3D Multi-scale Modelling Of Vascular Tumour Growth

Malignant tumor, also known as cancer, is now one of the most serious public issues in the world, which has been greatly endangering human health. Due to the complexity of the tumor biological experiments and clinical research, researchers are increasingly foc using on using mathematical model to explain and predict the biological phenomenon during tumor growth. Also, mathematical modeling and computational simulation has become a new way for studying tumor. In this paper, based on the existing models, a modeling about the process of vascular tumor cells is proposed.In this paper, we adopt the method of multi-scale, using three levels of inner cell scale, cellular scale and extracellular scale, to study the growth of tumor cell. At the inner cell scale we mainly consider how the oxygen concentration around the cell affect the cycle of tumor cell; at the cellular scale we mainly consider the division, migration, dormancy and death of cell, and using cellular automatic machine to model the behaviors of cel ls; at the extracellular scale we mainly consider the nutrient concentration that influence the growth of tumor, especially the diffusion of oxygen concentration, and use convection diffusion equation to model this type of diffusion process.Since the distribution of oxygen concentration will directly affects the growth of tumor cells, computation of the distribution of oxygen concentration is the foundation of the whole experiment. We use the Cellular Automatic Machine(CAM) to choice rulers to do the meshing, and solve the convection diffusion equation of oxygen diffusion, based on Finite Difference Method(FDM). This paper shows the simulations of avascular tumor and how the oxygen concentration affect vascular tumor growth in 3D space.Simulation results show that the proposed model can simulate avascular and vascular tumor growth well enough. In the growth of avascular tumor, when the tumor cells are small, tissue can provide sufficient oxygen to the tumor by diffusion. As the tumor cells begin to growth, the oxygen concentration of tissue will become lower and lower, which cause part of the cells of tumor enter dormant state due to lack of oxygen. Those cells that is in the center of tumor will die after a long time of dormancy. The internal structure of tumor will be three layers: proliferation layer in the outer, dormant layer in the middle and necrosis in the center. In vascular tumor growth, the cell the closer to the blood vessels, the faster it grow, and vice versa. As the number of tumor cells increase, the tumor cells away from the blood vessels enters the state of dormancy and death, and finally the tumor cells around the blood vessels can survive.In conclusion, the proposed model in this paper is well feasible, and it lays the foundation for the application of computer simulation and the development of drug effects on tumor cells.