# Benchmarking brachydose: Voxel based EGSnrc Monte Carlo calculations of TG-43 dosimetry parameters.

**ABSTRACT** In this study, BrachyDose, a recently developed EGSnrc Monte Carlo code for rapid brachytherapy dose calculations, has been benchmarked by reproducing previously published dosimetry parameters for three brachytherapy seeds with varied internal structure and encapsulation. Calculations are performed for two 125I seeds (Source Tech Medical Model STM1251 and Imagyn isoSTAR model 12501) and one l03Pd source (Theragenics Model 200). Voxel size effects were investigated with dose distribution calculations for three voxel sizes: 0.1 x 0.1 x 0.1 mm(3), 0.5 x 0.5 x 0.5 mm(3), and 1 X 1 X 1 mm(3). 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 X 0.1 x 0.1 mm(3) voxels for distances in the range of 0<r< or = l cm, 0.5 x0.5 0.5 mm(3) voxels for 1 <r< or =5 cm and 1 x 1 X 1 mm(3) voxels for 5<r< or = 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.

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**ABSTRACT:**The aim of this study is to determine effects of size deviations of brachytherapy seeds on two dimensional dose distributions around the seed. Although many uncertainties are well known, the uncertainties which stem from geometric features of radiation sources are weakly considered and predicted. Neither TG-43 report which is not completely in common consensus, nor individual scientific MC and experimental studies include sufficient data for geometric uncertainties. Sizes of seed and its components can vary in a manufacturing deviation. This causes geometrical uncertainties, too. In this study, three seeds which have different geometrical properties were modeled using EGSnrc-Code Packages. Seeds were designed with all their details using the geometry package. 5% deviations of seed sizes were assumed. Modified seeds were derived from original seed by changing sizes by 5%. Normalizations of doses which were calculated from three kinds of brachytherapy seed and their derivations were found to be about 3%–20%. It was shown that manufacturing differences of brachytherapy seed cause considerable changes in dose distribution.Reports of Practical Oncology and Radiotherapy 09/2014; - SourceAvailable from: Lucas Paixão
##### Conference Paper: MONTE CARLO CALCULATION OF DOSIMETRIC PARAMETERS OF A 125 I BRACHYTHERAPY SEED ENCAPSULATED WITH BIOCOMPATIBLE POLYMER AND A CERAMIC MATRIX AS RADIOGRAPHIC MARKER

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**ABSTRACT:**For prostate cancer treatments, there is an increasing interest in the permanent radioactive seeds implant technique. Currently, in Brazil, the seeds are imported at high prices, which prohibit their use in public hospitals. One of the seed models that have been developed at CDTN has a ceramic matrix as a radioisotope carrier and a radiographic marker; the seed is encapsulated with biocompatible polymer. In this work, Monte Carlo simulations were performed in order to assess the dose distributions generated by the prototype seed model. The obtained data was assessed as described in the TG-43U1 report by the AAPM. The dosimetric parameters dose rate constant, Λ, radial dose function, g L (r), and anisotropy function, F(r,θ), were derived from simulations using the MCNP5 code. The function g(r) shows that the seed has a lower decrease in dose rate on its transverse axis when compared to the 6711 model (one of the most used seeds in permanent prostate implants). F(r,θ) shows that CDTN's seed anisotropy curves are smoother than the 6711 model curves for θ ≤ 20° and 0.25 ≤ r ≤ 1 cm. As well, the Λ value is 15% lower than the Λ value of 6711. The results show that CDTN's seed model can deposit a more isotropic dose. Because of the model's characteristics, the seeds can be impregnated with iodine of lower specific activity which would help reducing costs.2011 International Nuclear Atlantic Conference - INAC 2011, Belo Horizonte, Brazil; 10/2011 - SourceAvailable from: David SarrutF. Baldacci, A. Mittone, A. Bravin, P. Coan, F. Delaire, C. Ferrero, S. Gasilov, J.M. Létang, D. Sarrut, F. Smekens, N. Freud[Show abstract] [Hide abstract]

**ABSTRACT:**Die Track-Length-Estimator (TLE)-Methode ist ein rechnerisch sehr effizientes Verfahren für Monte-Carlo (MC)-Simulationen, welches kürzlich in GATE 6.2 implementiert wurde. Sie wird zur Beschleunigung der Dosisberechnungen im Umfeld der niederenergetischen Röntgenstrahlung mit Hilfe der Kerma-Annährung eingesetzt. Über die Effizienzsteigerung der TLE-Mehode im Vergleich mit der analogen MC-Methode wurde in der Literatur im Bezug auf zahlreiche Anwendungen (darunter Strahlentherapie, Röntgenbildgebung) berichtet. Wir haben die TLE-Methode hinsichtlich statistischer Größen, Strahlendosisverteilungen und Recheneffizienz im Vergleich mit analogen MC-Simulationen untersucht. Zunächst wurden die statistischen Eigenschaften der abgegebenen Röntgendosis analysiert. Ausgehend vom jeweiligen Ausdruck der mit der Dosisabschätzung verbundenen Varianz bei der TLE- und der analogen MC-Methode, wurde der Varianzreduktionsfaktor der TLE- gegenüber der analogen MC-Methode hergeleitet. Zwei Testfälle wurden zum Vergleich der Leistungsfähigkeiten der TLE- und der analogen MC-Methode untersucht: (i) die Bestrahlung eines Kleintieres bei stereotaktischer Synchrotronstrahlentherapie und (ii) die Bestrahlung eines menschlichen Beckens bei einer Cone Beam - Computertomographie. Dosisverteilungen und Verteilungen der Effizienzsteigerungsfaktoren wurden analysiert. Letztere zeigen grosse Unterschiede innerhalb eines gegebenen Bestrahlungsfeldes und zwar in Abhängigkeit der geometrischen (Voxelgröße, Ballistik) und physikalischen (Material- und Strahleigenschaften) Parameter auf der Voxelskala. Typische Werte liegen zwischen 10 und 103, wobei niedrigere Werte in dichten Materialien (Knochen) außerhalb der bestrahlten Bereiche (nur Streudosis), und höhere Werte in weichen, direkt im Strahlenfeld liegenden Geweben festzustellen sind.Zeitschrift für Medizinische Physik 06/2014; · 1.81 Impact Factor

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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-thick walls,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

diameterand

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?.

446 Taylor, 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 BrachyDose 447

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 name AuthorMethod

? 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 scoringregionwasdecreased

??=0.690±0.002 cGy h−1U−1?

??=0.772±0.003 cGy h−1U−1?. Also shown on the plots are

to 0.1?0.1 cm2

to 0.1?0.1 cm2

from10?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 Imagyn125IThera 200103Pd

L=4.2 mm

r/cm

L=3.8 mmPoint

L=3.4 mmPoint 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?.

450 Taylor, 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

using voxels 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?

0.25 0.50.7512345 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?

0.250.5 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?

0.170

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

452Taylor, 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

Agreementwith thecalculations

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 Monroeand

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?

0.250.50.7512345 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?

0.604

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 BrachyDose 453

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 nameAuthor

?¯an

STM12501This 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.

454 Taylor, Yegin, and Rogers: Benchmarking the EGSnrc user-code BrachyDose 454

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

calculatedforthe STMsource 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?Electronic mail:

www.physics.carleton.ca/~drogers/

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