Feedback induced phase transitions in active porous media

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Abstract

Flow through passive porous media is typically described in terms of a linear theory relating current fluxes and driving forces, in the presence of a prescribed heterogeneous permeability. However, many porous systems such as glacial drainage networks, erosional river bed networks, vascular networks, social insect swarms and animal architectures such as termite mounds are continuously remodeled by the flow and thence modify the flow, i.e. they are active. Here we consider a minimal model for an active porous medium where flow and resistance are coupled to each other. Using numerical simulations, we show that this results in both channelization and wall-building transitions depending on the form of the feedback. A continuum model allows us to understand the qualitative features of the resulting phase diagram, and suggests ways to realize complex architectures using simple rules in engineered systems.

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Rules for biologically inspired adaptive network design.

Atsushi Tero, Seiji Takagi, Tetsu Saigusa … (2010)

Transport networks are ubiquitous in both social and biological systems. Robust network performance involves a complex trade-off involving cost, transport efficiency, and fault tolerance. Biological networks have been honed by many cycles of evolutionary selection pressure and are likely to yield reasonable solutions to such combinatorial optimization problems. Furthermore, they develop without centralized control and may represent a readily scalable solution for growing networks in general. We show that the slime mold Physarum polycephalum forms networks with comparable efficiency, fault tolerance, and cost to those of real-world infrastructure networks--in this case, the Tokyo rail system. The core mechanisms needed for adaptive network formation can be captured in a biologically inspired mathematical model that may be useful to guide network construction in other domains.

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Fluid forces control endothelial sprouting.

Weimin Song, Lance Munn (2011)

During angiogenesis, endothelial cells (ECs) from intact blood vessels quickly infiltrate avascular regions via vascular sprouting. This process is fundamental to many normal and pathological processes such as wound healing and tumor growth, but its initiation and control are poorly understood. Vascular endothelial cell growth factor (VEGF) can promote vessel dilation and angiogenic sprouting, but given the complex nature of vascular morphogenesis, additional signals are likely necessary to determine, for example, which vessel segments sprout, which dilate, and which remain quiescent. Fluid forces exerted by blood and plasma are prime candidates that might codirect these processes, but it is not known whether VEGF cooperates with mechanical fluid forces to mediate angiogenesis. Using a microfluidic tissue analog of angiogenic sprouting, we found that fluid shear stress, such as exerted by flowing blood, attenuates EC sprouting in a nitric oxide-dependent manner and that interstitial flow, such as produced by extravasating plasma, directs endothelial morphogenesis and sprout formation. Furthermore, positive VEGF gradients initiated sprouting but negative gradients inhibited sprouting, promoting instead sheet-like migration analogous to vessel dilation. These results suggest that ECs integrate signals from fluid forces and local VEGF gradients to achieve such varied goals as vessel dilation and sprouting.

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Random network peristalsis in Physarum polycephalum organizes fluid flows across an individual.

Karen Alim, Gabriel Amselem, François Peaudecerf … (2013)

Individuals can function as integrated organisms only when information and resources are shared across a body. Signals and substrates are commonly moved using fluids, often channeled through a network of tubes. Peristalsis is one mechanism for fluid transport and is caused by a wave of cross-sectional contractions along a tube. We extend the concept of peristalsis from the canonical case of one tube to a random network. Transport is maximized within the network when the wavelength of the peristaltic wave is of the order of the size of the network. The slime mold Physarum polycephalum grows as a random network of tubes, and our experiments confirm peristalsis is used by the slime mold to drive internal cytoplasmic flows. Comparisons of theoretically generated contraction patterns with the patterns exhibited by individuals of P. polycephalum demonstrate that individuals maximize internal flows by adapting patterns of contraction to size, thus optimizing transport throughout an organism. This control of fluid flow may be the key to coordinating growth and behavior, including the dynamic changes in network architecture seen over time in an individual.