Evaluating 241Am Ingrowth in an In Vivo Count cont'd

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DOE-STD-1128-98
by routine in vivo chest counting or in long-term monitoring of residual wound
content.
While many available internal dosimetry computer codes will calculate the projected
241Am lung content following an intake (accounting for ingrowth in the process),
none of the current codes will do curve-fitting from long-term data and at the same
time adjust the data for ingrowth. Therefore, the following simplistic method was
developed to assess that data.
An estimate of the 241Am ingrowth can be made by assuming that, at the time of
intake (t = 0), all the material that will compose the long-term component is
deposited in a single compartment and that the rate of transfer of material from the
compartment at any subsequent time t is proportional to the quantity of material
remaining in the compartment (i.e., simple exponential transport kinetics). The
following equation will then describe the buildup of 241Am in that compartment
following an initial deposition of 241Pu and 241Am and a given or assumed effective
clearance rate:
(e - k e, Pu t - e - k e, Am t) + A O, Am e - k e, Am t
A t, Am = λ  r, Am
A O Pu
(5.9)
k e, Am - k e, Pu
where At,Am = activity of 241Am at time t
λ  r,Am
= radiological decay constant for 241Am
A0,Pu
= activity of 241Pu at time 0
ke,Am
= effective clearance rate of 241Am
ke,Pu
= effective clearance rate of 241Pu
A0,Am
= activity of 241Am at time 0
t
= elapsed time
The effective clearance rate (ke) of any nuclide is the sum of the radiological decay
constant ( λ  r) and the biological clearance rate ( λ  bio). By assuming that the biological
clearance rate is constant for both parent and progeny nuclides, the equation reduces
to three unknowns: the initial amount of parent, the initial amount of progeny, and
the biological clearance rate. These unknowns can be dealt with by assuming a
standard isotopic composition at the time of intake and then solving the equation for
a biological clearance rate using an iterative process until the calculated result
matches the observed result at a given time t. A computer or calculator algorithm can
eliminate the need for lengthy hand calculations.
5-34

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