The linear no-threshold theory of radiation risks

Currently, much debate exists about the validity of the linear no-threshold theory (LNT) for radiation risks. For example, it appears that some radiation scientists connected with the Japanese nuclear industry and the ICRP remain strongly opposed to the LNT. See for example which lists a number of prominent ICRP scientists who do not appear to subscribe to the theory.

In addition, several media pundits in the UK newspaper, the Guardian, and on the BBC have implied – without adducing evidence – that radiation effects are exaggerated and that there are no observed effects below 100 mSv.

However, in an accompanying post, I’ve shown that a growing number of studies show radiation effects well below that level. Indeed, they show effects down to very low levels – even at background levels of radiation. In other words, there does not appear to be a threshold, ie a dose below which no effects are seen, apart from zero dose.

But is the dose-response relationship linear?

This post addresses the “linear” part of the LNT theory. Graph 1 below shows the different kinds of relationships which could exist, ie (a) linear, (b) supra-linear, (c) sub-linear, (d) threshold, and (e) hormetic.

Graph 1

Graph 1

To assess whether a linear dose-response relationship is valid, we need to examine both the epidemiological evidence at low doses and dose rates, and the evidence from radiobiology theory derived from the evidence in cell and animal studies.

A. Epidemiological Studies

Does the available epidemiological evidence show risks declining linearly with dose at low doses? Yes, several recent epi studies do indeed show this, and the important new points are that these are (a) very large studies with statistically significant results, and (b) at very low doses, even down to background levels. In other words, the usual caveats about the validity of the linear shape of the dose response relationship down to low doses are becoming less and less justified.

The most recent evidence is from Zablotska et al (2012). (See references at end)

Graph 2 below, reproduced from Zablotska et al, shows statistically significant risks for all leukemias and for chronic lymphocytic leukemia (CLL) in over 110,000 Chernobyl cleanup workers. It can also be seen that there are 6 data points showing increased risks below 100 mSv. The Excess Relative Risk (ERR) can be estimated as 2.3 per Gy, all cases, at 1 Gy.

Graph 2

Graph 2

Second is the very recent cohort study of radiation exposures from medical CT scans in the UK by Pearce et al (2012). 74 out of 178,604 patients diagnosed with leukaemia and 135 out of 176,587 patients diagnosed with brain tumours were analyzed. As shown in graph 3 reproduced from their study, the authors noted a positive association between radiation doses from CT scans and leukaemia (ERR per Gy = 36, 95% CI 5–120 p=0·0097) and brain tumours (ERR per Gy = 23,10–49; p<0·0001). The large dashed line showed a linear fit to the data with a 95% confidence interval shown by small dashed lines.

Graph 3

Graph 3

Third are the risks from background radiation. Kendall et al (2012) recently conducted a large UK record-based case–control study testing associations between childhood cancer and natural background radiation with over 27,000 cases and 37,000 controls. Surprisingly, they observed an elevated risk of childhood leukaemia with cumulative red bone marrow dose from natural background gamma radiation. ERR/Gy = 120 (95% CI: 30, 220).

In graph 4 below reproduced from their study, the x-axis represents cumulative gamma ray doses in mGy. The red line shows not merely a linear but a slightly supralinear curve fitted to the data. The small dotted lines mark a 95% confidence interval.

Graph 4

Graph 4

Fourth is the third analysis of the UK National Registry for Radiation Workers (NRRW). This study of observed 11,000 cancer cases and 8,000 cancer deaths in 175,000 UK radiation workers with an average individual cumulative dose of 25 mSv and an average follow-up of 22 years. Graph 5 reproduced from the study shows the relative risks for all solid cancers with the continuous blue line representing the NRRW data, and the continuous red line the results from the US BEIR VII report for comparison – the two are very similar, as can be seen. An estimated ERR of 0.27 per Gy at 1 Gy can be derived from this graph.


Graph 5

Fifth is the Cardis et al (2005) meta-analysis of 196 leukaemias and 5,024 other cancers among 400,000 nuclear workers in fifteen countries with an average follow-up of 12.7 years and a mean individual cumulative dose of 19.4 mSv. The study found ERRs for leukaemia of 1.93 (95% CI: <0, 8.47) per Sv (2-year lag) and 0.97 (95% CI: 0.14, 1.97) per Sv for solid cancers (10-year lag).

Sixth is the meta-analysis of 13 european studies in 9 EU countries on indoor radon exposure risks by Darby et al (2005). This examined lung cancer risks at measured residential Rn concentrations with over 7,000 cases of lung cancer and 14,000 controls. The action level for indoor radon in most EU countries is 200 Bq per m3, corresponding to about 10  mSv per year. (This is derived from a UNSCEAR (2000)  reference value of 9 nSv per Bq·h/m3. This means that people living 2/3rds of their time indoors (5,780 h/year) at a Rn concentration of 200 Bq/m3 would receive an effective dose of ~10 mSv/year.)

Graph 6 reproduced from the study shows elevated risks at concentrations well below this level. (The solid line is the authors’ linear fit to the data.)

Graph 6

Graph 6

B. Radiobiological Evidence

In addition, much current radiobiological theory is consistent with a linear dose-response relationship down to low doses (ie below 10 mSv).

The radiobiological rationale for linearity comes from the stochastic energy deposition of ionising radiation. It was explained by 15 of the world’s most eminent radiation biologists and epidemiologists in a famous article. (Brenner et al, 2003)

It stated as follows:

“1. Direct epidemiological evidence demonstrates that an organ dose of 10 mGy of diagnostic x-rays is associated with an increase in cancer risk.

2. At an organ dose of 10 mGy of diagnostic x-rays, most irradiated cell nuclei will be traversed by one or, at most, a few physically distant electron tracks. Being so physically distant, it is very unlikely that these few electron tracks could produce DNA damage in some joint, cooperative way; rather, these electron tracks will act independently to produce stochastic damage and consequent cellular changes.

3. Decreasing the dose, say by a factor of 10, will simply result in proportionately fewer electron tracks and fewer hit cells. It follows that those fewer cells that are hit at the lower dose will be subject to (i) the same types of electron damage and (ii) the same radiobiological processes as would occur at 10 mGy.

4. Thus, decreasing the number of damaged cells by a factor of 10 would be expected to decrease the biological response by the same factor of 10; i.e., the response would decrease linearly with decreasing dose. One could not expect qualitatively different biological processes to be active at, say, 1 mGy that were not active at 10 mGy, or vice versa. The argument suggests that the risk of most radiation -induced endpoints will decrease linearly, without a threshold, from ~10 mGy down to arbitrarily low doses.”

C. Official Reports

Both kinds of evidence (epidemiology and radiobiology) have been examined in five relatively recent international official reviews.

  • UNSCEAR (2008)
  • US NCRP Report No 136 (2001)
  • Académie Nationale de Médecine et Académie des Sciences Joint Report No 2 (2005)
  • US BEIR VII (2005) and
  • ICRP 99 (2006)

Four of these five reports emphatically confirmed the LNT as being the most prudent assumption for radiation protection purposes. The odd one out is the French Académie Nationale de Médecine et Académie des Sciences Joint Report No 2 (2005). However France relies on nuclear power for about 80% of its electricity, so this finding is perhaps not unexpected.

In 2009, Little et al  examined this matter in some detail and they concluded linearity was the best bet. They discussed: (i) the degree of curvature in the cancer dose response within the Japanese atomic bomb survivors and other groups, (ii) the consistency of risks between the Japanese and other low-dose cohorts, and (iii) biologic data on mechanisms.

D. The Importance of LNT in Radiation Protection

Regardless of dissenting views on LNT, the reality is that most if not all concepts used in radiation protection today are strongly based on the LNT theory. For example, LNT allows radiation doses (i) to be averaged within an organ or tissue, (ii) to be added from different organs, and (iii) to be added over time. The LNT also underpins the concepts of absorbed dose, effective dose, committed dose, and the use of dose coefficients (eg Sv per Bq of a radionuclide).

The use of the LNT also permits

  • the ICRP principle of limitation – ie annual dose limits/constraints
  • the ICRP principle of optimization -ie comparison of practices
  • radiation risk assessment at low and very low doses
  • individual dosimetry with passive detectors
  • the use of collective dose, and
  • the use of dose registers over long periods of time.

In fact, the LNT underpins all legal regulations in radiation protection. Indeed if the LNT were not used, it’s hard to imagine our current radiation protection systems existing at all.


Brenner David J, Richard Doll, Dudley T. Goodhead, Eric J. Hall, Charles E. Land, John B. Little, Jay H. Lubin, Dale L. Preston, R. Julian Preston, Jerome S. Puskin, Elaine Ron, Rainer K. Sachs, Jonathan M. Samet, Richard B. Setlow, and Marco Zaider (2003) Cancer risks attributable to low doses of ionizing radiation: Assessing what we really know. PNAS. vol.100 no.24. pp 13761-13766. www.pnas.orgjcgijdoij10.1073jpnas.2235592100

Cardis et al (2005) Risk of cancer after low doses of ionizing radiation: retrospective cohort study in 15 countries. BMJ. 2005 Jul 9;331 (7508).

Darby et al (2005) Radon in homes and risk of lung cancer: collaborative analysis of individual data from 13 European case-control studies. BMJ 2005;330:223.

Kendall G M, M P Little, R Wakeford, K J Bunch, J C H Miles, T J Vincent, J R Meara and M F G Murphy (2012) A record-based case–control study of natural background radiation and the incidence of childhood leukaemia and other cancers in Great Britain during 1980–2006. Leukemia (5 June 2012) | doi:10.1038/leu.2012.151.

Little MP, Wakeford R, Tawn EJ, Bouffler SD, Berrington de Gonzalez A. Risks associated with low doses and low dose rates of ionizing radiation: why linearity may be (almost) the best we can do. Radiology. 2009 Apr;251(1):6-12. doi: 10.1148/radiol.2511081686.

Muirhead et al (2009) Mortality and cancer incidence following occupational radiation exposure: third analysis of the National Registry for Radiation Workers. Br J Cancer 2009; 100: 206-212.

Pearce et al (2012) Radiation exposure from CT scans in childhood and subsequent risk of eukaemia and brain tumours: a retrospective cohort study. The Lancet. June 7, 2012. 380: 499-505. DOI:10.1016/S0140-6736(12)60815-0,

United Nations Scientific Committee on the Effects of Atomic Radiation (2000). UNSCEAR Report to the General Assembly, with scientific annexes – Annex B, § 153.

Zablotska et al (2012) Radiation and the Risk of Chronic Lymphocytic and Other Leukemias among Chornobyl Cleanup Workers. Environmental Health Perspectives Online 8 November 2012.

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