Robust Increase in Supply by Vessel Dilation in Globally Coupled Microvasculature

Configuration-independent thermal invariants under flow reversal in thin vascular systems

Modulating temperature fields is indispensable for advancing modern technologies: space probes, electronic packing, and implantable medical devices, to name a few. Bio-inspired thermal regulation achieved via fluid flow within a network of embedded vesicles is notably desirable for slender synthetic material systems. This far-reaching study-availing theory, numerics, and experiments-reveals a counter-intuitive yet fundamental property of vascular-based fluid-flow-engendered thermal regulation. For such thin systems, the mean surface temperature and the outlet temperature-consequently, the heat extracted by the flowing fluid (coolant)-are invariant under flow reversal (i.e. swapping the inlet and outlet). Despite markedly different temperature fields under flow reversal, our newfound invariance-a discovery-holds for anisotropic thermal conductivity, any inlet and ambient temperatures, transient and steady-state responses, irregular domains, and arbitrary internal vascular topologies, including those with branching. The reported configuration-independent result benefits thermal regulation designers. For instance, the flexibility in the coolant's inlet location eases coordination challenges between electronics and various delivery systems in microfluidic devices without compromising performance (e.g. soft implantable coolers for pain management). Last but not least, the invariance offers an innovative way to verify computer codes, especially when analytical solutions are unavailable for intricate domain and vascular configurations.

Anomalous Diffusion of Deformable Particles in a Honeycomb Network

Transport of deformable particles in a honeycomb network is studied numerically. It is shown that the particle deformability has a strong impact on their distribution in the network. For sufficiently soft particles, we observe a short memory behavior from one bifurcation to the next, and the overall behavior consists in a random partition of particles, exhibiting a diffusionlike transport. On the contrary, stiff enough particles undergo a biased distribution whereby they follow a deterministic partition at bifurcations, due to long memory. This leads to a lateral ballistic drift in the network at small concentration and anomalous superdiffusion at larger concentration, even though the network is ordered. A further increase of concentration enhances particle-particle interactions which shorten the memory effect, turning the particle anomalous diffusion into a classical diffusion. We expect the drifting and diffusive regime transition to be generic for deformable particles.

Elastohydrodynamic Relaxation of Soft and Deformable Microchannels

Hydrodynamic flows in compliant channels are of great interest in physiology and microfluidics. In these situations, elastohydrodynamic coupling leads to (i) a nonlinear pressure-vs-flow-rate relation, strongly affecting the hydraulic resistance; and (ii), because of the compliance-enabled volume storage, a finite relaxation time under a stepwise change in pressure. This latter effect remains relatively unexplored, even while the timescale can vary over a decade in typical situations. In this study we provide time-resolved measurements of the relaxation dynamics for thin and soft, rectangular microfluidic channels. We describe our data using a perturbative lubrication approximation of the Stokes equation coupled to linear elasticity, while taking into account the effect of compliance and resistance of the entrance. The modeling allows us to completely describe all of the experimental results. Our Letter is relevant for any microfluidic scenario wherein a time-dependent driving is applied and provides a first step in the dynamical description of compliant channel networks.

Dispersive transport dynamics in porous media emerge from local correlations

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.

Dispersive transport through complex media, relevant for semiconductors, liquid crystals, and biological soft matter, is influenced by their microscopic, porous structure. The authors consider the statistics of pore-junction units, in contrast to individual pores, to link morphology and macroscopic transport characteristics.

Control of low flow regions in the cortical vasculature determines optimal arterio-venous ratios

The energy demands of neurons are met by a constant supply of glucose and oxygen via the cerebral vasculature. The cerebral cortex is perfused by dense, parallel arterioles and venules, consistently in imbalanced ratios. Whether and how arteriole-venule arrangement and ratio affect the efficiency of energy delivery to the cortex has remained an unanswered question. Here, we show by mathematical modeling and analysis of the mapped mouse sensory cortex that the perfusive efficiency of the network is predicted to be limited by low-flow regions produced between pairs of arterioles or pairs of venules. Increasing either arteriole or venule density decreases the size of these low-flow regions, but increases their number, setting an optimal ratio between arterioles and venules that matches closely that observed across mammalian cortical vasculature. Low-flow regions are reshaped in complex ways by changes in vascular conductance, creating geometric challenges for matching cortical perfusion with neuronal activity.

Distribution Networks Achieve Uniform Perfusion through Geometric Self-Organization

A generic flow distribution network typically does not deliver its load at a uniform rate across a service area, instead oversupplying regions near the nutrient source while leaving downstream regions undersupplied. In this Letter we demonstrate how a local adaptive rule coupling tissue growth with nutrient density results in a flow network that self-organizes to deliver nutrients uniformly. This geometric adaptive rule can be generalized and imported to mechanics-based adaptive models to address the effects of spatial gradients in nutrients or growth factors in tissues.

Neurofluids-Deep inspiration, cilia and preloading of the astrocytic network

With the advent of real-time MRI, the motion and passage of cerebrospinal fluid can be visualized without gating and exclusion of low-frequency waves. This imaging modality gives insights into low-volume, rapidly oscillating cardiac-driven movement as well as sustained, high-volume, slowly oscillating inspiration-driven movement. Inspiration means a spontaneous or artificial increase in the intrathoracic dimensions independent of body position. Alterations in thoracic diameter enable the thoracic and spinal epidural venous compartments to be emptied and filled, producing an upward surge of cerebrospinal fluid inside the spine during inspiration; this surge counterbalances the downward pooling of venous blood toward the heart. Real-time MRI, as a macroscale in vivo observation method, could expand our knowledge of neurofluid dynamics, including how astrocytic fluid preloading is adjusted and how brain buoyancy and turgor are maintained in different postures and zero gravity. Along with these macroscale findings, new microscale insights into aquaporin-mediated fluid transfer, its sensing by cilia, and its tuning by nitric oxide will be reviewed. By incorporating clinical knowledge spanning several disciplines, certain disorders-congenital hydrocephalus with Chiari malformation, idiopathic intracranial hypertension, and adult idiopathic hydrocephalus-are interpreted and reviewed according to current concepts, from the basics of the interrelated systems to their pathology.

Hidden Topological Structure of Flow Network Functionality

The ability to reroute and control flow is vital to the function of venation networks across a wide range of organisms. By modifying individual edges in these networks, either by adjusting edge conductances or creating and destroying edges, organisms robustly control the propagation of inputs to perform specific tasks. However, a fundamental disconnect exists between the structure and function: networks with different local architectures can perform the same functions. Here, we answer the question of how changes at the level of individual edges collectively create functionality at the scale of an entire network. Using persistent homology, we analyze networks tuned to perform complex tasks. We find that the responses of such networks encode a hidden topological structure composed of sectors of nearly uniform pressure. Although these sectors are not apparent in the underlying network structure, they correlate strongly with the tuned function. The connectivity of these sectors, rather than that of individual nodes, provides a quantitative relationship between structure and function in flow networks.

Resilience of three-dimensional sinusoidal networks in liver tissue

Can three-dimensional, microvasculature networks still ensure blood supply if individual links fail? We address this question in the sinusoidal network, a plexus-like microvasculature network, which transports nutrient-rich blood to every hepatocyte in liver tissue, by building on recent advances in high-resolution imaging and digital reconstruction of adult mice liver tissue. We find that the topology of the three-dimensional sinusoidal network reflects its two design requirements of a space-filling network that connects all hepatocytes, while using shortest transport routes: sinusoidal networks are sub-graphs of the Delaunay graph of their set of branching points, and also contain the corresponding minimum spanning tree, both to good approximation. To overcome the spatial limitations of experimental samples and generate arbitrarily-sized networks, we developed a network generation algorithm that reproduces the statistical features of 0.3-mm-sized samples of sinusoidal networks, using multi-objective optimization for node degree and edge length distribution. Nematic order in these simulated networks implies anisotropic transport properties, characterized by an empirical linear relation between a nematic order parameter and the anisotropy of the permeability tensor. Under the assumption that all sinusoid tubes have a constant and equal flow resistance, we predict that the distribution of currents in the network is very inhomogeneous, with a small number of edges carrying a substantial part of the flow-a feature known for hierarchical networks, but unexpected for plexus-like networks. We quantify network resilience in terms of a permeability-at-risk, i.e., permeability as function of the fraction of removed edges. We find that sinusoidal networks are resilient to random removal of edges, but vulnerable to the removal of high-current edges. Our findings suggest the existence of a mechanism counteracting flow inhomogeneity to balance metabolic load on the liver.