A model for hepatocarcinogenesis treating phenotypical changes in focal hepatocellular lesions as epigenetic events

The major paradigm for mathematically describing the carcinogenic process has been through the use of multistage models. Multistage models are made up of numerous compartments representing cells in various stages on the way to malignancy and where movement from one cell class to another is assumed to have exponential waiting time. Once a cell is in a particular class, clonal expansion through a linear birth-death process increases the size of the compartment. These models are characterized by movement of single cells from one compartment to another rather than clonal colonies of cells. However, there is some evidence to suggest that, in certain organs for certain types of agents, preneoplastic lesions with different phenotypes arise directly from an entire clonal colony rather than from a single cell within that colony. This manuscript describes a simple mathematical model of carcinogenesis using both persistent changes of single or several cells (to start the process) and shifting of colonies to describe the stages of the model. Likelihoods for the use of the model with data on colonies of preneoplastic lesions are described and applied to real data.