Super-competition as a Novel Mechanism of the Dose-rate Effect in Radiation Carcinogenesis: A Mathematical Model Study

Data from animal experiments show that the radiation-related risk of cancer decreases if the dose rate is reduced, even though the cumulative dose is unchanged (i.e., a dose-rate effect); however, the underlying mechanism is not well understood. To explore factors underlying the dose-rate effect observed in experimental rat mammary carcinogenesis, we developed a mathematical model that accounts for cellular dynamics during carcinogenesis, and then examined whether the model predicts cancer incidence. A mathematical model of multistage carcinogenesis involving radiation-induced cell death and mutagenesis was constructed using differential equations. The mutation rate was changed depending on the dose rate. The model also considered competition among cells with various mutation levels. The main parameters of the model were determined using previous experimental data. The parameters of the model were consistent with experimental observations. A dose-rate effect on carcinogenesis became apparent when the relationship between dose rate and mutation rate was linear quadratic or quadratic. The dose-rate effect became prominent when cells with more mutations preferentially compensated for the radiation-induced death of cells with fewer mutations. The phenomenon by which mutated cells gain a competitive advantage over normal cells is known as super-competition. Here, we identified super-competition as a novel mechanism underlying the dose-rate effects on carcinogenesis. The data also confirmed the relevance of the shape of the relationship between dose rate and the mutation rate. Thus, this study provides new evidence for the mechanism underlying the dose-rate effect, which is important for predicting the cancer-related risks of low-dose-rate irradiation.