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

RADIATION DOSIMETRY 235
In most instances, biological elimination follows first-order kinetics. In this case, the
equation for the quantity of radioactive material within an organ at any time t after
deposition of a quantity Q0 is given by
Q = Q0e −λRt e −λBt , (6.48)
where λR is the radioactive decay constant and λB is the biological elimination constant.
The two exponentials in Eq. (6.48) may be combined
Q = Q0e −(λR+λB)t , (6.49)
and, if
λE = λR + λB, (6.50)
we have
Q = Q0e −λEt
where λE is called the effective elimination constant. The effective half-life is then
(6.51)
TE = 0.693
. (6.52)
λE
From the relationship among λE, λR, and λB, we have
or
1
TE
= 1
+
TR
1
, (6.53)
TB
TE = TR × TB
. (6.54)
TR + TB
In Example 6.14, for 35 S, TR = 87.1 days. TB, the biological half-life in the testis,
is reported to be 623 days. The effective half-life in the testis, therefore, is
TE =
87.1 × 623
= 76.4 days,
87.1 + 623
and the effective elimination rate constant is
λE = 0.693
76.4 days = 0.009 d−1 .
It should be noted that the effective half-life of 35 S in the testis is less than either
the radiological or the biological half-lives. This must be so because the quantity of
a radionuclide in the body is continually decreasing due to radioactive decay and
biological elimination. For this reason, the effective half-life can never be greater
than the shorter of either the biological or radiological half-life.