Modelling of 3D early blood vessel formation: Simulations and morphological analysis

Vascular networks form by a self-aggregation process of individual endothelial cells that differentiate at seemingly random sites in the embryo and collectively migrate toward each other forming a preliminary vascular plexus (vasculogenesis), followed by functional remodelling that gives rise to the final hierarchical system (angiogenesis). The study of this phenomenon is performed by biologists using in vitro and in vivo assays, both in two and three dimensional settings. The lack of direct biological evidence of the chemotactic autocrine loop that is thought to be the main responsible for the early aggregation, called for the development of mathematical models of this process, in order to study the possible effects of such a loop. After successful two-dimensional studies, the model was recently extended to a three dimensional setting and a suitably efficient approximation scheme for the numerical simulations has been developed, while three-dimensional images of embryo vascular networks are becoming available through confocal microscopy. This paper is concerned with the comparison of experimental and simulated data on embryo vascular plexi. Critical exponents of percolation, Euler-Poincaré characteristic, fractal dimension, power spectrum decay and maximum distance from a vessel are considered and compared.