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A new model for the emergence of blood capillary networks

Aceves-Sanchez, Pedro and Aymard, Benjamin and Peurichard, Diane and Kennel, Pol and Lorsignol, Anne and Plouraboué, Franck and Casteilla, Louis and Degond, Pierre A new model for the emergence of blood capillary networks. (2021) Networks & Heterogeneous Media, 16 (1). 91-138. ISSN 1556-1801

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Official URL: https://doi.org/10.3934/nhm.2021001

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.

Item Type:Article
Additional Information:Thanks to American Institute of Sciences Mathematical. This article is available at : https://www.aimsciences.org/article/doi/10.3934/nhm.2021001
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Etablissement Français du Sang - EFS Midi-Pyrénées (FRANCE)
Université de Toulouse > Ecole Nationale Vétérinaire de Toulouse - ENVT (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
French research institutions > Institut National de la Recherche en Informatique et en Automatique - INRIA (FRANCE)
French research institutions > Institut National de la Santé et de la Recherche Médicale - INSERM (FRANCE)
Other partners > Université Nice Sophia Antipolis (FRANCE)
Other partners > North Carolina State University (USA)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Imperial College London (UNITED KINGDOM)
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Deposited On:11 Mar 2021 08:33

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