A new model for the emergence of blood capillary networks

TL;DR

This paper introduces a novel computational model simulating blood capillary network formation by coupling fluid dynamics, oxygen transport, and endothelial cell behavior, revealing key mechanisms like oxygen gradients and shear stress in network emergence.

Contribution

The model uniquely integrates tissue porosity, fluid flow, oxygen transport, and discrete capillary agents without predefined connectivity, advancing understanding of vascular network development.

Findings

Oxygen gradient and shear stress are primary drivers of capillary formation.

The model successfully reproduces realistic capillary network patterns.

Mechanisms interact positively to promote network emergence.

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 intersticial 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.