Numerical simulation of hypoxic cell regulation in avascular tumor growth

Abstract

Avascular tumor is an early stage of tumor which does not have the blood vessels themselves and depends entirely on the cells around them to get the supply of nutrients such as oxygen and glucose. Hypoxia is a condition in which living cells are deprived of oxygen needed to maintain metabolism and growth. In avascular tumor, the hypoxic environment inhibits the cells proliferation and distinguishes the cellular dynamics into proliferative, quiescent and necrotic cells. In this paper, we present a numerical simulation of mathematical model describing these cellular dynamics using Matlab software with R2009a version. The model formulated in the form of one-dimensional parabolic partial differential equations depending on time and space. The discretization is based on forward differential respect to time and central differential respect to space of finite difference approximation. The results of simulation show that the distribution of proliferating, quiescent and necrotic cells within a tumor spheroid with respect to time and the cells regulation under different rates of nutrients consumptions in one-dimensional computational domain. In conclusion, in the hypoxic environment, the proliferative and quiescent cells grow slowly dependent on some parameter changes and the necrotic cells emerged at the tumor core.