Page 1
Benchmarking BrachyDose: Voxel based EGSnrc Monte Carlo calculations
of TG-43 dosimetry parameters
R. E. P. Taylor,a?G. Yegin, and D. W. O. Rogersb?
Ottawa Carleton Institute of Physics, Carleton University, Ottawa, Canada K1S 5B6
?Received 11 August 2006; revised 23 October 2006; accepted for publication 23 October 2006;
published 10 January 2007?
In this study, BrachyDose, a recently developed EGSnrc Monte Carlo code for rapid brachytherapy
dose calculations, has been benchmarked by reproducing previously published dosimetry param-
eters for three brachytherapy seeds with varied internal structure and encapsulation. Calculations
are performed for two125I seeds ?Source Tech Medical Model STM1251 and Imagyn isoSTAR
model 12501? and one103Pd source ?Theragenics Model 200?. Voxel size effects were investigated
with dose distribution calculations for three voxel sizes: 0.1?0.1?0.1 mm3, 0.5?0.5?0.5 mm3,
and 1?1?1 mm3. In order to minimize the impact of voxel size effects, tabulated dosimetry data
for this study consist of a combination of the three calculations: 0.1?0.1?0.1 mm3voxels for
distances in the range of 0?r?1 cm, 0.5?0.5?0.5 mm3voxels for 1?r?5 cm and 1?1
?1 mm3voxels for 5?r?10 cm. Dosimetry parameters from this study are compared with values
calculated by other authors using Williamson’s PTRAN code and to measured values. Overall,
calculations made with Brachydose show good agreement with calculations made with PTRAN
although there are some exceptions. © 2007 American Association of Physicists in Medicine.
?DOI: 10.1118/1.2400843?
I. INTRODUCTION
Yegin et al. have recently developed BrachyDose,1a Monte
Carlo ?MC? code for rapid brachytherapy dose calculations.
This code represents a valuable step forward since it allows
rapid ?5 min or less? Monte Carlo dose calculations for pros-
tate implants based on the well established EGSnrc3,4code.
The EGS Monte Carlo code has been used previously in
brachytherapy applications,5–12however, this is the first EGS
user code capable of modeling the more complicated geom-
etries found in many brachytherapy seeds. Although Will-
iamson’s PTRAN13,14code has been used for these applica-
tions for many years, it is valuable to have a completely
independent code. BrachyDose has the added advantage of
being able to model electron transport which is important for
modeling miniature x-ray sources being developed for
brachytherapy applications.15,16In this study, electron trans-
port is not done since at the energies relevant to the calcula-
tions here, the range of electrons is effectively zero and their
energy can be considered to be deposited locally.
The dosimetry protocol outlined by the AAPM’s Task
Group 4317,18recommends that investigators benchmark new
MC codes by reproducing previously published dosimetry
parameters for at least one widely used source. In this study,
BrachyDose has been used to calculate comprehensive
TG-43 dosimetry parameters for three sources with varied
internal structure and encapsulation. Calculations are per-
formed for two
STM125119–21and Imagyn isoSTAR model 1250122–25? and
one103Pd source ?Theragenics Model 2008,10,11,26–28?.
The majority of MC derived brachytherapy dosimetry pa-
rameters, available in the literature have been calculated us-
ing Williamson’s PTRAN13,14MC code. Unlike PTRAN,
BrachyDose calculates volume-averaged doses to voxels
125I seeds ?Source Tech Medical Model
rather than using a point kerma estimator. This makes it im-
perative that voxel size effects be considered. Both the
STM1251 and Model 200 seeds have highly anisotropic dose
distributions at small angles relative to the seed axis and thus
make good candidates for benchmarking a voxel based
Monte Carlo code like BrachyDose. To investigate the effect
of voxel size on dosimetry parameters, calculations were
made with three different voxel sizes. Dosimetry parameters
from the three sets of calculations are presented and com-
parisons are made with data calculated by other investigators
using PTRAN.
BrachyDose calculated dose rate constants, radial dose
functions and anisotropy data have been tabulated for the
three sources considered here. In a related study a compre-
hensive set of dosimetry data for 16 different seeds ?12125I
and 4103Pd? will be presented.
II. MATERIALS AND METHODS
A. BrachyDose code
BrachyDose1,2is a new EGSnrc Monte Carlo user code
capable of doing full brachytherapy prostate implant calcu-
lations in 5 min on a single CPU. BrachyDose may be used
to do calculations for192Ir,125I,103Pd and miniature x-ray
sources, the latter case requiring electron transport within the
source only. The incorporation of Yegin’s multi-geometry
package29into the BrachyDose code allows all of these dif-
ferent sources to be modeled in detail. In order to study the
effects of cross section uncertainties, BrachyDose also has
the capability to scale the cross section of any material by a
user-specified factor.
BrachyDose scores the collision kerma per history in vox-
els via a tracklength estimator. Due to the low energies in-
445 445Med. Phys. 34 „2…, February 20070094-2405/2007/34„2…/445/13/$23.00© 2007 Am. Assoc. Phys. Med.
Page 2
volved, charged particle equilibrium can be assumed and col-
lision kerma can be considered equal to the absorbed dose to
the medium. Dose is calculated as
Eiti??en
Dj= Kcol
j
=?
i
??
i?Vj,
?1?
where Djand Kcol
voxel, Eiis the energy of the ith photon, and tiis the track-
length of that photon in the voxel. The mass-energy absorp-
tion coefficient corresponding to energy Eiis??en
the volume of the voxel.
j
are the dose and collision kerma in the jth
??iand Vjis
B. Brachytherapy sources
Source geometries including both encapsulation and inter-
nal structure were modeled using Yegin’s multi-geometry
package.29This geometry package gives users the ability to
generate complex geometries composed of rectilinear, cylin-
drical, spherical and conical shapes. Figure 1 shows cross
sections of the three seeds modeled in this study. The figures
were generated using a separate code, MGview, which is part
of the multi-geometry package.
The STM1251125I source consists of a cylindrical gold
rod with 0.18 mm diameter which is inside of 3.81-mm-long
hollow aluminum wire with a diameter of 0.51 mm. The alu-
minum wire including the ends is coated with nickel
?1.9 ?m?, copper ?2.5 ?m? and radioactive iodine ?17 nm?.
The source is encapsulated in a titanium tube with 0.08
-mm-thickwalls, 0.81-mm-outer
0.13-mm-thick cylindrical end welds. All internal gaps are
filled with air for all the seeds. The overall source length is
4.5 mm. These are the same dimensions used in the study by
Kirov and Williamson.19
The Imagyn
coated with AgI, encapsulated in a titanium tube with ap-
proximately hemispherical end welds. The tube has 0.05
-mm-thick walls, a diameter of 0.8 mm and an overall length
of 4.5 mm. The thickness of the AgI coating on the internal
diameter and
125I source consists of five silver spheres
spheres is not listed in any of the relevant references and is
assumed to have negligible thickness in this study. There are
inconsistencies in the literature regarding the dimensions of
the silver spheres and the end welds for this source.
Gearheart22et al. report that the seed has 0.64 mm spheres
and 0.5-mm-thick end welds while Nath and Yue23report
0.65 mm spheres and 0.6-mm-thick end welds. TG43U1 lists
the diameter of the spheres as 0.56 mm and does not mention
the weld thickness.18Since comparisons are made with Gear-
heart et al.’s MC results, dimensions given in their paper
were used in this study.
The Model 200103Pd source consists of two cylindrical
graphite pellets coated with radioactive palladium and sepa-
rated by a cylindrical lead marker. The graphite cylinders
have a diameter of 0.56 mm and a length of 0.89 mm. The
lead marker is 1.09 mm long and 0.5 mm in diameter. The
thickness of Pd on the graphite is 2.2 ?m. The encapsulation
for the Model 200 seed is a thin titanium tube that is
0.826 mm in diameter with wall thickness of 0.056 mm and
length of 4.5 mm. The ends are sealed with hemispherical
titanium end cups that are 0.04 mm thick. The dimensions
are the same as those in Monroe and Williamson’s30study.
C. Monte Carlo calculations
For the calculations in this study, electrons were not trans-
ported and the photon cutoff energy was set to 1 keV. Ray-
leigh scattering, bound Compton scattering, photoelectric ab-
sorption and fluorescent emission of characteristic x rays
were all simulated. All calculations used photon cross sec-
tions from the XCOM31database and mass energy absorp-
tion coefficients were calculated using the EGSnrc user-code
g. Photon spectra recommended in TG-43U1 were used to
sample incident photon energies and probabilities for both
125I and
order to get 1? statistical uncertainties of 2% or less at a
distance of 10 cm for all sources.
Dose calculations were done with the source positioned at
the center of a rectilinear water phantom ?mass density of
0.998 g/cm3? with dimensions of 30?30?30 cm3?effec-
tive radius of 18.6 cm?. Melhus and Rivard32have recently
shown that a radius of 15 cm provides adequate scattering
medium for calculating the radial dose function at 10 cm
within 0.3±0.1% and 1.1±0.2% for
respectively. Dose distributions surrounding the source were
scored in a grid of cubic voxels on the plane defined by the
seed and transverse axis. To take advantage of the inherent
symmetry of the geometry and reduce calculation times, dose
values from the four identical quadrants of the scoring plane
were averaged.
Calculations of the air kerma per history were scored in
vacuo, avoiding the need to correct for attenuation by air.
Mass energy absorption coefficients were calculated for air
with the composition recommended by TG43U1 ?40% hu-
midity?. In principle this is incorrect because air kerma stan-
dards always refer to dry air, but the difference is less than
0.01% at these energies. Characteristic x rays originating
from the titanium encapsulation were suppressed by discard-
103Pd. Up to 4?1010histories were simulated in
125I and
103Pd seeds,
FIG. 1. Cross section of sources used in this study. Detailed descriptions of
each source are given in the text. From top to bottom the sources are: ?1?
Source Tech Medical Model STM1251 ?125I?, ?2? Imagyn isoStar 12501
?125I?, ?3? Theragenics Model 200 ?103Pd?. Images were generated using
MGview, a geometry visualization tool for Yegin’s geometry package ?Ref.
29?. Sources are all drawn to scale ?same scale for all sources?.
446Taylor, Yegin, and Rogers: Benchmarking the EGSnrc user-code BrachyDose446
Medical Physics, Vol. 34, No. 2, February 2007
Page 3
ing fluorescent emissions with energies ?5 keV, which in
this case is equivalent to using a photon cutoff energy of
5 keV.
D. Voxel size effects
Dose scored in voxels is a volume averaged estimate of
the dose at the center of a voxel. If the real dose distribution
is given by D?r? then the dose in a voxel, Dvox, scored in a
volume ?V is given by
?V?
?V
Dvox=
1
dVD?r?.
?2?
For an arbitrary curve in one dimension, binned in intervals
of width ?r, this expression can be written as
?r?
ro−??r/2?
Dvox=
1
ro+??r/2?
drD?r?.
?3?
Expanding using a Taylor series around the center of the bin,
ro, gives33
Dvox= D?ro??1 +
D??ro?
24D?ro??r2+ O??r4??,
?4?
i.e., the calculated dose in the voxel represents the dose at the
midpoint of the voxel when the second and higher order
terms in Eq. ?4? are negligible.
As a simple example, consider a point source with a dose
distribution of D?r?=
?r. Equation ?4? can be used to give the expression
Dvox? D?ro??1 +?r2
4ro
Do
r2 scored in spherical shells of width
2?.
?5?
Figure 2 shows the ratio of the dose scored in the voxel
calculated using Eq. ?5? to the point dose at the midpoint
radius for three different shell thicknesses. For this simple
case of a
thickness leads to dose overestimates of 2.8% and 0.25% at 3
and 10 mm, respectively. Decreasing the thickness of the
shell to 0.1 mm leads to dose overestimates of less than 0.1%
at the same two points.
While the above isotropic example serves to illustrate the
effect voxel size can have on calculated dose distributions,
estimating the errors introduced by scoring dose in voxels
surrounding brachytherapy seeds is less straightforward. The
dose distribution surrounding a realistic seed may deviate
greatly from
within the seed and due to attenuation and scatter in the
source and surrounding medium.
To investigate voxel size effects, dose distribution calcu-
lations were done with three voxel sizes: 0.1?0.1?0.1,
0.5?0.5?0.5, and 1?1?1 mm3. Figure 3 is a plot of the
anisotropy function of the SourceTech model STM1250 seed
at r=0.25 cm calculated for the three different voxel sizes. It
is apparent that calculations done with 1 and 0.5 mm voxels
are not capable of calculating a realistic dose profile in this
region. At a distance of 5 cm from the seed ?Fig. 4?, the
anisotropy function at 0°calculated with 1 mm voxels is ap-
proximately 20% higher than the value calculated using
0.5 mm voxels. At an angle of just 1° the difference between
the two calculations drops to 2%.
To minimize the impact of the voxel size effects discussed
above, tabulated dosimetry data for this study consist of a
combination of the three calculations. Voxel sizes were cho-
sen in the following way: 0.1?0.1?0.1 mm3voxels were
used for distances in the range of 0?r?1 cm, 0.5?0.5
?0.5 mm3voxels were used for 1?r?5 cm and 1?1
?1 mm3voxels were used for 5?r?10 cm.
1
r2 dose distribution, scoring in shells of 1 mm
1
r2due to the distribution of radioactive material
E. TG-43 dosimetry parameters
Data are tabulated as a function of distance from the seed
and polar angle relative to the seed axis. When tabulation
FIG. 2. Ratio of the average dose in spherical shells of thickness ?r ?calcu-
lated using Eq. ?5?? to dose at the midpoint of the shell for a point source
with a 1/r2distribution. Three different shell thicknesses are included. Scor-
ing in shells of 1 mm thickness leads to dose overestimates of 2.8% and
0.25% at 3 and 10 mm, respectively. Decreasing the thickness of the shell to
0.1 mm leads to overestimates of less than 0.1% at the same two points.
FIG. 3. Anisotropy function at r=0.25 cm for the STM12501 source. The
plot shows the anisotropy function calculated with voxels of ?0.1 mm?3,
?0.5 mm?3and ?1.0 mm?3as well as values calculated by Kirov and Will-
iamson ?Ref. 19?.
447 Taylor, Yegin, and Rogers: Benchmarking the EGSnrc user-code BrachyDose447
Medical Physics, Vol. 34, No. 2, February 2007
Page 4
points do not correspond with the center of a voxel, dose
values were interpolated bilinearly using the nearest neigh-
bors of the voxel that the point of interest falls within. To
improve the accuracy of the interpolation, all dose values
were first divided by their respective values of the geometry
function, GL?r,??. The geometry function is calculated using
the line source approximation given by
G??r,?? =?
?/Lr sin ?
where the angle ? ?=?2−?1in TG-43 notation? is given by
1/?r2− L2/4?
? = 0
if ? ? 0,
?6?
? =?
This geometry factor is equivalent to the definition given by
TG-43U1 and is used here because it is faster to calculate.
Williamson et al. have shown19,27,30that “Sources con-
taining radioactivity deposited on radio-opaque surfaces with
sharp corners give rise to distance- and angle-dependent self-
shielding phenomena with surprising dosimetric results, in-
cluding apparent inverse-square law breakdowns and signifi-
cant anisotropy near the transverse axis.”27This anisotropy
can lead to significant variations in the air kerma strength,
and hence the dose rate constant, depending on whether the
air kerma strength is scored at a point on the transverse axis
tan−1?Lr sin ?
tan−1?Lr sin ?
?/2
r2− L2/4?
r2− L2/4?+ ? r ? L/2
r ? L/2
r = L/2?
.
?7?
FIG. 5. Variation of the dose rate constant for the STM1251125I seed as a
function of the scoring volume for the air kerma strength per history. Dose
rate constants were determined using air kerma strengths averaged over
voxels that were 0.5 mm thick and faces with varying areas. The faces of the
scoring voxels were located 10 cm from the source. For comparison, values
of the dose rate constants calculated or measured by other authors ?Refs.
19–21? are also included. The WAFAC calculation by Kirov and Williamson
is shown at an area of 2.7?2.7 cm2. Kirov and Williamson’s point kerma
extrapolated estimate and TLD measurements are shown at 0 cm2. The re-
ported uncertainties on Kirov’s calculations, Li’s measurements and Chiu-
Tsao’s measurements are 2.5%, 7% and 5.5%, respectively.
FIG. 6. As in Fig. 5 except for the Imagyn125I source. Ibbott et al.’s ?Ref.
25? calculated value and TLD measurements ?Refs. 22–24? are shown at
0 cm2. The reported uncertainty on the TLD measurements by Gearheart et
al. ?Refs. 22 and 24? and Nath and Yue are 7.7% and 10%, respectively.
FIG. 7. As in Fig. 5 except for the Theragenics103Pd seed. The WAFAC
calculations by Monroe and Williamson ?Ref. 30? are shown at an area of
2.7?2.7 cm2. Monroe and Williamson’s point kerma extrapolated estimate
and Nath et al.’s ?Ref. 28? TLD measurements are shown at 0 cm2. The
reported uncertainties on Monroe and Williamson’s MC results are 3%.
FIG. 4. Anisotropy function at r=5 cm for the STM12501 source. The plot
shows the anisotropy function calculated with voxels of ?0.5 mm?3and
?1.0 mm?3as well as values calculated by Kirov and Williamson ?Ref. 19?.
There is a significant voxel size effect at 0° only.
448 Taylor, Yegin, and Rogers: Benchmarking the EGSnrc user-code BrachyDose448
Medical Physics, Vol. 34, No. 2, February 2007
Page 5
or averaged over a finite solid angle ?as in the wide angle
free air chamber ?WAFAC? measurements performed at the
National Institute of Standards and Technology ?NIST?34,35?.
To investigate the influence of the photon fluence aniso-
tropy on the determination of the dose rate constant, a num-
ber of calculations were done. The air kerma per history was
scored in rectilinear voxels with the face of the voxel located
10 cm from the source. The voxels used for scoring air
kerma per history were 0.5 mm thick and the area of the
voxel’s face was varied from 0.1?0.1 to 10?10 cm2?cen-
tered on the transverse axis?. As a comparison, the NIST
WAFAC primary collimator is 8 cm in diameter and is lo-
cated 30 cm from the source. The primary collimator would
subtend a circle with diameter of ?2.7 cm at a distance of
10 cm from the source.
Air kerma strength per history was calculated as
sK= k˙??d? ? d2? kr2,
?8?
where k˙?is the air kerma per history and d is the distance
from the source to the face of the scoring voxel. The factor
kr2 is the ratio of the average r2for the scoring volume to d2
and is a correction to account for the variation of the inverse
square law over the scoring region. This factor is used to
give a result at a given distance which is independent of
scoring volume size for a strictly point source and amounts
to giving the air kerma per history ?d2on the axis. This
correction factor can be calculated analytically as
kr2 =
1
d2· w2· t?
d
d+t?
−w/2
w/2?
−w/2
w/2
?x2+ y2+ z2?dx dy dz, ?9?
where t is the thickness of the voxel ?0.05 cm? and w is the
width of the voxel ?varied from 10 to 0.1 cm?. At 10 cm
from the source this amounts to a ?17.2% and 0.5% correc-
tion for the 0.05?10?10 and 0.05?0.1?0.1 cm3voxels,
respectively. The 10-cm-wide voxels are much larger than
would be used in practice but are included here to demon-
strate the dependence of the dose rate constant on the size of
the region used for scoring air kerma.
Dose rate constants, ?, are calculated as the dose to water
per history in a ?0.1 mm?3voxel centered on the reference
position ?1 cm,
divided by the air kerma strength per history.
The radial dose function, g?r?, is calculated using both
line and point source geometry functions and tabulated at
1 mm intervals for distances less than 1 cm from the source
and 0.5 cm intervals from 1 to 10 cm. Values at r
=0.25 mm and r=0.75 mm are also included.
Anisotropy functions are calculated using the line source
approximation and tabulated at radii of 0.25, 0.5, 0.75, 1, 2,
3, 4, 5, 7.5 and 10 cm. The same 32 polar angles used in
Monroe and Williamson’s study30of the Model 200
seed were used to provide high angular resolution near the
transverse axis and seed axis. The anisotropy factor, ?an?r?,
was calculated by integrating the solid angle weighted dose
rate over 0°???90° and the anisotropy constant, ?¯an, was
?
2? in the 30?30?30 cm3water phantom,
103Pd
TABLE I. Dose rate constants, ?, and uncertainties calculated in this study and from other authors. Uncertainties shown for the values calculated in this study
are statistical uncertainties only and do not include uncertainties in cross section or geometry.
Seed nameAuthor Method
? cGy h−1U−1
STM12501This study
This study
2.7?2.7?0.05 cm3voxel at 10 cm
0.1?0.1?0.05 cm3voxel at 10 cm
MC ?WAFAC sim.?
MC ?pt. extrapolation?
TLD
TLD
2.7?2.7?0.05 cm3voxel at 10 cm
0.1?0.1?0.05 cm3voxel at 10 cm
MC
TLD
TLD
Avg. of MC and TLD
2.7?2.7?0.05 cm3voxel at 10 cm
0.1?0.1?0.05 cm3voxel at 10 cm
MC ?WAFAC sim.?
MC ?pt. extrapolation?
TLD
Avg. of MC and TLD
1.012±0.002
1.045±0.003
0.980±0.024
1.041
1.039±0.073
1.07±0.06
0.924±0.003
0.923±0.003
0.92
0.92±0.07
0.95±0.095
0.940
0.694±0.002
0.772±0.003
0.691±0.02
0.797
0.680±0.05
0.686
Kirov and Williamsona
Kirov and Williamsona
Li and Williamsonb
Chiu-Tsaoc
This Study
This Study
Ibbottg
Gearheart et al.d,f
Nath and Yue
TG-43 Consensus
This study
This study
Monroe and Williamsoni
Monroe and Williamsoni
Nath et al.h
TG-43 Consensus
Imagyn
Theragenics
aReference 19.
bReference 20.
cReference 21.
dReference 22.
eReference 23.
fReference 24.
gReference 25.
hReference 28.
iReference 30.
449 Taylor, Yegin, and Rogers: Benchmarking the EGSnrc user-code BrachyDose449
Medical Physics, Vol. 34, No. 2, February 2007
Page 6
calculated as the inverse r-squared weighted average of
?an?r? for r?1 cm as recommended by TG-43U1.
III. RESULTS AND DISCUSSION
A. Dose rate constants
Figures 5–7 show the calculated dose rate constant versus
the width of the scoring region used for the air kerma
strength calculations. Variations of 4.6% in the dose rate con-
stant are seen for the STM1251 source as the area of the
air kerma scoring region is decreased from 10?10 cm2
??=0.999±0.002 cGy h−1U−1?
??=1.045±0.003 cGy h−1U−1?. The dose rate constant for
the Imagyn source shows very little variation as the area of
the air kerma scoring region is decreased from 10?10 cm2
??=0.925±0.003 cGy h−1U−1?
??=0.923±0.003 cGy h−1U−1?. The dose rate constant for
the Theragenics103Pd source increased by 11% as the area of
the scoringregionwas decreased
??=0.690±0.002 cGy h−1U−1?
??=0.772±0.003 cGy h−1U−1?. Also shown on the plots are
to0.1?0.1 cm2
to 0.1?0.1 cm2
from 10?10 cm2
0.1?0.1 cm2
to
TABLE II. Radial dose functions calculated using both line, gL?r?, and point, gP?r?, source approximations. Active lengths, L, used for calculating the geometry
function are also provided. Uncertainties for the125I sources are approximately 0.5% for r?1 cm, 0.7% at 5 cm and 1% at 10 cm. The uncertainties for the
Theragenics source are approximately 0.5% for r?1 cm, 1.0% at 5 cm and 2% at 10 cm.
gx?r?
Source nameSTM125I Imagyn125I Thera 200103Pd
L=4.2 mm
r/cm
L=3.8 mmPoint
L=3.4 mm Point Point
0.1
0.2
0.25
0.3
0.4
0.5
0.6
0.7
0.75
0.8
0.9
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
0.946
0.999
1.014
1.022
1.031
1.033
1.030
1.024
1.021
1.017
1.008
1.000
0.925
0.849
0.765
0.685
0.608
0.536
0.471
0.415
0.361
0.315
0.273
0.237
0.206
0.178
0.152
0.130
0.113
0.0976
0.548
0.810
0.878
0.925
0.977
1.002
1.012
1.015
1.012
1.015
1.011
1.000
0.937
0.862
0.778
0.697
0.617
0.548
0.480
0.423
0.366
0.320
0.277
0.241
0.209
0.181
0.154
0.132
0.115
0.0992
1.038
1.097
1.110
1.107
1.100
1.091
1.079
1.061
1.055
1.046
1.030
1.000
0.905
0.806
0.708
0.619
0.538
0.466
0.406
0.350
0.300
0.255
0.220
0.191
0.161
0.139
0.119
0.102
0.0886
0.0736
0.640
0.918
0.984
1.017
1.050
1.062
1.062
1.051
1.047
1.040
1.028
1.000
0.909
0.811
0.714
0.625
0.543
0.470
0.410
0.353
0.303
0.258
0.222
0.192
0.162
0.140
0.120
0.103
0.0894
0.0743
0.928
1.339
1.380
1.388
1.363
1.308
1.244
1.179
1.147
1.112
1.058
1.000
0.741
0.551
0.406
0.298
0.219
0.160
0.117
0.0865
0.0635
0.0469
0.0345
0.0256
0.0193
0.0147
0.0112
0.00837
0.00641
0.00513
0.503
1.045
1.162
1.227
1.273
1.256
1.213
1.162
1.135
1.104
1.055
1.000
0.755
0.563
0.416
0.305
0.224
0.164
0.120
0.0886
0.0653
0.0482
0.0355
0.0263
0.0198
0.0151
0.0115
0.00861
0.00660
0.00528
FIG. 8. Radial dose function gL?r?, for the three sources. Voxel sizes are:
?0.1 mm?3for r?1 cm, ?0.5 mm?3for 1 cm?r?5 cm, ?1.0 mm?3for
5 cm?r?10 cm. Lines are values calculated in this study and symbols are
values calculated by other authors ?Refs. 19, 22, and 30?.
450Taylor, Yegin, and Rogers: Benchmarking the EGSnrc user-code BrachyDose 450
Medical Physics, Vol. 34, No. 2, February 2007
Page 7
relevant dose rate constants calculated or measured by other
authors. For the STM and Theragenics sources, the depen-
dence of the dose rate constant on the size of region used for
scoring air kerma per history has been shown by Williamson
et al.19,27,30to be “a general feature of seeds containing in-
ternal components with sharp edges; composed of, or coated
with, radio-opaque materials; and with radioactivity distrib-
uted on or near the surface.”30Since the Imagyn source uses
spherical source elements, this same effect is not seen with
this seed.
Calculated dose rate constants and their statistical uncer-
tainties are listed in Table I. Included in the table are con-
sensus dose rate constants recommended by TG-43U1 and/or
relevant values calculated or measured by other authors. Our
values in the table are based on the dose to water per history
at 1 cm in a 0.1?0.1?0.1 mm3voxel and air kerma per
historyvalues calculated
?0.05 cm3?method 1? and 0.1?0.1?0.05 cm3?method 2?
located 10 cm from the source. The larger voxel size aver-
ages the air kerma per history over a region subtending
usingvoxels of2.7?2.7
TABLE III. Anisotropy function, F?r,??, and anisotropy factors, ?an?r?, for the STM1251 source calculated using the line source approximation with
L=3.8 mm. Uncertainties are approximately 0.2%, 0.5% and 1% at 1, 5 and 10 cm, respectively.
F?r,??
? ?deg?
r?cm?
0.250.50.7512345 7.510
0
1
2
3
5
7
10
12
15
20
25
30
35
40
45
50
55
60
65
70
73
75
78
80
82
84
85
86
87
88
89
90
?an?r?
0.865
0.860
0.856
0.836
0.804
0.843
0.756
0.731
0.808
0.898
0.931
0.950
0.964
0.945
0.943
0.962
0.973
0.981
0.987
0.992
0.995
0.996
0.997
0.998
0.999
0.999
0.999
0.999
0.999
0.999
1.000
1.000
1.211
0.514
0.505
0.481
0.547
0.659
0.588
0.564
0.578
0.617
0.693
0.760
0.816
0.864
0.904
0.934
0.956
0.972
0.984
0.994
0.974
0.983
0.988
0.993
0.994
0.996
0.997
0.998
0.999
0.998
0.998
0.999
1.000
0.982
0.432
0.427
0.500
0.644
0.601
0.559
0.560
0.580
0.619
0.689
0.753
0.805
0.851
0.889
0.921
0.948
0.968
0.981
0.992
1.001
1.005
0.998
0.987
0.991
0.996
0.998
0.999
0.999
0.999
0.999
1.000
1.000
0.951
0.409
0.410
0.581
0.659
0.587
0.560
0.571
0.590
0.628
0.695
0.757
0.807
0.849
0.885
0.916
0.942
0.963
0.979
0.990
0.998
1.003
1.005
1.007
0.987
0.991
0.995
0.995
0.998
0.997
0.998
0.996
1.000
0.940
0.462
0.593
0.654
0.657
0.608
0.597
0.613
0.631
0.666
0.724
0.775
0.820
0.859
0.891
0.918
0.941
0.962
0.979
0.990
1.000
1.004
1.005
1.008
1.010
1.011
1.008
1.000
0.994
0.995
0.995
0.997
1.000
0.937
0.514
0.665
0.702
0.672
0.633
0.629
0.646
0.662
0.695
0.746
0.792
0.834
0.869
0.899
0.923
0.948
0.965
0.980
0.994
1.002
1.010
1.011
1.013
1.014
1.014
1.015
1.015
1.011
1.001
0.999
0.999
1.000
0.948
0.550
0.693
0.712
0.685
0.655
0.651
0.668
0.682
0.715
0.758
0.808
0.843
0.876
0.904
0.929
0.952
0.966
0.985
0.999
1.004
1.012
1.010
1.018
1.014
1.019
1.017
1.017
1.021
1.015
1.003
1.002
1.000
0.948
0.571
0.711
0.711
0.688
0.661
0.664
0.676
0.693
0.723
0.762
0.804
0.846
0.872
0.899
0.923
0.944
0.960
0.978
0.996
0.998
1.001
1.005
1.007
1.009
1.006
1.009
1.011
1.013
1.013
1.001
1.000
1.000
0.943
0.665
0.722
0.716
0.694
0.682
0.685
0.698
0.706
0.740
0.775
0.810
0.843
0.875
0.899
0.925
0.940
0.952
0.973
0.983
0.992
0.991
0.997
1.005
1.004
0.999
1.007
1.001
1.004
1.001
0.999
1.001
1.000
0.942
0.691
0.730
0.729
0.718
0.693
0.701
0.707
0.720
0.742
0.779
0.824
0.845
0.883
0.904
0.929
0.936
0.957
0.969
0.983
0.979
0.988
0.987
1.002
1.004
0.998
0.996
1.000
0.999
1.009
1.001
0.998
1.000
0.939
FIG. 9. Comparisons of anisotropy data calculated for the STM1251
source with values calculated by Kirov and Williamson ?Ref. 19?. Voxel
sizes are ?0.1 mm?3at 1 cm and ?0.5 mm?3at 5 cm. See Fig. 3 for values at
0.25 cm.
125I
451 Taylor, Yegin, and Rogers: Benchmarking the EGSnrc user-code BrachyDose451
Medical Physics, Vol. 34, No. 2, February 2007
Page 8
roughly the same solid angle as subtended by the primary
collimator of the WAFAC. The small voxel serves to esti-
mate the air kerma per history at a point on the transverse
axis. It should be noted that Williamson et al. have shown
that for the Theragenics27,30and STM19sources, air kerma
strength calculated at a point on the transverse axis is depen-
dent on the distance of the point from the seed. As such, dose
rate constants calculated using the small voxel ?method 2? in
this study may not be directly comparable to the point ex-
trapolation method used in other studies of those two
sources.
The dose rate constant calculated for the STM source us-
ing the large voxel ?method 1? is 3.3% higher than the value
calculated by Kirov and Williamson using a full simulation
of the WAFAC. The source of this discrepancy has not been
identified. Kirov and Williamson’s dose rate constant based
on a point extrapolated air kerma strength is in much better
agreement ?within 0.4%? with the value calculated in this
study using the small voxel ?method 2?. Agreement of the
method 2 calculation with the value measured by Li and
Williamson20is also within 0.6%.
Dose rate constants calculated for the Imagyn source
showed very little dependence on the scoring region size.
Dose rate constants calculated with the two methods de-
scribed above agree with each other within 0.5%. Calculated
values show agreement with the values calculated and mea-
sured by Gearheart et al.22within 0.5%.
For the Theragenics source, the dose rate constant based
on the WAFAC simulation calculated by Monroe and
Williamson30is 0.4% lower than the value calculated in this
study using the large voxel ?method 1?. Monroe and William-
son’s dose rate constant based on their point extrapolated air
kerma strength is 3% higher than the value calculated in this
study using the small voxel ?method 2?. Again, this 3% dif-
ference for the method 2 calculation is not surprising as it
has been demonstrated in other studies of the Model 200
TABLE IV. Anisotropy function, F?r,??, and anisotropy factors, ?an?r?, for the Imagyn source calculated using the line source approximation with
L=3.4 mm. Uncertainties are approximately 0.4%, 0.7% and 1.4% at 1, 5 and 10 cm, respectively.
F?r,??
? ?deg?
r?cm?
0.25 0.50.7512345 7.5 10
0
1
2
3
5
7
10
12
15
20
25
30
35
40
45
50
55
60
65
70
73
75
78
80
82
84
85
86
87
88
89
90
?an?r?
0.170
0.171
0.173
0.176
0.187
0.203
0.252
0.293
0.383
0.528
0.641
0.730
0.797
0.847
0.882
0.908
0.930
0.950
0.962
0.974
0.979
0.984
0.988
0.991
0.993
0.995
0.996
0.997
0.997
0.998
0.999
1.000
1.024
0.207
0.207
0.207
0.209
0.225
0.236
0.268
0.299
0.353
0.445
0.532
0.613
0.688
0.755
0.812
0.863
0.910
0.944
0.965
0.981
0.987
0.992
0.996
0.996
0.998
0.998
0.998
0.999
1.000
1.001
1.001
1.000
0.886
0.240
0.239
0.242
0.252
0.260
0.273
0.306
0.337
0.383
0.466
0.543
0.617
0.684
0.747
0.804
0.855
0.901
0.936
0.965
0.986
0.991
0.993
0.997
0.997
1.000
1.000
1.000
1.000
1.001
1.001
0.999
1.000
0.868
0.268
0.271
0.277
0.288
0.290
0.307
0.341
0.370
0.415
0.489
0.563
0.634
0.698
0.759
0.814
0.865
0.909
0.947
0.978
0.998
1.007
1.006
1.010
1.011
1.011
1.008
1.011
1.008
1.013
1.010
1.010
1.000
0.873
0.345
0.352
0.357
0.361
0.366
0.381
0.412
0.436
0.474
0.537
0.600
0.659
0.715
0.767
0.814
0.859
0.899
0.934
0.963
0.983
0.990
0.992
0.996
0.996
0.997
0.999
1.000
1.000
1.000
1.000
1.000
1.000
0.867
0.395
0.402
0.408
0.409
0.415
0.428
0.457
0.479
0.514
0.570
0.626
0.679
0.735
0.778
0.824
0.865
0.905
0.939
0.963
0.982
0.990
0.991
0.992
0.998
0.998
1.001
1.000
1.003
1.002
0.999
1.000
1.000
0.874
0.425
0.438
0.440
0.440
0.447
0.459
0.486
0.511
0.538
0.594
0.646
0.696
0.746
0.790
0.833
0.870
0.906
0.943
0.968
0.989
0.993
0.992
0.996
0.997
1.002
1.002
1.004
1.004
1.000
1.005
1.000
1.000
0.881
0.448
0.457
0.454
0.458
0.463
0.475
0.504
0.523
0.547
0.605
0.655
0.697
0.741
0.789
0.830
0.869
0.903
0.927
0.959
0.977
0.984
0.985
0.991
0.988
0.995
0.991
0.997
0.999
0.989
0.998
0.992
1.000
0.877
0.498
0.503
0.505
0.502
0.511
0.522
0.553
0.562
0.588
0.635
0.679
0.724
0.766
0.811
0.850
0.886
0.917
0.944
0.970
0.987
0.993
0.997
1.002
1.000
1.006
1.016
1.013
1.008
1.016
1.007
1.008
1.000
0.894
0.508
0.534
0.526
0.527
0.536
0.544
0.562
0.575
0.604
0.647
0.696
0.742
0.773
0.812
0.854
0.887
0.917
0.958
0.975
0.990
0.992
0.992
1.005
1.007
1.006
1.007
1.006
1.004
1.010
1.015
0.997
1.000
0.898
452 Taylor, Yegin, and Rogers: Benchmarking the EGSnrc user-code BrachyDose452
Medical Physics, Vol. 34, No. 2, February 2007
Page 9
source that the air kerma strength determined at a point on
the transverse axis depends on the distance from the source.
In all comparisons with TLD measured values, it must be
noted the authors have all assumed the detector reading was
proportional to the dose in the TLD, whereas the results of
Davis et al.36imply the reading is high by up to 10% ?for a
30 kV x-ray spectrum? which suggests all previous measured
values may be systematically up to 10% high, although the
results of Davis et al. directly contradict the results of Das et
al.37This area requires further investigation.
B. Radial dose functions
Radial dose functions calculated using both the line
source and point source approximations are presented in
Table II. Figure 8 shows plots of gL?r? calculated in this
study as well MC data from other studies. Statistical uncer-
tainties for the two125I sources are ?0.5% and ?1% at 5
and 10 cm, respectively, while uncertainties for the Ther-
agenics source are ?1% and ?2% at 5 and 10 cm, respec-
tively.
The radial dose function calculated for the STM source in
this study agrees within 1% with the values calculated by
Kirov and Williamson19at all distances. For the Imagyn
source the radial dose function is approximately 1% higher
than the values reported by Gearheart et al.22for r?1 cm.
For 1?r?5 cm agreement is within 1%, with the values
calculated in this study being slightly greater than Gearheart
et al.’s. For 5?r?10 cm there is no obvious trend in the
differences between the two calculations. There is a differ-
ence of close to 7% at r=8 cm but calculations are within
2% at 10 cm. These differences likely reflect the 4% statis-
tical uncertainty reported for the value of Gearheart et al. for
the radial dose function.22
Agreement withthe calculations
Williamson30for the Theragenics103Pd source is better than
1% for 0.1?r?3 cm, however, there are some significant
differences at distances beyond 3 cm. Values calculated at 5,
7.5, and 10 cm in this study are lower than the values calcu-
lated by Monroe and Williamson by 2.5%, 6% and 16%,
respectively. Monroe and Williamson state that uncertainties
of Monroe and
TABLE V. Anisotropy function, F?r,??, and anisotropy factors, ?an?r?, for the Theragenics source calculated using the line source approximation with
L=3.4 mm. Uncertainties are approximately 0.3%, 1% and 2% at 1, 5 and 10 cm, respectively.
F?r,??
? ?deg?
r?cm?
0.25 0.5 0.7512345 7.510
0
1
2
3
5
7
10
12
15
20
25
30
35
40
45
50
55
60
65
70
73
75
78
80
82
84
85
86
87
88
89
90
?an?r?
0.604
0.605
0.607
0.607
0.599
0.552
0.317
0.232
0.322
0.522
0.679
0.795
0.877
0.929
0.949
0.945
0.941
0.976
0.984
0.983
0.973
0.959
0.974
0.989
0.998
1.003
1.003
1.003
1.002
1.001
1.001
1.000
1.142
0.688
0.683
0.671
0.647
0.596
0.548
0.492
0.469
0.446
0.451
0.512
0.601
0.680
0.748
0.804
0.849
0.887
0.917
0.930
0.931
0.917
0.940
0.955
0.958
0.950
0.958
0.972
0.982
0.988
0.995
0.999
1.000
0.889
0.601
0.597
0.583
0.573
0.532
0.512
0.488
0.480
0.477
0.489
0.532
0.596
0.673
0.739
0.798
0.843
0.884
0.919
0.945
0.962
0.964
0.967
0.949
0.967
0.976
0.975
0.970
0.976
0.992
0.998
0.999
1.000
0.867
0.553
0.559
0.545
0.540
0.512
0.498
0.486
0.488
0.493
0.511
0.550
0.606
0.676
0.742
0.799
0.845
0.887
0.925
0.955
0.976
0.983
0.982
0.987
0.984
0.973
0.990
0.986
0.983
0.981
0.993
1.000
1.000
0.865
0.522
0.515
0.512
0.509
0.500
0.496
0.501
0.507
0.520
0.545
0.582
0.632
0.689
0.750
0.806
0.854
0.896
0.933
0.962
0.989
1.002
1.009
1.017
1.020
1.020
1.012
1.003
0.995
0.995
0.992
0.993
1.000
0.871
0.517
0.515
0.520
0.515
0.510
0.511
0.516
0.526
0.543
0.571
0.610
0.656
0.711
0.771
0.823
0.871
0.912
0.950
0.978
1.005
1.020
1.027
1.035
1.039
1.044
1.036
1.029
1.019
1.006
1.007
1.001
1.000
0.888
0.516
0.527
0.526
0.524
0.520
0.520
0.531
0.539
0.557
0.590
0.625
0.676
0.724
0.779
0.833
0.882
0.921
0.955
0.985
1.015
1.029
1.039
1.047
1.051
1.057
1.047
1.044
1.034
1.024
1.011
1.011
1.000
0.899
0.511
0.528
0.524
0.530
0.527
0.529
0.535
0.546
0.561
0.596
0.635
0.685
0.733
0.789
0.838
0.885
0.924
0.956
0.978
1.007
1.030
1.034
1.046
1.048
1.048
1.047
1.033
1.030
1.016
1.013
1.008
1.000
0.899
0.544
0.556
0.557
0.558
0.557
0.559
0.572
0.584
0.602
0.634
0.667
0.707
0.757
0.804
0.851
0.892
0.935
0.965
0.989
1.006
1.023
1.026
1.037
1.045
1.041
1.044
1.044
1.032
1.021
1.013
0.998
1.000
0.907
0.632
0.643
0.631
0.625
0.634
0.644
0.656
0.671
0.673
0.707
0.747
0.749
0.804
0.849
0.872
0.907
0.936
0.970
0.973
1.012
1.002
1.012
1.025
1.037
1.036
1.047
1.039
1.024
1.011
1.022
1.018
1.000
0.923
453 Taylor, Yegin, and Rogers: Benchmarking the EGSnrc user-code BrachyDose453
Medical Physics, Vol. 34, No. 2, February 2007
Page 10
on their calculations are ?2% at distances far from the
source, making it unlikely that the differences are statistical
in nature. Radial dose functions were also calculated for an
unencapsulated point source and compared with values cal-
culated by Monroe and Williamson and by Melhus and
Rivard.32Agreement between these three sets of calculations
was within 1% for r?10 cm demonstrating that the differ-
ences in radial dose functions originate in modeling the
source.
To investigate the sensitivity of the results to cross sec-
tions, the radial dose function was recalculated with the cross
section of Pd reduced by 5%. While the absolute dose rate
increased by 0.6% at the reference position, ?1 cm, 90°?, the
re-calculated radial dose function agreed with the standard
calculation within statistical uncertainties for distances less
than 10 cm from the source. The differences between the
radial dose function calculations in this study and Monroe
and Williamson’s are unexplained given the good agreement
for the dose rate constant ?see Fig. 7? and anisotropy func-
tions ?see Fig. 11 below?.
C. Anisotropy data
Calculated anisotropy data including the anisotropy fac-
tors for all sources are shown in Tables III–V. The anisotropy
constants calculated in this study are shown in Table VI.
Figures 9–11 show anisotropy function data for the three
sources calculated at 1 and 5 cm as well as anisotropy data
published by other authors.
For the STM source ?Figs. 3 and 9?, agreement with Kirov
and Williamson’s19calculations is generally better than 1%.
However, larger differences of ?6% are seen for ?=2° at
r=1 and 2 cm ?2 cm data not shown? but these points are in
regions of very steep dose gradients and good agreement is
seen a short distance away. The anisotropy factors and con-
stant are all in agreement within 1% for the STM source.
For the Imagyn source ?Fig. 10?, our anisotropy data with
??20° generally agree within 2% with the values published
by Gearheart et al. At 10° the anisotropy function values
calculated in this study are 4% higher than those calculated
by Gearheart et al.22and at 0° the discrepancy is as large as
11% for r=1 cm. Anisotropy factors agree within 2% and
anisotropy constants are within 0.1% of each other.
The discrepancies in our F?r,0°? values and those of
Gearheart et al.22of up to 11% for the Imagyn source at 0°
do not appear to be caused by voxel size effects. Figure 11 is
a plot of dose profiles for the Imagyn IS-12501 source taken
perpendicular to the seed axis and offset 0.5 cm from the
source center. This figure shows the shadowing effect that
the end cap of the source encapsulation has ?diameter of
0.8 mm? and that the dose profile is relatively flat within the
shadow. Decreasing the voxel size even further should have
little effect on the dose values calculated near the source
axis. Also shown are calculations done with 0.5?0.5
?0.5 mm3voxels. The dose calculated in the two voxel
sizes is the same within uncertainties at 0°.
Since this region of space is where photons undergo the
most significant attenuation by the encapsulation, the dis-
crepancy between this study and previous studies may result
from differences in the photon cross sections used. Gearheart
et al. used the DLC-9938cross sections while all calculations
for this study were done using XCOM cross sections.31To
investigate the impact of cross section uncertainties a set of
calculations for the Imagyn source was done in which the
cross sections of the Ti encapsulation were increased by 1%.
Figure 12 shows the ratio of dose calculated with the stan-
dard cross section to the dose calculated with the increased
cross sections for Ti. Again the dose profiles for this plot
were taken perpendicular to the seed axis and offset 0.5 cm
from the source center. Increasing the cross section of Ti by
1% led to a decrease of dose of close to 0.8% at 0.5 cm
along the seed axis. At 0.5 cm along the transverse axis the
decrease in dose was only 0.2% giving a decrease in the
anisotropy function of 0.53±0.14% at ?r,??=?0.5 cm,0°?.
Discrepancies between the two calculations decreased as the
distance from the source and polar angles increased. No sig-
nificant differences were seen in the radial dose function for
the two calculations. These calculations show that differ-
ences in cross sections on the order of 1% lead to significant
differences in calculated anisotropy function data. We can
therefore deduce that a large discrepancy ??1%? in cross
section data may lead to large differences in calculated an-
isotropy data and may be the cause of the discrepancy be-
tween F?r,0°? values calculated in this study and those of
Gearheart et al.22
The Theragenics seed’s anisotropy data ?Fig. 13? show
very good agreement with the data calculated by Monroe and
Williamson.30The anisotropy function agrees within 1%–2%
at almost all angles and radii considered, with the one no-
table exception being for r=0.25 cm and 7°???20° where
there are discrepancies of 5% or more. This is the region
which has the steepest dose gradients and undergoes the
most significant attenuation due to the structure of the seed.
At 12° and 0.25 cm the anisotropy function value calculated
in this study is 20% higher than that calculated by Monroe
and Williamson while at 12° and 0.5 cm the difference has
dropped to less than 1%. These differences are in regions
where voxel size effects are most pronounced and are most
TABLE VI. Tabulated values of the one-dimensional anisotropy constant,
?¯an, calculated in this study and by other authors. The value attributed to
Gearheart was re-calculated ?using Eq. ?D2? of TG43U1 ?Ref. 18?? to in-
clude their data from 1 cm that was not presented in their original paper but
published later in Ibbott et al.’s letter to the editor ?Ref. 25?.
Seed name Author
?¯an
STM12501 This study 0.940
0.941
0.873
0.874
0.871
0.866
Kirov and Williamsonj
This study
Gearheartk
This study
Monroe and Williamsonl
Imagyn
Theragenics
jReference 19.
kReference 22.
lReference 30.
454Taylor, Yegin, and Rogers: Benchmarking the EGSnrc user-code BrachyDose454
Medical Physics, Vol. 34, No. 2, February 2007
Page 11
likely due to residual voxel size effects in our calculations.
The anisotropy factors and anisotropy constant all agree
within 1%.
IV. CONCLUSION
In order to benchmark the new EGSnrc Monte Carlo
code, BrachyDose, TG-43 dosimetry parameters were calcu-
lated for one103Pd and two125I sources. The three seeds in
this study were chosen because of their varied internal struc-
ture and encapsulation. The STM125I and Theragenics103Pd
seeds also make ideal candidates for benchmarking voxel
based dose calculations due to their highly anisotropic dose
distributions at small angles. Since the BrachyDose code is
able to accurately calculate the dose distribution surrounding
these two sources, we believe that, using the same voxel
sizes as presented in this study, BrachyDose is capable of
doing accurate dose calculations for any seed. A comprehen-
sive set of dosimetry parameters is being calculated for the
16 seeds listed in the Joint AAPM/Radiological Physics Cen-
ter ?RPC? Registry of Brachytherapy Sources.39
It was shown analytically that scoring the dose from a
point source in 1-mm-thick spherical shells leads to a signifi-
cant overestimate of dose at distances less than 1 cm from
the source. To minimize voxel volume effects it was found
that voxel sizes of 0.1?0.1?0.1 mm3were needed for
points less than 1 cm from the source. From 1 to 5 cm away
from the seed the voxel size was increased to 0.5?0.5
?0.5 mm3and beyond 5 cm from the seed dose was scored
in 1?1?1 mm3voxels. These voxel sizes should be suit-
able for doing calculations with other125I and103Pd seeds.
Cross section uncertainties play a significant role in cal-
culations of the anisotropy function. Increasing the cross sec-
tion of the titanium encapsulation for the Imagyn source by
1% resulted in a change of ?0.5% in the anisotropy function
for r?1 cm and ??15°. For the Theragenics source, de-
creasing the cross section of palladium by 5% resulted in an
increase of ?0.5% in the anisotropy function for ??5°. Un-
certainties in the geometry of the sources may also have a
significant impact on calculated dosimetry parameters but
have not been considered in this study. Combined uncertain-
ties in cross sections and geometry are larger than the statis-
tical uncertainties for the dosimetry parameters calculated in
this study.
When voxel sizes are chosen appropriately, dosimetry pa-
rameters calculated with BrachyDose generally show good
agreement with data calculated by other authors19,22,30using
Williamson’s PTRAN13,14code. This agreement demonstrates
BrachyDose’s ability to accurately calculate dose distribu-
tions surrounding brachytherapy seeds with widely varied
internal structure and encapsulation.
Although the vast majority of our comparisons with pre-
vious data show good agreement, there are three cases where
there are significant differences. First, the dose rate constant
calculated for theSTMsource usingthe2.7?2.7
FIG. 10. Comparisons of anisotropy data calculated for the Imagyn isoStar
125I source with values calculated by Gearheart et al. ?Ref. 22?. Voxel sizes
are ?0.1 mm?3at 1 cm and ?0.5 mm?3at 5 cm.
FIG. 11. Dose profile perpendicular to source axis located 0.5 cm from the
Imagyn source center. Voxels are ?0.1 mm?3and ?0.5 mm?3. It is evident
from this plot that decreasing the voxel size further would likely have no
effect on the anisotropy function values calculated at ?=0°.
FIG. 12. For the Imagyn isoStar
using the standard cross sections to dose calculated with the cross section of
the Ti encapsulation increased by 1%. The dose ratio profile shown was
taken perpendicular to the seed axis and 0.5 cm from the source center. A
1% increase in the cross section of titanium leads to a decrease in dose of
0.8% at 0°.
125I source, ratio of the dose calculated
455 Taylor, Yegin, and Rogers: Benchmarking the EGSnrc user-code BrachyDose455
Medical Physics, Vol. 34, No. 2, February 2007
Page 12
?0.05 cm3voxel is 3.3% higher than the value calculated by
Kirov and Williamson19using a full simulation of the
WAFAC. One might suspect that the more detailed model of
the WAFAC explains the difference except that for the Ther-
agenics seed our calculations agree very well with the more
detailed calculations by Monroe and Williamson.30Second,
BrachyDose calculated values of the radial dose function for
the Theragenics seed show significant differences beyond
5 cm when compared with the results of Monroe and
Williamson.30Finally, the anisotropy function calculated in
this study for the Imagyn source shows significant differ-
ences at small angles when compared with the results of
Gearheart et al.22Given the consistency in our approach for
the various seeds, we believe that our results are likely more
accurate, but this remains to be established.
ACKNOWLEDGMENTS
We wish to thank Dr. Yang Cai for pointing out the useful
equation ?Eq. ?7?? for calculating the angle ? in the line
source geometry function, as well as the members of the
Carleton Laboratory for Radiotherapy Physics ?CLRP? for
their helpful comments regarding this paper. Many of the
calculations in this study have made use of WestGrid com-
puting resources, which are funded in part by the Canada
Foundation for Innovation, Alberta Innovation and Science,
BC Advanced Education, and the participating research in-
stitutions. This work is partially funded by NSERC, The
Canada Research Chair’s program and Varian Inc. The help-
ful comments of the referees are gratefully acknowledged.
a?Electronic mail: rtaylor@physics.carleton.ca
b?Electronicmail:
www.physics.carleton.ca/~drogers/
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