Available via license: CC BY-NC-ND 4.0
Content may be subject to copyright.
NUKLEONIKA 2020;65(2):9598
doi: 10.2478/nuka-2020-0014 ORIGINAL PAPER
Introduction
The evaluation of internal exposure to 222Rn and
220Rn should rely on the equilibrium equivalent
concentration (EEC), rather than their concentra-
tions in the air, because the majority of the dose is
built up by their progenies. The EEC is specifi ed by
the concentrations of 222Rn and 220Rn progenies and
depends on their half-lives, indoor ventilation, and
deposition on the surface of all kinds of objects,
e.g., furniture, fl oor, ceiling, and wall. The half-life
of 220Rn (55.6 s) is relatively very short. Hence, it is
not homogeneously distributed, and its concentra-
tion decreases with increasing distance from the
source. For all these reasons, a direct technique for
the measurement of 222Rn and 220Rn progeny con-
centration is necessary for the correct assessment
of the internal exposure due to these radionuclides.
Recently, direct progeny measurement techniques
for the EEC of 222Rn and 220Rn were developed by
Tokonami et al. [1] and Mishra and Mayya [2]. The
application of the direct measurement technique for
determining their progeny concentrations depends
on the estimation of the effective deposition veloci-
ties of combinations of 222Rn and 220Rn progenies
in the typical indoor environment. Some research-
ers [2, 3] have used the experimental method
to estimate the geometric mean deposition velocity
and applied the data to the actual measurement
in the indoor environment. However, because of
Parameter sensitivity analysis
of the theoretical model
of a CR-39-based direct 222Rn/220Rn progeny
monitor
Jun Hu ,
Masahiro Hosoda,
Shinji Tokonami
J. Hu
Department of Radiation Sciences
Graduate School of Health Sciences
Hirosaki University
66-1 Hon-cho, Hirosaki, Aomori 036-8564, Japan
and Japan Society for the Promotion of Science
Tokyo, Japan
M. Hosoda
Department of Radiation Sciences
Graduate School of Health Sciences
Hirosaki University
66-1 Hon-cho, Hirosaki, Aomori 036-8564, Japan
and Institute of Radiation Emergency Medicine
Hirosaki University
66-1 Honcho, Hirosaki, Aomori 036-8564, Japan
S. Tokonami
Institute of Radiation Emergency Medicine
Hirosaki University
66-1 Hon-cho, Hirosaki, Aomori 036-8564, Japan
E-mail: tokonami@hirosaki-u.ac.jp
Received: 27 November 2019
Accepted: 3 February 2020
Abstract. The deposition-based direct indoor 222Rn and 220Rn progeny measurement techniques are mostly af-
fected by the indoor environmental conditions, such as the ventilation, concentration of condensation nuclei,
and reactions with the structure and its furnishings. In this study, a theoretical model of a direct 222Rn and 220Rn
progeny monitor based on allyl diglycol carbonate (ADC or CR-39) was established to analyse the factors that
infl uence the detection process by using the parameter sensitivity analysis. The aerosol parameters contributed
the highest to the variance, followed by the aerodynamic parameters. With respect to the result of the Spear-
man’s correlation analysis, the aerosol-related and the room-related parameters are positive, whereas the aero-
dynamic parameters – which affect the turbulence of indoor deposition – are negative. It means that both the
attachment process and the deposition process of 222Rn and 220Rn progenies are important to the performance
of the progeny monitor.
Keywords: 222Rn and 220Rn progeny • Parameter sensitivity analysis • Theoretical model
© 2020 J. Hu, M. Hosoda & S. Tokonami. This is an open access article distributed under the Creative
Commons Attribution-NonCommercial-NoDerivatives 3.0 License (CC BY-NC-ND 3.0).
96 J. Hu, M. Hosoda, S. Tokonami
the fl uctuation in environmental factors, the fi eld
measurement limitations often do not allow the
suffi ciently precise estimation of the particle depo-
sition velocities, and as a result, the uncertainty in
dose assessment increases. Therefore, in this study,
a theoretical model based on the measured value of
the environmental parameters has been established
to evaluate the factors that infl uence the direct 222Rn
and 220Rn progeny measurements.
Materials and methods
The direct 222Rn and 220Rn progeny monitor is
made up of a stainless steel plate, allyl diglycol
carbonate (ADC or CR-39) nuclear track detector,
and aluminium-vapourized Mylar film (Fig. 1).
Three thicknesses of the fi lms, viz., 7.10 mgcm–2,
5.05 mgcm–2, and 3.25 mgcm–2, are selected to allow
for the responding alpha energy to be higher than
that emitted by the progeny 212Po, 214Po, and 218Po
to form the tracks on CR-39, respectively. In the
behaviour of 222Rn and 220Rn progenies, the relation-
ship between the attached 222Rn and 220Rn progeny
deposition rate, J (atoms per square centimeter per
second), and the track density, N (tracks per square
centimeter), can be expressed as follows [3]:
(1)
where is the track registration effi ciency, which is
the multiplier of the branching ratio of its progeny
and the geometric effi ciency. For each channel, the
geometric effi ciency depends on the energies of
the incident -particle, the incident angles against
the absorbers, and the thickness of the absorbers.
And t is the exposure period (in seconds).
The effective deposition velocity of the progeny,
V
e (meters per second), is defi ned as follows:
(2)
where C is the atom concentration of the progeny
(atoms per cubic meter).
The effective deposition velocity combines the
contributions from both the unattached and the
attached fractions of each progeny species. By
considering the contributions of the two fractions,
the deposition velocity of each radionuclide can be
written as follows:
(3)
where pi denotes the unattached fraction of radio-
nuclide i; Vd
u and Vd
a are the deposition velocities
of the radioactive particles that belong to the unat-
tached and attached fractions, respectively, and are
dependent on the aerodynamic factors.
In the theoretical model, the particle deposition
velocity is one of the most important parameters in
the calculation process. Lai and Nazaroff’s three-
-layer model [4] is a commonly used method to
simulate particle deposition. The deposition velocity
for the attached fraction can be written as follows:
(4)
(5)
(6)
where
I
n the above formulas, the terms vd,u, v
d,d, and
vd,v are the deposition velocities of the upward hori-
zontal surface, downward horizontal surface, and
vertical surface, respectively; Sc =v/D, where v is
the kinematic viscosity of air; and D is the Brown-
ian diffusivity of the particle. Moreover, dp is the
particle diameter; u* is the friction velocity; and vS is
the gravitational settling velocity of the particle
.
After resolving the deposition velocity of the
radionuclides, the mass balance-based Jacobi room
model [5] is adopted to deduce the concentrations of
222Rn and 220Rn progenies and estimate the EEC. In
order to establish the Jacobi room model, the com-
position of the deposited progeny atoms should be
known. The deposited progeny atoms 212Bi and 212Pb
decay ultimately to 212Po and form tracks on CR-39.
Accordingly, 218Po, 214Bi, and 214Pb are deposited on
the surface of the monitor and decay to 214Po, form-
ing tracks on CR-39.
Since this progeny monitor is very sensitive to
environmental conditions, in this study, we use the
Monte Carlo sampling method to analyse the contri-
bution of the typical parameters to the EEC of each
Fig. 1. The schematic diagram of the CR-39-based direct
222Rn/220Rn progeny monitor.
N
Jt
e
J
VC
1
ua
iid id
VpV pV
*
,
*
1exp
du
S
u
vvI
u
*
,
*
exp 1
dd
S
u
vvI
u
.
*
dv
u
vI
2/3
3.64 39IScab
*/(2 )
p
rdu v
3
1/ 1/
1
1
211/
10.92 4.3 8.6 10.92
3tan
0.0609 3 10.92
ss
s
Sc Sc
aIn Sc Sc
3
1/3 1/3
1
1
2143 1/3
10.92 4.3 2 10.92
3tan
7.669 10 ( ) 3 10.92
Sc rSc
bIn
Sc r Sc
97Parameter sensitivity analysis of the theoretical model of a CR-39-based direct...
detecting channel and, moreover, analyse the factors
that infl uence the performance of the monitor.
Results
In this theoretical model, we set the aerosol particle
parameters, aerodynamic parameters, and room-
-related parameter as the main parameters to carry
out the parameter sensitivity analysis based on the
behaviour of the indoor 222Rn and 220Rn progenies.
The aerosol particle parameters include the activ-
ity median aerodynamic diameter (AMAD) for
the attachment fraction, the activity median ther-
modynamic diameter (AMTD) for the unattached
fraction, and the concentration of the condensation
nuclei, which indicates the aerosol distribution
and concentration in the indoor environment. The
aerodynamic parameters for sensitivity analysis
selected in this study are the friction velocity and
the ventilation rate. Both of the aerosol parameters
and the aerodynamic parameters are the main pa-
rameters used to estimate the deposition velocity of
the progeny radionuclide on the plate surface. The
room-related parameter in the theoretical model is
the correction coeffi cient of the surface area, which
decides the ratio of the progeny radionuclide de-
posed on the limited area of the surface of the plate
detector. Subsequently, the parameter sensitivity
analysis based on the Monte Carlo method was
implemented to analyse the contribution of the pa-
rameters to the values of the equilibrium equivalent
radon concentration (EERC) and the equilibrium
equivalent thoron concentration (EETC) for each
detecting channel. We set the uniform distribu-
tion to the range of 1–10 tracksmm–2 for the equal
contribution of each progeny radionuclide. Then,
100 000 samples from the uniform distributions of
the range (Table 1) for each parameter were ran-
domly extracted to run the theoretical model. Subse-
quently, the Spearman’s correlation coeffi cients and
their contribution to the variance were calculated
as shown in Fig. 2.
As a result, the friction velocity and ventilation
rate for all the channels were negative correlated
with the EEC. The other parameters had positive
correlations. With respect to the contribution to
variance, the aerosol particle parameters had the
highest contribution, followed by the aerodynamic
parameters and room-related parameter. According
to the separate parameters for each channel, six
parameters had the same ratio of contribution to
each channel. The concentration of the condensa-
tion nuclei had the highest contribution, with an
average around 21.21%, followed by the friction
velocity, which was around 20.79%. The other two
parameters of the aerosol particle, viz., the AMAD
for the attached and AMTD for the unattached frac-
tions, also contributed relatively greatly to the vari-
ance, which were 18.37% and 17.42%, respectively.
Conclusions
In this research, a theoretical model was applied
to simulate the mechanism of deposition based on
222Rn and 220Rn progeny measurements. Sensitivity
analysis of the parameters was carried out to analyse
the factors that infl uence the monitor. Since the
attachment process is a function of particle
size and the deposition velocity is mostly dependent
on the aerodynamic condition, according to the re-
sults of the sensitivity analysis, it is indicated that
both the deposition and the attachment processes
are important to the performance of the direct 222Rn
and 220Rn progeny measurement technique. In the
Table 1. The parameters of the sensitivity analysis
Variable Unit Minimum value Maximum value
Correction coeffi cient of surface area – 1 4
Ventilation rate (v)h–1 0.1 4
Friction velocity (u*) cms–1 110
AMAD for attachment fraction (dp)m 0.04 0.8
AMTD for unattached fraction (dp)m 0.001 0.01
Concentration of condensation nuclei (Cn)m–3 1.2 × 1091.2 × 1011
Fig. 2. The results of parameter sensitivity analysis.
98 J. Hu, M. Hosoda, S. Tokonami
actual measurement, it is recommended to use the
in-site measurement data of the aerosol parameters
to calibrate the monitor.
Acknowledgments. This work was supported by the
Japan Society for the Promotion of Science (JSPS)
KAKENHI vide grant numbers JP19J14291 and partial-
ly supported by grants JP16K15368 and JP16H02667.
ORCID
J. Hu http://orcid.org/0000-0002-9974-6958
References
1. Tokonami, S., Sun, Q., Yonehara, H., & Yamada, Y.
(2002). A simple measurement technique of equilib-
rium equivalent thoron concentration with a CR-39
detector. Jpn. J. Health Phys., 37(1), 59–63. DOI:
10.5453/jhps.37.59.
2. Mishra, R., & Mayya, Y. S. (2008). Study of a depo-
sition-based direct thoron progeny sensor (DTPS)
technique for estimating equilibrium equivalent
thoron concentration (EETC) in indoor environment.
Radiat. Meas., 43(8), 1408–1416. DOI: 10.1016/j.
radmeas.2008.03.002.
3. Zhuo, W., & Iida, T. (2000). Estimation of thoron
progeny concentration in dwellings with their deposi-
tion rate measurements. Jpn. J. Health Phys., 35(3),
365–370. DOI: 10.5453/jhps.35.365.
4. Lai, C. K., & Nazarff, W. (2000). Modeling indoor
particle deposition from turbulent fl ow onto smooth
surfaces. J. Aerosol Sci., 31(4), 463–476. DOI:
10.1016/S0021-8502(99)00536-4.
5. Jacobi, W. (1972). Activity and potential -energy
of 222Rn and 220Rn-daughters in different air at-
mospheres. Health Phys., 22(5), 441–450. DOI:
10.1097/00004032-197205000-00002.
