Early Career Award for Soft Matter Research (2021): How a functional distribution network builds itself

The basic function of a distribution network is to broadly deliver nutrients, solutes and other load to space. However, distribution networks that are designed to be the most efficient in terms of minimizing construction and operation costs, tend to do poorly at their basic function. In fact, implementing the most efficient design in terms of cost to build and dissipation, results in a single tube running from inlet to outlet - a network that is not space-filling and that leaves large areas without any nutrients. This architecture is in stark contrast to biological vascular networks that fill space and perfuse tissues rather uniformly. To address this apparent paradox, we solve for the solute distribution in a distribution network, and add “equiperfusion”, the equal distribution of nutrients to the “mechanical” objective functions of dissipation and building cost. By minimizing these objective functions together, we derive biologically plausible adaptation rules that rely only on local measurements of the current (or shear stress), the vessel diameter, and nutrient density at each location. We show that a network remodeling under these rules will reach a state which is both cost-effective and space-filling, equally distributing nutrients to the whole domain. We consider two sets of rules, one geometry based, where the network can continuously change the location of the nodes and the vessels but not the lumen diameter, and one topology based, where the geometry remains intact, but vessels can widen or disappear. These rules once more demonstrate how it is possible for biology to build optimal, robust and adaptable structures for a variety of functions with rather limited genetic information, by utilizing self-organization principles.