software for evaluation of epr-dosimetry performance

Radiation Protection Dosimetry Advance Access published May 29, 2014 Radiation Protection Dosimetry (2014), pp. 1–6

doi:10.1093/rpd/ncu167

SOFTWARE FOR EVALUATION OF EPR-DOSIMETRY PERFORMANCE E. A. Shishkina1,*, Yu. S. Timofeev1 and D. V. Ivanov2 1 Urals Research Centre for Radiation Medicine (URCRM), 68-AVorovsky Street, Chelyabinsk 454076, Russia 2 Institute of Metal Physics (IMP) of the Russian Academy of Sciences, 18 S. Kovalevsky Street, Yekaterinburg 620990, Russia *Corresponding author: [email protected]

INTRODUCTION Electron paramagnetic resonance (EPR) of tooth enamel is extensively applied for retrospective external dosimetry(1). Different research groups use different equipment, sample preparation procedures and spectrum processing algorithms. For comparison of metrological properties of different methods, a uniform algorithm of performance estimation need to be applied(2). Method performances can be described by quality indicators, such as critical values and detection limits(3 – 5). In addition to the performance parameters mentioned above, it is important to know the methodspecific dose-dependent uncertainty(6). For example, the data obtained by 11 methods used for EPR measurements of teeth in the long-term study of the Techa River population(7) can be combined and compared only taking into account the method-specific data quality. The importance of the data harmonisation served as a motivation (in many respects) for the development of a tool allowing a simple evaluation of the performances of the EPR methods, including the uncertainty as a function of a measurand. The preliminary studies have shown that the analytical models of uncertainty based on the empirical and semi-empirical approaches are not universal(8). A method-independent algorithm to evaluate the uncertainties was proposed based on Monte Carlo simulations reproducing the calibration experiment (9). The algorithm was improved and implemented in a new computer code ‘EPR-dosimetry performance’. The improvement consisted in accounting for the population-specific variability of dosimetric properties of tooth enamel,

viz., individual variability of background doses and variation of radiation sensitivity of the tooth enamel. The purpose of the paper is to present the computer code ‘EPR-dosimetry performance’, which is a userfriendly tool that provides a full description of method-specific capabilities of EPR tooth dosimetry, from metrological characteristics to practical limitations. The estimates of performances are based on experimental data, and they are valid for a fixed experimental design and a specific range of sample masses. The software was designed for scientists and engineers, and it has the following applications: support of method calibration by evaluation of calibration parameters and their precision; evaluation of critical value and detection limit for registration of radiation-induced signal (RIS) amplitude; estimation of critical value and detection limit for dose evaluation; estimation of minimal detectable value for anthropogenic dose assessment and description of method uncertainty. The software presented is available for free at the website of the Urals Research Centre for Radiation Medicine (http://www.urcrm.ru/eprdosimetry-performance). TERMS AND DEFINITIONS Performance parameters: – Critical level (critical value and detection decision) is a threshold below which there is practically no chance to distinguish an RIS from a blank response (Equation 1). Hereinafter, the critical level for amplitude detection is called the critical

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Electron paramagnetic resonance (EPR) with tooth enamel is a method extensively used for retrospective external dosimetry. Different research groups apply different equipment, sample preparation procedures and spectrum processing algorithms for EPR dosimetry. A uniform algorithm for description and comparison of performances was designed and implemented in a new computer code. The aim of the paper is to introduce the new software ‘EPR-dosimetry performance’. The computer code is a user-friendly tool for providing a full description of method-specific capabilities of EPR tooth dosimetry, from metrological characteristics to practical limitations in applications. The software designed for scientists and engineers has several applications, including support of method calibration by evaluation of calibration parameters, evaluation of critical value and detection limit for registration of radiation-induced signal amplitude, estimation of critical value and detection limit for dose evaluation, estimation of minimal detectable value for anthropogenic dose assessment and description of method uncertainty.

E. A. SHISHKINA ET AL.

amplitude (Ac); the critical level for dose evaluation is called the critical dose (Dc): ^ . Xc jX ¼ 0Þ 0:05; PðX

ð1Þ

– Detection limit (limit of detection and minimal detectable amount) is a threshold above which a measurement can be definitely interpreted as a response to radiation (Equation 2). Hereinafter, the limit of amplitude detection is indicated as LDA; the limit of dose evaluation is indicated as LDD: ^ Xc jX ¼ LDÞ ¼ 0:05: PðX

ð2Þ

Uncertainty components are classified as: (1) Measurement uncertainty (epistemic uncertainty) arises from experiment statement (related to instrumental noise and sensitivity, quality of sample preparation, signal processing and dose conversion); (2) Variability (aleatory uncertainty) arises from true heterogeneity among people (related to an individual’s history of background exposure and physiological properties of hydroxyapatite). –

Limit of individualisation (LI) is a threshold above which the value can be definitely interpreted as a response to exposure exceeding background level. This quality indicator is calculated by the same way that was applied in the calculation of the detection limit, but in contrast to LDD when the calculation was performed relative to the blank, the LI is evaluated relative to the background dose distribution.

Evaluation of metrological properties of EPR dosimetry (Ac, Dc, LDA, LDD) is based on a calibration experiment performed in a way ensuring minimisation of any influence of individual variability of dosimetric properties of tooth enamel. For this purpose, the calibration experiment should be performed using a carefully mixed enamel powder divided into portions (one-sample approach) as it is shown in Figure 1. The following input data should be arranged in the text file and downloaded: applied doses, sample masses and three amplitudes per sample portion. The range of applied doses and the number of exposed sample portions are not predetermined. However, the software includes an analysis of input data adequacy. In the case of insufficiency of input data, the program asks for additional experimental data suggesting an increase in the dose range or measurement statistics. A calibration system is elaborated for a narrow range of sample masses. A referent value of sample mass (M) from this range (the default value is 100 mg) should be indicated by the user. Estimation of the overall uncertainty as well as of LI is optional, and it needs additional information on the distribution of doses resulting from the background exposure and variation of individual radiation sensitivity of enamel (Figure 1). As was shown in previous studies(11, 12), both of these can be different in different regions or population groups. The distribution of background doses is assumed to be lognormal; the user-defined scale and shape parameters can be entered. By default, the parameters typical of the Urals rural population (m ¼ 4.99 and s ¼ 0.35) are fixed. Similarly, the individual variability of radiation sensitivity of enamel can be user-defined in terms of the coefficient of variation (CV); the value CVsenc ¼ 0.16(11) is used by default. Figure 2a represents the interface of the software. The numerical experiment imitating the detection of known RIS amplitudes simulates the distribution of

MATERIALS AND METHODS The software was developed in Cþþ Builder 6 for use on systems running Windows XP service pack 2 or later, Windows Vista, or Windows 7 and 8. The code implements a regression analysis and statistical analysis of repeatability of measurement results (input data). Stochastic modelling of measurement repeatability, errors of calibration and individual variability of radiation sensitivity of tooth enamel is performed using Monte Carlo simulations. Accounting for individual variability of background doses in assessing the overall uncertainty was conducted using two-dimensional Monte Carlo simulations. The generator of random variables of Borland Cþ þ Builder 6 (stdlib.h) was applied.

Figure 1. Accounting for the epistemic and aleatory sources of overall uncertainty.

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– Uncertainty is a non-negative parameter characterising the dispersion of the quantity values being attributed to a measurand, based on the information used(10).

INPUT DATA

SOFTWARE FOR EPR


Figure 2. Software interface: (a) the main window for data input, task selection and specification of the conditions for numerical experiment; (b) the report on the data processing and simulation results.

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EPR responses (Ym) to the measurand (m). In the numerical experiment, the number of triple measurements (N) of EPR amplitudes (Ai) (normalized per M ) is simulated for different ‘true’ amplitudes. In the software, the value N as well as the range of ‘true’ amplitudes and the amplitude step, all are userdefined. As a default, N is fixed as 1000.

DATA PROCESSING AND NUMERICAL MODELLING

Epistemic uncertainty Usually, the calibration curve is based on a limited number of EPR measurements, which are not enough to elaborate a reliable method-specific analytical model of amplitude-depending repeatability. Therefore, the model of amplitude repeatability is elaborated as a stochastic description of standard deviations of triple EPR measurements. It is described by a random value z distributed according to the Weibull function with the shape parameter m ¼ 2:

sðmÞ [ 6ðsðmÞÞ 6 ¼ sðmÞ ðln ð1 lÞÞ1=m ! 6 ¼ sðmÞ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ln ð1 lÞ; ð3Þ

where l is a uniformly distributed random value in the range from 0 to 1. The key parameter of the model is the scale parameter (s(m)) as a function of a known amplitude m. This parameter is proportional to the average standard deviations S(A) reflecting the repeatability of amplitude A detection: 1þ1 ¼ sðmÞ Gð1:5Þ; ð4Þ SðAÞ ¼ sðmÞ G m where D is a Gamma function (D(1.5) ¼ 0.886). Thus, s(m) is equal to S(A)/0.886. For evaluation of S(A), the software analyses the amplitude dependence of measurement repeatability and its variability. The measurement repeatability

Figure 3. Analysis of data dispersion: (a) the amplitude dependence of standard deviations of CV; (b) the amplitude dependence of measurement repeatability. Solid line indicates a model for average method repeatability (S(A)) depending on amplitude, presented according to Ivanov et al.(9).

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Simulation of the measurand m results in Ym ¼ distr ðA1 ; A2 ; :::; AN Þ; where Ai [ N½m; s is a normally distributed variable; s reflects the repeatability of triple measurement (related to epistemic uncertainty). Simulation of the amplitude to dose conversion is accounted for the uncertainty of calibration curve parameters. Preliminarily, the calibration curve is elaborated under linear assumption by fitting the dose dependence of normalising amplitudes by the leastsquare method. Errors of slop and intercept coefficients are evaluated. These errors are also related to the epistemic uncertainty.

is expressed in terms of CV of three repeated measurements. The variability of CVs for triple EPR measurements (sCV(A)) depending on the amplitude of RIS was calculated for three neighbouring CVs (similar to the method of running averaging) ranged by the average amplitudes. Starting with some value (I), the sCV can be assumed as a constant. This is illustrated by Figure 3a plotted based on the measurements performed in the Institute of Metal Physics(9)). The unfeasibility to reliably determine I is an indicator of insufficiency of the input data. The existence of the amplitude threshold I for stability of CV’s dispersion means that S(A) above and below I should be described in different ways. For amplitudes greater than I, S(A) can be described by a linear function with slope a and intercept b. Below I, S(A) is assumed to be constant c in the amplitude range from zero to I/2. The intermediate range of the amplitudes (from I/2 to I) was smoothed by a linear function to connect the previous and the next ranges. The model of amplitude dependence for the average standard deviation (s(A)) is formulated by the

SOFTWARE FOR EPR

following equation and illustrated by Figure 3b: 8 c; if A , I =2 > > < 2x I SðAÞ ¼ ðaI þ b cÞ c; if A , I : > I 1 2 > : a A þ b; if A I ð5Þ The uncertainty of the calibration is simulated taking into account the errors of coefficients of linear regression (slope k and intercept l ). The parameters are not independent, and they are simulated according to the following equation:

where Dm is the mid-range of doses applied, k0 and l0 are fitting coefficients of the regression and sk0 and sl0 are the errors of the regression coefficients.

Accounting for the aleatory uncertainties Simulation of an individual variation of radiation sensitivity is performed by an additional random drawing of the slope k independent of the intercept coefficient as norm(k0, sks), where sks ¼ k0 * CV senc. In contrast to the above-mentioned epistemic uncertainties contributed to the detection results (ordinate axes of dose–response), the individual variations of the background doses contribute to a dose assumed as a ‘true’ value (abscissa axes of dose–response). This uncertainty component is dose-independent and, therefore, it contributes mostly to low doses. Figure 4 illustrates the two-dimensional uncertainty.

The software develops a spline of 90 % confidence intervals calculated for each Ym(m) describing the extended uncertainty. The splines are used for the evaluation of the method performance. The upper border of 90 % confidence interval for zero ‘true’ amplitude reflects the Ac value. The LDA is estimated from the intercept of the level of critical amplitude and the corresponding low border of 90 % confidence interval. The critical dose and the dose detection limit are estimated in the same way, but in dose units, with account taken for the uncertainty of dose conversion and the individual variability (optional). The estimate of LI is performed using an approach similar to that applied for the limit of detection. Thus, the software output is represented by a report on the calibration curve, method-specific performance parameters for both amplitude detection and dose reconstruction, and optionally for description of the population-specific quality of dose reconstruction (overall uncertainty and LI). Additionally, the graphs illustrating the simulation results for separate sources of uncertainties are available. The raw data of numerical experiments are also available for users. Figure 2b presents an example of a software output.

CONCLUSIONS The uniform algorithm for description and comparison of performances of different EPR methods was designed and implemented in a new computer code. The computer code is a user-friendly tool that provides a full description of method-specific capabilities of EPR tooth dosimetry, from metrological characteristics to practical limitations. The software was designed for scientists and engineers and has several applications, including support of method calibration by evaluation of calibration parameters and their precision; evaluation of critical value and detection limit for registration of RIS amplitude; estimation of critical value and detection limit for dose evaluation; estimation of minimal detectable value for anthropogenic dose and description of method uncertainty. The software is available for free since January of 2014 at a website of Urals Research Centre for Radiation Medicine (http://www.urcrm.ru/ epr-dosimetry-performance).

ACKNOWLEDGEMENTS Figure 4. Illustration of a two-dimensional simulation of aleatory uncertainties: slope drawing along y-axes and background dose variation along x-axes.

The authors are very thankful to P. Fattibene, S. Della Monaka (ISS) and A. Wieser (HMGU) for fruitful discussions and for providing the raw data on calibration results.

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l ¼ normðl0 ; sl0 Þ ðl0 lÞ k¼ þ 2k0 normðk0 ; sk0 Þ; Dm

EVALUATION OF PERFORMANCE PARAMETERS AND SOFTWARE OUTPUT


FUNDING This work was supported by the Russian-American Project 1.1 and partially by the SOLO project.

REFERENCES

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