EXTRAPOLATING RADIATION-INDUCED CANCER RISKS
FROM LOW DOSES TO VERY LOW DOSES
David J. Brenner*
Abstract—There is strong evidence that ionizing radiation
increases cancer risks at high doses (e.g., >1 Gy), and persua-
sive, if controversial, epidemiological evidence that cancer
risks are increased at low doses (?10 mGy). Discussed here are
the issues related to extrapolating radiation risks from low
radiation doses to very low doses (<1 mGy) — for which
purpose we are forced to rely on radiobiological evidence and
biophysical arguments. At high doses, cells are typically hit by
many tracks of radiation, while at low doses most cells are
typically hit by a single track of radiation; at very low doses
proportionately fewer cells are hit, again only by a single track
of radiation. Thus, in comparing low doses to very low doses,
the damage to hit cells remains essentially the same (a single
radiation track passing through a cell), but what changes is the
number of cells that are subjected to this same damage, which
decreases linearly as the dose decreases. This is the argument
for a linear no-threshold (LNT) model. It is important to
emphasize that this LNT argument only applies to the extrap-
olation from low doses to very low doses, not from high to low
doses. Of course there are caveats to this argument, such as the
potential effects of phenomena such as inter-cellular commu-
nication and immunosurveillance, and the possibility of differ-
ent radiobiological processes at very low doses, compared to
low doses. However, there is little conclusive experimental
evidence about the significance of these phenomena at very low
doses, and comparative mechanistic studies at high doses vs. low
doses will not be informative in this context. At present, we do not
know whether such radiobiological phenomena would produce
or decrease cancer risks at very low doses, compared with the
prediction of a linear extrapolation from low doses.
Health Phys. 97(5):505–509; 2009
Key words: dose, low; extrapolation; radiation risk; National
Council on Radiation Protection and Measurements
THERE IS considerable uncertainty as to the extent to
which low or very low doses of radiation affect cancer
risks (NCRP 2001; Tubiana 2005; NRC 2006; UNSCEAR
2008). This is an important issue in a variety of contexts,
such as diagnostic radiology, nuclear power production,
and responses to a large-scale radiological event. There
exists a range of high radiation doses which demonstra-
bly increase cancer risks, and a lower dose range where
there is plausible (but controversial) evidence for an
increase in cancer risk; but almost by definition there is
a very low-dose range where there is no direct epidemi-
ological evidence, nor is there likely to be any in the
foreseeable future. This is because of the high “natural”
cancer rate in the general population of ?40%, which
essentially precludes practical epidemiological studies to
assess potential small radiation-induced changes in can-
cer risk. Without the possibility of direct measurements
of cancer risks at very low doses, and lacking a complete
mechanistic understanding of the processes involved in
radiation-induced cancer, or any other cancer process for
that matter, the only current option is to extrapolate
radiation-induced cancer risks from higher doses, where
the risks can be assessed epidemiologically, to lower doses.
Thus a key question becomes the most plausible method-
ology of extrapolating cancer risks from low doses, where
there is some evidence of an increased cancer risk, to very
METHODS AND RESULTS
The epidemiological data will not be discussed here
per se, but rather the focus will be on risk extrapolations
between dose regions. It will be convenient to divide the
relevant dose range into three regions: at high doses (e.g.,
?1 Gy) there is strong epidemiological evidence that
ionizing radiation increases cancer risks (Preston et al.
2007); at lower doses of the order of 10 mGy, there is
persuasive, if less definitive, epidemiological evidence that
cancer risks are increased (Doll and Wakeford 1997; Cardis
et al. 2007); at very low doses, however, epidemiological
studies cannot provide statistically useful information. Dis-
cussed here are the issues relating to extrapolating radiation
risks from low doses (?10 mGy) to very low doses (?1
mGy) — for which purpose we are forced to rely on
radiobiological evidence and biophysical arguments.
* Center for Radiological Research, Columbia University Medi-
cal Center, 630 West 168thStreet, New York, NY 10032.
For correspondence contact the author at the above address, or
email at email@example.com.
(Manuscript accepted 8 May 2009)
Copyright © 2009 Health Physics Society
Energy deposition patterns in cells in the three
As well as being associated with different levels of
confidence as to the associated cancer risks, the three
dose regions discussed above also correspond to different
patterns of energy deposition in individual cells, as
illustrated in Fig. 1. It will be argued, with caveats, that
these energy deposition patterns allow significant in-
sights into risk extrapolation approaches among the three
different dose ranges illustrated here.
As schematized in Fig. 1, at high doses (?1 Gy, Fig.
1A), mammalian cell nuclei are hit by multiple tracks of
radiation; for example, in an x-ray field, they would be
traversed by many incident x rays. By contrast, at low
doses (e.g., 10 mGy, Fig. 1B), cell nuclei are on average
hit by a single track of radiation [it is pertinent to note
that these generalizations actually depend both on the
x-ray energy and on the biological target size (ICRU
1983); here we have considered 80-kVp x rays, a typical
peak energy used in radiology, and have assumed the
target to be a typical human epithelial cell nucleus
(Altman and Katz 1976)]. At still lower doses (e.g., 1
mGy, Fig. 1C), the type of energy deposition to any
given hit cell does not change, still being a single
radiation track — but rather the number of hit nuclei
decreases, proportionately to the dose.
Extrapolating risks between the three dose regions
As can be intuitively seen from Figs. 1A and 1B,
there is unlikely to be a simple biophysically-based
argument to describe the extrapolation of risks from high
doses to low doses, because the basic type of cellular
damage to cells changes drastically, from many hits to
single hits — and indeed, as one might expect, there is
persuasive evidence of different types of radiobiological
Fig. 1. Schematic illustrations of radiation tracks in 10 typical human epithelial cell nuclei exposed to 80-kVp x rays, at doses of
high to low doses (A to B), but extrapolating risks from low to very low doses (B to C) may be more feasible.
506 Health Physics November 2009, Volume 97, Number 5
damage when comparing high and low radiation doses
(e.g., Yin et al. 2003; Portess et al. 2007).
By contrast, comparing low doses (e.g., 10 mGy, Fig.
1C) with very low doses (?1 mGy), the energy deposition
to the hit cells remains essentially the same (essentially a
single radiation track passing through a cell), but what
changes is the proportion of cells that are subjected to this
same damage, which decreases linearly as the dose de-
creases. In principle, therefore, extrapolating from low to
very low doses is expected to be easier than extrapolating
from high to low doses, because the type of damage does not
change, merely the proportion of cells subject to that damage.
The linear no-threshold (LNT) extrapolation from
low doses to very low doses
These considerations suggest a biophysically-based
rationale for an LNT extrapolation of risks from low
doses to very low doses, summarized as follows:
1. At low to very low doses, if a cell nucleus is traversed
by an x ray, it will be traversed by one or, at most, a
few physically-distant radiation tracks; and
2. Thus at low to very low doses, given that the type of
physical damage to cells does not change, the main
effect of a decrease in dose will be a proportionate
decrease in the number of cells subject to this same
type of physical damage, and thus a proportionate,
i.e., linear, decrease in risk.
Again it is emphasized that:
I. The rationale for the LNT model relates to extrapo-
lating risks from low doses (e.g., 5 to 20 mGy) to still
lower doses, not for extrapolating risks from high
doses to low doses; and
II. The LNT argument does not address the issue of
whether there are, in fact, increased cancer risks in
the low-dose range from 5 to 20 mGy, although there
are large-scale epidemiological studies suggesting
that this is indeed the case, such as the Oxford Survey
of Childhood Cancers, a case control study of 15,000
childhood cancers (Doll and Wakeford 1997), and
initial reports from the 15-country study of nuclear
industry workers (Cardis et al. 2007).
Potential confounders of the biophysical argument
There are several potential weaknesses to this bio-
physical argument for linearity, the most commonly
1. Possible confounding effects of inter-cellular commu-
2. Potential differential effects of immunosurveillance
when the number of (pre) malignant cells is low; and
3. The possibility of different types of biological dam-
age, and damage responses, dominating at very low
doses, compared to low doses.
Each of these potential confounders will be briefly
Intercellular communication. As described above,
the biophysical argument for linearity refers to the
development of monoclonal tumors by autonomous (in-
dependently developing) cells (Rossi and Kellerer 1972;
Brenner et al. 2003). By contrast, it is well known that,
while most tumors are monoclonal in origin (Fearon et al.
1987), cell-to-cell communication is a central component
of the process of carcinogenesis (Bhowmick and Moses
2005; Trosko et al. 2005).
Not all types of cell-to-cell communications would
invalidate the biophysical argument for linearity. For
example, if the interactions are between unirradiated
tissue and radiation-damaged cells, the argument for
linearity remains valid. However, the argument would
potentially not hold if other irradiated cells could signif-
icantly change the probability that a radiation-damaged
cell develops into a cancer in a way which is non-linear
with dose. But it would still then remain to be determined
whether such intercellular communication would de-
crease the cancer risk [suggested, for example, by
Barcellos-Hoff (2001)], or increase it [suggested, for
example, by Tubiana (2005) and colleagues], or indeed
would make any appreciable difference. One may note here
that the most studied intercellular communication phenom-
enon in the field of radiobiology is the so-called bystander
effect (Nagasawa and Little 1992; Brenner et al. 2001;
Ballarini et al. 2006), which generally results in risks per
unit dose that are higher at very low doses compared to low
doses (Sawant et al. 2001; Zhou et al. 2001).
Overall, our current understanding of the relevance
of intercellular communication to the biophysical argument
for LNT was well summarized by Trosko et al. (2005): “At
present, one cannot predict whether the [intercellular com-
munication] response is biologically relevant to any health
effect or even whether the effect on the affected cells could
be considered positive or negative.”
Immune surveillance. It has been suggested (Tubiana
2005) that immune surveillance and other systems are able
to eliminate small numbers of radiation-induced pre-
malignant cells, but would be overwhelmed by larger
numbers of such cells—which would lead to cancer risks
per unit doses which are lower at very low doses than at
higher doses. It is certainly true that innate and adaptive
immune effector cells and molecules can recognize and
destroy tumors (Gasser and Raulet 2006). However, it is
also clear that small numbers of pre-malignant cells can
507 Extrapolating radiation-induced cancer risks●D. J. BRENNER
survive immune surveillance (Willimsky et al. 2008), and
there is no evidence to suggest that the immune surveillance
system is more efficient when the number of pre-malignant
or malignant cells is low. To the contrary, there is consid-
erable evidence that small numbers of tumor cells can
escape immune surveillance more efficiently than larger
numbers, a phenomenon referred to as “sneaking through”
(Old et al. 1962) or “dilution escape” (Bonmassar et al. 1974),
al. 1973; Bonmassar et al. 1974; Mengersen et al. 1975).
An example of “sneaking through” is illustrated in
Fig. 2, which shows the incidence of BALB/c mastocy-
toma tumors in BALB/c mice injected with various
numbers of BALB/c mastocytoma tumor cells (Ko ¨lsch et
al. 1973); there is a very high tumor incidence when large
numbers (?500,000) of tumor cells are injected, and this
incidence decreases as the number of injected tumor cells is
reduced. But as the number of injected tumor cells is
reduced from 5,000 down to, in this case, 20 tumor cells,
there is no further decrease in the induced tumor incidence.
The possibility of different biological damage-
response processes dominating at very low doses,
compared to low doses. There has been considerable
recent interest in comparing biological damage-response
the validity of the LNT extrapolation. As discussed above
(see Fig. 1), one would expect different types of biological
damage in the Gy dose range as compared with mGy doses,
and thus different types of biological responses — and
indeed such has been reported by several investigators [e.g.,
Yin et al. (2003), Portess et al. (2007)]. It follows that
comparisons of mechanisms in the mGy vs. the Gy dose
range will not be informative regarding the validity of the
LNT approach, which is concerned with extrapolating from
risks at ?10 mGy to risks at doses of less than 1 mGy.
It is pertinent to point out here, in regard to radiobio-
logical experiments in the sub-mGy dose range, that they
are extraordinarily difficult to perform and interpret, partic-
ularly in light of the requirements that they be pertinent to
carcinogenesis and, ideally, in vivo. As an example, initial
studies by Rothkamm and Löbrich (2003) on DNA double
strand break (DSB) repair kinetics in the mGy dose range
initially suggested very different DNA repair kinetics at 1.2
mGy compared to 5 or 20 mGy. Such a result might argue
against LNT in that the initial energy deposition in hit cells
would be expected to be essentially the same for each of these
be expected to be the same. However, when the experiments
in repair kinetics were observed over the mGy dose range.
The LNT approach is a plausible mechanistically-
based approach for extrapolating radiation-induced can-
cer risks from low doses (e.g., 5 to 20 mGy) down to very
low doses (e.g., ?1 mGy). Two things it cannot do are (1)
extrapolate cancer risks from high doses (?1 Gy) to low
doses; or (2) establish whether there are, in fact, increased
cancer risks at doses in the range of, say, 5 to 20 mGy.
There are, of course, several key assumptions that
underlie the LNT approach. Three of the most commonly
discussed issues are the possible confounding effects of
intercellular communication; the potential differential
effects of immune surveillance when the number of
premalignant cells is low; and the possibility of different
radiobiological processes dominating at very low doses,
compared to low doses. As discussed here, there is
currently no strong evidence that any of these three
phenomena significantly affect the LNT argument,
though this may be in large part because essentially no
decisive experiments have been reported — in turn a
consequence of the difficulties of undertaking quantita-
tive radiobiological studies in the mGy dose range.
Finally, at least two different experimental ap-
proaches are possible to assess the validity of the LNT
approach. First, the LNT argument makes clear predictions
that the same types of biological damage and damage
responses should be dominant at doses ?1 mGy, compared
though the technical difficulties involved are formidable. It
is emphasized that comparisons of mechanisms at mGy vs.
Gy doses will not be informative in this context — the
Fig. 2. Incidence of BALB/c mastocytoma tumors in BALB/c
mice injected with a single dose of different numbers of BALB/c
mastocytoma tumor cells (based on Ko ¨lsch et al. 1973).
508 Health Physics November 2009, Volume 97, Number 5
Second, the LNT argument relies on an assumption
about single cells acting autonomously during carcino-
genesis, which is clearly not correct. However, we do not
currently know if deviations from the predictions of LNT
that are associated with intercellular communication will
be large or small, nor even whether they will increase or
decrease low-dose cancer risk estimates. This is likely to
be a central theme of future research in the field (Trosko
2005; Barcellos-Hoff 2008).
U19-AI67773, and NCI grant CA 49062. Illuminating discussions with Drs.
Mary-Helen Barcellos-Hoff and Noelle Metting are gratefully acknowledged.
Altman PL, Katz DD. Cell biology. Bethesda, MD: Federation
of American Societies for Experimental Biology; 1976.
Ballarini F, Alloni D, Facoetti A, Mairani A, Nano R, Ottolenghi
A. Modelling radiation-induced bystander effect and cellular
communication. Radiat Protect Dosim 122:244–251; 2006.
Barcellos-Hoff MH. It takes a tissue to make a tumor: epige-
netics, cancer and the microenvironment. J Mammary
Gland Biol Neoplasia 6:213–221; 2001.
Barcellos-Hoff MH. Cancer as an emergent phenomenon in sys-
tems radiation biology. Radiat Environ Biophys 47:33–38; 2008.
Bhowmick NA, Moses HL. Tumor-stroma interactions. Curr
Opin Genet Dev 15:97–101; 2005.
Bonmassar E, Menconi E, Goldin A, Cudkowicz G. Escape of
small numbers of allogeneic lymphoma cells from immune
surveillance. J Natl Cancer Inst 53:475–479; 1974.
Brenner DJ, Little JB, Sachs RK. The bystander effect in
radiation oncogenesis: II. A quantitative model. Radiat Res
Brenner DJ, Doll R, Goodhead DT, Hall EJ, Land CE, Little JB,
Lubin JH, Preston DL, Preston RJ, Puskin JS, Ron E, Sachs RK,
doses of ionizing radiation: assessing what we really know. Proc
Natl Acad Sci USA 100:13761–13766; 2003.
Cardis E, Vrijheid M, Blettner M, Gilbert E, Hakama M, Hill
C, Howe G, Kaldor J, Muirhead CR, Schubauer-Berigan M,
Yoshimura T, Bermann F, Cowper G, Fix J, Hacker C,
Heinmiller B, Marshall M, Thierry-Chef I, Utterback D,
Ahn YO, Amoros E, Ashmore P, Auvinen A, Bae JM,
Bernar J, Biau A, Combalot E, Deboodt P, Sacristan AD,
Eklof M, Engels H, Engholm G, Gulis G, Habib RR, Holan
K, Hyvonen H, Kerekes A, Kurtinaitis J, Malker H,
Martuzzi M, Mastauskas A, Monnet A, Moser M, Pearce
MS, Richardson DB, Rodriguez-Artalejo F, Rogel A, Tardy
H, Telle-Lamberton M, Turai I, Usel M, Veress K. The
15-country collaborative study of cancer risk among radia-
tion workers in the nuclear industry: estimates of radiation-
related cancer risks. Radiat Res 167:396–416; 2007.
Doll R, Wakeford R. Risk of childhood cancer from fetal
irradiation. Br J Radiol 70:130–139; 1997.
Fearon ER, Hamilton SR, Vogelstein B. Clonal analysis of
human colorectal tumors. Science 238:193–197; 1987.
Gasser S, Raulet DH. The DNA damage response arouses the
immune system. Cancer Res 66:3959–3962; 2006.
Hewitt HB. Studies of the quantitative transplantation of mouse
sarcoma. Br J Cancer 7:367–383; 1953.
International Commission on Radiation Units and Measure-
ments. Microdosimetry. Bethesda, MD: ICRU; 1983.
Ko ¨lsch E, Mengersen R, Diller E. Low dose tolerance prevent-
ing tumor immunity. Eur J Cancer 9:879–882; 1973.
Löbrich M, Rief N, Kuhne M, Heckmann M, Fleckenstein J,
Rube C, Uder M. In vivo formation and repair of DNA
double-strand breaks after computed tomography examina-
tions. Proc Natl Acad Sci USA 102:8984–8989; 2005.
Mengersen R, Schick R, Kölsch E. Correlation of “sneaking
through” of tumor cells with specific immunological im-
pairment of the host. Eur J Immunol 5:532–537; 1975.
Nagasawa H, Little JB. Induction of sister chromatid ex-
changes by extremely low doses of alpha particles. Cancer
Res 52:6394–6396; 1992.
National Council on Radiation Protection and Measurements. Eval-
radiation. Bethesda, MD: NCRP; Report No. 136; 2001.
National Research Council. Health risks from exposure to low
levels of ionizing radiation. Washington, DC: The National
Academies Press; BEIR VII; 2006.
Old LJ, Boyse EA, Clarke DA, Carswell EA. Antigenic
properties of chemically induced tumors. Ann NY Acad Sci
Portess DI, Bauer G, Hill MA, O’Neill P. Low-dose irradiation
of nontransformed cells stimulates the selective removal of
precancerous cells via intercellular induction of apoptosis.
Cancer Res 67:1246–1253; 2007.
Preston DL, Ron E, Tokuoka S, Funamoto S, Nishi N, Soda M,
Mabuchi K, Kodama K. Solid cancer incidence in atomic
bomb survivors: 1958–1998. Radiat Res 168:1–64; 2007.
Rossi HH, Kellerer AM. Radiation carcinogenesis at low
doses. Science 175:200–202; 1972.
Rothkamm K, Löbrich M. Evidence for a lack of DNA double-
strand break repair in human cells exposed to very low x-ray
doses. Proc Natl Acad Sci USA 100:5057–5062; 2003.
bystander effect in radiation oncogenesis: I. Transformation in
C3H 10T1/2 cells in vitro can be initiated in the unirradiated
neighbors of irradiated cells. Radiat Res 155:397–401; 2001.
Trosko JE. The role of stem cells and cell-cell communication
in radiation carcinogenesis: ignored concepts. BJR Suppl
Trosko JE, Chang CC, Upham BL, Tai MH. Low-dose ionizing
radiation: induction of differential intracellular signalling
possibly affecting intercellular communication. Radiat En-
viron Biophys 44:3–9; 2005.
Tubiana M. Dose-effect relationship and estimation of the
carcinogenic effects of low doses of ionizing radiation: The
joint report of the Acade ´mie des Sciences (Paris) and of the
Acade ´mie Nationale de Médecine. Int J Radiat Oncol Biol
Phys 63:317–319; 2005.
United Nations Scientific Committee on the Effects of Atomic
Radiation. 2006 Report Vol. 1: Effects of ionizing radiation.
New York: United Nations; 2008.
Willimsky G, Czeh M, Loddenkemper C, Gellermann J, Schmidt K,
Wust P, Stein H, Blankenstein T. Immunogenicity of premalig-
nant lesions is the primary cause of general cytotoxic T lympho-
cyte unresponsiveness. J Exp Med 205:1687–1700; 2008.
Yin E, Nelson DO, Coleman MA, Peterson LE, Wyrobek AJ. Gene
expression changes in mouse brain after exposure to low-dose
ionizing radiation. Int J Radiat Biol 79:759–775; 2003.
Zhou H, Suzuki M, Randers-Pehrson G, Vannais D, Chen G,
Trosko JE, Waldren CA, Hei TK. Radiation risk to low
fluences of alpha particles may be greater than we thought.
Proc Natl Acad Sci USA 98:14410–14415; 2001.
509Extrapolating radiation-induced cancer risks●D. J. BRENNER