Linear no-threshold model

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Alternative assumptions for the extrapolation of the cancer risk vs. radiation dose to low-dose levels, given a known risk at a high dose:
(A) supra-linearity, (B) linear
(C) linear-quadratic, (D) hormesis

The linear no-threshold model (LNT) is a model used in radiation protection to quantify radiation exposition and set regulatory limits. It assumes that the long term, biological damage caused by ionizing radiation (essentially the cancer risk) is directly proportional to the dose. This allows the summation by dosimeters of all radiation exposure, without taking into consideration dose levels or dose rates.[1] In other words, radiation is always considered harmful with no safety threshold, and the sum of several very small exposures are considered to have the same effect as one larger exposure (response linearity).

One of the organizations for establishing recommendations on radiation protection guidelines internationally, the UNSCEAR, has recently recommended policies that do not agree with the Linear No-Threshold model at exposure levels below background levels of radiation to the UN General Assembly from the Fifty-Ninth Session of the Committee. Its recommendation states that "the Scientific Committee does not recommend multiplying very low doses by large numbers of individuals to estimate numbers of radiation-induced health effects within a population exposed to incremental doses at levels equivalent to or lower than natural background levels." This is a reversal from previous recommendations by the same organization.[2]

Whether the model describes the reality for small-dose exposures is disputed. It opposes two competing schools of thought: the threshold model, which assumes that very small exposures are harmless, and the radiation hormesis model, which claims that radiation at very small doses can be beneficial. Because the current data are inconclusive, scientists disagree on which model should be used. Pending any definitive answer to these questions and the precautionary principle, the model is sometimes used to quantify the cancerous effect of collective doses of low-level radioactive contaminations, even though such practice has been condemned by the International Commission on Radiological Protection.[3]

The LNT model is sometimes applied to other cancer hazards such as polychlorinated biphenyls in drinking water.[4]


Increased Risk of Solid Cancer with Dose for A-bomb survivors, from BEIR report.

The linear-no-threshold model was first expressed by John Gofman, and rejected by the Department of Energy, according to Gofman, because it was "inconvenient".[5]

The National Academy of Sciences (NAS) Biological Effects of Ionizing Radiation (BEIR) report, NAS BEIR VII was an expert panel who reviewed available peer reviewed literature and writes, "the committee concludes that the preponderance of information indicates that there will be some risk, even at low doses".[6]

Radiation precautions and public policy[edit]

Radiation precautions have led to sunlight being listed as a carcinogen at all sun exposure rates, due to the ultraviolet component of sunlight, with no safe level of sunlight exposure being suggested, following the precautionary LNT model. According to a 2007 study submitted by the University of Ottawa to the Department of Health and Human Services in Washington, D.C., there is not enough information to determine a safe level of sun exposure at this time.[7]

If a particular dose of radiation is found to produce one extra case of a type of cancer in every thousand people exposed, LNT projects that one thousandth of this dose will produce one extra case in every million people so exposed, and that one millionth of the original dose will produce one extra case in every billion people exposed. The conclusion is that any given dose equivalent of radiation will produce the same number of cancers, no matter how thinly it is spread.

The model is simple to apply: a quantity of radiation can be translated into a number of deaths without any adjustment for the distribution of exposure, including the distribution of exposure within a single exposed individual. For example, a hot particle embedded in an organ (such as lung) results in a very high dose in the cells directly adjacent to the hot particle, but a much lower whole-organ and whole-body dose. Thus, even if a safe low dose threshold was found to exist at cellular level for radiation induced mutagenesis, the threshold would not exist for environmental pollution with hot particles, and could not be safely assumed to exist when the distribution of dose is unknown.

The linear no-threshold model is used to extrapolate the expected number of extra deaths caused by exposure to environmental radiation, and it therefore has a great impact on public policy. The model is used to translate any radiation release, like that from a "dirty bomb", into a number of lives lost, while any reduction in radiation exposure, for example as a consequence of radon detection, is translated into a number of lives saved. When the doses are very low, at natural background levels, in the absence of evidence, the model predicts via extrapolation, new cancers only in a very small fraction of the population, but for a large population, the number of lives is extrapolated into hundreds or thousands, and this can sway public policy.

A linear model has long been used in health physics to set maximum acceptable radiation exposures.

The United States based National Council on Radiation Protection and Measurements (NCRP), a body commissioned by the United States Congress, recently released a report written by the national experts in the field which states that, radiation's effects should be considered to be proportional to the dose an individual receives, regardless of how small the dose is.

Ramsar, located in Iran, is often quoted as being a counter example to LNT. Based on preliminary results, it was considered as having the highest natural background radiation levels on Earth, several times higher than the ICRP-recommended radiation dose limits for radiation workers, whilst the local population did not seem to suffer any ill effects.[8] Actually, the population of the high-radiation districts is small (about 1800 inhabitants) and only receive an average of 10 millisieverts per year,[9] so that cancer epidemiology data are too imprecise to draw any conclusions.[10] On the other hand, there may be non-cancer effects of the background radiation such as chromosomal aberrations[11] or female infertility.[12]


The LNT model and the alternatives to it each have plausible mechanisms that could bring them about, but definitive conclusions are hard to make given the difficulty of doing longitudinal studies involving large cohorts over long periods.

A 2003 review of the various studies published in the authoritative Proceedings of the National Academy of Sciences concludes that "given our current state of knowledge, the most reasonable assumption is that the cancer risks from low doses of x- or gamma-rays decrease linearly with decreasing dose."[13]

A 2005 study[14] of Ramsar, Iran (a region with very high levels of natural background radiation) showed that lung cancer incidence was lower in the high-radiation area than in seven surrounding regions with lower levels of natural background radiation. A fuller epidemiological study[15] of the same region showed no difference in mortality for males, and a statistically insignificant increase for females.

A 2007 study of Swedish children exposed to fallout from Chernobyl while they were fetuses between 8 and 25 weeks gestation has found that the reduction in IQ at very low doses was greater than expected, given a simple LNT model for radiation damage, indicating that the LNT model may be too conservative when it comes to neurological damage.[16] Neurological damage has a different biology than cancer, and for cancer rates there are conflicting studies.

In a 2009 study[17] cancer rates among UK radiation workers were found to increase with higher recorded occupational radiation doses. The doses examined varied between 0 and 500 mSv received over their working lives. These results exclude the possibilities of no increase in risk or that the risk is 2-3 times that for A-bomb survivors with a confidence level of 90%. The cancer risk for these radiation workers was still less than the average for persons in the UK due to the healthy worker effect.

A 2009 study focusing on the naturally high background radiation region of Karunagappalli, India concluded: "our cancer incidence study, together with previously reported cancer mortality studies in the HBR area of Yangjiang, China, suggests it is unlikely that estimates of risk at low doses are substantially greater than currently believed."[18] A 2011 meta-analysis further concluded that the "Total whole body radiation doses received over 70 years from the natural environment high background radiation areas in Kerala, India and Yanjiang, China are much smaller than [the non-tumour dose, "defined as the highest dose of radiation at which no statistically significant tumour increase was observed above the control level"] for the respective dose-rates in each district."[19]

In 2011 an in vitro time-lapse study of the cellular response to low doses of radiation showed a strongly non-linear response of certain cellular repair mechanisms called radiation-induced foci (RIF). The study found that low doses of radiation prompted higher rates of RIF formation than high doses, and that after low-dose exposure RIF continued to form after the radiation had ended.[20]


In recent years the accuracy of the LNT model at low dosage has been questioned and several expert scientific panels have been convened on this topic.

  • In 2005 the United States National Academies' National Research Council published its comprehensive meta-analysis of low-dose radiation research BEIR VII, Phase 2. In its press release the Academies stated:[24]

"The scientific research base shows that there is no threshold of exposure below which low levels of ionizing radiation can be demonstrated to be harmless or beneficial."

  • The United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) wrote in its 2000 report[26]

    Until the [...] uncertainties on low-dose response are resolved, the Committee believes that an increase in the risk of tumour induction proportionate to the radiation dose is consistent with developing knowledge and that it remains, accordingly, the most scientifically defensible approximation of low-dose response. However, a strictly linear dose response should not be expected in all circumstances.

  • the United States Environmental Protection Agency also endorses the LNT model in its 2011 report on radiogenic cancer risk:[27]

    "Underlying the risk models is a large body of epidemiological and radiobiological data. In general, results from both lines of research are consistent with a linear, no-threshold dose (LNT) response model in which the risk of inducing a cancer in an irradiated tissue by low doses of radiation is proportional to the dose to that tissue."

However, other organisations disagree with using the Linear no-threshold model to estimate risk from environmental and occupational low-level radiation exposure.

The French Academy of Sciences (Académie des Sciences) and the National Academy of Medicine (Académie nationale de Médecine) published a report in 2005 (at the same time as BEIR VII report in the United States) that rejected the Linear no-threshold model in favor of a threshold dose response and a significantly reduced risk at low radiation exposure:[28][29]

In conclusion, this report raises doubts on the validity of using LNT for evaluating the carcinogenic risk of low doses (< 100 mSv) and even more for very low doses (< 10 mSv). The LNT concept can be a useful pragmatic tool for assessing rules in radioprotection for doses above 10 mSv; however since it is not based on biological concepts of our current knowledge, it should not be used without precaution for assessing by extrapolation the risks associated with low and even more so, with very low doses (< 10 mSv), especially for benefit-risk assessments imposed on radiologists by the European directive 97-43.

The Health Physics Society's position statement first adopted in January 1996, as revised in July 2010, states:[30]

In accordance with current knowledge of radiation health risks, the Health Physics Society recommends against quantitative estimation of health risks below an individual dose of 5 rem (50 mSv) in one year or a lifetime dose of 10 rem (100 mSv) above that received from natural sources. Doses from natural background radiation in the United States average about 0.3 rem (3 mSv) per year. A dose of 5 rem (50 mSv) will be accumulated in the first 17 years of life and about 25 rem (250 mSv) in a lifetime of 80 years. Estimation of health risk associated with radiation doses that are of similar magnitude as those received from natural sources should be strictly qualitative and encompass a range of hypothetical health outcomes, including the possibility of no adverse health effects at such low levels.

The American Nuclear Society recommended further research on the Linear No Threshold Hypothesis before making adjustments to current radiation protection guidelines, concurring with the Health Physics Society's position that:[31]

There is substantial and convincing scientific evidence for health risks at high dose. Below 10 rem or 100 mSv (which includes occupational and environmental exposures) risks of health effects are either too small to be observed or are non-existent.

The US Nuclear Regulatory Commission "accepts the LNT hypothesis as a conservative model for estimating radiation risk" while noting that "public health data do not absolutely establish the occurrence of cancer following exposure to low doses and dose rates — below about 10,000 mrem (100 mSv). Studies of occupational workers who are chronically exposed to low levels of radiation above normal background have shown no adverse biological effects."[32]

Historical documents suggest that an early study invalidating the LNT model was intentionally ignored by Hermann Joseph Muller when he gave his 1946 Nobel Prize address.[33]

Recent fundamental research of the cellular repair mechanisms support the evidence against the linear no-threshold model.[34] According to its authors, this 2011 study published in the Proceedings of the National Academy of Sciences of the United States "casts considerable doubt on the general assumption that risk to ionizing radiation is proportional to dose".

Mental health effects[edit]

The consequences of low-level radiation are often more psychological than radiological. Because damage from very-low-level radiation cannot be detected, people exposed to it are left in anguished uncertainty about what will happen to them. Many believe they have been fundamentally contaminated for life and may refuse to have children for fear of birth defects. They may be shunned by others in their community who fear a sort of mysterious contagion.[35]

Forced evacuation from a radiation or nuclear accident may lead to social isolation, anxiety, depression, psychosomatic medical problems, reckless behavior, even suicide. Such was the outcome of the 1986 Chernobyl nuclear disaster in the Ukraine. A comprehensive 2005 study concluded that "the mental health impact of Chernobyl is the largest public health problem unleashed by the accident to date".[35] Frank N. von Hippel, a U.S. scientist, commented on the 2011 Fukushima nuclear disaster, saying that "fear of ionizing radiation could have long-term psychological effects on a large portion of the population in the contaminated areas".[36]

Such great psychological danger does not accompany other materials that put people at risk of cancer and other deadly illness. Visceral fear is not widely aroused by, for example, the daily emissions from coal burning, although, as a National Academy of Sciences study found, this causes 10,000 premature deaths a year in the US. It is "only nuclear radiation that bears a huge psychological burden — for it carries a unique historical legacy".[35]

See also[edit]


  1. ^ "In the absence of more conclusive data, scientists have assumed that even the smallest radiation exposure carries a risk." GAO study
  2. ^ [1] UNSCEAR Fifty-Ninth Session 21–25 May 2012 | Published 14 August 2012
  3. ^ ICRP publication 103, §66
  4. ^ Consumer Factsheet on: polychlorinated biphenyls US Environment Protection Agency.
  5. ^ Gofman on the health effects of radiation: "There is no safe threshold". Retrieved on 5 May 2012.
  6. ^ NAS BEIR VII Phase 2 Executive Summary retrieved 8 October 2008
  7. ^ Cranney A, Horsley T, O'Donnell S, et al. (August 2007). "Effectiveness and safety of vitamin D in relation to bone health". Evidence Report/technology Assessment (158): 1–235. PMID 18088161. 
  8. ^ High Background Radiation Areas of Ramsar, Iran, S. M. Javad Mortazavi, Biology Division, Kyoto University of Education, Kyoto 612-8522, Japan. Retrieved 4 September 2011.
  9. ^ Babapouran, Mozhgan (2005), "New public dose assessment from internal and external exposures in low- and elevated-level natural radiation areas of Ramsar, Iran", International Congress Series 1276: 169–174, doi:10.1016/j.ics.2004.11.102 
  10. ^ Mosavi-Jarrahi, Alireza; Mohagheghi, Mohammadali; Akiba, Suminori; Yazdizadeh, Bahareh; Motamedid, Nilofar; Shabestani Monfared, Ali (2005), "Mortality and morbidity from cancer in the population exposed to high level of natural radiation area in Ramsar, Iran", International Congress Series 1276: 106–109, doi:10.1016/j.ics.2004.11.109 
  11. ^ Zakeri, F.; Rajabpour, M. R.; Haeri, S. A.; Kanda, R.; Hayata, I.; Nakamura, S.; Sugahara, T.; Ahmadpour, M. J. (2011), "Chromosome aberrations in peripheral blood lymphocytes of individuals living in high background radiation areas of Ramsar, Iran", Radiation and Environmental Biophysics 50 (4): 571–578, PMID 21894441 
  12. ^ Tabarraie, Y.; Refahi, S.; Dehghan, M.H.; Mashoufi, M. (2008), "Impact of High Natural Background Radiation on Woman`s Primary Infertility", Research Journal of Biological Sciences 3 (5): 534–536 
  13. ^ Brenner, David J; et al. (10 November 2003). "Cancer risks attributable to low doses of ionizing radiation: Assessing what we really know". Proceedings of the National Academy of Sciences 100 (24): 13761–6. doi:10.1073/pnas.2235592100. PMC 283495. PMID 14610281. Retrieved 29 August 2007. 
  14. ^ S.M.J. Mortazavi, M. Ghiassi-Nejad, M. Rezaiean, Cancer risk due to exposure to high levels of natural radon in the inhabitants of Ramsar, Iran, International Congress Series, Volume 1276, February 2005, Pages 436–437, ISSN 0531-5131, 10.1016/j.ics.2004.12.012. [2]
  15. ^ Alireza Mosavi-Jarrahi, Mohammadali Mohagheghi, Suminori Akiba, Bahareh Yazdizadeh, Nilofar Motamedi, Ali Shabestani Monfared, [Mortality and morbidity from cancer in the population exposed to high level of natural radiation area in Ramsar, Iran], International Congress Series, Volume 1276, February 2005, Pages 106–109, ISSN 0531-5131, 10.1016/j.ics.2004.11.109.
  16. ^ Douglas Almond, Lena Edlund, Mårten Palme, "Chernobyl's Subclinical Legacy: Prenatal Exposure to Radioactive Fallout and School Outcomes in Sweden" August 2007, NBER working paper 13347, [3]
  17. ^ Muirhead, Colin R; et al. (13 January 2009). "Mortality and cancer incidence following occupational radiation exposure: third analysis of the National Registry for Radiation Workers". British Journal of Cancer 100 (1): 206–212. doi:10.1038/sj.bjc.6604825. PMC 2634664. PMID 19127272. 
  18. ^ Nair, R. R. K.; Rajan, B.; Akiba, S.; Jayalekshmi, P.; Nair, M. K.; Gangadharan, P.; Koga, T.; Morishima, H.; Nakamura, S.; Sugahara, T. (2009). "Background Radiation and Cancer Incidence in Kerala, India—Karanagappally Cohort Study". Health Physics 96 (1): 55–66. doi:10.1097/01.HP.0000327646.54923.11. PMID 19066487.  edit
  19. ^ Tanooka, H. (2011). "Meta-analysis of non-tumour doses for radiation-induced cancer on the basis of dose-rate". International Journal of Radiation Biology 87 (7): 645. doi:10.3109/09553002.2010.545862.  edit
  20. ^ Neumaier, Teresa; et al. (19 December 2011). "Evidence for formation of DNA repair centers and dose-response nonlinearity in human cells". Proceedings of the National Academy of Sciences 108. doi:10.1073/pnas.1117849108. PMC 3258602. PMID 22184222. Retrieved 20 December 2011. 
  21. ^ Health Risks from Exposure to Low Levels of Ionizing Radiation: BEIR VII Phase 2. Retrieved on 5 May 2012.
  22. ^ Society News Archive: BEIR VII Report Supports LNT Model. Retrieved on 5 May 2012.
  23. ^ quoted text available at. (1 June 2003). Retrieved on 5 May 2012.
  24. ^ NAS. Low Levels of Ionizing Radiation May Cause Harm. Press Release, June 29, 2005. Retrieved on 17 December 2012
  25. ^ NCRP report. Retrieved on 5 May 2012.
  26. ^ UNSCEAR 2000 REPORT Vol. II: Sources and Effects of Ionizing Radiation: Annex G: Biological effects at low radiation doses. page 160, paragraph 541. Available online at [4].
  27. ^ U.S. Environmental Protection Agency (April 2011). "EPA Radiogenic Cancer Risk Models and Projections for the U.S. Population". EPA. Retrieved 15 November 2011. 
  28. ^ Heyes et al. (1 October 2006). "Authors' reply". British Journal of Radiology (The British Medical Journal) 79 (946): 855–857. doi:10.1259/bjr/52126615. Retrieved 27 March 2008. 
  29. ^ Aurengo et al. (30 March 2005). Dose-effect relationships and estimation of the carcinogenic effects of low doses of ionizing radiation.. Académie des Sciences & Académie nationale de Médecine. Retrieved 27 March 2008. 
  30. ^ Health Physics Society, 2010. Radiation Risk in Perspective PS010-2 [5]
  31. ^ The American Nuclear Society, 2001. Health Effects of Low-Level Radiation. Position Statement 41 [6]
  32. ^ "Radiation Exposure and Cancer". Nuclear Regulatory Commission. 29 March 2012. Retrieved 11 December 2013. 
  33. ^ Calabrese, E. J. (30 June 2011). "Muller’s Nobel lecture on dose–response for ionizing radiation:ideology or science?". Archives of Toxicology (Springer) 81 (4): 1495–1498. doi:10.1007/s00204-011-0728-8. PMID 21717110. Retrieved 30 December 2011. 
  34. ^ Neumaier, T.; Swenson, J., Pham, C., Polyzos, A., Lo, A. T., Yang, P., Dyball, J., Asaithamby, A., Chen, D. J., Bissell, M. J., Thalhammer, S., Costes, S. V. (19 December 2011). "Evidence for formation of DNA repair centers and dose-response nonlinearity in human cells". Proceedings of the National Academy of Sciences 109 (2): 443–8. doi:10.1073/pnas.1117849108. PMC 3258602. PMID 22184222. 
  35. ^ a b c Andrew C. Revkin (March 10, 2012). "Nuclear Risk and Fear, from Hiroshima to Fukushima". New York Times. 
  36. ^ Frank N. von Hippel (September/October 2011 vol. 67 no. 5). "The radiological and psychological consequences of the Fukushima Daiichi accident". Bulletin of the Atomic Scientists. pp. 27–36. 

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