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

Abstract

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.

Keywords: Inhibition effect; LNT theory; Radiation hormesis.

Fig. 1

Graph of inhibition effect R(x) due to the inhibitor factor. The radiation dose is defined as x. The radiation dose at which R(x) reaches a maximum is defined as x₁. a Single point of inflection for x > x₁. b One single point of inflection for 0 < x < x₁ and another for x > x₁

Fig. 2

Graph of probability of developing cancer D(x). The radiation dose is defined as x. The linear dashed lines from the zero points indicate LNT (Eq. 1). a D(x) with hormesis region present. The value of x for the local minimum of D(x) is defined as x₂, for which Eq. 6 must be satisfied. b D(x) with no hormesis region present. c D(x) having negative values. d D(x) of type a. having the maximum hormesis region. The value of x for the local minimum of D(x) is defined as x₂, for which Eqs. 5 and 6 must be satisfied. The value of x for the local maximum of D(x) is defined as x₃, and the other value of x where D has the same value as the local maximum D(x₃) is defined as x₄ (ZEP). The hormesis region is x₃ < x < x₄

Fig. 3

Probability of developing cancer D(x) at the point where a hormesis region begins to appear. The radiation dose is defined as x. The value of x is defined as x₂, for which Eqs. 11 and 12 must be satisfied. The linear dashed line from the zero point indicates LNT (Eq. 1)