# Extensive study of radiation dose on human body at aviation altitude through
Monte Carlo simulation

Abhijit Roy  Ritabrata Sarkar<EMAIL_ADDRESS><EMAIL_ADDRESS>Choonsik Lee  Indian Centre for Space Physics, 43 Chalantika, Garia Station
Rd., Kolkata 700084, W.B., India  Division of Cancer Epidemiology and
Genetics, National Cancer Institute, National Institutes of Health, Bethesda,
MD 20852, USA

###### Abstract

The diverse near-Earth radiation environment due to cosmic rays and solar
radiation has direct impact on human civilization. In the present and upcoming
era of increasing air transfer, it is important to have precise idea of
radiation dose effects on human body during air travel. Here, we calculate the
radiation dose on the human body at the aviation altitude, also considering
the shielding effect of the aircraft structure, using Monte Carlo simulation
technique based on Geant4 toolkit. We consider proper 3D mathematical model of
the atmosphere and geomagnetic field, updated profile of the incoming particle
flux due to cosmic rays and appropriate physics processes. We use quasi-
realistic computational phantoms to replicate the human body (male/female) for
the effective dose calculation and develop a simplified mathematical model of
the aircraft (taking Boeing 777–200LR as reference) for the shielding study.
We simulate the radiation environment at the flying altitude (considering
geomagnetic latitude in the range of 45-50∘), as well as at various locations
inside the fuselage of the aircraft. Then, we calculate the dose rates in the
different organs for both male and female phantoms, based on latest
recommendations of International Commission on Radio logical Protection. This
calculation shows that the sex-averaged effective dose rate in human phantom
is 5.46 $\mu$Sv/h, whereas, if we calculate weighted sum of equivalent dose
contributions separately in female and male body: total weighted sum of
equivalent dose rate received by the female phantom is 5.72 $\mu$Sv/h and that
by the male phantom is 5.20 $\mu$Sv/h. From the simulation, we also calculate
the numerous cosmogenic radionuclides produced inside the phantoms through
activation or spallation processes which may induce long-term biological
effects.

###### keywords:

Radiation dose , Galactic Cosmic Ray , Atmospheric radiation , Radiation dose
at aviation altitude

††journal: Journal of LaTeX Templates

##  1 Introduction

Two major inputs controlling the near Earth space radiation environment are
Galactic Cosmic Radiation (GCR) and Solar Particle Events (SPEs). The
particles and radiation have a wide energy range spanning from few MeV to
above $10^{12}$ GeV with decreasing flux as the energy increases. The nature
and origin of these particles depend on their energy. The low energy radiation
observed below about 100 MeV are mainly from solar origin. However, during the
SPEs [Reames, 1999] the energy of the solar particles or radiation due to
coronal mass ejection or solar flares, can extend up to several GeVs and the
flux can last from an hour to days [Gopalswamy et al., 2006]. On the other
hand, GCRs of Galactic or extra-galactic origin, while propagating through the
heliosphere, interact with the electromagnetic field carried by the solar
energetic particles, which modifies the intensity of low energy GCR particles
up to the energy of several GeVs [Gaisser, 1990]. The heliospheric space-
radiation environment is highly dynamic and strongly correlated with solar
activities.

The intensity of space radiation near Earth depends on the strength and
spatial distribution of Earth’s magnetic field [Störmer, 1955]. The charged
particle (spectral and spatial) distribution is modified by the geomagnetic
field surrounding the Earth which also depends on the solar activity. There is
a strong dependence of the rigidity cut-off of the primary GCR and SPE
particles on the geomagnetic latitude and solar activity [Bazilevskaya &
Svirzhevskaya, 1998, Sarkar et al., 2017]. After entering the Earth’s
atmosphere, the radiation and particles interact with the atmospheric
molecules, producing a large number of secondary particles in cascade, which
is known as extensive air shower. Due to the balance between the production
rate of the secondary particles and their absorption in the atmosphere, the
particle flux has a maximum at around 15-20 km altitude (also depends on the
geomagnetic latitude), which is called the Regener-Pfotzer maximum [Regener &
Pfotzer, 1934]. The particle flux starts to decrease below this region.

The radiation environment in the atmosphere due to the primary Cosmic Ray (CR)
particles can produce serious biological hazard to high altitude travelers and
also can disrupt the microelectronics components in the aircraft. The
radiation intensity and hence the induced potential hazard generally increases
with altitude and geomagnetic latitude. The CR particles and radiation have
enough energy to give a serious amount of radiation dose on human body which
may lead to fatal cancer, eye cataracts, cardiovascular diseases, malfunctions
of the central nervous system etc. From the study of Bennett et al. [2013] on
Air Canada pilots shows that, most of them received annual dose about 3 mSv
even a few of them received approx 5 mSv, which is higher than the
International Commission on Radiological Protection (ICRP) recommended 1 mSv
per year limit for public radiation exposure. Due to this high exposure from
CR on flight crews, disorder in the reproductive system and high risk of
miscarriage among female flight attendants was also observed [Grajewski et
al., 2015, Lauria et al., 2006, Aspholm et al., 1999]. For these reasons
pilots and flight crews are considered as radiation workers by ICRP [ICRP,
2007]. Continuous exposure to this kind of radiation can also produce various
radioactive isotopes in our body [Brodzinski et al., 1969], where these could
cumulatively give radiation dose depending upon their half lives.

There are different protection and operational quantities used in radiation
dosimetry like: equivalent dose (HT) (in different organ type T), effective
dose (E) and ambient dose equivalent (H∗(10)). The definition of these
quantities can be found in ICRP publication 103 [ICRP, 2007]. As the
protection quantities like E, HT cannot be measured directly in the human
body, so the operational quantity (H∗(10)) is used for measurements, from
which the protection quantities can be derived using suitable conversion
coefficient. However, in many cases ambient dose equivalent cannot properly
estimate the effective dose [Ferrari et al., 1997, Sato et al., 1999].

There are different computer programs based on Monte Carlo calculation or
empirical models to calculate radiation dose at flight altitude [Bottollier-
Depois et al., 2012]. But there are significant number of uncertainties
associated with these kind of calculations which is summarized in ICRU [2010]
and EURADOS report [Lindborg et al., 2004a]. Also, there are a limited number
of studies that consider the effect of aircraft structure for dose calculation
[Battistoni et al., 2005, Ferrari et al., 2004, Dyer et al., 2003, Dyer & Lei,
2001]. These calculations also have several limitations associated with them
like, considering the isotropic distribution for fluence to dose calculation
and fixed vertical cut-off rigidity instead of direction dependence of cut-off
rigidity.

There is no experimental or calculated radiation dose data at individual
organs of flight crews and a few study on the shielding effect of aircraft
structure. These studies can be important for planning the radiological
protection. In this concern, we develop a computer simulation program based on
Geant4 [Agostinelli et al., 2003] Monte Carlo simulation toolkit to calculate
the absorbed dose rate, equivalent dose rate in individual organs, organ
weighted sum of equivalent dose rate for both male and female body as well as
the sex-average effective dose rate at aviation altitude radiation
environment. The change in particle fluxes inside the aircraft due to the
shielding effects of the aircraft structure also have been studied here
considering full-scale aircraft model.

In the following Sec. 2, we describe the simulation method for the calculation
of radiation dose at the aviation altitude. We present and discuss the
simulation results in Sec. 3. And finally conclude in Sec. 4.

##  2 Simulation Method for Dose Calculation

The overall simulation of radiation dose at flight altitude comprises a series
of calculations. First, we calculated the radiation environment at the
relevant altitude for which we need to consider proper models for the Earth’s
atmosphere, geomagnetic field and distribution of the primary GCR. To simulate
the radiation environment inside the aircraft, we need to consider a proper
structure of the aircraft. Similarly, to calculate the radiation dose in human
body, proper computational description of the human phantom is required. We
also need to consider the underlying physics processes properly to define the
radiation interactions with matter.

###  2.1 Simulation of secondary radiation environment in atmosphere

The secondary CR radiation environment at the Earth’s atmosphere is formed due
to the interaction of primary GCR with Earth’s atmosphere. Here, in this work
we did not consider the sporadic effects due to the high energy particles from
SPE. A detailed description of the simulation procedure for primary GCR
interaction with the Earth’s atmosphere to produce secondary radiation and
particle fluxes can be found in Sarkar et al. [2020]. For this simulation
purpose, we considered full 3D atmospheric and magnetospheric models and with
updated Local Interstellar Spectrum (LIS) [Herbst et al., 2017] for the
primary GCR. We used NRLMSIS-00 [Picone et al., 2002] atmospheric model to
define the Earth’s atmosphere up to 100 km altitude from the surface
subdivided into 100 concentric shells with thickness equal in logarithmic
scale. The Earth’s magnetosphere was defined using: (i) 12th generation IGRF
model [Thébault et al., 2015] for the inner magnetic field distribution and
(ii) Tsyganenko Model [Tsyganenko & Andreeva, 2016] for the external magnetic
field distribution, with proper input parameters.

A proper description of primary GCR LIS is very important in order to simulate
the shower of secondary particles in the Earth’s atmosphere. At the end of
2012, for the first time in situ measurement of unmodulated primary GCR was
possible by Voyager1 [Stone et al., 2013] after crossing the heliopause.
Complimenting the PAMELA [Adriani et al., 2013] and AMS-02 [Aguilar et al.,
2015] measurements with the Voyager1 measurement, a new model of very LIS,
before modulation by the heliospheric electromagnetic field, was proposed by
Vos & Potgieter [2015]. This LIS model was used to derive the differential GCR
flux at 1 AU by Herbst et al. [2017] based on forced-field approximation
[Caballero-Lopez & Moraal, 2004, Moraal, 2013]. We considered this model to
describe the GCR flux at the top of the atmosphere with an arbitrary value for
the solar modulation potential $\phi$ = 524 MV, (which corresponds to a solar
transitional phase from maximum to nearing a minimal activity).

The rigidity cut-off for the CR charged particles imposed by the geomagnetic
field distribution is an important factor for the calculation of secondary
radiation environment in the atmosphere. While, most of the other similar
program consider the vertical rigidity cut-off for the distribution of the
primary GCR at different locations, we considered the back-tracing method to
select the allowed tracks into the atmosphere from the isotropic distribution
of particles at the top of the atmosphere [Sarkar et al., 2020]. This method
takes care of the directional dependence and penumbra region of the rigidity
cut-off. However, for an example, Fig. 1 exhibits the positional distribution
of vertical rigidity cut-off at 10 km altitude. Due to high rigidity cut-off
at the geomagnetic equator, only the charged particles with enough rigidity
can penetrate the Earth’s magnetic field and interact with the atmospheric
nuclei, while the neutral particles are unaffected.

Figure 1: Distribution of vertical rigidity cut-off at 10 km altitude over the
total geographic region.

Using the geomagnetic field model and back-tracing method, the position
dependent geomagnetic modulation was inherently achieved in the simulation as
can be seen from Fig. 2. This plot shows primary GCR spectra (for protons and
alpha particles) at an altitude of 400 km, averaged over two different
geomagnetic latitude ranges 0-63.03∘ and 0-80.21∘, along with the very LIS at
122 AU and modified LIS at 1 AU (modulated by the electromagnetic field
carried by the solar wind). We recorded all the relevant information like:
position, momentum, energy, type (pdg number) etc. of the generated secondary
particles and radiation in this step of the simulation to be used afterward.

(a) Proton

(b) Alpha

Figure 2: Very LIS of primary GCR in interstellar medium (red); modulated
primary GCR in heliosphere at 1 AU (green); modulated primary GCR by
magnetosphere at 400 km in two different geomagnetic latitude range (blue,
cyan).

###  2.2 Human phantom and aircraft model

In the next stage of the calculation, we simulated the interaction of
secondary radiations produced in the atmosphere (along with the primaries
survived the geomagnetic cut-off) in the human body and with the aircraft to
see the structural effects on radiation dose.

The simulation of radiation dose received by human organs has been done
considering UF/NCI hybrid phantom models (PHANTOMS library), jointly developed
by the University of Florida and National Cancer Institute. These
computational models contain more than 100 organs or tissues. More details
about PHANTOMS and their compositions can be found in Lee et al. [2009],
Griffin et al. [2019] and references therein. We can calculate the energy
depositions separately in each of the organs and subsequently get the overall
effective dose in human body.

To find out the variation of radiation fluxes inside the aircraft structure,
we developed a simplified mass model of the aircraft structure in Geant4
simulation framework, based on Boeing 777–200LR [Boeing Co., 2020] aircraft
model. We sampled the radiation effects at different positions inside the
aircraft by placing dummy volumes (three spheres of 2 m diameter at the front,
middle and back sections of the fuselage). A representative picture of the
aircraft model along with the dummy spheres can be seen in Fig. 3. A
simplified description of the jet fuel, window glass, cockpit instrumentation
has been considered. For the aircraft structure construction, we mainly used 5
mm thick aluminum (1.35 g/cm2) and the composition and density of other
different materials (jet fuel, window glass, cockpit instrumentation) were
taken from Ferrari et al. [2004]. The full tanks of fuel (145,000 kg) were
placed inside the wings and lower half of the fuselage confined along only in
the region where the wings are connected to the fuselage. An additional
aluminum plate of 5 mm thickness comprised the floor of the passenger cabin,
thus rendering a total equivalent thickness of 2.7 g/cm2 for the upward going
particles.

Figure 3: Mass model structure of the aircraft used in the simulation with
three sampling dummy spheres placed at different sections inside the fuselage.

###  2.3 Physics list considered in the simulation

It is important to consider the right set of physics processes to describe the
radiation interactions with the atmosphere, aircraft structure and human
phantom. For this simulation, we considered QGSP_BIC_AllHP physics list
[Geant4, 2020] with updated TALYS-based Evaluated Nuclear Data Library
(TENDL), which is appropriate for hadronic interaction and isotope
productions. To handle electromagnetic interactions, electromagnetic_options3
physics list was used, which is suitable for space and medical purposes.

###  2.4 Simulation of radiation interaction in human phantom and aircraft
structure

From the knowledge of radiation environment at the flight altitude, we
simulated the radiation interactions in the human phantoms and the aircraft
structure. First, to calculate the radiation effect in human body we
irradiated the phantoms with different secondary GCR particles from upper and
lower hemispheres of 2 m radius (without considering the aircraft structure)
for both upward and downward going particles and calculated the corresponding
deposited doses. We used the standing posture of the phantoms for irradiation,
since there is no significant difference in radiation doses observed in the
sitting and standing postures [Alves et al., 2016].

To find out the variation of radiation inside the aircraft due to shielding
effects of aircraft structure, we irradiated the aircraft from two hemispheres
with 35 m radius along with three dummy spheres inside the fuselage at
different locations shown in Fig. 3 and recorded the information of each event
inside those spheres.

For the purpose of radiation dose calculation in human body, we irradiated
both male and female phantoms by 106 number of each different types of
particles; while for the simulation of radiation interactions in the aircraft,
we considered 107 particles from both upper and lower hemispheres. For both
simulations, we considered the particles with kinetic energy distribution in
the range of 10 keV to 800 GeV for downward going particles, while for upward
going particles the energy range is 10 keV to 10 GeV. This choice of energy
ranges can be justified by the simulated outcome of the secondary particle
fluxes in the atmosphere discussed later in Sec. 3.1.

##  3 Results and Discussions

###  3.1 Radiation at flight altitude

The primary GCR LIS is modified in the heliosphere, by the electromagnetic
field carried by the solar wind. At Earth’s vicinity, this modified GCR is
further modulated by the Earth’s magnetic field, while propagating towards
Earth through the magnetosphere. The primary particles with modified flux then
interact with the atmospheric nuclei to produce secondary particles and
radiation which in turn interact with the aircraft structure. The flux
distribution of all the different particles generated from the simulation at
the flight altitude (which we considered here at 10 km from the Earth’s
surface) is shown in Fig. 4. Though, due to the lack of direct experimental
measurements of the distribution of radiation flux components at aviation
altitude, it is not possible to directly verify the results shown in this
figure. Nevertheless, we compared the simulation results at satellite altitude
with AMS observation of proton flux and at balloon altitude with the
atmospheric radiation measurement by ICSP balloon borne experiment [Sarkar et
al., 2020]. Ferrari et al. [2005] mentioned the anisotropy in the distribution
of high energy radiation flux components for downward and upward particles at
aviation altitude, while low energy neutrons and photons $<$ 10 MeV are more
isotropically distributed. This fact is also evident from Fig. 4 and also can
be seen at balloon altitude as shown in Sarkar et al. [2020].

For the current purpose, we consider the fluxes of proton, neutron, $\gamma$,
$e^{-}$, $e^{+}$, $\mu^{-}$, $\mu^{+}$, $\pi^{-}$ and $\pi^{+}$ generated from
primary GCR interactions with atmosphere. In this simulation, we do not
consider the weakly interacting (e.g. neutrinos) and low abundant ($K^{-}$,
$K^{+}$, $\overline{p}$, $\overline{n}$ and others) particles, we also neglect
$\pi^{-}$, $\pi^{+}$ for upward and $\pi^{o}$ for both directions due to their
low flux. The atmospheric radiation calculations were done at 10 km altitude
(which is the typical cruise altitude of commercial aircraft, e.g., FL328) and
in $\sim$45∘–50∘ geomagnetic-latitude ($\theta_{M}$) region, since most
frequent flight paths pass through this region [ICAO, 2016].

(a) Downward

(b) Upward

Figure 4: Different secondary CR particle fluxes at 10 km altitude in the
geomagnetic latitude range of $\sim$45∘–50∘ for both downward and upward going
particles with respect to local zenith.

The dose calculation at other regions and altitudes can be done in the same
way and will be considered in future. However, the latitudinal and
longitudinal distribution of all the simulated atmospheric particles at 10 km
altitude can be seen from Fig. 5 over the whole geographic region.

Figure 5: Positional distribution of all the simulated particles and radiation
in the atmosphere at 10 km altitude over the whole geographic region.

###  3.2 Dose calculation in human body

Here in this study, we are to calculate the effective dose ($E$), equivalent
dose ($H_{T}$) and absorbed dose ($D_{R,T}$) rates in human body from
radiation interactions at aviation altitude, where $T$ refers to particular
organ or tissue type and $R$ refers to type of radiation. The effective dose
is calculated according to the equation:

$E=\sum_{T}w_{T}H_{T}=\sum_{T}w_{T}\sum_{R}w_{R}D_{R,T},$ (1)

where $w_{T}$ is the weighting factor for organ $T$ ($\sum_{T}w_{T}=1$),
$w_{R}$ is radiation weighting factor and $D_{R,T}$ is absorbed dose averaged
over the organ $T$ for particular radiation type $R$. The absorbed dose
$D_{R,T}$ is the energy deposited per unit mass.

The ICRP first introduced the set of $w_{R}$ values in ICRP [1991], which was
updated by a new value for proton and introducing more accurate energy
dependent continuous function of $w_{R}$ instead of a step function for the
neutrons in ICRP [2007]. But the consideration of constant $w_{R}$ values for
proton and other CR ions may not be correct at higher altitudes where the
energy and flux of these particles are higher [Banjac et al., 2019].

We calculated the total effective dose, as well as the individual
contributions from different omnidirectional radiation and particles of
atmospheric CRs mentioned in Sec. 3.1. The individual contributions from
different radiation components to the weighted sum of equivalent dose rate is
plotted in Fig. 6 for both male and female phantom along with their relative
contributions to the total weighted sum of equivalent dose rate. The same
values of weighted sum of equivalent dose rates along with their relative
contributions are tabulated in Table 1, separated for downward and upward
components of incident radiations. This calculation shows that most of the
weighted sum of equivalent dose received by the phantom is due to the downward
going particles (more than $\sim$95%), where maximum contribution comes from
neutrons followed by proton, $\gamma$, $e^{\pm}$, $\mu^{\pm}$ and $\pi^{\pm}$.

ICRP [2007] defined the sex-averaged effective dose for reference person as:

$E_{ref}=\sum_{T}w_{T}\left(\frac{H^{M}_{T}+H^{F}_{T}}{2}\right),$ (2)

$H^{M}_{T}$ and $H^{F}_{T}$ being the equivalent dose in different organs of
male and female body respectively. Since, the $w_{T}$ factor for both male and
female body in similar organs are considered same, Eqn. 2 can be rewritten as:

$E_{ref}=\frac{\sum_{T}w_{T}H^{M}_{T}+\sum_{T}w_{T}H^{F}_{T}}{2},$ (3)

which is the average of weighted sum of equivalent dose of reference male and
female. So, for the sake of comparison, we first calculated the total weighted
sum of equivalent dose rates in reference female and male phantoms and then
took the average to calculate the sex-averaged total effective dose rate.

(a) Male

(b) Female

Figure 6: Weighted sum of equivalent dose rates and their relative contributions in male and female phantoms due to different incident secondary CR particles and radiation. Table 1: Weighted sum of equivalent dose rates [and their relative contributions] for different incident particles and generated secondary particles in human (male/female) phantom for both downward and upward going particles. Particles |  Male ($\mu Sv/h$) [%] |  Female ($\mu Sv/h$) [%]
---|---|---
|  Down |  Up |  Down |  Up
$n$ |  1.841 [35.35] |  0.180 [3.46] |  2.246 [39.26] |  0.163 [2.85]
$p$ |  1.434 [27.53] |  0.008 [0.15] |  1.446 [25.27] |  0.009 [0.15]
$\gamma$ |  0.693 [13.32] |  0.025 [0.48] |  0.819 [14.32] |  0.024 [0.42]
$e^{-}$ |  0.377 [07.23] |  0.004 [0.09] |  0.363 [06.35] |  0.004 [0.08]
$e^{+}$ |  0.280 [05.37] |  0.003 [0.07] |  0.274 [04.80] |  0.003 [0.06]
$\mu^{-}$ |  0.159 [03.06] |  0.002 [0.05] |  0.166 [02.90] |  0.003 [0.05]
$\mu^{+}$ |  0.185 [03.56] |  0.002 [0.04] |  0.184 [03.23] |  0.003 [0.05]
$\pi^{-}$ |  0.003 [00.07] |  0.000 [0.00] |  0.004 [00.06] |  0.000 [0.00]
$\pi^{+}$ |  0.004 [00.08] |  0.000 [0.00] |  0.005 [00.08] |  0.000 [0.00]

Spatial distribution (frontal and side-wise view) of absorbed dose rate and
equivalent dose rate inside both male and female phantoms are plotted in Fig.
7 and 8. The contributions to absorbed dose rates and equivalent dose rates
from different primary incident particles in each organs, for both male and
female phantom, are also shown in Fig. 9, 10 and 11, 12. Under the same
irradiation condition, the dose received by the female phantom is slightly
higher than the male phantom. Noticeable difference in radiation dose rates at
different organs is quite apparent from these plots. Lund & Jevremovic [2019]
also find similar variation in organ dose using a human anatomical phantom for
Apollo 11 and Apollo 14 missions from trapped protons. Using a MC simulation
procedure with simplified phantom model in X-ray radiation environment for
medical purpose, Lewis et al. [1988] reported different absorption dose rates
in different organs indicating a ratio more than factor of 2 between colon and
stomach. In a recent study of organ dose estimation due to computed
tomography, De Mattia et al. [2020] also reported substantial difference of
radiation dose rates in different organs which also support our calculation.
However, Reitz et al. [2012] reported more or less flat distribution of
absorbed dose rate at different organs in human body at the radiation
environment on moon with only high energy primary GCRs and using ICRP phantom
model. We can speculate the differential organ doses due to radiation
environment at the aviation altitude and organ material distribution in the
phantoms (high density and relatively high Z bone material should play a role
here). The direct verification of the obtained result is difficult due to lack
of experimental knowledge and other calculations of dose rate for individual
organs at this level. Some future development in this concern with computation
or/and experiments can shed more light and verify the results obtained in the
current calculation.

The sex-averaged absorbed (equivalent) dose rate on eye lens is calculated as
1.84 $\mu$Gy/h (5.16 $\mu$Sv/h). The equivalent dose limit of eye lens for
occupational exposure and public exposure is 20 mSv and 15 mSv per year. So
from this simulation, it can be seen that this limit can be exceeded for
frequent fliers or aircrews which could increase the chance of eye cataracts.
The absorbed dose rate and equivalent dose rate received by the prostate
(uterus) of male (female) phantom is 1.25 (1.78) $\mu$Gy/h and 1.82 (3.21)
$\mu$Sv/h. A recent study by Grajewski et al. [2015] suggests that the risk of
miscarriage among the female flight attendant will increase for radiation dose
of or more than 0.1 mGy in week 9–13 from conception. The estimated threshold
dose for the gestational period can be found in Patel et al. [2007], which is
quite high but can be reached during severe solar particle events, Terrestrial
Gamma-ray Flash events [Dwyer et al., 2010] or frequent use of flights from
high altitude or long haul polar routes. So, all frequently flying pregnant
women or aircrews should take extra care of their fetus during their early
gestation.

Figure 7: Spatial distribution (frontal view; side-wise view) of absorbed dose
rate and equivalent dose rate in male phantom.

Figure 8: Spatial distribution (frontal view; side-wise view) of absorbed dose
rate and equivalent dose rate in female phantom. Figure 9: Absorbed dose rate
for different incident particles in different organs of male phantom. Figure
10: Absorbed dose rate for different incident particles in different organs of
female phantom. Figure 11: Equivalent dose rate for different incident
particles in different organs of male phantom. Figure 12: Equivalent dose rate
for different incident particles in different organs of female phantom.

The incident energetic particles and radiation produce different sub-atomic
secondary particles, as well as some radioactive nuclei, by interacting with
the human body. These radioactive nuclei are mainly produced by spallation
reaction of protons and activation by neutrons in our body [Brodzinski et al.,
1969]. The amount of radiation dose per hour imparted by these radionuclides
is negligible, but can be accumulated to give substantial dose for extended
exposure time or elevated radiation environment. Because of their radioactive
nature, these cosmogenic radio-isotopes are particularly important, as they
can be accumulated in some specific organs due to their physicochemical
nature, where it could cumulatively give radiation dose depending upon their
biological half-lives which may lead to stochastic detrimental effect like
cancer. Despite of the harmful characteristics of the cosmogenic
radionuclides, they could be used to accurately measure the radiation dose in
the human body [Brodzinski et al., 1969]. They have half-lives ranging from
less than a second to years. Internal radioactivity is particularly dangerous
than the external radiation as the decaying particles or radiations may kill
nearby tissue, cells or damage the DNA structure. In the current simulation
work we also have calculated the production of radioactive nuclei in human
body due to high energy particles or radiation interactions. Most abundant
nuclides among all the produced radionuclides in human body are listed in
Table 2 along with their half-life, mode of production and abundance.

Table 2: Total production of cosmogenic radionuclides per hour inside phantoms
from interaction of cosmic ray at aircraft altitude.

Radionuclide |  Half-life |  Mode of production∗ |  Atoms/hour
---|---|---|---
14C |  5700 y |  ${}^{14}N(n,p)^{14}C$ |  2.88$\times 10^{5}$
15O |  122.24 s |  ${}^{16}O(n,2n)^{15}O$ |  1.24$\times 10^{5}$
36Cl |  3.01$\times 10^{5}$ y |  ${}^{35}Cl(n,\gamma)^{36}Cl$ |  8.39$\times 10^{4}$
11C |  20.36 m |  ${}^{12}C(n,2n)^{11}C$ |  6.59$\times 10^{4}$
7Be |  53.22 d |  ${}^{12}C(n,2n+\alpha)^{7}Be$ |  3.20$\times 10^{4}$
40K |  1.24$\times 10^{9}$ y |  ${}^{39}K(n,\gamma)^{40}K$ |  1.91$\times 10^{4}$
14O |  12.5 ms |  ${}^{16}O(n,3n)^{14}O$ |  2.08$\times 10^{4}$
6He |  806.7 ms |  ${}^{12}C(n,p+\alpha+d)^{6}He$ |  1.45$\times 10^{4}$
16N |  7.13 s |  ${}^{16}O(n,p)^{16}N$ |  1.16$\times 10^{4}$
41Ca |  9.94$\times 10^{4}$ y |  ${}^{40}Ca(n,\gamma)^{41}Ca$ |  1.25$\times 10^{4}$
10Be |  1.51$\times 10^{6}$ y |  ${}^{12}C(n,2n+p)^{10}B$ |  1.27$\times 10^{4}$
12B |  20.20 ms |  ${}^{16}O(n,p+\alpha)^{12}B$ |  6.75$\times 10^{3}$
13N |  9.96 m |  ${}^{16}O(n,p+3n)^{13}N$ |  1.09$\times 10^{4}$
8Li |  839.9 ms |  ${}^{12}C(n,p+\alpha)^{8}Li$ |  8.20$\times 10^{3}$
37Ar |  35.01 d |  ${}^{40}Ca(n,\alpha)^{37}Ar$ |  6.97$\times 10^{3}$
12N |  11.0 ms |  ${}^{16}O(n,p+4n)^{12}N$ |  5.75$\times 10^{3}$
32P |  14.26 d |  ${}^{31}P(n,\gamma)^{32}P$ |  6.04$\times 10^{3}$
24Na |  14.99 h |  ${}^{23}Na(n,\gamma)^{24}Na$ |  4.03$\times 10^{3}$

∗ Only major production processes

Based on this result, we tried to have a rough estimation of the maximum limit
to the career exposure of the aircrews due to cosmogenic radionuclides listed
in Table 2. For this purpose, we considered the decay of the induced
radionuclides at their corresponding position of generation inside human body
as obtained from the simulation and calculated the absorbed dose from
different radionuclides. The total number of radionuclides accumulated in the
body is calculated considering overall occupational exposure for 20 and 30
years with 1000 flight hours per year. The number of radionuclides that decay
over the lifetime after the exposure (considering 50 years from the median age
of occupational exposure suffered) to give the radiation dose, depending on
the corresponding half lives of the radionuclides. This calculation yields the
carrier exposure of about 6 mSv and 9 mSv considering 20 and 30 years of
occupational exposures respectively. However, it should be emphasized here
that, this calculation is based on the physical half-lives of the
radionuclides. But due to various reasons their biological half-lives would be
different, which should be actually considered in the calculation. Again, the
production rates of these radionuclides depends on the location
(altitude/latitude) of exposure over the occupational career which also should
be considered.

###  3.3 Radiation flux inside aircraft structure

The simulated flux of different secondary particles at three different
positions inside the aircraft, along with the flux outside the aircraft
structure (i.e., in the free atmosphere), for both downward and upward going
particles can be seen from Fig. 13 and Fig. 14. Here, we discarded the
downward going $\pi^{\pm}$ due to their negligible contribution to the total
effective dose rate (see Table 1). The change (in %) of the integral flux
(particles $m^{-2}sr^{-1}s^{-1}$) for different individual secondary particles
(as well as for the total contribution) in both downward and upward directions
at different positions inside the fuselage with respect to the corresponding
flux outside the aircraft, is given in Table 3. The corresponding change (in
$\mu$Sv/h) in effective dose rate in human body is tabulated in Table 4.
However, to calculate the effective dose rate at different positions inside
the aircraft we considered the same fluence-to-dose-rate weighting factor
obtained from the dose rate calculation in human phantom in the atmosphere as
discussed in Sec. 3.2.

From these results, it is apparent that inside the aircraft fuselage the flux
of downward going particles are increased in general (with exception for the
muons). This may be attributed due to the secondary production by interaction
of high energy particles with the aircraft materials have overwhelmed the
absorption of the particles in the aircraft shell. On the other hand, a
significant reduction of particle flux inside the fuselage for upward going
particles is discernible from the results. Which is mainly due to the presence
of the floor and central fuel tank. But, since downward particles contribute
almost $\sim$96% to the total effective dose rate, while upward particles
contribute only $\sim$4% (see Table 1), the reduction of upward particle flux
could not effectively reduce the dose rate. In fact this calculation shows
about 9.7% increase of total effective dose rate at the center of the fuselage
compared to the free atmosphere, while effective dose rate due to neutrons
increase by $\sim$ 6%. The neutron dose rate measurement inside RB57-F
military aircraft shows about 10% increment in the radiation dose rate than
outside the aircraft Singleterry Jr et al. [1999]. In a previous calculation,
Ferrari et al. [2005] reported qualitatively similar findings of slight
increment (depending on the position along the fuselage) of radiation dose in
side the aircraft due to downward radiation, while the contribution from the
upward radiation decremented due to the presence of the fuel and cargo
content. However, the dose rate inside the fuselage may also change due to
absorption of radiation by the internal structures, seats, passengers and
other high-Z materials, which can be studied by MC simulation with detailed
geometrical structure of the aircraft from the manufacture and corresponding
measurements on board the aircraft.

Figure 13: Particle flux for different downward going secondary GCR particles
(proton, neutron, $\gamma$, $e^{-}$, $e^{+}$, $\mu^{-}$, $\mu^{+}$) at
aviation altitude and in four different positions (outside:Atmosphere, front,
middle and back side of the aircraft).

Figure 14: Particle flux for different upward going secondary GCR particles (proton, neutron, $\gamma$, $e^{-}$, $e^{+}$, $\mu^{-}$, $\mu^{+}$) at aviation altitude and in four different positions (outside:Atmosphere, front, middle and back side of the aircraft). Table 3: Percentage changes of integral flux (Particles $m^{-2}sr^{-1}s^{-1}$) for total and individual different secondary GCR particles in front, middle and back section of the fuselage with respect to the free atmosphere. Particles | Front (%) | Middle (%) | Back (%)
---|---|---|---
|  Down |  Up |  Down |  Up |  Down |  Up
$n$ |  04.51 |  -11.53 |  13.74 |  -86.87 |  05.59 |  -10.70
$p$ |  00.28 |  -49.61 |  05.83 |  -88.52 |  03.10 |  -40.39
$\gamma$ |  04.14 |  -30.87 |  27.15 |  -88.20 |  04.59 |  -26.64
$e^{-}$ |  12.25 |  -78.56 |  16.91 |  -94.03 |  13.85 |  -70.34
$e^{+}$ |  16.37 |  -42.29 |  29.90 |  -67.18 |  18.06 |  -29.28
$\mu^{-}$ |  -2.74 |  -15.86 |  01.77 |  -88.64 |  -1.20 |  -11.59
$\mu^{+}$ |  -2.56 |  -17.36 |  01.02 |  -88.06 |  02.30 |  -11.02
Total |  04.60 |  -29.58 |  24.76 |  -88.09 |  05.26 |  -25.62
Table 4: Variation of effective dose rate for different downward and upward going secondary GCR particles inside the aircraft fuselage. Particles | Front ($\mu$Sv/h) | Middle ($\mu$Sv/h) | Back ($\mu$Sv/h)
---|---|---|---
|  Down |  Up |  Down |  Up |  Down |  Up
$n$ |  0.0921 |  -0.0198 |  0.2808 |  -0.1493 |  0.1142 |  -0.0183
$p$ |  0.0040 |  -0.0042 |  0.0839 |  -0.0075 |  0.0446 |  -0.0034
$\gamma$ |  0.0313 |  -0.0075 |  0.2054 |  -0.0216 |  0.0347 |  -0.0065
$e^{-}$ |  0.0453 |  -0.0037 |  0.0626 |  -0.0045 |  0.0512 |  -0.0033
$e^{+}$ |  0.0454 |  -0.0015 |  0.0829 |  -0.0024 |  0.0501 |  -0.0010
$\mu^{-}$ |  -0.0044 |  -0.0004 |  0.0028 |  -0.0027 |  -0.001 |  -0.0003
$\mu^{+}$ |  -0.0047 |  -0.0004 |  0.0018 |  -0.0024 |  0.0042 |  -0.0003
Total |  0.2091 |  -0.0379 |  0.7206 |  -0.1906 |  0.2973 |  -0.0334
| 0.1712 | 0.5299 | 0.2638
Table 5: Dose rate as calculated from this simulation and using the dose
conversion coefficient from Pelliccioni [2000].

Particles |  Effective dose rate ($\mu Sv/h$) |  Effective dose rate∗ ($\mu Sv/h$) |  Ambient dose equivalent∗ ($\mu Sv/h$)
---|---|---|---
$n$ |  2.2159 |  2.0371 |  2.2398
$p$ |  1.4486 |  2.1885 |  0.7790
$\gamma$ |  0.7812 |  0.4644 |  0.1895
$e^{-}$ |  0.3751 |  0.1924 |  0.1704
$e^{+}$ |  0.2811 |  0.1454 |  0.2507
$\mu^{-}$ |  0.1660 |  0.0952 |  0.0935
$\mu^{+}$ |  0.1880 |  0.1154 |  0.1108
$\pi^{-}$ |  0.0039 |  0.0023 |  0.0015
$\pi^{+}$ |  0.0048 |  0.0072 |  0.0054
Total |  5.4651 |  5.2484 |  3.8408

∗ using fluence-to-dose conversion coefficients for isotropic irradiation

###  3.4 Comparison with previous dose calculations

This simulation yields that the total weighted sum of equivalent dose rate
received by the female phantom is 5.72 $\mu$Sv/h, whereas that by the male
phantom is 5.20 $\mu$Sv/h. So the sex-averaged effective dose rate is 5.46
$\mu$Sv/h. The experimental or calculated dose rates received by the
individual organs inside the human body (at aviation altitude), influenced by
the aircraft structure at the geomagnetic latitude and altitude considered in
this simulation are not available. So, we could not directly compare our
simulated results for absorbed and equivalent dose rates on each organ of the
male and female body. However, we bench-marked our simulation at different
stages of the calculation.

In Sec. 3.1, we have already mentioned about the validation of the simulated
proton flux at satellite altitude and atmospheric radiation flux at balloon
altitude. We also compared the simulated neutron fluence rate at the aviation
altitude with the experimental measurement reported by Goldhagen et al.
[2002]. Fig. 15 shows the neutron fluence rate per lethargy at 20 km altitude
and in 1.0 - 1.1 rad geomagnetic latitude, as obtained in this simulation and
compared to that measured by Goldhagen et al. [2002] in the same latitude and
altitude region. Considering this neutron fluence and conversion coefficients
from Pelliccioni [2000], we calculated the effective dose rate (ambient dose
equivalent rate) as 7.60 (9.12) $\mu$Sv/h which is within 10% deviation of the
measured value.

Figure 15: Neutron fluence rate at 20 km altitude and in 1.0 - 1.1 rad
geomagnetic latitude obtained in this simulation (black) and that measured by
Goldhagen et al. [2002] (gray).

The radiation dose in the human phantom depends on many factors like: material
distribution considered in the phantom, incident radiation spectra, energy
range of the radiation, angular distribution of the incident flux etc. For
example, Sato et al. [2009] showed the effect of using different source
geometries on radiation dose. Here, in this work, instead of using fluence to
dose conversion coefficients, using micro-dosimetric technique we explicitly
calculated the energy depositions in different organs for a wide range of
radiation types and energy considering different angular distributions for
downward and upward radiations. However, to compare our simulated dose rate,
we also calculated the effective dose rate using the common conversion
coefficients for isotropic irradiation from Pelliccioni [2000] and the values
for different radiation types are tabulated in Table 5. The comparison shows
that the total effective dose rate are within the acceptable uncertainty
range, although some deviations in the effective dose rate for different
particles are noticeable due to above mentioned factors.

Since, effective dose and equivalent dose are not measurable quantities, so
ambient dose equivalent ($H^{*}(10)$) used instead for measurements. In Table
5 we also presented the $H^{*}(10)$ values for different particles calculated
using corresponding conversion coefficients. The apparent underestimation of
total ambient dose equivalent rate compared to the total effective dose rate
can be understandable from the measurement of dose depth distribution aboard a
series of flights from Cologne (GER) to Washington, DC (USA) using a quasi
tissue-equivalent phantom sphere by Vana et al. [2003]. This measurement shows
that the maximum dose equivalent appears in a depth of 50 to 60 mm rather than
10 mm, implying that $H^{*}(10)$ underestimates the actual whole-body
radiation exposure. Similarly, Petoussi-Henss et al. [2010], Veinot & Hertel
[2011] showed that above few MeV, $H^{*}(10)$ can not provide a conservative
estimate of the protection quantities. In fact, whether $H^{*}(10)$ saturates
with energy, effective dose increases. Ferrari & Pelliccioni [1998] also
conclude that the only up to a limited energy range $H^{*}(10)$ gives a
conservative estimate of effective dose and for high energy neutrons. For the
validation of this simulation here we also compere the calculated ambient dose
equivalent rate (3.84 $\mu Sv/h$) in the simulated region ($\theta_{M}$ =
45∘–50∘, Altitude = 10 km, $\phi$ = 524 MV) with the other reported values of
ambient dose equivalent rate in Ploc et al. [2013], Lindborg et al. [2004b],
Bottollier-Depois et al. [2012], Lindborg et al. [2004a] which is determined
by in-flight measurements through several radiation monitors and in different
altitude, latitude as well as solar condition. We simply interpolate the
reported values for the comparison, which shows that our simulated dose rate
is well within the acceptable limit of 30% uncertainty.

##  4 Conclusions

The gender specific radiation dose on the human body and its internal organs
are calculated in this work through MC simulation, using most updated models
describing the atmosphere and magnetosphere, CR flux, human phantoms and organ
specific weighting factors. The calculation shows that, among all the incident
primary particles, most of the radiation effective dose received by the human
body is due to the neutrons, at the location of aviation altitude considered
in this simulation. By interacting with the human phantoms secondary CRs also
produce different cosmogenic radioactive nuclides with half lives ranging from
less than a second to years. These radionuclides may give negligible
contributions to the total effective dose received per hour during the flight,
but can gradually increase with increasing altitude, latitude and exposure
time and most importantly can have significant cumulative effect over the
human lifespan. The calculation also reveals that the dose received by the
human phantoms at flight altitude are mostly due to downward directed
particles with a small contribution by the upward particles. Comparison of the
calculated effective dose rate in this work with that calculated by various
other computer codes and measurement as reported in Ploc et al. [2013],
Lindborg et al. [2004b], Bottollier-Depois et al. [2012], Lindborg et al.
[2004a] shows an agreement well within the acceptable error limit. Study of
the shielding effect of the aircraft structure on the radiation dose is very
important in aviation safety as this helps us to better predict radiation dose
for radiological protection. By considering a detailed aircraft structure
Battistoni et al. [2005] showed that, inside the aircraft, decrease of ambient
dose equivalent is more significant than the decrease of effective dose
compared to free atmosphere. Based on this they conclude that effective dose
at the free atmosphere can be used for individuals risk assessment. On the
other hand great care should be taken to consider the shielding effect on the
ambient dose equivalent when compared the calculated value with the
measurement. Here, in this simulation, the consideration of the simplified
aircraft model structure with only the outer shell, gives apparently odd
result that the effective radiation dose is increased inside the aircraft. But
this is understandable from the fact that the high-energy particle fluxes are
converted to relatively low-energy particles by the shell material which
subsequently contribute to the received dose by the human body more
efficiently. However, this calculation can be improved by considering the the
actual particle flux distribution produced inside the aircraft to calculate
the energy depositions in the phantoms, rather than using the fluence-to-dose-
rate weighting coefficients obtained from the calculation at the atmosphere
outside the aircraft. Moreover, the calculation of radiation dose in human
body inside the aircraft can further be improved by considering more realistic
internal structure of the aircraft and passenger distribution, which is of
course practically very challenging to implement in this kind of simulation.

##  5 Acknowledgment

This work has been supported by the SERB (India) project EMR/2016/003870. We
also thank the Higher Education department of West Bengal, for a Grant-In-Aid
which allowed us to carry out the research activities at ICSP.

## References

  * Adriani et al. [2013] Adriani, O., Barbarino, G., Bazilevskaya, G., Bellotti, R., Boezio, M., Bogomolov, E., Bongi, M., Bonvicini, V., Borisov, S., Bottai, S. et al. (2013).  Time dependence of the proton flux measured by PAMELA during the 2006 July-2009 December solar minimum.  The Astrophysical Journal, 765(2), 91.
  * Agostinelli et al. [2003] Agostinelli, S., Allison, J., Amako, K. a., Apostolakis, J., Araujo, H., Arce, P., Asai, M., Axen, D., Banerjee, S., Barrand, G. . et al. (2003).  GEANT4—a simulation toolkit.  Nuclear instruments and methods in physics research section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 506(3), 250–303.
  * Aguilar et al. [2015] Aguilar, M., Aisa, D., Alpat, B., Alvino, A., Ambrosi, G., Andeen, K., Arruda, L., Attig, N., Azzarello, P., Bachlechner, A. et al. (2015).  Precision measurement of the proton flux in primary cosmic rays from rigidity 1 GV to 1.8 TV with the Alpha Magnetic Spectrometer on the International Space Station.  Physical Review Letters, 114(17), 171103.
  * Alves et al. [2016] Alves, M. C., Galeano, D. C., Santos, W. S., Lee, C., Bolch, W. E., Hunt, J. G., da Silva, A. X., & Carvalho, A. B. (2016).  Comparison of the effective dose rate to aircrew members using hybrid computational phantoms in standing and sitting postures.  Journal of Radiological Protection, 36(4), 885–901.
  * Aspholm et al. [1999] Aspholm, R., Lindbohm, M.-L., Paakkulainen, H., Taskinen, H., Nurminen, T., & Tiitinen, A. (1999).  Spontaneous abortions among Finnish flight attendants.  Journal of occupational and environmental medicine, 41(6), 486–491.
  * Banjac et al. [2019] Banjac, S., Heber, B., Herbst, K., Berger, L., & Burmeister, S. (2019).  On-the-Fly Calculation of Absorbed and Equivalent Atmospheric Radiation Dose in A Water Phantom with the Atmospheric Radiation Interaction Simulator (AtRIS).  Journal of Geophysical Research: Space Physics, 124(12), 9774–9790.
  * Battistoni et al. [2005] Battistoni, G., Ferrari, A., Pelliccioni, M., & Villari, R. (2005).  Evaluation of the doses to aircrew members taking into consideration the aircraft structures.  Advances in Space Research, 36(9), 1645–1652.
  * Bazilevskaya & Svirzhevskaya [1998] Bazilevskaya, G., & Svirzhevskaya, A. (1998).  On the stratospheric measurements of cosmic rays.  Space Science Reviews, 85(3-4), 431–521.
  * Bennett et al. [2013] Bennett, L., Lewis, B., Bennett, B., McCall, M., Bean, M., Doré, L., & Getley, I. (2013).  A survey of the cosmic radiation exposure of Air Canada pilots during maximum galactic radiation conditions in 2009.  Radiation measurements, 49, 103–108.
  * Boeing Co. [2020] Boeing Co. (2020).  Boeing 777-200LR / -300ER / -FreighterAirplane Characteristics for Airport Planning.  http://www.boeing.com/assets/pdf/commercial/airports/acaps/777_2lr3er.pdf.  [Online; accessed 02–April–2020].
  * Bottollier-Depois et al. [2012] Bottollier-Depois, J.-F., Beck, P., Latocha, M., Mares, V., Matthiä, D., Rühm, W., & Wissmann, F. (2012).  Comparison of codes assessing radiation exposure of aircraft crew due to galactic cosmic radiation.  EURADOS report 2012-03, (pp. 1–55).  ISBN 978-3-943701-02-9.
  * Brodzinski et al. [1969] Brodzinski, R., Wogman, N., & Perkins, R. (1969).  Cosmic-ray induced radioactivity in astronauts as a measure of radiation dose.  Space life sciences, 1(4), 545–553.
  * Caballero-Lopez & Moraal [2004] Caballero-Lopez, R., & Moraal, H. (2004).  Limitations of the force field equation to describe cosmic ray modulation.  Journal of Geophysical Research: Space Physics, 109(A1).
  * De Mattia et al. [2020] De Mattia, C., Campanaro, F., Rottoli, F., Colombo, P. E., Pola, A., Vanzulli, A., & Torresin, A. (2020).  Patient organ and effective dose estimation in ct: comparison of four software applications.  European radiology experimental, 4(1), 1–16.
  * Dwyer et al. [2010] Dwyer, J., Smith, D., Uman, M., Saleh, Z., Grefenstette, B., Hazelton, B., & Rassoul, H. (2010).  Estimation of the fluence of high-energy electron bursts produced by thunderclouds and the resulting radiation doses received in aircraft.  Journal of Geophysical Research: Atmospheres, 115(D9).
  * Dyer & Lei [2001] Dyer, C., & Lei, F. (2001).  Monte Carlo calculations of the influence on aircraft radiation environments of structures and solar particle events.  IEEE Transactions on Nuclear Science, 48(6), 1987–1995.
  * Dyer et al. [2003] Dyer, C., Lei, F., Clucas, S., Smart, D., & Shea, M. (2003).  Calculations and observations of solar particle enhancements to the radiation environment at aircraft altitudes.  Advances in Space Research, 32(1), 81–93.
  * Ferrari & Pelliccioni [1998] Ferrari, A., & Pelliccioni, M. (1998).  Fluence to dose equivalent conversion data and effective quality factors for high energy neutrons.  Radiation Protection Dosimetry, 76(4), 215–224.
  * Ferrari et al. [1997] Ferrari, A., Pelliccioni, M., & Pillon, M. (1997).  Fluence to effective dose conversion coefficients for neutrons up to 10 TeV.  Radiation Protection Dosimetry, 71(3), 165–173.
  * Ferrari et al. [2004] Ferrari, A., Pelliccioni, M., & Villari, R. (2004).  Evaluation of the influence of aircraft shielding on the aircrew exposure through an aircraft mathematical model.  Radiation protection dosimetry, 108(2), 91–105.
  * Ferrari et al. [2005] Ferrari, A., Pelliccioni, M., & Villari, R. (2005).  A mathematical model of aircraft for evaluating the effects of shielding structure on aircrew exposure.  Radiation protection dosimetry, 116(1-4), 331–335.
  * Gaisser [1990] Gaisser, T. K. (1990).  Cosmic rays and particle physics..  Cambridge University Press.
  * Geant4 [2020] Geant4 (2020).  Physics list guide.  http://geant4-userdoc.web.cern.ch/geant4-userdoc/UsersGuides/PhysicsListGuide/html/reference_PL/QGSP_BIC.html.  [Online; accessed 02–April–2020].
  * Goldhagen et al. [2002] Goldhagen, P., Reginatto, M., Kniss, T., Wilson, J., Singleterry, R., Jones, I., & Van Steveninck, W. (2002).  Measurement of the energy spectrum of cosmic-ray induced neutrons aboard an ER-2 high-altitude airplane.  Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 476(1-2), 42–51.
  * Gopalswamy et al. [2006] Gopalswamy, N., Mewaldt, R., & Torsti, J. (2006).  Solar eruptions and energetic particles: An introduction.  Solar Eruptions and Energetic Particles, (165), 1–5.
  * Grajewski et al. [2015] Grajewski, B., Whelan, E. A., Lawson, C. C., Hein, M. J., Waters, M. A., Anderson, J. L., MacDonald, L. A., Mertens, C. J., Tseng, C.-Y., Cassinelli, R. T. et al. (2015).  Miscarriage among flight attendants.  Epidemiology (Cambridge, Mass.), 26(2), 192.
  * Griffin et al. [2019] Griffin, K. T., Mille, M. M., Pelletier, C., Gopalakrishnan, M., Jung, J. W., Lee, C., Kalapurakal, J., Pyakuryal, A., & Lee, C. (2019).  Conversion of computational human phantoms into DICOM-RT for normal tissue dose assessment in radiotherapy patients.  Physics in Medicine & Biology, 64(13), 13NT02.
  * Herbst et al. [2017] Herbst, K., Muscheler, R., & Heber, B. (2017).  The new local interstellar spectra and their influence on the production rates of the cosmogenic radionuclides 10Be and 14C.  Journal of Geophysical Research: Space Physics, 122(1), 23–34.
  * ICAO [2016] ICAO (2016).  Global air navigation plan 2016–2030.  https://www.icao.int/airnavigation/documents/ganp-2016-interactive.pdf.  [Online; accessed 02–April–2020].
  * ICRP [1991] ICRP (1991).  1990 recommendations of the International Commission on Radiological Protection. ICRP publication 60.  Annals of the ICRP, 21, 1–3.
  * ICRP [2007] ICRP (2007).  The Recommendations of the International Commission on Radiological Protection. ICRP Publication 103.  Annals of the ICRP, 37, 2–4.
  * ICRU [2010] ICRU (2010).  Reference Data for the Validation of Doses from Cosmic-radiation Exposure of Aircraft Crew. ICRU Report 84 (prepared jointly with ICRP).  Journal of the ICRU, 10(2).
  * Lauria et al. [2006] Lauria, L., Ballard, T. J., Caldora, M., Mazzanti, C., & Verdecchia, A. (2006).  Reproductive disorders and pregnancy outcomes among female flight attendants.  Aviation, space, and environmental medicine, 77(5), 533–539.
  * Lee et al. [2009] Lee, C., Lodwick, D., Hurtado, J., Pafundi, D., Williams, J. L., & Bolch, W. E. (2009).  The UF family of reference hybrid phantoms for computational radiation dosimetry.  Physics in Medicine & Biology, 55(2), 339.
  * Lewis et al. [1988] Lewis, C., Smith, P., Stratton, I., Darby, S., & Doll, R. (1988).  Estimated radiation doses to different organs among patients treated for ankylosing spondylitis with a single course of x rays.  The British journal of radiology, 61(723), 212–220.
  * Lindborg et al. [2004a] Lindborg, L., Bartlett, D., Beck, P., McAulay, I., Schnuer, K., Schraube, H., & Spurny, F. (2004a).  Cosmic radiation exposure of aircraft crew: compilation of measured and calculated data.  EC Report Radiation Protection 140.  Final Report of EURADOS WG 5, Luxembourg, pp. 1–271 (ISBN 92-894-8448-9).
  * Lindborg et al. [2004b] Lindborg, L., Bartlett, D., Beck, P., McAulay, I., Schnuer, K., Schraube, H., & Spurny, F. (2004b).  Cosmic radiation exposure of aircraft crew: compilation of measured and calculated data.  Radiation protection dosimetry, 110(1-4), 417–422.
  * Lund & Jevremovic [2019] Lund, M., & Jevremovic, T. (2019).  Enhanced GEANT4 Monte Carlo simulations of the space radiation effects on the International Space Station and Apollo missions using high-performance computing environment.  Acta Astronautica, 165, 219–228.
  * Moraal [2013] Moraal, H. (2013).  Cosmic-ray modulation equations.  Space Science Reviews, 176(1-4), 299–319.
  * Patel et al. [2007] Patel, S. J., Reede, D. L., Katz, D. S., Subramaniam, R., & Amorosa, J. K. (2007).  Imaging the pregnant patient for nonobstetric conditions: algorithms and radiation dose considerations.  Radiographics, 27(6), 1705–1722.
  * Pelliccioni [2000] Pelliccioni, M. (2000).  Overview of fluence-to-effective dose and fluence-to-ambient dose equivalent conversion coefficients for high energy radiation calculated using the fluka code.  Radiation Protection Dosimetry, 88(4), 279–297.
  * Petoussi-Henss et al. [2010] Petoussi-Henss, N., Bolch, W., Eckerman, K., Endo, A., Hertel, N., Hunt, J., Pelliccioni, M., Schlattl, H., & Zankl, M. (2010).  ICRP Publication 116. Conversion coefficients for radiological protection quantities for external radiation exposures.  Annals of the ICRP, 40(2-5), 1–257.
  * Picone et al. [2002] Picone, J., Hedin, A., Drob, D. P., & Aikin, A. (2002).  NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues.  Journal of Geophysical Research: Space Physics, 107(A12), SIA–15.
  * Ploc et al. [2013] Ploc, O., Ambrozova, I., Kubancak, J., Kovar, I., & Dachev, T. P. (2013).  Publicly available database of measurements with the silicon spectrometer liulin onboard aircraft.  Radiation measurements, 58, 107–112.
  * Reames [1999] Reames, D. V. (1999).  Particle acceleration at the Sun and in the heliosphere.  Space Science Reviews, 90(3-4), 413–491.
  * Regener & Pfotzer [1934] Regener, E., & Pfotzer, G. (1934).  Intensity of the cosmic ultra-radiation in the stratosphere with the tube-counter.  Nature, 134(3383), 325–325.
  * Reitz et al. [2012] Reitz, G., Berger, T., & Matthiae, D. (2012).  Radiation exposure in the moon environment.  Planetary and Space Science, 74(1), 78–83.
  * Sarkar et al. [2017] Sarkar, R., Chakrabarti, S. K., Pal, P. S., Bhowmick, D., & Bhattacharya, A. (2017).  Measurement of secondary cosmic ray intensity at Regener-Pfotzer height using low-cost weather balloons and its correlation with solar activity.  Advances in Space Research, 60(5), 991–998.
  * Sarkar et al. [2020] Sarkar, R., Roy, A., & Chakrabarti, S. K. (2020).  Simulation of cosmic rays in the Earth’s atmosphere and interpretation of observed counts in an X-ray detector at balloon altitude near tropical region.  Advances in Space Research, 65(1), 189–197.
  * Sato et al. [1999] Sato, O., Yoshizawa, N., Takagi, S., Iwai, S., Uehara, T., Sakamoto, Y., Yamaguchi, Y., & Tanaka, S.-i. (1999).  Calculations of effective dose and ambient dose equivalent conversion coefficients for high energy photons.  Journal of nuclear science and technology, 36(11), 977–987.
  * Sato et al. [2009] Sato, T., Endo, A., Zankl, M., Petoussi-Henss, N., & Niita, K. (2009).  Fluence-to-dose conversion coefficients for neutrons and protons calculated using the phits code and icrp/icru adult reference computational phantoms.  Physics in Medicine & Biology, 54(7), 1997.
  * Singleterry Jr et al. [1999] Singleterry Jr, R. C., Shinn, J. L., Wilson, J. W., Maiden, D. L., Thibeault, S. A., Badavi, F. F., Conroy, T., & Braby, L. (1999).  Aircraft Radiation Shield Experiments—Preflight Laboratory Testing.  NASA STI/Recon Technical Report N.  https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.39.4978&rep=rep1&type=pdf.
  * Stone et al. [2013] Stone, E., Cummings, A., McDonald, F., Heikkila, B., Lal, N., & Webber, W. (2013).  Voyager 1 observes low-energy galactic cosmic rays in a region depleted of heliospheric ions.  Science, 341(6142), 150–153.
  * Störmer [1955] Störmer, C. (1955).  The polar aurora.  Clarendon Press.
  * Thébault et al. [2015] Thébault, E., Finlay, C. C., Beggan, C. D., Alken, P., Aubert, J., Barrois, O., Bertrand, F., Bondar, T., Boness, A., Brocco, L. et al. (2015).  International geomagnetic reference field: the 12th generation.  Earth, Planets and Space, 67(1), 79.
  * Tsyganenko & Andreeva [2016] Tsyganenko, N., & Andreeva, V. (2016).  An empirical RBF model of the magnetosphere parameterized by interplanetary and ground-based drivers.  Journal of Geophysical Research: Space Physics, 121(11), 10–786.
  * Vana et al. [2003] Vana, N., Hajek, M., & Berger, T. (2003).  Ambient dose equivalent H∗(d)- an appropriate philosophy for radiation monitoring onboard aircraft and in space?.  IRPA Regional Congress on Radiation Protection in Central Europe, (p. 573). Slovakia: Nuclear Regulatory Authority of the Slovak Republic.  https://inis.iaea.org/collection/NCLCollectionStore/_Public/36/097/36097704.pdf.
  * Veinot & Hertel [2011] Veinot, K., & Hertel, N. (2011).  Personal dose equivalent conversion coefficients for photons to 1 gev.  Radiation protection dosimetry, 145(1), 28–35.
  * Vos & Potgieter [2015] Vos, E. E., & Potgieter, M. S. (2015).  New modeling of galactic proton modulation during the minimum of solar cycle 23/24.  The Astrophysical Journal, 815(2), 119.