Complex systems display the ability to self-organize to generate stable spatio-temporal structures as a result of simple local interactions between agents. In this project, we study whether the formation of a vascular network (vasculogenesis) or the creation of new capillary blood vessels from an existing vessel network (angiogenesis) could be the result of a self-organization process between a reduced amount of agents and whether the topology of the created networks could be an emergent property.
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 intersticial fluid flows. Oxygen obeys a convection-diffusionreaction 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.
Collaborations:
RESTORE (Toulouse), IMFT (Toulouse), Imperial College London
Project publications:
P. Aceves-Sanchez, B. Aymard, D. Peurichard, P. Kennel, A. Lorsignol, F. Plouraboue, L. Casteilla, P. Degond , A new model for the emergence of blood capillary networks, Networks and Heterogeneous Media, (2021), 16:91-138