Mathematical Models of Tumor Growth and Angiogenesis

Abstract

In this paper we present several mathematical models of tumor growth and angiogenesis expressed by  systems of ODE’s encoding the most essential observations and assumptions about the complex hierarchical interactive processes of tumor neo-vascularization (angiogenesis). The simplest modeling option presented merely captures the three independent variables mentioned earlier-tumor size N, total vessel volume V and the amount of protein P. We modify this model assuming that the protein is additionally consumed by growing vessels and obtain a model with protein consumption. Next models with time-delays are introduced. To make our models more realistic, two more compartments representing more complex vascularity and protein effects are introduced. Hence five dimensional models are obtained.