# Modeling angiogenesis under Robin boundary conditions

## TL;DR

This paper presents a numerical model to simulate how blood vessels grow toward tumors under specific boundary conditions.

## Contribution

The novelty lies in applying Robin boundary conditions to the Keller–Segel system to study angiogenesis influenced by chemical flux.

## Key findings

- Stronger chemical flux delays angiogenesis by creating a more uniform matrix.
- Robin boundary conditions reduce the chemotactic gradient's effectiveness.
- Model parameters help identify key biological factors in angiogenesis behavior.

## 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.