Optimal counter-current exchange networks

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 ...

Biological transport networks are highly optimized structures that ensure power-efficient distribution of fluids across various domains, including animal vasculature and plant venation. Theoretically, these networks can be described as space-embedded graphs, and rich structures that align well with observations emerge from optimizing their hydrodynamic energy dissipation. Studies on these models typically use regular grids and focus solely on edge width optimization. Here, we...

One of the ways natural and synthetic systems regulate temperature is via circulating fluids through vasculatures embedded within their bodies. Because of the flexibility and availability of proven fabrication techniques, vascular-based thermal regulation is attractive for thin microvascular systems. Although preliminary designs and experiments demonstrate the feasibility of thermal modulation by pushing fluid through embedded micro-vasculatures, one has yet to optimize the p...

We present an asymptotic analysis of a mesoscale energy for bilayer membranes that has been introduced and analyzed in two space dimensions by the second and third author (Arch. Ration. Mech. Anal. 193, 2009). The energy is both non-local and non-convex. It combines a surface area and a Monge-Kantorovich-distance term, leading to a competition between preferences for maximally concentrated and maximally dispersed configurations. Here we extend key results of our previous anal...

In this paper, we investigate the physical mechanisms underlying one of the most efficient filtration devices: the kidney. Building on a minimal model of the Henle loop - the central part of the kidney filtration - we investigate theoretically the detailed out-of-equilibrium fluxes in this separation process in order to obtain absolute theoretical bounds for its efficiency in terms of separation ability and energy consumption. We demonstrate that this separation process opera...

For the problem of efficiently supplying material to a spatial region from a single source, we present a simple scaling argument based on branching network volume minimization that identifies limits to the scaling of sink density. We discuss implications for two fundamental and unresolved problems in organismal biology and geomorphology: how basal metabolism scales with body size for homeotherms and the scaling of drainage basin shape on eroding landscapes.

Intercellular exchange networks are essential for the adaptive capabilities of populations of cells. While diffusional exchanges have traditionally been difficult to map, recent advances in nanotechnology enable precise probing of exchange fluxes with the medium at single-cell resolution. Here we introduce a tiling-based method to reconstruct the dynamic unfolding of exchange networks from flux data, subsequently applying it to an experimental mammalian co-culture system wher...

A plethora of computational models have been developed in recent decades to account for the morphogenesis of complex biological fluid networks, such as capillary beds. Contemporary adaptation models are based on optimization schemes where networks react and adapt toward given flow patterns. Doing so, a system reduces dissipation and network volume, thereby altering its final form. Yet, recent numeric studies on network morphogenesis, incorporating uptake of metabolites by the...

A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for each of the fluid flows. A single design variable is used to describe the physical fields. The solid interface and the fluid domains are generated using an erosion-dilation based identification technique, which guarantees well-separated flu...

From the vasculature of animals to the porous media making up batteries, transport by fluid flow within complex networks is crucial to service all cells or media with resources. Yet, living flow networks have a key advantage over porous media: they are adaptive and can self-organize their geometry to achieve a homogeneous perfusion throughout the network. Here, we show that, through erosion, artificial flow networks self-organize to a geometry where perfusion is more homogene...