Ohtaki, M. and Niwa, O. A Mathematical Model of Radiation Carcinogenesis with Induction of Genomic Instability and Cell Death. Radiat. Res. 156, 672–677 (2001).

We developed a mathematical model of carcinogenesis that incorporates genomic instability, a feature characterized by long-term destabilization of the genome in irradiated cells that leads to an increase in cancer risk in the exposed individuals at the cancer-prone age. This model also considers the induction of cell death, another important effect of radiation on cells. It is assumed that cell killing by radiation may occur at all stages of the carcinogenic process. The resulting model can explain not only the paradoxical relationship between low mutation rates and high cancer incidence but also the low-order dose–response relationship of cancer risk.