Radiation Protection Dosimetry (2015), Vol. 167, No. 4, pp. 664 – 670
Advance Access publication 30 January 2015
doi:10.1093/rpd/ncu358
AN EMPIRICAL METHOD FOR DERIVING RBE VALUES
ASSOCIATED WITH ELECTRONS, PHOTONS AND
RADIONUCLIDES
M. Bellamy1, *, J. Puskin2, N. Hertel1 and K. Eckerman1
1
Oak Ridge National Laboratory, Center for Radiation Protection Knowledge, PO Box 2008, Oak Ridge,
TN 37831-6153, USA
2
Center for Science and Technology, Radiation Protection Division, ORIA (6608J), EPA, Washington,
DC 20460, USA
*Corresponding author: [email protected]
Received 13 October 2014; revised 17 November 2014; accepted 19 November 2014
There is substantial evidence to justify using relative biological effectiveness (RBE) values of >1 for low-energy electrons and
photons. But, in the field of radiation protection, radiation associated with low linear energy transfer has been assigned a radiation weighting factor wR of 1. This value may be suitable for radiation protection but, for risk considerations, it is important to
evaluate the potential elevated biological effectiveness of radiation to improve the quality of risk estimates. RBE values between
2 and 3 for tritium are implied by several experimental measurements. Additionally, elevated RBE values have been found for
other similar low-energy radiation sources. In this work, RBE values are derived for electrons based upon the fractional deposition of absorbed dose of energies less than a few kiloelectron volts. Using this empirical method, RBE values were also derived
for monoenergetic photons and 1070 radionuclides from ICRP Publication 107 for which photons and electrons are the primary
emissions.
INTRODUCTION
The relative biological effectiveness (RBE) of a radiation is frequently related to linear collisional stopping power (commonly known as Linear Energy
Transfer, LET)(1). The relationship between LET and
RBE is thought to exist because the densely clustered
collisions of high-LET radiation tends to cause more
complex DNA strand damage compared with lowLET radiation. Energetic electrons are considered to
be low LET and are normally ascribed an RBE of
unity regardless of the electron energy(2). However, as
with most charged particles, the LET varies with the
electron’s kinetic energy and rises sharply in the tail(s)
of the electron track before it comes to rest. Because
the LET rises sharply near the track end, this can be
considered to be the most significant portion with
respect to biological effect (3). This phenomenon has
been described as a sting in the tail of electron
tracks(4).
Electrons with a low initial kinetic energy have a
higher average LET than their higher energy counterparts(5). Both high- and low-initial energy electrons
have a relatively high-LET tail, but a larger fraction
of the dose deposited by low-initial energy electrons
occur in the high-LET region of the trail. This implies
that low-energy electrons should have a higher RBE
than high-energy electrons. This has been confirmed
experimentally in numerous studies involving lowenergy electron emitters and low-energy photon
sources(6 – 9). Photon sources are relevant to the
electron RBE discussion because they deposit their
energy in matter almost exclusively through electron
production and because low-energy photons generate
low-energy electrons in tissue. Furthermore, there is
evidence that low-energy electrons produce more
complex damage than high-energy electrons(10).
The International Commission on Radiological
Protection (ICRP) has acknowledged that photons
and electron sources may have RBE values greater
than unity but recommends a radiation weighting
factor (wR) of 1 for electrons and photons(11, 12).
Rather than adopting a series of discrete, energydependent wR values like those recommended for neutrons in ICRP Publication 103, the ICRP maintains
that for radiation protection purposes, a single value
of 1 is adequate for photons and electrons of all
energies. The reasoning behind this decision is that
variations in the underlying RBE values are up to
a few-fold at low doses. Additionally, there is also a
few-fold variation in the uncertainty of the risk coefficient for cancer, so the ICRP does not ascribe different values for wR to different low-LET radiations.
Despite this, there have been recommendations for an
elevated RBE for tritiated water even for radiation
protection purposes(13).
While an electron and photon wR value of 1 may be
appropriate for radiation protection calculations, this
value may not be appropriate for risk calculations.
Radiation protection organisations generally observe
ALARA (as low as reasonably achievable) and deal
Published by Oxford University Press 2015. This work is written by (a) US Government employee(s) and is in the public domain in the US.
ELECTRON RBE VALUES
with doses that are well below known radiation danger
levels. Risk calculations, on the other hand, generally
deal with specific exposure scenarios and health endpoints (cancer). Thus, these calculations need to be as
accurate as possible. Therefore, the best known RBE
value for the specific scenario should be used to
produce the RBE-weighted absorbed dose.
The biological effect of radiation, and thus the
RBE, depends on several factors including dose, dose
rate, biological endpoint, cell type and fractionation.
Thus, selecting a single RBE value for a risk calculation is a non-trivial task. The most appropriate RBE
values for use in risk calculations are those from
experiments that closely match the calculation conditions such as endpoint, cell type and dose rate.
However, RBE values produced under similar experimental conditions may not be available. In these circumstances, experimental RBE values produced
under nearly similar conditions may be used as a
surrogate. In the absence of human cell RBE measurements, values for different endpoints or organisms(14, 15) may be used as a surrogate. There are some
cases where no RBE information is available, and the
radiation weighting factor has then been used as a
default value.
One important area with radiation risk concerns is in
the use of X rays in routine mammography screenings.
Due to their very low energy (26–30 kVp), the X rays
are likely to produce greater levels of biological effect
than high-energy gamma rays for the same absorbed
dose(16). A substantial component of epidemiological
data used to determine radiation risk is derived from
high-energy gamma rays(17). Therefore, if elevated RBE
considerations are not taken into account when determining the risk associated with mammography X rays,
then poor choices regarding the risk–benefit ratio of the
procedure may be made. As Brenner et al.(18) notes,
‘Because of the low doses involved in screening mammography, the benefit–risk ratio for older women would
still be expected to be large, though for younger women
the increase in the estimated radiation risk suggests a
somewhat later age than currently recommended—by
about 5 to 10 years—at which to commence routine
breast screening.’ Radiation risk concerns such as mammography screenings justify further study of low-energy
photon and electron RBE.
The appropriate RBE for low-energy electrons and
photons was identified by the Environmental Protection
Agency(17) as an issue to be resolved before updating
Federal Guidance Report 13(19). In this paper, an electron track code is used to derive RBE values across
a range of electron energies from 1 keV to 1.0 MeV
following the empirical approach of Nikjoo and
Goodhead(3). As the absorbed dose from photons is
due to liberated electrons, photon RBE values are
derived from the electron RBEs. The reference radiation
in the analysis is taken to be 1-MeV electrons, not
photon radiation as used for practical reasons in
experimental studies. Uncertainties in the derived RBE
values arise from the computational parameters and the
empirical approach itself.
APPROACH
In this section, the authors describe the empirical relationship between the energy of monoenergetic electron and RBE. Then, they describe the methods of
calculating photon, beta spectrum and radionuclide
RBE values.
In formulating the empirical relationship between
initial electron energy and electron RBE, the authors
assume that there is an energy below which the electron may cause significant biological damage(3, 20, 21).
The authors term that energy the threshold energy Ec.
When an electron deposits energy in matter, the electron will deposit a portion of the absorbed dose both
while it is above and below the threshold energy. The
authors define the term active dose as the total energy
of all the deposition events associated with an electron with kinetic energy below the threshold energy.
Additionally, the authors define the term average
active fraction F (Ec, E0) as the statistical mean of the
quotient of the active dose of an electron divided by
the initial energy of that electron. This quantity is
computed by determining the average active fraction
over a large population of monoenergetic electrons.
Since the average active fraction only considers the
biologically significant component of the electron
tracks, the authors assume that the RBE of electrons
is proportional to average active fraction.
Based upon this formulation, the authors define
the RBE of electrons with initial energy using the following empirical relationship:
RBEðE0 Þ ¼
FðEc ; E0 Þ
FðEc ; ER Þ
ð1Þ
where F (Ec, E0) is the average active fraction of an
electron with initial energy E0 and threshold energy
Ec. F (Ec, ER) is the average active fraction of the reference radiation with threshold energy Ec.
For example, consider a 1-MeV electron travelling
through the medium which first deposits 0.5 MeV
through low-energy deposition events and then produces two delta rays of 0.25 MeV each. For this scenario, the 50 % of the dose is deposited by electrons
with kinetic energy of ,0.25 MeV.
F (Ec, E0) is derived for individual electrons using
the New Oak Ridge Electron Code (NOREC)(22). As
the electron travels in the absorbing medium, its
energy deposition events are recorded as a function of
its kinetic energy immediately before the event. In the
definition of active dose, excitation events associated
with very low-energy secondary electrons (,100 eV)
are considered to be a part of the primary electron
track. Benchmark studies of NOREC with other
665
M. BELLAMY ET AL.
Monte Carlo codes have shown general agreement
across most electron initial energies(23, 24). Detailed
cross section data are available for electron interactions in liquid water, which serves as an acceptable
surrogate for tissue.
Although from an experimental point of view,
photons are a convenient choice for the reference radiation, the authors have adopted 1-MeV electrons as
the reference radiation.
RESULTS AND DISCUSSION
Fractional cumulative absorbed dose distributions
were compiled from the NOREC simulation of 30
monoenergetic electrons ranging in energy from 0.001
to 1.0 MeV. The simulations were carried out for a
total emission of 1 GeV for each monoenergetic electron, i.e. the number of simulated electrons ranged
from 106 at 1 keV to 103 at 1 MeV. The resultant cumulative absorbed dose distributions at several electron energies are shown in Figure 1. As evident in the
figure, a significant fraction of the absorbed dose is
deposited by low-energy secondary electrons, and the
fraction increases with decreasing initial electron
energy. Analysis reveals that low-energy interactions
account for 40 % of the absorbed dose when tissue
is irradiated by 1-MeV electrons. The cumulative dose
curves produced by NOREC are consistent with
those obtained by Nikjoo et al.(3) using MOCA8b(25).
The RBE values for monoenergetic electrons have
been calculated based on equation 1, assuming 1-MeV
electrons as the reference radiation for energy cut-off
values, ranging from 1.5 to 6 keV. For monoenergetic
electrons of energy of .0.8 MeV, the RBE values are
unity for all energy cut-offs. The values gradually increase with decreasing initial electron energy and approach a maximum value at the cut-off energy. The
maximum values are 3.09, 3.01, 2.72, 2.66, 2.53 and
2.44 at energy cut-offs of 1.5, 2, 3, 4, 5 and 6 keV,
respectively. As shown in Figure 2, the values are
consistent with experimental results suggesting that
low-energy electrons have an elevated biological effectiveness(8, 9). The dashed lines in Figure 2 correspond to
the RBE values assigned by Kocher et al.(13), i.e. a
median value of 2.4 (95 % confidence interval of 1.1 to
6.1) for electrons of energies of ,15 keV and a single
value of 1.0 at higher energies. This assignment was
largely based on the data for low-energy photons.
Beta particles
The RBE pure beta-emitting radionuclides such as
tritium are obtained by folding their beta spectra(27)
over the electron RBE values as follows:
Ð1
RBEðE0 Þ ¼
SðEÞE½RBEðEÞ dE
0
Ð1
ð2Þ
SðEÞE dE
0
where S(E) is the beta spectrum and RBE(E) is the
RBE as a function of electron energy as shown in
Figure 2. The RBE values for the beta-emitters vary
little with the assumed energy cut-off values. For
example, the RBEs for 3H and 14C, both common are
low-energy beta-emitters, range from 1.7 to 2.1 and
1.2 to 1.3, respectively, depending on the choice of
energy cut-off. An RBE of 2.0 for the tritium is consistent with an energy cut-off of 5 keV, and that cutoff value is adopted in the authors’ recommendations.
Photons
Figure 1. The cumulative fraction of absorbed dose
deposited by primary and secondary electrons as a function
of electron kinetic energy for initial electrons 10 keV to
1 MeV. The fractional contribution to absorbed dose by
interactions entered into at energies below a cut-off of 5 keV
is projected by the horizontal lines on the y-axis.
The absorbed dose from photon radiations arises
from secondary electrons liberated by photons undergoing photoelectric, Compton and pair production
interactions. RBE values for photons were derived by
folding the spectrum of liberated secondary electrons
over the electron RBE values in a manner similar to
equation (2). Secondary electron spectra were generated by generating the down-scattered photons in an
infinite media where the incident photon energy was
entirely transferred to the media. Additional secondary electron spectra were generated considering only
the first collision (interaction) of the incident photon.
These two methods of generating the electron spectrum provide upper and lower bounds on the average
number of photon interactions in the human body.
The photon RBE values are consistent with the experimental studies of Fabry and Wambersie(28), Roos
666
ELECTRON RBE VALUES
Table 1. Estimated RBE values relative to 1 MeV of electrons
for X rays as a function of voltage and filtering.
Voltage (kVp)
20
40
80
160
250
20
40
80
160
250
Filter (mm)
RBEa
1.2 Al
1.2 Al
1.2 Al
1.2 Al
1.2 Al
1.2 Al and 1 Cu
1.2 Al and 1 Cu
1.2 Al and 1 Cu
1.2 Al and 1 Cu
1.2 Al and 1 Cu
1.56
1.47
1.50
1.52
1.52
1.50
1.47
1.55
1.55
1.52
a
Assuming a tungsten anode and a threshold energy of 5 keV.
Figure 2. Electron RBE as function of energy and values
reported in various studies. The reference radiation is 1 MeV of
electrons and energy cut-off of 5 keV. The data points in the
figure are from Friedland et al.(26) and Nikjoo et al.(9). The
dashed line represents the recommendations of Kocher et al.(13)
1.9 (95 % confidence interval of 1.0 to 4.7), and above
250 keV, they assign an RBE of 1.0. In a footnote,
Kocher et al. noted that Frankenberg et al.(32, 16, 33)
indicated that the RBE for 25- to 30-kVp X rays is 4
relative to 200 kVp of X rays and 8 relative to 60Co
gamma rays. Goggelmann et al.(30) report values for
29-kVp X rays of 2 with 95 % confidence interval of
1.4 to 2.6. The higher values for low-energy X rays
have been observed in in vitro studies. Goggelmann
et al. suggested that infrequent change in the culture
medium, as in the experiments by Frankenberg et al.,
can cause fluctuations in the observed transformation
rates. The energy dependences in the photon RBE
values of Figure 3 are based on biophysical and microdosimetric principles.
Atomic bomb spectra
Figure 3. Photon RBE as function of energy and values
reported in various studies. The reference radiation is 1 MeV
of electrons. The experimental studies include Fabry and
Wambersie(28), Roos and Schmid(29), Goggelman et al.(30)
and Krumrey(31). The median values of the RBE probability
distributions recommended by Kocher et al.(13) are also
shown.
and Schmid(29), Goggelman et al.(30) and Krumey(31)
as shown in Figure 3. Also shown are the median RBE
bands assigned by Kocher et al.(13) in their review of
experimental data. For photon energies of ,30 keV,
their probability distribution has a median value of 2.4
(95 % confidence interval of 1.1 to 6.1); for energies
of 30 to 250 keV, the median of the distribution is
Egbert et al.(34) have tabulated the ground-level photon
spectra at Hiroshima and Nagasaki as a function of
ground distances from the hypocentre. The tissue
kerma-weighted mean energy of the spectra is 3.2 and
3.3 MeV at Hiroshima and Nagasaki, respectively. The
spectrum of secondary electrons liberated by the
photons within the body at 1500 m of ground distance
was calculated using the MCNPX code(35), and the
RBE was derived for a cut-off energy of 5.0 keV. For
both cities, the resultant photon RBE was 1.01, slightly
less than the 1.06 value for the 60Co gamma rays.
Based on this work, 60Co gamma rays are slightly
more effective than Hiroshima and Nagasaki photon
spectra, but not to the extent suggested by Straume(36).
Machine-generated photons
RBE values for machine-generated X rays were derived
in a manner similar to equation (2) using X-ray spectra
generated by the SpekCalc software package(37) along
with monoenergetic photon RBE values. These values
are listed in Table 1 for various voltages and filtration
667
M. BELLAMY ET AL.
assuming a threshold energy of 5 keV. The data show a
moderate increase in RBE values from 120- to 20-kVp
X rays. The additional filtering of 1 mm of copper
hardens the beam sufficiently to result in a slightly
lower RBE value at all voltages. No appreciable difference in RBE is indicated for 20- and 250-kVp X rays;
the derived RBE is in the range 1.4–1.6, which is consistent with observations of Goggelmann et al.(30) and
the recently published measurements by Depuydt
et al.(38). Based on this work, X rays used in mammography examinations (25–30 kVp) have an RBE in the
range 1.4–1.6 relative to the high-energy photon
spectra at Hiroshima and Nagasaki.
Radionuclides
Radionuclide-specific RBE values were calculated for
the radionuclides of ICRP Publication 107(27) for
which alpha emission or spontaneous fission is not
indicated as a mode of decay. The calculations assume
the radionuclide is uniformly distributed in the soft
tissues of the adult male. The calculation of the risk
coefficients in the revision of Federal Guidance Report
13 will include the age and gender specifics of the US
population and the distributions of the radionuclide
within the tissues of the body at radiogenic risk following inhalation and ingestion intakes. For illustrative
purposes, the nuclide-specific RBE for the hypothetical
total-body distribution is calculated as follows:
GþDþV
CþQþL
1
ð
1
SðEÞRBEE ðEÞdE
G¼
M
RBE ¼
0
1 X
D¼
Ei RBEE ðEÞYi ðEi Þ
M i
V¼
1 X
Ei RBEP ðEÞYi ðEi ÞSAFðEi Þ
M i
C¼
1
M
1
ð
ð3Þ
Y ðEÞE dE
0
Q¼
X
Ei Yi ðEi Þ
i
L¼
X
Ei Yi SAFðEi Þ
i
where the first term of the numerator G is the contribution of beta emissions (if applicable) to the RBEweighted absorbed dose, the second term D is the
contribution of discrete electrons and the third term V
is the contribution of photons (X- and gamma-rays).
The denominator (C þ Q þ L) is the unweighted
Figure 4. Scatter plot of nuclide-specific RBE values. The
reference radiation is 1 MeV of electrons, and a 5 keV of
energy cut-off is assumed. The values were derived assuming
the radionuclide is uniformly distributed in the soft tissues of
the body. The majority of the radionuclides with RBE values
of .2 decay by EC, which is followed by a cascade of lowenergy Auger and Coster-Kronig electrons.
absorbed dose. The mass of the tissue over which the
dose is averaged is denoted by M and the energy and
yield of the emitted radiations by E and Y, respectively. S(E) denotes the beta emission intensity as a function of energy(27). SAF denotes the specific absorbed
fraction of the photon energy absorbed in the soft tissue
of the body per unit mass, and RBEE and RBEP are the
monoenergetic electron and photon RBE values.
The radionuclide-specific RBE values for 1070
radionuclides based on an energy cut-off of 5 keV are
shown graphically in Figure 4. For 56 % of the radionuclides, the RBE values are ,1.1. About 31 % have
RBEs between 1.1 and 1.3, and 7 % have RBEs
between 1.5 and 2. Seventeen radionuclides are identified with an RBE of 2 or higher as shown in Table 2.
The decay modes b2, bþ EC and IT denote beta
minus, beta plus, electron capture (EC) and isomeric
transition, respectively, and the units of the physical
half-lives abbreviated as m, d and y are minute, day
and year, respectively. The majority of the above
nuclides decay by EC, which is followed by a cascade
of low-energy Auger and Coster-Kronig electrons.
Only three of the nuclides (3H, 59Ni and 187Re) are
beta-emitters(27); 59Ni-dominant mode of decay is by
EC not by beta-plus (positron) emission. The average
energy of electrons emitted in the decay of 3H, 59Ni
and 187Re is 5.7, 4.5 and 0.62 keV, respectively.
Auger emitters are able to generate multiple shortradiation tracks starting at the same location and may
therefore have an increased potential to cause
complex DNA damage. This is particularly true if the
auger emitter is bound to the DNA strand. This effect
has not been addressed in this work, and these radiations are treated as regular electrons. Further effort
concerning the RBE of auger emitters is needed(1).
668
ELECTRON RBE VALUES
Table 2. Radionuclides identified with an RBE of 2 or
greater.
Radionuclide
3
H
Ar
41
Ca
49
V
53
Mn
55
Fe
59
Ni
68
Ge
71
Ge
123
Te
142
Pr
157
Tb
163
Ho
187
Re
193
Pt
194
Hg
205
Pb
37
Decay mode
Half-life
b2
EC
EC
EC
EC
EC
EC b þ
EC
EC
EC
IT
EC
EC
b2
EC
EC
EC
12.32 y
35.04 d
1.02` 105 y
330 d
3.7` 106 y
2.737 y
1.01` 105 y
270.95 d
11.43 d
6.00` 1014 y
14.6 m
180 y
4570 y
4.12` 1010 y
50 y
440 y
1.53` 107 y
upon the same approach using a threshold energy of 5
keV. This energy cut-off value is consistent with the one
that yielded a tritium RBE of 2. Based upon the electron and photon RBE values estimated as a function of
energy, the authors have produced radionuclide-specific
RBE estimates for 1070 radionuclides. For 56 % of
the radionuclides, the RBE values are ,1.1. About 31
% have RBEs between 1.1 and 1.3, and 7 % have
RBEs between 1.5 and 2. Seventeen radionuclides are
identified with an RBE of 2 or higher. Most of the
radionuclides with an RBE of .2 decay by EC followed by a cascade of auger electrons. The authors have
estimated RBE values in the range 1.4–1.6 for X rays
used in mammography examinations.
ACKNOWLEDGEMENTS
This work was supported by the U.S. Environmental
Protection Agency Office of Air and Radiation and
was prepared by Oak Ridge National Laboratory,
managed by UT-Battelle, LLC, for the U.S.
Department of Energy.
Summary
Uncertainties in the derived RBE values arise from
several sources including the empirical model, using
water as a tissue surrogate, and the electron code.
The major source of uncertainty is from the use of
the simple empirical model. This model does not incorporate the mechanics of the underlying biological
processes involved in the RBE endpoint and relies
on a simple empirical assumption about the electron
track and biological effect. Another source of uncertainty is the use of water cross sections for the electron transport instead of tissue cross sections. At the
time that this work was done, water electron cross
section data were the most appropriate data set to use
as tissue cross section data were unavailable. Another
set of uncertainty is the set of assumptions made in
the electron transport code used to simulate the track
information.
CONCLUSION
Complex damage to DNA caused by passing electrons
has been shown to be greatly enhanced near track ends
where there is an increase in ionisation density. Thus, it
is reasonable to assume that RBE of electrons and
photons may be strongly associated with the fraction of
dose deposited by electrons below some threshold
energy. In this work, RBE values were derived based
on this assumption. This led to an estimated RBE of
2 for tritium beta particles relative to gamma rays of
1 MeV or greater. The value 2 is in reasonable agreement with radiobiological data published on tritium
RBE values.
Additionally, the authors have estimated the RBE of
electrons and photons as a function of energy based
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