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

Table 3.1.20 Exponents and coefficients of analytical functions for the urinary excretion rate
of Plutonium after ingestion (Model-b ).
Index i f 1 = 5•10 -4
1 4.77•10 -6
2 3.06•10 -7
3 5.63•10 -8
4 -4.18•10 -9
5 8.55•10 -9
6 9.06•10 -8
7 -8.24•10 -8
121
f 1 = 1•10 -4
f 1 = 1•10 -5
c i λ i[d -1 ] c i λ i[d -1 ] c i λ i[d -1 ]
7.5•10 -1
9.5•10 -2
8.2•10 -3
1.2•10 -3
8•10 -4
1•10 -5
8•10 -6
9.54•10 -7
6.12•10 -£
1.13•10 -8
-8.36•10 -10
1.71•10 -9
1.81•10 -8
-1.65•10 -8
7.5•10 -1
9.5•10 -2
8.2•10 -3
1.2•10 -3
8•10 -4
1•10 -5
8•10 -6
9.54•10 -8
6.12•10 -9
1.13•10 -9
-8.36•10 -11
1.71•10 -10
1.81•10 -9
-1.65•10 -9
7.5•10 -1
9.5•10 -2
8.2•10 -3
1.2•10 -3
8•10 -4
1•10 -5
8•10 -6
For an intake via inhalation the exponents of the first three terms describing the shortterm
excretion are equal under all the conditions of exposure. The exponents of the last four
terms depend on the type of absorption, but turn out to be almost independent on the AMAD
of the aerosol. The exponential expression deviates from the exact analytical solution of the
model by less than 5% for the first 10 days post-intake and less than 2% up to 20,000 days
post-intake. In case of ingestion it was possible to obtain reasonably good fitting using the
same exponents for all the standard f 1 values. The coefficients of the exponential terms were
firstly calculated for the analytical function of the Plutonium urinary excretion relating to f 1 =
5•10 -4 . The same coefficients can be used for the analytical functions relating to the other two
f 1 values (1•10 -4 and 1•10 -5 ). In the latter cases the coefficients for f 1 = 5•10 -4 should be
multiplied by factors derived from the f 1 values (1•10 -4 /5•10 -4 = 0.2 and 1•10 -5 /5•10 -4 = 0.02).
Even with this extreme simplification the exponential expression deviates from the exact
analytical solution of the model by less than 15% for the first 10 days post-intake and less
than 10% up to 20,000 days post-intake.
3.1.5.3 Sensitivity analysis
A sensitivity analysis was applied to the opimized model in order to pick out the most
significant parameters for the urinary excretion of Plutonium. To a lesser extent fecal
excretion and activity in blood were also considered. Respiratory tract and gastrointestinal
compartmental models connected to the systemic model were considered as well, and the
sensitivity analysis was applied to their parameters too, in order to consider real cases of
contamination via ingestion or inhalation. The results of the present sensitivity analysis have
two main applications. First of all it allows to identify the transfer rates and in a certain way
the physiological processes whose alteration could explain possible significant deviations of
the measurements of the excreted activity from the model predictions. Secondly they will be
used as a screening method to reduce the number of model parameters that must be
considered in the subsequent analysis of the uncertainty of the model predictions for
Plutonium excretion in urine. As usual great importance was placed on the urinary excretion
of Plutonium because the monitoring of the internal contamination following an intake of a
Pu-radioisotope is mainly based on measurements of activity in biological samples, more