title: Solutions of a linearized mathematical model for capillary formation in tumor angiogenesis: an initial data perturbation approximation.
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.
authors.affiliation: Department of Mathematics, University of Kocaeli, Umuttepe Campus, Kocaeli, Izmit, Turkey. spamuk@kocaeli.edu.tr
authors.forename: Serdal
authors.initials: S
authors.lastname: Pamuk
mesh_terms: D002196:Capillaries / Q000378:metabolism / Q000473:pathology*; D002465:Cell Movement; D003198:Computer Simulation; D042783:Endothelial Cells / Q000473:pathology / Q000502:physiology; D005353:Fibronectins / Q000378:metabolism; D006801:Humans; D016014:Linear Models; D055641:Mathematical Concepts; D008955:Models, Cardiovascular; D009369:Neoplasms / Q000098:blood supply*; D009389:Neovascularization, Pathologic; D017711:Nonlinear Dynamics
chemical_list: D005353:Fibronectins
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