  The experimental actualisation of organoids modelling organs from brains to
pancreases has revealed that much of the diverse morphologies of organs are
emergent properties of simple intercellular "rules" and not the result of
top-down orchestration. In contrast to other organs, the initial plexus of the
vascular system is formed by aggregation of cells in the process known as
vasculogenesis. Here we study this self-assembling process of blood vessels in
three dimensions through a set of simple rules that align intercellular
apical-basal and planar cell polarity. We demonstrate that a fully connected
network of tubes emerges above a critical initial density of cells. Through
planar cell polarity our model demonstrates convergent extension, and this
polarity furthermore allows for both morphology-maintaining growth and
growth-induced buckling. We compare this buckling to the special vasculature of
Islets of Langerhans in the pancreas and suggest that the mechanism behind the
vascular density-maintaining growth of these islets could be the result of
growth-induced buckling.
