A model of multiple tumorigenesis allowing for cell death: Quantitative insight into biological effects of urethane

This paper considers the utility of a stochastic model of carcinogenesis proposed by Yakovlev and Polig [Math. Biosci. 132 (1996) 1–33] in the analysis of experimental data on multiple tumors induced by chemical carcinogens. The model provides a good description of published data on multiple tumors developing in the lungs of mice in response to different schedules of urethane. The distribution of pulmonary tumor counts appears to be negative binomial for each period of time after exposure to urethane. Our results suggest that the rate of administration of urethane has little effect both on the mean number of initiated cells per unit dose and on the rate of formation of lesions responsible for cell death. As our estimates show, more than 80% of initiated cells die in the course of tumor promotion. The model is robust to variations in the rate of urethane excretion given a fixed total dose of the carcinogen. Some prospects for further development of the model to allow for expansion of promoted cell clones are discussed.