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To explain the known differences in the dose and age dependences of radiogenic mortality from leukemia and solid tumors after single exposure, a model was developed, which is a modification of the Kellerer-Rossi theory of dual radiation action. The model assumes formation in a cell of both single and double primary damages due to radiation and other carcinogens, while the recovery rate of single damages (φ) significantly exceeds that for double ones (ψ). Upon achieving a certain stage of the cell cycle (the critical age of cell – T), double damages become permanent and with probability of А can be inherited to daughter cells as “premalignant” defects. In contrast, in the Kellerer-Rossi theory, permanent damage is formed immediately after formation of the second damage at the next energy absorption event in the cell, i.e. ψ=0 .On the assumption that the premalignant defects only occur based on the double primary damages, i.e. φ>>ψ, the expressions for А were derived for the prompt radiation exposure and radiation exposure at a constant dose rate. They reproduce the effect increasing with decreasing of T, whereas the influence of T on the linear term of the dose expression in both cases is the same, but with decreasing of T the quadratic term increases faster for exposure at a constant dose rate than that for the prompt one. Thus, presence of the quadratic term in the dose expression for leukemia and its virtual complete absence for solid tumors may be due to lower T-value for hemopoietic stem cells. Predicted by the model dose rate influence on the quadratic term does not depend on the dose, so the reduction factor should be only applied to the quadratic term of the dose expression. This follows as well from the original version of the Kellerer-Rossi theory.

A mathematical model for radiogenic increasing of mortality was proposed, taking into account spontaneous background damages of the genetic material, that always occur in cells due to the influence of non-radiation internal and environmental factors. The model is based on the representation of indistinguishability between radiogenic andspontaneous cancers and on the postulates of the Kellerer-Rossi dual action theory. It was proposed that duringformation of premalignant damages dual interactions occur both between primary radiation damages, and betweenradiation and spontaneous primary damages (hybrid interactions). The role of the latter is particularly important at low levels exposure that corresponds to a linear dependence of cancer incidence on dose. Their significance is indicated by the following factor: at the adopted value of the nominal (radiation) risk factor (0,05 Sv-1) and cancer mortality share among the population (0,15–0,2), the contribution of non-radiative carcinogenic factors for the total life is equivalent to radiation dose of 3–4 Sv or radiation at a constant dose rate of 40–50 mSv / year.The model assumes formation in DNA of both spaced apart (single) damages with high probability of recovery, and nearby (double) damages, which are more likely to interact, entering into the permanent state. Permanent damages being formed in certain portions of DNA can be inherited to daughter cells as premalignant defects. The relative role of spontaneous primary damages is greater the more single damages are formed as compared to double ones within the area of potential interaction.It was shown within this model that the presence of background cancer mortality for initial and finite population in the used by ICRP expression for interpopulation risk transfer has logical and biophysical justifications. Accounting of spontaneous primary damages and hybrid interactions enhances the capabilities for development of radiation risk models.