Linear no-threshold model

Linear no-threshold model

The linear no-threshold model (LNT) is a method for predicting the long term, biological damage caused by ionizing radiation and is based on the assumption that the risk is directly proportional to the dose at all dose levels. In other words, the sum of several very small exposures have the same effect as one larger exposure. The LNT model therefore predicts higher risks than either the threshold model, which assumes that very small exposures are negligible, or the radiation hormesis model, which predicts the least risk by assuming that radiation at very small doses can be beneficial. Because the current data are inconclusive, scientists disagree on which method should be used.[1]

LNT, or at least "no threshold", is sometimes applied to other cancer hazards such as polychlorinated biphenyls in drinking water.[2]



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".[3]

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".[4]

Radiation precautions and public policy

If a particular dose of radiation is found to produce one extra case of a type of cancer in every thousand people exposed, LNT predicts that one thousandth of this dose will produce one extra case in every million people so exposed, and that one millionth of this dose will produce one extra case in every billion people exposed. This means that any given quantity 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 calculate by extrapolation, the expected number of extra deaths caused by exposure to environmental radiation, and it therefore has a great impact on public policy. The model allows any radiation release, like that from a dirty bomb, to be translated into a number of lives lost, while any reduction in radiation exposure, for example as a consequence of radon detection, can be immediately 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 can easily reach 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.

As a counter example to LNT, Ramsar in Iran is noted for having the highest natural background radiation levels on Earth and they are a few times higher than the ICRP recommended radiation dose limits for radiation workers. The local population does not seem to suffer any ill effects.[5].


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 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."[6]

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.[7] Neurological damage has a different biology than cancer, and for cancer rates there are conflicting studies.


In recent years, the accuracy of the LNT model at low dosage has been questioned. Some believe that if radiation is distributed evenly enough, so that the levels are comparable to the natural levels, it has no harmful health effects.

Several expert scientific panels have been convened on the topic of the Linear no-threshold model.

  • the United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) wrote in its 2000 report[12]

    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:[13]

    "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:[14][15]

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:[16]

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 in one year or a lifetime dose of 10 rem above that received from natural sources. Doses from natural background radiation in the United States average about 0.3 rem per year. A dose of 5 rem will be accumulated in the first 17 years of life and about 25 rem 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 [17] :

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

Dr John DeSesso, academic expert in teratology writes,[18]

When conducting risk assessments, the US Environmental Protection Agency (EPA) does not currently consider the beneficial effects from exposure to concentrations of agents below the no observed adverse effect level (NOAEL). If such benefits were observed, and if the beneficial and toxicological mechanisms of action were identical, this would probably be represented as a ‘j–shaped’ hormetic dose–response curve. If such data are available, they should be considered when assigning uncertainty factors for safe exposure calculations.

See also


  1. ^ "In the absence of more conclusive data, scientists have assumed that even the smallest radiation exposure carries a risk." GAO study
  2. ^ Consumer Factsheet on: polychlorinated biphenyls US Environment Protection Agency.
  3. ^ Gofman on the health effects of radiation: "There is no safe threshold"
  4. ^ NAS BEIR VII Phase 2 Executive Summary retrieved 8 October 2008
  5. ^ 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.
  6. ^ Brenner, David J; et al. (2003-11-10). "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 2007-08-29. 
  7. ^ 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, [1]
  8. ^ Health Risks from Exposure to Low Levels of Ionizing Radiation: BEIR VII Phase 2
  9. ^ Society News Archive: BEIR VII Report Supports LNT Model
  10. ^ quoted text available at: [2]
  11. ^ NCRP report
  12. ^ 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 [3].
  13. ^ U.S. Environmental Protection Agency (April 2011). "EPA Radiogenic Cancer Risk Models and Projections for the U.S. Population". EPA. Retrieved Nov 15, 2011. 
  14. ^ Heyes et al. (2006-10-01). "Authors' reply". British Journal of Radiology (The British Medical Journal) 79 (946): 855–857. doi:10.1259/bjr/52126615. Retrieved 2008-03-27. 
  15. ^ Aurengo et al. (2005-03-30). Dose-effect relationships and estimation of the carcinogenic effects of low doses of ionizing radiation.. Académie des Sciences & Académie nationale de Médecine. Retrieved 2008-03-27. 
  16. ^ Health Physics Society, 2010. Radiation Risk in Perspective PS010-2 [4]
  17. ^ The American Nuclear Society, 2001. Health Effects of Low-Level Radiation. Position Statement 41 [5]
  18. ^ The case for integrating low dose, beneficial responses into US EPA risk assessments Human & Experimental Toxicology journal.

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