linear no-threshold model linear no-threshold model the linear no-threshold model (lnt) is a dose-response model used in radiation protection to estimate stochastic health effects such as radiation-induced cancer, genetic mutations and teratogenic effects on the human body due to exposure to ionizing radiation. the model statistically extrapolates effects of radiation from very high doses (where they are observable) into very low doses, where no biological effects may be observed. the lnt model lies at a foundation of a postulate that all exposure to ionizing radiation is harmful, regardless of how low the dose is, and that the effect is cumulative over lifetime. different assumptions on 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 lnt model is commonly used by regulatory bodies as a basis for formulating public health policies that set regulatory dose limits to protect against the effects of radiation. the model has also been used in the assessment of cancer risks of mutagenic chemicals. the validity of the lnt model, however, is disputed, and other significant models exist: the threshold model, which assumes that very small exposures are harmless, the radiation hormesis model, which says that radiation at very small doses can be beneficial, and the supra-linear model based on observational data. whenever the cancer risk is estimated from real data at low doses, and not from extrapolation of observations at high doses, the supra-linear model is verified. it has been argued that the lnt model may have created an irrational fear of radiation. different organizations take different approaches to the lnt model. for example, the us nuclear regulatory commission and united states environmental protection agency endorse the model, while a number of other bodies deprecate it. one of the organizations for establishing recommendations on radiation protection guidelines internationally, the united nations scientific committee on the effects of atomic radiation (unscear) that previously supported the lnt model, no longer supports the model for very low radiation doses. introduction stochastic health effects are those that occur by chance, and whose probability is proportional to the dose, but whose severity is independent of the dose. the lnt model assumes there is no lower threshold at which stochastic effects start, and assumes a linear relationship between dose and the stochastic health risk. in other words, lnt assumes that radiation has the potential to cause harm at any dose level, however small, and the sum of several very small exposures is just as likely to cause a stochastic health effect as a single larger exposure of equal dose value. in contrast, deterministic health effects are radiation-induced effects such as acute radiation syndrome, which are caused by tissue damage. deterministic effects reliably occur above a threshold dose and their severity increases with dose. because of the inherent differences, lnt is not a model for deterministic effects, which are instead characterized by other types of dose-response relationships. lnt is a common model to calculate the probability of radiation-induced cancer both at high doses where epidemiology studies support its application, but controversially, also at low doses, which is a dose region that has a lower predictive statistical confidence. nonetheless, regulatory bodies, such as the nuclear regulatory commission (nrc), commonly use lnt as a basis for regulatory dose limits to protect against stochastic health effects, as found in many public health policies. whether the lnt model describes the reality for small-dose exposures is disputed, and challenges to the lnt model used by nrc for setting radiation protection regulations were submitted. nrc rejected the petitions in 2021 because "they fail to present an adequate basis supporting the request to discontinue use of the lnt model". the lnt model 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. a 2016 peer-reviewed meta-analysis rejected the lnt on the basis of a lack of empirical evidence supporting it, and that it ignores biological effects, especially the self-correcting mechanisms in dna which are effective up to a certain level of mutagenic agent. because the current data is inconclusive, scientists disagree on which model should be used. pending any definitive answer to these questions, the lnt model is applied through the precautionary principle. the model is sometimes used to quantify the cancerous effect of collective doses of low-level radioactive contaminations, which may produce estimates of excess deaths at levels that may have had zero deaths or saved lives in the two other models. such practice has been criticized by the international commission on radiological protection since 2007. the lnt model is sometimes applied to other cancer hazards such as polychlorinated biphenyls in drinking water. origins increased risk of solid cancer with dose for a-bomb survivors, from beir report. notably, this exposure pathway occurred from essentially a massive spike or pulse of radiation, a result of the brief instant that the bomb exploded, which while somewhat similar to the environment of a ct scan, is wholly unlike the low dose rate of living in a contaminated area such as chernobyl, where the dose rate is orders of magnitude smaller. lnt does not consider dose rate and is an unsubstantiated one size fits all approach based solely on total absorbed dose. when the two environments and cell effects are vastly different. likewise, it has also been pointed out that bomb survivors inhaled carcinogenic benzopyrene from the burning cities, yet this is not factored in. the association of exposure to radiation with cancer had been observed as early as 1902, six years after the discovery of x-rays by wilhelm röntgen and radioactivity by henri becquerel. in 1927, hermann muller demonstrated that radiation may cause genetic mutation. he also suggested mutation as a cause of cancer. gilbert n. lewis and alex olson, based on muller's discovery of the effect of radiation on mutation, proposed a mechanism for biological evolution in 1928, suggesting that genomic mutation was induced by cosmic and terrestrial radiation and first introduced the idea that such mutation may occur proportionally to the dose of radiation. various laboratories, including muller's, then demonstrated the apparent linear dose response of mutation frequency. muller, who received a nobel prize for his work on the mutagenic effect of radiation in 1946, asserted in his nobel lecture, the production of mutation, that mutation frequency is "directly and simply proportional to the dose of irradiation applied" and that there is "no threshold dose". the early studies were based on higher levels of radiation that made it hard to establish the safety of low level of radiation. indeed, many early scientists believed that there may be a tolerance level, and that low doses of radiation may not be harmful. a later study in 1955 on mice exposed to low dose of radiation suggests that they may outlive control animals. the interest in the effects of radiation intensified after the dropping of atomic bombs on hiroshima and nagasaki, and studies were conducted on the survivors. although compelling evidence on the effect of low dosage of radiation was hard to come by, by the late 1940s, the idea of lnt became more popular due to its mathematical simplicity. in 1954, the national council on radiation protection and measurements (ncrp) introduced the concept of maximum permissible dose. in 1958, the united nations scientific committee on the effects of atomic radiation (unscear) assessed the lnt model and a threshold model, but noted the difficulty in acquiring "reliable information about the correlation between small doses and their effects either in individuals or in large populations". the united states congress joint committee on atomic energy (jcae) similarly could not establish if there is a threshold or "safe" level for exposure; nevertheless, it introduced the concept of "as low as reasonably achievable" (alara). alara would become a fundamental principle in radiation protection policy that implicitly accepts the validity of lnt. in 1959, the united states federal radiation council (frc) supported the concept of the lnt extrapolation down to the low dose region in its first report. by the 1970s, the lnt model had become accepted as the standard in radiation protection practice by a number of bodies. in 1972, the first report of national academy of sciences (nas) biological effects of ionizing radiation (beir), an expert panel who reviewed available peer reviewed literature, supported the lnt model on pragmatic grounds, noting that while "dose-effect relationship for x rays and gamma rays may not be a linear function", the "use of linear extrapolation . . . may be justified on pragmatic grounds as a basis for risk estimation." in its seventh report of 2006, nas beir vii writes, "the committee concludes that the preponderance of information indicates that there will be some risk, even at low doses". radiation precautions and public policy