Physics and Radiobiology of Nuclear Medicine

(Jeff_L) #1

Using Eq. (3.4)


At= 150 ×e−0.1155×^5
= 150 ×e−0.5775
= 150 ×0.5613
=84.2 mCi (3.1 GBq) at 3 p.m.

Problem 3.3
If a radionuclide decays at a rate of 30%/hr, what is its half-life?


Answer


l=0.3 hr−^1

Problem 3.4
If 11% of 99mTc-labeled diisopropyliminodiacetic acid (DISIDA) is elimi-
nated via renal excretion, 35% by fecal excretion, and 3.5% by perspiration
in 5 hr from the human body, what is the effective half-life of the radio-
pharmaceutical (Tp=6 hr for 99mTc)?


Answer


Total biological elimination =11% +35% +3.5%
=49.5% in 5 hr
Therefore,Tb≈5hr
Tp=6hr

Successive Decay Equations


General Equation


In the preceding section, we derived equations for the activity of any
radionuclide that is decaying. Here we shall derive equations for the activ-
ity of a radionuclide that is growing from another radionuclide and at the
same time is itself decaying.
If a parent radionuclide pdecays to a daughter radionuclide d, which in
turn decays to another radionuclide (i.e.,p→d→), then the rate of growth
of dbecomes


T

TT

TT

e

bp
bp

=

×

+

=

×

+

==

56

56

30

11

27.hr

t 12

0 693 0 693

03

== = 231

..

.

.

l

hr hr

l=

0 693

12

.

t

Successive Decay Equations 29
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