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Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ryan Thiessen & Thomas Hillen, 2021. "Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models," Mathematics, MDPI, vol. 9(13), pages 1-22, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1561-:d:587578
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    References listed on IDEAS

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    1. Matthias Osswald & Erik Jung & Felix Sahm & Gergely Solecki & Varun Venkataramani & Jonas Blaes & Sophie Weil & Heinz Horstmann & Benedikt Wiestler & Mustafa Syed & Lulu Huang & Miriam Ratliff & Kianu, 2015. "Brain tumour cells interconnect to a functional and resistant network," Nature, Nature, vol. 528(7580), pages 93-98, December.
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