Modeling angiogenesis under Robin boundary conditions

Abstract

In this study, we show an example of a numerical model based on the Keller-Segel system of equations to simulate angiogenesis in response to chemotaxis under Robin boundary conditions, which represent the presence of flux at the tumor. Different parameters of the model are modified to identify key biological factors relevant to the behavior of angiogenesis. The results show that in the presence of a stronger flux, angiogenesis occurs later owing to the chemical flux that creates a more uniform and homogeneous matrix, decreasing the pronunciation of the gradient and reducing the potential of chemotaxis.

Keywords

angiogenesis / Keller-Segel / Robin boundary condition

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RIGHTS & PERMISSIONS

The Author(s). Quantitative Biology published by John Wiley & Sons Australia, Ltd on behalf of Higher Education Press.