Opposition to the Linear No-Threshold Model

Sydney Lance
March 22, 2018

Submitted as coursework for PH241, Stanford University, Winter 2018

The Linear No-Threshold Model

Fig. 1: A graphical representation of the Linear No-threshold Model. The red line is the model (linear relationship between cancer and radiation exposure) and the green line is the natural occurrence of cancer (Source: S. Lance).

For low levels of radiation exposure, below an exposure of 50 to 100 millisieverts (mSv), the effects of radiation are not entirely known. [1] There are many theories as to how low levels of radiation exposure effect organisms, and perhaps the most prominent of these theories is the linear no-threshold model. [1-3] The linear no-threshold model (Fig. 1) suggests that the damage to an organism from radiation, more specifically the presence of cancer, is directly proportional to the dose. However, the model does not take into account the rate of the dosage or the amount of the dose. [1,2]

The theory initially gained support in the 1970s after the Committee on the Biological Effects of lonizing Radiation used studies involving the extrapolation of radiation exposure data from those who experienced higher levels of radiation exposure and animal studies to support this theory. The model has largely affected radiation policy in the United States ever since despite the fact that many find problems with the model. [1,3,4] This widespread adoption of the model is due to both the fact that it is a relatively safe assumption to make and that various sets of data fit the model relatively well. [1,5] Since no other theory has definitively been proven and there are so many confounding variables that can influence the results of studies at low levels of radiation, this safer model is still widely used. [1]

Opposition to the Model

Many find the linear no-threshold model to be conservative, meaning that they believe the model is an overestimation of radiation risks at lower radiation levels. [1,2,4] Although this is beneficial in some aspects, relating to safety, there are consequences to spreading the information that all radiation is dangerous at any level or exposure. [4]

The main justifications for the linear no-threshold model stem from the concepts that small amounts of radiation can cause DNA damage and that a greater number of mutations is linked to a greater risk of cancer. Radiation and mutations do somewhat follow a linear model, however, this model does not take into account the human response to low levels of radiation, which can actually prevent further DNA damage. The body responds to smaller amounts of DNA damage with increased defenses, which, in turn, actually lowers the risk of cancer overall. [4] Recent evidence also suggests that instances of cancer do not increase with an increased number of mutations. Essentially, if more mutations are caused by radiation, it does not necessarily lead to a higher occurrence of cancer. [6] Therefore, some of the key aspects of the linear no-threshold model are flawed.

Various studies also find that lower levels of radiation are not entirely harmful and that there possibly is a threshold for radiation exposure danger. For humans, there do not appear to be carcinogenic effects due to long-term exposure to radiation for doses under 500 mSv and for short-term exposure for doses under 100 mSv. This data comes from a variety of sources and locations varying from atomic blast survivors to occupational exposure to those undergoing diagnostic X-rays. [4] The data from many of these studies also suggests that at low levels, the duration and dose of the exposure play a significant role in the effects on the organism, which the linear no-threshold model does not account for. [1,4]


Radiation exposure and its effects on organisms are difficult to understand at low levels with so many confounding factors and varying data. The linear no-threshold model is, on occasion, aligned with radiation data, but all of the factors have led many scientists to believe that the issue is too complicated for a simple linear model and that it is possible that no one model will ever fit all radiation exposure data. [1] Although it is safe to use the linear no threshold model, the consequences for its use could possibly be worse than the benefits. For example, the overestimation of radiation effects during the Chernobyl disaster led to between 100,000 and 200,000 abortions that were likely unnecessary and about 1,250 suicides. [4] Upon investigating radiation exposure relating to risk, it seems that radiation exposure is too complicated and varied to be modeled with the linear no-threshold model. It will likely take some time to develop a model that is highly accurate in predicting low-level radiation risks.

© Sydney Lance. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] "Radiation Standards: Scientific Basis Inconclusive, and EPA and NRC Disagreement Continues," U.S. General Accounting Office, GAO/RCED-00-152, June 2000.

[2] L. Yang, "Low Level Radiation on Human Health," Physics 241, Stanford University, Winter 2016.

[3] E. Calabrese, "The Threshold vs LNT Showdown: Dose Rate Findings Exposed Flaws in the LNT Model Part 2. How a Mistake Led BEIR I to Adopt LNT," Environ. Res. 154, 452 (2017).

[4] M. Tubiana et al., "The Linear No-Threshold Relationship Is Inconsistent with Radiation Biologic and Experimental Data," Radiology 251, 13 (2009).

[5] C. Vandevoorde et al., "γ-H2AX Foci as in Vivo Effect Biomarker in Children Emphasize the Importance to Minimize X-Ray Doses in Paediatric CT Imaging," Eur. Radiol. 25, 800 (2015).

[6] I. Martincorena et al., "Tumor Evolution. High Burden and Pervasive Positive Selection of Somatic Mutations in Normal Human Skin," Science 348, 880 (2015).