Computer simulation of cell growth governed by stochastic processes: application to clonal growth cancer models

Cancer is a multistage process in which cell proliferation determines the growth of cells within stages and is associated with the transition of cells from one stage to the next. The usual model for cancer risk assessment, the linearized multistage model, does not explicitly include cell proliferation. More realistic cancer models are needed to reduce uncertainty in cancer risk assessment and to provide basic insights into the quantitative roles of cell proliferation and mutation. This report describes a simulation model for the transition of cells from one stage to the next and for clonal growth within stages. The model is intended to facilitate the use of experimental data on cell replication and preneoplastic lesions in risk assessment. When a population of cells is small its growth may be governed by stochastic processes. Such a population may disappear by chance even when the probability of cell division on a given time interval exceeds the probability of cell death. Procedures for estimating cell proliferation and mutation parameters from data for use in risk assessment should account for this random aspect of growth. The present model describes cell growth governed by stochastic processes, is consistent with earlier analytical expressions for such growth (Dewanjii et al., Risk Anal. 9, 179, 1989), and is flexible with respect to time-dependent data. A data set for spontaneous basophilic clones in male F344 rats (Popp et al., Fundam. Appl. Toxicol. 5, 314, 1985) is analyzed and predictions are made for (a) the probability of mutation to the basophilic genotype per division of a normal hepatocyte (3.5 x 10(-8)), (b) number of basophilic clones too small to be detected, and (c) number of basophilic clones that disappear by chance. This work illustrates the potential of computer simulation for quantitative analysis of the roles of cell division, cell death, and mutation in cancer.