A simple algorithm for solving the inverse problem of interpretation of uncertain individual measurements in internal dosimetry

The individual monitoring of internal exposure of workers comprises two steps: measurement and measurement interpretation. The latter consists in reconstructing the intake of a radionuclide from the activity measurement and calculating the dose using a biokinetic model of the radionuclide behavior in the human body. Mathematically, reconstructing the intake is solving an inverse problem described by a measurement-model equation. The aim of this paper is to propose a solution to this inverse problem when the measurement-model parameters are considered as uncertain. For that, an analysis of the uncertainty on the intake calculation is performed taking into account the dispersion of the measured quantity and the uncertainties of the measurement-model parameters. It is shown that both frequentist and Bayesian approaches can be used to solve the problem according to the measurement-model formulation. A common calculation algorithm is proposed to support both approaches and applied to the examples of tritiated water intake and plutonium inhalation by a worker.

Internal dosimetry: towards harmonisation and coordination of research

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.

Internal dose assessments: uncertainty studies and update of ideas guidelines and databases within CONRAD project

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.

Evaluation of scattering factor values for internal dose assessment following the IDEAS guidelines: preliminary results

The IDEAS Guidelines for the assessment of internal doses from monitoring data suggest default measurement uncertainties (i.e. scattering factors, SFs) to be used for different types of monitoring data. However, these default values were mainly based upon expert judgement. In this paper, SF values have been calculated for different radionuclides and types of monitoring data using real data contained in the IDEAS Internal Contamination Database. Results are presented.

Estimation of the uncertainty in internal dose calculation for two contamination cases

The assessment of internal dose is subject to a large uncertainty due to the limits of measuring technique and to the assumptions made by the expert. Here, we propose an approach to report the confidence interval associated with the evaluated dose. The sources of uncertainties considered so far include the date of intake, the physico-chemical characteristics of the radioactive material, the counting error and the stochastic variability of excretion. Three successive levels of approximation are suggested, depending on the expected dose, for which increasingly realistic parameter values should be sought and applied. Finally, the results of a Monte Carlo dose calculation are presented in the form of a statistical distribution of possible dose values. This approach has been applied to two cases of uranium and caesium exposure.

Analysis of the uncertainty in internal dose estimate resulting from biological stochastic variability of excretion

A method for investigating the uncertainty in internal dose estimate resulting from biological stochastic variability of excretion is proposed in the paper. The method is based on analysing generated cases of individual monitoring data using Monte Carlo simulation technique. In case of a single intake and assumption of stochastic variability of excretion is a single source of uncertainty it was shown that the intake (dose) uncertainty depends exclusively on the uncertainty of the bioassay data and the number of daily urine (faeces) measurements. Assuming a log-normal distribution for describing the variability of excretion a simple expression for calculating the uncertainty was proposed. In case of routine monitoring data it was shown that the uncertainty of annual intake (dose) estimate would depend on biological stochastic variability of excretion, type of excretion function and the number of monitoring intervals in a year. By the example of Pu and U aerosols it was shown that the effects of decreasing uncertainty in the dose estimate resulting from increasing the number of monitoring intervals in a year and from decreasing the uncertainty of bioassay data (performing a number of successive daily measurements, once in a year) should be estimated to optimise the routine monitoring program.

Coordination of research on internal dosimetry in Europe: the CONRAD project

The EUropean RAdiation DOSimetry Group (EURADOS) initiated in 2005 the CONRAD Project, a Coordinated Network for Radiation Dosimetry funded by the European Commission (EC), within the 6th Framework Programme (FP). The main purpose of CONRAD is to generate a European Network in the field of Radiation Dosimetry and to promote both research activities and dissemination of knowledge. The objective of CONRAD Work Package 5 (WP5) is the coordination of research on assessment and evaluation of internal exposures. Nineteen institutes from 14 countries participate in this action. Some of the activities to be developed are continuations of former European projects supported by the EC in the 5th FP (OMINEX and IDEAS). Other tasks are linked with ICRP activities, and there are new actions never considered before. A collaboration is established with CONRAD Work Package 4, dealing with Computational Dosimetry, to organise an intercomparison on Monte Carlo modelling for in vivo measurements of (241)Am deposited in a knee phantom. Preliminary results associated with CONRAD WP5 tasks are presented here.

Dependence of the dose estimate on the time pattern of intake by the example of tritiated water intakes

The uncertainties related to activity measurement and time pattern of intake in routine monitoring of internal exposure are considered through the example of tritiated water intakes. For this purpose, a combination of intake-to-bioassay and bioassay-to-intake calculations with Monte Carlo integration technique is introduced as a method of investigation. The time pattern of intake and the measured activity are defined as random input quantities. The probability density functions (PDFs) of the input quantities are defined and a Monte Carlo integration is performed to obtain the PDF of the output quantity which is either the value of intake estimated from a measured value of activity or the estimated activity from a given value of intake. Different possible estimates of the intake are considered: some represent the parameters of the PDF of the output quantity, others are derived from the commonly used constant chronic, I(CC), and mid-point, I(1/2), methods. The combinations of activity and intake estimates that would provide a stable estimate of the initial intake in intake-to-bioassay and bioassay-to-intake calculations were studied. Several intake estimates satisfying this requirement can be chosen depending on the task to be solved by adjusting the proper activity estimate.

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.

Dosimetry of heavy charged particles with thermoluminescence detectors--models and applications

Lithium fluoride thermoluminescent (TL) detectors, with Li-7 isotope and various activators (MTS-7 LiF:Mg,Ti, MTT-7 LiF:Mg,Ti with enhanced Ti concentration and MCP-7 LiF:Mg,Cu,P) were used for dosimetry of heavy charged particles, within the ICHIBAN experiment. The microdosimetric model has been applied to calculate detection efficiency, eta, relative to gamma-ray dose, of these detectors after proton and heavy charged particle (HCP) irradiation for ion charges ranging from Z = 1 to Z = 6 and in the energy range from 0.3 to 20 MeV amu(-1). The calculated ratio eta(MCP-7)/eta(MTS-7) lies in the range between 0.2 and 1.0 for protons and between 0.2 and 0.4 for HCP with Z > 1. The calculated value of eta(MTT-7)/eta(MTS-7) for protons was found range between 1.0 and 1.45 and, for Z > 1, between 1.3 and 2. These relationships can be applied to derive information about the 'effective LET' in an unknown HCP field and to correct the TLD readings for dose evaluation.

Uncertainty analysis in the task of individual monitoring data

Assessment of internal doses is an essential component of individual monitoring programmes for workers and consists of two stages: individual monitoring measurements and interpretation of the monitoring data in terms of annual intake and/or annual internal dose. The overall uncertainty in assessed dose is a combination of the uncertainties in these stages. An algorithm and a computer code were developed for estimating the uncertainty in the assessment of internal dose in the task of individual monitoring data interpretation. Two main influencing factors are analysed in this paper: the unknown time of the exposure and variability of bioassay measurements. The aim of this analysis is to show that the algorithm is applicable in designing an individual monitoring programme for workers so as to guarantee that the individual dose calculated from individual monitoring measurements does not exceed a required limit with a certain confidence probability.

Proton dosimetry intercomparison based on the ICRU report 59 protocol

BACKGROUND AND PURPOSE

A new protocol for calibration of proton beams was established by the ICRU in report 59 on proton dosimetry. In this paper we report the results of an international proton dosimetry intercomparison, which was held at Loma Linda University Medical Center. The goals of the intercomparison were, first, to estimate the level of consistency in absorbed dose delivered to patients if proton beams at various clinics were calibrated with the new ICRU protocol, and second, to evaluate the differences in absorbed dose determination due to differences in 60Co-based ionization chamber calibration factors.

MATERIALS AND METHODS

Eleven institutions participated in the intercomparison. Measurements were performed in a polystyrene phantom at a depth of 10.27 cm water equivalent thickness in a 6-cm modulated proton beam with an accelerator energy of 155 MeV and an incident energy of approximately 135 MeV. Most participants used ionization chambers calibrated in terms of exposure or air kerma. Four ionization chambers had 60Co-based calibration in terms of absorbed dose-to-water. Two chambers were calibrated in a 60Co beam at the NIST both in terms of air kerma and absorbed dose-to-water to provide a comparison of ionization chambers with different calibrations.

RESULTS

The intercomparison showed that use of the ICRU report 59 protocol would result in absorbed doses being delivered to patients at their participating institutions to within +/-0.9% (one standard deviation). The maximum difference between doses determined by the participants was found to be 2.9%. Differences between proton doses derived from the measurements with ionization chambers with N(K)-, or N(W) - calibration type depended on chamber type.

CONCLUSIONS

Using ionization chambers with 60Co calibration factors traceable to standard laboratories and the ICRU report 59 protocol, a distribution of stated proton absorbed dose is achieved with a difference less than 3%. The ICRU protocol should be adopted for clinical proton beam calibration. A comparison of proton doses derived from measurements with different chambers indicates that the difference in results cannot be explained only by differences in 60Co calibration factors.