MODELING AND SIMULATION OF AVASCULAR TUMOR GROWTH: THE EFFECT OF CELL MIGRATION

摘要

A quantitative analysis of tumor growth at the tumor scale may be of value to therapeutic strategies that aim to control disease extension into surrounding healthy tissue. Our aim is to model avascular tumor growth due to directed cell motions and investigate the role of different taxis and biophysical parameters on tumor growth. Using one dimensional numerical simulation, we will present the results of a parameter study of tumor growth with a range of biophysical and taxis parameters and investigate the causal link between these parameters on tumor growth and the internal tumor structure. We will consider the evolution of live and dead tumor cells using a sharp interface model where species movement depends on oncotic pressure from cell proliferation, adhesion forces between cell-cell and cell- extracellullar matrix (ECM), and relative strength of chemotaxis, due to the nutrient gradient and soluble ECM gradient, and haptotaxis due to the gradient of insoluble ECM. Using our multispecies tumor model, it is possible to estimate, for a given initial tumor, how far it will invade and thus allow for both qualitative and quantitative comparisons with experimental and clinical data. The results show that the tumor biophysical parameters (e.g., cell viability limit, rate of necrosis and degradation of the necrotic core) has a great impact on the quantitative aspects of the tumor progression, such as the size of viable region, necrotic region, the amount of invasion into the host tissue, the rate of growth and internal structure of the tumors. Among the taxis parameters, the haptotaxis due to intact ECM gradients affects strongly the tumor equilibrium radius compared to the chemotaxis due to soluble ECM gradients and nutrient gradients. Chemotaxis of soluble ECM gradient works against invasion but at a negligible rate.