Flow systems in nature, whether animate or inanimate, have evolved in time toward greater efficiency by adapting, or ‘morphing’, their configuration to decrease resistance to the currents flowing through them. Observations at various scales indicate that the distribution of flow, i.e. the connection of a point (source/sink) to a volume (sink/source) or vice-versa, is the most efficient when it happens through a dendritic architecture. Flow channels function in concert with the structures around them, as a combination of long and fast flows along the channels, with short and slow flows through the surrounding medium. The ability to predict flow patterns enables engineers to propose flow designs for heat, mass, and fluid flows. Our previous work theorized the deterministic nature of morphing and showed how to obtain efficient flow configurations for combined and sometimes competing objectives.

In this talk we will discuss the blood flow architecture of the liver, the largest organ in the body. The superimposition of three different types of networks (hepatic artery and portal vein trees as inflows, and hepatic vein tree as outflow) leads to a very complex hierarchical structure made of several millions to billions of blood vessels. Out of the complexity of the blood flow system, invoking the principles mentioned above, we can predict the main features of this flow system and represent the hepatic blood circulatory system as a deterministic combination of dendritic networks and porous systems made of rigid or elastic vessels.

Next, we will consider the design of capillary networks for the cooling of high-power electronic components and how, incidentally, we understood that our theoretical approaches could also predict hydrotropism, the growth of plant roots towards areas with high moisture level. While the mechanisms are complex and involve several drivers, we extracted a conceptual understanding of how a plant root system evolves in time to connect more and more water sources while morphing its entire vasculature at every growth step. The network volume grows with the network, but the volume distribution throughout all the channels morphs to allow enough capillary pressure in each branch and minimum friction losses to pull the maximum flow rate out of the system.