Life and functioning of higher organisms depends on the continuous supply of metabolites to tissues and organs. What are the requirements on the transport network pervading a tissue to provide a uniform supply of nutrients, minerals or hormones? To theoretically answer this question, we present an analytical scaling argument and numerical simulations on how flow dynamics and network architecture control active spread and uniform supply of metabolites by studying the example of xylem vessels in plants. We identify the fluid inflow rate as the key factor for uniform supply. While at low inflow rates metabolites are already exhausted close to flow inlets, too high inflow flushes metabolites through the network and deprives tissue close to inlets of supply. In between these two regimes, there exists an optimal inflow rate that yields a uniform supply of metabolites. We determine this optimal inflow analytically in quantitative agreement with numerical results. Optimizing network architecture by reducing the supply variance over all network tubes, we identify patterns of tube dilation or contraction that compensate sub-optimal supply for the case of too low or too high inflow rate.

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 explain analytically. We show that local coupling of vessels promotes spatially correlated increased supply by dilation.Vascular networks pervade all organs of animals and are the paradigm of adaptive transport networks. Their self-organized architecture continuously inspires the search for their underlying physical principles [1][2][3][4] and at the same time serves as a template for designing efficient networks in engineering [5]. The blood flowing through vessels transports nutrients, hormones, and metabolites to adjacent tissues. Metabolite exchange primarily occurs within the fine vessel meshwork formed by microvasculature. In the brain, local metabolite demand can abruptly rise due to an increase in neural activity [6], altering blood flow [7,8] in the same brain region, observable in fMRI [9]. During the process of increased neuronal activity, neurons signal their increased demand to adjacent astrocyte cells, which in turn trigger small ring muscles surrounding blood vessels to relax [10]. Thus, neural activity drives local dilation of a vessel [11,12], and hence regulates metabolite supply [7,13]. However, from a fluid dynamics perspective there is a mystery: blood vessels form a highly interconnected network in the microvasculature [8], resulting in a global coupling of blood flow. A single dilating vessel can potentially change the metabolite supply in a broad region of the networkand thus the local increase due to dilation is a function of specific network topology. Quantitatively, how much control over changes in blood-based supply resides in a single dilating vessel?Models considering metabolite spread in tissue date back more than a hundred years to A. Krogh [14]. Krogh's model estimates the supply pattern in a tissue enclosed by vessels assuming that supply is constant on all vessel walls. Yet, on a larger tissue scale, supply spatially varies along the vasculature since resources supplied upstream are not available downstream. Alternative models consider vessel-based transport [15], yet only diffusive transport is taken into account. The combined importance of advection and diffusion for transporting solutes in a single tube was discovered by G.I. Taylor [16,17], with subsequent work outlining modifications due to solute absorption at the tube boundary [18][19][20]. Yet, there has been much less work capturing the coupling of advection and diffusion in tubular network struc-tures [21,22], including solute absorption [23]. The impact of a dilating vessel is hard to estimate since not only the absorption dynamics on the level of sing...

Understanding and controlling transport through complex media is central for a plethora of processes ranging from technical to biological applications. Yet, the effect of micro-scale manipulations on macroscopic transport dynamics still poses conceptual conundrums. Here, we demonstrate the predictive power of a conceptual shift in describing complex media by local micro-scale correlations instead of an assembly of uncorrelated minimal units. Specifically, we show that the non-linear dependency between microscopic morphological properties and macroscopic transport characteristics in porous media is captured by transport statistics on the level of pore junctions instead of single pores. Probing experimentally and numerically transport through two-dimensional porous media while gradually increasing flow heterogeneity, we find a non-monotonic change in transport efficiency. Using analytic arguments, we built physical intuition on how this non-monotonic dependency emerges from junction statistics. The shift in paradigm presented here broadly affects our understanding of transport within the diversity of complex media.

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