RADIATION RESEARCH 182, 587–598 (2014)0033-7587/14 $15.00
Ó2014 by Radiation Research Society.
All rights of reproduction in any form reserved.
DOI: 10.1667/RR13663.1

Accounting for Neutron Exposure in the Japanese Atomic Bomb Survivors
Harry M. Cullings,a,1 Donald A. Pierceb and Albrecht M. Kellerer caRadiation Effects Research Foundation, Hiroshima and Nagasaki, Japan; b Oregon Health Sciences University, Portland, Oregon; and c LudwigMaximilians University, Munich, Germany

INTRODUCTION
Cullings, H. M., Pierce, D. A. and Kellerer, A. M.
Accounting for Neutron Exposure in the Japanese Atomic
Bomb Survivors. Radiat. Res. 182, 587–598 (2014).

The Life Span Study (LSS) of late effects such as theincreased incidence of leukemia and of solid cancers among
the atomic bomb survivors in Hiroshima and Nagasaki has
long been the major basis for radiation risk assessment.
Although this large epidemiological study of the Radiation
Effects Research Foundation (RERF) has successfully
evolved for more than half a century, it continues toprovide new insights and to improve the methods ofanalysis. However, one critical issue that continues to be
discussed is the impact of the neutron dose on risk
assessment because even though neutrons contribute only
a very small fraction to the absorbed dose in A-bombradiation, it nevertheless must be taken into account because
neutrons are a densely ionizing radiation that create more
effect per unit dose than the predominant c rays.
The primary motivation for considering the neutron
effects in the LSS data is to account for them in order tomore precisely estimate the c-ray effects. To assess the dose
contribution of neutrons, information on their relative
biological effectiveness (RBE) is required for comparison
to the high-energy c rays of the A-bomb radiation. It is wellknown that the neutron doses in the LSS data are too small
and are too highly correlated with the c-ray doses to allow
useful estimation of the RBE from the late effects data.
In published articles by Shimizu et al. and othercolleagues (1–4) the obtained neutron dose estimates havevery broad confidence limits. Several of these studies
attribute any city differences in late effects to the larger
neutron doses in Hiroshima, which is questionable. Little(3) for example, used tentative revised Hiroshima neutron
estimates that turned out to be much too large. It should also
be noted that analyses outside of RERF have been done
without access to neutron and c-ray dose estimates forindividual survivors, using instead the mean values in crosstabulations based on weighted total dose described below.
In view of increasing statistical capabilities and improved
dose estimates in recent years, RERF analysts havecontinued to assess this matter. The most recent work
remains unpublished, further demonstrating the difficulty ofthis approach. These new findings confirm that, as is typicalwith such highly collinear variables, statistical methods forthis purpose are non-robust and unsatisfactory [e.g., see

The Japanese atomic bomb survivors that were directly
exposed to both c rays and neutrons have been followed by
the Radiation Effects Research Foundation (RERF). The
estimation of the c-ray risks requires some adjustment for
the greater biological effect of the neutrons per unit dose.
Because the small neutron doses and the predominant c-ray
doses are highly correlated, the neutron relative biologicaleffectiveness (RBE) cannot be reliably estimated from thesurvivors’ data and information from radiobiology must be
invoked. As data became available on neutron doses, RERF
has used a constant neutron RBE value of 10, even thoughradiobiological studies indicate that the RBE values appear
to have considerably larger values at low doses. The approximation RBE = 10 assumes that if the RBE is variable ittakes roughly this value in the range of total dose most
relevant for linear risk estimation, namely about 1 Gy. We
consider some possible RBE functions to explain the correct
use and the impact of a dose-dependent RBE. However, we
do not advocate any particular choice or even that a variable
RBE be employed. Rather we show that the assumed
neutron RBE, within a wide range of choices, is far lessimportant to the outcome of risk assessment of the RERF
data than generally believed. Some of these misperceptions
have been related to the consideration of variable RBE
functions, and without due attention to the fact that in thecase of the A-bomb survivors’ data, the mixed field of
neutrons and c rays must be considered. Therefore, the RBE
value of neutrons is much lower than the RBE in pureneutron fields that are used in radiobiological experiments.
Thus, applying the pure neutron field RBE to the mixedfield A-bomb radiation can lead to an overestimation of theactual neutron RBE for moderate total dose levels of 1 Gy
by a factor of more than four. While in a pure neutron
exposure the RBE depends on the neutron dose, in the mixed
field it depends on both components of exposure, and inparticular, we show that in the RERF setting the RBE
depends mainly on the accompanying c-ray dose. Ó 2014 by
Radiation Research Society

1 Address for correspondence: Statistics Department, Radiation
Effects Research Foundation, 5-2 Hijiyama Park, Minami-ku,
Hiroshima 732-0815 Japan; e-mail: hcull@rerf.or.jp.

587

588

CULLINGS, PIERCE AND KELLERER

section 3.8 of ref. (5)]. In particular, it was found that theestimation of RBE remains grossly oversensitive to small
portions of the data.
Since there are no other data available in humans forleukemia or solid cancers caused by exposure to neutronradiation we must rely on the dose-effect relationships forcell damage obtained in experimental radiation studies.
These dose relationships are often linear quadratic forsparsely ionizing radiations, such as c rays; the initial slope
is small, but there is substantial upward curvature, i.e., theadded effect of an increment of dose increases as the dose
increases. For densely ionizing radiation, such as neutrons,
the dose relationships are steep but roughly linear, and theeffect per unit dose is high but does not increase with dose.
Under these circumstances the efficiency of neutrons
relative to c rays is large at lower doses of c rays anddecreases at higher doses. How to potentially utilize such
experimental information for neutron RBE will be outlined
later in this article.
It is important to note that RBE is similar to, but must be
distinguished from the radiation weighting factor, wR, which
was adopted by the International Commission on Radiological Protection (ICRP) for radiation protection purposes.
wR relates to low doses and/or low dose rates, and isintended as a regulatory factor rather than for risk
estimation. In this article, we use the term ‘‘RBE’’ to referto the function that takes on values R to be applied as weightfactors for the neutron component in the A-bomb radiation.
The concept of neutron RBE does not merely refer to low
doses or low dose rates, nor is it restricted to the comparison of
a neutron dose with the equivalent c-ray dose. Suppose that,for a given biological end point, the effect of a joint dose (Dc,
Dn) is the same as that of a c-ray dose Dc þ D alone. Then the
additional c-ray dose, D, is equivalent to the neutroncomponent and the RBE value is defined as R = D/Dn. Notethat this implies that R will generally depend on both Dc and
Dn. The product RDn equals the additional c-ray dose, D,
equivalent to Dn, and is here termed the ‘‘weighted dose’’ dueto the neutrons. The sum Dc þ RDn is the total weighted doseand equals the c-ray dose that is equivalent to Dc þ Dn.
If the dose-effect relationships are linear both for neutronsand c rays, the RBE is dose independent. Otherwise, if forexample the c-ray response is upward curved and theneutron response is linear, R decreases with increasing c-ray
dose since decreasing increments of c-ray dose are thenrequired to produce a given increase in effect. While R
decreases with the increase of the neutron dose when a pureneutron exposure is compared to a c-ray exposure, the RBEof a neutron dose decreases with increase of both theneutron dose and c-ray dose when a neutron dose isaccompanied by a c-ray dose, as in the A-bomb survivor
setting (Fig. A3). The RBE function will thus be different
for the two settings: (1) converting a pure neutron dose to an
equivalent c-ray dose; and (2) converting the neutron doseto an equivalent additional increment of c rays when the
exposure is already a combination of neutrons and c rays(for details about this distinction, see the Appendix section).
For clarification, the term ‘‘pure neutron RBE’’ refers to aneutron exposure alone, while the term ‘‘mixed-field
neutron RBE’’ refers to the neutrons in the combined
exposures to the A-bomb radiation.
The dependence of the RBE on neutron and c-ray dose iscentral to our analysis, because there have been several
instances where the pure neutron RBE has been applied tomixed-field A-bomb radiation and the decrease of the RBE
due to the simultaneous, much larger c-ray dose has been
disregarded. This has led, for example, Sasaki et al. (7) toconclude that neutrons are responsible for more than 40% of
the solid cancer risks in Hiroshima. This type of error,
confusing the pure neutron RBE with the mixed-field
neutron RBE, was also made by Rossi and Zaider (6).
Even though it was anticipated that the DS02 revision
would lead to substantially increased neutron doses, [e.g.,
Straume et al. (9)], this did not materialize, and the belief ina substantial neutron contribution to the late effects among
the A-bomb survivors remained because of the confusion
discussed above. In the current analysis the dosimetric data
for the LSS cohort are employed to elucidate the choice of
the RBE function and to demonstrate that, within broad
limits, it has such a small effect on the RBE-weighted dosesthat it cannot appreciably affect the c-ray risk estimatesobtained from the LSS late effects data.
We present the main results here not in terms of actual
risk estimation, which would require a very different type ofarticle, but by considering merely the change of weighted
dose caused by different RBE functions. A minimal
exception is made for some comments on Figs. 2 and 3,
where the specific points are best supported by cancer risk
estimates.
OVERVIEW OF THE c-RAY AND NEUTRON DOSESTO THE A-BOMB SURVIVORS

Scatter Plots of Individual Doses in the Life Span Study(LSS) Cohort

The dosimetry data used in this study are the current
dosimetry system DS02 colon dose estimates used foranalysis of all solid cancers together, with some suitable
downward adjustment for dose estimation errors (10). The
data are described in an earlier article on the DS02 doses(11). The adjustment for dose estimation errors applies
equally to the neutrons and the c rays, and it varies with
dose, ranging from none at total doses around 0.05 Gy toabout a 10–15% dose reduction in the higher part of thedose range. The LSS cohort comprises 120,321 individuals,of whom 26,580 were not in either city at the time ofbombing, and another 7,070 do not have calculated dose
estimates due to difficult shielding situations. After omitting
317 survivors with unweighted total (neutron þ c ray)shielded kerma estimates greater than 4 Gy as calculated bydosimetry system DS02, there were 58,324 survivors who

ACCOUNTING FOR NEUTRONS IN ATOMIC BOMB SURVIVORS

589

FIG. 1. Neutron/c-ray ratios, qn vs. c-ray dose for Hiroshima (left panel) and Nagasaki (right panel). The
points represent individual survivors. The three gray curves indicate the median and the 10 and 90% quantile ateach c-ray dose.

were in Hiroshima and 28,030 survivors who were in
Nagasaki at the time of the bombing and have dose
estimates. Many of these have very small or zero doses andfor most purposes here we restrict to those with unweighted
total (neutron þ c ray) colon dose estimates above 0.05 Gy:
19,307 survivors in Hiroshima and 4,961 in Nagasaki. For
some plots, such as the first one, we further restrict ouranalysis to those with colon doses greater than 0.1 Gy.
Figure 1 shows scatter diagrams pertaining to theseadjusted colon-dose estimates in Hiroshima and in Nagasaki. Logarithmic dose scales are employed on both axes forbetter readability at low doses, and furthermore the graph is
simplified by plotting the neutron/c-ray dose ratios, qn, on
the ordinate, instead of the neutron dose. The three graycurves indicate the median, 10% quantile and 90% quantile
at each c-ray dose, obtained by a suitable nonparametricsmoothing procedure.
The fractional contribution of the neutrons to the absorbed
dose is roughly 5 times larger in Hiroshima than in
Nagasaki. In Nagasaki the neutron doses are too small
relative to the c-ray doses to be of much interest, howevereven in Hiroshima they are only about 0.2% of the c-ray
dose at a c-ray dose of 0.1 Gy, 0.7% at 1 Gy and about 1%
at 2 Gy. The ratios qn for shallow organs such as thyroid andbreast are somewhat larger than those for colon, but not somuch that the conclusions of the following analysis would
be affected. Neutron doses are proportionally smaller atlarger distances and lower c-ray doses because neutrons are
more rapidly attenuated in air than c rays.
The equation:
qn =Dn =Dc =0:007D0:5cð1Þ

with dose expressed in Gy, serves as a rough parametricapproximation for the average neutron/c-ray ratio in
Hiroshima. The standard deviation of the neutron dose ata specified c-ray dose is of the order of 30% of the mean,
due to differences in radiation shielding among individual
survivors.
ASSESSMENT IN TERMS OF CONSTANT RBE

We begin with the simplest treatment of neutron
effectiveness: a constant RBE for neutrons as found witheffects such as point mutations where the dose relationships
are linear both for sparsely ionizing and densely ionizing
radiation. For the purpose of the current analysis, we leave
open whether a constant or a variable RBE applies.
Information from experimentally observed linear-quadratic
dose relationships for photons and linear relationships forneutrons will be considered in the subsequent sections.

590

CULLINGS, PIERCE AND KELLERER

Although a constant RBE need not apply to the lateeffects in the LSS, this is a very conservative approach thathas served as a reasonable approximation in the major
analyses at RERF. The rationale has been that even if the
RBE varies with dose, the value R = 10 represents its value
in the dose range most influential for linear risk estimation,
namely about 1 Gy. An alternative, conservative choice fora constant R at the value 20 will be considered later.
According to Eq. (1) the average weighted dose due toneutrons in Hiroshima is approximately:
RDn =0:007RD1:5
c ;

ð2Þ

for dose in Gy. With the customary RERF choice of aconstant R = 10, the weighted dose from neutrons is 5% of
the c-ray dose when the c-ray dose is 0.5 Gy, 7% at 1 Gy
and 10% at 2 Gy. For R = 20 these values are doubled. This
gives a perspective on the fraction of effect attributable toneutrons. Since the neutron/c-ray dose ratio increases withc-ray dose, the inferred relative contribution of neutrons isgreatest at high doses if the value of R is taken as constant.
However, there are reasons to believe that the true RBE is
not constant, but decreases with increasing dose, and it is theconcept of such a variable RBE that has given rise to most of
the issues that we intend to address. The appropriate low-dose
RBE to use for the LSS cancer data is uncertain, but could well
be close to 100. The rest of this article mainly concerns thesignificance of such a variable RBE for the many RERF
purposes.
ASSESSMENT IN TERMS OF VARIABLE NEUTRON
RBEParameters Inferred from Radiobiology

In a wide range of experimental radiation studies, and inline with microdosimetric parameters, the dose-effectrelationships for cell damage, such as chromosome
aberrations, have been linear quadratic with linear terms
substantially dependent on the linear energy transfer (LET)of the radiation. We review here potential implications for
the RBE of neutrons, although they need not necessarily
apply to the cancer risk estimation from the LSS data.
At the energies prevalent in the A-bomb radiation the linear
term of the dose response for (high-LET) neutrons dominates
sufficiently that the quadratic term can be disregarded.
Accordingly the effect, E, of a combined exposure with c-ray
dose Dc and neutron dose Dn is taken to be:EðDc ; Dn Þ = bðDc þ Rmax Dn þ hD2c Þ:ð3ÞThe coefficient b is the initial slope of the dose-effectrelationship for c rays. With this factorization, the formulafor RBE involves the two parameters Rmax and h. The
parameter Rmax is the ratio of the initial slopes for neutronsand c rays. Rmax equals as indicated by the notation, themaximal neutron RBE at low doses. The other parameter his the ratio of the coefficients of the quadratic and thelinear term in the dose relationship for c rays. Although h
has the dimension Gy1, it is termed ‘‘curvature’’ because alarge value implies a strongly curved dose-effect relationship. Its reciprocal is referred to as the crossover dose,since 1/h is the dose where the quadratic term equals thelinear term.
With the RERF data in view, Sasaki et al. (7, 8) have
performed an in-depth study of chromosome aberrations byneutrons and c rays in human lymphocytes. The parameters
they inferred were roughly Rmax = 90, h = 4 Gy1. These
parameters agree well with data for chromosomal aberrations obtained in earlier studies with neutrons and c rays
(12–14). They are also consistent with LET data andmicrodosimetric parameters for neutron and photon radiation (15). Detailed investigations on the yield of chromosome aberrations in dependence on neutron and photon
energy (16–18) suggest that the above parameters apply tothe hard c rays and the moderately energetic neutrons (,1MeV) that prevailed in the A-bomb radiation.
In addition to deriving precise results for chromosome
aberrations, Sasaki et al. (8) sought to obtain data fromanimal cancer experiments in the literature. From eightstudies on solid cancers in rodents they inferred widely
varying parameters with mean values, Rmax = 87 6 35 and h= (4.5 6 2.1) Gy1 that were consistent with those forchromosome aberrations. Therefore, they applied essentiallythe same parameters to their analysis of the chromosome
aberration and the solid cancer data in the A-bomb
survivors. For comparison, Brenner and Hall (19) in theirassessment of the neutron contamination in proton therapy
beams referred to the analysis in NCRP Report No. 104 (20)and the majority of Ullrich’s mouse data which, likewise,provided widely varying values of 59, 36, 6, 19 and 33 forRmax.
The parameters from the animal studies must be viewed
with caution not only because of their inherent differences,
but because they are derived under the assumption of linear
and linear-quadratic dose relationships although the observed relationships for cancer in rodents bend over at
moderate and high doses and tend to be poorly defined at
low doses. This also underscores the need to distinguish thedose relationship for primary cellular lesions and that for theultimate late effects that develop at much later time periods.
Primary Lesions vs. Late Effects

A variable RBE may appear implausible for humancancer, because the excess cancer rate in the LSS is far
more linear than that seen in chromosome aberration
studies or in animal tumor studies. For all solid cancers
together in the RERF data the upward curvature on 0–2
Gy is quite small, and on the full dose range there isdistinct leveling off above that dose range [see Fig. 2
from ref. (10)]. For leukemia there is somewhat morecurvature but nothing like that seen in chromosome
aberration experiments.

ACCOUNTING FOR NEUTRONS IN ATOMIC BOMB SURVIVORS

However, there is no reason to assume that the excess
relative risk (ERR) for late effects must be proportional to
the number of initial lesions. The observed increase of
ERR may have less curvature than the dependence of theinitial lesions because of intervening processes, such as the
body’s mechanisms for dealing with malignant cells. To
the extent that such mechanisms act independently ofradiation quality, the appropriate RBE for analysis ofcancer will still be that for the initial cellular damage. The
studies with neutrons and X rays on the incidence of
mammary tumors in rats by Shellabarger et al. (21, 22) area case in point. These experiments were specificallyfocused on low neutron doses and they demonstrated that
depending on the end points considered, e.g., tumor
incidence at specified time after exposure or mean time tothe tumor, the dose relationships differed substantially. But
even when the dose relationship was roughly linear for X
rays and roughly proportional to the square root of theneutron dose, high values of R max near 100 wereconsistently obtained, as was the decrease of RBE withincreasing dose.
The need to distinguish the dose relationship for initiallesions and for late effects appears to have been overlooked
when a highly variable RBE was rejected in view of thenearly linear cancer rates in the LSS. However, weemphasize that even if a dose-dependent RBE is used, the‘‘risk extrapolation’’ from moderate to low c-ray doses must
be based on the observed dose relationships for the end
point in question and not, as is often assumed, on a
postulated linear-quadratic dependence for initial lesions.
In the subsequent sections we evaluate the impact of theneutrons on the LSS data in terms of some parameter setsthat are representative of the range suggested by theexperimental results. For this purpose we do not invoke
definitive parameter estimates for human cancer. The aim is
to demonstrate the impact on the c-ray risk estimates interms of a wide range of potential values.
Parameters to be Considered in the Analysis

We provide an equation in the appendix section [Eq.
(A3)] for the mixed-field neutron RBE, as appropriate forthe LSS data. For comparison we also present an equation in
the appendix section [Eq. (A5)] for the pure neutron RBE
because it was used by Sasaki for the A-bomb survivors’
data, in spite of the mixed-field setting, which resulted inmuch larger values of R than does Eq. (A3). As it happens,
Eq. (A3) is rather complicated, however, the RBE for the
relatively small neutron doses in the mixed-field A-bomb
exposures can be well approximated by the simpler
relationship in Eq. (A4), which means that it depends only
on the c-ray dose as in Eq. (4):
Rmax
:
R=
1 þ 2hDc

ð4Þ

591

The magnitude of the RBE at 1 Gy is particularly relevant
to RERF linear risk estimates, i.e., to estimates based on
the assumption of linear dose relationships. Statisticians at
RERF have long realized (22) that nearly the same linear
risk estimate is obtained whether one uses a dose
dependent or a constant RBE, provided the values areequal at 1 Gy. The linear risk estimate is simply rescaledby the inverse value of the weighted dose at 1 Gy. This
result is specific to the particulars of the LSS cohort, where
the neutron fraction is vanishingly small at low doses (seeFig. 1), and it applies to linear risk estimation that uses
most of the available dose range. For cancer risk
estimation with constant RBE, changing R from 10 to 20
reduces the linear risk estimate by about 5%, which isabout half of the standard error of the risk estimate.
According to the reasoning just given, this reduction factor
will also roughly apply for variable RBEs with R values of
20 instead of 10 at a 1 Gy total dose.
The RBE at 1 Gy total dose being the essential reference
value, we can use instead of (Rmax,h) the more directly
descriptive parameters (Rmax, R1), where R1 = Rmax/(1 þ 2h)
is, according to Eq. (4), the RBE at 1 Gy for the mixed fieldwith dominant c-ray contribution. Eq. (4) is then reexpressed as
R=Rmax =ð1 þ ðRmax =R1  1ÞDc Þ

ð5Þwith Dc in Gy.
There has been a consensus view that the value of avariable RBE suitable for the middle range of doses for Abomb survivors, namely about 1 Gy, should be around 10 or
20. The chromosome aberration experiments provide interms of Eqs. (4) or (5) the value R1 = 10. A mixed-field
neutron RBE of about R1 = 10 is also the correct result of
the Sasaki (8) synopsis of the eight experiments involving
solid cancer in rodents, although those authors obtained amuch larger value by employing the formula for a pureneutron RBE.
The parameter pair Rmax = 90, h = 4 Gy1 is equivalent toRmax = 90, R1 = 10 and the corresponding RBE is denotedby RBE(90,10). However, for our purposes in thesubsequent sections of this article, we will utilize a rather
wide range of RBE functions that have been chosen toreflect the possibilities indicated by the results considered
above. We will express these choices in terms of theparameter pair Rmax, R1 as RBE(100,10), RBE(100,20),
RBE(10,10), RBE(20,20). The wide range of Rmax is in linewith the chromosomal and solid cancer experiments, and thetwo values of R1 are employed because this variation affects
the risk estimation differently.
THE LIMITED IMPACT OF THE NEUTRONS

To judge the impact of the use of various RBE functions
one can compare the total weighted dose, Dw = Dc þ RDn,for various assumed RBE functions. In Fig. 2, three

592

CULLINGS, PIERCE AND KELLERER

FIG. 2. The total weighted dose, Dw = Dc þ RDn, that results for Hiroshima with the mean neutron doses [Eq.
(1)] and the RBE according to Eq. (5) with RBE(100,20) (upper solid line) or RBE(100,10) (lower solid line),
i.e. with RBEmax = 100 and with RBE at 1 Gy equal to 20 or 10; the corresponding curvature parameters h are
2 Gy1 and 4.5 Gy1. The points represent the individual values obtained with constant R = 10. The comparison
shows that there is small difference between the use of the variable and the constant RBE.

alternative total weighted doses for Hiroshima are plottedversus Dc. The solid lines give the median total weighted
dose, Dw, which results with the choices of RBE(100,10),
upper curve and RBE(100,20), lower curve. The narrowcloud of points represents the total weighted doses for the
A-bomb survivors obtained with the RBE(10,10) commonly assumed in the analyses of the LSS data. The
scatter of the points is entirely due to the variations of theneutron/c-ray ratio for individual survivors due toshielding.
The risk estimation changes corresponding to thealternative weighted doses in Fig. 2 are well within thestatistical uncertainties of risk estimation from these
epidemiological data. For the cancer mortality data of LSS
Report 12 (23) the coefficient of variation of nonparametric
ERR estimation (i.e., smoothing of dose-category ERRs) is
about 20% for doses over 0.25 Gy, about 60% for doses ofaround 0.15 Gy, and greater than 80% for doses of 0.05 Gyor less. For the most recently evaluated cancer incidence
data (24), the corresponding coefficients of variation areabout two thirds of those for the cancer mortality.
Figure 3 illustrates the comparison (left and right panels)in terms of ratios rather than differences. The panels show
the ratio of the total weighted dose computed with thevariable RBE and with constant R = 10. The variable RBE

corresponds to the parameters of RBE(100,10) (left panel)or RBE(100,20) (right panel). The gray lines represent themedians of the dose ratios.
It was noted above that the magnitude of the RBE
adjustment at 1 Gy is particularly relevant to linear cancer
risk estimates from the LSS data. Either choice,RBE(100,20) or RBE(20,20) results in about 5% smaller
excess relative risk estimates than the choices ofRBE(100,10) or RBE(10,10), respectively. This is roughly
one half the standard error of the risk estimates. On the other
hand, linear risk estimates for choices RBE(100,10) andRBE(10,10) differ by less than 0.5%, and the same applies
for choices RBE(100,20) and RBE(20,20). These relationships hold for either Hiroshima or both cities together.
The variation in Fig. 3 raises the question of whether with
RBE(100,10) or RBE(100,20) the larger weighted doses
under 0.5 Gy might alter perceptions about low-dose cancer
risks from c rays based on the constant R = 10, that is,perceptions regarding possible thresholds or low-dose
linearity. However, this is not the case, largely because
the neutron/c-ray ratio is so small for small doses [see Eq.
(1)]. For either of those variable RBE functions the excess
relative risk estimates for low-dose ranges of 0–0.025 Gy,
0–0.05 Gy and 0–0.075 Gy decrease by about 3%, andthose for low-dose ranges of 0–0.10 Gy, 0–0.15 Gy and 0–

ACCOUNTING FOR NEUTRONS IN ATOMIC BOMB SURVIVORS

593

FIG. 3. The ratio of the total weighted doses, Dw, computed with variable RBE to the weighted dose obtainedwith the constant R = 10. The points represent the values obtained with RBE(100,10) (left panel) andRBE(100,20) (right panel), the corresponding curvature parameters h are 4.5 Gy1 and 2 Gy1. The gray lines are
based on the median neutron doses.

0.20 Gy decrease by about 6%. These risk estimates arecomputed from the dataset of this article, we used the same
methodology as that used for Fig. 5 from the LSS Report 14(25), which has long been standard in RERF reports. These
3 and 6% reductions are very small relative to the risk
estimation standard errors in these low-dose ranges,
resulting in no change of perceptions regarding low-dose
cancer risks from c rays.
Figure 4 compares the constant R = 10 (left panel) to thevariable RBE(100,10) (right panel) in terms of the ratio of
total weighted dose, Dw, to absorbed dose. This ratio can betermed the ‘‘net RBE’’ of the radiation in Hiroshima, and isabout 1.07 in the most relevant dose range, confirming
again that the neutrons are not a critical issue in the risk
estimates derived from the LSS data.
The essential finding we have made here is that it makes
little difference whether the simple approach in terms of aconstant R = 10 or a variable neutron RBE is used. Past
suggestions that the neutrons have substantially contributed
to the late health effects were based on the large RBE values
that are inferred by using the pure neutron RBE instead ofthe mixed-field RBE. As mentioned, based on a wide arrayof experimental data, Sasaki et al. (7, 8) arrived at an RBEfunction with approximately Rmax = 90 and curvatureparameter h = 4.5 Gy1, which corresponds approximately
to our RBE(100,10). By using the RBE formula for pureneutron exposures [see Eq. (A5)], they arrived at a value ofabout R1 = 40, rather than the value R1 = 10 that would
actually be calculated from parameter values in the mixedfield radiation equations. Thus their conclusions correspondroughly to an RBE function we would denote asRBE(100,40). Because LSS risk estimation hinges substantially on the RBE at 1 Gy, this led to considerably
underestimated cancer risk estimates for c rays and to theirclaim of a substantial contribution of the neutrons to the lateeffects in the LSS.
CONCLUSION

The findings presented here indicate that c-ray risk
estimation from the LSS data is affected very little by the
choice of the RBE for neutrons. We refer here to the use of aconstant RBE versus variable, dose-dependent RBE that has
been suggested based on radiobiological experiments. This
topic may benefit from the clarification provided here,
because many observers have been skeptical of RERF’s useof a constant RBE in light of evidence from experimentsthat the low-dose neutron RBE tends to be larger than atintermediate or high doses. In addition, there has been somemisperception about the formulation of a variable RBE thatis suitable for LSS data, because the distinction between
pure-neutron and mixed-field exposures has been neglected.

594

CULLINGS, PIERCE AND KELLERER

FIG. 4. The ratio of total weighted dose, Dw, to absorbed dose, i.e., the ‘‘net RBE’’ of the A-bomb radiation in
Hiroshima, as it is obtained in terms of the constant R = 10 (left panel) and the dose-dependent RBE(100,10)(right panel).

We hope that the findings in this article will be helpful to
RERF.
We believed that our primary investigation should, to theextent possible, be based on the effect of the RBE function
on the total weighted doses used in risk estimation, rather
than on fitting specific risk models. Thus, Fig. 2 indicatesthat for linear risk estimation over a wide dose range,
results will be nearly equivalent for a constant RBE of 10
versus a variable one with the same value of 10 at 1 Gy,
but much larger values at low doses. We express the value
at 1 Gy as R1 and the limiting value at low doses as Rmax.
RBE functions with R1 = 20 versus R1 = 10, somewhat
independently of Rmax, do result in a modest decrease inlinear risk estimates of about 5%. This decrease is nottotally negligible in comparison to the inherent uncertaintyof the risk estimation, since it is about one half of thestandard deviation in the risk estimate.
However, it is difficult to be sure that in every respect therisk estimation would be negligibly affected by assuming alarge low-dose RBE, such as Rmax = 100. This is the reason
that we investigated the distinction in low-dose risk
estimates presented in relationship to Fig. 3. Those results
support the general conclusions above, but we do not wantto overstate the position that for nearly all risk estimation
purposes, the choice of RBE function matters little.
Postulating a plausible dose-dependent RBE function
remains conjectural, but guidance by the family of LQ

models of Eq. (3) is valuable and it provides the RBE
function given by Eq. (A3). The fact that this equation israther complicated may be one reason for the repeatederror of using in its place the simpler Eq. (A5) that
corresponds to the familiar experimental setting wherepure neutron doses are compared to pure c-ray exposures.
Fortunately, a much simpler formula based on Eq. (A4)and Fig. A3 applies to the LSS data, where the neutroncomponent is always relatively small. In those circumstances, the RBE depends only on the c-ray dose, andas seen in Eq. (5), the Rmax at small doses and R1 at 1
Gy.
Our use of LQ models corresponding to Rmax = 100 and
R1 = 10 or 20 involves far more curvature than is seen in the
LSS cancer data, while it is not uncommon for experimental
settings for either chromosome aberrations or cancer
induction in animals. The concepts of a highly variable
RBE, and approximate linearity in dose of the cancer risk,
can be reconciled by the hypothesis that the unobserved
initial cellular damage had dose response curvature as seen
in radiobiological experiments, while the loss of curvaturein the cancer response is due to subsequent repair andsuppression processes. If such mechanisms depend on thelevel of the initial cellular damage, but not on the quality of
the radiation, the appropriate RBE function for analysis of
the late cancer effects will be that applied for the initial
cellular damage. This rationale applies only to the neutron

ACCOUNTING FOR NEUTRONS IN ATOMIC BOMB SURVIVORSRBE issue, and the extrapolation of c-ray risk estimatesfrom moderate to low doses must still be based on theobserved dose relationship.
APPENDIX
General RBE RelationshipIn this appendix we review in detail the RBE functions related to thelinear-quadratic dose-response functions. For current purposes it would be
sufficient to disregard, in line with Eq. (3), the quadratic component in thedose response for neutrons. On the other hand, it is useful to have theformula for the general case, because it permits the comparison not only toearlier investigations by Rossi and Zaider (6, 26), but also to the extensive
analysis by Sasaki et al. (7, 8) who included in their considerations highenergy neutrons (..1 MeV) for which the quadratic component cannot
be disregarded. The linear-quadratic relationship for a mixed-field
exposure is then:hiðA1ÞEðDc ; Dn Þ=b Dc þ Rmax Dn þ hðDc þ Dn Þ2 :Setting E(Dc,Dn) equal to E(Dc þ D, 0) one obtains the relationship:RðDc ; Dn Þ=

D
=
Dn

2c
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
1 þ 2g þ ð1 þ 2gÞ2 þ 4nc

ðA2Þ

with the abbreviations: g = hDc, n = hDn; c = Rmax þ 2g þ n (if thesquared term is included in the neutron dose response); and c = Rmax (if nosquared term is included in the neutron dose response). These
abbreviations are used to make the complicated equation more readable.
Special Cases
Below are three important special cases obtained by setting to zero,
respectively, the quadratic term for the neutron dose response, the neutron
dose and the c-ray dose.
Mixed-field radiation with linear relationship for the neutrons (c = Rmax):RðDc ; Dn Þ=

2Rmax
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
1 þ 2g þ ð1 þ 2gÞ2 þ 4nRmax

ðA3Þ

Limit of small neutron doses (n = 0):RðDc Þ=cRmax=
1 þ 2g 1 þ 2hDc

ðA4ÞEquation (A4), is important as a suitable approximation for the LSS data
where the neutron dose is small relative to the c-ray dose and is further
justified below.
Pure neutron exposure (g = 0):RðDn Þ =

1þ

2c
2Rmax
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ =1 þ 4nc 1 þ 1 þ 4hDn Rmax

ðA5ÞThe above equation [Eq. (A5)] corresponds to the one employed by
Sasaki (8), it is important to note that the RBE for such pure neutron
exposure is often confused with that for the mixed-field exposures of the
A-bomb survivors.
With different notation and in different form, Eq. (A3) has been given
by Rossi and Zaider (26) in an analysis that inferred, on the basis of therevised dosimetry system DS86 (1) that the mixed-field weighted dose in
Hiroshima did not exceed the c-ray dose anywhere by more than a factorof 1.25.

595

In a later assessment the same authors (6) mistakenly used the RBE forpure neutron exposure when they referred to tentative activation data by
Straume et al. (9) and to the implied larger neutron doses. They concluded
that the neutron contribution to the weighted dose exceeded the c-ray
contribution in Hiroshima at distances less than about 1,200 m fromground zero. Pierce et al. (27) objected to this conclusion, since it had been
incorrectly based on neutron RBE values that were obtained from therelationship for pure neutron exposures, i.e., a relationship that
corresponded to Eq. (A5) rather than to Eq. (A3) for the mixed-fieldradiation.
Sasaki et al. (7, 8) derived, in careful studies of the RBE of neutrons forchromosomal aberrations, a relationship that corresponded correctly to Eq.
(A5). Since they were also concerned with neutrons of high energy, i.e.,with intermediate LET, they included the quadratic term for the neutrons.
However, they too applied this relationship, which is valid for thecomparison of the neutron experiments to the c-ray experiments, andsubsequently to the mixed c-ray and neutron exposures in Hiroshima.
Thus, they disregarded the decrease of the RBE due to the simultaneous cray dose, which led to a substantial overestimate of the neutron
contribution.
Figure A1 shows the magnitude of the error that is incurred when theformula for a pure neutron exposure is applied to the mixed-field
exposures in Hiroshima. The lower curve gives the RBE values from Eq.
(A3) for the parameters Rmax = 100 and h = 4.5 Gy1. The upper broad
scatter cloud of values shows the much larger values that result, again for
Rmax = 100 and h = 4.5 Gy1, when Eq. (A5) for a pure neutron exposureis erroneously applied to the neutron doses in Hiroshima. The neutron
contribution is then overestimated by a factor between 3 and 7 in therelevant dose range of 0.5–2 Gy.
Figure A2 shows the corresponding diagram for the weighted dose inanalogy to Fig. 2 but with the upper point cloud of values resulting fromthe erroneous use of Eq. (A5). Compared to the lower point cloud, whichcorresponds to Eq. (A3), it is again shown that the resultant point cloudconsiderably overestimates the proper mixed-field weighted doses for theparameters Rmax = 100 and h = 4.5 Gy1.
Simplified Formula for the Neutron RBE when Neutron Doses are
Relatively Small
The exposure situation of the atomic bomb survivors allows the RBE to
be approximated very well by a simplified formula that depends only on cray dose, because the survivors’ neutron doses are much less than their cray doses. Figure A3 gives for Rmax = 100 and h = 4.5 Gy1 the resulting
contours of constant R(Dc,Dn) versus Dn and Dc using Eq. (A3).
For small neutron doses the RBE is close to 10 at the 1 Gy c-ray dose,
which is notable because the constant R = 10 has been used in the major
studies at RERF to account for the effectiveness of the neutrons. Since
there is agreement at 1 Gy, and linear fits over a range up to 1.5 or 2 Gylargely depend on the point at 1 Gy, the use of the constant RBE is atolerable approximation in spite of the fact that the diagram shows RBE
values for small neutron doses from 25 down to 5 in the dose range 0.3–2
Gy.
The superimposed scatter diagram corresponds to the data in Fig. 1 andrepresents the individual dose estimates (Dc,Dn), for Hiroshima. Notably
all points lie on the vertical part of the contours of constant RBE. Their
associated RBE values are thus close to the limit, R(Dc,0), for small
neutron doses. This confirms the considerably simplified treatment interms of Eq. (A4) that is applicable to the A-bomb radiation since theneutrons contribute only a minor fraction of the absorbed dose. Equation(A4) agrees with Eqs. (4) and (5).
The gray curves in Fig. A4 correspond to Eq. (5) for the cases
RBE(100,10) and RBE(100,20). They correspond to the parameters Rmax =100 and h = 4.5 Gy1 and Rmax = 100 and h = 2 Gy1. The exact values
according to Eq. (A3) for the individual dose estimates (Dc,Dn), of thesurvivors in Hiroshima are represented by the bands of points. The

596

CULLINGS, PIERCE AND KELLERER

FIG. A1. The RBE of the neutrons in Hiroshima vs. the concomitant c-ray doses. Both curves represent theparameter pair Rmax = 100 and h = 4.5 Gy1. The lower series of points gives the individual RBE values obtainedcorrectly from Eq. (A3). The upper broad cloud of points gives the much larger values inferred in terms of theEq. (A5) which does not account for the concomitant c-ray exposures.

FIG. A2. Diagram of the total weighted dose as in Fig. 2 for the parameters Rmax = 100 and h = 4.5 Gy1(lower cloud of points) and, for comparison, the total weighted doses that result with the same parameters fromthe incorrect use of Eq. (A5) (upper cloud of points).

ACCOUNTING FOR NEUTRONS IN ATOMIC BOMB SURVIVORS

FIG. A3. Lines of constant R(Dc,Dn) for Rmax = 100 and h = 4.5 Gy1 according to Eq. (A3) andsuperimposed, the scatter diagram of the individual neutron doses, Dn, for Hiroshima. Of note, all RBE values
for the individual neutron doses are close to the limit for small neutron doses, and the same applies a fortiori toNagasaki where the neutron/c ratios are considerably smaller.

FIG. A4. The gray curves give the RBE of small neutron doses for Rmax = 100 and h = 4.5 Gy1 (upper curve)
or Rmax = 100 and h = 2 Gy1 (lower curve) versus the accompanying c-ray dose [Eq. (A4)]. The exact values of
the RBE according to Eq. (A3) for the individual dose estimates (Dc, Dn) of the survivors in Hiroshima arerepresented by the points and they agree well with Eq. (A4).

597

598

CULLINGS, PIERCE AND KELLERER

relationship for the RBE at small neutron doses is seen to be a good
approximation.

ACKNOWLEDGMENTS
The Radiation Effects Research Foundation (RERF), Hiroshima andNagasaki, Japan is a private, nonprofit foundation funded by the Japanese
Ministry of Health, Labour and Welfare (MHLW) and the U.S.
Department of Energy (DOE), the latter in part through DOE Award
DE-HS0000031 to the National Academy of Sciences that supported
HMC and DAP. This publication was supported by RERF ResearchProtocol RP #18–59. The views of the authors do not necessarily reflect
those of the two governments.
Received: January 8, 2014; accepted: June 25, 2014; published online:
November 19, 2014

REFERENCES
1. Shimizu Y, Kato H, Schull WJ, Preston DL, Fujita S, Pierce DA.
Studies of the mortality of A-bomb survivors: 9. Mortality, 1950–
1985: Part 1. Comparison of risk coefficients for site-specificcancer mortality based on the DS86 and T65DR shielded kerma
and organ doses. Radiat Res 1988; 118:502–24.
2. Kellerer AM, Rühm W, Walsh L. Indications of the neutron effectcontribution in the solid cancer data of the A-bomb survivors.
Health Phys 2006; 90:554–64.
3. Little MP. Estimates of neutron relative biological effectivenessderived from the Japanese atomic bomb survivors. Int J Radiat
Biol 1997; 72:715–26.
4. Walsh, L. Neutron relative biological effectiveness for solid cancer
incidence in the Japanese A-bomb survivors: an analysis
considering the degree of independent effects from c-ray andneutron absorbed doses with hierarchical partitioning. Radiat
Environ Biophys 2013; 52:29–36.
5. Meyers RH. Classical and modern regression with applications,
2nd ed. Boston: Duxbury; 1990.
6. Rossi HH, Zaider M. Comment on the contribution of neutrons tothe biological effect at Hiroshima. Radiat Res 1996; 146:590–1.
7. Sasaki MS, Endo S, Ejima Y, Saito I, Okamura K, Oka Y, et al.
Effective dose of A-bomb radiation in Hiroshima and Nagasaki asassessed by chromosomal effectiveness of spectrum energy
photons and neutrons. Radiat Environ Biophys 2006; 45:79–91.
8. Sasaki MS, Nomura T, Ejima Y, Utsumi H, Endo S, Saito I, et al.
Experimental derivation of relative biological effectiveness of Abomb neutrons in Hiroshima and Nagasaki and implications forrisk assessment. Radiat Res 2008; 170:101–17.
9. Straume T, Egbert D, Woolson A, Finkel RC, Kubik PW, Grove
HE, et al. Neutron Discrepancies in the DS86 Hiroshima dosimetry
system. Health Phys 1992; 63:421–6.
10. Pierce DA, Vaeth M, Cologne JB. Allowance for random dose
estimation errors in atomic bomb survivor studies: a revision.
Radiat Res 2008; 170:118–26.
11. Preston DL, Pierce DA, Shimizu Y, Cullings HM, Fujita S,

Funamoto S, Kodama K. Effect of recent changes in atomic bomb
survivor dosimetry on cancer mortality risk estimates. Radiat Res
2004; 162:377–89.
12. Lloyd DC, Purrott RJ, Dolphin GW, Edwards AA. Chromosome
aberrations induced in human lymphocytes by neutron irradiation.
Int J Radiat Biol 1976; 29:169–82.
13. Edwards AA, Lloyd DC, Purrott RJ, Prosser JC. The dependence ofchromosome aberration yields on dose rate and radiation quality. In:
Research and development report, 1979–1981, RAD 4. Chilton,
UK: National Radiological Protection Board; 1982. p. 83–5.
14. Dobson RI, Straume T, Carrano AV, Minkler JL, Deaven LL,
Littlefield LG, et al. Biological effectiveness of neutrons from
Hiroshima bomb replica: Results of a collaborative cytogenetic
study. Radiat Res 1991; 128:142–9.
15. Kellerer AM, Rossi HH. The theory of dual radiation action.
Current Topics in Radiation Research Quarterly 1974; 8:85–158.
16. Schmid E, Schlegel D, Guldbakke S, Kapsch RP, Regulla D. RBEof nearly monoenergetic neutrons at energies of 36 keV – 14.6
MeV for induction of dicentrics in human lymphocytes. Radiat
Environ Biophys 2003; 42:87–94.
17. Schmid E, Regulla D, Kramer HM, Harder D. The effect of 29 kV
x-rays on the dose response of chromosome aberrations in human
lymphocytes. Radiat Res 2002; 158:771–7.
18. ICRP Relative biological effectiveness (RBE), quality factor (Q),and radiation weighting factor (wR). Annals of the ICRP,
Publication No. 92. Oxford: Pergamon Press; 2003.
19. Brenner DJ, Hall EJ. Secondary neutrons in clinical proton
radiotherapy: A charged issue. Radiother Oncol 2008; 86:165–70.
20. The relative biological effectiveness of radiations of different
quality. NCRP Report No. 104. Bethesda: MD: National Council
on Radiation of Radiation Protection and Measurements; 1990.
21. Shellabarger CJ, Chmelevsky D, Kellerer AM. Induction of
mammary neoplasms in the Sprague-Dawley rat by 430 keV
neutrons and x-rays. J Natl Cancer Inst 1980; 64:821–32.
22. Shellabarger CJ, Chmelevsky D, Kellerer AM, Stone JP, Holtzman
S. Induction of mammary neoplasms in the ACI rat by 430-keV
neutrons, x-rays, and diethylstilbestrol. J Natl Cancer Inst 1982;
69:1135–46.
23. Pierce DA, Preston DL. Radiation-related cancer risks at low doses
among atomic bomb survivors. Radiat Res 2000; 154:178–96.
24. Preston DL, Ron E, Tokuoka S, Funamoto S, Nishi N, Soda M, etal. Solid cancer incidence in atomic bomb survivors: 1958–1998.
Radiat Res 2007; 168:1–64.
25. Ozasa K, Shimizu Y, Suyama A, Kasagi F, Soda M, Grant EJ, etal. Studies of the mortality of Atomic bomb survivors, Report 14,
1950–2003: An overview of cancer and noncancer diseases. Radiat
Res 2012; 177:229–43.
26. Rossi HH, Zaider M. The contribution of neutrons to the biologicaleffects at Hiroshima. Health Phys 1990; 58:645–7.
27. Pierce DA, Shimizu Y, Preston DL, Vaeth M, Mabuchi K.
Response to the letter of Drs. Rossi and Zaider. Radiat Res 1996;
146:591–34.