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Updated: May 8, 2026

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment
Published on: December 1, 2023
Solutions of a linearized mathematical model for capillary formation in tumor angiogenesis: an initial data
1Department of Mathematics, University of Kocaeli, Umuttepe Campus, Kocaeli, Izmit, Turkey. spamuk@kocaeli.edu.tr
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.
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