 |
Center for Nonlinear Studies |
Tumors become especially dangerous after they induces blood vessel growth, because the new blood vessels can not only carry oxygen and nutrition that further facilitate tumor growth but also act as passages for tumor cells to spread to other sites of the body. Thus tumor growth can be divided into two phases: avascular and vascular growth. Avascular tumor models have been studied extensively, either on a macro-level chemical distribution or on a microscopic cellular level, and recently both. Although almost all studies reach similar conclusions that avascular tumor can only grow up to a limited size,the saturation mechanisms that are assumed in different models are not the same. I use a simple mathematical model to study the differences between distinct mechanisms of avascular tumor growth, and address this intriguing question of tumor saturation. Vascular tumor growth is much more complicated due to the complex structure of the blood vessel network, which makes pure mathematical analysis impossible. Aiming to obtain some insight into the problem without the cost of numerical simulations, I simplify the problem to study the oxygen concentrations provided by a few parallel blood vessels, relate biological phenomenon at the boundaries to the mathematical boundary conditions, and use this model to investigate analytically different hypotheses of tumor and normal tissue cell response to oxygen deprivation.
Host: Yi Jiang T-07