Plutonium Biokinetics in Human Body A. Luciani - Kit-Bibliothek - FZK

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The use of such values allows to characterize the uncertainty of the output variable by two numbers. In comparison to other uncertainty analysis techniques [169] (such as Taylor series based differential analysis, response surface methodology or Fourier amplitude test), Monte Carlo procedures have some important advantages: • The full range of each input variable is sampled and then used as input for calculating model predictions; • The uncertainty is evaluated without using surrogate models, i.e. an approximating model that resembles the original model under study and on which the uncertainty analysis can be performed more effectively; • The full stratification over the range of each input variable facilitates the identification of non-linearities, thresholds and discontinuities; • The approach is conceptually simple and can be easily implemented in iterative procedures. The most relevant drawback of using Monte Carlo techniques for uncertainty analyses is the fact that a large number of model evaluations are required. Therefore if the model is computationally expensive to evaluate or many input variables are considered and for each variable many values are sampled, the time and cost for performing the required calculations may be too large. In this context results of the above sensitivity analysis can be used for screening purposes in order to reduce the number of input variables that are considered in the uncertainty analysis [170]. Only those input variables that significantly affect model predictions for a certain output variable should be considered. Furthermore computational time and cost needs for uncertainty analysis can be reduced by adopting an effective procedure for the generation of the random values of the input variables. The Latin Hypercube Sampling (LHS) procedure [170] rather than random sampling techniques will improve the efficiency of random values generation. The LHS procedure is a stratified sampling technique that generates a sample of size m for each of the n input parameters in the following way: • The range of each input variable is divided into m non-overlapping intervals on the basis of equal probability. Such a division will therefore depend on the statistical distribution assumed for the input variable; • One value from each interval is randomly generated according to the statistical distribution in this interval; • The previous two steps are repeated for each of the n input variables; • The m values obtained for the x 1 input variable are paired in random manner with the m values of the x 2 input variable. These m pairs are combined in a random manner with the m values of the x 3 input variable and so on until all the n input variables are considered. The main advantage of the LHS procedure is that the full range of input parameters is sampled, whereas in a simple random sampling scheme, combinations of input parameter values could easily come from the same subintervals. In adopting the LHS procedure the choice of the sample size m should be carefully considered in relation to the number n of input variables. It is preferable that m (the size of the sample, i.e. the number of values sampled for each input variable) be greater than or equal to (4/3)•n [171]. Of course, if the model is simple and can be run quickly , then m could even be larger. The sensitivity analysis has already pointed out the main significant transfer rates for the urinary excretion, fecal excretion and blood content of Plutonium predicted by the optimized model (Model-b). These parameters represent the input variables of the uncertainty analysis. In accordance with similar recent studies [166] a log-normal distribution for the input variable was assumed. The range of variation of the transfer rates was set at the 1 st and 99 th percentile of the log-normal distribution centred around the base case values. 130
Geometric standard deviations ranging from 1.25 to 2.25 (at 0.25 intervals) were preliminarily assumed for the log-normal distribution of the input variables. The aim was to find out the geometric standard deviation (GSD) for the input variable distribution that would determine a urinary excretion of Plutonium (or fecal excretion or blood content) predicted by the model with an uncertainty comparable to the observed uncertainty of data from different human subjects. Therefore, assuming a certain geometric standard deviation for the transfer rates, the variance and the mean of Plutonium urinary excretion (or fecal excretion or blood content) predicted by the model were compared to the corresponding variance and mean for the experimental data. A variance comparison test was firstly performed by considering the ratio of the two estimates of variance, one calculated on the basis of the experimental data and the second one on model's predictions. If the variances turn out to be statistically equal, a mean comparison test was successively performed to test if the mean too can be considered statistically equal [172]. In order to use the previous statistical test a normal distribution of the data should be assumed. As model predictions of activity in urine, feces and blood (tested with a χ 2 test, [172]) and the bioassays (as reported in literature [111]) can be considered log-normally distributed, the statistical tests were performed on the logarithm of the values. Sufficient experimental data for calculating variances and means at each time point after injection are only available up to about 100 days post intake. Therefore only the most significant transfer rates in determining the activity in urine, feces and blood at short time (10 and 100 days post injection, in Figure 3.1.22, Figure 3.1.23 and Figure 3.1.24) were considered. They are summarized in Table 3.1.22. The results of the statistical analysis of means and variances are given in Table 3.1.23. It turns out that, in case of transfer rates with a GSD = 1.50, for 98% of the considered time points the model predicts a variance for the urinary excretion of Plutonium that doesn’t significantly differ from the variance based on the experimental data. Furthermore for 88% of all time points the means do not significantly differ as well. In case of a GSD = 1.75, the agreement is a little worse for the urinary excretion, but the fecal excretion and the blood activity predicted by the model significantly improve their agreement with experimental data. For 94% of the considered time points, the model predicts a variance for the fecal excretion of Plutonium that doesn’t significantly differ from the variance based on the experimental data. For 39% of the time points the mean doesn’t significantly differ as well. The corresponding values for the activity in blood are 57% and 50%, respectively. For higher values of the GSD the urinary excretion predicted by the model agrees less and less with the variance and the mean values based on the experimental data. Therefore a GSD = 1.75 can be reasonably assumed as a realistic parameter for the geometric standard deviation of the Model-b transfer rates, to reproduce the dispersion of the subjects’ values experimentally observed at short time. It is particularly interesting to point out that this choice is coherent with the factors suggested by ICRP 66 in Annex E [57] to estimate the uncertainty of several respiratory tract model parameters. For the remaining transfer rates affecting the model’s predictions at longer time, the aforementioned GSD (1.75) was assumed. The final Model-b predictions for the daily percentage urinary and fecal excretion and for the blood percentage content are presented in Figure 3.1.28, Figure 3.1.29 and Figure 3.1.30, respectively, with the relating uncertainties: the 16 st and 84 th percentiles (1 GSD) and the 1 st and 99 th percentiles. It turns out that the geometric mean of the values calculated on the basis of model’s predictions for log-normally distributed transfer rates coincide with the model’s predictions when basic values of the transfer rates are assumed. This was observed in all the following evaluations based on different scenarios of contamination. 131
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Forschungszentrum Karlsruhe in der
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Für diesen Bericht behalten wir un
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i ABSTRACT The biokinetic model pre
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ZUSAMMENFASSUNG Das von der Interna
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1 INDEX OF CONTENTS INDEX OF SYMBOL
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3 INDEX OF SYMBOLS Here a short glo
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Chapter 1 Introduction 5
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the duties of the Department for Ra
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adionuclide. Therefore only isotope
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stabilise the +4 oxidation state [1
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techniques adopted in the early pha
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present in spent and MOX reactor fu
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INTRAVENOUS INJECTION skin WOUND bl
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functions, defined as retained and
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the contamination event, of such as
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Table 1.3.2 Indicative 239 Pu detec
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The kinetics of Plutonium in the ki
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1.4.2 COMMENTS ON THE ICRP 67 MODEL
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Chapter 2 Data and measurements 31
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Therefore the radiolysis process, m
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Recent technologic developments in
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eu(t) = 0.19e −0.272t + 0.023e
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function for each of the considered
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the minimum detectable activity of
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2.2.2 AVAILABLE MEASUREMENTS Immedi
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Table 2.2.4 Daily fecal excretion o
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elements the spectral distribution
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The phoswich detector is based on t
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HPGe crystals are produced in cylin
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This quantity is normally expressed
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The peak is located in the region B
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To introduce the second quantity, t
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117 cm 3 h -1 for the incoming and
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Figure 2.3.8 The Lawrence Livermore
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three detectors are used. Two detec
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Table 2.3.4 Efficiency factors of p
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• the necessity of performing mea
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Table 2.3.7 Impulses in the measure
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2.4 ACTIVITY MEASUREMENTS IN BIOASS
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If more then one radionuclide is ma
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L A is the air layer in µgcm -2 ;
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The electrodeposition cell used for
Page 90 and 91: Table 2.4.1 238 Pu, 239 Pu and 241
Page 93 and 94: 3.1.1 MATHEMATICAL TOOLS 3.1.1.1 So
Page 95 and 96: calculating the amount of Plutonium
Page 97 and 98: 3.1.2 ANALYSIS OF THE ICRP 67 MODEL
Page 99 and 100: empirical curves given by Langham,
Page 101 and 102: the worst performance of the group.
Page 103 and 104: leave the total clearance from the
Page 105 and 106: Figure 3.1.4 shows that the use of
Page 107 and 108: 3.1.3 MODIFICATION OF ICRP 67 MODEL
Page 109 and 110: The structure of Polig’s skeleton
Page 111 and 112: Percentage daily urinary excretion
Page 113 and 114: of 0.693d -1 . The values of the F
Page 117 and 118: the basis of all the reference data
Page 119 and 120: Table 3.1.10 Transfer rates of the
Page 121 and 122: 3.1.4 VERIFICATION OF THE OPTIMIZED
Page 123 and 124: Table 3.1.13 Intakes and percentage
Page 125 and 126: soft tissue ST2 soft tissue ST0 sof
Page 127 and 128: For the routine application of Mode
Page 129 and 130: excreted by individuals aged sixty
Page 131 and 132: Table 3.1.20 Exponents and coeffici
Page 133 and 134: tract [57] to consider a contaminat
Page 135 and 136: The sensitivity coefficients for th
Page 137 and 138: Sensitivity coefficients S i Figure
Page 139: transfer rates on the Plutonium uri
Page 147 and 148: 3.2 APPLICATION OF THE OPTIMIZED MO
Page 149 and 150: lymph nodes, as in the LLNL phantom
Page 151 and 152: Americium in the lungs [Bq] 1000 10
Page 153 and 154: Daily urinary excretion [Bqd -1 ] 1
Page 155 and 156: long time is not yet described by t
Page 157 and 158: excretion that is one of the main i
Page 159 and 160: The comparison of model’s predict
Page 161 and 162: Americium in the lungs [Bq] 1000 10
Page 163 and 164: 153 CONCLUSIONS The optimized model
Page 165 and 166: Annex Quantities used in Radiologic
Page 167 and 168: present. As the radiation weighting
Page 169 and 170: w R is the radiation weighting fact
Page 171 and 172: 161 BIBLIOGRAPHY 1. Plutonium. W. K
Page 173 and 174: 29. Nenot, J.-C. and Stather, J. W.
Page 175 and 176: 55. International Atomic Energy Age
Page 177 and 178: 81. Crowley, J., Lanz, H., Scott, K
Page 179 and 180: 107. Hempelmann, L.H., Langham,W.H.
Page 181 and 182: 137. Breitestein, B.D., Newton, C.E
Page 183 and 184: 167. Harrison, J.D., Khursheed, A.,
Page 185 and 186: JOURNALS OWN PUBLICATIONS RELATED T
Page 187 and 188: 177 ACKNOWLEDGEMENTS Special thanks
Page 189 and 190: Name: Andrea Luciani Date and place
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Plutonium Biokinetics in Human Body A. Luciani - Kit-Bibliothek - FZK

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