International Journal of Medical Physics, Clinical Engineering and Radiation Oncology, 2013, 2, 117-124
Published Online November 2013 (http://www.scirp.org/journal/ijmpcero)
http://dx.doi.org/10.4236/ijmpcero.2013.24016
Open Access IJMPCERO
The Reproducibility of Patient Setup for Head and Neck
Cancers Treated with Image-Guided and
Intensity-Modulated Radiation Therapies Using
Thermoplastic Immobilization Device
Akihiro Nakata1,2, Kunihiko Tateoka1,3*, Kazunori Fujimoto1,4, Yuichi Saito1, Takuya Nakazawa1,
Tadanori Abe1, Masaki Yano1, Koichi Sakata1,3
1Department of Medical Physics, Graduate School of Medicine, Sapporo Medical University, Sapporo, Japan
2Nikko Memorial Hospital, Muroran, Japan
3Department of Radiology, Sapporo Medical University, Sapporo, Japan
4Radiation Therapy Research Institute, Social Medical Corporation Teishinkai, Sapporo, Japan
Received July 30, 2013; revised August 25, 2013; accepted September 10, 2013
Copyright © 2013 Akihiro Nakata et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
The reproducibility of patient setup is an important issue for head and neck cancers treated with intensity-modulated
radiation therapy (IMRT). In this study, an image-guided radiation therapy (IGRT) system has been used to minimize
the uncertainty of patient setup while standard thermoplastic masks were used to provide adequate immobilization for
the head and neck. However, they do not provide sufficient immobilization of the shoulders, which is an important re-
quirement in comprehensive nodal irradiation. Therefore, we investigated the setup and rotational shifts in head and
neck cancer patients undergoing IMRT for which this immobilization device had been used together with an IGRT sys-
tem. The setup and rotational shifts of patients were analyzed using the ExacTrac X-ray 6D IGRT system. The patients
were classified as having head and neck tumors in the upper or lower regions. The upper neck nodes included lymph
nodal level II while the lower neck nodes included lymph nodal levels III and IV. Clinical data from 227 treatment ses-
sions of 12 head and neck cancer patients were analyzed. The random translational error in inter- and intra-fraction er-
rors of the anterio-posterior (AP) direction might influence the rotational errors of pitch and roll in the upper region. At
the same time, the random translational error in the inter- and intra-fraction errors of the AP direction might influence
the rotational error of roll in the lower region. We believe that these random translational errors should be considered
during treatment. We found variability in random translational errors for different regions in the anatomy of head and
neck cancer patients due to rotational shifts. Depending on the location of the primary lesion or the selected nodal
treatment targets, these relative positional variations should be considered when setup and rotational shifts are corrected
with IGRT systems before treatment.
Keywords: IMRT; IGRT; Radiation Therapy; Immobilization; Head and Neck Cancer
1. Introduction
The primary goal of radiation therapy is to deliver the
desired radiation dose accurately to the desired target
volume throughout the course of treatment. Technologi-
cal advances in conformal radiation therapy have made it
possible to tailor treatment to match the shape and posi-
tion of the target, and thereby minimizing normal tissue
damage to a greater extent than previously possible. One
technique, intensity-modulated radiation therapy (IMRT),
has yielded significant gains in tumor control and toxic-
ity reduction [1-3]. Another technique, image-guided
radiation therapy (IGRT), has focused on the characteri-
zation and control of patient movement, organ motion,
and anatomical deformation, which introduce geometric
uncertainty and limit the effectiveness of high-precision
treatment.
Target localization performed with appropriate tech-
nologies and frequency is a critical component of treat-
*Corresponding author.

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118
ment quality assurance. For example, the target position
relative to the beams has been inferred from surface
marks on the patient’s skin or through an immobilization
device and verified using megavoltage radiographs of the
treatment portal. With IGRT, imaging technology has
made it possible to image soft tissue volumes and bones
using x-rays (kV) in the treatment setting. Enhancing
localization practices reduces treatment errors, permits
the monitoring of anatomical changes, and minimizes un-
certainties that could influence clinical outcomes [4].
Analysis of the reproducibility of patient setup is an
important issue for radiation treatments employing IMRT
and IGRT. In particular, the standard thermoplastic mask
provides adequate immobilization of the head and neck.
However, it fails to provide sufficient immobilization of
the shoulders which is an important requirement when
IMRT and IGRT systems are used for comprehensive
nodal irradiation [5,6].
In Engelsman et al. [7] investigation of the intra-frac-
tion patient motion before IMRT treatment of the head
and neck, it was found that translational motion of less
than 1 mm is possible, depending on the characteristics
of the immobilization device used. However, they re-
ported a limitation in determining the accuracy of patient
setup, since their method only implemented two-dimen-
sional (2D)/2D matching using 2D portal images and 2D
digitally reconstructed radiographs (DRRs) [5,6,8]. There
is an important flaw in this technique because it is not
always possible to distinguish mismatches due to transla-
tional shifts from these images due to rotational dis-
placements. Inter-fraction motion before IMRT treatment
of the head and neck analyzed through 2D/2D matching
of portal images and DRRs is also discussed in other
literatures [9,10].
Zhang et al. [6] investigated inter-fraction patient mo-
tion as the deviations between the daily computed tomo-
graphy (CT) and the planning CT of a region of interest
with respect to a reference point, as determined by three
radiopaque markers on the thermoplastic mask before
IMRT treatment of the head and neck. Inter-fraction pa-
tient motions, including translations and rotations, for
three individual bony landmarks in the head and neck
region were separately registered in the daily CTs with
respect to their positions in the reference planning CT.
The study quantified inter-fraction patient motions in a
three-dimensional (3D) manner, but they did not report
intra-fraction patient motions. With the recent availabil-
ity of IGRT systems, it is possible to correct the patient
setup error just before treatment and/or before the deliv-
ery of each IMRT field with the patient immobilized in
the treatment position. Data on the intra-factional motion
of patients under specific immobilization methods will
provide a measure of the reproducibility of patient setup
when these devices are used. Additionally, the range of
inter-fractional motion of individual treatment sites will
provide an important data in order to set acceptable tol-
erances when these devices are used. The aim of this
study was to evaluate the reproducibility of patient setup
for head and neck cancers treated with image-guided
IMRT using thermoplastic immobilization device.
2. Materials and Methods
2.1. IGRT System
Step-and-shoot IMRT beams having five segments Inter-
and intra-fraction patient motions were analyzed using
the ExacTrac x-ray 6D IGRT systems (BrainLAB AG,
Feldkirchen, Germany) with system software version 3.5.
The ExacTrac x-ray 6D system consists of infrared (IR)
tracking and x-ray components. The infrared tracking
component includes two IR cameras, passive IR reflect-
ing spheres placed on the patient or the immobilization
device, and a plastic mask molded to the patient’s con-
tour. The IR cameras are rigidly mounted to the ceiling,
and they emit a low IR signal that is reflected and ana-
lyzed for positional information. Patient setup can then
be easily achieved by moving the couch to match the
marker’s position with those recorded in a CT image.
The software also provides rotational offsets along three
primary axes. The external markers must be positioned in
a relatively stable location to achieve accurate setup. The
x-ray component consists of two floor-mounted kV x-ray
tubes that project in an oblique angle medially, anteriorly,
and inferiorly onto two corresponding amorphous silicon
flat panel detectors mounted on the ceiling (Figure 1).
Two stereoscopic images produced by the two kV x-ray
tubes are obtained after the patient is initially set up
with the ExacTrac (infrared) system. These images are
then compared with the corresponding isocenter of each
patient’s 3D CT simulation images in the form of
DRRs.
The software provides several options for matching the
images. One of the methods is the six degrees of freedom
(6D) fusion method assume that the patient is set up with
rotational offsets. Corresponding DRRs are generated at
fixed angles, and position adjustment in three transla-
tional and three rotational directions (6D) is performed
on the DRRs to best match the x-ray images. The soft-
ware then compares these DRRs with the corresponding
x-ray images to obtain the set of DRRs with maximal
similarity to the corresponding x-ray images. The best
match is thus determined, and the three translational and
three rotational position variations used to generate the
set of DRRs are the 6D offsets used to fuse the images.
Jian et al. demonstrated in a phantom study that the
maximal random error of this system was ±0.6 mm in
each direction with 95% confidence interval while sys-
tematic error of approximately 0.4mm was found in the

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Figure 1. (a) The ExacTrac X-ray 6D IGRT systems showing the infrared camera, flat panel, and kV tube; (b) Head, neck
and shoulder thermoplastic immobilization system (S-Type, Medtec, Orange City, IA) and plastic mask.
longitudinal direction [11]. Vertical, longitudinal, and la-
teral displacements of the table as well as couch angles
(roll, pitch, and yaw) are calculated by the system to
correct for the differences in the actual patient setup and
the patient setup when the reference CT was taken. The
entire imaging, analysis, and patient shift require 3 to 5
min of additional setup time than that needed for patients
undergoing no image guidance [8,12].
2.2. Analysis of Patient Motions
Twelve patients with head and neck cancers treated with
IMRT were selected for this study. Their planning CT
was taken at a spatial resolution of 0.94 mm per pixel in
the transverse plane, and the slice thickness was 1 mm.
Before beam delivery they patient images were also ta-
ken with the ExacTrac x-ray 6D IGRT systems, of which
227 pairs of stereoscopic images were used for the study.
Head and neck IMRT patients are immobilized at our
institution by using a head-neck-shoulder thermoplastic
immobilization system (S-Type, Medtec, Orange City,
IA) with patient-specific neck cushions. IMRT treat-
ments were performed using 6MV x-rays from a Sie-
mens Mevatron Primus (Siemens, Munich, Germany)
with 80 leaf pairs of 1 cm projected width at the iso-
center.
For head and neck IMRT patients, we use a generic
isocenter, which is typically located around the C2 to C4
vertebrae. Although individual bony structures are rigid,
bony structures in the head and neck region collectively,
are not simple rigid objects. Zhang et al. [6] reported that
regions of interest (ROIs) in different locations in the
head and neck region were needed to analyze patient
motion. Patient motions were analyzed by separating the
head and neck cancers into two ROIs for nasopharyngeal,
oropharyngeal, and hypopharyngeal cancers. The first
region was comprised of the primary tumor and upper
neck nodes (upper region, close to the clivus and C3 ver-
tebra (C3) regions). The upper neck nodes included
lymph nodal level II of the neck. The second region was
comprised of the lower neck nodes (lower region, close
to the C5 vertebra (C5) and supraclavicular regions). The
lower neck nodes included lymph nodal levels III and IV
of the neck. The clivus to C3 region represents the tumor
to subclinical disease for head and cancer patients. The
C5 to supraclavicular region represents the supraclavicu-
lar lymph nodes that are occasionally treated with IMRT.
Therefore, to analyze the set-up reproducibility of head
and neck cancers, the region of interest was separated
into upper region and lower region.
All patient setup were performed with aid of the Ex-
acTrac system. The necessary shifts to move the patient
to the isocenter were acquired with the position of the
infrared markers placed on top of the thermoplastics used
as bases for patient set-up localization. Stereoscopic x-
ray images from two directions were taken. In the analy-
sis of the upper region, the lower region of the images
was masked using the system software. Likewise, in the
analysis of the lower region, the upper regions in the
stereoscopic images were masked as shown in Figure 2.
The images were automatically registered to the DRR
generated from the planning CT image set. The ExacTrac
system software then computed the shifts necessary to
move the patient to the calculated isocenter for upper and
lower regions respectively. These were defined as the
pretreatment shifts. The couch was adjusted when the
computed translational and rotational shifts were more
than 1.0 mm and 1.0 degree, respectively (the mean shift
is about 1 mm according to rotational error of one degree
in this study).
When the computed translational and rotational shifts
for the upper and lower regions were in opposite direc-
tions, the patient had to be repositioned in the thermo-
plastic mask and stereoscopic images were re-taken to re-
calculate the pre-treatment shifts. Another set of stereo-
scopic images was taken after the completion of every
fraction of treatment in order to obtain the post-treatment
shifts.Inter-fractional motion, both in translational and
rotational directions, was determined from all the pre-
treatment shifts. On the other hand, intra-fractional mo-

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(a) (b)
Figure 2. Two verification kV x-ray images for evaluating the localization accuracy, which is determined by measuring the
distance of isocenter between the x-ray system and the treatment for the upper region (a) and lower region (b). The dark gray
region not fused image is masked.
tion, both in the translational and rotational directions,
was derived from the pre- and post-treatment shifts ob-
tained within the same day (or treatment fraction). The
translational shifts were calculated along the anterio-
posterior (AP), cranio-caudal (CC) and left-light (LR)
directions while the rotational shifts in roll, pitch and
yaw directions. The mean error (
X
), systematic error
(∑), and random error (δ) for the inter- and intra-frac-
tional motions were defined as the mean of the variation
inter- or intra-fractional motion of the entire patients, the
standard deviation of inter- or intra-fractional motion of
patient-to-patient, and the mean of the observed random
standard deviations of the entire patients in the study,
respectively [13].
3. Results
3.1. The Mean Translational and Rotational
Errors (upper
trans
X,upper
rot
X), Systematic Errors
(upper
trans
,upper
rot
), and Random Errors
(upper
trans
 ,upper
rot
 ) for the Upper Region
The translational errors are given in Table 1, which quan-
titatively summarizes the pre-treatment (Before), post-
treatment (After), and intra-translation (Intra) mean
upper
trans
X, systematic upper
trans
, and random errors upper
trans

(mm) and their ranges in the LR, CC, and AP directions
for the upper region of the patient population.
Table 1 shows that the translational mean and system-
atic error of the upper region before treatment of the en-
tire patient population (12 patients) were small (less than
0.26 mm) in all directions, indicating that there was no
significant systematic error between the treatment simu-
lation and the actual treatment. In the LR and CC direc-
tions, the translational systematic errors after treatment
and the intra-fraction error were consistent (less than
0.59 mm) with the pre-treatment values; however, that of
the AP direction was slightly larger, with a range of 1.02
to 1.22 mm. Moreover, the pre-treatment, post-treatment,
and intra-fraction random translational errors exhibited
ranges of 0.65 to 0.76 mm in the CC direction and 0.83
to 2.04 mm in the AP and LR directions.
The rotational errors are given in Table 2, which quan-
titatively summarizes the pre-treatment (Before), post-
treatment (After), and intra-fraction (Intra) upper
rot
X, sys-
tematic upper
rot
, and random errors upper
rot
 (degree) and
their ranges in the roll, pitch and yaw directions for the
upper region of the patient population.
Table 2 shows that the range of the pre-treatment,
post-treatment, and intra-fractionation mean rotational,
rotational systematic and random rotational errors was
−0.69 to 1.04 degree in the yaw and pitch directions;
therefore, the effect of the roll and yaw directions was
small. The range of the mean rotational error was consis-
tent in all three directions, but the ranges of the rotational
systematic and random rotational errors were larger in
the pitch direction than in the roll and yaw directions.
That is, the rotational errors for the upper regions were
small in all directions excluding the post-treatment and
inter-fraction rotational systematic and random errors in
the roll direction. The systematic and random errors of
translation and rotation for the upper region in all direc-
tions exhibited approximately normal probability distri-
butions.

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Table 1. Translation error (mm) of the upper and lower regions
X
, Σ and δ are mean, systematic and random errors, re-
spectively. (a) Before treatment; (b) After treatment; (c) Intra-translation error.
LR CC AP
(a) Before (b) After Intra (a) Before(b) After Intra (a) Before (b) After Intra
upper trans
upper
trans
X 0.07 −0.07 −0.11 0.07 −0.14 −0.18 0.08 1.02 1.08
upper
trans
 0.17 0.36 0.39 0.10 0.59 0.58 0.26 1.07 1.22
upper
trans
 0.83 1.17 1.13 0.65 0.76 0.65 1.10 1.79 2.04
lower trans
lower
trans
X 0.04 0.00 0.39 0.40 0.48 0.26 0.66 0.54 0.61
lower
trans
 0.28 0.56 0.54 0.59 0.67 0.31 0.90 0.88 0.80
lower
trans
 1.32 1.54 1.51 0.89 0.95 0.86 1.78 2.68 2.82
Table 2. Rotational error (degree) of the upper and lower regions
X
, Σ and δ are mean, systematic and random errors, re-
spectively. (a) Before treatment; (b) After treatment; (c) Intra-rotational error (degree).
roll pitch yaw
(a) Before (b) After Intra (a) Before(b) After Intra (a) Before (b) After Intra
upper rot
upper
rot
X −0.01 −0.27 −0.21 0.10 −0.69 −0.72 −0.69 0.06 0.06
upper
rot
 0.22 0.46 0.42 0.18 1.55 1.54 0.09 0.14 0.11
upper
rot
 0.97 0.84 1.04 0.81 1.07 1.03 0.61 0.75 0.82
lower rot
lower
rot
X 0.32 1.12 0.28 1.10 1.12 0.34 0.25 0.14 0.16
lower
rot
 0.44 0.49 0.37 1.60 1.63 0.48 0.29 0.20 0.23
lower
rot
 1.07 1.15 1.13 1.59 1.64 1.53 0.95 1.00 0.80
3.2. The Mean Translational and Rotational
Errors (lower
trans
X, lower
rot
X), Systematic Errors
(lower
trans
,lower
rot
), and Random Errors
(lower
trans
 ,lower
rot
 ) for the Lower Region
The translational errors are given in Table 1, which
quantitatively summarizes the pre-treatment (Before),
post-treatment (After) and intra-fraction (Intra) mean
lower
trans
X, systematiclower
trans
 and random errors lower
trans

(mm) and their ranges in the LR, CC, and AP directions
for the lower regions of the patient population.
Table 1 shows that the pre-treatment, post-treatment,
and intra-fraction mean translational and systematic er-
rors of the lower regions of the entire patient population
(12 patients) were relatively small (less than 0.90 mm) in
all directions, thereby, indicating that there is no signifi-
cant difference between the upper and lower regions.
In the CC direction, the pre-treatment, post-treatment,
and intra-fraction random translational errors were simi-
lar (less than 0.95 mm) to the mean translational and
systematic errors; however, those of the LR and AP di-
rections were relatively large, with a range of 1.32 to
2.82 mm. Therefore, there were many variations between
the treatment simulation and actual treatment and during
treatment variables in the lower region.
The rotational errors are given in Table 2, which
quantitatively summarizes the pre-treatment (Before),
post-treatment (After), and intra-fraction (Intra) mean
lower
rot
X, systematic lower
rot
, and random errors lower
rot

(degree) and their ranges in the roll, pitch and yaw direc-
tions for the lower region of the patient population.
Table 2 shows that the range of the pre-treatment,
post-treatment, and intra-fraction mean rotational and
rotational systematic errors was 0.16 to 1.12 degree in
the yaw and pitch directions. The ranges of the mean
rotational and rotational systematic errors were similar in
the yaw, pitch, and roll directions, whereas the ranges of
the mean rotational and rotational systematic errors were
larger in the roll direction than in the yaw and pitch di-
rections. Moreover, the post-treatment and intra-fraction
random rotational errors were relatively large in all di-
rections; these values ranged from 0.80 to 1.59 degree.
The random rotational error of the lower region was lar-
ger than that of the upper region. The systematic and
random errors of translation and rotation for the lower
region exhibited approximately normal probability dis-
tributions in all directions.

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4. Discussion
In this study, we investigated the setup reproducibility in
head and neck cancer therapy for two different regions
using from ExacTrac X-ray 6D IGRT data acquired
while patients were immobilized in the treatment posi-
tion.
Recent work by Court et al. [5] and Zhang et al. [6] in-
dicated that bony landmarks C2, C6, and the palatine
process of maxilla (PPM) were independently chosen as
alignment targets to represent these landmarks in most
head and neck cancer patients. In this way, bony struc-
tures are used as landmarks for alignment in head and
neck cancer patients. For this reason, it was assumed that
the position of targets or avoidance structures relative to
bony landmarks is consistent between fractions for head
and neck cancer patients [5,6]. However, it may be diffi-
cult to concurrently correct patient setup errors of upper
region and lower region using these three landmarks in-
dependently.
Our landmarks for patient motions were analyzed by
separating the head and neck cancers into two ROIs; the
first region included the primary tumor + upper neck
nodes (upper region, close to the clivus and the C3 ver-
tebra (C3) region), whereas the second region included
the lower neck nodes (lower region, close to the C5 ver-
tebra (C5) region and the supraclavicular region). In par-
ticular, the upper region (the clivus to C3 region) repre-
sents the subclinical representation of the tumor for na-
sopharyngeal, oropharyngeal, and hypopharyngeal can-
cers.
Zhang et al [6] reported that the range of motion in the
translational direction of the bony landmarks C3, C6 and
PPM were generally between −0.5 cm to 0.5 cm at a 90%
confidence interval. The range of motion was slightly
worse for C6 in the LR direction at −0.68 cm to 0.62cm
and for the PPM in the CC direction at −0.5 cm to 1.15
cm. They reported no significant difference when using
the S-board or conventional facemask. Moreover, after
C2 alignment using IGRT, they reported a 90% confi-
dence range of −5.4 to 3.3 mm for C6 in each direction
and −7.5 to 9.0 mm for PPM in each direction. The re-
sults of Court et al. [5] were similar to those of Zhang et
al. Therefore, they described that some patients exhibit
large uncertainties in the C6 or supraclavicular region
that were useful for evaluating patient setup shifts. More-
over, they described that the lack of significant shoulder
shifts in the first week of treatment does not necessarily
indicate that few/no shoulder shifts will be observed later
during treatment because one patient had no shoulder
shifts larger than 5 mm until the 32nd fraction but had
large shifts for every fraction thereafter (total treatment,
35 fractions) and other patients had large shifts from the
start of treatment. The method of correcting patient setup
errors for the lower region is to treat the lower region
using a conventional anterior field. However, Thorstad et
al. [14] indicated that a cold match line between conven-
tional and IMRT fields can be a significant cause of re-
currences when implemented to treat the lower region
using a conventional anterior field. For that reason, plan-
ning target volume (PTV) margins are a geometric con-
cept defined to ensure that, in the presence of setup and
other uncertainties, the prescribed dose is actually deliv-
ered to the clinical target volume (CTV) is not difficult to
define using the published formulations for calculating
the necessary PTV basis of normal probability distribu-
tion for patient setup error [15-17]. Therefore, a correc-
tion method for head and neck cancer patients described
online re-planning to correct all shifts and rotations in
different regions or physically repositioning the patient in
the mask [5,6]. These reports are critical when treatment
is given using IGRT systems to be able to reposition the
patient.
In our IGRT assisted evaluation of the mean transla-
tional and systematic errors, the range of motion of the
upper and lower regions of head and neck cancer patients
were about 1 mm which was consistent with the other
published results [5,6]. Our patient setup error data ex-
hibited an approximately normal probability distribution.
The random translational error was larger than the
mean translational and systematic errors for the upper
and lower regions of head and neck cancer patients in all
directions. This is because the translational error in the
AP direction strongly influences the pitch and rolls rota-
tions. The pitch and roll rotations are more associated
with the translational error in the CC and LR directions,
respectively, and yaw rotation is determined by the trans-
lational error in the LR and CC directions. Although it
appears that large rotational errors were observed in all
directions, the effects of these three rotations indicated
that the effect of random translational error was larger
than those of mean and systematic translational errors
(Tables 1 and 2); the mean and systematic rotational
errors were slightly influenced by the mean and system-
atic translational errors in the all directions. Therefore,
the post-treatment and intra-fraction translational errors
in the AP direction influence the rotational errors of pitch
and roll in the upper region. At the same time, the post-
treatment and intra-fraction translational errors in the AP
direction influence the rotational error of roll in the lower
region. For this reason, even if head and neck cancer
patients were treated with IGRT and immobilization de-
vice, they do not provide sufficient reproducibility of
patient setup for head and neck region, which is an im-
portant requirement in comprehensive nodal irradiation.
We believe that these random translational errors
should be considered in the course of treatment. Our use
of IGRT is straightforward and only adds approximately
5 min to the delivery of each fraction. In addition, global
population data might permit the creation of a class solu-

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tion to calculate PTV margins.
5. Conclusions
In this study, we used the ExacTrac X-ray 6D IGRT sys-
tem and two regions (the upper and lower region) analy-
sis method to quantify the intra-fractionation error for
patient setup with head and neck cancer patients who
underwent fractionated external beam radiotherapy using
a commercially available immobilization device.
Setup and rotational shifts in the upper and lower re-
gion for the head and neck cancer patients were analyzed.
We found variability in random translational errors for
different regions of the anatomy in the head and neck
cancer patient as a consequence of rotational shifts. De-
pending on the location of the primary lesion or the se-
lected nodal treatment targets, these relative positional
variations should be considered when setup and rota-
tional shifts are corrected with IGRT system and immo-
bilization device before treatment.
6. Acknowledgements
The author(s) expresses their appreciation to Prof. Jun
Takada (Radiation Protection Laboratory, Sapporo Medi-
cal University) for his support and insightful comments
regarding this study. We likewise acknowledge the con-
tributions to this work by Dr. Kenichi Tanaka (Radiation
Protection Laboratory, Sapporo Medical University), Dr.
Kenichi Kamo (Mathematics and Information Sciences,
Sapporo Medical University).
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