282 Radiation Dosimetry: Instrumentation and Methods
The capsule is 5 mm long and 1.1 mm in overall diameter
and its distal end is a steel cap with a 0.55-mm radius. The
dose calculation formalism proposed by AAPM Task Group
43 has been followed. Dose rate (r,
), in medi-um at point
(r,
), where r is the distance in cm from the active source
center and
is the polar angle relative to the longitudinal
axis of the source, is expressed as:
(4.56)
where
S
k
is the source air-kerma strength in units of U (1 U
l
Gym
2
h
1
1 cGy cm
2
h
-1
). is the dose rate constant
defined as the dose rate in the medium per unit source
strength at radial distance r
0
1 cm along the transverse
axis, and
0
/2, so that
(4.57)
G(r,
) is the geometry function in units of cm
2
which
accounts for the variation of relative dose due only to the
spatial distribution of activity within the source, ignoring
photon absorption and scattering in the source structure.
At distances greater than approximately 2–3 times the
active source dimension (i.e., for the given source greater
than approximately 1 cm), the geometry function is well-
approximated (within 1%) by the inverse-square law used
in point-source approximation. g(r) is the dimensionless
radial dose function which accounts for photon attenuation
and scattering in the medium and encapsulation along the
transverse axis (
0
/2) and is by definition unity at r
0
1 cm, i.e., g(1) 1, so that
(4.58)
F(r,
) is the dimensionless dose anisotropy function
which accounts for photon attenuation and scattering at
any polar angle
, relative to that for
0
/2, and is by
definition unity at
0
/2; i.e., F(r,
/2) 1, so that
(4.59)
An equivalent dose calculation formalism in terms
of the tissue attenuation factor,
T(r), is also used in
many computer-assisted brachytherapy treatment-planning
systems:
(4.60)
In this expression the product g(r) of Equation (4.56)
has been replaced by the product fT(r). The factor f is
the air kerma in air to water kerma in air conversion
factor, which is equal to the ratio of mean mass energy
absorption coefficients for water and air. This ratio is
almost constant and has a value of 1.11 for energies
between 150 keV and 4 MeV. Thus, f is also equal to 1.11
for the
192
Ir primary energy range. The factor T(r) is well-
approximated by the ratio of water kerma in water to
water kerma in air and accounts for the combined atten-
uation and scattering in water. It is noted that for the given
source, the formalism of Equation (4.60) is valid at radial
distances greater than approximately 1 cm, where, as
mentioned above, the geometry factor G(r,
) is well-
approximated by the inverse-square law.
TLDs were placed in small cylindrical TLD polysty-
rene receptors (3 mm in diameter and 6 mm long) having
a cylindrical hole of 1-mm diameter in their centers to
accommodate the dosimeters. A 30
30 1.1-cm
3
slab
of polystyrene, prepared in a milling machine with an
accuracy of 0.1 mm, was constructed to accommodate
TLD receptors and a plastic catheter (2-mm outer diame-
ter), inside which the source was driven. This slab was
sandwiched between other identical polystyrene slabs to
build a 30 30 30-cm
3
phantom which approximates
the water spherical phantom of 30-cm diameter used in
MC calculations. [59]
In Figure 4.80, radial dose functions calculated for
spherical water phantoms of different diameters (d
10–50 cm) are presented. The figure demonstrates that
phantom dimensions significantly affect the radial func-
tions at radial distances near phantom edges, where devi-
ations of up to 25% are observed. This effect is due to the
reduction of scatter contribution to overall dose at the
edges of the phantom and should be taken into account in
the case of estimating the dose near the body edges.
Using the MC code and the CSDA electron ranges
proposed by ICRU Report 37, the average starting energy
of the electrons generated in the TLD material was found
to be less than 100 keV over the whole range of measure-
ment distances and angles, and the corresponding
R was
less than 0.006 cm, thus giving the value of factor d less
than 0.02. As a result of this, the TLD material behaves
like a large cavity in
192
Ir
-rays, and the LiF TLD
response can be calculated using the simplified equation:
(4.61)
where
E
i
is the energy of the ith photon in the point of
measurement, (
en
/
)E
i,LiF
is the mass energy absorption
D
˙
D
˙
r
,() S
k
Gr,
()
Gr
0
,
0
()
---------------------
Fr,
()gr()
D
&
r
0
,
0
()S
k
gr()
D
˙
r,
0
()Gr
0
,
0
()
D
˙
r
0
,
0
()Gr,
0
()
-----------------------------------------
Fr
,()
D
˙
r,
()Gr,
0
()
D
˙
r,
0
()Gr,
()
------------------------------------
D
˙
r
,() S
k
f
1
r
2
----
Tr()Fr
,()
D
LiF TLD
D
water
--------------------
en
-------
water
LiF
E
i
en
-------
E
i,LiF
i
E
i
en
-------
E
i, water
i
Ch-04.fm Page 282 Friday, November 10, 2000 12:01 PM