Introduction
The output factor (OF) measurements of a medical linear
accelerator are one of the most critical parameters affecting the accuracy of radiation therapy. Incorrect
acquisition of this factor causes an error in the determination
of the Monitor Unit (MU) therefore incorrect
radiation treatment.
The OF is defined as the ratio of the adjusted electrometer
readings in the non-reference condition to the
measurement in the reference condition.[] Dose profiles,
percentage depth doses (PDD), and OFs should
be measured using suitable detectors and techniques in
all energies for varied field sizes. The selection of the
appropriate detector is important, especially for the
small fields, because of the detector size limitation that
causes lateral charge particle disequilibrium.[,]
For many years, researchers have focused on measurements
and reducing the uncertainties of OFs. Thus,
various methods have been proposed over time. Besides
the experimental methods, Monte Carlo (MC) simulation
is a useful and reliable method for investigating the
variables effecting the calculation of the OFs. The characterizations
of the different detectors were evaluated
for small cone or square fields using the MC method in
the literature.[-] Furthermore, the modeling of detector
sizes and materials has been examined. In a previous
study by Haryanto et al.[] four different materials
were used to simulate sensitive volumes of detectors
to show the detector reaction during dose deposition
due to their sensitive materials. In addition, 1 mm and
5 mm voxel sizes were chosen to model the size of the
detectors. The authors of the study have reported that
a good agreement was obtained between the measured
and the calculated OFs for 6 MV photon beam energy
by ignoring the effects of the voxel size and the material
of the detector for the field sizes larger than 1×1 cm2.
[] In another study that the OFs of MC and real-time
measurement have been compared for FFF beams,
Cheng et al.[] simulated and calculated the OFs with
the voxel sizes of 0.25 mm and 0.5 mm for the conical
fields of 4 mm and 5 mm. The differences have been
reported as smaller than 1%. It has been expressed that
there is no volume-averaging effect between different
voxel sizes for MC simulations. In some other studies,
OFs have been investigated for square and rectangular
fields with various widths and lengths. In these studies,
the authors found that the OF differences between the
MC simulations and the real-time measurements were
within 1.5% for the field sizes varying from 4×4 cm2 to
40×40 cm2. It is also indicated that photon OFs can be
predicted accurately using the MC method.[]
In the literature, EGS/BEAMnrc, PENELOPE,
and MCNP codes were frequently used to obtain the
OFs, PDDs, or dose profiles.[-] The small number
of GEANT4 studies have been published, in contrast
to other MC codes, motivated this study was done.
This study aims to widely demonstrate the energy and
field size-related differences between cylindrical ionization chambers commonly used in the clinical applications
of the radiation therapy to avoid inaccurate
measurement of the OFs. The OFs were calculated by
using GEANT4 simulations for five different photon
beams with the field sizes ranging from 0.6x0.6 cm2 to
30x30 cm2. OFs calculated by GEANT4 simulations
were compared to those OFs measured by three different
cylindrical ionization chambers with the Varian
Truebeam STx treatment machine. The cylindrical
ionization chambers, which are commonly preferred in
clinical applications of point dose measurements, were
particularly chosen. Besides the studies that have been
investigated in the literature, an extended investigation
of the OF comparisons for both flattened (6 MV, 10
MV, 15 MV) and flattening filter-free (6 MV, 10 MV)
beams were reported in means of this study. GEANT4
(for Geometry And Tracking),[] which has been developed
for use in CERN (Conseil Européen pour la
Recherche Nucléaire) applications, was preferred for
MC simulations throughout the study.
The validation of GEANT4 simulations was performed
within a good agreement by comparing calculated
and measured PDDs, inplane, and crossplane
profiles. The energy and the field size-related responses
of three different cylindrical ionization chambers
were examined for the varied energies and the field
sizes that declared above and the results are reported
in this study.
Methods
We note that this study does not aim to find correction
factors required to use in small field dosimetry. The
goal is that making contribution to the literature-expanded
assessment of energy and field size-related responses
of the most common detector types frequently
used in radiation therapy by means of GEANT4.
Treatment Unit
The real-time measurements were performed on a
Varian TrueBeam STx medical linear accelerator (Varian
Medical Systems, Palo Alto, CA) with commissioned
X-ray beams of 6 MV, 6 MV-FFF (Flattening
Filter Free), 10 MV, 10 MV-FFF, and 15 MV. The accelerator
collimator contains 2 pairs of Jaws made by
using tungsten alloy (95% W, T-21014, class 3) in X and
Y dimensions and a High Definition (HD) 120 Multi-
Leaf Collimator (MLC), which consisting of 120 pairs
of tungsten alloy (95% W, T-21014, class 3) leaves. The
outer leaves of HD 120 MLC have 14 pairs on either side with 5 mm-projected width on the isocenter. The
HD 120 MLC has central leaves of 32 pairs with 2.5
mm-projected width on the isocenter. The collimator
can be adjusted with the variable width over field sizes
of 22×40 cm2 and 40×40 cm2 with and without HD 120
MLC, respectively.
Detectors
Three different cylindrical ionization chambers, which
are 0.6 cc Farmer (PTW 30013, Germany), 0.125 cc
Semiflex (PTW 34010, Germany), and 0.015 cc Pin-
Point (PTW 31006, Germany) were used. The basic
characteristics of the ionization chambers are shown
in Table 1. The readings were obtained using PTW
Unidos Webline electrometer at +400 V. All ionization
chambers were calibrated with electrometer by the Secondary
Standards Dosimetry Laboratory. Water equivalent
RW3 slab phantoms (Sun Nuclear RW3 (Goettingen
White Water)) with dimensions of 30x30x1 cm3
and motorized remote-controlled 3D water phantom
(PTW MP3 Water Phantom) were used for the acquisition
of the real-time measurements.
Table 1: Basic specification of ionization chamber detectors used in this study
The lack of lateral charged particle equilibrium (rLCPE
) is induced If the full width-half maximum or the
radius of the photon beam is smaller than the maximum range of secondary electrons that have to contributed
to dose deposition.[] A formula explained
in the International Atomic Energy Agency (IAEA)
Technical Reports Series (TRS) No.483 defines the relationship
between photon energy and rLCPE in smallfield
dosimetry. The minimum field sizes that the cylindrical
ionization chambers used in this study can be
used to measure the dose deposition without the need
for any correction are tabulated in Table 2. The calculated
square fields given in Table 2 were at source-axis
distance of 100 cm.
Table 2: FWHMmin of ionization chamber detectors used in this study
The OF Measurement
The point doses were acquired on a Varian TrueBeam
STx medical linear accelerator with 6 MV, 6 MV-FFF,
10 MV, 10 MV-FFF, and 15 MV. Real-time measurements
were performed in water-equivalent slab phantoms
at a depth of 10 cm on the central axis (CAX) of
the field sizes with source-surface (phantom surface)
distance (SSD) of 100 cm by delivering 100 MU. The
orientation of the ionization chambers was perpendicular
to the CAX. During these measurements of
OFs, Varian TrueBeam STx medical linear accelerator
was operated at Dose Rate (DR) of 400 MU/min. As
described in IAEA TRS No. 398, a depth of 10 cm is recommended, particularly to eliminate the contamination
of secondary electrons from collimators of the
linear accelerator.[] The varied field sizes adjusted
by X-Y jaws of 0.6×0.6, 1×1, 2×2, 3×3, 4×4, 5×5, 8×8,
10×10, 15×15, 20×20, 25×25, and 30×30 cm2 projected
on the isocenter were used for 6 MV, 6 MV-FFF, 10
MV, 10 MV-FFF, and 15 MV, respectively. The HD 120
MLC was retracted to the park position during the data
acquisition. Farmer, semiflex, and pinpoint ionization
chambers operated at +400 V were used in real-time
measurements. The acquired data of point doses were
normalized to readings of 10×10 cm2 for all energies
separately to determine OFs.
Monte Carlo Simulations
GEANT4 simulation application based on the MC
algorithm and C++ programming language was used
to model the Varian TrueBeam STx medical linear accelerator.
GEANT4 is a toolkit used for simulating the
passage of particles through matter that includes all the
functionalities such as building complex geometry, expanded
physics models, tracking, and hits. It has been
used in applications related to particle physics, nuclear
physics, accelerator design, space engineering, and
medical physics. Many medical physicists working on
particle interactions use GEANT4 simulation application
for complex geometry design and suitable physics
list selection. In GEANT4, there are diverse physics models on the interactions of particles with the matter
with a broad energy range.[]
The simulation was performed on Linux CentOS
version 7 using the GEANT4 v.10.7.2 application built
on C++ advanced programming language. The computer
that consists of Intel® Xeon E5-2630 v3 processor,
32 GB RAM was used in MC calculations. Through
the GEANT4 multi-thread feature, 32 threads of CPU
were run in parallel during the MC simulations.
IAEA formatted phase-space files[] produced by
Varian Medical Systems[] using GEANT4 were used
as the generator of photon beams of 6 MV, 6 MV-FFF,
10 MV, 10 MV-FFF, and 15 MV. Photons, electrons, and
positrons used in phase-space were scored on a planar
surface with 6.5×6.5 cm2 at 26.7 cm below the source.
The field size of phase space projected on isocenter was
48.6×48.6 cm2. Many phase-space files were merged to
avoid latent variance problem and also to obtain better
statistics on the particle distribution.[,] A total of
36.9×109, 26.6×109, 21.3×109, 13.3×109, and 24.6×109
original histories were simulated for 6 MV, 6 MV-FFF,
10 MV, 10 MV-FFF, and 15 MV, respectively.
The X-Y Jaws, HD 120 MLCs, Baseplate, and water
phantom were modeled below the phase-space. The
simulated materials of the accelerator and the phantom
used in GEANT4 were provided by the National
Institute of Standards and Technology. The geometric
dimensions and the positions of the X-Y Jaws, HD 120 MLCs, and Baseplate were obtained from Varian
Medical Systems. Varian Medical Systems also provided
the movement trajectory of X-Y Jaws and MLCs.
The 3D water phantom modeled at the dimensions of
40×40×40 cm3 was placed at the SSD of 100 cm. The
general design of the accelerator used in this GEANT4
study is shown in Figure 1.
Fig. 1: The simulation geometry in GEANT4.
The G4EmStandardPhysics (Option 4) electromagnetic
physics package that consists of many particles
(photons, electrons, positrons, etc.) was used utilizing
GEANT4 electromagnetic physics library. G4Em-
StandardPhysics (Option 4) is the most accurate electromagnetic physics package in terms of the particle
energies used in this study. The set-cut values defined
by GEANT4 as default were used and these values are
tabulated in Table 3. During the GEANT4 simulations,
"HepJamesRandom" pseudo-random number generator[] was used to choose which particle to be consecutively
produced. No variance reduction techniques
were used in this study.
Table 3: Set-cut values of range and energy for simulated materials
The 3D water phantom designed in the simulation
was divided into voxels of 5×5×5 mm3 and 1×1×5 mm3
as mesh structures. The voxel size of 5×5×5 mm3 was
chosen due to Semiflex's sensitive volume size for the validation of the simulation model. The voxel size of
1×1×5 mm3 mesh geometry was used for the calculations of the OFs. Dose scoring was performed in the
medium of water. Primitive dose scorers were assigned to these meshes to store the dose deposition released by
the particles. The dose deposition scored by primitive
scorers was printed out as the format of 3D dose and
analyzed using in-house codes written in Matlab.[]
Results
Verification of Monte Carlo Simulations
GEANT4 simulations were performed by defining
variable field sizes for all energies to validate the simulation
model of the Varian TrueBeam STx with actual
measurements. Voxelized 3D water phantom was
used to acquire PDDs, inplane, and crossplane profiles
for the validation of the GEANT4 simulation model.
The 3D water phantom and semifex ionization chamber
were used to verify PDDs, inplane, and crossplane
profiles of 6 MV, 6 MV-FFF, 10 MV, 10 MV-FFF, and
15 MV with MC calculations. Verification of the dose
profiles was done by field size of 10×10 cm2 at a depth
of 10 cm with SSD of 100 cm. PDD validations were
accomplished with a field size of 10×10 cm2.
Figure 2 shows comparisons between calculated
and measured profiles at a depth of 10 cm with a
field size of 10×10 cm2. Calculated values were normalized
to the CAX and Dmax of measured profiles of
inplane-crossplane and PDD, respectively. The Trapezoidal
Rule technique was used to calculate percentage
differences between calculated and measured
inplane-crossplane and PDD profiles. inplane and
crossplane profiles measured by the Semiflex ionization
chamber in the 3D water phantom were agreed
well with profiles calculated by GEANT4.
The maximum differences of 1.4%, 1.5%, 0.5%,
0.8%, and 0.8% were achieved between the calculated
and measured profiles of inplane-crossplane of 6 MV, 6
MV-FFF, 10 MV, 10 MV-FFF, and 15 MV, respectively.
The largest deviation of agreement between calculated
and measured profiles was at the penumbra (80-20%)
and end of the penumbra regions (<20%). The sharpness
of the real-time inplane-crossplane profiles might
be lost at the edge of the field sizes due to Semiflex air
cavity volume and its continuous collection during data
acquisition. Also, the real-time measurements were affected
by different factors, namely the disturbance in
the electron transportation within the detector, the
energy and DR dependencies of the detector, and the
finite size of the detector.[]
PDDs calculated by GEANT4 were in 0.9%, 0.1%,
0.7%, 0.7%, and 0.05% agreement with PDDs measured
by Semiflex with the field size of 10×10 cm2 for 6 MV,
6 MV-FFF, 10 MV, 10 MV-FFF, and 15 MV, respectively.
Tissue-Phantom Ratio (TPR20,10) was calculated to
determine the quality of energy differences between
the measured and calculated. TPR20,10 values calculated
by GEANT4 were in 0.7%, 0.6%, 1.3%, 0.6%, and 1.2%
agreement with the field size of 10x10 cm2 for 6 MV, 6
MV-FFF, 10 MV, 10 MV-FFF, and 15 MV, respectively.
The comparison of PDDs can be seen in Figure 3.
As shown in Figures 2 and 3, the comparison results
of PDDs, inplane, and crossplane profiles show that the
phase-space data and the simulation model of the Varian
TrueBeam STx machine used in the GEANT4 simulation
are consistent with the actual Varian TrueBeam
STx machine used in this study.
Fig. 2: (a) Comparison of inplane profiles between measured and calculated at a depth of 10 cm with a field size of 10X10
cm2 for all flattened beams. (b) Same as (a) but for FFF beams. (c) Comparıson of corssplane profiles between measured
and calculated at a depth of 10 cm with the field size of 10X10 cm2 for flattened beams. (d) Same as (c) but for
FFF beams.
Fig. 3: (a) Comparison of PDDs between measured by using Semiflex ionization chamber with the field size of 10X10 cm2
and calculated by GEANT4 for flattened beams. (b) The same as (a) but for FFF beams.
Comparison of the OFs
The comparison results of OFs between measured by
three different ionization chambers and calculated by
GEANT4 simulations are shown in Figures 4 and 5. The results are also shown in Tables 4 and 5 as tabulated.
In addition, OFs and the statistical errors in the
GEANT4 simulations are given in Tables 6 and 7 as
tabulated. The relative deviations in the OF measurements for the field sizes between 4×4 cm2 and 30×30
cm2 present good agreement within 1.5%. The Farmer
ionization chamber had the maximum deviation
of 5.5% and 22% for the field sizes of 3×3 cm2 and
2×2 cm2, respectively. Semiflex and Pinpoint ionization
chambers were in the agreement within 2% and
5.5% for 3×3 cm2 and 2×2 cm2, respectively. Pinpoint
ionization chamber was kept using to acquire dose
deposition for smaller fields than 2x2 cm2 due to its
smaller sensitive volume and its results had the deviations
of 11% and 19% at field sizes of 1×1 cm2 and
0.6×0.6 cm2, respectively. The number of the relative
deviations of the OFs of the ionization chambers can
be seen in Figure 6.
Table 4: Percentage differences in measured OFs of three different ionization chambers relative to calculated OFs by GEANT4
for flattened beams. Here a, b, and c stand for Farmer, Semiflex, and Pinpoint, respectively
Table 5: Percentage differences in measured OFs of three different ionization chambers relative to calculated OFs by GEANT4
for FFF beams. Here a, b, and c stand for Farmer, Semiflex, and Pinpoint, respectively
Table 6: OFs for flattened beams. Here a, b, c and d stand for Farmer, Semiflex, Pinpoint and MC, respectively. Statistical errors of the GEANT4 Simulations are given with MC
Table 7: OFs for FFF beams. Here a, b, c and d stand for Farmer, Semiflex, Pinpoint and MC, respectively. Statistical errors of
the GEANT4 Simulations are given with MC
Fig. 4: (a) Measured of results of three different ionization
chamber detectors relative to the calculated
OF results of Monte Carlo simulations for 6 MV.
(b) Sema as (a) but for 10 MV. (c) Same as (a)
but for 15 MV.
Fig. 5: (a) Measured OF results of three different ionization chamber dedectors relative to calculated OF results of Monte
Carlo simulations for 6 MV-FFF. (b) Sema as (a) but for 10 MV-FFF.
Fig. 6: (a) Percentage deviations between measured OFs
of three different ionization chamber dedectors
and calculated OFs Monte Carlo simulations for
Farmer (b) the same as (a) but for Semiflex and
(c) Same as but for Pinpoint.
Discussion
A geometrical model of a Varian TrueBeam STx
medical linear accelerator has been designed by using
GEANT4 simulation software and validated by
comparing differences between calculated PDDs and
profiles with the real-time measurements. The calculated
OFs were compared with three different cylindrical
ionization chambers to investigate detector's
responses depending on the field size and photon
beam energy. This study yields that it is important to
pay attention to detector selection. The three different
sizes of detectors used in this study were particularly
selected because they are most basic chamber types
frequently preferred by the users. These detectors to
be used to obtain OFs should be selected properly.
It is known that the lack of lateral electronic equilibrium
can cause errors in dose measurements, especially
for the fields smaller than the sensitive volume of
the detector. As Tyler et al.[] and Azangwe et al.[]
reported that if the ionization chamber size is larger
than the uniform region of the field size, the underestimation
of the dose at the center of the axis of the beam
is measured with differences up to 20-30% due to the
detector size. The results declared in this study for the
fields smaller than 4×4 cm2 show that the percentage
differences in OFs between measured and calculated
increase up to 22% regarding sensitive volume of the
ionization chamber.
Haryanto et al.[] reported that the Pinpoint ionization
chamber detector reads a slightly higher dose
due to over-response of this detector to low-energy
scatter for the larger field sizes. Martens et al.[] also
present that the Pinpoint ionization chamber has an
unwanted signal that can be increased as large as 2.5%
at CAX because of irradiated cable length. Nevertheless,
no such an impact of the Pinpoint detector was
observed in this study.
The formula expressed in IAEA TRS No.483 leads
us to the minimum square fields regarding the photon
energy are required without loss of LCPE during point
dose acquisition should be approximately between
field sizes of 3.7×3.7 cm2 - 5.7×5.7 cm2, 2.3×2.3 cm2 -
4.2×4.2 cm2 and 2.2×2.2 cm2 - 4.1×4.1 cm2 for Farmer,
Semiflex, and Pinpoint, respectively. However, the results
in this study show that Farmer could measure
dose deposition reliably until the field size of 4×4 cm2 for all photon energies. In addition, the Farmer ionization
chamber can be ignored for the fields smaller
than 4×4 cm2 due to its sensitive volume. Semiflex and
Pinpoint chambers could be used to measure the dose
deposition until a field size of 3×3 cm2. Nevertheless,
Semiflex and Pinpoint chambers were observed to have
poor performance at the field sizes smaller than 3x3
cm2. Furthermore, the deviations in Pinpoint chamber
were up to 5%, 11%, and 19% without any correction
applied at field sizes of 2×2 cm2, 1×1 cm2, and 0.6×0.6
cm2, respectively. Papaconstadopoulos et al.[] found
that the uncertainties of 1.3% in OFs could be observed
because of the jaw-defined field sizes, particularly
for small fields. Even though the uncertainties
in small field OFs calculated by GEANT4 simulations
in this study would be combined with the uncertainties
of 1.3% caused by jaw positioning, the deviations
are not small enough to use Pinpoint detector for the
field sizes of 1×1 cm2 and 0.6×0.6 cm2 depending to
photon energy. As tabulated in the Tables 4 and 5, the
percentage differences in OFs increased by increasing
the value of TPR20,10. Although the correction factors
tabulated in IAEA TRS No. 483 are the same for the
energies of 6 MV, 6 MV-FFF, 10 MV, and 10 MV-FFF
and the field sizes varied between 3×3 cm2 and 1.5×1.5
cm2, the results in this study show that percentage differences
in OFs differ according to TPR20,10. Therefore,
it is strongly recommended to investigate the correction
factor in more detail by considering the photon
energy for Semiflex and Pinpoint ionization chambers
if they are used during OF measurements with field
sizes equal to or smaller than 3×3 cm2.
The ionization chambers used in this study perform
well within 1.5% agreement at all photon energies
for the field sizes between 4×4 cm2 and 30×30 cm2.
Moreover, Semiflex and Pinpoint chambers were in
2% agreement up to the field size of 3×3 cm2. To obtain
accurate OFs for the field sizes smaller than 3×3
cm2 require smaller sensitive volume of detector rather
than the three different cylindrical-type ionization
chambers used in this study.
Limitations of This Study
The number of particles used in this study was limited.
More particles are needed for use in simulations
to acquire dose deposition more precisely particularly
for small voxel sizes. Because the number of particles
that interact in the voxel decreases with decreasing
voxel size and it causes larger statistical errors in
calculations.
Peer-review: Externally peer-reviewed.
Conflict of Interest: All authors declared no conflict of interest.
Financial Support: None declared.
Authorship contributions: Concept - O.A.; Design - O.A.;
Supervision - O.A., K.A.; Data collection and/or processing
- O.A., R.K., G.Ş., C.A.; Data analysis and/or interpretation
- O.A., C.A.; Literature search - O.A., R.K., K.A.; Writing -
O.A., C.A.; Critical review - K.A., L.Z.A.A.
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