Numerical Simulation Of Avascular Tumor Growth And Tumor-induced Angiogenesis

Tumor negatively impacts the health of human beings. Understanding how cancerdevelops has a profound and far reaching significance since it can help to guide clinicaldiagnosis and treatment. Tumor growth is a complex and continuous process and iscategorized into three phases namely: avascular growth phase, angiogenesis phase, andvascular tumor growth phase. Based on the existing models, two models which describe theavascular tumor growth phase and angiogenesis phase respectively are proposed in this thesis.The mathematical model of avascular tumor growth and development is a hybrid modelbased on finite element method which spans two distinct scales. At the extracellular level,reaction-diffusion equations describe the chemical dynamics including the nutrients whichdetermine the proliferation of tumor cell as well as nutrients which affect tumor cell migrationand necrotic. At the cellular level, a probabilistic cellular automata model is used to modelcell proliferation, motility and death. In addition, shedding of the cells at the surface of thetumor spheroid is considered. Compared to the traditional uniform mesh, using the finiteelement method can be adapted to a more flexible mesh, and thus more realistic simulation oftumor morphology.A hybrid mathematical model to understand the mechanisms behind tumor-inducedangiogenesis is presented. The model describes uptake of tumor angiogenic factor atextracellular level, uses partial differential equation to describe the evolution of endothelialcell density including endothelial cell proliferation, chemotaxis to tumor angiogenic factor,and haptotaxis to extracellular matrix. In addition, the phenomenon of blood perfusion in themicro-vessels is considered in this model.The numerical simulation results indicate that the models presented in this thesis canreflect the primary features of avascular tumor growth and tumor-induced angiogenesis. Atthe avascular tumor growth phase, the model shows that the spatial structure composed of acentral necrotic core, an inner rim of quiescent cells and a narrow outer shell of proliferatingcells which is in agreement with biological data. And the total number curves of tumor cellsin avascular growth stage follows the trend of exponential growth in the early period and thenlinear growth. The model of angiogenesis produces sprout formation with realisticmorphological and dynamical features, including the so-called “brush border effect”, thedendritic branching and fusing of the capillary sprouts forming a vessel network. Therefore,the models proposed in this thesis have better viability and can lay the foundation for further studies of drugs on tumor cells.