A Monte Carlo method for calculating Bayesian uncertainties in internal dosimetry

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.     

The quantification of uncertainties in internal doses assessed from monitoring measurements

A novel method is described for the assessment of total uncertainties in intakes and internal doses assessed from in vivo and bioassay monitoring measurements. Using the information on uncertainties in intake patterns, measurements and biokinetic model parameters, the probability distribution functions for assessed intake and dose were generated using Monte-Carlo simulations. The method was implemented using software written in MS Visual Basic 6.0. Preliminary results are presented for the example of routine tritium-in-urine monitoring. It was shown that the uncertainty in the assessed dose first decreases with increasing monitoring interval, reaching a minimum at approximately 14 d, and then increases as the monitoring interval is increased beyond 14 d. The distribution describing the ratio of assessed-dose-to-true-dose becomes very asymmetric at longer monitoring intervals. In principle, this method should allow realistic uncertainties to be placed on assessed internal doses.     

Assessment of occupational doses from internal contamination with 241Am

A group of workers with occupational intakes of 241Am, which occurred a long time ago, has been followed for some time. Results of in vivo measurement and bioassay of excreta are compared with the values predicted by the ICRP Publication 78 model. The observed skeletal content is, as a rule, higher than the predicted one. The ratio of excreted activity in urine to that in faeces is in very good agreement with the model prediction. Another group of workers from a waste management department, who were internally contaminated in July 2001, has also been followed. In some cases, there is quite a large difference in calculated intake between excretion by urine and that by faeces. The contaminant was presumably the same as that in the group of workers with old intakes, but its physical and chemical form could be influenced by a fixating lacquer used to prevent the spread of contamination.     

A simple method for assessing that internal doses are below action levels

The accidental or deliberate dispersal of radioactive aerosols into the public environment may require urgent assessments of radiation dose to be made to aid decisions on whether treatment should be implemented, or to reassure the public that doses are acceptably low. However, rapid assessments will be difficult due to lack of information on factors such as the particle size distribution and biokinetic characteristics of the aerosol. A procedure is described that relates the amount of activity of a radionuclide in the body and excreta to time after intake for a specified dose, taking into account the likely variations in aerosol size and differences in the biokinetic behaviour of the same or different chemical forms of the radionuclide. The implementation of the procedure for an intake of caesium-137 and a dose level of 1 mSv is described and the information presented graphically. Figures for other specified dose levels can be produced by simply scaling the data by an appropriate factor. The figures can also be used to assess the most appropriate monitoring procedure and indicate the uncertainty in the assessed dose according to the parameter and parameter values used. This approach is proposed for rapid decisions on public reassurance when potentially large numbers of people are involved. It is not intended as a substitute for individual dose assessment.     

An approach to reduction of uncertainties in internal doses reconstructed for the Techa River population

A methodology was developed for reduction of uncertainties in estimates of internal dose for residents of the Techa Riverside communities, who were exposed as a result of releases of radionuclides from the Mayak plutonium production facility in 1949-56. The 'Techa River Dosimetry System' (TRDS) was specifically elaborated for reconstruction of doses. A preliminary analysis of uncertainty for doses estimated using the current version of the TRDS showed large ranges in the uncertainty of internal absorbed dose and led to suggestions of methods to reduce uncertainties. The new methodological approaches described in this paper will allow for significant reduction of uncertainties of 90Sr-dose. The major sources of reduction are: making use of individual measured values of 90Sr and through development of a Household Registry to associate unmeasured persons with measured persons living in the same household(s).     

A method of calculating the temperature distribution in a complex structure

A mathematical model is given for the temperature distribution in a structure when the temperatures in the individual elements are described by one-dimensional heat-conduction equations.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 29, No. 1, pp. 140–144, July, 1975.     

A method for calculating meshless finite difference weights

An exact method for calculating the finite difference weights for arbitrary distributed points in multiple dimensions is presented. The method avoids the numerical ill conditioning associated with a small‐scale factor (ε) by delaying the limiting of ε → 0. The Gaussian Radial Basis function is approximated by a Taylor's series expansion in the variable ε, and the resultant matrix equation is solved using the Fraction Free LU decomposition method. Copyright © 2007 John Wiley & Sons, Ltd.     

A Bayesian method for oscillator stability analysis

The power spectral density of frequency fluctuations of an oscillator is generally modeled as a sum of power laws with integer exponents (from -2 to +2). However, a power law with a fractional exponent may exist. We propose a method for measuring the level of such a noise process and determining the probability density of the exponent. This yields a criterion for compatibility with an integer exponent. This method is based on a Bayesian approach called the reference analysis of Bernardo-Berger. The application to a sequence of frequency measurement from a quartz oscillator illustrates this paper.     

一种非分层海洋中的声线计算方法

在浅海环境中,声速剖面和海底深度在水平方向上的变化都会对声传播产生较大的影响。将声速剖面用前几阶经验正交函数来表示,在一定范围的海域各阶经验正交函数系数可以近似为随水平距离线性变化,提出了一种非分层海洋中的声线计算方法,可以计算到达接收水听器的本征声线和传播时间。该方法计算速度快,计算精度较高,可以用于海洋中的声速剖面快速反演。     

A method for calculating stress intensities in bimaterial fracture

A numerical method is presented for obtaining the values of K^* ₁,K ^* _II and K^* _III in the elasticity solution at the tip of an interface crack in general states of stress. The basis of the method is an evaluation of theJ-integral by the virtual crack extension method. Individual stress intensities can then be obtained from further calculations ofJ perturbed by small increments of the stress intensity factors. The calculations are carried out by the finite element method but minimal extra computations are required compared to those for the boundary value problem. Very accurate results are presented for a crack in the bimaterial interface and compared with other methods of evaluating the stress intensity factors. In particular, a comparison is made with stress intensity factors obtained by computingJ by the virtual crack extension method but separating the modes by using the ratio of displacements on the crack surface. Both techniques work well with fine finite element meshes but the results suggest that the method that relies entirely on J-integral evaluations can be used to give reliable results for coarse meshes.

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Résumé On présente une méthode numérique en vue d'obtenir les valeurs de K^* ₁, K^* _II et K^* _III relatives à la solution élastique d'application à l'extrémité d'une fissure d'interface sujette à un état de contraintes général. La méthode repose sur l'évaluation de l'intégraleJ par la technique d'extension virtuelle de la fissure. On peut ensuite obtenir les intensités de contraintes individuelles à partir de calculs deJ subséquents, correspondant à des perturbations introduites par de petits accroissements des facteurs d'intensité de contraintes.Les calculs sont accomplis par la méthode des éléments finis, mais, par rapport aux calculs à mettre en oeuvre dans le problème des valeurs aux limites, il ne faut procéder qu'à quelques calculs supplémentaires.On présente des résultats très précis pour le cas d'une fissure dans un interface entre deux matériaux, et on les compare avec ceux provenant d'autres méthodes d'évaluation des facteurs d'intensité de contraintes.En particulier, on fait une comparaison pour des facteurs d'intensité de contraintes obtenus en calculant J par la méthode d'extension virtuelle d'une fissure, mais en séparant les modes selon le rapport des déplacements de la surface de la fissure.Les deux techniques fonctionnent de manière satisfaisante avec des maillages fins d'éléments finis; cependant, les résultats suggèrent que la méthode qui repose entièrement sur les évaluations de l'intégraleJ peut être utilisée afin d'obtenir des résultats fiables dans les réseaux à mailles grossières.

     

A new numerical method for the inverse source problem from a Bayesian perspective

In this work, a new numerical method for the inverse problem of determining a spacewise‐dependent heat source for a parabolic heat equation is developed. We reconstruct the unknown heat source by an augmented Tikhonov regularization (a‐TR) method derived from a Bayesian perspective. The a‐TR method could determine the regularization parameter and detect the noise level automatically. Numerical results for several benchmark test problems indicate that the a‐TR method is an accurate and flexible method to determine the unknown spacewise‐dependent heat source. Copyright © 2010 John Wiley & Sons, Ltd.     

一种颗粒系超声衰减谱的改进计算方法

Epstein和Carhart,Allegra和Hawley先后研究建立起的超声谱颗粒粒径测量的经典理论模型——ECAH,针对直接求解ECAH理论模型预测颗粒两相系中物理量声衰减系数时出现的困难,通过构造与Bessel（Hankel）函数有关的新变量,改造原有系数矩阵,降低矩阵的条件数,避免了数值溢出问题,拓展该模型的计算范围至频率100MHz和毫米级颗粒,通过与BLBL（Bouguer-Lambert-Beer-Law）散射方法的比较验证了文中提出的改进方法的有效性。     

A method for calculating the freezing point of dairy products

Using the method of Leighton, an approximate method of predicting the freezing point of milk products, including ice cream, is developed. It takes account only of the concentrations of sugar and serum. Predictions are tested against a range of experimental measurements and the error is found to be generally less than 0.05°C.     

一种高次光学非球面度的计算方法

针对现有光学非球面度计算方法不统一的问题,在分析常用方法特点的基础上,对于高次光学非球面度的计算提出最小最大残差法。寻找最接近球面,使其沿法线方向与非球面的最大偏离量最小,此时的最大偏离量即为非球面的最大非球面度。该方法适于计算机编程,计算结果准确,且可完全统一二次曲面和高次非球面的非球面度计算。     

A molecular fraction method for measuring personnel radiation doses

This work represents a development in fast and albedo neutron and gamma ray dosimetry, using cellulose nitrate, as a tissue equivalent material, in which radiation damage was registered.The changes in molecular fractions of the polymer were measured after irradiation with neutron fluences from a ²⁵²Cf source in the range 10⁵−10¹⁰ n/cm² and gamma doses in the range 10⁻⁴–10⁻¹ Gy through the use of gel filtration chromatography.Effects of irradiation on phantom, phantom to dosimeter distance, phantom thickness and storage at extreme environmental conditions were studied on the detector response and readout.The results showed that main chain scission followed by formation of new molecular configurations is the predominant effect of radiation on the polymer. The method enables measurements of neutron fluences and gamma doses in mixed radiation fields. Empirical formulae for calculating the absorbed dose from the measured changes in molecular fraction intensities are given.     

A family of statistical distributions for modelling occupational radiation doses in low dose occupations

New statistical distributions have been defined to describe occupational exposures to ionising radiation. These distributions are particularly useful in modelling occupations where most doses are low. The maximum likelihood method was used for parameter estimation and has been adapted to allow doses that are recorded as zero to be included in the calculations. The method can then be applied to estimate true doses from the complete set of recorded dose values when the a priori dose distribution and the dose measurement distributions have been derived previously. This application is important in epidemiological cohort studies where it can improve the accuracy of excess relative risk estimates.