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

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

= 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