization in the presence of internal noise typically adopt a two-step approach: (a) fitting a response model as a function of the set value and (b) using Monte Carlo methods to account for internal noise while optimizing the response. In this article, motivated by a problem in optimizing alignment of carbon nanotubes (CNT), we propose a Bayesian approach for response surface optimization in the presence of internal noise. A unit-free and interpretable measure to quantify the strength of internal noise is proposed. Suitable objective functions or performance measures consistent with the overall goal of optimizing the response function are identified, methods for estimating them from available experimental data are suggested, and simulations are conducted to compare them with respect to their ability to account for internal noise in the optimization problem. The loss accrued by ignoring the internal noise in the optimization problem is quantified and studied via simulation. The proposed method is demonstrated through its application in the CNT alignment problem.     

A fully Bayesian approach for combining multi-level information in multi-state fault tree quantification

This paper presents a fully Bayesian approach that simultaneously combines non-overlapping (in time) basic event and higher-level event failure data in fault tree quantification with multi-state events. Such higher-level data often correspond to train, subsystem or system failure events. The fully Bayesian approach also automatically propagates the highest-level data to lower levels in the fault tree. A simple example illustrates our approach.     

Obtaining an unbiased estimate of intake in routine monitoring when the time of intake is unknown

A common problem in internal dosimetry occurs in routine monitoring, when it is required to estimate an intake from a measurement made at the end of a monitoring interval, and the time of intake is unknown. ICRP suggests that, in these cases, it should be assumed that the intake occurred in the middle of the monitoring period. However, it has been shown that this will, in the long term, lead to biased estimates of a worker's intake and dose. In order to overcome this biasing, the United States Department of Energy (USDOE) recommends a different method based on calculating the intakes for all possible intake-times in the interval, and then taking an arithmetic average. In this paper, it is shown that both the ICRP and USDOE methods are biased. An alternative method is suggested, which assumes a constant chronic intake throughout the monitoring interval. Monte Carlo simulations are used to estimate the magnitude of bias for two realistic monitoring programmes using all three methods. It is shown that the proposed method is unbiased and also yields estimates of intake that are generally closer to the actual intake, than the other two. The Monte Carlo conclusions are backed up by a theoretical analysis of bias. Finally, the source of bias in the apparently intuitive approach of the USDOE method is revealed by viewing the problem from a Bayesian perspective.     

Technical basis for using nose swab bioassay data for early internal dose assessment

One of the challenges to the dose assessment team in response to an inhalation incident in the workplace is to provide the occupational physicians, operational radiation protection personnel and line managers with early estimates of radionuclide intakes so that appropriate consequence management and mitigation can be done. For radionuclides such as Pu, where in vivo counting is not adequately sensitive, other techniques such as the measurement of removable radionuclide from the nasal airway passages can be used. At Los Alamos National Laboratory (LANL), nose swabs of the ET1 region have been used routinely as a first response to airborne Pu releases in the workplace, as well as for other radionuclides. This paper presents the results of analysing over 15 years of nose swab data, comparing these with dose assessments performed using the Bayesian methods developed at LANL. The results provide empirical support for using nose swab data for early dose assessments. For Pu, a rule of thumb is a dose factor of 0.8 mSv Bq(-1), assuming a linear relationship between nasal swab activity and committed effective dose equivalent. However, this value is specific to the methods and models used at LANL, and should not be applied directly without considering possible differences in measurement and calculation methods.     

Developing instruments for measurement of plutonium activity in the environmental samples in the case of radiation accident

According to the Russian norms, the permissible specific activity of 239Pu in the air and water are the lowest. Still the problem of low (compared to permissible) Pu activity measurement for environmental samples arises, for instance, in the case of radiation accident during transportation or storage of excess weapons-grade plutonium transferred to the civil sphere of utilisation. The base method of Pu activity measurement is alpha spectrometry by using silicon detector. A new model of alpha spectrometer, based on silicon surface-barrier detector with background level less than 1-3 pulses per day has been developed. A simple unfolding method for the determination of Pu activity of samples with various thickness based on alpha spectrum measurement has been also developed. L-X photon detection is also used for reducing the measurement threshold of Pu activity determination. A method based on detecting L-X photons of Pu, excited by X rays and beta particles, is applied for further reducing the threshold.     

Analysis of a computational problem involving complex voxel geometries

This communication briefly summarises the results obtained from the 'International comparison on MC modeling for in vivo measurement of Americium in a knee phantom' organised within the EU Coordination Action CONRAD (Coordinated Network for Radiation Dosimetry) as a joint initiative of EURADOS working groups 6 (computational dosimetry) and 7 (internal dosimetry). Monte Carlo simulations using the knee voxel phantom proved to be a viable approach to provide the calibration factor needed for in vivo measurements.     

基于贝叶斯理论的钢筋混凝土框架中节点抗剪强度计算

我国现行设计规范中钢筋混凝土框架中节点抗剪强度计算为半经验半理论计算公式,由于试验数据的有限性和钢筋混凝土材料的离散性,规范建议公式缺乏明确的理论模型。该文以贝叶斯动态信息更新思路,根据主观经验信息选定先验模型,将国内外已完成101组钢筋混凝土框架中节点试件的试验结果作为数据库,应用贝叶斯参数估计方法综合两类信息进行推断,建立了基于贝叶斯理论的多元线性钢筋混凝土中节点抗剪强度概率模型,进而采用贝叶斯后验模型参数剔除理论,剔除影响节点抗剪强度的次要因素,对概率模型进行动态更新,得到中节点抗剪强度简化模型,并将抗剪模型计算值与试验值和美国ACI 352R-02中钢筋混凝土节点抗剪强度的计算公式进行了对比。研究表明：贝叶斯方法继承了先验信息的完备性和大量试验数据的准确性,建议的中节点贝叶斯概率抗剪模型与试验值吻合良好,且较规范值能够更准确地预测钢筋混凝土中节点抗剪强度,可用于该类节点的抗剪强度计算。     

Optimization of structures under material parameter uncertainty using evidence theory

An evidence-based approach is developed for optimization of structural components under material parameter uncertainty. The approach is applied to evidence-based design optimization (EBDO) of externally stiffened circular tubes under axial impact load using an isotropic–elastic–plastic plasticity model to simulate dynamic material behaviour. Uncertainty modelling considers the changes in material parameters that are caused by variability in material properties as well as incertitude and errors in experimental data and procedure to determine the material parameters. Spatial variation of material parameters across the structural component is modelled using a field joint belief structure and propagated for the calculation of evidence-based objective function and design constraints. Surrogate models are used in both uncertainty propagation and solution of the optimization problem. The methodology and the solution to the EBDO example problem are presented and discussed.     

Integration of external and internal dosimetry in Switzerland

Individual monitoring regulations in Switzerland are based on the ICRP60 recommendations. The annual limit of 20 mSv for the effective dose applies to the sum of external and internal radiation. External radiation is monitored monthly or quarterly with TLD, DIS or CR-39 dosemeters by 10 approved external dosimetry services and reported as H(p)(10) and H(p)(0.07). Internal monitoring is done in two steps. At the workplace, simple screening measurements are done frequently in order to recognise a possible incorporation. If a nuclide dependent activity threshold is exceeded then one of the seven approved dosimetry services for internal radiation does an incorporation measurement to assess the committed effective dose E(50). The dosimetry services report all the measured or assessed dose values to the employer and to the National Dose Registry. The employer records the annually accumulated dose values into the individual dose certificate of the occupationally exposed person, both the external dose H(p)(10) and the internal dose E(50) as well as the total effective dose E = H(p)(10)+E(50). Based on the national dose registry an annual report on the dosimetry in Switzerland is published which contains the statistics for the total effective dose, as well as separate statistics for external and internal exposure.     

Calculation of Measurement Uncertainty Using Prior Information

We describe the use of Bayesian inference to include prior information about the value of the measurand in the calculation of measurement uncertainty. Typical examples show this can, in effect, reduce the expanded uncertainty by up to 85 %. The application of the Bayesian approach to proving workpiece conformance to specification (as given by international standard ISO 14253-1) is presented and a procedure for increasing the conformance zone by modifying the expanded uncertainty guard bands is discussed.