Topological evolution of sprouting vascular networks: from day-by-day analysis to general growth rules.

Engineering tissues with an embedded vasculature of well-controlled topology remains one of the basic problems in biofabrication. Still, little is known about the evolution of topological characteristics of vascular networks over time. Here, we perform a high-throughput day-by-day analysis of tens of microvasculatures that sprout from endothelial-cell coated micrometric beads embedded in an external fibrin gel. We use the bead-assays to systematically analyze (i) macroscopic observables such as the overall length and area of the sprouts, (ii) microscopic observables such as the lengths of segments or the branching angles and their distributions, as well as (iii) general measures of network complexity such as the average number of bifurcations per branch. We develop a custom angiogenic image analysis toolkit and track the evolution of the networks for at least 14 days of culture under various conditions, e.g., in the presence of fibroblasts or with added endothelial growth factor (VEGF). We find that the evolution always consists of three stages: (i) an inactive stage in which cells remain bound to the beads, (ii) a sprouting stage in which the sprouts rapidly elongate and bifurcate, and (iii) the maturation stage in which the growth slows down. We show that higher concentrations of VEGF lead to an earlier onset of sprouting and to a higher number of primary branches, yet without significantly affecting the speed of growth of the individual sprouts. We find that the mean branching angle is weakly dependent on VEGF and typically in the range of 60-75 degrees suggesting that, by comparison with the available Laplacian growth models, the sprouts tend to follow local VEGF gradients. Finally, we observe an exponential distribution of segment lengths, which we interpret as a signature of stochastic branching at a constant bifurcation rate (per unit branch length). Our results, due to high statistical relevance, may serve as a benchmark for predictive models and reveal how the external means of control, such as VEGF concentration, could be used to control the morphology of the vascular networks. We provide guidelines for the fabrication of optimized microvasculatures with potential applications in drug testing or regenerative medicine.