Biodynamic Modeling and Simulation of Multistage Cell Mutations

Abstract

The aim of this study is to present a mathematical computer simulation model for multistage carcinogenesis. The population genetic model is developed based on the reaction diffusion, logistic behavior, and Hollings Type II interactions between normal, benign, and premalignant cells. The simple form of the Fisher-Haldane-Wright equation of the genetic model of tumor suppressor gene and oncogenes is used to describe this type of interaction. Through computer simulation, we observe the behavior, stability, and traveling wave solution of the premalignant stage mutation as well as its survival under natural selection pressure. As a simple case of this model, the interaction between normal and tumor cells with one or two stages of mutations is analyzed.