Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models

Ryan Thiessen and Thomas Hillen
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Ryan Thiessen: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G2G1, Canada
Thomas Hillen: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G2G1, Canada

Mathematics, 2021, vol. 9, issue 13, 1-22

Abstract: 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.

Keywords: chemotaxis; anisotropy; kinetic transport equation; parabolic scaling; pattern formation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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