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

Serdal Pamuk | Zendy

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

Author(s) -

Serdal Pamuk

Publication year - 2013

Publication title -

computational and mathematical methods in medicine

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.462

H-Index - 48

eISSN - 1748-6718

pISSN - 1748-670X

DOI - 10.1155/2013/789402

Subject(s) - capillary action , perturbation (astronomy) , nonlinear system , matlab , differential equation , mathematics , angiogenesis , mathematical analysis , computer science , physics , thermodynamics , medicine , quantum mechanics , operating system

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.

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