The prospective mathematical idea satisfying both radiation hormesis under low radiation doses and linear non-threshold theory under high radiation doses

It has yet to be determined whether or not the probability of developing cancer due to radiation exposure levels of low doses is proportional to the dose. Herein, for radiation hormesis occurring at low doses, mathematical models using functions that take a mountain-like shape having two inflection points are considered. The following perspectives were obtained: (i) When the probability of developing cancer decreases at radiation levels above the natural background dose, the radiation hormesis effect occurs up to ~ 12.4 mSv. (ii) When there is a proportional relationship at ≥750 mSv, the radiation hormesis effect occurs up to ~ 225 mSv. Thus, by performing studies at the molecular and cellular levels for radiation doses at ≤16.8 or 307 mSv, it is possible to investigate carcinogenesis resulting from low radiation doses.