Radiation Environment and Medicine 2023 Vol.12, No.2 99–106

Regular Article

Effect of Off-axis Ion Recombination Factor on the Beam Profile
in Flattening Filter-free Photon Beams
Yuki Tanimoto1, 2, Masataka Oita3*, Shohei Yoshida1, Atsuki Nakahira1,
Kazunobu Koshi1 and Hirofumi Honda4
Department of Radiological Technology, National Hospital Organization (NHO) Shikoku Cancer Center,
160 Minamiumemotomachi, Matsuyama, Ehime 791-0280, Japan
2
Graduate School of Interdisciplinary Science and Engineering in Health Systems, Okayama University,
3-1 Tsushimanaka, 3-chome, Kita-ku, Okayama, Okayama 700-8530, Japan
3
Faculty of Interdisciplinary Science and Engineering in Health Systems, Okayama University,
3-1 Tsushimanaka, 3-chome, Kita-ku, Okayama, Okayama 700-8530, Japan
4
Department of Radiological Technology, Ehime University Hosipital, Shitsukawa, Toon, Ehime 791-0204, Japan
1

Received 19 January, 2023; revised 26 May, 2023; accepted 2 June, 2023

The ion recombination factor (ks) of a beam without a flattening filter differs from that of a filteredbeam. In this study, we examined the effect of changing the measurement conditions on ks in theoff-axis direction, and clarified the effect on the beam profile. We calculated ks using the Jaffe
plot and two-voltage method (TVM) by varying the measurement conditions, adding ks,rel, off-ax
to the beam profile, and comparing the changes via local gamma analysis. The central value of
ks increased with X-ray energy, and the effect become more pronounced when the measurement
depth is varied. For the beam profile with high energy and a field size of 40×40 cm2, the resultsof the local gamma analysis are lower than the reference value. At the maximum dose depth, theresults are poor, even when the field size is 30×30 cm2. At 40×40 cm2, the results are lower than
the reference value even when the criteria are further relaxed. Our results indicate that ks differs
depending on the measurement method, and thus, ks,rel,off-ax should be considered when measuring
beam profiles with field sizes larger than 30×30 cm2.
Key words: ion recombination factor, FFF beams, beam profile, off-axis, local gamma analysis

1. Introduction
X-rays generated by a target have an intensity distribution
with a sharp center1, 2). However, in recent years, linear
accelerators that irradiate beams without flattening filters(flattening filter-free beams, FFF beams) have become*Masataka Oita: Faculty of Interdisciplinary Science and Engineering in Health
Systems, Okayama University, 3-1 Tsushimanaka, 3-chome, Kita-ku, Okayama,
Okayama 700-8530, Japan
E-mail: oita-m@cc.okayama-u.ac.jp
https://doi.org/10.51083/radiatenvironmed.12.2_99
Copyright © 2023 by Hirosaki University. All rights reserved.

popular3).
The FFF beam can be irradiated at a higher dose rate
than a beam with a flattening filter beam (WFF beam)4),
and various differences have been reported because ofchanges in the beam quality5, 6). Among them, the dose
per pulse (DPP) increases and the ion collection efficiency
decreases; thus, the ion recombination factor (ks) shows adifferent behavior from that of WFF7, 8).
Kry et al. reported that ks measured with TN30013
changed from 1.005 to 1.008 and from 1.011 to 1.013 at
a depth of 10 cm and dmax at 6 MV and 10 MV FFF,
respectively9). Chang et al. also studied the variation of

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ks in the depth and off-axis directions and stated thatby using CC13, ks varied by 1.2% (1.015 ± 0.002 to 1.002 ±0.001) for 6 MV FFF and by 2.0% (1.023±0.006 to 1.002± 0.001) for 10 MV FFF10). Jonathan et al. reported thatthe off-axis ks changed by up to 1.2% at 10 MV FFF whenmeasured at intervals of 5 cm from the center in an
irradiation field of 40×40 cm2 at a depth of 5 cm using
TN3001311).
The change in ks affects the shape of the beam profile,such as the percentage depth dose (PDD) and off-center
ratio (OCR). Jonathan et al. reported that local gamma
analysis of 40 × 40 cm2 profiles (5 and 10 cm depths)
acquired with 10 MV FFF using A1SL and CC04 with andwithout correction in ks showed a gamma pass rate of 94%( >5% of the points had a gamma index greater than 1)11).
In an FFF beam, t he prof ile shape is convex
and approximates the WFF only near the center 12).
Additionally, the convex shape varies as the irradiation
field size changes; the smaller the field size, the steeper
the convex shape13).
In recent years, multiple off-axis targets have been
irradiated with a single isocenter for metastatic brain
tumors, and the effects of patient position rotation error
and isocenter misalignment on the target dose have been
investigated14, 15). However, the off-axis ks that affects the
OCR should not be ignored16, 17). Changes in the depth
direction of ks in FFF beams have been actively studied;however, studies on changes in the off-axis direction
are limited. As the shape and quality of OCR varydepending on the measurement conditions, such as thesize and depth of the irradiation field, previous studies are
insufficient, and more detailed research is necessary.
This study had three objectives: (1) investigate
the effectiveness of the two-voltage method (TVM)
measurements in the off-axis direction, (2) investigate theeffects of changing the measurement conditions on ks
in the off-axis direction, and (3) investigate the effect ofchanges in the ks value on the shape of the beam profile,and examine whether it should be taken into accountwhen measuring beam data.
2. Materials and methods
We used a Farmer ionization chamber (TN30013,
volume 0.6 cm3, PTW) and a small ionization chamber(Semiflex 3D, volume 0.07 cm3, PTW), listed in Table 1.
We used a RAMTEC Duo (Toyo Medic) electrometer.
The target radiation was 6 MV and 10 MV X-rays(VARIAN TrueBeam STx) measured using FFF andWFF for comparison. A three-dimensional scanning water
phantom, BEAMSCAN (PTW), was used. We stored thewater phantom in the irradiation room at least one day
before measurements to equalize with the temperature,and brought the ionization chamber into the irradiation

room at least 3 h before the measurements.
To stabilize the measured values, we performed 1000
MU of pre-irradiation after applying the voltage. If thecoefficient of variation (CV) exceeded 0.05%, multiple
measurements were performed until the CV stabilized18, 19).
We measured the applied voltage at five points: +100,+150, +200, +250, and +300 V because the American
Association of Physicists in Medicine (AAPM) TG51
addendum recommends +300 V as the upper voltage20).
2.1. Method for calculating the ion recombination factor
W e ca lc ula t ed a nd com pa r ed t he v a l ue of ion
recombination factor ks using the inverse charge (1/Q)
inverse voltage (1/V) (Jaffe-plot), and TVM21-22). ks can becalculated using TVM as follows.
M1

(M )

M1

(M )

ks = a0 + a1 ―― + a2 ―― 2
2

2

(1)

where M1 and M2 are the measured values of the applied
voltages V1 and V2, respectively, and the voltage ratio V1/V2 was set to 3.0 (300 V/100 V). The parameters a0, a1, anda2 represent correction factors: a0 = 1.198, a1 = –0.875, anda2 = 0.677.
2.2. Measurement conditions for ks
The source-to-surface distance (SSD) was maintained
at 100 cm. The ionization chamber (Semiflex 3D) was
placed at a depth of 10 cm and dmax with field sizes of 10
×10, 20×20, 30×30, and 40×40 cm2, respectively. ks forvarious depth and field sizes were measured at the center
axis (CAX) as the reference value for each condition.
The measurement conditions for ks at off-axis points (i.e.,
distances from the CAX) were 2, 4, and 5 cm for the 10
× 10 cm2 field; 0, 4, 8, 9, and 10 cm for the 20×20 cm2
field; 0, 4, 8, 12, 14, and 15 cm for the 30×30 cm2 field;
and 0, 4, 8, 12, 16, 19, and 20 cm for the 40×40 cm2 field.
The measurement of each field edge (the distance fromthe CAX was half of each field size) was excluded at thedepth of dmax because the chamber volume was not fully
contained in the field.
First, we examined the effect of measurement depth on
ks. We measured ks for field sizes of 10×10, 20×20, 30×30, and 40×40 cm2, at depth of 10 cm and dmax, for 6 MV
and 10 MV FFF. Next, to examine the changes due to thetype of detector, we compared the ks values measured
using Semiflex 3D and TN30013 at depths of 10 cm anddmax for field sizes of 10 ×10, 20 ×20, and 30 ×30 cm2 at
10 MV FFF. Further, to examine the difference between
WFF and FFF beams, we measured and compared ks of
WFF and FFF beams at a depth of 10 cm for a field sizeof 30×30 cm2 at 6 MV and 10 MV.
The shape of a beam profile changes with themeasurement direction10). Therefore, we measured onlyYuki Tanimoto et al. / Radiation Environment and Medicine 2023 Vol.12, No.2 99–106

101

Table 1. Speciﬁcations of the ionization chambers
Factors
Nominal volume (cm3)Length of sensitive volume (mm)Radius of sensitive volume (mm)Collection time (μsec)
Nominal response (nC/Gy)

PTW Semiﬂex 3D 31021
0.07
4.8
2.4
118
2.0

PTW Farmer 300
0.6
23.0
3.05
140
0.2

Fig. 1. ks at each measurement point at 6 MV FFF, 10 cm depth, andfield sizes of 10 × 10 , 20 × 20, 30 × 30, and 40 × 40 cm2 (+/– direction
indicates the R/L direction).

Fig. 2. ks at each measurement point at 6 MV FFF, depth dmax, andfield sizes of 10 × 10, 20 × 20, 30 × 30, and 40 × 40 cm2 (+/– direction
indicates the R/L direction).

for field sizes 30×30 and 40×40 cm2 in the In-line direction
at depths of 10 cm and dmax and compared the results withthose in the Cross-line direction. To examine the effect of
the change in the dose rate on ks in the off-axis direction,
we performed measurements with a 6 MV FFF beam
(1400 and 400 MU/min) and 10 MV FFF beam (2400 and
400 MU/min) for a field size of 30×30 cm2.

Additionally, we performed smoothing to remove systemdependent noise in the measurement 23). Next, for theks calculated under the conditions of section 2.2, wecomplemented the intervals between the measured points
using linear interpolation and added them to the beamprofile. We performed a local gamma analysis before
and after the addition to calculate the gamma index todetermine the effect of ks on beam profile. The analysis
was performed using the software tool, BEAMSCAN.
Judgement criteria were 0.5 mm/0.5%, 0.5 mm/1%, 1
mm/1%, and 2 mm/1%, with failure defined as a gamma
pass rate of less than 95%. Points outside the field were
excluded because of uncertainties other than ks.
The beam profiles were measured five times insuccession under identical conditions, gamma analysis
was performed for each measurement, and the averagevalue of gamma pass rate was calculated.

2.3. Calculation of relative ion recombination of f -axis
factors
From the obtained k s obtained under the conditions
described in section 2.2, we calculated the relative ion
recombination off-axis correction factor k s,rel,off-ax forarbitrary points (x, y) at a depth d using Eq. (2). We set(x0, y0) as the beam CAX.
ks,(x, y, d)
ks, rel, of f-ax = ――――――
ks,(x0, y0, d)(2)

2.4. Ef fect on beam profile
Using Semiflex 3D, we measured the beam profile witha measurement interval of 0.5 mm, depths of 10 cm anddmax for field sizes 10×10, 20×20, 30×30, and 40×40 cm2
in the Cross-line direction and 30×30 and 40×40 cm2 in
the In-line direction. We measured the energy with 6 MV
FFF and 10 MV FFF and used CAX for normalization.

3. Results
3.1. Comparison of Jaf fe-plot and TVM
The Jaffe-plot and TVM results agreed within 0.1% withno tendency to overestimate or underestimate the other.
In addition, no trends were observed in any of the fields,
dose rates, measurement directions, or measurement
points.

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Fig. 3. ks at each measurement point at 10 MV FFF, 10 cm depth,
and field sizes of 10 × 10, 20 × 20, 30 × 30, and 40 × 40 cm2 (+/– direction
indicates the R/L direction).

Fig. 4. ks at each measurement point at 10 MV FFF, depth dmax, andfield sizes of 10 × 10, 20 × 20, 30 × 30, and 40 × 40 cm2 (+/–indicates R/L
direction).

Table 2. ks at each measurement point at a depth of 10 cm, 10 MV FFF, dmax, and ﬁeld sizes of 10×10, 20×20, and 30×30 cm2 due to the difference indetectors (+/– indicates the R/L direction.)
Semiﬂex 3D
Depth Field size
(cm)
(cm2)
15
14
12
10
10
10
20
1.007
30
1.005 1.005 1.006 1.007
10
20
dmax
30
1.008 1.009 1.010

9
1.008
1.008
1.009
1.011

8
1.008
1.008
1.010
1.011

5
1.008
1.009
1.010
1.012
1.012

Distance from CAX (cm)
4
2
0
-2
-4
1.009 1.009 1.010 1.009 1.008
1.009 1.009 1.010 1.009 1.009
1.010 1.009 1.010 1.009 1.009
1.011 1.012 1.013 1.012 1.012
1.012 1.013 1.013 1.012 1.011
1.012 1.013 1.014 1.013 1.012

-5
1.007
1.009
1.009
1.011
1.012

-8
1.008
1.008
1.009
1.010

-9
-10
-12
-14
-15
1.008 1.007
1.008 1.008 1.007 1.006 1.006
1.009
1.010 1.010 1.009 1.008-

TN30013
Depth Field size
(cm)
(cm2)
15
14
12
10
10
10
20
1.006
30
1.005 1.005 1.006 1.007
10
20
dmax
30
1.007 1.007 1.008

9
1.006
1.007
1.008
1.009

8
1.006
1.007
1.009
1.009

5
1.007
1.008
1.007
1.011
1.011

4
1.008
1.009
1.008
1.011
1.011
1.011

-5
1.007
1.009
1.008
1.011
1.011

-8
1.007
1.006
1.009
1.010

-9
-10
-12
-14
-15
1.007 1.006
1.006 1.006 1.005 1.005 1.004
1.008
1.008 1.008 1.007 1.007-

3.2. Variation of ks under each measurement condition
By changing the depth from 10 cm to dmax, the ks of the
6 MV FFF changed from 1.006 to 1.008 at the center(approximately 0.2%) and increased from 1.004 to 1.005
at the field edges (approximately 0.1%), as shown in
Figures 1 and 2. The 10 MV FFF showed an increase of
approximately 0.4% from 1.01 to 1.014 at the center, andan increase of approximately 0.2% from 1.004 to 1.006 in
the limbus, as shown in Figures 3 and 4. Both the 6 MV
and 10 MV FFF showed little change when compared at
the same measurement point, even when the field size
was changed. The edge of the field was less affected bychanges in depth and energy and did not change relative
to the central part.

2
1.009
1.009
1.009
1.012
1.012
1.012

0
1.009
1.009
1.009
1.013
1.013
1.013

-2
1.008
1.009
1.009
1.012
10.12
1.012

-4
1.008
1.009
1.008
1.012
1.011
1.011

No trend was observed when TN30013 and Semiflex
3D were compared. TN30013 had a ks value of 1.009 at a
depth of 10 cm, which changed by 0.2% at the field edge
and 0.4% at the center when the depth was changed todmax, as presented in Table 2.
The average value of ks at each measurement pointin the WFF was 1.004 (±0.0004) for the 6 MV WFF and1.004 (±0.0004) for the 10 MV WFF, with little change
between the center and edge of the field.
For the 6 MV FFF, the mean value of all measured
points was 1.006 at the center and 1.004 at 15 cm fromthe center, and 1.005 (±0.0008) overall. For the 10 MV
FFF, the mean value of all measured points was 1.01 at
the center and 1.006 at 15 cm from the center. The mean

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103

Table 3. ks at each measurement point with a depth of 10 cm, 10 MV FFF, dmax, and ﬁeld sizes of 30×30 and 40×40 cm2 according to thedifference in measurement direction (+/– indicates the R/L direction.)
Cross-line
Depth Field size
(cm)
(cm2)
20
19
16
15
30
1.005
10
40
1.004 1.005 1.005 1.005
30
dmax
40
1.006 1.006 1.007

14
1.005
1.006
1.008
1.007

12
1.006
1.006
1.009
1.008

Distance from CAX (cm)
8
4
0
-4
-8
1.008 1.010 1.010 1.009 1.008
1.008 1.009 1.010 1.008 1.007
1.011 1.012 1.014 1.012 1.010
1.009 1.012 1.014 1.012 1.010

-12
1.007
1.007
1.009
1.008

-14
-15
-16
-19
-20
1.006 1.006
1.006 1.006 1.005 1.004 1.004
1.008
1.007 1.007 1.006 1.006-

In-lineDepth Field size
(cm2)
(cm)
20
19
16
15
30
1.005
10
40
1.004 1.004 1.005 1.005
30
dmax
40
1.006 1.007 1.007

14
1.005
1.006
1.007
1.008

12
1.006
1.006
1.008
1.008

Distance from CAX (cm)
8
4
0
-4
-8
1.007 1.009 1.010 1.008 1.007
1.008 1.009 1.010 1.009 1.007
1.009 1.012 1.013 1.011 1.009
1.009 1.011 1.013 1.011 1.009

-12
1.006
1.006
1.008
1.008

-14
-15
-16
-19
-20
1.005 1.005
1.006 1.005 1.005 1.004 1.004
1.007
1.008 1.007 1.007 1.006-

Fig. 6. Local gamma analysis in the Cross-line direction at 10 MV
FFF, depth 10 cm, and field sizes of 10 × 10, 20 × 20, 30 × 30, 40 × 40
cm2.

Fig. 5. ks, rel, off-ax in the Cross-line and In-line directions for 10 MV
FFF, depth dmax, and irradiation field size of 40 × 40 cm2 (+indicates the
R and Gun directions; – indicates the L and Target directions).

value for all measurement points was 1.007 (±0.0018).
Compared with WFF, FFF had a higher value of ks at
the center, and the convex shape is more pronounced at
higher energies. As shown in Table 3, ks varied only 0.1%
at most when the measurement direction changed.
A maximum change of 0.1% was observed in both 6 MV
and 10 MV FFF when the dose rate was changed. As ks
does not depend on the irradiation field size, we observed
the same trend for ks, rel, off-ax. Figure 5 shows the results of
ks, rel, off-ax in the Cross-line and In-line directions at a 10 MV
FFF, depth of dmax, and irradiation field size of 40×40 cm2.

Fig. 7. Local gamma analysis in the Cross-line direction at 10 MV
FFF, depth dmax, and field sizes of 10 × 10, 20 × 20, 30 × 30, and 40 ×
40 cm2.

Fig. 8. Local gamma analysis in the In-line direction at 10 MV FFF,
depth 10 cm, and field sizes of 30 × 30 and 40 × 40 cm2.

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Fig. 9. Local gamma analysis in the In-line direction at 10 MV FFF,
depth dmax, and field sizes of 30 × 30 and 40 × 40 cm2.

3.3. Ef fect on Beam Profile
In the 6 MV FFF, the gamma pass rate was 100% under
all conditions. In the 10 MV FFF, the pass rate was 94.79%
when the depth was 10 cm with 0.5 mm/0.5% and fieldsize 40×40 cm2, as shown in Figure 6. At dmax, the change
was more pronounced than that at a depth of 10 cm(76.91% at 1 mm/0.5 %), as shown in Figure 7. For a fieldsize of 30×30 cm2, the pass rate was 96.84%, as shown in
Figure 7.
The gamma pass rates in the Cross-line direction andIn-line directions were 57.66% and 75.57%, respectively,
at 10 MV FFF, a field of 40×40 cm2, and 1 mm/0.5%. As
shown in Figures 7–9, the gamma pass rate significantly
worsens in the Cross-line direction. The position closest
to the center, where a gamma index of 1.0 or higher wascounted, did not depend on the size of the field; however,dmax appeared closer to the center, as listed in Table 4.
Toward the field edge, the uncorrected and correctedbeam profiles were not aligned.
4. Discussion
The Jaffe-plot and TVM results were reported to bewithin 0.3% by Jonathan et al., which is a larger deviation
than the 0.1% in our study11). They used an applied voltageof –250 V, which resulted in a higher ks than the ks in
our experiments performed at +300 V. In their study,
the upper limit of the applied voltage was 400 V, andthe minimum applied voltage was –50 V, which caused
uncertainties because of the small amount of charge.
We consider that the lack of change in ks in the WFF
beam resulted from a significant change in DPP in the
FFF beam. This means that the DPP changes with depth
and is higher at dmax. However, in the off-axis direction,
the DPP did not change as much at the field edges as it
did at the CAX. When correcting for ks, understanding thechange in the DPP in the off-axis direction is necessaryfor each profile measured at each depth.
ks using TN30013 was 1.009 at a depth of 10 cm and1.013 at dmax in the central region. These values are
consistent with those reported in previous studies9, 10).
The size of the penumbra region varied as themeasurement direction changed, becoming larger in
the In-line direction. The convex slope of the FFF beam
depends on the field size; however, it does not affect ks.
This, together with the lack of change observed in thecomparison of dose rates, confirms the results of previous
studies showing that ks depends on DPP in the off-axis
direction10).
In the analysis of beam profile, the gamma index
worsened as the field size increased. Although the
gamma pass rate was satisfactory ( >95%), we considered
performing the correction by k s necessary whenmeasuring fields larger than 30×30 cm2.
Even with the worst gamma index profile, the gamma
pass rate from 0.5 mm/1% was less than 95%, whichis inconsistent with the results of Jonathan et al. whofound a gamma pass rate of 94% at 40×40 cm2 and 2
mm/1%11). A possible reason for the discrepancy is thatthe measurement interval in Jonathan et al. was longer (2mm) than the 0.5 mm interval in our study, with the datainterpolated between the measurement points, thereby
resulting in uncertainties.
Under the conditions of 40×40 cm2 and 1 mm/0.5%,
the gamma pass rate in the Cross-line direction wasmuch worse than that in the In-line direction. One of thepossible explanations is the different CAX values. Whenmeasuring the Cross-line and In-line directions, the water
phantom is often needed to be repositioned such that theTable 4. Position closest to the center, counting gamma index 1 or more in each measurement direction,
depth, ﬁeld sizes of 30×30 and 40×40 cm2, and 10 MV FFF (Cross-line: +/– indicates the R/L) (In-line: +/–indicates the Gun/Target direction).
Direction
Cross-line

In-line

Depth
(cm)
dmax
10
dmax
dmax
10
dmax

Field size(cm)
30
40
40
30
40
40

Criteria
0.5 mm/0.5%-129.7130.75-169.2
194.9
-96.4
108.9
-128.2129.1-169.8167.2-135.2133.5

1 mm/0.5%-116.5117.9-159.1
146.5

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105

Table 5. Gamma analysis for each measurement direction and depth for a ﬁeld size of 40×40 cm2 and 10 MV FFF whenvarying a subset of analyzed beam proﬁles.
Direction

Depth
(cm)
10

Cross-line
dmax
10
In-linedmax

Subset of profiles
All profile
Outside of 15cm
All profile
Outside of 15cm
All profile
Outside of 15cm
All profile
Outside of 15cm

Criteria
1.0 mm/0.5%
0.5 mm/0.5%
Avg. gamma pass rate ± SD
Avg. gamma pass rate±SD0.440 ± 0.239
0.546 ± 0.301
0.742 ± 0.064
0.930 ± 0.070
0.667 ± 0.370
0.835 ± 0.457
1.131 ± 0.067
1.407 ± 0.043
0.447 ± 0.268
0.556 ± 0.334
0.773 ± 0.058
0.969 ± 0.07
0.561 ± 0.282
0.702 ± 0.349
0.904 ± 0.061
1.127 ± 0.064

short axis of the chamber faces the direction of off-axis
movement. This may have caused a partial volume effect.
Another possibility is that the differences in the profile
shapes owing to differences in the measurement direction
caused variations in the amount of charge. Furthermore,
as presented in Table 5, the gamma index approaches
1.0 beyond 15 cm from CAX. As the beam profile wasnormalized by CAX, the slight change in the ks value
between the center and field edges may have affected the
gamma pass rate at the edges. However, this variationin ks in CAX was considered acceptable because it was
equal to or less than the variation reported in the study
by Chang et al10).
As the value of ks does not change when the irradiation
field size changes, the same values of ks, rel, off-ax wereadded at each point. In addition, the gradient was steeper
in 40×40 cm2 than in 30×30 cm2. Therefore, the position
where the gamma index exceeds 1.0 was considered to
be closer to the center. However, as presented in Table 4,
the position near the center, where one or more gamma
indices were counted, did not depend on the size of the
field, probably because the effect of the profile slope wasminimal.
The gamma index varied significantly between 1
mm/0.5% and 1 mm/1%, with the latter having no effectat all. Venselaar et al. reported that an accuracy of
0.5% reproducibility for deep doses is desirable. Theysuggested that the measurement relative depth-dose
data should be 0.5% 24). As treatment of micro-brain
metastases of less than 1 cm3 was also being performed,
more detailed beam data measurement was needed, andthe setting of this criterion was considered appropriate25).
Additionally, registering the beam data by adding ks, rel, off-ax
to the profile in case of acquisition of the beam data
was considered necessary. The results of this study alsosuggest the need for more detailed data acquisition,although the AAPM Task Group 53 reported that theaccuracy of the inner beam measurement in a square
irradiation field is within 1.5%26).

A limitation of this study is that slight variations in ks
occurred when the measurement direction and irradiation
field size varied. However, we were able to demonstrate
the necessity of adding ks, rel, off-ax when measuring beamprofiles. Further studies should utilize the beam data of 10
MV FFF, where the value of ks is particularly large, andverify the influence of clinical treatment planning cases.
5. Conclusion
This study revealed that TVM can be used to measureks in the off-axis direction. In the FFF beam, ks changed
with the off-axis displacement from the center, and its
rate of change became more pronounced when the depthchanged; however, the other measurement conditions did
not affect the change in ks. We showed that ks,rel,off-ax must
be considered when measuring profiles with a field size of
30×30 cm2 or larger, and that performing measurementswith strict criteria, such as 1 mm/0.5%, is necessary.
Conflict of Interest
The authors have no conflicts of interest.
Author Contribution
Yuki Tanimoto, Masataka Oita, Shohei Yoshida, Atsuki
Nakahira, Kazunobu Koshi, and Hirof umi Honda
designed the study. Yuki Tanimoto, Masataka Oita and
Hirofumi Honda drafted the manuscript. All the authors
reviewed the results and approved the final version of themanuscript.
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