Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models

• Main Authors: Ryan Thiessen, Thomas Hillen
• Format: Article
• Language: English
• Published: MDPI AG 2021-07-01
• Series: Mathematics
• Subjects: chemotaxis; anisotropy; kinetic transport equation; parabolic scaling; pattern formation
• Online Access: https://www.mdpi.com/2227-7390/9/13/1561

For this paper, we are interested in network formation of endothelial cells. Randomly distributed endothelial cells converge together to create a vascular system. To develop a mathematical model, we make assumptions on individual cell movement, leading to a velocity jump model with chemotaxis. We use scaling arguments to derive an anisotropic chemotaxis model on the population level. For this macroscopic model, we develop a new numerical solver and investigate network-type pattern formation. Our model is able to reproduce experiments on network formation by Serini et al. Moreover, to our surprise, we found new spatial criss-cross patterns due to competing cues, one direction given by tissue anisotropy versus a different direction due to chemotaxis. A full analysis of these new patterns is left for future work.