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

The exponents relating to the physical decay are given in Table 3.1.18
Table 3.1.18 Physical decay constants to be used in the analytical function for the urinary
excretion of Plutonium (exp(- R t)).
238 Pu
λ R [d -1 ] 2.17•10 -5
239 Pu
7.89•10 -8
120
240 Pu
2.91•10 -7
241 Pu
1.32•10 -4
In order to calculate the other exponential terms the urinary excretion curves
calculated on the basis of Model-b were plotted in a semi-logaritmic graph to reveal the
conspicuous slopes that could be mathematically described with suitable exponents. A linear
fitting procedure was then carried out to calculate the coefficients of the exponential terms.
The whole procedure has two main advantages:
• It was avoided to using non-linear fitting procedures, as they are strongly depending on
the initial values of the parameters and therefore subjected to a close local minimum;
• The preliminary graphical analysis allowed to see some common trends among the
excretion curves for different scenarios of contamination. It was therefore possible to limit
the variation of parameters when different scenarios were considered, making it easier to
implement the analytical curves in the monitoring practice.
The coefficients and the exponents for the exponential terms relating to the biokinetic
transfers of the radionuclide in the body are given in Table 3.1.19 and Table 3.1.20 in case of
inhalation and ingestion, respectively. In part they were already published in a recent
publication [163].
Table 3.1.19 Exponents and coefficients of analytical functions for the urinary excretion rate
of Plutonium after inhalation (Model-b ).
Index i Type M
f 1 = 5•10 -4
AMAD = 1 μm AMAD = 5 μm
Type S
f 1 = 1•10 -5
Type M
f 1 = 5•10 -4
Type S
f 1 = 1•10 -5
c i λ i[d -1 ] c i λ i[d -1 ] c i λ i[d -1 ] c i λ i[d -1 ]
1 3.03•10 -4 8.8•10 -1
2 8.81•10 -6
3 -2.18•10 -6
4 1.06•10 -5
5 1.69•10 -6
91•0 -2
11•0 -2
6•10 -3
1•10 -3
6 1.71•10 -5 1•10- 5
7 -1.56•10 -5 8•10- 6
2.94•10 -6 8.8•10 -1
5.07•10 -8
3.91•10 -9
9•10 -2
1•10 -2
-1.34•10 -7 1.5•10 -3
1.89•10 -7
-8.91•10 -8
2.44•10 -7
8•10 -4
2•10 -4
4•10 -5
3.60•10 -4 8.8•10 -1
1.20•10 -5
1.61•10 -6
4.81•10 -6
1.12•10 -6
1.17•10 -5
-1.07•10 -5
9•10 -2
1•10 -2
6•10 -3
1•10 -3
1•10 -5
8•10 -6
3.57•10 -6 8.8•10 -1
1.03•10 -7
2.84•10 -8
9•10 -2
1•10 -2
-7.36•10 -8 1.5•10 -3
1.03•10 -7
-5.11•10 -8
1.30•10 -7
8•10 -4
2•10 -4
4•10 -5