Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models
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 us...
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doaj-c09fcccd4dfd407dbdb78a4a7774a83f2021-07-15T15:41:42ZengMDPI AGMathematics2227-73902021-07-0191561156110.3390/math9131561Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis ModelsRyan Thiessen0Thomas Hillen1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G2G1, CanadaDepartment of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G2G1, CanadaFor 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.https://www.mdpi.com/2227-7390/9/13/1561chemotaxisanisotropykinetic transport equationparabolic scalingpattern formation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ryan Thiessen Thomas Hillen |
spellingShingle |
Ryan Thiessen Thomas Hillen Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models Mathematics chemotaxis anisotropy kinetic transport equation parabolic scaling pattern formation |
author_facet |
Ryan Thiessen Thomas Hillen |
author_sort |
Ryan Thiessen |
title |
Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models |
title_short |
Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models |
title_full |
Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models |
title_fullStr |
Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models |
title_full_unstemmed |
Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models |
title_sort |
anisotropic network patterns in kinetic and diffusive chemotaxis models |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2021-07-01 |
description |
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. |
topic |
chemotaxis anisotropy kinetic transport equation parabolic scaling pattern formation |
url |
https://www.mdpi.com/2227-7390/9/13/1561 |
work_keys_str_mv |
AT ryanthiessen anisotropicnetworkpatternsinkineticanddiffusivechemotaxismodels AT thomashillen anisotropicnetworkpatternsinkineticanddiffusivechemotaxismodels |
_version_ |
1721298905638895616 |