Numerical Analysis of Mathematical Model of Tumor Treatment by Anti-Angiogenesis

Abstract

Explanation of cell movement and cell population in biology is one of the most interesting themes of the mathematical oncology. This study targets to produce numerical solutions of the system of equation produced by the process of angiogenesis in the development of tumor from vascular to avascular and then metastasis. We consider a situation in which anti-angiogenesis treatment is administered before a tumor is vascularized. This involves the treatment by preventing the angiogenesis by anti-angiogenic agent namely said an anti-angiogenic factor (AAF). We developed the governing equations for the conservation of endothelial cells, tumor angiogenic factors and fibronectin concentrations. To solve these equations a finite Difference method is applied. Which is considered to be very reliable and stable for parabolic partial differential equations. After the discretization process of equations, we get the matrics which solve by Matlab simulations. We have used the previously published parametric values which are chosen to suit this study. Results obtained designate that when we applied the antiangiogenic term to the equation for endothelial cell concentration, endothelial cells concentration declines identically. This can make huge inferences for cancer treatment