Biomedical Engineering Reference
In-Depth Information
specific effective energies for a newborn and children of ages 1 y, 5 y, 10 y, and
15 y as well as a 58-kg adult female and the 70-kg adult reference man. The reader
is referred to Section 16.13 for additional information on decay-scheme data for
internal dosimetry.
16.9
Number of Transformations in Source Organs over 50 Y
The final step needed in the methodology for obtaining the committed quantities
is the determination of the numbers of transformations
U
S
that occur in source
organs and tissues S during the 50 y following the intake of a radionuclide. We
present some detailed calculations for a two-compartment model, consisting of the
body fluids (transfer compartment
a
) and a single additional compartment
b
.
After the intake of an initial activity
A
0
of a radionuclide into compartment
a
at time
t
0 (with no prior activity present), Eqs. (16.37) and (16.38) describe the
time-dependent activities in
a
and
b
. We obtain the number of transformations
U
a
and
U
b
of the nuclide in the two compartments from time
t
=
=
0
to any subsequent
time
T
by integrating the activities:
λ
a
e
-(λ
R
+λ
a
)
t
T
T
A
0
λ
R
+
U
a
(
T
)
=
q
a
(
t
)d
t
=
-
(16.46)
0
0
A
0
λ
R
+
λ
a
(1-e
-(λ
R
+λ
a
)
T
)
=
(16.47)
and
T
U
b
(
T
)
=
q
b
(
t
)d
t
(16.48)
0
1-e
-(λ
R
+λ
a
)
T
λ
R
+
λ
a
.
-
1-e
-(λ
R
+λ
b
)
T
λ
R
+
λ
b
λ
a
A
0
λ
b
-
λ
a
b
=
(16.49)
The numbers of transformations
U
a
and
U
b
in compartments
a
and
b
for a ra-
dionuclide with decay constant
λ
R
can thus be evaluated explicitly for the commit-
ted equivalent dose (
T
=
50
y), given the metabolic parameters
λ
a
,
λ
b
,and
b
.
Example
Use the two-compartment model just described for a radionuclide having a half-life
of 0.430 d. The metabolic half-life in the body fluids (compartment
a
)is0.25d,the
fraction
b
=
0.22 of the nuclide goes to organ
b
when it leaves
a
, the metabolic half-life
in
b
is 9.8 y, the organ weighting factor for
b
is
w
T
=
0.05, and the mass of
b
is 144 g.
Calculate the number of transformations
U
a
and
U
b
of the radionuclide in the two
compartments during the 50 y following the single entrance of 1 Bq of the radionu-
clide into compartment
a
at time
t
=
0. If the radionuclide emits only beta particles
with an average energy
E
=
0.255 MeV, what are the resulting committed equivalent
