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Article

Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models

Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G2G1, Canada
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Author to whom correspondence should be addressed.
Academic Editor: Alessandro Niccolai
Mathematics 2021, 9(13), 1561; https://doi.org/10.3390/math9131561
Received: 29 April 2021 / Revised: 19 June 2021 / Accepted: 25 June 2021 / Published: 2 July 2021
(This article belongs to the Special Issue Mathematical Models for Cell Migration and Spread)
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. View Full-Text
Keywords: chemotaxis; anisotropy; kinetic transport equation; parabolic scaling; pattern formation chemotaxis; anisotropy; kinetic transport equation; parabolic scaling; pattern formation
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MDPI and ACS Style

Thiessen, R.; Hillen, T. Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models. Mathematics 2021, 9, 1561. https://doi.org/10.3390/math9131561

AMA Style

Thiessen R, Hillen T. Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models. Mathematics. 2021; 9(13):1561. https://doi.org/10.3390/math9131561

Chicago/Turabian Style

Thiessen, Ryan, and Thomas Hillen. 2021. "Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models" Mathematics 9, no. 13: 1561. https://doi.org/10.3390/math9131561

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