Blood flow and red blood cell deformation in nonuniform capillaries: effects of the endothelial surface layer

Glycocalyx-targeted therapy ameliorates age-related arterial dysfunction

Advanced age is accompanied by arterial dysfunction, as well as a diminished glycocalyx, which may be linked to reduced high molecular weight-hyaluronan (HMW-HA) synthesis. However, the impact of glycocalyx deterioration in age-related arterial dysfunction is unknown. We sought to determine if manipulations in glycocalyx properties would alter arterial function. Tamoxifen-induced hyaluronan synthase 2 (Has2) reduction was used to decrease glycocalyx properties. Three weeks post-tamoxifen treatment, glycocalyx thickness was lower in Has2 knockout compared to wild-type mice (P<0.05). Has2 reduction induced arterial dysfunction, demonstrated by impaired endothelium-dependent dilation (EDD) and elevated aortic stiffness (P<0.05). To augment glycocalyx properties, old mice received 10 weeks of a glycocalyx-targeted therapy via Endocalyx™ (old+ECX), which contains HMW-HA and other glycocalyx components. Compared to old control mice, glycocalyx properties and EDD were augmented, and aortic stiffness decreased in old+ECX mice (P<0.05). Old+ECX mice had a more youthful aortic phenotype, demonstrated by lower collagen content and higher elastin content than old control mice (P<0.05). Functional outcomes were repeated in old mice that underwent a diet supplemented solely with HMW-HA (old+HA). Compared to old controls, glycocalyx properties and EDD were augmented, and aortic stiffness was lower in old+HA mice (P<0.05). We did not observe any differences between old+HA and old+ECX mice (P>0.05). Has2 reduction phenocopies age-related arterial dysfunction, while 10 weeks of glycocalyx-targeted therapy that restores the glycocalyx also ameliorates age-related arterial dysfunction. These findings suggest that the glycocalyx may be a viable therapeutic target to ameliorate age-related arterial dysfunction.

Influence of the vessel wall geometry on the wall-induced migration of red blood cells

The geometry of the blood vessel wall plays a regulatory role on the motion of red blood cells (RBCs). The overall topography of the vessel wall depends on many features, among which the endothelial lining of the endothelial surface layer (ESL) is an important one. The endothelial lining of vessel walls presents a large surface area for exchanging materials between blood and tissues. The ESL plays a critical role in regulating vascular permeability, hindering leukocyte adhesion as well as inhibiting coagulation during inflammation. Changes in the ESL structure are believed to cause vascular hyperpermeability and entrap immune cells during sepsis, which could significantly alter the vessel wall geometry and disturb interactions between RBCs and the vessel wall, including the wall-induced migration of RBCs and the thickening of a cell-free layer. To investigate the influence of the vessel wall geometry particularly changed by the ESL under various pathological conditions, such as sepsis, on the motion of RBCs, we developed two models to represent the ESL using the immersed boundary method in two dimensions. In particular, we used simulations to study how the lift force and drag force on a RBC near the vessel wall vary with different wall thickness, spatial variation, and permeability associated with changes in the vessel wall geometry. We find that the spatial variation of the wall has a significant effect on the wall-induced migration of the RBC for a high permeability, and that the wall-induced migration is significantly inhibited as the vessel diameter is increased.

The Endothelial Glycocalyx and Retinal Hemodynamics

PURPOSE

Previous studies suggest that the endothelial glycocalyx adds to vascular resistance, inhibits thrombosis, and is critical for regulating homogeneous blood flow and ensuring uniform red blood cell (RBC) distribution. However, these functions and consequences of the glycocalyx have not been examined in the retina. We hypothesize that the endothelial glycocalyx is a critical regulator of retinal hemodynamics and perfusion and decreases the propensity for retinal thrombus formation.

METHODS

Hyaluronidase and heparinase, which are endothelial glycocalyx-degrading enzymes, were infused into mice. Fluorescein isothiocyanate-dextran (2000 kDa) was injected to measure lumen diameter, while RBC velocity and distribution were measured using fluorescently labeled RBCs. The diameters and velocities were used to calculate retinal blood flow and shear rates. Mean circulation time was calculated by measuring the difference between arteriolar and venular mean transit times. Rose Bengal dye was infused, followed by illumination with a green light to induce thrombosis.

RESULTS

The acute infusion of hyaluronidase and heparinase led to significant increases in both arteriolar (7%) and venular (16%) diameters in the retina, with a tendency towards increased arteriolar velocity. In addition, the degradation caused a significant decrease in the venular shear rate (14%). The enzyme infusion resulted in substantial increases in total retinal blood flow (26%) and retinal microhematocrit but no changes in the mean circulation time through the retina. We also observed an enhanced propensity for retinal thrombus formation with the removal of the glycocalyx.

CONCLUSIONS

Our data suggest that acute degradation of the glycocalyx can cause significant changes in retinal hemodynamics, with increases in vessel diameter, blood flow, microhematocrit, pro-thrombotic conditions, and decreases in venular shear rate.

Biphasic flow dynamics and polarized mass transportation in branched hepatic sinusoids

In fatty liver diseases, such as liver fibrosis and liver cirrhosis, blood flow in hepatic sinusoids, an elementary building block of the liver lobule, tends to bypass through collateral vessels inside sinusoids and presents distinct sinusoidal flows compared to normal physiological flows. It remains unclear in those flow characteristics in branched sinusoids and the correlation of pathological flows with liver lesions, mainly due to the difficulty of direct hemodynamics measurements in the sinusoids. Here, we developed a dual-branched theoretical model of hepatic sinusoidal flow to elucidate the relevant flow dynamics and mass transport. Numerical simulations, based on the lattice Boltzmann method, indicated that the flow velocity distribution in hepatic sinusoids is mainly dominated by endothelium permeability and presents a non-monotonic variation with the permeability at the fusion segment of these branched sinusoids. Flow-induced shear stress on the endothelium at the side of the Disse space exhibited a biphasic pattern, yielding a low shear stress region at the junctional site. Meanwhile, a highly polarized distribution of lipoproteins concentration was also presented at the low shear stress region, indicating a localized accumulation of typical hepatic serum proteins. Thus, this work provides the basic understanding of blood flow features and mass transport regulations in branched hepatic sinusoids.

Dependence of red blood cell dynamics in microvessel bifurcations on the endothelial surface layer's resistance to flow and compression

Red blood cells (RBCs) make up 40-45% of blood and play an important role in oxygen transport. That transport depends on the RBC distribution throughout the body, which is highly heterogeneous. That distribution, in turn, depends on how RBCs are distributed or partitioned at diverging vessel bifurcations where blood flows from one vessel into two. Several studies have used mathematical modeling to consider RBC partitioning at such bifurcations in order to produce useful insights. These studies, however, assume that the vessel wall is a flat impenetrable homogeneous surface. While this is a good first approximation, especially for larger vessels, the vessel wall is typically coated by a flexible, porous endothelial glycocalyx or endothelial surface layer (ESL) that is on the order of 0.5-1 µm thick. To better understand the possible effects of this layer on RBC partitioning, a diverging capillary bifurcation is analyzed using a flexible, two-dimensional model. In addition, the model is also used to investigate RBC deformation and RBC penetration of the ESL region when ESL properties are varied. The RBC is represented using interconnected viscoelastic elements. Stokes flow equations (viscous flow) model the surrounding fluid. The flow in the ESL is modeled using the Brinkman approximation for porous media with a corresponding hydraulic resistivity. The ESL's resistance to compression is modeled using an osmotic pressure difference. One cell passes through the bifurcation at a time, so there are no cell-cell interactions. A range of physiologically relevant hydraulic resistivities and osmotic pressure differences are explored. Decreasing hydraulic resistivity and/or decreasing osmotic pressure differences (ESL resistance to compression) produced four behaviors: (1) RBC partitioning nonuniformity increased slightly; (2) RBC deformation decreased; (3) RBC velocity decreased relative to blood flow velocity; and (4) RBCs penetrated more deeply into the ESL. Decreasing the ESL's resistance to flow and/or compression to pathological levels could lead to more frequent cell adhesion and clotting as well as impaired vascular regulation due to weaker ATP and nitric oxide release. Potential mechanisms that can contribute to these behaviors are also discussed.

Multifunctional manipulation of red blood cells using optical tweezers

Serving as natural vehicles to deliver oxygen throughout the whole body, red blood cells (RBCs) have been regarded as important indicators for biomedical analysis and clinical diagnosis. Various diseases can be induced due to the dysfunction of RBCs. Hence, a flexible tool is required to perform precise manipulation and quantitative characterization of their physiological mechanisms and viscoelastic properties. Optical tweezers have emerged as potential candidates due to their noncontact manipulation and femtonewton-precision measurements. This review aimed to highlight the recent advances in the multifunctional manipulation of RBCs using optical tweezers, including controllable deformation, dynamic stretching, RBC aggregation, blood separation and Raman characterization. Further, great attentions have been focused on the precise assembly of functional biophotonics devices with trapped RBCs, and a brief overview was offered for the growing interests to manipulate RBCs in vivo.

Influence of microflow on hepatic sinusoid blood flow and red blood cell deformation

Hepatic sinusoids present complex anatomical structures such as the endothelial sieve pores and the Disse space, which govern the microscopic blood flow in the sinusoids and are associated with structural variations in liver fibrosis and cirrhosis. However, the contributions of the permeability of endothelial and collagen layers and the roughness of hepatocyte microvilli to the features of this microflow remain largely unknown. Here, an immersed boundary method coupled with a lattice Boltzmann method was adopted in an in vitro hepatic sinusoidal model, and flow field and erythrocyte deformation analyses were conducted by introducing three new source terms including permeability of the endothelial layer, resistance of hepatocyte microvilli and collagen layers, and deformation of red blood cells (RBCs). Numerical calculations indicated that alterations in endothelial permeability could significantly affect the flow velocity and flow rate distributions in hepatic sinusoids. Interestingly, a biphasic regulating pattern of shear stress occurred simultaneously on the surface of hepatocytes and the lower side of endothelium, i.e., the shear stress increased with increased thickness of hepatocyte microvilli and collagen layer when the endothelial permeability was high but decreased with the increase of the thickness at low endothelial permeability. Additionally, this specified microflow manipulates typical RBC deformation inside the sinusoid, yielding one-third of the variation of deformable index with varied endothelial permeability. These simulations not only are consistent with experimental measurements using in vitro liver sinusoidal chip but also elaborate the contributions of endothelial and collagen layer permeability and wall roughness. Thus, our results provide a basis for further characterizing this microflow and understanding its effects on cellular migration and deformation in the hepatic sinusoids.

Vascular permeability of skeletal muscle microvessels in rat arterial ligation model: in vivo analysis using two-photon laser scanning microscopy

Peripheral artery disease (PAD) in the lower limb compromises oxygen supply due to arterial occlusion. Ischemic skeletal muscle is accompanied by capillary structural deformation. Therefore, using novel microscopy techniques, we tested the hypothesis that endothelial cell swelling temporally and quantitatively corresponds to enhanced microvascular permeability. Hindlimb ischemia was created in male Wistar rat's by iliac artery ligation (AL). The tibialis anterior (TA) muscle microcirculation was imaged using intravenously infused rhodamine B isothiocyanate dextran fluorescent dye via two-photon laser scanning microscopy (TPLSM) and dye extravasation at 3 and 7 days post-AL quantified to assess microvascular permeability. The TA microvascular endothelial ultrastructure was analyzed by transmission electron microscopy (TEM). Compared with control (0.40 ± 0.15 μm3 × 106), using TPLSM, the volumetrically determined interstitial leakage of fluorescent dye measured at 3 (3.0 ± 0.40 μm3 × 106) and 7 (2.5 ± 0.8 μm3 × 106) days was increased (both P < 0.05). Capillary wall thickness was also elevated at 3 (0.21 ± 0.06 μm) and 7 (0.21 ± 0.08 μm) days versus control (0.11 ± 0.03 μm, both P < 0.05). Capillary endothelial cell swelling was temporally and quantitatively associated with elevated vascular permeability in the AL model of PAD but these changes occurred in the absence of elevations in protein levels of vascular endothelial growth factor (VEGF) its receptor (VEGFR2 which decreased by AL-7 day) or matrix metalloproteinase. The temporal coherence of endothelial cell swelling and increased vascular permeability supports a common upstream mediator. TPLSM, in combination with TEM, provides a sensitive and spatially discrete technique to assess the mechanistic bases for, and efficacy of, therapeutic countermeasures to the pernicious sequelae of compromised peripheral arterial function.

Morphometric, Hemodynamic, and Biomechanical Factors Influencing Blood Flow and Oxygen Concentration in the Human Lamina Cribrosa

Purpose

We developed a combined biomechanical and hemodynamic model of the human eye to estimate blood flow and oxygen concentration within the lamina cribrosa (LC) and rank the factors that influence LC oxygen concentration.

Methods

We generated 5000 finite-element eye models with detailed microcapillary networks of the LC and computed the oxygen concentration of the lamina retinal ganglion cell axons. For each model, we varied the intraocular pressure (IOP) from 10 mm Hg to 55 mm Hg in 5-mm Hg increments, the cerebrospinal fluid pressure (13 ± 2 mm Hg), cup depth (0.2 ± 0.1 mm), scleral stiffness (±20% of the mean values), LC stiffness (0.41 ± 0.2 MPa), LC radius (1.2 ± 0.12 mm), average LC pore size (5400 ± 2400 µm²), the microcapillary arrangement (radial, isotropic, or circumferential), and perfusion pressure (50 ± 9 mm Hg). Blood flow was assumed to originate from the LC periphery and drain via the central retinal vein. Finally, we performed linear regressions to rank the influence of each factor on the LC tissue oxygen concentration.

Results

LC radius and perfusion pressure were the most important factors in influencing the oxygen concentration of the LC. IOP was another important parameter, and eyes with higher IOP had higher compressive strain and slightly lower oxygen concentration. In general, superior–inferior regions of the LC had significantly lower oxygen concentration than the nasal–temporal regions, resulting in an hourglass pattern of oxygen deficiency.

Conclusions

To the best of our knowledge, this study is the first to implement a comprehensive hemodynamical model of the eye that accounts for the biomechanical forces and morphological parameters of the LC. The results provide further insight into the possible relationship of biomechanical and vascular pathways leading to ischemia-induced optic neuropathy.

The role of the endothelial glycocalyx in advanced age and cardiovascular disease

The endothelial glycocalyx is a gel-like structure that is bound to the luminal surface of the vascular endothelium. At the interface between flowing blood and endothelial cells, the glycocalyx has several functions that are critical for the maintenance of a healthy vasculature, particularly in regard to the vascular endothelium. Within the vasculature, the glycocalyx modulates vascular resistance to maintain blood flow homogeneity in the microcirculation, mechanotransduces fluid shear stress to the endothelium, and buffers endothelial cells from plasma oxidants, cytokines, and circulating immune cells. In advanced age and cardiovascular disease (CVD), the glycocalyx is deteriorated. Moreover, glycocalyx deterioration may precede traditional measurements of age-related vascular dysfunction, such as impaired endothelium-dependent dilation and large artery stiffness, suggesting that a deteriorated glycocalyx could initiate age-related CVD pathology.

Biofabrication strategies for creating microvascular complexity

Design and fabrication of effective biomimetic vasculatures constitutes a relevant and yet unsolved challenge, lying at the heart of tissue repair and regeneration strategies. Even if cell growth is achieved in 3D tissue scaffolds or advanced implants, tissue viability inevitably requires vascularization, as diffusion can only transport nutrients and eliminate debris within a few hundred microns. This engineered vasculature may need to mimic the intricate branching geometry of native microvasculature, referred to herein as vascular complexity, to efficiently deliver blood and recreate critical interactions between the vascular and perivascular cells as well as parenchymal tissues. This review first describes the importance of vascular complexity in labs- and organs-on-chips, the biomechanical and biochemical signals needed to create and maintain a complex vasculature, and the limitations of current 2D, 2.5D, and 3D culture systems in recreating vascular complexity. We then critically review available strategies for design and biofabrication of complex vasculatures in cell culture platforms, labs- and organs-on-chips, and tissue engineering scaffolds, highlighting their advantages and disadvantages. Finally, challenges and future directions are outlined with the hope of inspiring researchers to create the reliable, efficient and sustainable tools needed for design and biofabrication of complex vasculatures.

Advanced age results in a diminished endothelial glycocalyx

Age-related microvascular dysfunction is well characterized in rodents and humans, but little is known about the properties of the microvascular endothelial glycocalyx in advanced age. We examined the glycocalyx in microvessels of young and old male C57BL6 mice (young: 6.1 ± 0.1 mo vs. old: 24.6 ± 0.2 mo) using intravital microscopy and transmission electron microscopy and in human participants (young: 29 ± 1 yr vs. old: 60 ± 2 yr) using intravital microscopy. Glycocalyx thickness in mesenteric and skeletal muscle microvessels was 51-54% lower in old compared with young mice. We also observed 33% lower glycocalyx thickness in the sublingual microcirculation of humans in advanced age. The perfused boundary region, a marker of glycocalyx barrier function, was also obtained using an automated capture and analysis system. In advanced age, we observed a 10-22% greater perfused boundary region in mice and humans, indicating a more penetrable glycocalyx. Finally, using this automated analysis system, we examined perfused microvascular density and red blood cell (RBC) fraction. Perfused microvascular density is a marker of microvascular function that reflects the length of perfused microvessel segments in a given area; RBC fraction represents the heterogeneity in RBC presence between microvessel segments. Compared with young, the perfused microvascular density was 16-21% lower and RBC fraction was 5-14% lower in older mice and in older humans. These data provide novel evidence that, across mammalian species, a diminished glycocalyx is present in advanced age and is accompanied by markers of impaired microvascular perfusion. Age-related glycocalyx deterioration may be an important contributor to microvascular dysfunction in older adults and subsequent pathophysiology. NEW & NOTEWORTHY Advanced age is characterized by microvascular dysfunction that contributes to age-related cardiovascular diseases, but little is known about endothelial glycocalyx properties in advanced age. This study reveals, for the first time, lower glycocalyx thickness and barrier function that is accompanied by impaired microvascular perfusion in both mice and humans in advanced age.

Red blood cell dynamics in biomimetic microfluidic networks of pulmonary alveolar capillaries

The pulmonary capillary networks (PCNs) embody organ-specific microvasculatures, where blood vessels form dense meshes that maximize the surface area available for gas exchange in the lungs. With characteristic capillary lengths and diameters similar to the size of red blood cells (RBCs), seminal descriptions coined the term "sheet flow" nearly half a century ago to differentiate PCNs from the usual notion of Poiseuille flow in long straight tubes. Here, we revisit in true-scale experiments the original "sheet flow" model and devise for the first time biomimetic microfluidic platforms of organ-specific PCN structures perfused with RBC suspensions at near-physiological hematocrit levels. By implementing RBC tracking velocimetry, our measurements reveal a wide range of heterogonous RBC pathways that coexist synchronously within the PCN; a phenomenon that persists across the broad range of pressure drops and capillary segment sizes investigated. Interestingly, in spite of the intrinsic complexity of the PCN structure and the heterogeneity in RBC dynamics observed at the microscale, the macroscale bulk flow rate versus pressure drop relationship retains its linearity, where the hydrodynamic resistance of the PCN is to a first order captured by the characteristic capillary segment size. To the best of our knowledge, our in vitro efforts constitute a first, yet significant, step in exploring systematically the transport dynamics of blood in morphologically inspired capillary networks.

Local membrane length conservation in two-dimensional vesicle simulation using a multicomponent lattice Boltzmann equation method

We present a method for applying a class of velocity-dependent forces within a multicomponent lattice Boltzmann equation simulation that is designed to recover continuum regime incompressible hydrodynamics. This method is applied to the problem, in two dimensions, of constraining to uniformity the tangential velocity of a vesicle membrane implemented within a recent multicomponent lattice Boltzmann simulation method, which avoids the use of Lagrangian boundary tracers. The constraint of uniform tangential velocity is carried by an additional contribution to an immersed boundary force, which we derive here from physical arguments. The result of this enhanced immersed boundary force is to apply a physically appropriate boundary condition at the interface between separated lattice fluids, defined as that region over which the phase-field varies most rapidly. Data from this enhanced vesicle boundary method are in agreement with other data obtained using related methods [e.g., T. Krüger, S. Frijters, F. Günther, B. Kaoui, and J. Harting, Eur. Phys. J. 222, 177 (2013)10.1140/epjst/e2013-01834-y] and underscore the importance of a correct vesicle membrane condition.

Modeling microcirculatory blood flow: current state and future perspectives

Microvascular blood flow determines a number of important physiological processes of an organism in health and disease. Therefore, a detailed understanding of microvascular blood flow would significantly advance biophysical and biomedical research and its applications. Current developments in modeling of microcirculatory blood flow already allow to go beyond available experimental measurements and have a large potential to elucidate blood flow behavior in normal and diseased microvascular networks. There exist detailed models of blood flow on a single cell level as well as simplified models of the flow through microcirculatory networks, which are reviewed and discussed here. The combination of these models provides promising prospects for better understanding of blood flow behavior and transport properties locally as well as globally within large microvascular networks.

Flow structures and red blood cell dynamics in arteriole of dilated or constricted cross section

Vessel with 'circular' or 'star-shaped' cross sections are studied, representing respectively dilated or constricted cases where endothelial cells smoothly line or bulge into the lumen. Computational haemodynamics simulations are carried out on idealised periodic arteriole-sized vessels, with red blood cell 'tube' hematocrit value=24%. A further simulation of a single red blood cell serves for comparison purposes. The bulk motion of the red blood cells reproduces well-known effects, including the presence of a cell-free layer and the apparent shear-thinning non-Newtonian rheology. The velocity flow field is analysed in a Lagrangian reference frame, relative to any given red blood cell, hence removing the bulk coaxial motion and highlighting instead the complex secondary flow patterns. An aggregate formation becomes apparent, continuously rearranging and dynamic, brought about by the inter-cellular fluid mechanics interactions and the deformability properties of the cells. The secondary flow field induces a vacillating radial migration of the red blood cells. At different radial locations, the red blood cells express different residence times, orientation and shape. The shear stresses exerted by the flow on the vessel wall are influenced by the motion of red blood cells, despite the presence of the cell-free layer. Spatial (and temporal) variations of wall shear stress patters are observed, especially for the 'circular' vessel. The 'star-shaped' vessel bears considerable stress at the protruding endothelial cell crests, where the stress vectors are coaxially aligned. The bulging endothelial cells hence regularise the transmission of stresses on the vessel wall.

A boundary-integral representation for biphasic mixture theory, with application to the post-capillary glycocalyx

We describe a new boundary-integral representation for biphasic mixture theory, which allows us to efficiently solve certain elastohydrodynamic–mobility problems using boundary element methods. We apply this formulation to model the motion of a rigid particle through a microtube which has non-uniform wall shape, is filled with a viscous Newtonian fluid, and is lined with a thin poroelastic layer. This is relevant to scenarios such as the transport of small rigid cells (such as neutrophils) through microvessels that are lined with an endothelial glycocalyx layer (EGL). In this context, we examine the impact of geometry upon some recently reported phenomena, including the creation of viscous eddies, fluid flux into the EGL, as well as the role of the EGL in transmitting mechanical signals to the underlying endothelial cells.

Circulatory bubble dynamics: from physical to biological aspects

Bubbles can form in the body during or after decompression from pressure exposures such as those undergone by scuba divers, astronauts, caisson and tunnel workers. Bubble growth and detachment physics then becomes significant in predicting and controlling the probability of these bubbles causing mechanical problems by blocking vessels, displacing tissues, or inducing an inflammatory cascade if they persist for too long in the body before being dissolved. By contrast to decompression induced bubbles whose site of initial formation and exact composition are debated, there are other instances of bubbles in the bloodstream which are well-defined. Gas emboli unwillingly introduced during surgical procedures and ultrasound microbubbles injected for use as contrast or drug delivery agents are therefore also discussed. After presenting the different ways that bubbles can end up in the human bloodstream, the general mathematical formalism related to the physics of bubble growth and detachment from decompression is reviewed. Bubble behavior in the bloodstream is then discussed, including bubble dissolution in blood, bubble rheology and biological interactions for the different cases of bubble and blood composition considered.

Red blood cell dynamics in polymer brush-coated microcapillaries: A model of endothelial glycocalyx in vitro

The confined flow of red blood cells (RBCs) in microvasculature is essential for oxygen delivery to body tissues and has been extensively investigated in the literature, both in vivo and in vitro. One of the main problems still open in microcirculation is that flow resistance in microcapillaries in vivo is higher than that in vitro. This discrepancy has been attributed to the glycocalyx, a macromolecular layer lining the inner walls of vessels in vivo, but no direct experimental evidence of this hypothesis has been provided so far. Here, we investigate the flow behavior of RBCs in glass microcapillaries coated with a polymer brush (referred to as "hairy" microcapillaries as opposed to "bare" ones with no coating), an experimental model system of the glycocalyx. By high-speed microscopy imaging and image analysis, a velocity reduction of RBCs flowing in hairy microcapillaries as compared to bare ones is indeed found at the same pressure drop. Interestingly, such slowing down is larger than expected from lumen reduction due to the polymer brush and displays an on-off trend with a threshold around 70 nm of polymer brush dry thickness. Above this threshold, the presence of the polymer brush is associated with an increased RBC deformation, and RBC velocity is independent on polymer brush thickness (at the same pressure drop). In conclusion, this work provides direct support to the hypothesis that the glycocalyx is the main factor responsible of the higher flow resistance found in microcapillaries in vivo.

Blood viscosity in microvessels: experiment and theory

The apparent viscosity of blood flowing through narrow glass tubes decreases strongly with decreasing tube diameter over the range from about 300 μm to about 10 μm. This phenomenon, known as the Fåhraeus-Lindqvist effect, occurs because blood is a concentrated suspension of deformable red blood cells with a typical dimension of about 8 μm. Most of the resistance to blood flow through the circulatory system resides in microvessels with diameters in this range. Apparent viscosity of blood in microvessels in vivo has been found to be significantly higher than in glass tubes with corresponding diameters. Here we review experimental observations of blood's apparent viscosity in vitro and in vivo, and progress towards a quantitative theoretical understanding of the mechanisms involved.

Multiple-component lattice Boltzmann equation for fluid-filled vesicles in flow

We document the derivation and implementation of extensions to a two-dimensional, multicomponent lattice Boltzmann equation model, with Laplace law interfacial tension. The extended model behaves in such a way that the boundary between its immiscible drop and embedding fluid components can be shown to describe a vesicle of constant volume bounded by a membrane with conserved length, specified interface compressibility, bending rigidity, preferred curvature, and interfacial tension. We describe how to apply this result to several, independent vesicles. The extended scheme is completely Eulerian, and it represents a two-way coupled vesicle membrane and flow within a single framework. Unlike previous methods, our approach dispenses entirely with the need explicitly to track the membrane, or boundary, and makes no use whatsoever of computationally expensive and intricate interface tracking and remeshing. Validation data are presented, which demonstrate the utility of the method in the simulation of the flow of high volume fraction suspensions of deformable objects.

Motion of red blood cells near microvessel walls: effects of a porous wall layer

A two-dimensional model is used to simulate the motion and deformation of a single mammalian red blood cell (RBC) flowing close to the wall of a microvessel, taking into account the effects of a porous endothelial surface layer (ESL) lining the vessel wall. Migration of RBCs away from the wall leads to the formation of a cell-depleted layer near the wall, which has a large effect on the resistance to blood flow in microvessels. The objective is to examine the mechanical factors causing this migration, including the effects of the ESL. The vessel is represented as a straight parallel-sided channel. The RBC is represented as a set of interconnected viscoelastic elements, suspended in plasma, a Newtonian fluid. The ESL is represented as a porous medium, and plasma flow in the layer is computed using the Brinkman approximation. It is shown that an initially circular cell positioned close to the ESL in a shear flow is deformed into an asymmetric shape. This breaking of symmetry leads to migration away from the wall. With increasing hydraulic resistivity of the layer, the rate of lateral migration increases. It is concluded that mechanical interactions of RBCs flowing in microvessels with a porous wall layer may reduce the rate of lateral migration and hence reduce the width of the cell-depleted zone external to the ESL, relative to the cell-depleted zone that would be formed if the interface between the ESL and free-flowing plasma were replaced by an impermeable boundary.

Excessive erythrocytosis compromises the blood-endothelium interface in erythropoietin-overexpressing mice

Elevated systemic haematocrit (Hct) increases risk of cardiovascular disorders, such as stroke and myocardial infarction. One possible pathophysiological mechanism could be a disturbance of the blood-endothelium interface. It has been shown that blood interacts with the endothelial surface via a thick hydrated macromolecular layer (the 'glycocalyx', or 'endothelial surface layer'--ESL), modulating various biological processes, including inflammation, permeability and atherosclerosis. However, the consequences of elevated Hct on the functional properties of this interface are incompletely understood. Thus, we combined intravital microscopy of an erythropoietin overexpressing transgenic mouse line (tg6) with excessive erythrocytosis (Hct 0.85), microviscometric analysis of haemodynamics, and a flow simulation model to assess the effects of elevated Hct on glycocalyx/ESL thickness and flow resistance. We show that the glycocalyx/ESL is nearly abolished in tg6 mice (thickness: wild-type control: 0.52 μm; tg6: 0.13 μm; P < 0.001). However, the corresponding reduction in network flow resistance contributes <20% to the maintenance of total peripheral resistance observed in tg6 mice. This suggests that the pathological effects of elevated Hct in these mice, and possibly also in polycythaemic humans, may relate to biological corollaries of a reduced ESL thickness and the consequent alteration in the blood-endothelium interface, rather than to an increase of flow resistance.

Tank-treading of erythrocytes in strong shear flows via a nonstiff cytoskeleton-based continuum computational modeling

We develop a computationally efficient cytoskeleton-based continuum erythrocyte algorithm. The cytoskeleton is modeled as a two-dimensional elastic solid with comparable shearing and area-dilatation resistance that follows a material law (Skalak, R., A. Tozeren, R. P. Zarda, and S. Chien. 1973. Strain energy function of red blood cell membranes. Biophys. J. 13:245-264). Our modeling enforces the global area-incompressibility of the spectrin skeleton (being enclosed beneath the lipid bilayer in the erythrocyte membrane) via a nonstiff, and thus efficient, adaptive prestress procedure which accounts for the (locally) isotropic stress imposed by the lipid bilayer on the cytoskeleton. In addition, we investigate the dynamics of healthy human erythrocytes in strong shear flows with capillary number Ca =O(1) and small-to-moderate viscosity ratios 0.001 ≤ λ ≤ 1.5. These conditions correspond to a wide range of surrounding medium viscosities (4-600 mPa s) and shear flow rates (0.02-440 s(-1)), and match those used in ektacytometry systems. Our computational results on the cell deformability and tank-treading frequency are compared with ektacytometry findings. The tank-treading period is shown to be inversely proportional to the shear rate and to increase linearly with the ratio of the cytoplasm viscosity to that of the suspending medium. Our modeling also predicts that the cytoskeleton undergoes measurable local area dilatation and compression during the tank-treading of the cells.

Microvascular Rheology and Hemodynamics

The goal of elucidating the biophysical and physiological basis of pressure-flow relations in the microcirculation has been a recurring theme since the first observations of capillary blood flow in living tissues. At the birth of the Microcirculatory Society, seminal observations on the heterogeneous distribution of blood cells in the microvasculature and the rheological properties of blood in small bore tubes raised many questions on the viscous properties of blood flow in the microcirculation that captured the attention of the Society's membership. It is now recognized that blood viscosity in small bore tubes may fall dramatically as shear rates are increased, and increase (dramatically with elevations in hematocrit. These relationships are strongly affected by blood cell deformability and concentration, red cell aggregation, and white cell interactions with the red cells anti endothelium. Increasing strength of red cell aggregation may result in sequestration of clumps of red cells with either reductions or increases in microvascular hematocrit dependent upon network topography. During red cell aggregation, resistance to flow may thus decrease with hematocrit reduction or increase due to redistribution of red cells. Blood cell adhesion to the microvessel wall may initiate flow reductions, as, for example, in the case of red cell adhesion to the endothelium in sickle cell disease, or leukocyte adhesion in inflammation. The endothelial glycocalyx has been shown to result from a balance of the biosynthesis of new glycans, and the enzymatic or shear-dependent alterations in its composition. Flow-dependent reductions in the endothelial surface layer may thus affect the resistance to flow and/or the adhesion of red cells and/or leukocytes to the endothelium. Thus, future studies aimed at the molecular rheology of the endothelial surface layer may provide new insights into determinants of the resistance to flow.

Numerical simulation of blood flow through microvascular capillary networks

A numerical method is implemented for computing blood flow through a branching microvascular capillary network. The simulations follow the motion of individual red blood cells as they enter the network from an arterial entrance point with a specified tube hematocrit, while simultaneously updating the nodal capillary pressures. Poiseuille's law is used to describe flow in the capillary segments with an effective viscosity that depends on the number of cells residing inside each segment. The relative apparent viscosity is available from previous computational studies of individual red blood cell motion. Simulations are performed for a tree-like capillary network consisting of bifurcating segments. The results reveal that the probability of directional cell motion at a bifurcation (phase separation) may have an important effect on the statistical measures of the cell residence time and scattering of the tube hematocrit across the network. Blood cells act as regulators of the flow rate through the network branches by increasing the effective viscosity when the flow rate is high and decreasing the effective viscosity when the flow rate is low. Comparison with simulations based on conventional models of blood flow regarded as a continuum indicates that the latter underestimates the variance of the hematocrit across the vascular tree.

Unloading oxygen in a capillary vessel under a pathological condition

In this work, we study theoretically the unloading of oxygen from a hemoglobin molecule to the wall of a typical capillary vessel, considering that the hemoglobin under pathological conditions, obeys the rheological Maxwell model. Based on recent experimental evidences in hypertension, we consider that the red blood cells (RBCs) are composed by a single continuous medium in contrast with the classical particulate or discrete RBC models, which are only valid under normal physiological conditions. The analysis considers the hemodynamic interactions between the plasma and the hemoglobin, both circulating in a long horizontal capillary. We apply numerical and analytical methods to obtain the main fluid-dynamic characteristics for both fluids in the limit of low Reynolds and Womersley numbers. A diffusion boundary layer formulation for the oxygen transport in the combined plasma-hemoglobin core region is presented. The main aspects derived are the time and spatial evolution of the membrane. The hemoglobin and plasma velocities and the pressure distributions are shown. For the oxygen unloading the results are the oxy-hemoglobin saturation, the oxygen flux and the oxygen concentration in the cell-free plasma layer. The volume fraction of red blood cells and the Strouhal number have a great influence on the hemodynamic interactions.

Tank-tread frequency of the red cell membrane: dependence on the viscosity of the suspending medium

Single human red cells were suspended in media with viscosities ranging from 12.9 to 109 mPa s and subjected to shear flow ranging from 1/s to 290/s in a rheoscope. This is a transparent cone-plate chamber adapted to a microscope. The motion of the membrane around red cells oriented in a steady-state fashion in the shear field (tank-tread motion) was videotaped. The projected length and width of the cells as well as the frequency of tank-tread motion were measured. One-thousand eight-hundred seventy-three cells of three blood donors were evaluated. The frequency increased with the mean shear rate in an almost linear fashion. The slope of this dependence increased weakly with the viscosity of the suspending medium. No correlation was found between the frequency and four morphological red cell parameters: the projected length and width of the cells as well as the ratio and the square root of the product of these quantities. The energy dissipation within the red cell membrane was estimated based on the measured parameters and compared to the energy dissipation in the undisturbed shear flow. At constant mean shear rate the rise of the energy dissipation with viscosity is slower whereas at constant viscosity the rise with the shear rate is steeper than in the undisturbed shear flow. A fit of the data collected in this work to a theoretical red cell model might allow one to determine intrinsic mechanical constants in the low deformation regime.

Normal endothelium

In recent decades, it has become evident that the endothelium is by no means a passive inner lining of blood vessels. This 'organ' with a large surface (approximately 350 m2) and a comparatively small total mass (approximately 110 g) is actively involved in vital functions of the cardiovascular system, including regulation of perfusion, fluid and solute exchange, haemostasis and coagulation, inflammatory responses, vasculogenesis and angiogenesis. The present chapter focusses on two central aspects of endothelial structure and function: (1) the heterogeneity in endothelial properties between species, organs, vessel classes and even within individual vessels and (2) the composition and role of the molecular layer on the luminal surface of endothelial cells. The endothelial lining of blood vessels in different organs differs with respect to morphology and permeability and is classified as 'continuous', 'fenestrated' or 'discontinuous'. Furthermore, the mediator release, antigen presentation or stress responses of endothelial cells vary between species, different organs and vessel classes. Finally there are relevant differences even between adjacent endothelial cells, with some cells exhibiting specific functional properties, e.g. as pacemaker cells for intercellular calcium signals. Organ-specific structural and functional properties of the endothelium are marked in the vascular beds of the lung and the brain. Pulmonary endothelium exhibits a high constitutive expression of adhesion molecules which may contribute to the margination of the large intravascular pool of leucocytes in the lung. Furthermore, the pulmonary microcirculation is less permeable to protein and water flux as compared to large pulmonary vessels. Endothelial cells of the blood-brain barrier exhibit a specialised phenotype with no fenestrations, extensive tight junctions and sparse pinocytotic vesicular transport. This barrier allows a strict control of exchange of solutes and circulating cells between the plasma and the interstitial space. It was observed that average haematocrit levels in muscle capillaries are much lower as compared to systemic haematocrit, and that flow resistance of microvascular beds is higher than expected from in vitro studies of blood rheology. This evidence stimulated the concept of a substantial layer on the luminal endothelial surface (endothelial surface layer, ESL) with a thickness in the range of 0.5-1 microm. In comparison, the typical thickness of the glycocalyx directly anchored in the endothelial plasma membrane, as seen in electron micrographs, amounts to only about 50-100 microm. Therefore it is assumed that additional components, e.g. adsorbed plasma proteins or hyaluronan, are essential in constituting the ESL. Functional consequences of the ESL presence are not yet sufficiently understood and acknowledged. However, it is evident that the thick endothelial surface layer significantly impacts haemodynamic conditions, mechanical stresses acting on red cells in microvessels, oxygen transport, vascular control, coagulation, inflammation and atherosclerosis.

Effect of erythrocyte aggregation at normal human levels on functional capillary density in rat spinotrapezius muscle

Previous studies have shown that functional capillary density (FCD) is substantially reduced by erythrocyte aggregation. However, only supranormal levels of aggregability were studied. To investigate the effect of erythrocyte aggregability at the level seen in healthy humans, the FCD of selected capillary fields in rat spinotrapezius muscle was determined with high-speed video microscopy under normal (nonaggregating) conditions and after induction of erythrocyte aggregation with Dextran 500 (200 mg/kg). To examine shear rate dependence, the effect was studied both at normal and reduced arterial pressures (50 and 25 mmHg), the latter achieved by short periods of hemorrhage. In a separate study, volume flow was determined in arterioles (52.1 ± 3.7 μm) under the same conditions. Before Dextran 500 infusion, FCD fell to 91% and 76% of control values, respectively, when arterial pressure was reduced to 50 and 25 mmHg. After Dextran 500 infusion, FCD was 96% at normal arterial pressure and fell to 79% and 37% of normal control values at 50 and 25 mmHg. All FCD values were significantly lower after dextran infusion. FCD reduction after lowering arterial pressure or dextran infusion appeared to be due to plasma skimming rather than capillary plugging. Reduction of FCD by dextran at reduced pressure was compensated by increased red blood cell flux in capillaries with red blood cell flow. We conclude that the level of aggregability seen in healthy humans is an important determinant of FCD only at reduced arterial pressure.

A Novel Three-Dimensional Computer-Assisted Method for a Quantitative Study of Microvascular Networks of the Human Cerebral Cortex

OBJECTIVE

Detailed information on microvascular network anatomy is a requirement for understanding several aspects of microcirculation, including oxygen transport, distributions of pressure, and wall shear stress in microvessels, regulation of blood flow, and interpretation of hemodynamically based functional imaging methods, but very few quantitative data on the human brain microcirculation are available. The main objective of this study is to propose a new method to analyze this microcirculation.

METHODS

From thick sections of india ink-injected human brain, using confocal laser microscopy, the authors developed algorithms adapted to very large data sets to automatically extract and analyze center lines together with diameters of thousands of brain microvessels within a large cortex area.

RESULTS

Direct comparison between the original data and the processed vascular skeletons demonstrated the high reliability of this method and its capability to manage a large amount of data, from which morphometry and topology of the cerebral microcirculation could be derived.

CONCLUSIONS

Among the many parameters that can be analyzed by this method, the capillary size, the frequency distributions of diameters and lengths, the fractal nature of these networks, and the depth-related density of vessels are all vital features for an adequate model of cerebral microcirculation.

Microvascular blood viscosity in vivo and the endothelial surface layer

The apparent viscosity of blood in glass tubes declines with decreasing diameter (Fåhraeus-Lindqvist effect) and exhibits a distinctive minimum at 6-7 microm. However, flow resistance in vivo in small vessels is substantially higher than predicted by in vitro viscosity data. The presence of a thick endothelial surface layer (ESL) has been proposed as the primary cause for this discrepancy. Here, a physical model is proposed for microvascular flow resistance as a function of vessel diameter and hematocrit in vivo; it combines in vitro blood viscosity with effects of a diameter-dependent ESL. The model was developed on the basis of flow distributions observed in three microvascular networks in the rat mesentery with 392, 546, and 383 vessel segments, for which vessel diameters, network architecture, flow velocity, and hematocrit were determined by intravital microscopy. A previously described hemodynamic simulation was used to predict the distributions of flow and hematocrit from the assumed model for effective blood viscosity. The dependence of ESL thickness on vessel diameter was estimated by minimizing deviations of predicted values for velocities, flow directions, and hematocrits from measured data. Optimal results were obtained with a layer thickness of approximately 0.8-1 microm for 10- to 40-microm-diameter vessels and declined strongly for smaller diameters, with an additional hematocrit-dependent impact on flow resistance exhibiting a maximum for approximately 10-microm-diameter vessels. These results show that flow resistance in vivo can be explained by in vitro blood viscosity and the presence of an ESL and indicate the rheologically effective thickness of the ESL in microvessels.

Microcirculation and Hemorheology

Major experimental and theoretical studies on microcirculation and hemorheology are reviewed with the focus on mechanics of blood flow and the vascular wall. Flow of the blood formed elements (red blood cells (RBCs), white blood cells or leukocytes (WBCs) and platelets) in individual arterioles, capillaries and venules, and in microvascular networks is discussed. Mechanical and rheological properties of the formed elements and their interactions with the vascular wall are reviewed. Short-term and long-term regulation of the microvasculature is discussed; the modes of regulation include metabolic, myogenic and shear-stress-dependent mechanisms as well as vascular adaptation such as angiogenesis and vascular remodeling.

An investigation of the influence of cell topography on epithelial mechanical stresses during pulmonary airway reopening

The goal of this study is to assess the local mechanical environment of the pulmonary epithelium in a computational model of airway reopening. To this end, the boundary element method (BEM) in conjunction with lubrication theory is implemented to assess the stationary-state behavior of a semi-infinite bubble traveling through a liquid-occluded parallel plate flow chamber lined with epithelial cells. The fluid occlusion is assumed to be Newtonian and inertia is neglected. The interactions between the microgeometry of the model airway's walls and the interfacial kinematics surrounding the bubble's tip result in a complex, spatially and temporally dependent stress distribution. The walls' nonplanar topography magnifies the normal and shear stresses and stress gradients. We find that decreasing the bubble's speed serves to increase the maximum normal stress and stress gradient but decrease the maximum shear stress and stress gradient. Our results give credence to the pressure-gradient-induced epithelial damage theory recently proposed by Bilek et al. [J. Appl. Physiol. 94, 770 (2003)] and Kay et al. [J. Appl. Physiol. 97, 269 (2004)]. We conclude that the amplified pressure gradients found in this study may be even more detrimental to the airway's cellular epithelium during airway reopening.

Adenosine A 3 Receptor Activation Modulates the Capillary Endothelial Glycocalyx

The endothelial glycocalyx is a dynamic extracellular matrix composed of cell surface proteoglycans, glycoproteins, and adsorbed serum proteins that has been implicated in the regulation and modulation of capillary tube hematocrit, permeability, and hemostasis. High tissue adenosine levels have been shown to adversely affect microvascular function and tissue survival after an ischemic episode, and previous work in this laboratory has shown that adenosine causes arteriolar constriction and degranulation of mast cells via the A3 receptor (A3AR). We hypothesized that adenosine exerts at least part of its effect through modification of the glycocalyx via the A3AR. We used an in vivo cremaster model (hamster and mouse) in which circulating plasma was labeled with a 70-kDa FITC-dextran, and the capillaries were examined before and after superfusion with varying concentrations of adenosine (or other vasoactive molecules). Measurements of the dextran exclusion from an endothelial cell surface layer and red cell separation from the endothelial cell surface were made for up to 30 minutes. Our data indicate that adenosine causes a rapid and profound decrease in the ability of the glycocalyx to exclude dextran but only affects red blood cell exclusion at pharmacological levels. Knockout mice deficient in the A3AR were completely protected from glycocalyx changes attributable to adenosine. These data show a potential link between a known vasoactive tissue metabolite, adenosine, and regulation of the glycocalyx, which may be important during (patho)physiological changes in microvascular function during inflammatory insults.