Photon-beam subsource sensitivity to the initial electron-beam parameters
Michael K. Fix,a! Paul J. Keall, and Jeffrey V. Siebers
Department of Radiation Oncology, Virginia Commonwealth University, P.O. Box 980058, Richmond,
Virginia 23298
!Received 30 November 2004; revised 10 February 2005; accepted for publication 11 February 2005;
published 29 March 2005"
One limitation to the widespread implementation of Monte Carlo !MC" patient dose-calculation
algorithms for radiotherapy is the lack of a general and accurate source model of the accelerator
radiation source. Our aim in this work is to investigate the sensitivity of the photon-beam subsource
distributions in a MC source model !with target, primary collimator, and flattening filter photon
subsources and an electron subsource" for 6- and 18-MV photon beams when the energy and radial
distributions of initial electrons striking a linac target change. For this purpose, phase-space data
!PSD" was calculated for various mean electron energies striking the target, various normally
distributed electron energy spread, and various normally distributed electron radial intensity distributions. All PSD was analyzed in terms of energy, fluence, and energy fluence distributions, which
were compared between the different parameter sets. The energy spread was found to have a
negligible influence on the subsource distributions. The mean energy and radial intensity significantly changed the target subsource distribution shapes and intensities. For the primary collimator
and flattening filter subsources, the distribution shapes of the fluence and energy fluence changed
little for different mean electron energies striking the target, however, their relative intensity compared with the target subsource change, which can be accounted for by a scaling factor. This study
indicates that adjustments to MC source models can likely be limited to adjusting the target subsource in conjunction with scaling the relative intensity and energy spectrum of the primary collimator, flattening filter, and electron subsources when the energy and radial distributions of the
initial electron-beam change. © 2005 American Association of Physicists in Medicine.
#DOI: 10.1118/1.1884385$
Key words: Monte Carlo simulation, photon beam, beam characteristics
I. INTRODUCTION
Monte Carlo !MC" methods have been used extensively in
medical physics for modeling linear accelerators and for radiation therapy dose calculations.1–26 MC methods used for
the latter purpose produce accurate results in the vicinity of
tissue heterogeneities, such as air cavities and surface irregularities, and are considered the most accurate method for
predicting dose distributions for treatment-planning purposes. Given the availability of fast radiotherapy-specific
MC codes and ever-increasing computer speed, a major barrier to the extensive clinical implementation of MC dose
calculations is the lack of a generalized source model of the
accelerator radiation source. In particular, such a source
model should allow a user with an arbitrary linear accelerator
to commission an MC dose-calculation algorithm that meets
a predetermined accuracy requirement !such as 2% or 2
mm27 or better" for patient dose calculations. A generalized
source model that can be tuned to match the output of a
general user’s accelerator is needed to overcome these limitations.
Several possible approaches are described and discussed
in detail in previous publications.17,28 One approach of a
source model is to characterize the beam analytically, as described by Jiang et al.29 and more recently by Fippel et al.30
A disadvantage of these source model types is their ability to
model physically unreal conditions.29 Another approach is to
1164
Med. Phys. 32 „4…, April 2005
perform full MC simulations of the radiation transport
through the accelerator head.9,24 Thereby, phase-space data
!PSD" is generated that contains the necessary data !position,
momentum, energy, and charge" for each particle traversing
the phase-space- !PS-" scoring plane. The PS plane is usually
perpendicular to the beam axis and above the irradiated body.
This PSD provides particle distributions in the PS plane,
thus, in this sense, PSD files can be used directly as source
models.3,4,21–23 It has been shown that by adjusting the parameters of the electron beam above the target, followed by
the full transport of particles through the beam-generating
devices to the PS plane, the dose calculation using that PSD
file is able to accurately match the measured
dose.9,15,20,23,24,31–33 However, the flexibility of directly using
a PSD file is limited when adjusting the data for use with
accelerators with slightly different outputs. The parameters
of the initial electron beam are treated as adjustable parameters, since they are not known in advance. Hence, the beam
characterization is done iteratively by adjusting the incident
electron-beam parameters to best match calculated dose distributions with measurements. Thus, researchers from several
institutions have conducted studies that result in different
parameters for the initial electron beam hitting the target in
order to match their own accelerators’ output.5,8,9,11,15,16,19–24
Applying this method in general requires local expertise in
implementing the MC PSD simulation, including the imple-
0094-2405/2005/32„4…/1164/12/$22.50
© 2005 Am. Assoc. Phys. Med.
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Fix et al.: Sensitivity of photon-beam subsource characteristics
1165
TABLE I. Parameter settings for the initial electron beam for the phase-space !PS" calculation of the 6-MV beam.
The bold numbers define the standard parameter set. The first column indicates to which group number the
parameter set belongs.
Group
Mean energy: Ee in MeV
Energy spread: !E in % of Ee
Radial intensity: !r in mm
I
I, II, III
I
II
II
II
III
III
III
5.0
6.2
7.0
6.2
6.2
6.2
6.2
6.2
6.2
1.28
1.28
1.28
1.28
1.28
1.28
0.0
0.64
2.56
0.96
0.96
0.96
0.0
0.48
1.92
0.96
0.96
0.96
mentation of an accurate geometric model of the local linear
accelerator. Furthermore, each iteration—using different
electron source parameters—is both labor intensive and time
consuming. However, recently Kawrakow et al.34 demonstrated that fast treatment head simulations can be performed, which has the potential to speed up iterative commissioning in the future or to replace the need for source
models altogether.
Apart from using analytical source models or the PSD file
itself as a source model, another approach is to create a
histogram-based source model from the PSD.8,11,14–17 For
these source models, the PSD is divided in subsource PSDs,
each representing a main component of the beam defining
system within the accelerator head, such as the target, the
primary collimator, or the flattening filter. By sampling the
initial parameters of a particle from these histogram distributions, these source models reconstruct the photon beam at the
PS plane. However, histogram source models suffer from the
same disadvantages as full PSD models in terms of adjusting
the model to match to a given user’s accelerator unless a
method is developed to adjust the histogrammed subsources
to match measurements. This requires knowledge of the sensitivity of the accelerator output when the initial electron
source parameters change, i.e., to identify how each subsource needs to be changed and what the suitable ranges for
these changes are. Adjustable histogram-based source models should allow matching to an individual user’s accelerator
beams without having to reperform the entire MC simulation; only scaling of subsource histogram distributions from
a standard precomputed MC simulation would be required to
tune the source model to match a user’s beam. Therefore, our
aim in this work is to investigate the sensitivity of the subsource characteristics as a function of initial electron parameters for 6- and 18-MV photon beams. For this purpose, PSD
was calculated for a variety of parameter sets of the initial
electron-beam data, including the radiation transport of photons, electrons, and positrons !photonuclear and neutron interactions were ignored". The PSD was analyzed in terms of
energy, fluence, and energy fluence distributions on a
subsource-by-subsource basis at source-to-surface distances
!SSDs" of 50, 100, and 200 cm. Hence, in this study we
Medical Physics, Vol. 32, No. 4, April 2005
provide information about the extent and within what ranges
each subsource is affected by changes of the initial electronbeam parameters.
II. METHODS AND MATERIALS
In this section, the creation of the PSD for the multiple
parameter sets is described in detail followed by a description of the analysis of the PSD in terms of energy, fluence
and energy fluence distributions.
A. Creation of phase-space data
MC simulations of the radiation transport for 6- and
18-MV photon modalities of a Varian Clinac 21EX !Varian
Oncology Systems, Palo Alto, CA 94304" were performed
using BEAMnrc.4 The treatment-head geometry and materials
used as input were based on data supplied by the accelerator’s manufacturer and previous publications.15,17,24 Simulations were initiated with electrons perpendicularly striking
the target. Primary and secondary particles including photons, electrons, and positrons were transported through the
beam-defining system, which contains the target, primary
collimator !PC", vacuum window, flattening filter !FF",
monitor chamber, field light mirror, and intervening air below the vacuum window. Particles were transported to a
plane directly above the secondary collimator jaws, where
their coordinates were saved in a PSD file. Several studies
have shown that the initial electron fluence above the linear
accelerator target can be described by three parameters,
namely, the mean electron energy Ee, the electron energy
spread !E, typically assumed to be normally distributed, and
the radial intensity spread !r of the electrons, also typically
assumed to be normally distributed.21–24 The angular distribution of the electron beam incident on the target is ignored
in this work, since Sheikh–Bagheri and Rogers23 concluded
in their study that credible divergences of up to 0.5°, show
no observable effect on dose and in-air off axis factors. In
this study, the three parameters, Ee , !E, and !r, were used to
define groups in which the parameter in question were modified while keeping the other parameters fixed. In group I, Ee
1166
Fix et al.: Sensitivity of photon-beam subsource characteristics
1166
TABLE II. Parameter settings for the initial electron beam for the phase-space !PS" calculation of the 18-MV
beam. The bold numbers correspond to define the standard parameter set. The first column indicates to which
group number the parameter set belongs.
Group
Mean energy: Ee in MeV
Energy spread: !E in % of Ee
Radial intensity: !r in mm
I
I, II, III
I
II
II
II
III
III
III
17.0
18.0
19.0
18.0
18.0
18.0
18.0
18.0
18.0
1.28
1.28
1.28
1.28
1.28
1.28
0.0
0.64
2.56
0.64
0.64
0.64
0.0
0.32
1.28
0.64
0.64
0.64
was varied, in group II, !r was varied, and in group III, !E
was varied. Table I and Table II give an overview of the
combinations for which PSD was computed for the 6- and
18-MV beams, respectively. An energy spread of !E
= 1.28% corresponds with a full width half maximum
!FWHM" of 3%, and a radial intensity spread !r of 0.96 mm
corresponds with an FWHM of 2.27 mm. A standard parameter set !SPS" was defined for each beam energy, and for this
set of parameters, previous dose calculations in water agreed
to within 1% or 1 mm with measurements in a water
phantom.24 On the basis of these SPS, the mean energy was
varied by about ±1 MeV, and the radial intensity as well as
FIG. 1. Energy spectra of the 6-MV beam for group I !Ee". !a" Target subsource. !b" Primary collimator subsource. !c" Flattening filter subsource. !d" Electron
subsource. Additionally, for better legibility, an error bar is only plotted at 0.9 MeV. The energy spectra are normalized so that the sum of all bin values is
equal to one. The legend refers to the mean energy Ee of the initial electron beam in MeV.
Medical Physics, Vol. 32, No. 4, April 2005
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Fix et al.: Sensitivity of photon-beam subsource characteristics
TABLE III. Fractional fluence components for the flattening filter !FF", primary collimator !PC", and electron subsources relative to the fluence for the
target !T" subsource for the 6-MV beam. The bold numbers refer to the
standard parameter set !SPS". The first column indicates to which group
number the parameter set belongs. The numbers in parentheses are the relative changes of the fluence ratios with respect to the SPS. The statistical
uncertainty is less than 1%.
Group Phsp E_!E_!r
I
SPS
I
II
II
II
5.0_1.28_0.96
6.2_1.28_0.96
7.0_1.28_0.96
6.2_1.28_0.00
6.2_1.28_0.48
6.2_1.28_1.92
$FF % $T
0.0603
0.0612
0.0626
0.0570
0.0592
0.0630
!0.985"
(1.000)
!1.024"
!0.939"
!0.968"
!1.030"
$PC % $T
0.0338 !0.96"
0.0352 (1.000)
0.0363 !1.032"
0.0285 !0.810"
0.0315 !0.896"
0.0434 !1.235"
$electrons % $photons
0.001 56
0.001 86
0.002 06
0.001 80
0.001 83
0.001 92
!0.839"
(1.000)
!1.104"
!0.967"
!0.982"
!1.029"
the energy spread were varied by factors of 0, 0.5, and 2.0.
These parameter ranges cover most of the parameter settings
used for PSD calculations at several research
institutions.5,8,9,11,14,15,17,19,21–24 In the remainder of this paper, each group is referred with the particular parameter
changed shown in parentheses. For example, group I !Ee"
refers to the parameter sets within group I, in which the mean
energy of the initial electron beam Ee was changed.
For all of the MC simulations, the threshold energies for
electron and photon transport, ECUT and PCUT, were set to
0.70 and 0.010 MeV, respectively, except in the target for the
18-MV beam, where the value of PCUT was increased to 0.15
MeV, which had been previously shown to negligibly impact
the PSD.17,24 The discrete electron and photon creation
thresholds, AE and AP, were set to 0.70 and 0.010 MeV, respectively. The default bremsstrahlung cross sections, i.e.
Bethe-Heitler, were used for all MC simulations. To reduce
the calculation time, the “uniform bremsstrahlung splitting”
variance reduction technique was applied with a bremsstrahlung splitting number of 20. The splitting number was not
applied to higher-order bremsstrahlung and annihilation photons. For the 6 and 18-MV beams, at least 100" 106 and
20" 106 histories, respectively, were simulated leading to at
least 106" 106 !6 MV" and 95" 106 !18 MV" particles in the
PSD files directly above the secondary collimator jaws.
The PSD file contains the following data for each particle
crossing the PS-scoring plane at a given z coordinate:
P = #x,y,u, v,E,q,weight,LATCH$,
!1"
where x and y are the position coordinates of the particle; u
and v are the direction cosines in the x and y directions,
respectively; E is the energy; q is the charge; weight is the
particle statistical weight; and LATCH is a tag that records
the history of the previous particle interaction locations. The
total PSD was separated into PSD files for the target, PC and
FF, based on the location of the last interaction of the photons. With these three subsource PSDs, over 99.5% of all
photons scored in the total PSD file were used. The remaining 0.5% of the photons had their last interaction in air or in
one of the other head components !ionization chamber, mirror, etc.". As a result, they were excluded from this study. In
Medical Physics, Vol. 32, No. 4, April 2005
1167
addition, a PSD file for the contaminant electrons was separated from the total PSD.
B. Analysis of subsource phase-space characteristics
The phase-space analysis was limited to PSD particles
that have the potential to contribute to the patient’s radiation
dose for field sizes up to 42" 42 cm2 at the isocenter plane
!the maximum field size achievable with this accelerator is
40" 40 cm2 at the isocenter plane". This was accomplished
by determining the intersection of each particle’s trajectory
with the isocenter plane !SSD 100 cm" for each particle from
the subsource PSD, presuming the material between the PSD
plane and the isocenter plane was a vacuum, and by keeping
all particles within a radius #30 cm of the central axis at the
isocenter plane. For an analysis of the directional distributions at SSDs of 50 and 200 cm, particles within 15 cm !SSD
50 cm" and 60 cm !SSD 200 cm" of the central axis were
used.
Subsource PSD data was analyzed in terms of fractional
fluence and energy fluence components for each parameter
set within a group. The fractional fluence and energy fluence
components for the PC and FF were defined as ratios at the
isocenter plane of the planar fluence and planar energy fluence contributions from the PC and FF subsources to those
for the target. The fractional components for the electron
subsource were determined as a ratio at the isocenter of the
planar electron fluence and energy fluence to those from the
three photon subsources together. For these ratios the fluence
and energy fluence was determined over the full region, i.e.,
30 cm diameter at the isocenter. In addition, the energy distributions for each subsource and parameter set were determined, and, thereby, the energy spectra, averaged over the
whole field, were established. Apart from these energy spectra, the mean energy as a function of the off-axis distance
was evaluated. Furthermore, the beams were characterized in
terms of radial fluence and radial energy fluence distributions
for all parameter sets, each subsource, and both beam energies. Within this analysis, the energy spectra, the radial mean
energy, the radial fluence, and the radial energy fluence distributions were evaluated in the form of histograms. The
number of bins depended on the subsource and the considered quantity, whereas the bin widths changed with off-axis
distance for the radial distributions to achieve similar statistical uncertainties in each bin. Changing the initial electronbeam parameters, especially Ee, affected the photon yield,
and consequently the fluence and energy fluence distributions. Hence, to compare the shape of the radial energy fluence between parameter sets, the radial energy fluence was
normalized to the integral value calculated for the SPS !integral normalization".
III. RESULTS AND DISCUSSION
The results are structured in sections where each section
contains the results of the parameter groups for one physical
quantity.
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Fix et al.: Sensitivity of photon-beam subsource characteristics
TABLE IV. Fractional fluence components for the flattening filter !FF", primary collimator !PC", and electron subsources relative to the fluence for the
target !T" subsource for the 18-MV beam. The bold numbers refer to the
standard parameter set !SPS". The first column indicates to which group
number the parameter set belongs. The numbers in parentheses are the relative changes of the fluence ratios with respect to the SPS. The statistical
uncertainty is less than 1%.
Group Phsp E_!E_!r
I
SPS
I
II
II
II
17_1.28_0.64
18_1.28_0.64
19_1.28_0.64
18_1.28_0.00
18_1.28_0.32
18_1.28_1.28
$FF % $T
0.1039
0.1056
0.1077
0.1014
0.1031
0.1099
!0.984"
(1.000)
!1.019"
!0.960"
!0.976"
!1.041"
$PC % $T
0.0369
0.0371
0.0374
0.0334
0.0350
0.0425
!0.994"
(1.000)
!1.008"
!0.901"
!0.944"
!1.144"
$electrons % $photons
0.004 80
0.005 04
0.005 27
0.004 99
0.005 00
0.005 08
!0.955"
(1.000)
!1.047"
!0.991"
!0.993"
!1.010"
1168
TABLE V. Fractional energy fluence components for the flattening filter !FF",
primary collimator !PC", and electron subsources relative to the target !T"
subsource fluence for the 6-MV beam. The bold numbers refer to the standard parameter set !SPS". The first column indicates to which group number
the parameter set belongs. The numbers in parentheses are the relative
changes of the fluence ratios compared with those for the standard parameter
set, for which the ratio was set to one. The statistical uncertainty is less than
1%.
Group Phsp E_!E_!r
I
SPS
I
II
II
II
5.0_1.28_0.96
6.2_1.28_0.96
7.0_1.28_0.96
6.2_1.28_0.00
6.2_1.28_0.48
6.2_1.28_1.92
&FF % &T
0.0469
0.0456
0.0451
0.0430
0.0443
0.0468
!1.029"
(1.000)
!0.989"
!0.944"
!0.974"
!1.028"
&PC % &T
0.0329
0.0316
0.0309
0.0261
0.0286
0.0387
!1.040"
(1.000)
!0.976"
!0.827"
!0.906"
!1.223"
&electrons % &photons
0.002 35
0.002 75
0.003 01
0.002 71
0.002 73
0.002 77
!0.854"
(1.000)
!1.095"
!0.984"
!0.994"
!1.014"
A. Fractional fluence
The fractional fluence components for the parameter sets
of group I !Ee" and group II !!r" are given in Table III and
Table IV for the 6 and 18-MV beams, respectively. For the
FF and PC subsources, the largest variations in the fractional
fluence occurred in group II !!r" with !r set to its extreme
values. Compared with the SPS, the FF fractional fluence
component changed from a decrease of 6% !6 MV" and 4%
!18 MV" with !r = 0 to an increase of 3% !6 MV" and 4% !18
MV" with !r at the maximum value tested. For the same
case, the PC subsource showed a decrease of 19% !6 MV"
and 10% !18 MV" and an increase of 24% !6 MV" and 14%
!18 MV". This is due to the fact that as !r increases, more
particles from the target strike the PC due to the increased
radial geometric proximity of the PC with respect to the
photon source. This, in turn, produces increasing scatter for
the PC subsource and decreases the fluence for the target
subsource. Then, more particles strike the thinner part of the
FF, and the scatter from the FF decreases. However, this
decrease is less compared with the decrease of the target
fluence. For group I !Ee" the geometry remains constant,
leading to smaller changes in the relative fluences compared
with those for group II !!r". The largest deviation for the
electron subsource was observed for group I !Ee", with a
decrease of %16% !6 MV" and %4% !18 MV" at the minimum Ee of the group and an increase of %10% !6 MV" and
%5% !18 MV" at the maximum Ee of the group. This is
because higher-energy photons produce higher-energy, more
forward directed electrons. Overall, the fractional fluence
variations were lower for the 18-MV beam compared with
those of the 6-MV beam—within the range used in the parameters sets. The variation of the fractional fluence with Ee
and !r indicates that the relative weights of the subsources
change when the initial electron beam on the target changes
!i.e., for different parameter sets" and, hence, needs to be
taken into account when tuning the source model to match
measurements. The effects on the fractional fluence components in group III !!E" was negligible, i.e., the results agree
to within two standard deviations, hence, they were not listed
in Table III and Table IV.
Medical Physics, Vol. 32, No. 4, April 2005
B. Fractional energy fluence
Table V and Table VI show the results for the fractional
energy fluence for the 6 and 18-MV beams, respectively.
Since the mean energy for the target subsource photons is
higher than for the FF and PC subsource photons, their fractional energy fluence components are lower than their corresponding fractional fluence components. The fractional energy fluence for different parameter sets in group II !!r",
compared with the SPS, shows the same trends as those for
the fractional fluence: For increasing !r in group II !!r", the
fractional energy fluence for the FF subsource changed from
a decrease of 6% !6 MV" and 4% !18 MV" with !r = 0 to an
increase of 3% !6 MV" and 4% !18 MV" with !r at the
maximum value used. For the PC subsource, these values
changed from a decrease of 17% !6 MV" and 10% !18 MV"
to an increase of 22% !6 MV" and 16% !18 MV".
The group I !Ee" fractional energy fluence results, however, show opposite trends compared with those found for
the fractional fluences. This is due to the fact that for increasing incident photon energy, the fraction of energy retained by
the Compton photon decreases, on average. As Ee increases,
the ratio of the mean photon energies decreases more rapidly
TABLE VI. Fractional energy fluence components for the flattening filter
!FF", primary collimator !PC", and electron subsources relative to the target
!T" subsource fluence for the 18-MV beam. The bold numbers refer to the
standard parameter set !SPS". The first column indicates to which group
number the parameter set belongs. The numbers in parentheses are the relative changes of the fluence ratios compared with those for the standard
parameter set, for which the ratio was set to one. The statistical uncertainty
is less than 1%.
Group Phsp E_!E_!r
I
SPS
I
II
II
II
17_1.28_0.64
18_1.28_0.64
19_1.28_0.64
18_1.28_0.00
18_1.28_0.32
18_1.28_1.28
&FF % &T
0.0609
0.0608
0.0608
0.0586
0.0595
0.0630
!1.002"
(1.000)
!1.001"
!0.964"
!0.979"
!1.037"
&PC % &T
0.0194
0.0189
0.0186
0.0170
0.0178
0.0220
!1.021"
(1.000)
!0.981"
!0.896"
!0.940"
!1.157"
&electrons % &photons
0.006 62
0.007 00
0.007 39
0.006 98
0.006 99
0.006 99
!0.947"
(1.000)
!1.056"
!0.997"
!0.997"
!0.999"
1169
Fix et al.: Sensitivity of photon-beam subsource characteristics
1169
FIG. 2. Radial mean energy distributions in the isocenter plane for group I !Ee". !a" Target subsource of the 6-MV beam. !b" All nontarget subsources of the
6-MV beam. !c" Target subsource of the 18-MV beam. !d" All nontarget subsources of the 18-MV beam. The numbers in the plot correspond with the
according Ee in MeV. Where no error bars are visible, the statistical uncertainties are smaller than the linewidth used for plotting. The legend refers to the mean
energy Ee of the initial electron beam in MeV. PC: primary collimator; FF: flattening filter.
than the corresponding ratio of the photon fluences increase
!see Table III and Table IV", causing the fractional energy
fluences to decrease.
Again, the fractional energy fluence for the electrons
changed most for group I !Ee" and resulted in deviations of
up to 14%. The analysis showed virtually no changes, i.e.,
the results agree to within two standard deviations, for the
fractional fluence and fractional energy fluence components
for group III !!E"; thus, they were not listed in Table V and
Table VI.
C. Energy spectra and mean energy
Figure 1 illustrates the energy spectra for each subsource
for the 6-MV beam of group I !Ee". These spectra show the
largest changes in shape for all parameter groups investigated. The energy spectra are normalized so that the sum of
all bin values is equal to one; thus, each bin value represents
its probability. For increasing Ee, photons with higher energy
were produced and, consequently, the fraction of low-energy
photons is reduced in the photon energy spectra, leading to
an increase of the mean photon energy. This can also be seen
by the mean energy as a function of off-axis distance in Fig.
2!a" and Fig. 2!b" for group I !Ee". The mean energy deMedical Physics, Vol. 32, No. 4, April 2005
creases about 20% and increases about 10% when an Ee of
5.0 or 7.0 MeV is used instead of 6.2 MeV in the SPS,
respectively. The analogous results for the 18-MV beam are
depicted in Fig. 2!c" and Fig. 2!d". The impact of the PC on
the target subsource is clearly visible at off-axis distances
greater than 25 cm, beyond which the beam is attenuated by
the PC !see Fig. 4". However, whereas beam hardening appears for the 6-MV beam, beam softening due to the increased attenuation of high-energy photons in the PC occurred in the 18-MV beam. Note, for the electrons the mean
of the total energy is depicted and does not include energy
loss in air between the plane where the PSD was acquired
and the isocenter. The changes of the energy distributions for
group III !!E" were negligible. These results agree with those
published by others.13,15,22 For example, for a 10" 10-cm2
field size, Ma et al.13 determined that the mean energy for the
FF subsource is around 1.3 MeV for a Varian Clinac
2300C/D 6 MV photon beam. For a 40" 40-cm2 field size,
Fix et al.15 obtained results similar to Fig. 2!b" for the FF and
PC subsources. In this latter study, slightly higher and lower
mean energies were reported for the target and electron subsource, respectively. However, the plane where the mean energy distributions were evaluated is not the isocenter plane as
used in our present study, but rather a plane directly below
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Fix et al.: Sensitivity of photon-beam subsource characteristics
1170
FIG. 3. Radial fluence distribution in the isocenter plane. !a" Target subsource of the 6-MV beam for group I !Ee". !b" The same as !a", but normalized to the
same integral value of the standard parameter set !6.2_1.28_0.96". !c" The same as !a" for the 18-MV beam. !d" The same as !c", but normalized to the same
integral value of the standard parameter set !18_1.28_0.64". Where no error bars are visible, the statistical uncertainties are smaller than the linewidth used for
plotting. The legend refers to the mean energy Ee of the initial electron beam in MeV.
FIG. 4. Radial fluence distribution in the isocenter plane. !a" Target subsource of the 6-MV beam for group II !!r". !b" The same as !a" for the 18-MV beam.
Where no error bars are visible, the statistical uncertainties are smaller than the linewidth used for plotting. The legend refers to the radial electron intensity
distribution !r in mm.
Medical Physics, Vol. 32, No. 4, April 2005
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Fix et al.: Sensitivity of photon-beam subsource characteristics
1171
FIG. 5. Radial fluence distribution in the isocenter plane for the primary collimator !PC", the flattening filter !FF", and the electron subsources for group I !Ee".
!a" For the 6-MV beam. !b" The same as !a", but normalized to the same integral value of the standard parameter set !6.2_1.28_0.96". !c" For the 18-MV beam.
!d" The same as !c", but normalized to the same integral value as the one for the standard parameter set !18_1.28_0.64". The numbers in the plot correspond
with the according Ee in MeV, where Ee refers to the mean energy of the initial electron beam. Where no error bars are visible, the statistical uncertainties are
smaller than the linewidth used for plotting.
the secondary collimator jaws. In the study by SheikhBagheri et al.,22 the mean energy distributions for the target
subsource agree with the present study’s data for the 6- and
18-MV beams. The decreasing mean energy as the off-axis
distance increases for the combined beam is in agreement
with other studies.3,8,9,11–13,15,22 However, none of these previous studies show how the mean energy distribution is affected by changing the initial electron source nor show the
data for the subsources.
D. Radial fluence distributions
Figure 3 shows the sensitivity of the target subsource fluence as a function of the off-axis distance at the isocenter
plane for different parameter sets. The fluence increased significantly for group I !Ee", where the mean energy Ee was
increased #Fig. 3!a" and Fig. 3!c"$. This is due to the fact that
the radiation yield increases and is more forward directed
with increasing electron energy. As a consequence, the
shapes of the radial fluence distributions for the target subsource change significantly with an increase of the central
Medical Physics, Vol. 32, No. 4, April 2005
axis fluence relative to the off axis fluence, as shown in Fig.
3!b" and Fig. 3!d". In Fig. 4!a" and Fig. 4!b", the radial fluence distributions for group II !!r" are shown. The maximum
fluence is shifted to larger off-axis distances for decreasing
!r of the initial electron beam. The deviation for the maximum fluence is up to about 20% compared with the SPS.
These changes in the fluence distributions result from the
effect that more bremsstrahlung photons are absorbed or
scattered by the PC as !r increases. The radial fluence distributions for the PC, the FF, and the electron subsource for
group I !Ee" are illustrated in Fig. 5. The general behavior is
the same as for the target subsource, i.e., increasing the mean
initial electron energy Ee results in increased radial fluence
distributions. This is because the increased fluence from the
target impinging on the FF and the PC result in increased
scatter radiation from these subsources. However, whereas
the shape of the radial fluence distribution changes significantly for the target subsource, Fig. 5!b" and Fig. 5!d" demonstrate that for nontarget subsources the distribution shapes
remain the same. Note, in Fig. 5!b" and Fig. 5!d", the integral
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Fix et al.: Sensitivity of photon-beam subsource characteristics
1172
FIG. 6. Radial fluence distribution in the isocenter plane for the primary collimator !PC", the flattening filter !FF", and the electron subsources for group II !!r".
!a" For the 6-MV beam. !b" For the 18-MV beam. Where no error bars are visible, the statistical uncertainties are smaller than the linewidth used for plotting.
The legend refers to the radial electron intensity distribution !r in mm.
normalization was applied. The normalized radial fluence
distributions are within their statistical uncertainty, i.e.,
within about 1% !1 SD".
For the nontarget subsources, Fig. 6 illustrates the radial
fluence distribution for group II !!r". The fluence distributions for this group compared with those for the SPS vary by
16% for 6 MV and 4% for 18 MV. The integral normalization of these distributions demonstrates that the shapes of the
radial fluence distributions for each subsource remain within
their statistical uncertainty of about 1%. This is an important
result that will be discussed later in this paper.
The normalized data for the FF, PC, and electron subsources for group I !Ee" and group II !!r", but evaluated at
SSDs of 50 and 200 cm, shows that the deviation between
the normalized fluence distributions is within 1.5% for all
SSDs analyzed and both beam energies. Hence, this data
suggests that while the target subsource characteristics are
strongly sensitive to the parameter set used, the changes for
the nontarget subsources could be described by changing the
relative weight of the subsources relative to the target subsource.
E. Radial energy fluence distributions
Figure 7 shows the radial energy fluence as a function of
the off-axis distance for the target subsource for group I !Ee"
and group II !!r". The energy fluence distributions change in
values and shape due to the changes in the radial mean energy and fluence distributions. For the same two parameter
groups, Fig. 8 illustrates the results for the nontarget subsources. The radial energy fluence increased with increasing
Ee in group I !Ee" for all subsources and both beam energies.
For example, the energy fluence at the central axis increases
by a factor of about 2.5 when Ee is increased from 5.0 to 7.0
MeV. The FF, PC, and electron subsources show less sensitivity in terms of the energy fluence distributions for the
range of !r used in this work #Fig. 8!b" and Fig. 8!d"$. The
shapes of the radial energy fluence for all nontarget subMedical Physics, Vol. 32, No. 4, April 2005
sources were found to be virtually constant !within their statistical uncertainty of about 1.5%" after integral normalization was applied.
The results for the radial energy fluence distributions for
the parameter sets within group III !!E", where the energy
spread of the initial electron beam !E was changed, show
that the deviations of the energy fluence, compared with
those for the SPSs for all subsources, were within the statistical uncertainties of about 1.5% !1 SD".
IV. SUMMARY AND CONCLUSIONS
In this work, the impact of the initial electron-beam parameters on the photon-beam subsource distributions was investigated. For this purpose, the initial electron beam impinging the target for 6- and 18-MV photon beams was
described by the mean electron energy, the electron energy
spread, and the radial intensity distribution of the electrons.
Parameter sets were defined, changing one parameter at a
time and grouped according to the parameter changed. For
each parameter set, PSD was computed using full MC simulations of the radiation transport through the accelerator head
and afterward separated into subsource PSDs. Subsource-bysubsource comparisons of the subsource characteristics were
performed in terms of energy, radial mean energy, radial fluence, and radial energy fluence distributions for SSDs of 50,
100, and 200 cm. The parameter changes showed a larger
influence on the 6-MV beam compared with the influence on
the 18-MV beam for the range used within the parameter
sets.
Changing the parameter Ee resulted in the largest changes
for the energy distributions as well as for the values of the
fluence and energy fluence distributions for both beam energies. Whereas varying the parameter !r led to a significant
change in the shape of the radial fluence and the radial energy fluence distributions of the target subsources for the 6and 18-MV beams, at each SSD these distributions retained
their shape for the FF, the PC, and the electron subsources.
The deviations for all quantities used to characterize the pho-
1173
Fix et al.: Sensitivity of photon-beam subsource characteristics
1173
FIG. 7. Radial energy fluence distribution in the isocenter plane. !a" Target subsource of the 6-MV beam for group I !Ee". !b" Target subsource of the 6-MV
beam for group II !!r". !c" The same as !a" for the 18-MV beam. !d" The same as !c" for the 18-MV beam. Where no error bars are visible, the statistical
uncertainties are smaller than the linewidth used for plotting. The legend refers to the mean energy Ee of the initial electron beam in MeV and to the radial
electron intensity distribution !r in mm, respectively. El: electron; Fl: fluence.
ton beams, when the parameter !E was changed, were within
their statistical uncertainties, i.e., the subsource characteristics of the 6- and 18-MV beams were not sensitive on !E for
the range of !E used. Since this study explicitly used the
geometry and materials for a specific accelerator design !the
Varian 21EX" at specific energies, the results are not necessarily generalizable to other beam energies or linear accelerator designs, although presumably with qualitatively comparable results, e.g., Sheigk-Bagheri and Rogers22 as well as
Faddegon et al..35
The results of this study contain valuable information for
the commissioning procedure of MC source models. The
data obtained suggests that besides the target subsource, only
the relative weight to the target subsource and the energy
spectrum need to be changed for the other subsources in
order to adjust the source model to match differently tuned
accelerators. This has the potential to ease the MC source
model commissioning procedure substantially. In addition,
this study provides information about the range that subsources should be changed; for example, Fig. 1 shows the
Medical Physics, Vol. 32, No. 4, April 2005
energy spectrum variations for each subsource when different mean energies for the initial electrons are used. For a
histogram-based source model, the variation can be accounted for by scaling the energy histogram distributions that
represent the subsource to be tuned. Furthermore, an iterative
procedure similar to that described by Sheigk-Bagheri and
Rogers23 to determine the optimal parameters for the initial
electron beam could be applied to histogram-based source
models such as that described in Fix et al.17 via the following:
!a"
!b"
Starting with the source model for the SPS.
Matching calculated and measured depth-dose
curves; select an Ee and modify the histograms affected by this parameter in the source model, i.e.,
scaling the subsource energy spectra according the
data from Sec. III C while simultaneously adjusting
the relative subsource intensity for the scattered subsources by interpolating the data from Sec. III A.
Select a different Ee until depth-dose curves match.
1174
Fix et al.: Sensitivity of photon-beam subsource characteristics
1174
FIG. 8. Radial energy fluence distribution in the isocenter plane for the primary collimator !PC", the flattening filter !FF", and the electron subsources for group
I !Ee". !a" For the 6-MV beam and group I !Ee". !b" For the 6-MV beam and group II !!r". !c" For the 18-MV beam and group I !Ee". !d" For the 18-MV beam
and group II !!r". The numbers in the plot correspond with the according Ee in MeV, where Ee refers to the mean energy of the initial electron beam, and the
legend refers to the radial electron intensity distribution !r in mm. Where no error bars are visible, the statistical uncertainties are smaller than the linewidth
used for plotting. El: electron; Fl: fluence.
!c"
!d"
Matching calculated and measured in-air off-axis
factors; select an !r and modify the histograms affected by this parameter in the source model according to the change in !r of group II !see Sec. III D",
i.e., adjusting the histogram describing the radial
fluence distribution of the target subsource while simultaneously adjusting the relative subsource intensity for the scattered subsources by interpolating the
data from Sec. III A. Note that the scattered subsource histogram distributions could remain constant. Select a different !r until in-air off-axis factors match.
Iterate the procedure !b" to !c" until the acceptance
criteria are fulfilled.
The data presented in this study provides the basic information and the ranges within the source model histograms
should be adjusted during the tuning process.
In this publication, only a subset of all analyzed data is
presented, since there is a high volume of data for the energy
spectra, mean energy, fluence, and energy fluence distributions. However, a full set of results is available from the
authors upon request.
Medical Physics, Vol. 32, No. 4, April 2005
ACKNOWLEDGMENTS
The authors wish to recognize and thank Dr. Radhe Mohan for his efforts in developing the VCU Monte Carlo program. We appreciate Dr. Bruce Libby for establishing the
initial Monte Carlo head modeling used at VCU. The clarity
of this article was much improved by Devon Stein’s careful
review. Varian Medical Systems provided us with the engineering diagrams and material specifications required for the
modeling of the linear accelerators. We acknowledge the financial support of Philips Medical Systems, ACS Grant No.
IRG-73-001-28 and NIH Grant No. 1R01CA098524.
a"
Address for correspondence: Michael Fix, Department of Radiation Oncology, Virginia Commonwealth University, 401 College Street, P.O. Box
980058, Richmond, Virginia 23298.
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