Investigation of Uncertainty Sources in the Determination of Gamma Emitting Radionuclides in the WBC

Transcription

1 Investigation of Uncertainty Sources in the Determination of Gamma Emitting Radionuclides in the WBC A. Specification Whole body counting method is used to detect the gamma rays emitted by radio nuclides, which have been deposited in a human body. The radio nuclides are identified and their activity is calculated. Measurement procedure The BEGe detectors are calibrated for energy and efficiency using BOMAB phantom (#PM95- A) for the high energy and the JAERI lung phantom for the low energy arrange. The BOMAB phantom was prepared by the homogeneous dispersion of a mixture of gamma emitters (Cs-137, Ba-133 and Co-60) in Uralite Polyurethane Elastomer. The phantom volume is ml and the density is 1.06 g/ml. The calibration reports are filed in the detectors folder. The JAERI lung phantom was designed for calibration by the Japan Atomic Energy Research Institute. Polyurethane and epoxy resin were used to simulate major body tissues, including lung. The density of the foamed Polyurethane is g/ml. The torso phantom has the following lung sets: Natural Uranium 3% Enriched Uranium Plutonium 38 Americium 41 Thorium 3 To simulate the different chest wall thickness, the JAERI lung phantom is provided with overlays. 1

2 The specific information on how to calibrate and measure are given in the WI-3-WB-03. The measure consists of the following stages: Body height determination Body weight determination Background count WBC count Calibration RESULT Figure 1: WBC - count Calculation The measurand is the nuclide activity, which is given by: A Ei N ε t γ = E [Bq] in the high energy arrange E d A Ei N ε t γ = E [Bq] in the low energy arrange ' E d where: A Ei = the activity concentration of nuclide I based on energy E = the net peak area for peak at energy E N Ei = the detector efficiency at energy E ε E ε E = the attenuation corrected detector efficiency at energy E t = the live time γ d = the branching ratio for energy E of this Nuclide

3 B. Identifying and Analysing Uncertainty Sources The estimation of uncertainties contains the following steps: Exploration of all factors influencing the measurement, Quantification of the uncertainties connected to each factors by measurement results or by expert judgment if applicable, Estimation of the overall uncertainty of the measurement. Uncertainty Sources: Net Peak Area Detector Efficiency Branching Ratio Measuring time Temperature Attenuation Corrected Detector Efficiency Chest Wall Thickness The different effects and their influences are shown as a cause and effect diagram in Figure and 3. Quantifying the uncertainty components Net Peak Area Determined by the spectrum evaluation software Background correction N = G B where: G = Gross sum of the counts within the peak region (ROI), B = background area counts for the peak. n B = 1 + n 1 ( B B )

4 The uncertainty in background area counts. where: n B1 B u ( B) = + n1 n n = number of channels in the ROI, BB1 = Area of left background region, width n1 channels, B B = Area of right background region, width n channels. If the background regions are of equal width (n 1 = n), the uncertainty in background area counts reduces to: u n + ( B ) ( B) = 1 B n 1 In the spectrometry practice the statistical uncertainty of the net peak area, in connection with the Poisson distribution, is commonly expressed as: u ( N ) + B = G u( ) (1.a) Subtraction of Peak Environmental Background N = ( G B) I The environmental background interference peak is calculated as I = t t B I B where: I = number of count due to the environmental background t B B = the live time of background spectrum I B B = the net peak area of the peak in the background The variance of the background interference can be calculated as: u = ( I ) u( I B tb t u(i B ) B = the uncertainty of the net peak area for the interference peak, it can be calculated by equation (1.a). In case of the presence of an interference peak, i.e. a residual area in the ROI due to environmental background radiation or detector contamination, etc. determined by a separate background measurement, the following equation shall be used instead of (1.a): ( G + u( B) u( ) ) ) u ( N ) = + I (1.b)

5 The quantification of peak area uncertainty is well described in Genie 000 Customization Tools G V.1./ p Non-statistical errors connected with the calculation of net peak area and uncertainty of net peak area Determined by the spectrum evaluation software Expert comments: The calculation of net area and net area uncertainty is also associated with no pure statistical errors, as: - Set of ROI, i.e. peak width, - Set of width of background regions, - Curve fitting for the photopeak. Detector Efficiency Determined by the spectrum evaluation software The efficiency calibration consists of the following steps: collection of spectrum of the calibration standard, evaluation of the spectrum, calculation of photo peak efficiencies and fit of the energyefficiency curve. ε E = A Ei N E t γ K d i Where: K = the decay correction for radionuclide I, i K ln t e T1/ = e t e = the elapsed time between the start of acquisition and the stated reference time in the certificate T 1/ = the half-life of this nuclide Uncertainty Sources in the Efficiency Calibration: Activity in the reference standard, Preparation of calibration standard, Peak areas in calibration spectrum, Decay correction, Fitting of energy-efficiency curve,

6 Difference in calibration and measurement geometry, Shift of the peak energy. Branching ratio Activity and preparation of the calibration standard The combined uncertainty of the activity of radionuclides in a reference standard and preparation of the calibration geometry shall be given in the certificate attached with it. The value of relative uncertainties does not exceed 1- percent, generally. If the reported uncertainty is given with confidence level, it has to be divided by the appropriate percentage point on the normal distribution for the level of confidence given to calculate the standard deviation. Without confidence level, it is normally appropriate to assume a rectangular distribution. The uncertainty should be divided by 3 1/ to calculate the standard deviation. Net Peak Area Determined by the spectrum evaluation software Expert comments: The statistical uncertainty of net peak areas of calibration spectrum shall be reduced by use of high activity standards and long measuring time. However, the use of very high activities should also be avoided, because of the possible uncertainty from pile-up in the measuring equipment. In practice, a dead time up to 3-5 percent is quite acceptable. Due to the summation effect the use of radionuclides with cascade decay scheme needs careful investigation for some measuring geometries. It can be stated, however that for the commonly used geometries at the IAEA WBC (in-vivo) the relative uncertainty from the summation effect is well below 1- percent. The relative statistical uncertainty of the net peak areas in the calibration spectrum can be kept below 5 percent, usually. The variation of background plays only role in case of interference peaks, when the correction of the peak net area is based on a separate background measurement. Therefore, the frequency of background measurement shall be high enough to exclude the deterministic or systematic uncertainty and the measuring time long enough to reduce the relative statistical uncertainty to less than 5-10 percent. For the calculation of it the equation (1.a) or (1.b) can be used. Decay correction Determined by the spectrum evaluation software The uncertainty of the decay correction factor is calculated as K ln() t u( K) = e u( T1/ ) ( T ) 1/ In all cases, if the u(t 1/ ) is not available, it is set to zero.

7 Fitting of energy-efficiency curve Determined by the spectrum evaluation software Expert Comments: Most of the spectrum evaluation software offer the possibility to fit different energy-efficiency curves on the measured values. To decide the goodness of fit of the efficiency curve the following criteria shall be evaluated: chi-square value of fit and systematic difference between the fitted curve and several measuring points in any energy regions. The relative uncertainty associated with the efficiency curve fit shall not exceed -3 percent. Difference in calibration and measurement geometry Determined by expert judgment. The equality of calibration and measurement geometries shall refer to the following factors in general: distribution of radionuclide, volume, shape or dimensions, mass, density, atomic number or effective atomic number, mass number. The problem is rather complex for in vivo-measurements. The preparation of a calibration standard, so called phantom shall take into consideration as many factors as it possible. In the practice it means, that the phantom should be anthropomorphic, made from tissue equivalent material of the same density as the human body. Based on calibration results the relative uncertainty arising from the use of efficiency of the closest, but not exactly the same mass of phantom is well within 5 percent, assuming 15 kg steps of mass increase in the set of calibration phantoms. The most serious uncertainty is associated with the distribution of radionuclides in the human body. In practice several approaches are used: homogeneous distribution, lung, skull, thyroid measuring geometries. As the real distribution of the radionuclide in the person to be measured is unknown the only possibility to use the measuring geometry, which is the best approximation considering the intake route, biokinetic characteristics of radionuclide and its chemical compound. It should be noted, that exist methods to get information on the distribution of radionuclide in the body, however these cannot be used routinely. However, the overall relative uncertainty arising from the unknown and possible different from the calibration phantom distribution of the radionuclide is less than about percent except of low energy photons, i.e. for energies below kev. Shift of the peak energy Determined by expert judgment. The shift of the photopeak energy has only minor influence on the efficiency, usually. The maximum of the derivative of the efficiency curve, except of again the energies below kev, is about 10-7 /kev, which is negligible comparing the efficiency of approx However, the synchronization of spectra of multiple detector assemblies shall be ensured to avoid the uncertainty arising from the incorrect fit for wide and non-gaussian peaks. In practice, the shift of peaks of the spectra summed up is acceptable up to 1- kev.

8 Combined standard uncertainty for the efficiency calibration The standard uncertainty u(ε) of the detector efficiency can be calculated as: u( N) u( A) u( γ ) u( K) u( ε ) = ε N A γ K Branching ratio Determined by the spectrum evaluation software Expert comments: There are many nuclide libraries, data sets containing gamma photon emission probabilities (yields) for radionuclides. The spectrum evaluation software contains also editable nuclide library, usually. There could be no remarkable differences of yields given in different data sources, at least for string peaks of commonly used radionuclides. However, it is worth to mention, that the gamma emission probabilities are given for the decay of the radionuclide and not the parent nuclide, generally. A simple example: 137 C is a pure beta-emitting radionuclide, the gamma photons of kev are emitted by the radioactive daughter, 137m Ba. The yield of the gamma line of the above energy is for 137m Ba, however the 137 Cs transition to 137m Ba has a branching fraction of It means, that the gamma emission probability for the decay of 137 Cs is 0.898x0.946 = 0.85, instead of 0.898, even if the parent and daughter radionuclides are in radioactive equilibrium. Finally, it can be concluded, that following a careful check of nuclide library of the spectrum evaluation software, the uncertainty associated with the gamma emission probability is usually negligible. Measuring time Determined by expert judgment. Although, the dead time of the ADC is compensated for each measuring equipment (live-time correction) the very high count rates, resulting dead time higher than about 5-10 percent without pile up rejection shall be avoided. In normal spectrometry practice the count rates are very low usually, therefore the uncertainty of the measuring time is negligible. Environmental effects Determined by expert judgment. The most important environmental factor, which might influence the measurement result, is temperature. However, the change of temperature can cause mainly the change of amplification, which results in peak shift. As it was stated above the peak shift has only minor effect on efficiency. Otherwise, the temperature stability of the spectrometers are high enough to ensure that there is no observable peak shift for the temperature range of normal laboratory conditions.

9 Attenuation Corrected Efficiency Lung counting efficiency varies greatly with chest wall thickness. A facility must have chest wall thickness correction factors available to make an accurate estimate of activity in a subject's lung. The JAERI phantom can be used with an overlay plate that will increase the chest wall thickness. The range of thicknesses (Muscle Equivalent Chest Wall thickness) that can be simulated varies from cm (no overlay) to 3.36 cm. Chest Wall Thickness Determined by expert judgment CWT weight[ kg] = height[ cm] The uncertainty is assumed to be 15%.

10 Calculation of the combined standard uncertainty of the measuring result in the high arrangement ) ( ) ( ) ( ) ( Ej u u N N u A A u = γ γ ε ε Where: Ej = combined uncertainty for the expert judgment

11 Practical Example High Energy Arrangement For the Cs kev line of the file CNF, the calculations can be illustrated as follow File Cs-137 activity [Bq] 5.73 Total reported uncertainty [%] Reference Date :46 Measuring date: :46 Method Description Uncertainty in Percent Net Peak Area (includes *) statistical (Poisson distribution) and * Non-statistical (set of ROI, peak fitting) * Spectrum Evaluation Software GENIE 00 Efficiency (includes *) 1.03 Activity in the reference standard (certificate) * Curve fitting * Decay correction * Net Peak Area (statistical and non-statistical) * Branching ratio * Nuclide data (includes *) < 0.1 Decay correction * Branching ratio * Square of combined uncertainty of the above factors difference in calibration and measurement geometry 15 Cascade summing (calibration) - Expert Judgment shift of photopeak energy < 0.1 gamma emission probability < 0.1 measuring time( dead time) < 0.1 stability against environmental effects < 0.1 Square of combined uncertainty of the above factors 5 The overall combined uncertainty for the activity in this example is: u ( A) = = 4.50% instead of 19.37%

12 N E Sample γ Ei Sample Expert judgment Background Correction Attenuation N Ei Standard K Standard Attenuation A Ei Standard Live time Dead time γ Ei Standard A Ei T 1/ ε E MEQ-CWT CWT Figure : Uncertainties in WBC for the low energy arrangement 1

13 N E Sample γ Ei Sample Expert Judgment Background Correction Attenuation N Ei Standard Attenuation A Ei Standard A Ei γ Ei Standard Dead time K Standard T 1/ ε E Live Time Figure 3 Uncertainties in WBC for the high energy arrangement

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