A new model for the emergence of blood capillary networks
File(s)
Accepted version
Author(s)
Type
Journal Article
Abstract
We propose a new model for the emergence of blood capillary networks. We assimilate the tissue and extra cellular matrix as a porous medium, using Darcy's law for describing both blood and interstitial fluid flows. Oxygen obeys a convection-diffusion-reaction equation describing advection by the blood, diffusion and consumption by the tissue. Discrete agents named capillary elements and modelling groups of endothelial cells are created or deleted according to different rules involving the oxygen concentration gradient, the blood velocity, the sheer stress or the capillary element density. Once created, a capillary element locally enhances the hydraulic conductivity matrix, contributing to a local increase of the blood velocity and oxygen flow. No connectivity between the capillary elements is imposed. The coupling between blood, oxygen flow and capillary elements provides a positive feedback mechanism which triggers the emergence of a network of channels of high hydraulic conductivity which we identify as new blood capillaries. We provide two different, biologically relevant geometrical settings and numerically analyze the influence of each of the capillary creation mechanism in detail. All mechanisms seem to concur towards a harmonious network but the most important ones are those involving oxygen gradient and sheer stress. A detailed discussion of this model with respect to the literature and its potential future developments concludes the paper.
Date Issued
2021-03-01
Date Acceptance
2020-11-23
Citation
Networks and Heterogeneous Media, 2021, 16 (1), pp.91-138
ISSN
1556-1801
Publisher
American Institute of Mathematical Sciences (AIMS)
Start Page
91
End Page
138
Journal / Book Title
Networks and Heterogeneous Media
Volume
16
Issue
1
Copyright Statement
© 2021 American Institute of Mathematical Sciences.
Sponsor
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Grant Number
WM130048
EP/M006883/1
EP/N014529/1
Subjects
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
Applied Mathematics
Publication Status
Published