Mathematical modelling of tumor growth

The carcinogenesis is a very complex multistage phenomenon, including a large number of variables with specific activities and interacting between them. This review intends to present very briefly the main stages in a tumor evolution. A model with three types of cells (proliferating, quiescent and dead cells) in a macroscopic tumor is presented in more detail. Their densities are satisfying partially differential equations of reaction-diffusion type, with coefficients depending on the nutrient concentration. The space and time evolution of the nutrient is governed by a diffusion equation. Free boundary conditions have to be considered, as the tumor radius is changing in time. For the very simplified model of a single component, the stationary state and the tumor radius are explicitly calculated.