Year-end Sale % OFF 
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.
Highlights
Network formation is an important process in many biological tissues
The spatial interaction of moving endothelial cells leads to a spontaneous network formation, in a process that is not based on a trail following mechanism but rather arises as macroscopic pattern formation in a chemotaxis system
We analyzed two effects that can lead to directional orientation of moving particles: chemotaxis and anisotropy
Summary
Network formation is an important process in many biological tissues. For example, in angiogenesis, blood vessels sprout and grow to form functioning vascular networks [1], or lung tissue, which forms a complex network of bronchioli. The spatial interaction of moving endothelial cells leads to a spontaneous network formation, in a process that is not based on a trail following mechanism but rather arises as macroscopic pattern formation in a chemotaxis system. In this paper, we generalize Serini’s et al approach and consider a chemotaxis-transport equation model, which is based on detailed microscopic cell movement patterns often referred to as “run and tumble” [9,10,11,12,13]. The anisotropic chemotaxis model balances two causes of anisotropy, the directionality of the underlying tissue and the orientation of the chemotactic gradient These two effects compete, leading to interesting criss-cross patterns, which have never been observed before in a mathematical model.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
