Flow rate of transport network controls uniform metabolite supply to tissue

The prevailing theory for metabolic scaling is based on area-preserved, space-filling fractal vascular networks. However, it's known both theoretically and experimentally that animals' vascular systems obey Murray's cubic branching law. Area-preserved branching conflicts with energy minimization and hence the least-work principle. Additionally, while Kleiber's law is the dominant rule for both animals and plants, small animals are observed to follow the 2/3-power law, large a...

Transport is an important function in many network systems and understanding its behavior on biological, social, and technological networks is crucial for a wide range of applications. However, it is a property that is not well-understood in these systems and this is probably due to the lack of a general theoretical framework. Here, based on the finding that renormalization can be applied to bio-networks, we develop a scaling theory of transport in self-similar networks. We d...

Cardiovascular networks span the body by branching across many generations of vessels. The resulting structure delivers blood over long distances to supply all cells with oxygen via the relatively short-range process of diffusion at the capillary level. The structural features of the network that accomplish this density and ubiquity of capillaries are often called space-filling. There are multiple strategies to fill a space, but some strategies do not lead to biologically ada...

Vascular networks are used across the kingdoms of life to transport fluids, nutrients and cellular material. A popular unifying idea for understanding the diversity and constraints of these networks is that the conduits making up the network are organized to optimize dissipation or other functions within the network. However the general principles governing the optimal networks remain unknown. In particular Durand showed that under Neumann boundary conditions networks, that m...

Many biological, geophysical and technological systems involve the transport of resource over a network. In this paper we present an algorithm for calculating the exact concentration of resource at any point in space or time, given that the resource in the network is lost or delivered out of the network at a given rate, while being subject to advection and diffusion. We consider the implications of advection, diffusion and delivery for simple models of glucose delivery throug...

Neuronal activity induces changes in blood flow by locally dilating vessels in the brain microvasculature. How can the local dilation of a single vessel increase flow-based metabolite supply, given that flows are globally coupled within microvasculature? Solving the supply dynamics for rat brain microvasculature, we find one parameter regime to dominate physiologically. This regime allows for robust increase in supply independent of the position in the network, which we expla...

We study transport in synthetic, bi-disperse porous structures, with arrays of microchannels interconnected by a nanoporous layer. These structures are inspired by the xylem tissue in vascular plants, in which sap water travels from the roots to the leaves to maintain hydration and carry micronutrients. We experimentally evaluate transport in three conditions: high pressure-driven flow, spontaneous imbibition, and transpiration-driven flow. The latter case resembles the situa...

The phloem vascular system facilitates transport of energy-rich sugar and signaling molecules in plants, thus permitting long range communication within the organism and growth of non-photosynthesizing organs such as roots and fruits. The flow is driven by osmotic pressure, generated by differences in sugar concentration between distal parts of the plant. The phloem is an intricate distribution system, and many questions about its regulation and structural diversity remain un...

Network flows often exhibit a hierarchical tree-like structure that can be attributed to the minimisation of dissipation. The common feature of such systems is a single source and multiple sinks (or vice versa). In contrast, here we study networks with only a single source and sink. These systems can arise from secondary purposes of the networks, such as blood sugar regulation through insulin production. Minimisation of dissipation in these systems lead to trivial behaviour. ...

Distribution networks -- from vasculature to urban transportation systems -- are prevalent in both the natural and consumer worlds. These systems are intrinsically physical in composition and are embedded into real space, properties that lead to constraints on their topological organization. In this study, we compare and contrast two types of biological distribution networks: mycelial fungi and the vasculature system on the surface of rodent brains. Both systems are alike in ...