Imperial College London
Alternate

ProfessorPierreDegond

Faculty of Natural Sciences, Department of Mathematics

Visiting Professor
 
 
 
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Contact

 

p.degond Website

 
 
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Location

 

Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Aceves:2021:10.3934/nhm.2021001,
author = {Aceves, Sanchez P and Aymard, B and Peurichard, D and Kennel, P and Lorsignol, A and Plouraboué, F and Casteilla, L and Degond, P},
doi = {10.3934/nhm.2021001},
journal = {Networks and Heterogeneous Media},
pages = {91--138},
title = {A new model for the emergence of blood capillary networks},
url = {http://dx.doi.org/10.3934/nhm.2021001},
volume = {16},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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.
AU  - Aceves,Sanchez P
AU  - Aymard,B
AU  - Peurichard,D
AU  - Kennel,P
AU  - Lorsignol,A
AU  - Plouraboué,F
AU  - Casteilla,L
AU  - Degond,P
DO  - 10.3934/nhm.2021001
EP  - 138
PY  - 2021///
SN  - 1556-1801
SP  - 91
TI  - A new model for the emergence of blood capillary networks
T2  - Networks and Heterogeneous Media
UR  - http://dx.doi.org/10.3934/nhm.2021001
UR  - http://hdl.handle.net/10044/1/85904
VL  - 16
ER  -
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