t
= time post-onset of uptake, days,
X
= instantaneous fraction of atoms decaying per unit time, day~!
p° = initial atom ingestion rate, atoms day~!,
K; = instantaneous fraction of atoms removed from compartment i by
physiological mechanisms, day~!,
Xj = compartment i deposition fraction,
x; = the number of atoms in compartment i relative to the number in all
compartments at the onset ef declining continuous uptake, (t=0),
U
= instantaneous urine activity concentration, Bq gol,
Ue = subject urine excretion rate, 2% day~!,
fi = fraction from GI tract to blood,*
fi = fraction excreted by the urine pathway,
Kg = instantaneous fraction of atoms removed or added to the atom uptake
per unit time, day7!, due to factors other than radioactive decay,
q
= instantaneous body burden, Bq,
q
= body burden at the onset of uptake, Bq,
D
= the number of disintegrations in all compartments occurring during
the uptake interval, Bq days.
The development of Eqs. (1), (2),~hmd (3) was based on the following convolution integral.
At some variable time, T, defined during a fixed uptake
interval, T, the daily activity ingestion rate crossing the gastrointestinal
tract to blood is given by
Af,P o e
-(kgtaA)T ‘