Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis

Öz

In this work, we obtain the regular perturbation solutions of a mathematical model in tumor angiogenesis in one and two space dimensions. Our results show that the solutions we have obtained are in good agreement with the solutions obtained by other methods. We also present our results in Matlab generated figures.

Anahtar Kelimeler

• Endothelial Cell,Mathematical Model,Perturbation Solutions,Tumor Angiogenesis

Kaynakça

1. Paweletz N., Knierim M., 1989. Tumor-related angiogenesis. Critical Reviews in Oncology, 9(3), 197-242.
2. Levine H. A., Sleeman B. D., 2000. A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis. Mathematical Biosciences, 168, 77-115.
3. Pamuk S., Gürbüz A., 2004. Stability analysis of the steady-state solution of a mathematical model in tumor angiogenesis. Global Analysis and Applied Mathematics, 729, 369-373.
4. Pamuk S., 2003. Qualitative analysis of a mathematical model for capillary formation in tumor angiogenesis. Mathematical Models and Methods in Applied Sciences, 13(1), 19-33.
5. Pamuk S., 2004. Steady-state analysis of a mathematical model for capillary network formation in the absence of tumor source. Mathematical Biosciences, 189, 21-38
6. Bender C.M., Orszag S.A., 1999. Advanced Mathematical Methods for Scientists and Engineers, Springer, New York.
7. Hunter J.K., 2004. Asymptotic Analysis and Singular Perturbation Theory, University of California at Davis, California.
8. Rice R. G., Do D. D., 1995. Applied Mathematics And Modeling For Chemical Engineers, John Wiley and Sons Inc., New York.