Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation


Pamuk S.

COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE, 2013 (SCI İndekslerine Giren Dergi) identifier identifier identifier

  • Basım Tarihi: 2013
  • Doi Numarası: 10.1155/2013/789402
  • Dergi Adı: COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE

Özet

We present a mathematical model for capillary formation in tumor angiogenesis and solve it by linearizing it using an initial data perturbation method. This method is highly effective to obtain solutions of nonlinear coupled differential equations. We also provide a specific example resulting, that even a few terms of the obtained series solutions are enough to have an idea for the endothelial cell movement in a capillary. MATLAB-generated figures are provided, and the stability criteria are determined for the steady-state solution of the cell equation.