Radiation Measurements 42 (2007) 1538 – 1544
www.elsevier.com/locate/radmeas
Estimation of Argon-41 concentrations in the vicinity of a high-energy
medical accelerator
J.H. Chao a , W.S. Liu b , C.Y. Chen c,∗
a Nuclear Science and Technology Development Center, National Tsing Hua University, 30013 Hinchu, Taiwan, ROC
b Department of Radiation Oncology, Chung Shan Medical University Hospital, Taichung, 40201 Taiwan, ROC
c Department of Medical Imaging and Radiological Sciences, Chung Shan Medical University, Taichung, 40201 Taiwan, ROC
Received 9 October 2006; received in revised form 13 February 2007; accepted 19 June 2007
Abstract
This study presents the estimation of 41Ar concentrations using the neutron activation method. The distribution of thermal neutron flux in
a 15 MV medical accelerator (linac) treatment room was determined and contoured by measuring the radioactivities of indium foils irradiated
by thermal neutrons. The 41Ar concentrations were calculated based on the spatial distribution of thermal neutrons. The evolution of 41Ar
concentration with time in the treatment room was predicted and the corresponding radiation dose associated with 41Ar was derived and shown to
be insignificant for both patients and workers, being below the regulatory level. Indium foil activation method showed high detection sensitivity
for estimating the low-level 41Ar in the vicinity of medical accelerators, yielding a minimum detectable concentration of less than 10 Bq m−3 .
© 2007 Elsevier Ltd. All rights reserved.
Keywords: Argon-41; Indium foils; Thermal neutron flux; Neutron activation; Medical accelerators
1. Introduction
High-energy electron accelerators including the electron
linear accelerator and the betatron are routinely used to produce
high-energy electrons and X rays for cancer therapy. Accelerators operated at above 10 MeV can produce neutrons through
photonuclear reactions in the target, field-flattening filters,
beam-defining collimators and other accelerator components,
resulting in a mixed radiation field in the beam and the treatment room. The calculation of photoneutron yields and the subsequently induced photons in different components of medical
accelerators and barriers has been extensively investigated to
design shielding to protect personnel outside treatment rooms
(Kase et al., 1998; Mao et al., 1996, 1997; McGinley, 1992).
The contribution of neutrons and photons can be estimated for
therapeutic and radiation safety purposes. Neutron fluences and
the corresponding dose can also be measured experimentally
∗ Corresponding author. Tel.: +886 4 24730022x17216;
fax: +886 4 23248186.
E-mail address: [email protected] (C.Y. Chen).
1350-4487/$ - see front matter © 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.radmeas.2007.06.002
and compared to the calculated results (Lin et al., 2001; Paredes
et al., 1999; Palta et al., 1984; Gur et al., 1978; McGinley et al.,
1976; Uwamino et al., 1986). Although the dose of photoneutrons is less than 0.5% of that of photons on the beam central
axis at the depth of dose maximum, and less than 1% in treatment rooms (Paredes et al., 1999), the photoneutrons can also
produce activation of materials in treatment rooms to generate
radioactive substances, which raise a concern about radiation
safety. To date, little attention has been paid to the gaseous radionuclide 41Ar, which can be generated by thermal neutron
activation of stable 40Ar in air, although its contribution to the
radiation dose of both patients and workers may be negligible.
Measurement of 41Ar concentration using a gamma-ray
spectrometer following the collection of an air sample in a
sealed container is convenient but impractical because the 41Ar
concentration is generally lower than the detection limit of the
counting system. In situ monitoring of gaseous radionuclides
using a gamma-ray spectrometric system may be effective for
an air source of infinite space (Chung et al., 1998; Chung and
Tsai, 1996) but is not applicable to a treatment room with an
air volume of specific geometry. Accordingly, almost no data
on 41Ar concentration near a medical accelerator has been
J.H. Chao et al. / Radiation Measurements 42 (2007) 1538 – 1544
reported. In this work, the concentration of 41Ar in a treatment
room equipped with a 15 MV accelerator was determined. Initially, the thermal neutron flux, or thermal neutron fluence rate,
was estimated with the activation method using indium foils.
Therefore, the variation of the concentration of 41Ar with time
and the corresponding dose were calculated for radiation safety
assessment.
2. Materials and methods
2.1. Neutron activation of indium foils
The activation technique has been widely used for measurement of neutron fluxes and the corresponding doses (Knoll,
1989). Fast and thermal neutrons can be discriminated by irradiating appropriate foil materials and measuring the induced
radioactivities (Lin et al., 2001; Paredes et al., 1999; Palta
et al., 1984; Deye and Young, 1977; Price and Holeman, 1978;
Gur et al., 1978; McGinley et al., 1976; Uwamino et al.,
1986). In the measurement of thermal neutrons, indium
foils are commonly used due primarily to indium’s high
cross-section and suitable half life (t1/2 = 54.1 m) (Reus
and Westmeier, 1983). In this study, indium foils were used to
contour the distribution of thermal neutrons around a medical
accelerator. The thermal neutron flux is defined and determined
by measuring the induced radioactivities of indium foils, as
follows:
m×a
A = th × In × NA ×
(1)
× (1 − e−ti ) × e−tc ,
M
where th is the thermal neutron flux (cm−2 s−1 ); In is the
cross-section of the activation reaction (161 barns); NA is the
Avogadro’s number (6.02 × 1023 in atoms per g-atom); m is
the mass of indium foil (g); a the isotopic abundance of 115 In
(95.7%); M is the atomic weight of indium (114.82); is the
disintegration rate of 116m In (2.135 × 10−4 s−1 ); ti is the irradiation time, and tc is the time duration between irradiation
and measurement.
2.2. Neutron irradiation
Twenty indium foils (purity > 99.9%; 25 mm L×25 mm W ×
1 mm H) with an averaged mass of (4.86 ± 0.07) g were used
in the experiment. The foils were placed and distributed evenly
in the vicinity of a medical accelerator (Clinac 21EX, Varian,
Palo Alto, CA) for neutron irradiation. The electron accelerator
provides dual photoenergies with accelerating voltages of 6
and 15 MV. The beam intensity was controlled by changing the
pulse interval. Fig. 1 displays a floor plan of the radiotherapy
facility. The accelerator was operated at 15 MV for 2.5 min,
delivering a dose of 1000 cGy at depth of dose maximum in
a water-equivalent phantom with source-surface distance of
100 cm and the collimator open to a field size of 20 × 20 cm2 .
For batch irradiation, all measured values were normalized
to a reference foil, which was placed at the isocenter (0,0,0),
which is exactly 100 cm below the X-ray target, such that the
relative intensity of the thermal neutron in the treatment room
1539
can be simply described. The thermal neutron flux can be averaged by integrating thermal neutron flux with distance from
the reference point.
2.3. Radioactivity measurement
The irradiated foils were immediately transferred to a
gamma-ray spectrometric system, which consisted of a 30%
high-purity germanium detector (GC3520, Canberra Industries,
Meriden, CT, USA). The measured gamma-ray spectra were
collected with a multichannel analyzer (35-Plus, Canberra
Industries, Meriden, CT, USA) and were further analyzed by
gamma-ray spectrum software. The foils were placed immediately on the face of the detector for counting; the efficiency
was determined to be 4.0% at the characteristic gamma-ray
energy of 417 keV emitted from the activated nuclide 116m1 In.
2.4. Calculation of
41 Ar
concentrations
Argon-41 is produced through the neutron capture reaction
(n, ) 41Ar in air. The argon-40 concentration in air is
derived as
P
NAr (m−3 ) =
(2)
× fAr × NA ,
RT
where P is the atmospheric pressure (1 atm); fAr is the fraction of Ar molecules (1.28%); R is the universal gas constant
(8.2 × 10−5 atm m3 mol−1 K −1 ), and T is the temperature in
the treatment room (295 K). Therefore, NAr was calculated to
be 3.18 × 1023 m−3 .
The accumulation of 41Ar concentration (CAr ) by neutron
irradiation in the treatment room with irradiation time ti is given
by
40Ar
CAr (Bq m−3 ) = F × ¯ th × Ar × NAr × (1 − e−Ar ti ),
(3)
where th is the averaged thermal neutron flux in the room; Ar
is the neutron capture cross-section of argon (0.64 barns); and
Ar is the disintegration rate of 41Ar (1.05 × 10−4 s−1 ) (Reus
and Westmeier, 1983). The neutron capture cross-sections of
In in Eq. (1) and Ar in Eq. (3) were obtained from the published data (Lederer and Shirly, 1977). A correction factor F is
introduced in Eq. (3) to accommodate the neutron energy distribution of the medical accelerator. The F can be estimated by
relating the thermal neutron flux, determined by Eq. (1), to the
41Ar concentration, measured at the same irradiation positions
(as described in detail in the following section).
2.5. Estimation of the
dose
41 Ar
concentration and corresponding
An air-filled Marinelli cylindrical container ( = 25 cm; H =
20 cm) with a volume of 9.2 L was irradiated together with an
indium foil in the treatment room, but placed outside the direct
radiation beam to prevent fast neutron interference, to determine the correction factor F in Eq. (3). Prolonged irradiation
(10 min) was conducted to ensure that the 41Ar concentration
in the container was measurable. After irradiation, the foil and
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J.H. Chao et al. / Radiation Measurements 42 (2007) 1538 – 1544
Earth
concrete
2.2 m
concrete
*
Earth
2.7 m
Y axis
2.2 m
X axis
* isocenter
(0,0,0)
Door with
10 cm polyethylene
1 cm Pb
250 mm Pb
1.0 m
Fig. 1. Sechematic diagram of accelerator (Clinac 21EX) and room layout.
the container were measured offline with the germanium detector, individually. The detection efficiency at the photopeak of
1294 keV for 41Ar measurement in the Marinelli container was
calibrated as 0.2% and a minimum detectable concentration
(MDC) of 2000 Bq m−3 was obtained by counting for 15,000 s.
The count over the counting period must be decay-corrected
by introducing a multiplicative factor Fb (Fb = t/(1 − e−t ))
(ASTM, 1998), which was determined to be 1.988. Accordingly, 41Ar concentrations can be calculated by Eq. (3) once
the thermal neutron flux is determined.
The removal rate of 41Ar in the treatment room was determined by in situ measurement with the germanium detector following irradiation. The detector when facing a volume source
of the 41Ar has high-detection efficiency, but cannot provide an
absolute measurement of 41Ar concentration due to difficulty in
efficiency determination for a specified volume source (Chung
and Tsai, 1996).
According to the ICRP report (ICRP, 1991), the derived air
concentration (DAC) for 41Ar is 1 × 105 Bq m−3 , revealing that
workers will receive the 50 mSv annual dose limit of occupational exposure for radiation worker, if they work 2000 h in a
year in the treatment room. Thus, the radiation dose D for a
worker due to inhalation of 41Ar can be estimated as
D=
t
CAr
×
× 50,
DAC 2000
(4)
where CAr is the 41Ar concentration (Bq m−3 ), and t the working time (hour) in the treatment room per year.
3. Results and discussion
3.1. Thermal neutron flux distribution
The thermal neutron flux (th ) around the medical accelerator in the treatment room was determined by measuring
the radioactivities of the indium foils and then calculated by
Eq. (1). The thermal neutron flux at the linac isocenter, in the
beam field, was determined to be 1.31×104 cm−2 s−1 , which is
approximately the averaged value in the beam field over an area
of 20×20 cm2 . Fig. 2 presents the profile of the thermal neutron
flux along the X-axis, varied from 8×103 to 1.4×104 cm−2 s−1
with higher values in the beam field than outside it. Fig. 3
presents the profile of the thermal neutron flux along the Y-axis
(0, y, 0): the thermal neutron flux slightly declined with distance from the isocenter. It was remarkably shielded to under
2 × 103 cm−2 s−1 in the maze and 5.9 × 103 cm−2 s−1 near the
wall behind the accelerator. The thermal neutron flux between
the gantry head and the ceiling was 20–50% higher than that
at the isocenter because the neutrons were scattered and moderated with the lead shield in the gantry head, as illustrated in
Fig. 4. The maximal value of 2.0 × 104 cm−2 s−1 in the treatment room was measured 1.5 m above the gantry head. The
thermal neutron flux was slightly raised near the ground because the neutrons were moderated by scattering in the concrete material. The thermal neutron flux, ranging from 8 × 103
to 2 ×104 cm−2 s−1 , seemed to be roughly uniform in the treatment room except in the maze (less than 2 × 103 ). Integrating
the thermal neutron flux distribution relative to the reference
J.H. Chao et al. / Radiation Measurements 42 (2007) 1538 – 1544
1541
Thermal neutron flux (cm-2 s-1)
1.4x104
Varian 21Ex
Clinac
1.2x104
100 cm
30 cm
1.0x104
8.0x103
6.0x103
4.0x103
-4
-3
-2
-1
0
1
X- axis (x,0,0) ,m
2
4
3
Fig. 2. Profile of thermal neutron flux along the X-axis.
Thermal neutron flux (cm-2 s-1)
1.4x104
shield
1.2x104
isocenter
1.0x104
8.0x103
wall
6.0x103
z
4.0x103
maze
5.9 m
wall
3m
2.0x103
-7
-6
-5
-4
-3
-2
-1
0
Y axis (0,y,0), m
y
1m
isocenter
1
2
3
4
Fig. 3. Profile of thermal neutron flux along the Y -axis.
position yields an estimate of averaged neutron flux ¯ th in the
room, 1.02 × 104 cm−2 s−1 .
Fig. 5 compares the gamma-ray spectra for the irradiated
indium foils placed inside and outside the beam field. The
photopeak at 336 keV in Fig. 5(a) was from 115m In, and was
associated mainly with high-energy photon interaction through
an 115 In (, ) 115m In reaction (Chao et al., 2001).
3.2. Variation of 41 Ar with time
The 41Ar produced by neutron irradiation in the treatment
room will decrease with time through radioactive decay and
ventilation. The variation of 41Ar , in terms of count rate (cps)
at 1294 keV peak, can be monitored in situ and recorded with
time to determine the removal rate R of 41Ar and the ventilation
rate Rv (or air exchange rate of the room), which are related by
R = Ar + Rv ,
or
1
1
1
=
+ ,
TR
T1/2
Tv
(5)
(6)
where T1/2 =ln 2/Ar , Tv =ln 2/v , and TR =ln 2/R. The decline
of 41Ar was plotted against time after 2.5 min of irradiation, as
illustrated in Fig. 6. A removal half life TR was estimated to
be 48 min and the corresponding ventilation rate Rv was also
determined by Eq. (5) to be 138 m3 h−1 . The evolution of 41Ar
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J.H. Chao et al. / Radiation Measurements 42 (2007) 1538 – 1544
concentration in the treatment room can be predicted in detail
in case the treatment schedule is arranged.
3.3. Radiation dose from
41 Ar
2.0x104
Gantry head
1.6x104
ground
1.2x104
z Gantry head
isocenter
8.0x103
3.4. Other remarks
The MDC of 41Ar depends on the lowest thermal neutron flux
detectable using the indium foils. The detection limit of thermal
100
Count rate (cps)
Thermal neutron flux (cm-2 s-1)
The correction factor F in Eq. (3) was experimentally determined to be 9.4, and used to relate 41Ar concentrations to the
average neutron flux in the treatment room. The activated 41Ar
was assumed to diffuse rapidly and to be uniformly distributed
in the treatment room, regardless of the variation of the thermal neutron flux. Fig. 7 plots the evolution of the 41Ar concentration for a typical treatment schedule with operating voltage
of 15 MV. During therapy, the 41Ar concentration linearly increased to a maximum value at the end of irradiation. Thereafter, it declined exponentially with a removal half life of 48 min
until the next irradiation. As a whole, the 41Ar concentration
calculated by Eq. (3) would not exceed 2.52×103 Bq m−3 . The
averaged 41Ar concentration during working hours was about
1 × 103 Bq m−3 —far lower than the DAC (1 × 105 Bq m−3 ).
If the daily working period of a radiotherapist in the treatment
room is four hours, then a radiation dose of less than 0.3 mSv
per year would be predicted, which is negligible in relation to
the dose limit for occupational exposure. In case of prolonged
treatment, for example during 1-h therapy, the 41Ar concentration can accumulate to 6 × 103 Bq m−3 , which does not exceed
the DAC.
10-1
y
isocenter
ground
10-2
0
4.0x103
-2
-1
0
Z axis (0,0,z), m
1
Fig. 4. Profile of thermal neutron flux along the Z-axis.
50
100
150
Time (min)
200
250
2
Fig. 6. Removal of 41Ar with time by radioactive decay and ventilation.
The 41Ar concentration, represented as the count rate at 1294 keV peak, was
monitored in situ using the germanium detector.
105
(a)
116m1
336(115mIn) 116m1
417(
In)
1097(116m1In) 1294(
In)
104
103
1460(40K)
102
Counts
101
104
100
103
102
101
100
(b)
0
1000
2000
Channel Number
3000
4000
Fig. 5. Gamma-ray spectrum of the irradiated indium foils placed (a) inside and (b) outside the beam field. Both gamma-ray energies (keV) and the respective
radionuclides are indicated.
J.H. Chao et al. / Radiation Measurements 42 (2007) 1538 – 1544
1543
2000
1500
1000
41Ar
Concentration (Bq.m-3)
2500
500
21:00
20:00
19:00
18:00
17:00
16:00
15:00
14:00
13:00
12:00
11:00
10:00
09:00
08:00
0
Time (of clock)
Fig. 7. Evolution of 41Ar concentration for a typical treatment schedule with operating voltage of 15 MV.
neutron flux is estimated to be 100 cm−2 s−1 under the experimental condition in this study (Currie, 1968), corresponding
to a 41Ar concentration of less than 10 Bq m−3 , which is much
lower than that obtained by counting an air sampling container.
The operating energy, the shielding design and the geometry of
the accelerator in treatment rooms can shape the neutron energy spectrum. This problem can be solved by experimentally
determining the correction factor F in Eq. (3). The measurement of low-level 41Ar in the vicinity of medical accelerators
with various neutron energies seems to be more practical if the
indium foil activation technique is conducted.
4. Conclusions
This study proposes a neutron activation approach for estimating 41Ar concentrations in the vicinity of a medical accelerator and predicting the radiation dose received by workers.
Nowadays, the shielding of a medical accelerator can be well
designed based on sophisticated calculations, and the radiation
dose to workers due to neutron/photon leakage from the shielding concrete is negligible. Therefore, 41Ar may be an important
contributor to the radiation dose to workers in the treatment
room, although the predicted dose is much lower than the allowed level. The indium activation technique is more sensitive
than other methods in estimation of low-level 41Ar around a
high-energy accelerator.
Acknowledgements
The authors would like to thank the National Science Council of the Republic of China, Taiwan (Contract no. NSC-952623-7-040-001-NU). Radiotherapists C.C. Lu and S.T. Hsu of
CSMUH are appreciated for their assistance in the operation of
the accelerator.
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