A new model for the emergence of blood capillary networks

We propose a new model for the emergence of blood capillary networks. assimilate tissue and extra cellular matrix as porous medium, using Darcy's law describing both interstitial fluid flows. Oxygen obeys convection-diffusion-reaction equation advection by blood, diffusion consumption tissue. Discrete agents named elements modelling groups endothelial cells are created or deleted according to different rules involving oxygen concentration gradient, velocity, sheer stress element density. Once created, locally enhances hydraulic conductivity matrix, contributing local increase velocity flow. No connectivity between is imposed. The coupling flow provides positive feedback mechanism which triggers network channels high we identify capillaries. provide two different, biologically relevant geometrical settings numerically analyze influence each creation in detail. All mechanisms seem concur towards harmonious but most important ones those gradient stress. A detailed discussion this with respect literature its potential future developments concludes paper.