Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics



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BibTex format

author = {Aceves-Sanchez, P and Aymard, B and Peurichard, D and Kennel, P and Lorsignol, A and Plouraboue, F and Casteilla, L and Degond, P},
title = {A new model for the emergence of blood capillary networks},
url = {},

RIS format (EndNote, RefMan)

AB - We propose a new model for the emergence of blood capillary networks. Weassimilate the tissue and extra cellular matrix as a porous medium, usingDarcy's law for describing both blood and intersticial fluid flows. Oxygenobeys a convection-diffusion-reaction equation describing advection by theblood, diffusion and consumption by the tissue. Discrete agents named capillaryelements and modelling groups of endothelial cells are created or deletedaccording to different rules involving the oxygen concentration gradient, theblood velocity, the sheer stress or the capillary element density. Oncecreated, a capillary element locally enhances the hydraulic conductivitymatrix, contributing to a local increase of the blood velocity and oxygen flow.No connectivity between the capillary elements is imposed. The coupling betweenblood, oxygen flow and capillary elements provides a positive feedbackmechanism which triggers the emergence of a network of channels of highhydraulic conductivity which we identify as new blood capillaries. We providetwo different, biologically relevant geometrical settings and numericallyanalyze the influence of each of the capillary creation mechanism in detail.All mechanisms seem to concur towards a harmonious network but the mostimportant ones are those involving oxygen gradient and sheer stress. A detaileddiscussion of this model with respect to the literature and its potentialfuture developments concludes the paper.
AU - Aceves-Sanchez,P
AU - Aymard,B
AU - Peurichard,D
AU - Kennel,P
AU - Lorsignol,A
AU - Plouraboue,F
AU - Casteilla,L
AU - Degond,P
TI - A new model for the emergence of blood capillary networks
UR -
ER -