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Computational and Mathematical Methods in Medicine
Volume 2013, Article ID 789402, 7 pages
http://dx.doi.org/10.1155/2013/789402
Research Article

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

Department of Mathematics, University of Kocaeli, Umuttepe Campus, Kocaeli, 41380 Izmit, Turkey

Received 24 May 2013; Accepted 12 July 2013

Academic Editor: Henggui Zhang

Copyright © 2013 Serdal Pamuk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.