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.
Funder
Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Cited by
3 articles.
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