The effects of spatial inhomogeneities on flow through the endothelial surface layer

Flow through the endothelial surface layer (the glycocalyx and adsorbed plasma proteins) plays an important but poorly understood role in cell signaling through a process known as mechanotransduction. Characterizing the flow rates and shear stresses throughout this layer is critical for understanding how flow-induced ionic currents, deformations of transmembrane proteins, and the convection of extracellular molecules signal biochemical events within the cell, including cytoskeletal rearrangements, gene activation, and the release of vasodilators. Previous mathematical models of flow through the endothelial surface layer are based upon the assumptions that the layer is of constant hydraulic permeability and constant height. These models also assume that the layer is continuous across the endothelium and that the layer extends into only a small portion of the vessel lumen. Results of these models predict that fluid shear stress is dissipated through the surface layer and is thus negligible near endothelial cell membranes. In this paper, such assumptions are removed, and the resultant flow rates and shear stresses through the layer are described. The endothelial surface layer is modeled as clumps of a Brinkman medium immersed in a Newtonian fluid. The width and spacing of each clump, hydraulic permeability, and fraction of the vessel lumen occupied by the layer are varied. The two-dimensional Navier-Stokes equations with an additional Brinkman resistance term are solved using a projection method. Several fluid shear stress transitions in which the stress at the membrane shifts from low to high values are described. These transitions could be significant to cell signaling since the endothelial surface layer is likely dynamic in its composition, density, and height.     

Drag-reducing polymers diminish near-wall concentration of platelets in microchannel blood flow

The accumulation of platelets near the blood vessel wall or artificial surface is an important factor in the cascade of events responsible for coagulation and/or thrombosis. In small blood vessels and flow channels this phenomenon has been attributed to the blood phase separation that creates a red blood cell (RBC)-poor layer near the wall. We hypothesized that blood soluble drag-reducing polymers (DRP), which were previously shown to lessen the near-wall RBC depletion layer in small channels, may consequently reduce the near-wall platelet excess. This study investigated the effects of DRP on the lateral distribution of platelet-sized fluorescent particles (diam. = 2 μm, 2.5 × 10?/ml) in a glass square microchannel (width and depth = 100 μm). RBC suspensions in PBS were mixed with particles and driven through the microchannel at flow rates of 6-18 ml/h with and without added DRP (10 ppm of PEO, MW = 4500 kDa). Microscopic flow visualization revealed an elevated concentration of particles in the near-wall region for the control samples at all tested flow rates (between 2.4 ± 0.8 times at 6 ml/h and 3.3 ± 0.3 times at 18 ml/h). The addition of a minute concentration of DRP virtually eliminated the near-wall particle excess, effectively resulting in their even distribution across the channel, suggesting a potentially significant role of DRP in managing and mitigating thrombosis.     

血浆层对血管壁剪应力和剪应力梯度的影响

在细小血管中,由于血细胞明显的趋轴效应,管中的血液分为两个不同的区域,即具有血细胞的核心区和邻近管壁和血浆层。应用两相分层流模型,研究在相同的流量和管径下,当核心区中的血液分别为牛顿流体和Casson流体时,不同的血浆层厚度对细小血管壁剪应力和剪应力梯度的影响。结果表明,血浆层的存在对壁剪应力和壁剪应力梯度有较大影响,当血浆层厚度仅为血管半径的1％和3％时,壁剪应力梯度分别下降约10％和20％。     

Local hemodynamics affect monocytic cell adhesion to a three-dimensional flow model coated with E-selectin.

Monocyte adhesion to the endothelium depends on concentrations of receptors/ligands, local concentrations of chemoattractants, monocyte transport to the endothelial surface and hemodynamic forces. Monocyte adhesion to the inert surface of a three-dimensional perfusion model was shown to correlate inversely with wall shear stress, but was also affected by flow patterns which influenced the near-wall cell availability. We hypothesized that (a) under the same flow conditions, insolubilized E-selectin on the model's surface may mediate adhesive interactions at higher wall shear stresses, compared to an uncoated model, and (b) pulsatile flow may modify the adhesion profile obtained under steady flow. An axisymmetric flow model with a stenosis and a sudden expansion produced a range of wall shear stresses and a separated flow with recirculation and reattachment. Pre-activated U937 cells were perfused through the model under either steady (Re = 100, 140) or pulsatile (Remean = 107) flow. The velocity field was characterized through computational fluid dynamics and validated by inert particle tracking. Surface E-selectin greatly increased cell adhesion in all regions at Re = 100 and 140, compared to an uncoated model under the same flow conditions. In regions where the cells near the wall were abundant (taper and stenosis), adhesion to E-selectin correlated with the reciprocal of local wall shear stress when flow was steady. Pulsatile flow distributed the adherent cells more evenly throughout the coated model. Hence, characterizing both the local hemodynamics and the biological activity on the vessel wall is important in leukocyte adhesion.     

Effect of the endothelial surface layer on transmission of fluid shear stress to endothelial cells

Responses of vascular endothelial cells to mechanical shear stresses resulting from blood flow are involved in regulation of blood flow, in structural adaptation of vessels, and in vascular disease. Interior surfaces of blood vessels are lined with a layer of bound or adsorbed macromolecules, known as the endothelial surface layer (ESL). In vivo investigations have shown that this layer has a width of order 1 microm, that it substantially impedes plasma flow, and that it excludes flowing red blood cells. Here, the effect of the ESL on transmission of shear stress to endothelial cells is examined using a theoretical model. The layer is assumed to consist of a matrix of molecular chains extending from the surface, held in tension by a slight increase in colloid osmotic pressure relative to that in free-flowing plasma. It is shown that, under physiological conditions, shear stress is transmitted to the endothelial surface almost entirely by the matrix, and fluid shear stresses on endothelial cell membranes are very small. Rapid fluctuations in shear stress are strongly attenuated by the layer. The ESL may therefore play an important role in sensing of shear stress by endothelial cells.     

On the Helical MHD Mode in a Finite-Conductivity Tokamak Plasma

A helical MHD perturbation in a finite-conductivity tokamak plasma has been considered in the straight-cylinder model in a situation where there is no resonance surface q = m/n in plasma. The radial eigenfunction of the helical mode, in addition to the large-scale component described at σ_||→ ∞ by the ideal MHD equation, contains a small-scale component localized near the wall and near discontinuities in the radial profiles of the unperturbed quantities. At smooth profiles, the small-scale component is attached to the wall and is smaller in magnitude than the large-scale component. Therefore, beyond a thin near-wall plasma layer, the mode is close to the large-scale ideal MHD mode. The presence of the small-scale component is necessary to satisfy the boundary conditions for the perturbed field on the wall.     

Shear stress induces a transient and VEGFR-2-dependent decrease in the motion of injected particles in endothelial cells

Vascular endothelial cells form the inner lining of all blood vessels and play a central role in vessel physiology and disease. Endothelial cells are highly responsive to the mechanical stimulus of fluid shear stress that is exerted by blood flowing over their surface. In this study, the immediate micromechanical response of endothelial cells to physiological shear stress was characterized by tracking of ballistically injected, sub-micron, fluorescent particles. It was found that the mean squared displacement (MSD) of the particles decreases by a factor 1.5 within 10 min after the onset of shear stress. This decrease in particle motion is transient, since the MSD returns to control values within 15-30 min after the onset of shear. The immediate micromechanical stiffening is dependent on activation of the vascular endothelial growth factor receptor (VEGFR)-2, because inhibition of the receptor abrogates the micromechanical response. This work shows that the cytoskeleton is actively involved in the acute, functional response of endothelial cells to shear stress.     

Acute cerebral artery constriction in the spontaneously hypertensive rat following blood and plasma administration into the subarachnoid space

The purpose of the present study was to demonstrate, using a vascular casting technique, acute vasoconstrictive changes in the cerebral vasculature 1 h following whole-blood or plasma infusion into the subarachnoid space of conscious spontaneously hypertensive rats. Vascular casts from animals infused (over 20 min) with 0.45 ml of heparinized autologous arterial blood or plasma exhibited incomplete filling, while casts from saline-infused controls exhibited virtually no filling defects. Significant elevations in intracranial pressure were noted in blood, but not in plasma- or saline-infused rats. Two characteristic forms of constriction occurred, depending upon the vessel lumen diameter. Vessels with lumen diameters >100 µm were flattened longitudinally with deep endothelial nuclear imprints, while smaller vessels had focal circular constrictions resembling beads. Arterial cast filling terminated in vessels with lumen diameters from 70 to 20 µm with focal signs of constriction at or near the point of cast termination. The results indicate that the presence of both blood and plasma in the subarachnoid space produces acute small-artery constriction. This phenomenon is due to a noncellular blood component and does not correlate with increases in intracranial pressure.     

Expression of connexin 37, 40 and 43 in rat mesenteric arterioles and resistance arteries

Connexins are the protein constituents of gap junctions which mediate intercellular communication in most tissues. In arterioles gap junctions appear to be important for conduction of vasomotor responses along the vessel. Studies of the expression pattern of connexin isoforms in the microcirculation are sparse. We investigated the expression of the three major vascular connexins in mesenteric arterioles (diameter <50 micro m) from male Sprague-Dawley rats, since conducted vasomotor responses have been described in these vessels. The findings were compared with those obtained from upstream small resistance arteries. Indirect immunofluorescence techniques were used on whole mounts of mesenteric arterioles and on frozen sections of resistance arteries (diameter approximately 300 micro m). Mesenteric arterioles expressed Cx40 and Cx43 in the endothelial layer, and Cx37 was found in most but not all vessels. Connexins were not demonstrated in the media. In resistance arteries endothelial cells expressed Cx37, Cx40 and Cx43. Ultrastructural studies of mesenteric arterioles confirmed that gap junction plaques between endothelial cells are present, whereas myoendothelial, or smooth muscle cell gap junctions could not be demonstrated. The findings suggest that smooth muscle cells in mesenteric arterioles may not be well coupled and favour that conducted vasomotor responses in these vessels are propagated through the endothelial cell layer.     

Spatiotemporal analysis of flow-induced intermediate filament displacement in living endothelial cells

The distribution of hemodynamic shear stress throughout the arterial tree is transduced by the endothelium into local cellular responses that regulate vasoactivity, vessel wall remodeling, and atherogenesis. Although the exact mechanisms of mechanotransduction remain unknown, the endothelial cytoskeleton has been implicated in transmitting extracellular force to cytoplasmic sites of signal generation via connections to the lumenal, intercellular, and basal surfaces. Direct observation of intermediate filament (IF) displacement in cells expressing green fluorescent protein-vimentin has suggested that cytoskeletal mechanics are rapidly altered by the onset of fluid shear stress. Here, restored images from time-lapse optical sectioning fluorescence microscopy were analyzed as a four-dimensional intensity distribution function that represented IF positions. A displacement index, related to the product moment correlation coefficient as a function of time and subcellular spatial location, demonstrated patterns of IF displacement within endothelial cells in a confluent monolayer. Flow onset induced a significant increase in IF displacement above the nucleus compared with that measured near the coverslip surface, and displacement downstream from the nucleus was larger than in upstream areas. Furthermore, coordinated displacement of IF near the edges of adjacent cells suggested the existence of mechanical continuity between cells. Thus, quantitative analysis of the spatiotemporal patterns of flow-induced IF displacement suggests redistribution of intracellular force in response to alterations in hemodynamic shear stress acting at the lumenal surface.     

Chemotaxis of granulocytes across bovine pulmonary artery intimal explants without endothelial cell injury

Emigration of granulocytes from vessel lumen to a site of injury is a hallmark of acute inflammation but whether this migration is necessarily associated with vascular damage is not clear. To follow the structural changes associated with granulocyte migration across an intact endothelial cell layer and to assess changes in vascular permeability, an in vitro technique was developed in which intimal explants were stripped from bovine pulmonary artery and mounted in chemotaxis chambers. All explants studied had granulocytes and trace amounts of 3H-water, 14C-sucrose and 125I-albumin in the upper well of the chambers. Experimental explants had zymosan-activated plasma in the lower well and control explants had either serum in the lower well or zymosan-activated plasma in the upper well. Explants were incubated at 37 degrees C for periods from 15 min to 3 hr. When the chemoattractant was added to the lower well, granulocytes migrated into the explants. Transmission and scanning electron microscopy showed an orderly sequence of granulocyte--endothelial interactions throughout which the two cell types maintained close opposition--granulocyte adherence to and exploration of the endothelial surface; penetration and migration through the interendothelial cell junction; reapposition and reformation of the luminal 'tight' junctions and finally passage of granulocytes through the endothelial basal lamina. After 60 min incubation, the majority of granulocytes seen in each section was through the endothelial cell layer and after 2 hr, they were through the basal lamina. Structural evidence of granulocyte or endothelial cell damage was not found at any of the times examined, neither was there any demonstrable increase in intimal permeability. In control explants, granulocyte migration was strikingly less frequent at 2 hr (approximately 10% of that seen towards the chemoattractant). Thus, granulocyte migration across an endothelial cell layer towards a chemoattractant is not necessarily associated with structural evidence of endothelial cell injury or increased vascular permeability.     

Analysis of early embryonic great-vessel microcirculation in zebrafish using high-speed confocal μPIV

In the developing cardiovascular system, hemodynamic vascular loading is critical for angiogenesis and cardiovascular adaptation. Normal zebrafish embryos with transgenically-labeled endothelial and red blood cells provide an excellent in vivo model for studying the fluid-flow induced vascular loading. To characterize the developmental hemodynamics of early embryonic great-vessel microcirculation in the zebrafish embryo, two complementary studies (experimental and numerical) are presented. Quantitative comparison of the wall shear stress (WSS) at the first aortic arch (AA1) of wild-type zebrafish embryos during two consecutive developmental stages is presented, using time-resolved confocal micro-particle image velocimetry (μPIV). Analysis showed that there was significant WSS difference between 32 and 48 h post-fertilization (hpf) wild-type embryos, which correlates with normal arch morphogenesis. The vascular distensibility of the arch wall at systole and the acceleration/deceleration rates of time-lapse phase-averaged streamwise blood flow curves were also analyzed. To estimate the influence of a novel intermittent red-blood cell (RBC) loading on the endothelium, a numerical two-phase, volume of fluid (VOF) flow model was further developed with realistic in vivo conditions. These studies showed that near-wall effects and cell clustering increased WSS augmentation at a minimum of 15% when the distance of RBC from arch vessel wall was less than 3 μm or when RBC cell-to-cell distance was less than 3 μm. When compared to a smooth wall, the WSS augmentation increased by a factor of ~1.4 due to the roughness of the wall created by the endothelial cell profile. These results quantitatively highlight the contribution of individual RBC flow patterns on endothelial WSS in great-vessel microcirculation and will benefit the quantitative understanding of mechanotransduction in embryonic great vessel biology, including arteriovenous malformations (AVM).     

Dynamical clustering of red blood cells in capillary vessels

We have modeled the dynamics of a 3-D system consisting of red blood cells (RBCs), plasma and capillary walls using a discrete-particle approach. The blood cells and capillary walls are composed of a mesh of particles interacting with harmonic forces between nearest neighbors. We employ classical mechanics to mimic the elastic properties of RBCs with a biconcave disk composed of a mesh of spring-like particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, translational and angular momenta. Realistic behavior of blood cells is modeled by considering RBCs and plasma flowing through capillaries of various shapes. Three types of vessels are employed: a pipe with a choking point, a curved vessel and bifurcating capillaries. There is a strong tendency to produce RBC clusters in capillaries. The choking points and other irregularities in geometry influence both the flow and RBC shapes, considerably increasing the clotting effect. We also discuss other clotting factors coming from the physical properties of blood, such as the viscosity of the plasma and the elasticity of the RBCs. Modeling has been carried out with adequate resolution by using 1 to 10 million particles. Discrete particle simulations open a new pathway for modeling the dynamics of complex, viscoelastic fluids at the microscale, where both liquid and solid phases are treated with discrete particles. Figure A snapshot from fluid particle simulation of RBCs flowing along a curved capillary. The red color corresponds to the highest velocity. We can observe aggregation of RBCs at places with the most stagnant plasma flow.     

Surface activity in vitro: role of surfactant proteins

Pattle, who provided some of the initial direct evidence for the presence of pulmonary surfactant in the lung, was also the first to show surfactant was susceptible to proteases such as trypsin. Pattle concluded surfactant was a lipoprotein. Our group has investigated the roles of the surfactant proteins (SP-) SP-A, SP-B, and SP-C using a captive bubble tensiometer. These studies show that SP-C>SP-B>SP-A in enhancing surfactant lipid adsorption (film formation) to the equilibrium surface tension of approximately 22-25 mN/m from the 70 mN/m of saline at 37 degrees C. In addition to enhancing adsorption, surfactant proteins can stabilize surfactant films so that lateral compression induced through surface area reduction results in the lowering of surface tension (gamma) from approximately 25 mN/m (equilibrium) to values near 0 mN/m. These low tensions, which are required to stabilize alveoli during expiration, are thought to arise through exclusion of fluid phospholipids from the surface monolayer, resulting in an enrichment in the gel phase component dipalmitoylphosphatidylcholine (DPPC). The results are consistent with DPPC enrichment occurring through two mechanisms, selective DPPC adsorption and preferential squeeze-out of fluid components such as unsaturated phosphatidylcholine (PC) and phosphatidylglycerol (PG) from the monolayer. Evidence for selective DPPC adsorption arises from experiments showing that the surface area reductions required to achieve gamma near 0 mN/m with DPPC/PG samples containing SP-B or SP-A plus SP-B films were less than those predicted for a pure squeeze-out mechanism. Surface activity improves during quasi-static or dynamic compression-expansion cycles, indicating the squeeze-out mechanism also occurs. Although SP-C was not as effective as SP-B in promoting selective DPPC adsorption, this protein is more effective in promoting the reinsertion of lipids forced out of the surface monolayer following overcompression at low gamma values. Addition of SP-A to samples containing SP-B but not SP-C limits the increase in gamma(max) during expansion. It is concluded that the surfactant apoproteins possess distinct overlapping functions. SP-B is effective in selective DPPC insertion during monolayer formation and in PG squeeze-out during monolayer compression. SP-A can promote adsorption during film formation, particularly in the presence of SP-B. SP-C appears to have a superior role to SP-B in formation of the surfactant reservoir and in reinsertion of collapse phase lipids.     

Computational modelling of emboli travel trajectories in cerebral arteries: influence of microembolic particle size and density

Ischaemic stroke is responsible for up to 80 % of stroke cases. Prevention of the reoccurrence of ischaemic attack or stroke for patients who survived the first symptoms is the major treatment target. Accurate diagnosis of the emboli source for a specific infarction lesion is very important for a better treatment for the patient. However, due to the complex blood flow patterns in the cerebral arterial network, little is known so far of the embolic particle flow trajectory and its behaviour in such a complex flow field. The present study aims to study the trajectories of embolic particles released from carotid arteries and basilar artery in a cerebral arterial network and the influence of particle size, mass and release location to the particle distributions, by computational modelling. The cerebral arterial network model, which includes major arteries in the circle of Willis and several generations of branches from them, was generated from MRI images. Particles with diameters of 200, 500 and 800  $\upmu \hbox {m}$ and densities of 800, 1,030 and 1,300 $\hbox {kg/m}^{3}$ were released in the vessel’s central and near-wall regions. A fully coupled scheme of particle and blood flow in a computational fluid dynamics software ANASYS CFX 13 was used in the simulations. The results show that heavy particles (density large than blood or a diameter larger than 500  $\upmu \hbox {m}$ ) normally have small travel speeds in arteries; larger or lighter embolic particles are more likely to travel to large branches in cerebral arteries. In certain cases, all large particles go to the middle cerebral arteries; large particles with higher travel speeds in large arteries are likely to travel at more complex and tortuous trajectories; emboli raised from the basilar artery will only exit the model from branches of basilar artery and posterior cerebral arteries. A modified Circle of Willis configuration can have significant influence on particle distributions. The local branch patterns of internal carotid artery to middle cerebral artery and anterior communicating artery can have large impact on such distributions.     

Towards the prediction of flow-induced shear stress distributions experienced by breast cancer cells in the lymphatics

Tumour metastasis in the lymphatics is a crucial step in the progression of breast cancer. The dynamics by which breast cancer cells (BCCs) travel in the lymphatics remains poorly understood. The goal of this work is to develop a model capable of predicting the shear stresses metastasising BCCs experience using numerical and experimental techniques. This paper models the fluidic transport of large particles (\(\eta =d_{\mathrm{p}}/W=0.1-0.4\) where \(d_{\mathrm{p}}\) is the particle diameter and W is the channel width) subjected to lymphatic flow conditions (\({ Re}=0.04\)), in a \(100\times 100\,\upmu \hbox {m}\) microchannel. The feasibility of using the dynamic fluid body interaction (DFBI) method to predict particle motion was assessed, and particle tracking experiments were performed. The experiments found that particle translational velocity decreased from the undisturbed fluid velocity with increasing particle size (5–14% velocity lag for \(\eta =0.1-0.3\)). DFBI simulations were found to better predict particle behaviour than theoretical predictions; however, mesh restrictions in the near-wall region (\(0.2\,\mathrm{W}>y>0.8\,\mathrm{W}\)) result in computationally expensive models. The simulations were in good agreement with the experiments (\(<12\%\) difference) across the channel (\(0.2\,\mathrm{W}\le y\le 0.8\,\mathrm{W}\)), with differences up to 25% in the near-wall region. Particles experience a range of shear stresses (0.002–0.12 Pa) and spatial shear gradients (\(0.004-0.137\,\hbox {Pa}/\upmu \hbox {m}\)) depending on their size and radial position. The predicted shear gradients are far in excess of values associated with BCC apoptosis (\(0.004-0.023\,\hbox {Pa}/\upmu \hbox {m}\)). Increasing our understanding of the shear stress magnitudes and gradients experienced by BCCs could be leveraged to elucidate whether a particular BCC size or location exists that encourages metastasis within the lymphatics.     

Control of endothelial cell gene expression by flow

The vessel wall is constantly subjected to, and affected by, the stresses resulting from the hemodynamic stimuli of transmural pressure and flow. At the interface between blood and the vessel wall, the endothelial cell plays a crucial role in controlling vessel structure and function in response to changes in hemodynamic conditions. Using bovine aortic endothelium monolayers, we show that fluid shear stress causes simultaneous differential regulation of endothelial-derived products. We also report that the downregulation of endothelin-1 mRNA by flow is a reversible process, and through the use of uncharged dextran supplementation demonstrate it to be shear stress-rather than shear rate-dependent. Recent work on the effect of fluid shear stress on endothelial cell gene expression of a number of potent endothelial products is reviewed, including vasoactive substances, autocrine and paracrine growth factors, thrombosis/fibrinolysis modulators, chemotactic factors, surface receptors and immediate-early genes. The encountered patterns of gene expression responses are classified into three categories: a transient increase with return to baseline (type I), a sustained increase (type II) and a biphasic response consisting of an early transient increase of varying extent followed by a pronounced and sustained decrease (type III). The importance of the dynamic character of the flow stimulus and the magnitude dependence of the response are presented. Potential molecular mechanisms of shear-induced gene regulation, including putative shear stress response elements (SSRE), are discussed. These results suggest exquisite modulation of endothelial cell phenotype by local fluid shear stress and may offer insight into the mechanism of flow-dependent vascular remodeling and the observed propensity of atherosclerosis formation around bifurcations and areas of low shear stress.