A mathematical analysis of a 2D model for tumor angiogenesis: An initial data perturbation approximation

Year 2018, Volume: 3 Issue: 1, 13 - 27, 30.04.2018

Serdal Pamuk İrem Cay

Abstract

We present a 2D - mathematical model for tumor angiogenesis and solve it by linearizing it using an initial data perturbation approximation method. This method is a well-known and highly effective method to obtain solutions of coupled non-linear differential equations. This method shows that a few terms of the obtained approximate solution are enough to get an idea about the movement of endothelial, macrophage and pericyte cells in the extra cellular matrix, which are needed for the initiation of tumor angiogenesis.  MATLAB-generated figures are provided.

Keywords

Tumor angiogenesis, linearization, perturbation

References

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