Mathematical modeling of MMPS in canser

Abstract

New approaches like mathematical modeling appeared in biology to explain the accumulation of extensive data about complex biological systems like tumors. Mathematical models of tumors which have been studied for over 50 years, aimed to explore the dynamics and characteristics of tumor progression and to make predictions by combining the elementary principles of biology to clinical and experimental data. During cancer progression, genetical and microenvironmental factors mutually affect each other in molecular scales and, this results in a behavior in tissue scale which threatens the patients’ life. What happens in molecular and tissue scales, are mostly known, but the relation between these two is impossible to discover with linear thinking. The discovery of how these events are linked, helps us to see the potential targets for treatments and to experiment on current treatments. With this motivation, we build a mathematical model of tumor growth in this thesis. We used continuous modeling approach and model the tumor progression within the framework of mixture theory. We focused on the activity of matrix degrading enzyme, MMP and its inhibition. In order to study delivery of MMP inhibitors, we set up a structure for a dynamic vessel web which also can help us to simulate activities of other substances and chemicals delivered by blood.