Incorporating phenotype-dependent growth rates into the color-shift model for preneoplastic hepatocellular lesions

Multi-stage models occupy a central position in modeling the carcinogenesis process. These models formalize the hypothesis that cells have to undergo several transformations on their way to malignancy. This hypothesis assumes that a preneoplastic cell of a later stage arises through a mutational event of a single cell of a previous stage and that preneoplastic cells proliferate clonally. However, there is some evidence that multi-stage models cannot adequately describe the formation and the progression of preneoplastic lesions at least in certain organs [Math. Biosci. 168 (2000) 167]. An alternative model assuming that all cells in a colony of altered hepatocytes change their phenotype more or less simultaneously rather than by mutation of single cells has already been introduced [Math. Biosci. 148 (1998) 181] and is called color-shift model (CSM). This model assumed deterministic phenotype-independent growth for the foci once they are generated. An expansion of the CSM allowing for variability between deterministic growth behaviour of phenotypically different colonies is presented (modCSM) and the model is applied to focal lesion data from a rat hepatocarcinogenesis experiment. The fit of the originally proposed and the modCSM are compared with respect to their ability to predict numbers and radii of preneoplastic cell foci.