Laboratoire Matière et Systèmes Complexes

Life above a certain size relies on a circulatory system for oxygen and nutrient delivery. Without it, no complex animal would exceed a few millimeters: by diffusion alone, oxygen would not be able to travel more than 100μm in the tissue. Plants, animals and fungi have developed circulatory systems of striking complexity to solve the formidable problem of nutrient delivery and waste removal. Typically, biological transport networks have to satisfy competing demands to operate efficiently and robustly while confronted with an ever-changing environment. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function. In this talk we present some general models regarding the development and function of biological transport networks, from the reticulate vascular architecture of the leaf, to the hierarchies of the veins and arteries in our brain. We first discuss how a hierarchically organized vascular system can develop under constant or variable flow and show how time-dependent flow can stabilize anastomoses and lead to a topology dominated by cycles. We demonstrate that the network topologies generated represent a trade-off between optimizing power dissipation, construction cost, and damage robustness and identify the Pareto-efficient front that evolution is expected to favor and select for. We show that the typical fluctuation length scale controls the position of the networks on the Pareto front and thus on the spectrum of venation phenotypes. Finally, inspired by hemodynamic fluctuations in the brain, we examine how networks dynamically adapt to reroute flow to prescribed network locations.