Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

RADIATION SAFETY GUIDES 401
segment to be as listed in Figure 8-19. Furthermore, the movement of the contents
between compartments is assumed to follow first-order kinetics, with compartmental
clearance rates as shown in Figure 8-19. The time rate of change of the contents of
each of the four compartments can be calculated on the basis of mass balance. The
increase or decrease in the quantity of radionuclide in any of the compartments is
simply equal to the difference between what goes in and what goes out:
Rate of change of contents = rate in − rate out. (8.43)
If we have a constant input rate, ˙
I per day, as in the case of continuous ingestion of
radioactivity in food or continuous inhalation of a radioactive aerosol that is cleared
from the lung into the GI tract, then the mass balance equation for the stomach
becomes
dq
dt
St
= ˙
I − λStqSt − λRqSt, (8.44)
where q may be measured either in SI units or in traditional units and λ is the turnover
rate per day. When the amount of activity entering into the stomach is equal to the
amount leaving, we have a steady-state condition, and (dq/dt)ST becomes equal to
zero. Under this condition, Eq. (8.44) becomes
˙
I = λStqSt + λRqSt. (8.45)
The stomach contents empty into the small intestine, whose kinetics are similar to
those of the stomach. The time rate of change of the contents, therefore, is described
by the difference between what enters from the stomach and what leaves the small
intestine. Material is cleared from the small intestine by two pathways:
1. by peristalsis into the upper large intestine, and
2. by molecular diffusion into the blood vessels in the inner surface of the small
intestine.
The difference between what goes into the small intestine and what leaves it is
expressed mathematically by
dq
= λStqSt − λSIqSI − λRqSI − λBqSI, (8.46)
dt
SI
where λB is the transfer rate of the radionuclide from the small intestine into the
blood and is given by Eq. (8.42). The dosimetric model of the GI tract assumes that
only water is absorbed into the bloodstream from the large intestine. The rate of
change of the radioactivity in the upper large intestine, therefore, is given by
dq
= λSIqSI − λULIqULI − λRqULI, (8.47)
dt
ULI
and for the lower large intestine, from which the radioactivity leaves the body, we
have
dq
= λULIqULI − λLLIqLLI − λRqLLI. (8.48)
dt LLI