Determining the incident electron fluence for Monte Carlo-based photon
treatment planning using a standard measured data set
Paul J. Keall,a) Jeffrey V. Siebers, Bruce Libby, and Radhe Mohan
Department of Radiation Oncology, Virginia Commonwealth University, P.O. Box 980058, Richmond,
Virginia 23298
!Received 5 September 2002; accepted for publication 28 January 2003; published 25 March 2003"
An accurate dose calculation in phantom and patient geometries requires an accurate description of
the radiation source. Errors in the radiation source description are propagated through the dose
calculation. With the emergence of linear accelerators whose dosimetric characteristics are similar
to within measurement uncertainty, the same radiation source description can be used as the input
to dose calculation for treatment planning at many institutions with the same linear accelerator
model. Our goal in the current research was to determine the initial electron fluence above the linear
accelerator target for such an accelerator to allow a dose calculation in water to within 1% or 1 mm
of the measured data supplied by the manufacturer. The method used for both the radiation source
description and the patient transport was Monte Carlo. The linac geometry was input into the Monte
Carlo code using the accelerator’s manufacturer’s specifications. Assumptions about the initial
electron source above the target were made based on previous studies. The free parameters derived
for the calculations were the mean energy and radial Gaussian width of the initial electron fluence
and the target density. A combination of the free parameters yielded an initial electron fluence that,
when transported through the linear accelerator and into the phantom, allowed a dose-calculation
agreement to the experimental ion chamber data to within the specified criteria at both 6 and 18 MV
nominal beam energies, except near the surface, particularly for the 18 MV beam. To save time
during Monte Carlo treatment planning, the initial electron fluence was transported through part of
the treatment head to a plane between the monitor chambers and the jaws and saved as phase-space
files. These files are used for clinical Monte Carlo-based treatment planning and are freely available
from the authors. © 2003 American Association of Physicists in Medicine.
#DOI: 10.1118/1.1561623$
Key words: Monte Carlo, initial electron fluence, beam modeling
I. INTRODUCTION
Rigorous Monte Carlo treatment planning will transport particles from the entrance of the accelerator target until they
and their progeny are absorbed in or exit the patient geometry or the patient. To obtain accurate dose calculation in the
patient, the characteristics of the electron beam above the
target need to be accurately modeled and the particles accurately transported through the beam-generating and beammodifying devices. Errors in determining the electron fluence incident on the target will directly cause a systematic
error in every dose calculation, whether the dose calculation
uses a phase-space file, or a source model based on the
phase-space file. !The term phase-space file, as used here,
means a list of particles specified at a plane with records
describing the charge, energy, position and direction of each
particle."
For treatment planning, the ICRU1,2 reports suggest that
the maximum error in dose calculation should be 2% of the
absolute dose !or within 2 mm of the absolute dose in highdose gradient regions". This 2% error needs to be shared
among many uncertainties, such as the radiation source determination !the subject of this article", the dosimetric effects
of the CT number to density conversion and the accuracy of
transport in the heterogeneous patient. Further Monte Carlospecific potential sources of error are energy cut-offs,
574
Med. Phys. 30 „4…, April 2003
density-to-material conversion, dose-to-material to dose-towater conversion, etc. Thus, in order to calculate dose to the
patient to within 2% or 2 mm we estimate that the source
modeling error should be within 1% or 1 mm. This value is
below the estimated 1.5% uncertainty of absolute dosimetry
protocols.3
The accurate characterization of linear acceleratorproduced radiation is becoming more appropriate now, due
to the dosimetric similarity of modern machines produced by
the same vendor with beam parameters with observed variations (between linear accelerators of the same vendor) being
approximately equivalent to the precision of measurement.4
Indeed, one linear accelerator vendor is offering a CD containing a ‘‘standard’’ set of beam data for one type of linear
accelerator. The data set contains depth-dose curves and dose
profiles for a variety of field sizes including open field and
wedged fields. This beam data was used as the measurement
set for which the source modeling results were compared.
Thus, one single source description can be used for dose
calculation by many centers.
Over the years, much effort has been devoted to Monte
Carlo modeling of linear accelerators.5–34 Arguably, the most
comprehensive studies have been performed by SheikhBagheri and Rogers,28,29 who have studied the sensitivity of
photon beam simulations to the initial electron fluence pa-
0094-2405Õ2003Õ30„4…Õ574Õ9Õ$20.00
© 2003 Am. Assoc. Phys. Med.
574
575
Keall et al.: Determining the incident electron fluence
rameters and characterized the phase space from nine megavoltage beams. They have concluded that the two most important parameters for simulating photon radiotherapy beams
are the mean energy and the radial spread of the incident
electron beam; these parameters comprise two of the three
parameters being studied in this work !the other being target
density". The niche of the current research is that unlike previous work, the beam modeling is for a standard data set and
thus is widely applicable to the radiotherapy community.
Our aims in this work were to !1" determine the electron
fluence above the target that, when transported through the
treatment head and used for dosimetric calculations, can reproduce a standard dosimetric measured data set in water to
within 1% or 1 mm; !2" use this electron fluence to transport
particles through the target, flattening filter, etc., and, up to
the first treatment dependent component, i.e., the movable
jaws, to create a patient independent phase-space file for use
in Monte Carlo treatment planning; and !3" make this phasespace file available for use by other researchers.
II. METHOD AND MATERIALS
A. Accelerator
The accelerator treatment head modeled here was that of
type Varian Clinac 21EX !Varian Oncology Systems, Palo
Alto, CA 94304 USA". This accelerator has a standing waveguide and a 270° bending magnet. Both photon modalities !6
and 18 MV" were investigated.
B. Measured data
Varian provides a measured data set for the 21EX !Varian
Oncology Systems, Clinac EX Precommissioning Data
Package". This data set contains depth-dose and lateral profile curves for a variety of field sizes and wedge angles.
Measured data for our 21EX showed no significant difference to the Varian data set. For generality, we used the Varian
data set, rather than our own measurements, as the calculation benchmark, so that the phase space developed in this
work could be applicable to all accelerators of this type.
The Varian measurements were performed in a 48
!48!48 cm3 water tank using a Wellhöfer IC15 ionization
chamber !Scanditronix Wellhöfer, Bartlett, TN 38133". The
SSD was 100 cm. Due to water tank size constraints, the
largest beam with its central axis aligned with the tank center
was 25!25 cm2 .
C. Initial electron fluence assumptions
The initial distribution of electrons, %!E,x,y,&,'", just
above the target !known z-position" is a 5-dimensional function, which can be described by the variables E, the kinetic
energy; x and y, the lateral positions !z is fixed"; &, the polar
angle; and ', the azimuthal angle. To determine the electron
distribution, four assumptions were made. These assumptions and their justifications are explained below.
Medical Physics, Vol. 30, No. 4, April 2003
575
1.The x and y spatial distributions are Gaussian
Karzmark et al.35 in their discussion of electron beam optics of magnet systems showed that the current density of the
electron beam above the target is centrally peaked with tails
distributed approximately normally on either side of the
peak. Also, a Gaussian-shaped distribution can be observed
in the results of Jaffray et al.,36 who measured the distribution of the bremsstrahlung focal radiation.
The distribution of the bremsstrahlung focal radiation is a
convolution of the initial electron distribution and the spread
of the electrons before the bremsstrahlung events. Our Monte
Carlo calculations for a monodirectional electron point
source upon the target have determined that the full width
half maximum !FWHM" of the spread of the electrons before
the bremsstrahlung events is (5 )m at 6 MV and (20 )m
at 18 MV. Because the spread of the electrons is small in
comparison with the spot size !order of mm", we can conclude that the initial electron distribution is approximately
equal to the bremsstrahlung radiation distribution. Thus, we
can limit our allowable initial electron distributions to the
limits measured by Jaffray et al.,36 i.e., 1.2 to 1.4 mm
FWHM at 6 MV and 0.9 to 1.6 mm FWHM at 18 MV. Note
that the values of Jaffray et al. measured from a 2100C and
the 21EX are modeled here. However, due to similar accelerator and bending magnet structure design, the 2100C and
21EX initial electron distributions are expected to be similar.
2. The x and y spatial distributions are equal
The measured data set contained only cross-plane !x"
dose-profile curves. Thus, in the absence of more information here, we assumed that the x and y spatial distributions
are equal. The results of Jaffray et al.37 indicate a reasonable
degree of symmetry for the Varian 2100 linear accelerators,
especially at low energy. Using this assumption, the x and y
reduce to a single variable, r" !x 2 #y 2 , which determines
the spatial distribution in the radial direction.
3. The electrons are monodirectional
Karzmark et al.35 have provided the typical beam transport acceptance values for the initial electron angle as 1–5
mradian !0.06 –0.3 degrees". This angle is very close to 0
!cos 5 mradian"1.0000". Hence, we assume monodirectionality.
4. The spread of the electrons about the mean
energy is Gaussian and has a FWHM of 3%
Using a magnetic spectrometer, Tanabe and Hamm38 measured the electron spectrum from the accelerating waveguide
for a Varian Clinac 1800 to have a FWHM of about 3% for
both the 6 and 18 MV modes. It was assumed that the linear
accelerator modeled here had a similar energy spread. This
value may change with waveguide type and also between
accelerators with bending magnets and those ‘‘in-line.’’
Using the assumptions above, the initial 5-dimensional
electron fluence, %(E,x,y, & , ' ), is reduced to two dimensions, %„E ,G(r)…, where E is the mean electron energy
Keall et al.: Determining the incident electron fluence
576
above the target, and G(r) is the initial electron radial Gaussian width, which can be characterized by FWHMrad. However, there is also variation in the density of the tungsten
alloy used for the target !$ 0.5 g cm%3 ) given by the manufacturer. Thus, the third unknown to be determined is the
target density, * target .
The density and composition of the target backing and
flattening filter are machined to tighter specifications than the
target. We assume that all beam-collimating devices have
been machined according to the engineering diagrams.
ues for the target and backing were determined by plotting
the energy of the parent particles against the last interaction
point for the particle !zlast". An insignificant number of particles that contributed to the phase space were created from
parent particles below the above-stated cut-offs. Thus, we
felt it justified to set ECUT and PCUT to these new values.
The reason for the cut-off value differences for the target and
the backing between modalities !apart from the obvious energy difference" was the different target/backing thickness
ratio. The increased energy cut-off reduced the calculation
time for the creation of the patient independent phase space
by approximately 40% for both energies.
576
D. Calculation details
The EGS439 usercode BEAM20 !BEAM 97" was used for the
beam-line particle transport. The geometry was input to
BEAM from proprietary diagrams supplied by Varian for the
Clinac 21EX. The entered geometry was checked visually
for gross errors using the BEAM gui package and validated
using the method of Libby et al.12 The EGS4 results were also
validated using an independent Monte Carlo code,13 MCNP.40
BEAM was adapted to allow a Gaussian radial source and
energy spread.
Particles were transported through the x-ray target, flattening filter, and ionization chamber to obtain a phase space
stored between the monitor chambers and the jaws. This
phase space was then used as input to a second calculation
that transported the particles through the air gap and jaws.
Particles were then transported in a water phantom using
the Cartesian geometry usercode DOSXYZ,41 and the dose
deposition was tallied. As with the measurements, the water
phantom used for the calculations was 48!48!48 cm3 . The
field size chosen for the calculations to determine the electron fluence was 25!25 cm2 , the largest field for which the
measured field central axis was aligned with the tank center.
A large field was chosen because, in our !and others’" experience, matching calculations with measured data is more
difficult for large fields than small fields. The SSD was 100
cm, and the voxel size was 2!2!2 cm3 . The voxel size was
chosen such that the dose distribution did not change significantly over the voxel within the dose volume analyzed. For
all calculations, the statistical uncertainties for the calculations were less than 2% of the D max dose. The statistical
uncertainty used allowed the calculation of the depth dose
and dose profile curves slopes !see Sec. II F" with a standard
error of the slope significantly smaller than the acceptance
criteria.
The discrete threshold energies for electron and photon
creation, AE and AP, were set to 0.70 MeV and 0.010 MeV,
respectively. The electron and photon transport thresholds
ECUT and PCUT were also set to 0.70 MeV and 0.010 MeV,
respectively, except in the target where the values were increased to 1.5 MeV and 0.15 MeV for the 6 MV target and
backing. For the 18 MV beam, the values in the target were
3.6 MeV and 0.15 MeV and 1.0 MeV and 0.15 MeV in the
target backing. These energy cut-off values were determined
using a method similar to that described by Schach von Wittenau et al.8 BEAM was modified to score the energy of the
parent particles of those in the phase space. The cut-off valMedical Physics, Vol. 30, No. 4, April 2003
E. Determining the mean initial electron energy, the
radial spread of these electrons and the target
density
The final dose distribution is a complex function of the
mean electron energy, E , the radial spread of these electrons,
FWHMrad and the target density, * target . Each of these parameters affects the depth-dose and lateral profile curves in
different ways. Thus, sensitivity calculations were performed
by varying one parameter and fixing the other two. For the
calculations where the energy was varied, MWHMrad was 1.3
mm and * target was 18.0 g cm%3 . For the calculations where
MWHMrad was varied, E was 6.0 MeV !6 MV" or 18.0 MeV
!18 MV" and * target was 18.0 g cm%3 . For the calculations
where the target density was varied, E was 6.0 MeV !6 MV"
or 18.0 MeV !18 MV" and MWHMrad was 1.3 mm.
F. Acceptance criteria
As stated earlier, to achieve 2% accuracy in patient dose
calculations, we estimate that in-water calculations should
agree with measurements to within 1%. The measured data
consists of depth-dose and dose-profile curves. Because each
Monte Carlo-calculated dose point has statistical uncertainty
and the uncertainty is inversely proportional to the square
root of the number of uncorrelated events, the more points
that are averaged over, the lower the overall uncertainty of
the estimated value will be. For this reason, instead of comparing individual points on a depth-dose curve, the slope of
the difference between the measured and calculated curves
was used. Thus, if the slope of the difference between the
measured and calculated data is zero, the two curves can be
considered identical to within statistical error. This slope of
the difference technique was applied to depth-dose and doseprofile curves.
If we assume that the measured and calculated depth-dose
and dose-profile curves have the same shape, then the measured and calculated curves can be compared by computing
the slope of the difference of the curves. A large difference in
slope will manifest itself as depth-dose/dose-profile curve
discrepancies between calculated and measured data. Similarly, a small difference in slope will yield depth-dose and
dose-profile curves that match each other. To obtain a difference of &1% for water over !0,40" cm depth, the slope of the
difference between the measured and calculated depth-dose
Keall et al.: Determining the incident electron fluence
577
TABLE I. Pass/fail results for acceptability of depth-dose and dose-profile
curve comparisons for a nominal 6 MV beam as electron energy, electron
FWHM and target density are varied. The fraction of the acceptance criteria
is given in brackets. The bold numbers correspond with the parameter varied. The italicized fields correspond to the energy, electron FWHM and
density combinations that are acceptable by both depth-dose and doseprofile criteria.
TABLE II. Pass/fail results for acceptability of depth-dose and dose-profile
curve comparisons for a nominal 18 MV beam as electron energy, electron
FWHM and target density are varied. The fraction of the acceptance criteria
is given in brackets. The bold numbers correspond with the parameter varied. The italicized fields correspond with energy, electron FWHM and density combinations that are acceptable by both depth-dose and dose-profile
criteria.
577
Acceptable? !fraction of
acceptance criteria"
Acceptable? !fraction of
acceptance criteria"
Energy
!MeV"
Electron FWHM
!mm"
Target density
!g cm%3 )
Depth
dose
Dose
profiles
Energy
!MeV"
Electron
FWHM !mm"
Target density
!g cm%3 )
Depth
dose
Dose
profiles
5.6
5.8
6.0
6.2
6.4
1.3
1.3
1.3
1.3
1.3
18
18
18
18
18
No !%1.33"
Yes !%0.63"
Yes !0.23"
Yes !0.06"
No !1.36"
No !5.5"
No !3.9"
No !2.3"
Yes !%0.68"
No !%1.9"
17.0
17.5
18.0
18.5
19.0
1.3
1.3
1.3
1.3
1.3
18
18
18
18
18
Yes !%0.89"
Yes !%0.97"
Yes !%0.55"
Yes !0.70"
Yes !0.46"
Yes !0.54"
No !%1.4"
No !%3.4"
No !%6.0"
No !%7.8"
6.0
6.0
6.0
1.2
1.3
1.4
18
18
18
Yes !%0.07"
Yes !0.23"
Yes !%0.24"
No !2.5"
No !2.3"
No !2.0"
18.0
18.0
18.0
0.9
1.3
1.6
18
18
18
Yes !%0.76"
Yes !%0.55"
Yes !0.21"
No !%2.3"
No !%3.4"
No !%5.1"
6.0
6.0
1.3
1.3
17
18
Yes !%0.07"
Yes !0.23"
Yes !0.59"
No !2.3"
18.0
18.0
1.3
1.3
17
18
Yes !0.29"
Yes !%0.55"
No !%3.1"
No !%3.4"
curves must be less than 0.01 D max /(40/2), or 0.0005D max
cm%1 . Similarly, to obtain a difference of &1% for water
over a 40!40 cm2 field size, the slope of the difference of
the dose-profile curves must be less than 0.01
!D max /(20/2), or 0.001D max cm%1 from the central axis.
These values were used as the acceptance criteria. The
ranges used to compute the slope difference between the
measured and calculated data were #5,25$ cm for the depthdose curves and #0,10$ cm for the lateral dose-profile curves.
The lower bound of the depth-dose curve range !5 cm" was
chosen, as it is beyond the range of contaminant electrons at
both 6 and 18 MV. !Build-up region discrepancies between
measurement and Monte Carlo have plagued many
researchers,6,26,28,29 and a recent article by Ding42 concludes
‘‘a new explanation for the unresolved discrepancy remains
to be found.’’" The upper bound was limited by the maximum depth of the measured depth-dose curves. The doseprofile curve range was only out to 10 cm to ensure that the
comparisons were in the umbral region of the 25!25 cm2
measured dose-profile curves, and thus not affected by electronic disequilibrium. The choice of the 25!25 cm2 is explained in Sec. II D.
If an initial electron fluence distribution is found that,
when transported into a phantom, yields both depth-dose
curves and dose-profile curves within the acceptance criteria
!see Table I and Table II", then we have determined an acceptable initial electron fluence, suitable for use for Monte
Carlo-based treatment planning in clinics that have linear
accelerators whose characteristics match those of the standard data set.
G. Verification calculations
The derived values of E , MWHMrad and * target were verified by comparing calculations at 6 MV and 18 MV for 5!5
Medical Physics, Vol. 30, No. 4, April 2003
cm2 and 10!10 cm2 open fields, and 10!10 cm2 60°
wedged fields with measured results. The voxel size used for
these calculations was 0.4!0.4!0.4 cm3 . This voxel size
was chosen, since a 0.4!0.4 cm2 square has a similar effective cross-sectional area to that of the Farmer-type ionization
chamber used for the measurements !Wellhöfer IC15". An
absolute dose !cGy/MU" was calculated to allow a direct
comparison with ionization chamber measurements.
The wedges were calculated in the BEAM simulation with
the wedge created by stacking layers of component module
JAWS. The geometry for the wedges was based on engineering diagrams and material specifications provided by the
manufacturer.
Although calculations performed starting with the determined initial electron fluence are validated for several field
sizes, full commissioning of Monte Carlo treatment planning
!following the guidelines of, e.g., TG 5343" is outside the
scope of this article.
III. RESULTS
A. Depth-dose results: Initial mean electron energy
Figure 1 shows the measured and calculated depth-dose
curves for both 6 and 18 MV. This figure highlights the insensitivity of the initial electron energy on the depth-dose
curve past the depth of maximum dose. The use of the
build-up region for energy determination is possible, however, due to the inability to accurately correlate the ion chamber reading with the dose in the build-up region, the accuracy
of the results would be questionable.
The differences between the various calculations and
measurements are quantified in Table I !6 MV" and Table II
!18 MV". Table I shows that the depth-dose curves from 5.8
to 6.2 MeV are within the acceptance criteria. As the initial
578
Keall et al.: Determining the incident electron fluence
FIG. 1. A comparison of ion-chamber-measured 6 and 18 MV depth-dose
curves with those calculated for !a" initial E values of 5.6 and 6.4 MeV, and
!b" initial E values of 17.0 and 19.0 MeV.
578
FIG. 2. Comparisons of ion-chamber-measured 6 and 18 MV dose-profile
curves at 10 cm depth with those calculated for !a" initial E values of 5.6
and 6.4 MeV, and !b" initial E values of 17.0 and 19.0 MeV.
C. Dose-profile results: initial mean electron energy
electron beam energy is increased from 5.6 MeV, the agreement with measurement improves until after 6.2 MeV, where
the discrepancy increases. Table II shows that all the tested
energies from 17.0 to 19.0 MeV yield acceptable depth-dose
curves.
B. Depth-dose results: initial electron radial FWHM
and target material density
Table I and Table II show the depth-dose curve comparisons, as the initial electron radial FWHM is varied for the 6
MV and 18 MV beams, respectively. Although the depthdose curve changes as the FWHM changes, the calculations
agree with measurement to within the acceptance criteria.
Similar conclusions can be drawn for the target material density. The change in density does affect the depth-dose curve,
but this change is not significant.
Due to the relative insensitivity of the depth-dose curves
to the initial mean electron energy, radial FWHM and target
density, dose profiles give a more sensitive determination of
these parameters.
Medical Physics, Vol. 30, No. 4, April 2003
Figure 2 shows the measured and calculated dose-profile
curves for both 6 and 18 MV beam energies. Figures 2!a"
and 2!b" show that the initial electron energy affects the
shape of the dose-profile curve, both near the central axis of
the beam and the edge of the field. The agreement between
calculation and measurement for the dose profiles is quantified in Table I and Table II. Table I shows that, for the calculations where the energy was varied, the 6.2 MeV initial
energy gives the only profile that is within the acceptance
criteria. Similarly, in Table II, there is one energy value !17.0
MeV" that gives dose profiles within the acceptance criteria.
D. Dose-profile results: Initial electron radial FWHM
Table I and Table II show that for the electron beam
FWHM radial calculations, none of the dose profiles are
within the acceptance criteria, indicating that either the electron energy used !6.0 MeV and 18.0 MeV" or the target
density !18.0 g cm%3 ) is incorrect. These results do show,
however, that as the FWHM increases, the size of the doseprofile ‘‘horns’’ will decrease. This effect is the same as that
579
Keall et al.: Determining the incident electron fluence
FIG. 3. A comparison of calculated !histograms" and ion-chamber-measured
!symbols" depth-dose curves for 4!4 and 10!10 cm2 open fields and a
10!10 cm2 60° wedge field at !a" 6 MV and !b" 18 MV. The cross at !5,0.6"
represents the acceptance criteria of $1 mm or $1% of d max dose. Inset is
the same plot with the x-axis from 0 to 3 cm. For the inset, the box at
!1.5,0.5" represents the acceptance criteria of $1 mm or $1% of d max dose.
of increasing energy !see Table I, Table II and Fig. 2", where
the size of the dose-profile horns decreases as energy increases.
E. Dose-profile results: Target material density
Table I and Table II show that for the calculations where
the target density was varied, the 17.0 g cm%3 calculated
profiles are acceptable at 6 MV, but not at 18 MV. For the 6
MV case, the higher target density resulted in larger horns,
whereas at 18 MV, the higher target density resulted in
smaller horns. This difference could be due to the energy
dependent attenuation coefficient values resulting in the target hardening the beam at 6 MV and softening the beam at
18 MV.
From Table I and Table II, of those tested, the best input
parameters to use for the Monte Carlo calculations are E
"6.2 MeV and 17.0 MeV !for the 6 and 18 MV beams,
respectively" and FWHMrad"1.3 mm and * target"18.0 g
cm%3 . These input parameters were used for the verification
Medical Physics, Vol. 30, No. 4, April 2003
579
FIG. 4. A comparison of calculated !histograms" and ion-chamber-measured
!symbols" dose-profile curves at 10 cm depth for 4!4 and 10!10 cm2 open
fields and a 10!10 cm2 60° wedge field at !a" 6 MV and !b" 18 MV. The
cross at !0,0.5" represents the acceptance criteria of $1 mm or $1% of d max
dose.
calculations. Note that for the 6 MV case, there were two
acceptable energy, FWHM and density combinations to
choose from. We chose the combination with * target"18.0 g
cm%3 to be consistent between 6 and 18 MV, as obviously
the target density is independent of beam energy.
F. Verification calculations
Figure 3 and Fig. 4 show a comparison of calculated and
measured depth-dose and dose-profile curves. At 6 MV, the
curves agree well with the experiment and are within the 1%
or 1 mm criteria. For the 18 MV calculations, the curves
agree to within the specified criteria after the contamination
electron range, however, at the maximum electron range, the
calculated results are higher than the experiment. There are
several reasons for this difference. Sheikh-Bagheri et al.5
found that correcting for the effective point of measurement
of the ion chamber reduces much of the discrepancy in the
build-up region and up to 2 cm beyond d max for 10 and 20
MV beams. Part of the discrepancy is because the measured
580
Keall et al.: Determining the incident electron fluence
580
TABLE III. A comparison of this work with other studies that have used Monte Carlo methods to model Varian accelerators.
Accelerator
Nominal
energy !MV"
Mean
electron
energy !MeV"
FWHM electron
energy spread
!% of mean"
Ding !Ref. 26"
2100EX
6
6.02
17%
Ding !Ref. 26"
2100EX
18
18.00
6%
Clinac 2100C/D
Clinac high energy
6
6
6.05
6.2
0
0
Clinac high energy
18
18.5
0
Liu et al. !Ref. 27"
2100C
6
6.5
0
Liu et al. !Ref. 27"
2100C
18
20.0
0
Clinac high energy
6
5.7
3%
Clinac high energy
18
18.3
3%
2100EX
6
6.2
3%
2100EX
18
17.0
3%
Author
Fix et al. !Ref. 24"
Hartmann-Siantar et al.
!Ref. 6"
Hartmann-Siantar et al.
!Ref. 6"
Sheikh-Bagheri and Rogers
!Refs. 28 and 29"
Sheikh-Bagheri and Rogers
!Refs. 28 and 29"
This work
This work
ionization curves have not been converted to dose using variable water/air stopping power ratios. This ratio is fairly constant after the build-up depth, however, at depths below this
point, the stopping power ratios vary.44
IV. DISCUSSION
The initial electron fluence above the linear accelerator
target has been determined for two photon energies !6 and 18
MV" of one linear accelerator model that, when transported
into phantoms, yields dose distributions within 1% or 1 mm
of the experimental measurements, except near the surface.
These initial electron fluences have been transported to a
plane between the monitor chambers and the jaws of the
linear accelerator and scored in the form of phase-space files.
These phase-space files are used in the Monte Carlo system
at our clinic for dosimetric verification of every IMRT patient treated, with the results documented, signed and included in the patient chart. These phase-space files have also
formed the basis for Monte Carlo calculations of multileaf
collimator transport, which have been experimentally verified in several publications.45– 47
The dosimetric effects of !1" the mean electron energy of
the initial electron fluence, !2" the radial spread of the initial
electron fluence and !3" the target density were studied. The
initial electron energy, initial electron radial spread and target
density all affect the depth-dose and dose-profile curves. An
increase in beam energy increases the penetration of the
depth-dose and decreases the horns of the dose-profile
curves. An increase in the radial FWHM also decreases the
Medical Physics, Vol. 30, No. 4, April 2003
Electron radial
distribution
1.2 mm FWHM
Gaussian function
1.5 mm FWHM
Pencil beam
2 mm diameter
cylindrical function
2 mm diameter
cylindrical function
4 mm diameter
cylindrical function
4 mm diameter
cylindrical function
2.0 mm FWHM
Gaussian function
1.1 mm FWHM
Gaussian function
1.3 mm FWHM
Gaussian function
1.4 mm FWHM
Gaussian function
Depth-dose
agreement
with measurement
Good
Measured dose high
for large fields
and shallow depths
Good
Good
Measured dose high
for large fields
and shallow depths
Not shown
Not shown
Good
Measured dose high
for shallow depths
Good
Measured dose high
for shallow depths
horns of the dose-profile curves. An increase in target density
has the effect of hardening the 6 MV depth-dose curve and
softening the 18 MV depth-dose curve.
Based on our results of modeling the ‘‘standard’’ measured data set of the input variables tested, the best parameters to use for the EGS4 calculations to model the Cl21EX
linear accelerator are initial mean electron energy 6.2 MeV
and 17.0 MeV for 6 and 18 MV beams, respectively, with a
FWHM of the radial spread of these electrons of 1.3 mm and
a target density of 18.0 g cm%3 . Calculations performed using these phase-space files agree with measurements past the
build-up region to within 1% or 1 mm over the 4!4 to
25!25 cm2 field size range tested. However, in the build-up
region, the 18 MV depth-dose curves were significantly
higher than those of the ion chamber measured curves. The
disagreement between the measured data highlights the need
for benchmark data sets, such as those to be conducted under
the auspices of AAPM Task Group 67.
A comparison of the derived parameters from this work
with that of previous publications relating to the Monte Carlo
modeling of Varian linear accelerators is shown in Table III.
It is interesting to note that even though each approach is
unique and the parameters used vary, the dosimetric results
are similar. Each group achieved the 6 MV beam modeling,
but none of the groups, as of yet, has accurately modeled the
18 MV beam for shallow depths and large field sizes. This
inability to accurately model the high-energy beams could be
due to several factors, such as the cross sections and transport methods used by the Monte Carlo codes, inaccurate geometrical specifications by the manufacturer, erroneous as-
Keall et al.: Determining the incident electron fluence
581
sumptions of the initial electron fluence distribution above
the target and the conversion from measured ionization to
dose.
Currently, the phase-space files store the particles below
the monitor chamber. Thus, in our Monte Carlo implementation, we need to perform an empirical correction to account
for the backscatter to the monitor chambers from the
collimators.48 Future work will concentrate on storing the
phase space above the monitor chambers so that the backscatter to the monitor chambers can be calculated directly.
The final phase-space files are freely available from the
authors !a 4-CD set". The 6 MV phase space contains 60
million particles, and the 18 MV phase space contains 45
million. Note that the phase spaces determined here have
only been tested for the EGS4 Monte Carlo code. Other codes
using different transport methodologies and cross sections
may yield differing results.
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581
ACKNOWLEDGMENTS
The authors wish to thank Alexis Schach von Wittenau of
Lawrence Livermore National Laboratory for sharing experiences and ideas. We appreciate Dr. Michael Fix, Dr. Christine Hartmann-Siantar and Helen Liu for providing us details
of the electron fluence parameters used in their Monte Carlo
publications. The clarity of this article was much improved
by Devon Murphy’s careful review. Varian Medical Systems
kindly provided us with the engineering diagrams and material specifications required for the modeling of the linear accelerators. The authors acknowledge the financial support of
NIH Grant No. CA 74158.
a"
Author to whom correspondence should be addressed. Phone: !804" 628
0980; fax: !804" 828 6042; electronic mail: [email protected]
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