Flow rate of transport network controls uniform metabolite supply to tissue

Capillary washboarding during slow drainage of a frictional fluid

Numerous natural and industrial processes involve the mixed displacement of liquids, gases and granular materials through confining structures. However, understanding such three-phase flows remains a formidable challenge, despite their tremendous economic and environmental impact. To unveil the complex interplay of capillary and granular stresses in such flows, we consider here a model configuration where a frictional fluid (an immersed sedimented granular layer) is slowly drained out of a horizontal capillary. Analyzing how liquid/air menisci displace particles from such granular beds, we reveal various drainage patterns, notably the periodic formation of dunes, analogous to road washboard instability. Considering the competitive role of friction and capillarity, a 2D theoretical approach supported by numerical simulations of a meniscus bulldozing a front of particles provides quantitative criteria for the emergence of those dunes. A key element is the strong increase of the frictional forces, as the bulldozed particles accumulate and bend the meniscus horizontally. Interestingly, this frictional enhancement with the attack angle is also crucial in small-legged animals' locomotion over granular media.

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.

Measuring of water transport selectively along the plant root plasmodesmata using gradient nuclear magnetic resonance with paramagnetic doping

In this study, we measured translational water diffusion selectively along symplast pathway through plasmodesmata in maize roots, and the effective plasmodesmata permeability coefficient (P) was determined using a nuclear magnetic resonance (NMR) spin echo method. Measuring of water transport selectively along the plant root plasmodesmata was achieved with paramagnetic complexes (PCs) of high relaxation efficiency. PCs penetrate into the intercellular space of root tissue, but not into cells, and accelerate the magnetic relaxation processes of intercellular water, thereby excluding the contribution of intercellular water to the registered NMR diffusion echo attenuation. In result, NMR control of translational diffusion can be applied to the signal of the water moving along the symplast pathway through plasmodesmata, where the PCs do not penetrate. Diethylenetriaminepentaacetic acid (GdDTPA), Mn²⁺-trans-1,2-diaminocyclohexane-N,N,N',N'-tetraacetic acid (MnDCTA), and GdCl₃ were used as PCs. An increase in the PCs concentration led to a side effect in the form of a varying decrease in diffusive water transport in the roots. The P was determined by extrapolating the concentration dependence to zero concentration of PCs. Among the PCs studied, MnDCTA had the least side effects on the water transport when the concentration dependence was linear. When MnDCTA was used, the P accounted for 30-35% of the total cell water permeability (by transmembrane and symplast pathways). The rate of water flow along the plasmodesmata in the approximation of the piston mode of flow along the linear cell chain was estimated to range from 4.5 × 10^-7 to 8.8 × 10^-7 m/s.

Morphology and Transport in Eukaryotic Cells

Transport of intracellular components relies on a variety of active and passive mechanisms, ranging from the diffusive spreading of small molecules over short distances to motor-driven motion across long distances. The cell-scale behavior of these mechanisms is fundamentally dependent on the morphology of the underlying cellular structures. Diffusion-limited reaction times can be qualitatively altered by the presence of occluding barriers or by confinement in complex architectures, such as those of reticulated organelles. Motor-driven transport is modulated by the architecture of cytoskeletal filaments that serve as transport highways. In this review, we discuss the impact of geometry on intracellular transport processes that fulfill a broad range of functional objectives, including delivery, distribution, and sorting of cellular components. By unraveling the interplay between morphology and transport efficiency, we aim to elucidate key structure-function relationships that govern the architecture of transport systems at the cellular scale. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Network-driven anomalous transport is a fundamental component of brain microvascular dysfunction

Blood microcirculation supplies neurons with oxygen and nutrients, and contributes to clearing their neurotoxic waste, through a dense capillary network connected to larger tree-like vessels. This complex microvascular architecture results in highly heterogeneous blood flow and travel time distributions, whose origin and consequences on brain pathophysiology are poorly understood. Here, we analyze highly-resolved intracortical blood flow and transport simulations to establish the physical laws governing the macroscopic transport properties in the brain micro-circulation. We show that network-driven anomalous transport leads to the emergence of critical regions, whether hypoxic or with high concentrations of amyloid-β, a waste product centrally involved in Alzheimer's Disease. We develop a Continuous-Time Random Walk theory capturing these dynamics and predicting that such critical regions appear much earlier than anticipated by current empirical models under mild hypoperfusion. These findings provide a framework for understanding and modelling the impact of microvascular dysfunction in brain diseases, including Alzheimer's Disease.

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.

Spectral graph theory efficiently characterizes ventilation heterogeneity in lung airway networks

This paper introduces a linear operator for the purposes of quantifying the spectral properties of transport within resistive trees, such as airflow in lung airway networks. The operator, which we call the Maury matrix, acts only on the terminal nodes of the tree and is equivalent to the adjacency matrix of a complete graph summarizing the relationships between all pairs of terminal nodes. We show that the eigenmodes of the Maury operator have a direct physical interpretation as the relaxation, or resistive, modes of the network. We apply these findings to both idealized and image-based models of ventilation in lung airway trees and show that the spectral properties of the Maury matrix characterize the flow asymmetry in these networks more concisely than the Laplacian modes, and that eigenvector centrality in the Maury spectrum is closely related to the phenomenon of ventilation heterogeneity caused by airway narrowing or obstruction. This method has applications in dimensionality reduction in simulations of lung mechanics, as well as for characterization of models of the airway tree derived from medical images.

Robust Increase in Supply by Vessel Dilation in Globally Coupled Microvasculature

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.