Optimization of nutrient transport in active and adaptive networks

Animal and plant vasculature is characterized by a rich hierarchical structure that is though to minimize dissipation, and when loops exist, provide robustness to damage and fluctuating load. The qualitative features of these networks can be reproduced by simple "use-it or lose-it" rules, which use local mechanical information, such as the shear stress of the vessel wall, to modify the lumen diameter of the vessels. However, these models ignore the importance of solutes: the flow carries oxygen and other nutrients that need to be distributed to the tissue according to the metabolic demands. In this talk we propose a local adaptation rule that accounts for homogeneous perfusion, in addition to energy dissipation and material cost. The competition between these terms produces rich network morphologies. We show that our local rule is consistent with the vascular architecture seen in the rat mesentery network.