Author(s)

Lujun Zhang, Kai Han and Yonggui Xu

Corresponding Author

Yonggui Xu

Abstract

With the aid of computer technology and the use of mathematical physical method, it is of special significance to construct a tumor growth model, to obtain the knowledge of tumor biology behaviors and to assistant clinical treatment. Based on the solid tumor biochemical environment, the proposed model focused on three factors: the concentration of nutrient, extracellular matrix giant molecules, and also tumor surrounding tissue environment characteristics, which were combined to diffusion terms, convection terms and reaction terms of a diffusion-convection-reaction equation which was the foundation of the model. The tumor cells were divided into two groups of proliferating cells and necrotic cells. The proposed model established a coupling model which had respective equations for these two groups of tumor cells, to show the dynamic tumor growth process with the interaction effect of these two groups. The simulation results demonstrated that the proposed model could show the process of tumor growth, and the interaction between the tumor growth and the various factors, and also coincided with the actual tumor biological behaviors.

Keywords

Solid tumor growth, mathematical modeling, diffusion-convection-reaction equation, tumor biochemical environment.