International Journal of Medical Physics, Clinical Engineering and Radiation Oncology, 2013, 2, 69-75
http://dx.doi.org/10.4236/ijmpcero.2013.23010 Published Online August 2013 (http://www.scirp.org/journal/ijmpcero)
Comparison of the Motion Accuracy of a Six Degrees of
Freedom Radiotherapy Couch with and without Weights
Akihiro Takemura1, Shinichi Ueda2, Kimiya Noto2, Hironori Kojima2, Naoki Isomura2
1Faculty of Health Sciences, Institute of Medical, Pharmaceutical and Health Sciences, Kanazawa University, Kanazawa, Japan
2Department of Radiology, Kanazawa University Hospital, Kanazawa, Japan
Received May 17, 2013; revised June 18, 2013; accepted July 5, 2013
Copyright © 2013 Akihiro Takemura et al. This is an open access article distributed under the Creative Commons Attribution Li-
cense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
In this study, we compared the motion accuracy of six degrees of freedom (6D) couch for precision radiotherapy with or
without weights attached to the couch. Two digital cameras were focused on the iso-center of a linear accelerator. Im-
ages of a needle which had been fixed to the 6D couch were obtained using the cameras when the couch moved in
translation and rotation around each axis. The three-dimensional (3D) coordinates of the needle were calculated from
coordinate values in the images. A coordinate error of the needle position relative to the theoretical position was calcu-
lated. The errors were obtained with or without a 60 kg weight attached to the 6D couch, and these errors were com-
pared with each other. The mean distance of the 3D error vectors for the weighted test was 0.21 ± 0.11 mm, and ˃0.16 ±
0.09 mm for the non-weighted test (p < 0.05). However, the difference of two values was 0.06 mm which is smaller
than the minimum distance the 6D couch system can move correctly. The variance of 0.16 mm for the Y coordinate
errors for the weighted test only was larger than that for the non-weighted test, which was 0.06 mm (p < 0.05). We
found that a total weight of 60 kg did not affect the accuracy of the 6D couch clinically. However, the variance of the Y
coordinate errors was increased. This might suggest that the addition of this weight increase the uncertainty of the mo-
tion of the 6D couch.
Keywords: 6D Couch; IGRT; Accuracy Assessment
1. Introduction
A six degrees of freedom (6D) couch with an infrared
system is an effective system for the precise correction of
patient setup errors in image guided radiation therapy
(IGRT). To use a 6D couch for precision IGRT, accurate
evaluation of the 6D couch should be performed. The
accuracy and uncertainty involved in the use of a 6D
couch with an infrared system were usually evaluated us-
ing a linear accelerator (LINAC) integrated imaging sys-
tem, such as an X-ray radiography system or cone-beam
computed tomography (CBCT) system. A 6D couch
combined with an ExacTrac system (BrainLAB AG,
Feldkirchen, Germany) has been evaluated with regard to
uncertainty in its precision in several studies [1-4]. These
evaluations were undertaken using the Wiston-Lutz test
or by means of image registration software for ExacTrac
X-ray images and for CBCT images. However, the Wis-
ton-Lutz test only evaluates the origin of the 6D couch
motion.
Another 6D couch, HexaPOD evo (Elekta AB, Stock-
holm, Sweden) was also evaluated regarding its accuracy
using its image registration software with CBCT images
[5]. The degree of accuracy depended on the resolution,
especially in relation to CBCT, which has a voxel size of
1 mm × 1 mm × 1 mm. However, in general the 6D
couch can move or recognize a distance of 0.1 mm at
minimum. Hayashi et al. reported uncertainty regarding a
6D couch system on iso-centric rotation with a section
sheet and a high-resolution digital camera [6]. Addition-
ally, the accuracy and uncertainty of 6D couch systems
reported in previous papers were evaluated without the
use of an attached weight. A 6D couch with a patient on
it should move accurately; consequently the accuracy of
a 6D couch with attached weights should be evaluated.
In the present study, we have compared the accuracy
of 6D couch motion with or without the use of an at-
tached weight.
2. Materials and Methods
A HexaPOD evo as a 6D couch system was evaluated for
C
opyright © 2013 SciRes. IJMPCERO

A. TAKEMURA ET AL.
70
accuracy of motion regarding translation and rotation.
The 6D couch is an add-on to the base couch system. The
add-on 6D and the base couch systems can independently
move in relation to each other. In the current study we
have only evaluated the accuracy of the add-on 6D
couch.
The motion of the 6D couch with regard to translation
and rotation were evaluated in each axis of the coordinate
system, namely translation along the X, Y and Z axis
(TX, TY and TZ, respectively) and rotation around the X,
Y and Z axis (RX, RY and RZ, respectively). In addition,
evaluation of the accuracy of translation and rotation was
carried out under non-weighted and weighted conditions.
In the weighted evaluation, six metal blocks each weigh-
ing 10 kg (total 60 kg) were laid on the top of the 6D
couch at constant distance of 30 cm from the gantry-side
(Figure 1).
The HexaPOD evo has an official limitation regarding
its translation range and rotation angle, which is ±30 mm
for the X and Y translation, ±40 mm for the Z translation
and ±3.0 degrees of rotation around each axis. This mo-
tion limitation is based on the center of motion of the 6D
couch system; this is not the iso-center and is located at
about 1 m from the gantry end of the couch. Thus, the
actual limitations based on the iso-center as being the
origin are different from the official limitations. In the
current evaluation, the actual limitations were −20 mm to
+29 mm for the TX, −18 mm to +30 mm for the TY, −30
mm to 24 mm for the TZ, −1.1 degrees to 1.5 degrees for
the RX, −2.9 degrees to +29 degrees for the RY and −1.3
degrees to +1.3 degrees for the RZ. The 6D couch system
can detect a minimum positional difference of 0.1 mm on
each axis and a minimum angle difference of 0.1 degree
around each axis.
IGRT systems have several coordinate systems, for
example a LINAC coordinate system, a CBCT coordi-
nate system and so on. All coordinate systems usually
have the same origin (iso-center), but some directions of
the axis or angle differ from each other coordinate sys-
tem; thus, in the present study all three-dimensional (3D)
positions and angles were described in terms of the left
hand coordinate system (Figure 1(a)).
Two Nikon D5000 (Nikon Corporation, Tokyo) digital
cameras with an AF-S Micro NIKKOR 60 mm f/2.8G
ED lens (Nikon Corporation, Tokyo) were used to meas-
ure the positional errors of the 6D couch. This camera
has a 23.6 × 15.8 mm complementary metal oxide semi-
conductor image sensor and can take a 4288 × 2848 ma-
trix image (i.e. the minimum pixel size was about 0.0055
mm). 3D coordinates for the needle tip were obtained
from the two images obtained from the two cameras
along two orthogonal axes in the 6D couch coordinate
system. The needle was secured to the 6D couch. Images
of the needle were obtained before and after each couch
motion, and the relative 3D position from the position
before motion was calculated using these two images.
The needle was attached to the end of a metal rod and the
other end of the rod was attached to the end of the couch.
The rod was positioned so that it had approximately a 45˚
angle relative to each axis in the coordinate system. This
approach enabled the needle tip to be easily recognized
in the images. A description of the evaluation of the
translation and rotation of the 6D couch is detailed be-
low.
2.1. Evaluation for Translation
The needle tip pointing at the iso-center was located us-
ing the laser localizer in the LINAC room. This needle
tip position (couch position) was the initial position used
in the evaluation of translation. Here, our assumption
was that the origin of the 6D couch motion can be indi-
cated by the laser localizer. Camera positions for each
translational motion are shown in Figure 2(a). For TX,
in which the needle is moved along the X axis, the cam-
eras were positioned on the Y and Z axes; for TY they
were positioned on the X and Z axes. For TZ, the cam-
eras were oriented to portrait and were positioned on the
X and Y axes. Relative 3D coordinates were obtained
from a pair of images with an orthogonal view angle.
To ensure its location on the X or Y axis, the camera
was attached to a tripod and made level with the level of
the camera platform; it was directed to the iso-center,
which was indicated by the tip of the needle. The dis-
tance from the iso-center to the sensor plane of the digital
camera was about 280 mm. This distance made the aper-
ture size at the iso-center ˃ 60 mm, which covered the
translational motion range of the 6D couch; the spatial
resolution at the iso-center in the images was approxi-
mately 0.015 mm/pixel. This resolution was sufficient
because the 6D couch’s infrared system can recognize a
minimum distance of 0.1 mm.
After the camera had been correctly located, a fishing
line (diameter, 0.074 mm) with a weight was suspended
from the LINAC gantry at the iso-center and an image of
the line was obtained from each camera to measure roll-
ing angle roll

of an image. The angle roll

of the line
from the vertical axis of the image was measured to cor-
rect for rolling of the camera position. Coordinates in the
image affected by camera rolling can be corrected using
the affine transformation as follows:
roll rollraw
rollrollrawraw
cossin 0
sincos 0
10 011
ii
qjq j



 
 

 
 
 
(1)
where, qraw(iraw, jraw, 1) is a measured position in an im-
age, i and j were lateral coordinate and vertical coordi-
nate, respectively (Figure 1(b)), and q(i, j, 1) is a

A. TAKEMURA ET AL. 71
(a)
(b)
Figure 1. Diagrammatic representation of the weights and
the coordinate system used for the 6D couch. The arrow in
image (a) represents the needle which was used to measure
table position. Image (b) shows an image taken by the digi-
tal camera and its coordinates system.
corrected position which is rotated byroll

.
A card type micrometer (TYK-15, EIGER TOOL, Ja-
pan) was placed at the iso-center and a image of the mi-
crometer was taken by each camera to calculate the spa-
tial resolution (mm/pixel) at the iso-center. When the
camera position was changed, both the rolling angle and
the spatial resolution were obtained again.
When a camera was located on the Z axis, the sensor
plane of the camera should be made level. We placed the
camera below the iso-center, directed it to the iso-center,
and then checked the level at the front of the lens using a
level tool. And to realize the rolling angle of camera, a
board was placed in the aperture of the camera on the Z
axis instead of fishing line. The laser line along the Y
axis was reflected on it; then an image of the board re-
flecting the laser localizer was obtained to measure roll-
ing angle, roll

of images. The angle roll

was used to
correct the rolling with the Equation (1) as well.
The 6D couch and the needle were moved every 10
mm from 0 mm (the iso-center) along each axis. When
the next moving distance overran the limitation of the
translational motion of the 6D couch, the limitation value
was evaluated as the moving distance; −20 mm to 29 mm
for the TX, −18 mm to +30 mm for the TY and −30 mm
to +24 mm for the TZ. An image of the needle at the ini-
tial position was obtained, the couch with the needle was
moved along only one of the axes from the initial posi-
tion by entering a moving distance value into the 6D
couch system and then another image of the needle was
obtained. After this procedure had been completed the
couch was returned to its initial position and an image of
the needle was obtained for the next motion. This process
was repeated for both the positive and negative directions
of the couch motion and each movement was performed
at a time once.
To obtain qraw, which was the coordinates of a needle
tip in an image, the manual measurement was performed
three times and the mean of the three measured coordi-
nates was used as the coordinate. The measurements
were carefully performed by sufficiently magnifying the
image. The coordinate values obtained in pixels were
transformed to coordinate values expressed in mm by
multiplying the spatial resolution at the iso-center ob-
tained from an image of the micrometer. After this, a
correction for camera rolling angle (Equation (1)) was
applied to the coordinates qraw.
The i and j of q(i, j) corresponded with any two of x, y
and z of the p(x, y, z) in the 3D coordinate system. In the
TX, i and j of the q(i, j) in the image which was taken
with the camera on the Y axis were used as x and z of the
p(x, y, z), respectively; j in the image which was taken
with the camera on the Z axis was used as y of the p(x, y,
z). In the TY, i and j of the q(i, j) in the image with the
camera on the X axis were used as x and z of the p(x, y,
z); j in the image which was taken with the camera on the
Z axis was used as x of the p(x, y, z). In the TZ, j and i of
the q(i, j) in the image which was taken with the camera
on the X axis were used as y and z of the p(x, y, z); j in
the image which was taken with the camera on the Y axis
was used as x of the p(x, y, z). In the RX, i and j of the q(i,
j) in the image which was taken with the camera on the X
axis were used as y and z of the p(x, y, z); j in the image
which was taken with the camera on the Y axis was used
as x of the p(x, y, z). In the RY, i and j of the q(i, j) in the
image which was taken with the camera on the Y axis
were used as x and z of the p(x, y, z); j in the image which
was taken with the camera on the X axis was used as y of
the p(x, y, z). In the RZ, j and i of the q(i, j) in the image
which was taken by the camera on the Z axis were used
as x and y of the p(x, y, z); j in the image which was taken
by the camera on the Y axis was used as z of the p(x, y, z).
When the direction of i and j coordinates were opposite
to the direction of the corresponding coordinates in the
3D space, i and j were changed to −i and −j.
Coordinate error (xerror, yerror and zerror), namely the dif-
ference between the measured coordinate and the theo-
retical calculated coordinate p
calc(xcalc, y calc, z calc), was
calculated for each motion (Equation (2)). The pcalc(xcalc,

A. TAKEMURA ET AL.
72
ycalc, zcalc) was calculated by adding the moving distance
to the coordinates of initial position. The distance of a 3D
error vector was also calculated from the X, Y and Z
coordinate errors (Equation (3)).
  
errorerror errorcalccalccalc calc
,, ,,,,Exyzpxyz pxyz

(2)
22
vecerrorerror error
Dxyz
2

(3)
where, is 3D error vector and Dvec
is distance of a 3D error vector.

errorerror error
,,Exy z
2.2. Evaluation of Rotation
In the evaluation of couch rotation the needle tip was
shifted by 10 mm from the iso-center as the initial posi-
tion. The needle was attached to the couch in an identical
manner to that used for the evaluation of translation. A
second needle was pointed to the iso-center and was se-
cured to the LINAC gantry; thus, this second needle con-
tinuously indicated the position of the iso-center. The
positions of the cameras and the needle tip in the evalua-
tion of rotational motion are shown in Figure 2(b). The
needle was moved down by 10 mm from the iso-center to
recognize the rotational motion of the needle tip for the
RX and RY. For the RZ the needle tip was shifted to the
right by 10 mm.
(a)
(b)
Fi gure 2. Camera positions and alignments. Im age (a) sho ws
the camera positions used in the evaluation of translation
motion, TX, TY and TZ. Image (b) shows the camera posi-
tions used in the evaluation of rotation motion, RX, RY and
RZ. The red arrows in image (a) and image (b) represent
the needles which were tracked to obtain table positions.
The gray arrows in image (b) represent the second needle
which points out the iso-center.
In the evaluation of rotation preparation of the camera
settings, distance from the iso-center to the camera sen-
sor plan, direction of the optic axis to the iso-center and
so on, were the same as for the evaluation of translation.
The rotation angle of the couch was set every 1 degree
from 0 degrees for each axis until the limitation of the
rotation was reached; −1.1 degrees to +1.7 degrees for
the RX, −2.9 degrees to +2.0 degrees for the RY and
−1.4 degrees to +1.4 degrees for the RZ. In common with
the evaluation for translation, the 6D couch was rotated
and returned to the initial position repeatedly. The im-
ages of the needle tip were obtained from the cameras at
the initial position and then at the new position. Each
movement was performed at a time once.
The method used for the measurement of the needle tip
coordinates in the images was the same as that used for
the measurement of the needle tip coordinates in the
evaluation of translation; the coordinates were measured
three times and were averaged, and the averaged coordi-
nate was translated from pixels to mm and applied to the
correction of camera rolling.
Coordinate errors, which were differences between the
measured coordinates and the theoretical calculated co-
ordinates of the needle tip, were calculated in the evalua-
tion of rotation. To calculate the theoretical estimated
position of the needle tip, the initial position init was
applied to a 3D Affine transformation using the 6D
couch-entered angle, input
p

. The origin of this rotation
was the position of the iso-center indicated by the second
needle. The 3D Affine transformation for rotation of each
axis is defined as follows:
Rotation around the X axis;
calc
calcinput input
calc init
calcinput input
000 0
0cossin 0
0sincos 0
10001 1
x
x
yy
pp
zz


 
 

 

 
 
 






1
(4)
Rotation around the Y axis;
calc inputinput
calc
calc init
calcinput input
cos0 sin0
0100
sin0 cos0
10001
x
x
yy
pp
zz


 
 
 

 

 
 






1
(5)
Rotation around the Z axis;
calcinput input
calcinput input
calc init
calc
cossin0 0
sincos0 0
0010
10001
x
x
yy
pp
zz



 
 
 

 
 
 






(6)
where, pinit(x, y, z, 1) is an initial position before rotation
and pcalc(xcalc, ycalc, zcalc, 1) is a theoretical calculated posi-
tion that is rotated by the hexapod-entered angle, input

.

A. TAKEMURA ET AL. 73
Distance of 3D error vector of the coordinate error was
also calculated.
3. Results
Mean coordinate errors for the non-weighted and wei-
ghted tests are detailed in Table 1. The coordinate errors
were differences between the measured coordinates and
the theoretical calculated coordinates of the needle tip.
The errors for the non-weighted and the weighted tests
were compared using the paired t-test.
On the translation in Table 1, the 60 kg weights did
not affect the accuracy of the 6D couch motion. All of
the mean coordinate errors for the translation did not
exceed ±0.1 mm, which is the minimum value recog-
nized by the 6D couch system; there was no significant
difference in each coordinate error between the non-
weighted and the weighted tests (p > 0.05).
On the rotation in Table 1, The X coordinate error of
−0.13 ± 0.15 mm for the rotation of the couch with the
weight attached was obtained, and the error was signifi-
cantly different from the X coordinate error for the rota-
tion of the non-weighted couch (p < 0.01). The other
coordinate errors did not exceed ±0.1 mm. However, the
Y coordinate errors for the rotation with or without
weight attached, which were 0.02 ± 0.04 mm and −0.06
± 0.05 mm, respectively, were also significantly different
from each other (p < 0.01).
With regard to the overall results, calculated from both
the translation and rotation measurements, all of the
mean coordinate errors did not exceed ±0.1 mm. How-
ever, the Y coordinate errors between the non-weighted
and weighted couch differed significantly (p < 0.05).
Figure 3 shows the mean distances of the 3D error
vectors for each motion. The translation result included
all results for the TX, TY and TZ, and the rotation result
included the results for the RX, RY and RZ.
The mean distance of the 3D error vector for the couch
rotation with the weight attached was 0.22 ± 0.14 mm
(Figure 3(c)), and this was larger than the distance of
0.19 ± 0.12 mm for the non-weighted couch (p < 0.05).
Considering the overall results, including the results of
Table 1. Mean coordinate errors for the weighted and non-
weighted 6D couch.
X (mm) Y (mm) Z (mm)
Non-weighted 0.04 ± 0.09 −0.03 ± 0.06 −0.01 ± 0.13
Translation
Weighted 0.03 ± 0.08 −0.06 ± 0.16 0.00 ± 0.10
Non-weighted −0.04 ± 0.19** 0.02 ± 0.04** 0.07 ± 0.09
Rotation
Weighted −0.13 ± 0.15** −0.06 ± 0.05** 0.08 ± 0.13
Non-weighted 0.00 ± 0.15 −0.01 ± 0.05* 0.02 ± 0.12
Overall
Weighted −0.04 ± 0.15 −0.06 ± 0.12* 0.04 ± 0.12
Data are presented as the mean ± standard deviation. *p < 0.05; **p < 0.01.
(a)
(b)
(c)
Figure 3. Mean distance of the 3D error vectors. Image (a)
shows the results for each translation, and image (b) for
each rotation. Image (c) shows the total data for translation
and rotation and the overall data. Error bars represent
standard deviation of distances of 3D error vectors.
the translation and the rotation motion, the mean distance
of the 3D error vectors for the weighted couch was 0.21
± 0.11 mm (Figure 3(c)); this was larger than the mean
distance of 0.16 ± 0.09 mm for the non-weighted couch
(p < 0.05). With regard to the other motions, there was
no significant difference between the results for the non-
weighted and the weighted couch.
Error distribution for each translation and rotation mo-
ion was evident as an important 2D plane (Figure 4). t

A. TAKEMURA ET AL.
74
(a) (b)
(c) (d)
(e) (f)
(g) (h) (i)
Figure 4. Distributions of coordinate errors. Images (a) and (b) show the error distribution for the TX in 2D graphs, images
c) and (d) for the TY, images (e) and (f) for the TZ and images (g), (h) and (i) for the RX, RY and RZ, respectively. (

A. TAKEMURA ET AL. 75
The points in the graphs in Figure 4 represent errors of
the movements. For instance, Figure 4(a) shows five
points for each of non-weighted and weighted and these
points represents the error for −20 mm, −10 mm, 10 mm
20 mm and 29 mm translations. The 3D errors were rep-
resented in two 2D graphs. The Y coordinate errors in the
TX and TY for the weighted couch were more widely
spread than for the non-weighted couch, although there
was no significant difference in the mean error of the
translation motion, as shown in Table 1. The error dis-
tributions for the rotation motion, RX, RY and RZ, for
both the non-weighted and weighted couch were un-
evenly spread. Thus, a significant difference between the
non-weighted and weighted couch in terms of the X and
Y coordinate errors for the rotation motion would occur.
4. Discussion
The mean X coordinate error in the rotation and the mean
Y coordinate error in the rotation and the overall error for
the weighted couch significantly differed from those for
the non-weighted couch. However, all differences did not
exceeded 0.1 mm which is the correctable minimum dis-
tance of the 6D couch system.
With regard to the overall results, the mean distance of
the 3D error vectors for the weighted couch was 0.21 ±
0.11 mm, which was larger than the mean distance of the
3D error vectors of 0.16 ± 0.09 mm for the non-weighted
couch. There was a significant difference between these
values. However, the difference was only 0.05 mm. The
difference in the mean 3D distance for the rotation mo-
tion between the non-weighted and the weighted couch
was also low at only 0.03 mm.
Significant differences were observed in the results of
the mean distance of the 3D error vectors with regard to
the rotation and overall and the mean coordinate error
along X and Y axes. All of these differences between the
non-weighted and weighted couch were smaller than the
minimum correctable distance of the 6D couch system.
Thus, a 60 kg weight does not actually affect accuracy of
the 6D couch motion in the clinical situation.
Although the mean error of the Y coordinate in the
translation did not differ significantly, the distribution of
the Y coordinate errors with regard to the weighted
couch seemed to spread more widely than was the case
for the non-weighted couch. The standard deviations of
the Y coordinate errors for the non-weighted and wei-
ghted couches were 0.06 mm and 0.16 mm, respectively.
A significant difference was found between the variances
of these distributions using the F-test (p < 0.01). This
suggested that the uncertainty of motion, especially con-
cerning the Y coordinate, could be increased by the at-
tachment of the 60 kg weight, and that this uncertainty
might possibly be further increased by the use of a heav-
ier weight.
The variance of a coordinate of the needle tip in
three time manual measurements from an image was up
to one pixel (approximately 0.015 mm). It was enough
smaller than the motion errors of the 6D couch.
5. Conclusion
We found that attaching a weight of 60 kg to the 6D
couch only slightly increased the error regarding the ac-
curacy of motion. The amount of increase of the error is
smaller than the minimum correctable distance of the 6D
couch system. Thus, the 6D couch can correct setup error
for a patient with body weight of about 60 kg or lighter.
However, we also found that the distribution of the Y
coordinate errors for the weighted couch was greater than
those for the non-weighted couch. This might suggest
that a weight of more over 60 kg would increase the un-
certainty of motion.
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