An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows

In this paper, we develop an immersed boundary lattice Boltzmann approach to simulate deformable capsules in flows. The lattice Boltzmann method is utilized to solve the incompressible flow field over a regular Eulerian grid, while the immersed boundary method is employed to incorporate the fluid-membrane interaction with a Lagrangian representation of the capsule membrane. This algorithm was validated for the Laplace relationship, the dispersion relationship for interfacial waves and the drag coefficient for cylinders; excellent agreement with theoretical results was observed. Furthermore, simulations of single and multiple red blood cells in shear and channel flows were performed. Several characteristic hemodynamic and hemorheological features were successfully reproduced, including the tank-treading motions, cell migration from the vessel wall, slipper-shaped cell deformation, cell-free layers, blunt velocity profiles and the Fahraeus effect. These simulations therefore demonstrate the potential usefulness of this computational model for microscopic biofluidic systems. However, extension of this algorithm to three-dimensional situations is necessary for more realistic simulations.     

Transendothelial flow inhibits neutrophil transmigration through a nitric oxide-dependent mechanism: potential role for cleft shear stress

Endothelial cells in vivo are well known to respond to parallel shear stress induced by luminal blood flow. In addition, fluid filtration across endothelium (transendothelial flow) may trigger nitric oxide (NO) production, presumably via shear stress within intercellular clefts. Since NO regulates neutrophil-endothelial interactions, we determined whether transendothelial flow regulates neutrophil transmigration. Interleukin-1beta-treated human umbilical vein endothelial cell (HUVEC) monolayers cultured on a polycarbonate filter were placed in a custom chamber with or without a modest hydrostatic pressure gradient (DeltaP, 10 cm H(2)O) to induce transendothelial flow. In other experiments, cells were studied in a parallel plate flow chamber at various transendothelial flows (DeltaP = 0, 5, and 10 cm H(2)O) and luminal flows (shear stress of 0, 1, and 2 dyn/cm(2)). In the absence of luminal flow, transendothelial flow reduced transmigration of freshly isolated human neutrophils from 57% to 14% (P < 0.05) and induced an increase in NO detected with a fluorescent assay (DAF-2DA). The NO synthase inhibitor L-NAME prevented the effects of transendothelial flow on neutrophil transmigration, while a NO donor (DETA/NO, 1 mM) inhibited neutrophil transmigration. Finally, in the presence of luminal flow (1 and 2 dyn/cm(2)), transendothelial flow also inhibited transmigration. On the basis of HUVEC morphometry and measured transendothelial volume flow, we estimated cleft shear stress to range from 49 to 198 dyn/cm(2). These shear stress estimates, while substantial, are of similar magnitude to those reported by others with similar analyses. These data are consistent with the hypothesis that endothelial cleft shear stress inhibits neutrophil transmigration via a NO-dependent mechanism.     

IQ Domain GTPase-Activating Protein 1 is Involved in Shear Stress-Induced Progenitor-Derived Endothelial Cell Alignment

Shear stress is one of mechanical constraints which are exerted by blood flow on endothelial cells (ECs). To adapt to shear stress, ECs align in the direction of flow through adherens junction (AJ) remodeling. However, mechanisms regulating ECs alignment under shear stress are poorly understood. The scaffold protein IQ domain GTPase activating protein 1 (IQGAP1) is a scaffold protein which couples cell signaling to the actin and microtubule cytoskeletons and is involved in cell migration and adhesion. IQGAP1 also plays a role in AJ organization in epithelial cells. In this study, we investigated the potential IQGAP1 involvement in the endothelial cells alignment under shear stress. Progenitor-derived endothelial cells (PDECs), transfected (or not) with IQGAP1 small interfering RNA, were exposed to a laminar shear stress (1.2 N/m²) and AJ proteins (VE-cadherin and β-catenin) and IQGAP1 were labeled by immunofluorescence. We show that IQGAP1 is essential for ECs alignment under shear stress. We studied the role of IQGAP1 in AJs remodeling of PDECs exposed to shear stress by studying cell localization and IQGAP1 interactions with VE-cadherin and β-catenin by immunofluorescence and Proximity Ligation Assays. In static conditions, IQGAP1 interacts with VE-cadherin but not with β-catenin at the cell membrane. Under shear stress, IQGAP1 lost its interaction from VE-cadherin to β-catenin. This “switch” was concomitant with the loss of β-catenin/VE-cadherin interaction at the cell membrane. This work shows that IQGAP1 is essential to ECs alignment under shear stress and that AJ remodeling represents one of the mechanisms involved. These results provide a new approach to understand ECs alignment under to shear stress.     

Proliferation, differentiation, and tube formation by endothelial progenitor cells in response to shear stress.

Endothelial progenitor cells (EPCs), circulating in peripheral blood, migrate toward target tissue, differentiate, and contribute to the formation of new vessels. In this study, we report that shear stress generated by blood flow or tissue fluid flow can accelerate the proliferation, differentiation, and capillary-like tube formation of EPCs. When EPCs cultured from human peripheral blood were subjected to laminar shear stress, the cells elongated and oriented their long axes in the direction of flow. The cell density of the EPCs exposed to shear stress was higher, and a larger percentage of these cells were in the G2-M phase of the cell cycle, compared with EPCs cultured under static conditions. Shear stress markedly increased the EPC expression of two vascular endothelial growth factor receptors, kinase insert domain-containing receptor and fms-like tyrosine kinase-1, and an intercellular adhesion molecule, vascular endothelial-cadherin, at both the protein and mRNA levels. Assays for tube formation in the collagen gels showed that the shear-stressed EPCs formed tubelike structures and developed an extensive tubular network significantly faster than the static controls. These findings suggest that EPCs are sensitive to shear stress and that their vasculogenic activities may be modulated by shear stress.     

The equation for platelet aggregation rate

A platelet aggregation model in shear flow taking into account the kinetics of intercellular fibrinogen bond formation limited by aggregated platelets rotation time was considered. For this consideration the average duration of platelets interaction in flow with shear rate value G is shown to be pi/4G. One fibrinogen bond is sufficient to form a solid aggregate between two platelets. The equation for single platelets disappearance rate concerned with intercellular fibrinogen bond formation, stochastic character of bond distribution in collided platelets and hydrodynamically controlled interaction time was obtained. The Hill's approximation for the obtained aggregation rate dependences was suggested and appropriate constants were determined. The qualitative criterion of platelets aggregating systems behavior was introduced.     

Effects of shear rate and suspending viscosity on deformation and frequency of red blood cells tank-treading in shear flows

The tank-treading rotation of red blood cells (RBCs) in shear flows has been studied extensively with experimental, analytical, and numerical methods. Even for this relatively simple system, complicated motion and deformation behaviors have been observed, and some of the underlying mechanisms are still not well understood. In this study, we attempt to advance our knowledge of the relationship among cell motion, deformation, and flow situations with a numerical model. Our simulation results agree well with experimental data, and confirm the experimental finding of the decrease in frequency/shear-rate ratio with shear rate and the increase of frequency with suspending viscosity. Moreover, based on the detailed information from our simulations, we are able to interpret the frequency dependency on shear rate and suspending viscosity using a simple two-fluid shear model. The information obtained in this study thus is useful for understanding experimental observations of RBCs in shear and other flow situations; the good agreement to experimental measurements also shows the potential usefulness of our model for providing reliable results for microscopic blood flows.     

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When the liver is damaged, hepatic stellate cells (HSCs) can change into an activated, highly migratory state. The migration of HSCs may be affected by shear stress due not only to sinusoidal flow but also by the flow in the space of Disse because this space is filled with blood plasma. In this study, we evaluated the effects of shear stress on HSC migration in a scratch-wound assay with a parallel flow chamber. At regions upstream of the wound area, the migration was inhibited by 0.6 Pa and promoted by 2.0 Pa shear stress, compared to the static condition. The platelet-derived growth factor (PDGF)-BB receptor, PDGFR-β, was expressed in all conditions and the differences were not significant. PDGF increased HSC migration, except at 0.6 Pa shear stress, which was still inhibited. These results indicate that another molecular factor, such as PDGFR-α, may act to inhibit the migration under low shear stress. At regions downstream of the wound area, the migration was smaller under shear stress than under the static condition, although the expression of PDGFR-β was significantly higher. In particular, the migration direction was opposite to the wound area under high shear stress; therefore, migration might be influenced by the intercellular environment. Our results indicate that HSC migration was influenced by shear stress intensity and the intercellular environment.     

Relationship between erythrocyte aggregate size and flow rate in skeletal muscle venules

In previous studies we showed that intravenous infusion of Dextran 500 in the rat causes blunting of the velocity profile of red blood cells in venules at low shear rates. To determine whether this blunting is associated with the formation of red blood cell aggregates, we measured the length and width of particles in the venular flow stream at systemic hematocrits up to 20% with a high-speed video camera and a new image analysis technique. Data were obtained at various shear rates under normal (nonaggregating) conditions as well as after infusion of Dextran 500. Under normal conditions, particle length (parallel to the vessel axis) was 6.5 +/- 2.7 microm and width (perpendicular to the axis) was 6.1 +/- 1.7 microm, in agreement with published dimensions of individual red blood cells for this species. After Dextran 500 infusion, particle length and width increased significantly to 8.7 +/- 5.1 and 10.4 +/- 4.4 microm, respectively. Particle dimensions were greater in the central region of the flow stream for both normal and dextran-treated blood and increased at low flow rates with dextran-treated blood. This study provides direct confirmation of aggregate formation at low shear in venules with high-molecular-weight dextran as well as an estimate of aggregate size and range.     

Flow-conditioned HUVECs support clustered leukocyte adhesion by coexpressing ICAM-1 and E-selectin

Endothelial sequestration of circulating monocytes is a key event in early atherosclerosis. Hemodynamics is proposed to regulate monocyte-endothelial cell interactions by direct cell activation and establishment of flow environments that are conducive or prohibitive to cell-cell interaction. We investigated fluid shear regulation of monocyte-endothelial cell adhesion in vitro using a disturbed laminar shear system that models in vivo hemodynamics characteristic of lesion-prone vascular regions. Human endothelial cell monolayers were flow conditioned for 6 h before evaluation of monocyte adhesion under static and dynamic flow conditions. Results revealed a distinctive clustered cell pattern of monocyte adhesion that strongly resembles in vivo leukocyte adhesion in early- and late-stage atherosclerosis. Clustered monocyte cell adhesion correlated with endothelial cells coexpressing intercellular adhesion molecule-1 (ICAM-1) and E-selectin as result of a flow-induced, selective upregulation of E-selectin expression in a subset of ICAM-1-expressing cells. Clustered monocyte cell adhesion assayed under static conditions exhibited a spatial variation in size and frequency of occurrence, which demonstrates differential regulation of endothelial cell adhesiveness by the local flow environment. Dynamic adhesion studies conducted with circulating monocytes resulted in clustered cell adhesion only within the disturbed flow region, where the monocyte rate of motion is sufficiently low for cell-cell interaction. These studies provide evidence and reveal mechanisms of local hemodynamic regulation of endothelial adhesiveness and endothelial monocyte interaction that lead to localized monocyte adhesion and potentially contribute to the focal origin of arterial diseases such as atherosclerosis.     

The Spontaneously Adhesive Leukocyte Function-associated Antigen-1 (LFA-1) Integrin in Effector T Cells Mediates Rapid Actin- and Calmodulin-dependent Adhesion Strengthening to Ligand under Shear Flow

Integrins in effector T cells are highly expressed and important for trafficking of these cells and for their effector functions. However, how integrins are regulated in effector T cells remains poorly characterized. Here, we have investigated effector T cell leukocyte function-associated antigen-1 (LFA-1) regulation in primary murine effector T cells. These cells have high LFA-1 integrin expression and display high spontaneous binding to intercellular adhesion molecule-1 (ICAM-1) ligand under static conditions. In addition, these cells are able to migrate spontaneously on ICAM-1. Atomic force microscopy measurements showed that the force required for unbinding of integrin-ligand interactions increases over time (0.5–20-s contact time). The maximum unbinding force for this interaction was ∼140 piconewtons at 0.5-s contact time, increasing to 580 piconewtons at 20-s contact time. Also, the total work required to disrupt the interaction increased over the 20-s contact time, indicating LFA-1-mediated adhesion strengthening in primary effector T cells over a very quick time frame. Effector T cells adhered spontaneously to ICAM-1 under conditions of shear flow, in the absence of chemokine stimulation, and this binding was independent of protein kinase B/Akt and protein kinase C kinase activity, but dependent on calcium/calmodulin signaling and an intact actin cytoskeleton. These results indicate that effector T cell integrins are highly expressed and spontaneously adhesive in the absence of inside-out integrin signaling but that LFA-1-mediated firm adhesion under conditions of shear flow requires downstream integrin signaling, which is dependent on calcium/calmodulin and the actin cytoskeleton.     

An Investigation on Platelet Transport during Thrombus Formation at Micro-Scale Stenosis

This paper reports on an investigation of mass transport of blood cells at micro-scale stenosis where local strain-rate micro-gradients trigger platelet aggregation. Using a microfluidic flow focusing platform we investigate the blood flow streams that principally contribute to platelet aggregation under shear micro-gradient conditions. We demonstrate that relatively thin surface streams located at the channel wall are the primary contributor of platelets to the developing aggregate under shear gradient conditions. Furthermore we delineate a role for red blood cell hydrodynamic lift forces in driving enhanced advection of platelets to the stenosis wall and surface of developing aggregates. We show that this novel microfluidic platform can be effectively used to study the role of mass transport phenomena driving platelet recruitment and aggregate formation and believe that this approach will lead to a greater understanding of the mechanisms underlying shear-gradient dependent discoid platelet aggregation in the context of cardiovascular diseases such as acute coronary syndromes and ischemic stroke.     

Computational Analysis of Dynamic Interaction of Two Red Blood Cells in a Capillary

The dynamic interaction of two red blood cells (RBCs) in a capillary is investigated computationally by the two-fluid model, including their deformable motion and interaction. For characterization of the deformation, the RBC membrane is treated as a curved two-dimensional shell with finite thickness by the shell model, and allowed to undergo the stretching strain and bending deformation. Moreover, a Morse potential is adopted to model the intercellular interaction for the aggregation behavior, which is characterized as the weak attraction at far distance and strong repulsion at near distance. For validation of the present technique, the dynamic interaction of two RBCs in static blood plasma is simulated firstly, where the RBCs aggregate slowly until a balanced configuration is achieved between the deformation and aggregation forces. The balanced configuration is in good agreement with the results reported previously. Three important effects on the dynamic behavior of RBCs are then analyzed, and they are the initial RBC shape, RBC deformability, and the intercellular interaction strength. It is found that the RBC is less deformed into a well-known parachute shape when the initial RBC shape is larger. Similarly, if the elastic shear modulus and bending stiffness of RBC membrane increase, the RBC resistance to deformation becomes higher, such that the RBC is less deformed. The simulation results also demonstrate that the RBC deformability strongly depends on the intercellular interaction strength. The RBCs deform more easily as the intercellular interaction strength increases.     

Computational fluid dynamics of aggregating red blood cells in postcapillary venules

Aggregate formation of red blood cells (RBCs) in a postcapillary venular bifurcation is investigated with three-dimensional computer simulations using the Chimera grid method. Interaction energy between the RBCs is modelled by a depletion interaction theory; RBCs are modelled as rigid oblate ellipsoids. The cell–cell interactions of RBCs are strongly dependent on vessel geometry and shear rates. The experimental data on vessel geometry, pseudoshear rates, and Dextran concentration obtained in our previous in vivo RBC aggregation study in postcapillary venules of the rat spinotrapezius muscle were used to simulate RBC aggregation. The computational results were compared to the experimental results from the in vivo study. The results show that cells have a larger tendency to form an aggregate under reduced flows. Aggregate formation also depends on the angle and location of the cells before they enter the bifurcation region. Comparisons with experimental data are discussed.     

Biorheological views of endothelial cell responses to mechanical stimuli

Vascular endothelial cells are located at the innermost layer of the blood vessel wall and are always exposed to three different mechanical forces: shear stress due to blood flow, hydrostatic pressure due to blood pressure and cyclic stretch due to vessel deformation. It is well known that endothelial cells respond to these mechanical forces and change their shapes, cytoskeletal structures and functions. In this review, we would like to mainly focus on the effects of shear stress and hydrostatic pressure on endothelial cell morphology. After applying fluid shear stress, cultured endothelial cells show marked elongation and orientation in the flow direction. In addition, thick stress fibers of actin filaments appear and align along the cell long axis. Thus, endothelial cell morphology is closely related to the cytoskeletal structure. Further, the dynamic course of the morphological changes is shown and the related events such as changes in mechanical stiffness and functions are also summarized. When endothelial cells were exposed to hydrostatic pressure, they exhibited a marked elongation and orientation in a random direction, together with development of centrally located, thick stress fibers. Pressured endothelial cells also exhibited a multilayered structure with less expression of VE-cadherin unlike under control conditions. Simultaneous loading of hydrostatic pressure and shear stress inhibited endothelial cell multilayering and induced elongation and orientation of endothelial cells with well-developed VE-cadherin in a monolayer, which suggests that for a better understanding of vascular endothelial cell responses one has to take into consideration the combination of the different mechanical forces such as exist under in vivo mechanical conditions.     

Multiscale modeling of blood flow: from single cells to blood rheology

Mesoscale simulations of blood flow, where the red blood cells are described as deformable closed shells with a membrane characterized by bending rigidity and stretching elasticity, have made much progress in recent years to predict the flow behavior of blood cells and other components in various flows. To numerically investigate blood flow and blood-related processes in complex geometries, a highly efficient simulation technique for the plasma and solutes is essential. In this review, we focus on the behavior of single and several cells in shear and microcapillary flows, the shear-thinning behavior of blood and its relation to the blood cell structure and interactions, margination of white blood cells and platelets, and modeling hematologic diseases and disorders. Comparisons of the simulation predictions with existing experimental results are made whenever possible, and generally very satisfactory agreement is obtained.     

Sublethal Supraphysiological Shear Stress Alters Erythrocyte Dynamics in Subsequent Low-Shear Flows

Blood is a non-Newtonian, shear-thinning fluid owing to the physical properties and behaviors of red blood cells (RBCs). Under increased shear flow, pre-existing clusters of cells disaggregate, orientate with flow, and deform. These essential processes enhance fluidity of blood, although accumulating evidence suggests that sublethal blood trauma—induced by supraphysiological shear exposure—paradoxically increases the deformability of RBCs when examined under low-shear conditions, despite obvious decrement of cellular deformation at moderate-to-higher shear stresses. Some propose that rather than actual enhancement of cell mechanics, these observations are “pseudoimprovements” and possibly reflect altered flow and/or cell orientation, leading to methodological artifacts, although direct evidence is lacking. This study thus sought to explore RBC mechanical responses in shear flow using purpose-built laser diffractometry in tandem with direct optical visualization to address this problem. Freshly collected RBCs were exposed to a mechanical stimulus known to drastically alter cell deformability (i.e., prior shear exposure (PSE) to 100 Pa × 300 s). Samples were subsequently transferred to a custom-built slit-flow chamber that combined laser diffractometry with direct cell visualization. Cell suspensions were sheared in a stepwise manner (between 0.3 and 5.0 Pa), with each step being maintained for 15 s. Deformability and cell orientation indices were recorded for small-scatter Fraunhofer diffraction patterns and also visualized RBCs. PSE RBCs had significantly decreased visualized and laser-derived deformability at any given shear stress ≥1 Pa. Novel, to our knowledge, observations demonstrated that PSE RBCs had increased heterogeneity of direct visualized orientation with flow vector at any shear, which may be due to greater vorticity and thus instability in 5-Pa flow compared with unsheared control. These findings indicate that shear exposure and stress-strain history can alter subsequent RBC behavior in physiologically relevant low-shear flows. These findings may yield insight into microvascular disorders in recipients of mechanical circulatory support and individuals with hematological diseases that alter physical properties of blood.     

Visualization study of motion and deformation of red blood cells in a microchannel with straight,divergent and convergent sections

The size of red blood cells (RBC) is on the same order as the diameter of microvascular vessels. Therefore, blood should be regarded as a two-phase flow system of RBCs suspended in plasma rather than a continuous medium of microcirculation. It is of great physiological and pathological significance to investigate the effects of deformation and aggregation of RBCs on microcirculation. In this study, a visualization experiment was conducted to study the microcirculatory behavior of RBCs in suspension. Motion and deformation of RBCs in a microfluidic chip with straight, divergent, and convergent microchannel sections have been captured by microscope and high-speed camera. Meanwhile, deformation and movement of RBCs were investigated under different viscosity, hematocrit, and flow rate in this system. For low velocity and viscosity, RBCs behaved in their normal biconcave disc shape and their motion was found as a flipping motion: they not only deformed their shapes along the flow direction, but also rolled and rotated themselves. RBCs were also found to aggregate, forming rouleaux at very low flow rate and viscosity. However, for high velocity and viscosity, RBCs deformed obviously under the shear stress. They elongated along the flow direction and performed a tank-treading motion.     

Aggregation and disaggregation of red blood cells

The aggregation of red blood cells may be analyzed as an interaction of an adhesive surface energy and the elastic stored energy which results from deformation of the cell. The adhesive surface energy is the work required to separate a unit adhered area and is the resultant of adhesive forces due to the bridging molecules that bind the cells together and the electrostatic repulsion due to surface charge. The elastic strain energy in the case of the red blood is associated with the membrane elasticity only since the interior of the cell is liquid. The membrane elasticity is due both to bending stiffness and shear. The area expansion is small and may be neglected. These assumptions allow realistic computation of red cell shapes in rouleaux. The disaggregation of rouleaux requires an external force which must overcome the adhesive energy and also supply additional elastic energy of deformation. Depending on the geometry, the initial effect of elastic energy may tend to aid disaggregation. In a shear flow, the stresses on a suspended rouleau alternately tend to compress and to disaggregate the cells if they are free to rotate. This introduces a time dependence so that viscous effects due to the viscosity of the cell membrane, the cell cytoplasm and the external fluid may play a role in determining whether disaggregation proceeds to completion or not.     

Mixed Exciton-Charge-Transfer States in Photosystem II: Stark Spectroscopy on Site-Directed Mutants

Sickle erythrocytes exhibit abnormal morphology and membrane mechanics under deoxygenated conditions due to the polymerization of hemoglobin S. We employed dissipative particle dynamics to extend a validated multiscale model of red blood cells (RBCs) to represent different sickle cell morphologies based on a simulated annealing procedure and experimental observations. We quantified cell distortion using asphericity and elliptical shape factors, and the results were consistent with a medical image analysis. We then studied the rheology and dynamics of sickle RBC suspensions under constant shear and in a tube. In shear flow, the transition from shear-thinning to shear-independent flow revealed a profound effect of cell membrane stiffening during deoxygenation, with granular RBC shapes leading to the greatest viscosity. In tube flow, the increase of flow resistance by granular RBCs was also greater than the resistance of blood flow with sickle-shape RBCs. However, no occlusion was observed in a straight tube under any conditions unless an adhesive dynamics model was explicitly incorporated into simulations that partially trapped sickle RBCs, which led to full occlusion in some cases.