804
TURNER
where
D, is the number of grams of food consumed and C; is the
amount of '!I per gram of food. This series does not represent the
amount in the thyroid after 30 days. The '"I that reaches the thyroid is
lost by both secretion and radioactive decay; therefore it declines
exponentially with an effective half-life reflecting these two processes,
Hence the amount that reaches the thyroid on the first day is reduced
by the end of 30 days to
FD,C,E”
(2)
where E equals ('4)!/> and b, the effective half-life of '*'I in the thyroid
in days, equals 0.693/2 g- The term et equals Et, The amount ingested
on the i¢h day after fallout and remaining 30 days afterward is
FD,C, E%+!-i
(3)
The required series for 30 days is thus
A= FD,C,E™ + FD,C,E?? ... + FD39C49E
(4)
So far C,; has been taken as the amount of 13ty per gram of food at
the time of consumption. Yet we wish to derive C, from the amount
deposited on vegetation on the first day. The loss of ‘I from vegetation is approximately exponential, but the effective half-life, v,, Varies
from day to day. The relation between the amount of '*/I on vegetation
consumed on the second day and the original amount on vegetation may
be expresSed as
Cy = XV,
(5)
where x, is the original amount of }*I on the vegetation making up the
meal consumed on the second. day and
V; = (A)iv
(6)
On the ith day, the relation would be
C, = x,V,VoV3..- Vig
i
(7)
-
or
inl
c,=x, II v.
(8)
jer?
The expression for A given in Eq. 4 can now be rewritten
29
A = F(D,x,E™ + D)x,V,E?? + Dyx,V,V,E"®... + DgpXg0E I V;) @)