Application of a color-shift model with heterogeneous growth to a rat hepatocarcinogenesis experiment

Several hypotheses are established to describe the formation and progression of foci of altered hepatocytes (FAH). A common model of hepatocarcinogenesis is the mutation model (MM), which is based on the assumption that cells have to undergo multiple successive changes on their way from the normal to the malignant stage. This model describes growth and phenotype change of foci on the cellular level and is based on the assumption that single cells change their phenotype through mutation into the next stage and proliferate according to a linear stochastic birth-death process. In contrast, the color-shift model (CSM) was introduced by Kopp-Schneider et al. to describe that whole colonies of altered hepatocytes simultaneously alter their phenotype. In this paper two modifications of the color-shift model are considered which allow the growth rate to vary from focus to focus. All four models are compared with respect to their ability to predict number and radii of foci in a rat hepatocarcinogenesis experiment, in which rats were treated with the carcinogens N-nitrosomorpholine, 2-acetylaminofluoren and Phenobarbital. Maximum likelihood parameter estimates are given, and predicted and empirical FAH size distributions are visualized. The Cramer-von-Mises distance is used as a measure for the discrepancy between empirical and theoretical size distributions.