The whole body retention at any time t-Tt of the fraction of initial radioactivity
inputed at time Tt is
E.y.e A tKi) (t-)
bel
Thus, the instantaneous activity at time t-T that remains following input during
dt is
oO
Af P e
-(Kgta)t Exe CED dt.
It follows that the instantaneous activity at time t-T that remains following
input during T is
T
J ° A£,PPe
-(Kpt)\)t
r.x.e
i*i
C0 +K;) (t-1)
dt .
The solution of the integral yields a general expression that depends on
the user defining t.
For example, if t is the fixed uptake interval, T, plus an
additional fixed post uptake interval, $, then the body burden at T + @ is
given by
AP°£) Lixi Ce
-(A+Kp)T
-e
“O4K))T) oe OK) ¢
K, ~ K.
As previously stated, Eq. (2) applied at Rongelap and Utirik, it was
for the situation that variable time t was the uptake interval.
Additionally,
persons who returned to the atolls in June 1954 and June 1957 did so with an initial body burden, q°.
The behavior of this contribution to body burden,
q, was embodied in the q° term of Eq. (2).
A similar model was used to relate