論文の公開元へPredictive gamma passing rate for three-dimensional dose verification with finite detector elements via improved dose uncertainty potential accumulation model
概要
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Predictive gamma passing rate for three-dimensional dose verification with finite detector elements via improved dose
uncertainty
potential accumulation model
un
uncerta
E
Eiji Sh
Shiba
Department
of Radiation Oncology, Hospital of the University of Occupational and Environmental Health, Fukuoka 807D
Depar
8556, JJapan
Department
of Radiation Oncology, Graduate School of Biomedical and Health Sciences, Hiroshima University,
D
Depar
Hiroshima
734-8551, Japan
H
Hirosh
Saito
A
Akito
Department
of Radiation Oncology, Hiroshima University Hospital, Hiroshima 734-8551, Japan
D
Depar
Makoto
Furumi
M
Makot
Department
of Radiation Oncology, Hospital of the University of Occupational and Environmental Health, Fukuoka 807D
Depar
8556, JJapan
85
Daisuke
Kawahara
D
Daisuk
Department
of Radiation Oncology, Graduate School of Biomedical and Health Sciences, Hiroshima University,
D
Depar
Hiroshima
734-8551, Japan
H
Hirosh
Kentaro
Miki
K
Kentar
Department
of Radiation Oncology, Hiroshima University Hospital, Hiroshima 734-8551, Japan
D
Depar
Yuji Murakami
Y
M
Department of Radiation Oncology, Graduate School of Biomedical and Health Sciences, Hiroshima University,
Depar
Hiroshima 734-8551, Japan
Hirosh
Takayuki
Ohguri
Ta
Takayu
Department
of Radiation Oncology, Hospital of the University of Occupational and Environmental Health, Fukuoka 807D
Depar
8556, JJapan
85
Shuichi
Ozawa
Sh
Shuich
Hiroshima
High-Precision Radiotherapy Cancer Center, Hiroshima 732-0057, Japan
H
Hirosh
T aarticle has been accepted for publication and undergone full peer review but has not been
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through the copyediting, typesetting, pagination and proofreading process, which may lead to
th
throu
differences between this version and the Version of Record. Please cite this article as doi:
10.1002/MP.13985
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Department of Radiation Oncology, Graduate School of Biomedical and Health Sciences, Hiroshima University,
Accepted Article
Hiroshima 734-8551, Japan
M
asato Tsuneda
Masato
D
Depar
Department
of Radiation Oncology, Tokyo Women’s Medical University, Shinjuku, Tokyo 162-8666, Japan
K
Katsuy
Katsuya
Yahara
D
Depar
Department
of Radiation Oncology, Hospital of the University of Occupational and Environmental Health, Fukuoka 80785
8556, JJapan
T
Teiji N
Nishio
Depar
Department of Medical Physics, Graduate School of Medical Science, Tokyo Women’s Medical University, Tokyo 16286
8666, JJapan
Y
Yukun
Yukunori
Korogi
Depar
Department of Radiation Oncology, Hospital of the University of Occupational and Environmental Health, Fukuoka 80785
8556, JJapan
Y
Yasush
Yasushi
Nagata
D
Depar
Department
of Radiation Oncology, Graduate School of Biomedical and Health Sciences, Hiroshima University,
H
Hirosh
Hiroshima
734-8551, Japan
C
Corre
Corresponding
author
A
Akito
Saito, PhD
Depart
Department of Radiation Oncology, Hiroshima University Hospital
1-2-3 K
Kasumi, Minami, Hiroshima, Hiroshima 734-8551, Japan
T
Tel: +8
+81-82-257-1545
Fax: +
+81-82-257-1546
Fa
E-mail:
akito@hiroshima-u.ac.jp
E
E-mail
Running
title
R
Runni
Predictive 3D GPR via improved DUP model
Keywords
dose uncertainty
gamma passing rate
complexity metric
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Accepted Article
Abstract
Abs
Pur
Purpose: We aim to develop a method to predict the gamma passing rate (GPR) of a three-dimensional (3D) dose
distribution
measured by the Delta4 detector system using the dose uncertainty potential (DUP) accumulation model.
dist
Methods:
Sixty head-and-neck intensity-modulated radiation therapy (IMRT) treatment plans were created in the
Me
XiO treatment planning system. All plans were created using nine step-and-shoot beams of the ONCOR linear
accelerator. Verification plans were created and measured by the Delta4 system. The planar DUP (pDUP)
acc
man
manifesting on a field edge was generated from the segmental aperture shape with a Gaussian folding on the
bea
beam’s-eye view. The DUP at each voxel ( )ݑwas calculated by projecting the pDUP on the Delta4 phantom with its
atte
attenuation considered. The learning model (LM), an average GPR as a function of the DUP, was approximated by
an exponential function ܽ
ሺݑሻ ൌ ݁ ି௨ to compensate for the low statistics of the learning data due to a finite
num
number of the detectors. The coefficient ݍwas optimized to ensure that the difference between the measured and
pred
predicted GPRs (݀
) was minimized. The standard deviation (SD) of the ݀
was evaluated for the optimized
LM
LM.
Res
Results: It was confirmed that the coefficient ݍwas larger for tighter tolerance. This result corresponds to the
exp
expectation that the attenuation of the ܽ
ሺݑሻ will be large for tighter tolerance. The
and ݉
were
obs
observed to be proportional for all tolerances investigated. The SD of ݀
was 2.3, 4.1, and 6.7% for tolerances of
3%
3%/3 mm, 3%/2 mm, 2%/2 mm, respectively.
Con
Conclusion: The DUP-based predicting method of the GPR was extended to 3D by introducing DUP attenuation
and an optimized analytical LM to compensate for the low statistics of the learning data due to a finite number of
dete
detector elements. The precision of the predicted GPR is expected to be improved by improving the LM and by
invo
involving other metrics.
This article is protected by copyright. All rights reserved
Accepted Article
1. Introduction
I
Inte
Intensity-modulated radiation therapy (IMRT) has become immensely popular in modern radiation therapy as it
realizes a high dose conformality on the target volume. Since IMRT utilizes a complex intensity-modulation (IM)
real
using a multileaf collimator (MLC) system, the patient-specific quality assurance (QA) has been emphasized as the
usin
prepre-treatment
verification. In practice, the patient-specific QA is typically performed using a pin-point ionization
chamber
for absolute dose verification and a two-dimensional (2D) or three-dimensional (3D) detector array to
cha
veri the shape of the dose distribution. Preparation for the patient-specific QA requires time and cost for the
verify
generation
of the verification plan, measurements of the absolute dose and the dose distribution, and subsequent
gen
ana
analysis
with a certain occupation of the treatment machine. Thus, improving the efficiency of IMRT preparation is
an essential
concern to be addressed to meet the increasing demand for IMRT. Moreover, it is not feasible to use the
e
IMR for progressive diseases as the preparation of the IMRT takes longer than 3D conformal radiation therapy.
IMRT
The
Therefore,
reducing the effort for IMRT preparation attracts attention in these contexts. In practice, the number of
inst
institutions performing the measurement-based patient-specific QA is dropping.1 For example, the verification
measurement for specific treatment sites such as the prostate or breast, in which a successful result is highly
mea
exp
expected, has been reduced or stopped in some institutions. However, there is a need to develop a verification
method that can substitute the currently used gamma analysis2 without losing the safety level in the IMRT delivery.
met
Recently, a variety of attempts have been made to estimate the IM complexity and to investigate their
relationship
between the IM and gamma passing rate (GPR), which may potentially help to omit the patient-specific
rela
QA and to improve the efficiency of the clinical QA practice. A complexity metric (CM) that may be related to the
GPR has been proposed by several authors,3–10 resulting in limited predictability of the GPR. Deep learning (DL)bas
based prediction showed a good performance for the planar dose distribution measured using the film. 11 Recently,
mac
machine
learning (ML) technique was used to attempt the GPR prediction using the CMs as input data.12
In our previous study, we developed a novel method to predict the GPR using a dose uncertainty potential
(DU accumulation technique.13 The concept of the DUP was first introduced by Kim et al.14 Jin et al. further
(DUP)
developed
the concept15, 16 and demonstrated its application to clinical data.17 The essential result of our previous
dev
stud
d 13 was that a good performance of the DUP-based prediction of the GPR was demonstrated for a planar dose
study
dist
distribution
with a pixel size of 1 ൈ 1 mm2. This method is based on a hypothesis that the ߛ value depends on the
DU at each dose voxel. In this study, we aim to extend the application of our DUP-based method to 3D dose
DUP
dist
distribution
analyzed using the gamma analysis with a finite number of detector elements. We introduced two
tech
techniques
to apply our DUP-based method to the 3D data in this study. One is the DUP attenuation while
esti
estimating
the 3D DUP distribution. Another is an optimized analytical learning model to compensate for the low
stat
statistics
of the learning data due to a limited number of detectors in the device.
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Accepted Article
2. Materials
M
and Methods
2.A
2.A. Clinical equipment, treatment plans, and patient-specific verification data
Figure 1 shows a schematic of the workflow. Sixty head-and-neck IMRT treatment plans were created in the
XiO treatment planning system (TPS) (Elekta AB, Stockholm, Sweden). All plans were created using nine step-andshoot beams of the ONCOR linear accelerator (Siemens Medical Systems, Concord, CA). The optimization was
sho
perf
performed with the maximum iteration of 60 and the convergence criterion of 0.001%. The dose computation was
performed with the grid spacing of 3 mm. Total number of segments in each plan is shown in Fig. 2(a) and the
perf
mon
monitor unit (MU) of each segment is shown in Fig. 2(b). The minimum segmental MU among 60 plans was 2. The
treatment plan and dose distribution were exported from the TPS in the digital imaging and communications in
trea
med
medicine (DICOM) format.
We used the Delta4 system that comprises of 1069 p-type Si semiconductors with an active area of 0.0078 cm2.
The phantom has a cylindrical shape with a 22-cm diameter and 40-cm length. The detector elements are arranged
on two oblique planes at 50ι and 320ι on the axial view. The detectors are arranged in 20 ൈ 20 cm2 area on each
plan
plane. The detector spacing was 0.5 cm within the inner area of 6 ൈ 6 cm2 while 1 cm for the area outside of 6 ൈ 6
cm2.
Verification plans were created and measured by Delta4 (ScandiDos, Inc., Ashland, VA, USA).18 The
measured
dose distribution (ܦ୫ ) was compared with the calculated dose distribution (ܦୡ ) using the gamma analysis.
mea
The ߛ distribution was calculated from ܦୡ and ܦ୫ on the detector elements on the oblique planes. The GPR was
then calculated from the ߛ distribution and was exported to our in-house software (GPR analyzer).
The DICOM RT Plan was also used for generating the 3D DUP distribution using another in-house software
(DUP
(DU generator) described in Sect. 2.B. The 3D DUP distribution was exported to the GPR analyzer which predicts
the GPR. The GPR analyzer used the GPR from the Delta4 system and the 3D DUP distribution from the DUP
gen
generator
to calculate the predicted GPR.
2.B Generation of the three-dimensional distribution of dose uncertainty potential
2.B.
A planar DUP (pDUP) distribution of each beam was generated using the same method developed in our
prev
previous study13 using the segmental MLC shape and monitor unit extracted from the DICOM RT Plan. The width
of the
t Gaussian folding was 3.9 mm as per the analysis of our previous study13 but with the lateral profile of the 3 ൈ
3-cm2 MLC field at 11-cm depth with a source-to-surface distance (SSD) of 89 cm, which is the same as the center
t Delta4 device.
of the
The attenuation of the DUP in the Delta4 phantom needs to be accounted for when the pDUP distribution is
proj
projected
on the Delta4 phantom. The attenuation of the DUP was estimated using a dose distribution of a 3 ൈ 3-cm2
MLC field with the SSD = 89 cm. The dose distribution of the MLC field [Fig. 3(a)] was obtained, and the
ML
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differential of the dose distribution ݑሺ݀ǡ ݔሻ = ݀ܦሺ݀ǡ ݔሻΤ݀ ݔwas calculated [Fig. 3(b)]. The depth profile of the DUP
diff
ܷሺ݀
ܷሺ݀ሻ is defined by
ܷሺ݀ሻ ൌ ሼݑሺ݀ǡ ݔሻሽ ሼݔሽ.
(1)
Nor
Normalized depth profiles of ܦሺ݀ǡ Ͳሻ and ܷሺ݀ሻ were created using
ሺ݀ሻ ൌ ܦሺ݀ǡ ͲሻΤሼܦሺ݀ǡ Ͳሻሽ ሼ݀ሽ and
ܦ
(2)
ሺ݀ሻ ൌ ܷሺ݀ሻΤሼܷሺ݀ሻሽ ሼ݀ሽ.
ܷ
(3)
ሺ݀ሻ (dashed line). Gray filled area shows the depth range in which the
ሺ݀ሻ (solid line) and ܷ
Fig
Figure
3(c) shows ܦ
ሺ݀ሻ and ܷ
ሺ݀ሻ at the center of the Delta4 device (݀
Delta4 detectors are located (݀ = 1–21 cm). The attenuation of ܦ
Del
is larger than ܦ
by 9.5%
= 111 cm; dotted line in Fig. 3(c)) were 0.474 and 0.519, respectively. The attenuation of ܷ
(
(~ (0.519
– 0.474) / 0.474 ൈ 100).
Figure 4 shows the flow of the generation of the 3D DUP distribution. The pDUP was projected on the Delta4
pha
phantom
by taking the divergence into account [Fig. 4(a)]. In this projection, the Gaussian folding width was
assu
assumed
to be proportional to the source-to-voxel distance. The depth profile of the DUP was considered using Eq.
(1). The projection was performed for all segments in all beams [Fig. 4(b)]. This calculation was performed with 1 ൈ
1 ൈ 1-mm3 voxels. The DUP was quadratically accumulated using
ଶ
ଶ ൌ σా σൣܷాǡ ൫݀ాǡ ൯൧ ,
(4)
where
whe ݅ , ݅ୗ , and ݅ are the identifiers of the beam, segment, and voxel, respectively, ݀ాǡ is the depth of the ݅ ’th
vox for the ݅ ’th beam, ܷాǡ is the DUP for each set of ሺ݅ ǡ ݅ୗ ǡ ݅ ሻ. The DUP values on the detector elements
voxel
(ob
(oblique lines in Fig. 4(c)) were extracted and were used to predict the 3D GPR.
2.C
2.C. Prediction of gamma passing rate
Figure 5 shows a diagram of the GPR prediction. The learning data comprises of a set of the ߛ distribution [Fig.
5(a)
5(a)] and DUP [ ]ݑdistribution [Fig. 5(b)]. The ߛ distribution was translated to the measured GPR [݉
] for the
tole
tolerance of 3%/3 mm, 3%/2 mm, and 2%/2 mm, which were obtained from the Delta4 software. The DUP
hist
t
histogram
[ܨ ሺݑሻ, Fig. 5(c)] was obtained from the DUP distribution [Fig. 5(b)] (Step #1).
Our method is based on the hypothesis that the ߛ histogram depends on the DUP value. In our previous study,
we demonstrated that this hypothesis is applicable for a planar dose distribution with 1 ൈ 1-mm2 pixel size.13 One of
the developments in this study is to apply our method to the gamma analysis using a fewer number of data points.
Our previous study predicted the GPR using a full numerical data array of the ߛ and ݑdistributions with 1 ൈ 1-mm2
pixels. The learning model (LM), an average GPR for a given DUP [ܽ
ሺݑሻ], was calculated from a large number
pixe
p
of pixel
data of ߛ and ݑvalues. On the other hand, this study predicts the GPR from the finite number of detector
elem
elements
in Delta4. The LM was assumed to be an exponential function to avoid a statistical fluctuation due to the
fini number of detectors [Fig. 5(d)].
finite
The predicted GPR [ ]
was calculated using the DUP histogram [Fig. 5(c)] and the LM [Fig. 5(d)]. The
LM is defined as
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ܽ
ሺݑሻ ൌ ݁ ି௨ ,
(5)
whe ݍis a parameter to optimize. The
is calculated by
where
ൌ σൣܨ ሺݑ ሻܽ
ሺݑ ሻ൧ൗσ ܨ ሺݑ ሻ,
(6)
where
whe ݆ is the identifier of the learning data and ݈ is the suffix for ݑ. A squared sum of the difference between
and ݉
for all data except for the evaluated data (݅’th data) is calculated by
ܵ ൌ σஷ ݀
ଶ ,
(7)
݀
ൌ ݉
െ
(8)
whe
where
(Ste
(Step #3). In practice, ܵ depends on the parameter ݍ, as illustrated in Fig. 5(e). Thus, the parameter ݍwas optimized
୭୮୲
to give
g the minimum value of ܵ . The optimized value of ݍ[ ݍ ] was then used to determine the optimized LM [Fig.
5(f)
5(f)] (Step #4). The optimized LM was applied to the evaluated data (݅’th data).
The evaluated data comprised the same data set as the learning data: the ߛ distribution [Fig. 5(g)] and ݑ
dist
distribution [Fig. 5(h)]. The ݑdistribution was translated to the ݑhistogram [Fig. 5(i)]. The
of the ݅’th data
୭୮୲
was calculated using the same equation as Eq. (6), but with ݍ
(Step #5). The
was then compared with the
݉
from the Delta4 software [Fig. 5(j)]. The leave-one-out cross-validation was realized by excluding the
݉
evaluated
data from the optimization of the LM. This procedure was performed for all sixty data with the 3%/3-mm,
eva
3%/2-mm,
and 2%/2-mm tolerances. The
was evaluated in comparison with the ݉
. Standard deviation
3%
(SD)
(SD of the ݀
was calculated as a function of
.
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Accepted Article
3. Results
R
Figure 6(a) shows an example of ܵ as a function of [ ݍEq. (7)] for each tolerance. Red, blue, and green lines
are data of the 3%/3-mm, 3%/2-mm, and 2%/2-mm tolerances. The filled circles show the minimum point for each
tolerance. The ݍ value to give the minimum value of ܵ was the optimized ݍ . Figure 6(b) shows the exponential
tole
functions
corresponding to the optimized ݍ for each tolerance. The larger value of ݍ corresponds to the larger
fun
attenuation
atte
of the exponential function. Larger attenuation was observed for tighter tolerance.
The correlation between ݉
and
is shown in Fig. 7(a). Red, blue, and green symbols show data for
the 3%/3-mm, 3%/2-mm, and 2%/2-mm tolerances, respectively. This correlation is translated to the relationship
betw
between
the ݀
and
shown in Fig. 7(b). The SD of the ݀
for each
domain with 5% pitch is
sho in Fig. 7(c). The corresponding area of this SD is shown with a filled gray area in Fig. 7(b). Note that the SD
shown
for <
85% was not calculated as the data had low statistics. Mean SD for the 3%/3-mm, 3%/2-mm, and 2%/2-
mm tolerances were 2.3%, 4.1%, and 6.7%. The systematic error of the ݀
for the 3%/3-mm, 3%/2-mm, and
2%
2%/2-mm
tolerances were 0.05%, 0.1%, and 0.3%.
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4. Discussion
D
The DUP-based prediction of the 3D GPR was realized by introducing two techniques. One is the behavior of
the DUP in the Delta4 phantom. The width of the penumbra, which was involved as the Gaussian folding width
previously,
was also assumed to be proportional to the source-to-voxel distance. This width affects the depth profile
prev
of the
t DUP because the amplitude obtained in Eq. (1) depends on the width at each depth. Technically, the
difference between ܦሺ݀ǡ Ͳሻ and ܷሺ݀ሻ is due to the larger widths at larger depths. The depth profile of ܷ should be
diff
correctly
involved for estimating the 3D DUP distribution since the attenuation of ܷ is larger than ܦ. It should also
corr
that the IM beam has several apertures with different shape and size, which may produce a different depth
be noted
n
pro
profile of each aperture. For simplicity, we assumed that the depth profile of the DUP is the same as the one for 3 ൈ
3-cm2 MLC field for all apertures.
The DUP was used in our model as the only metric for predicting the ݉
. Technically, the DUP, an
acc
accumulated dose gradient at each voxel, is expected to have a direct impact on the resulting dose accuracy. In
prac
practice, the decrease of the ݉
occurs due to a discrepancy between ܦୡୟ୪ୡ and ܦ୫ୣୟୱ . The performance of the
DU
DUP-based
prediction of GPR is supported by the ab initio approach originally introduced by Kim et al.14 and
dev
developed by Jin et al.15–17 Though the current study showed a limited performance, our previous and current results
demonstrated an efficacy of using DUP for predicting GPR. While we consider the DUP is a good candidate for the
dem
effective metric for GPR prediction, there are other candidates for the good metric for predicting GPR. For example,
effe
the dose discrepancy is observed for small MLC fields which are often used in IMRT. Though this study included
the location and intensity of the DUP, the field size was not taken into account. The field size affects both the
penumbra width and the depth profile of the DUP. Therefore, precision in predicting the GPR is expected to be
pen
improved by taking into account the aperture size in each segment.
imp
A simple exponential function with a single parameter [Eq. (5)] was chosen as the LM in this study. It helps to
restrict
ܽ
within the realistic range of 0–100%. The ܽ
for = ݑ0 is fixed at 100% and decreases for larger ݑ.
rest
The fact that ݍ is larger for tighter tolerance is consistent with the expectation that the attenuation of ܽ
is larger
for tighter tolerance [Fig. 6(b)]. The approximation using the exponential function also helps to compensate for the
low statistics of the sampling due to the finite number of detectors. It is expected that the prediction performance
may be improved by adjusting the shape of the LM.
GPR prediction has been investigated by several authors in previous studies. These are roughly classified into
two approaches. One is a complexity metric showing an average characteristic of the complexity of the IM beam.
Tot monitor unit,5 the modulation complexity score developed by McNiven et al.,3 total leaf travel4 were
Total
inve
investigated
in comparison with the GPR. The other approach is a direct estimation of the GPR. Our DUP-based
13
met
the DL-based method,11 and the ML-based method12 are classified into this direct estimation. This
method,
app
approach utilizes some parameters which have characteristics of the IM beam and good proportionality to the GPR.
Our previous and current studies can be used to understand the performance of the DUP for predicting the GPR.
One example is a comparison with the ML-based method. In this study, we obtained SD = 2.3% and 6.7% for
the 3%/3 mm and 2%/2 mm tolerances, which are close to the ML-based methods which analyzed data of a helical
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Accepted Article
diode array with a 1-cm pitch and achieved SD = 2.1–2.4% and 5.4–5.8% for the 3%/3 mm and 2%/2 mm tolerances
diod
by involving 28 complexity metrics as input parameters.12 We consider that the DUP is an effective metric for
predicting
pred
GPR since the DUP-based method achieved current results only with the DUP. The performance of our
method
is expected to be improved by involving other parameters such as the field size.
met
Another example is a comparison with the DL-based method as an ultimate approach which automatically
involves
multiple characteristics. Tomori et al.11 analyzed data of composite dose distributions measured using a
invo
gafchromic film and obtained a root mean square error of 1.11%, 1.50%, and 2.24% for the 3%/3 mm, 3%/2 mm,
gafc
and 2%/2 mm tolerances, which were smaller than our results (2.3, 4.1, and 6.7%) by factor of 2, 3, and 3,
respectively. Since our data were obtained from the Delta4 system with a 5-mm pitch detector array, direct
resp
com
comparisons of these results do not provide an exact goal to achieve. Applying multiple predicting methods (e.g. the
DUP-based, ML-based, and DL-based methods) to the same data set of the GPR may provide useful insight to
DU
und
understand how dominant the DUP is within the metrics for GPR prediction.
The SD of ݀
was evaluated in this study as well as our previous study. While the performances of the GPR
predictions in previous studies were evaluated using Pearson’s correlation coefficient ݎ, a careful consideration is
pred
needed to employ the ݎfor inter-comparison of the performance of the GPR predictions. The range of ݉
may
nee
differ among different combinations of the TPS, linear accelerator, and QA device. The quality of the beam model
diff
dire
directly affects the range of the resulting ݉
and subsequent ݎvalue. Thus, we employed the SD of ݀
in our
curr
current and previous studies.
The use of SD for evaluating
is also useful for considering the clinical application of the GPR prediction.
The decision to use a predicting method may be based on the accuracy and precision of
. In our previous study,
we introduced an example consideration for estimating a threshold for
corresponding to ݉
90% for a
give
given confidence level.13 This technique may be useful for considering a clinical use of
with good accuracy
and precision. Since we obtained a limited performance in this study, the consideration for the clinical use was left
for our future study.
Sixty head-and-neck IMRT cases were used to develop the 3D GPR prediction method in this study. The
evaluation of the necessary number of the learning data is left for our future study since other improvements such as
eva
usin
using correct aperture size instead of the fixed 3ൈ3 cm2 and involving the effect of the field size may have larger
imp
impact in our development of the GPR prediction. It is necessary to test this method for other treatment sites such as
in the
th brain, thorax, abdomen, and pelvis. Since the complexity of the treatment plan differs among treatment sites, it
is eexpected that the quality of the LM will depend on the treatment site. It should also be noted that the DUP
dist
distribution differs among different IM techniques (e.g., step and shoot vs. sliding window, flattening filter vs.
flat
flattening filter free, IMRT vs. VMAT). Specifically, the VMAT delivery involves continuous and dynamic motion
of the
t gantry and MLC. It is necessary to examine the application of our technique to VMAT since we generate the
com
composite DUP by accumulating segmental DUPs as static gantry angle and the MLC shape at each segment. Thus,
the LM needs to be generated and examined for each IM technique. The DUP distribution also differs among
diff
different TPSs and the accompanying algorithm. Therefore, further investigations are needed to obtain a general
und
understanding of the DUP and its application to the GPR prediction.
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5. Conclusion
C
We developed and demonstrated a DUP-based method to predict the GPR of the 3D dose distribution measured
by a commercial 3D detector array system. The pDUP was extended to 3D by including the depth profile of the
DUP.
DU An approximated LM was employed to compensate for the finite statistics of the learning data. It is expected
that this method can provide the predicted GPR prior to the verification measurements of the IMRT delivery.
Acknowledgement
We would like to thank Editage (www.editage.jp) for English language editing.
Disclosure of Conflict of Interest
The authors have no conflicts to disclose.
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Accepted Article
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Figure Legends
Fig
Fig
Fig. 1. The workflow of this study.
Fig
Fig. 2. (a) Total number of segments in each plan and (b) the monitor unit of each segment.
Fig
Fig. 3. (a) Dose distribution [ܦሺ݀ǡ ݔሻ] and (b) ݀ܦሺ݀ǡ ݔሻΤ݀ ݔof a 3 ൈ 3-cm2 MLC field. (c) Normalized depth profile
ሺ݀ሻ] and the DUP [ܷ
ሺ݀ሻ]. Gray area shows the range in which the Delta4
of tthe dose along the central axis [ܦ
dete
detectors
are located (݀ = 1–21 cm).
Fig 4. Generation of the 3D distribution of the DUP.
Fig.
Fig 5. Diagram of the prediction of the gamma passing rate.
Fig.
Fig 6. (a) An example of ܵ as a function of [ ݍEq. (7)]. Filled circles show the minimum point for each tolerance.
Fig.
୭୮୲
(b) Exponential functions corresponding to the ݍ . The red, blue, and green lines represent data for the 3%/3-mm,
3%
3%/2-mm,
and 2%/2-mm tolerances, respectively.
Fig 7. (a) Correlation between the ݉
and
. Red, blue, and green plots are data of the 3%/3-mm, 3%/2-mm,
Fig.
and 2%/2-mm tolerances, respectively. (b) Difference between ݉
and
as a function of
. A filled
gray area shows the range of a standard deviation (SD) for each domain of pGPR. (c) SD of the ݀
as a function
of
.
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