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.     

Time-dependent rheological behaviour of blood flow at low shear in narrow horizontal tubes

Magnitude and time-dependence of the effects of red cell aggregation and sedimentation on the rheology of human blood were studied during low shear (tau W 2.5 to 92 mPa) flow through horizontal tubes (ID 25 to 105 microns). Immediately following reduction of perfusion pressure to a low value the red cell concentration near the tube walls decreases as a result of red cell aggregation. This is associated with a transient increase of centerline velocity. Simultaneously, sedimentation begins to occur and eventually leads to the formation of a cell-free supernatant plasma layer. Time-course and extent of this sedimentation process are strongly affected by wall shear stress variation, particularly in the larger tubes. At the lower shear stresses, centerline velocity decreases (flow resistance increases) with time following the initial acceleration period, due to sedimentation of red cells. This is followed by a further increase of resistance caused by the elevation of hematocrit occurring because of the reduction of cell/plasma velocity ratio. The time dependence of blood rheological behaviour under these flow conditions is interpreted to reflect the net effect of the partially counteracting phenomena of sedimentation and red cell aggregation.     

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.     

Dielectric approach to investigation of erythrocyte aggregation. II. Kinetics of erythrocyte aggregation-disaggregation in quiescent and flowing blood

A method based on dielectric properties of dispersed systems was applied to investigate the kinetics of RBC aggregation and the break-up of the aggregates. Experimentally, this method consists of measuring the capacitance at a frequency in the beginning of the beta-dispersion. Two experimental protocols were used to investigate the aggregation process. In the first case, blood samples were fully dispersed and then the flow was decreased or stopped to promote RBC aggregation. It was found that the initial phases of RBC aggregation are not affected by the shear rate. This finding indicates that RBC aggregation is a slow coagulation process. In the second case, RBCs aggregated under flow conditions at different shear rates and after the capacitance reached plateau levels, the flow was ceased. The steady-state capacitance of the quiescent blood and the kinetics of RBC aggregation after stoppage of shearing depend on the prior shear rate. To clarify the reasons for this effect, the kinetics of the disaggregation process was studied. In these experiments, time courses of the capacitance were recorded under different flow conditions and then a higher shear stress was applied to break up RBC aggregates. It was found that the kinetics of the disaggregation process depend on both the prior and current shear stresses. Results obtained in this study and their analysis show that the kinetics of RBC aggregation in stasis consists of two consecutive phases: At the onset, red blood cells interact face-to-face to form linear aggregates and then, after an accumulation of an appropriate concentration of these aggregates, branched rouleaux are formed via reactions of ends of the linear rouleaux with sides of other rouleaux (face-to-side interactions). Branching points are broken by low shear stresses whereas dispersion of the linear rouleaux requires significantly higher energy.     

Factors influencing the nonuniform localization of monocytes in the arterial wall

Adhesion of monocytes to arterial endothelium may contribute to the asymmetric distribution of atherosclerotic lesions. Possible mechanisms for adhesion in the relatively high shear stress environment found in arteries include greater monocyte deformation and/or more frequent penetration of microvilli through steric and charge barriers. In vivo, secondary flows generate forces acting normal to the endothelial cell surface. These forces may cause compression of the microvilli or enable cells to overcome steric or electrostatic barriers, increasing adhesion. To investigate this, we examined monocyte adhesion to activated endothelium in recirculating flow. Adhesion was characterized by short arrests in a narrow region on either side of the reattachment line. The median arrest time was longer than that observed at comparable shear stresses in a linear shear flow. The lifetimes of adhesion were analyzed using a model for multiple bond formation. For cells adhering near the reattachment line, the bond number per cell was greater than the value found for similar shear stresses under shear flow. Thus, multiple bond formation arising from greater normal forces in recirculating flow permits monocytes to adhere at higher shear stresses.     

Aggregation of human red blood cells after moderate heat treatment

The aggregation behaviour of normal and heat treated (48.4 degrees C, 48.8 degrees C, 49.5 degrees C) red blood cells (RBCs) suspended in dextran-saline solutions (Dx 70, Dx 173) was investigated by a laser light reflectometric method over a wide range of bridging energies. The characteristic times of rouleau formation were found to be increased after RBC heat treatment. The disaggregation shear stress is not significantly different between normal RBCs and heat treated RBCs. The loss of cell deformability is nevertheless shown to improve slightly the dissociation efficiency of the flowing liquid in a shear flow resulting in a small reduction of the disaggregation shear rate after heat treatment. Heat treatment is also shown to alter the structure of RBC network at equilibrium. These results indicate that heat induced alterations of erythrocytes only affects the mechanical properties of the cell membrane without significant changes in the macromolecular bridging energy.     

Critical stresses for cancer cell detachment in microchannels

We present experiments involving cancer cells adhering to microchannels, subjected to increasing shear stresses (0.1–30 Pa). Morphological studies were carried out at different shear stresses. Cells exhibit spreading patterns similar to those observed under static conditions, as long as the shear stress is not too high. At critical wall shear stresses (around 2−5 Pa), cell-substrate contact area decreases until detachment at the larger stresses. Critical shear stresses are found to be lower for higher confinements (i.e. smaller cell height to channel height ratio). Fluorescent techniques were used to locate focal adhesions (typically 1 μm² in size) under various shearing conditions, showing that cells increase the number of focal contacts in the region facing the flow. To analyze such data, we propose a model to determine the critical stress, resulting from the competition between hydrodynamic forces and the adhesive cell resistance. With this model, typical adhesive stresses exerted at each focal contact can be determined and are in agreement with previous works.     

Biomechanics of leukocyte rolling

Leukocyte rolling on endothelial cells and other P-selectin substrates is mediated by P-selectin binding to P-selectin glycoprotein ligand-1 expressed on the tips of leukocyte microvilli. Leukocyte rolling is a result of rapid, yet balanced formation and dissociation of selectin-ligand bonds in the presence of hydrodynamic shear forces. The hydrodynamic forces acting on the bonds may either increase (catch bonds) or decrease (slip bonds) their lifetimes. The force-dependent 'catch-slip' bond kinetics are explained using the 'two pathway model' for bond dissociation. Both the 'sliding-rebinding' and the 'allosteric' mechanisms attribute 'catch-slip' bond behavior to the force-induced conformational changes in the lectin-EGF domain hinge of selectins. Below a threshold shear stress, selectins cannot mediate rolling. This 'shear-threshold' phenomenon is a consequence of shear-enhanced tethering and catch bond-enhanced rolling. Quantitative dynamic footprinting microscopy has revealed that leukocytes rolling at venular shear stresses (>0.6 Pa) undergo cellular deformation (large footprint) and form long tethers. The hydrodynamic shear force and torque acting on the rolling cell are thought to be synergistically balanced by the forces acting on tethers and stressed microvilli, however, their relative contribution remains to be determined. Thus, improvement beyond the current understanding requires in silico models that can predict both cellular and microvillus deformation and experiments that allow measurement of forces acting on individual microvilli and tethers.     

A 3-D computational model predicts that cell deformation affects selectin-mediated leukocyte rolling

Leukocyte recruitment to sites of inflammation is initiated by their tethering and rolling on the activated endothelium under flow. Even though the fast kinetics and high tensile strength of selectin-ligand bonds are primarily responsible for leukocyte rolling, experimental evidence suggests that cellular properties such as cell deformability and microvillus elasticity actively modulate leukocyte rolling behavior. Previous theoretical models either assumed cells as rigid spheres or were limited to two-dimensional representations of deformable cells with deterministic receptor-ligand kinetics, thereby failing to accurately predict leukocyte rolling. We therefore developed a three-dimensional computational model based on the immersed boundary method to predict receptor-mediated rolling of deformable cells in shear flow coupled to a Monte Carlo method simulating the stochastic receptor-ligand interactions. Our model predicts for the first time that the rolling of more compliant cells is relatively smoother and slower compared to cells with stiffer membranes, due to increased cell-substrate contact area. At the molecular level, we show that the average number of bonds per cell as well as per single microvillus decreases with increasing membrane stiffness. Moreover, the average bond lifetime decreases with increasing shear rate and with increasing membrane stiffness, due to higher hydrodynamic force experienced by the cell. Taken together, our model captures the effect of cellular properties on the coupling between hydrodynamic and receptor-ligand bond forces, and successfully explains the stable leukocyte rolling at a wide range of shear rates over that of rigid microspheres.     

Light transmission through blood in oscillatory flow

Measurements were made of the intensity of light transmitted through various thicknesses of normal human blood confined between two parallel plane surfaces, one fixed and the other oscillating in its own plane. When the light propagation direction is perpendicular to the direction of shear flow the transmitted intensity contains a steady component and a dominant second harmonic of the oscillation frequency. For a thin layer of blood, the steady intensity is a minimum value when the oscillation amplitude produces unit strain. The second harmonic is very small at small strains, but increases rapidly near unit strain where it is approximately in phase with the strain. For thicker layers, the effects of viscoelastic shear waves reduce the size of the second harmonic and modify its phase. Changes in light transmission are interpreted by relating the optical density of the blood to the total amount of contact between red cells. In oscillatory flow at low strains (less than 1) cell-to-cell contact is reduced by disaggregation of cell groups, and light transmission decreases. Near unit strain, disaggregation becomes complete, cell alignment occurs, and light transmission is minimized. At higher strains cell-to-cell contact is increased by formation of aligned layers of compacted cells separated by parallel plasma layers, and light transmission increases.     

The Multistep Process of Homotypic Neutrophil Aggregation: A Review of the Molecules and Effects of Hydrodynamics

Homotypic adhesion of neutrophils stimulated with chemoattractant is analogous to capture on vascular endothelium in that both processes are supported by L-selectin and β₂-integrin adhesion receptors. Under hydrodynamic shear, cell adhesion requires that receptors bind sufficient ligand over the duration of intercellular contact to withstand the hydrodynamic stresses. Using cone and plate viscometry to apply a uniform linear shear field to suspensions of neutrophils and flow cytometry to quantitate the size distribution of aggregates formed over the time course of formyl peptide stimulation, we conducted a detailed examination of the affect of shear rate and shear stress on the kinetics of cell aggregation. The efficiency of aggregate formation was fit from a mathematical model based on Smoluchowski's two-body collision theory. Over a range of venular shear rates (400–800 s^-1), β90% of the single cells are recruited into aggregates ranging from doublets to groupings larger than sextuplets. Adhesion efficiency fit to the kinetics of aggregation increased with shear rate from β20% at 100s^-1 to a maximum level of β80% at 400 s^-1. This increase to peak adhesion efficiency was dependent on L-selectin and β₂-integrin, and was resistant to shear stress up to β7 dyn/cm². When L-selectin was blocked with antibody, β₂-integrin (CD11a, b) supported adhesion at low shear rates (< 400 s^-1). Aggregates formed over the rapid phase of aggregation remain intact and resistant to shear up to 120 s. At the end of this plateau phase of stability, aggregates spontaneously dissociate back to singlets. The rate of cell disaggregation is linearly proportional to the applied shear rate. The binding kinetics of selectin and integrin appear to be optimized to function within discrete ranges of shear rate and stress, providing an intrinsic mechanism for the transition from neutrophil tethering to firm but reversible adhesion.     

Separation and characterization of red blood cells with different membrane deformability using steric field-flow fractionation

Human red blood cells were treated in different ways to alter their membrane deformability, and the hydrodynamic behavior of these altered cells was studied using the steric field-flow fractionation (FFF) technique. The relationships between cell retention in the FFF channel, flow-rate of the carrier fluid and the applied field strength were studied for normal and glutaraldehyde-fixed human red cells, and separation conditions were optimized. The effect of flow-induced hydrodynamic lift forces on red cell retention in the steric FFF channel was studied, and the results suggest that the membrane deformability of the red cell is an important factor contributing to the lift force, besides other previously described effects due to density and flow velocity. Using steric FFF, a mixture of normal and glutaraldehyde-fixed human red cells was completely separated with a resolution twice that found in published d ata from gel permeation, another hydrodynamic separation technique. Partial loss of membrane deformability, induced by different degrees of glutaraldehyde-fixation, by diamide, or by a thermal treatment, has also been studied. Steric FFF is thus shown to have potential for rapid separation and differentiation of red cells with different density and membrane deformability, conditions known to be associated with, e.g., cell senescence and certain hematological diseases.     

Magnetic resonance microscopy determined velocity and hematocrit distributions in a Couette viscometer

Magnetic resonance microscopy is used to non-invasively measure the radial velocity distribution in Couette flow of erythrocyte suspensions of varying aggregation behavior at a nominal shear rate of 2.20 s(-1) in a 1 mm gap. Suspensions of red blood cells in albumin-saline, plasma and 1.48% Dextran added plasma at average hematocrits near 0.40 are studied, providing a range of aggregation ability. The spatial distribution of the red blood cell volume fraction, hematocrit, is calculated from the velocity distribution. The hematocrit profiles provide direct measure of the thickness of the aggregation and shear rate dependent red blood cell depletion at the Couette surfaces. At the nominal shear rate studied hematocrit distributions for the red blood cells in plasma show a depletion zone near the inner Couette wall but not the outer wall. The red blood cells in plasma with Dextran show cell depletion regions of approximately 100 mum at both the inner and outer Couette surfaces, with greater depletion at the inner wall, but approach the normal blood hematocrit distribution with a doubling of shear rate due to decreased aggregation. The material response of the blood is spatially dependent with the shear rate and the hematocrit distribution non-uniform across the gap.     

A numerical analysis of forces exerted by laminar flow on spreading cells in a parallel plate flow chamber assay

Exposure of spreading anchorage-dependent cells to laminar flow is a common technique to measure the strength of cell adhesion. Since cells protrude into the flow stream, the force exerted by the fluid on the cells is a function of cell shape. To assess the relationship between cell shape and the hydrodynamic force on adherent cells, we obtained numerical solutions of the velocity and stress fields around bovine aortic endothelial cells during various stages of spreading and calculated the force required to detach the cells. Morphometric parameters were obtained from light and scanning electron microscopy measurements. Cells were assumed to have a constant volume, but the surface area increased during spreading until the membrane was stretched taut. Two-dimensional models of steady flow were generated using the software packages ANSYS (mesh generation) and FIDAP (problem solution). The validity of the numerical results was tested by comparison with published results for a semicircle in contact with the surface. The drag force and torque were greatest for round cells making initial contact with the surface. During spreading, the drag force and torque declined by factors of 2 and 20, respectively. The calculated forces and moments were used in adhesion models to predict the wall shear stress at which the cells detached. Based upon published values for the bond force and receptor number, round cells should detach at shear stresses between 2.5 and 6 dyn/cm(2), whereas substantially higher stresses are needed to detach spreading and fully spread cells. Results from the simulations indicate that (1) the drag force varies little with cell shape whereas the torque is very sensitive to cell shape, and (2) the increase in the strength of adhesion during spreading is due to increased contact area and receptor densities within the contact area. (c) 1993 John Wiley & Sons, Inc.     

Mechanics of transient platelet adhesion to von Willebrand factor under flow

A primary and critical step in platelet attachment to injured vascular endothelium is the formation of reversible tether bonds between the platelet glycoprotein receptor Ibalpha and the A1 domain of surface-bound von Willebrand factor (vWF). Due to the platelet's unique ellipsoidal shape, the force mechanics involved in its tether bond formation differs significantly from that of leukocytes and other spherical cells. We have investigated the mechanics of platelet tethering to surface-immobilized vWF-A1 under hydrodynamic shear flow. A computer algorithm was used to analyze digitized images recorded during flow-chamber experiments and track the microscale motions of platelets before, during, and after contact with the surface. An analytical two-dimensional model was developed to calculate the motion of a tethered platelet on a reactive surface in linear shear flow. Through comparison of the theoretical solution with experimental observations, we show that attachment of platelets occurs only in orientations that are predicted to result in compression along the length of the platelet and therefore on the bond being formed. These results suggest that hydrodynamic compressive forces may play an important role in initiating tether bond formation.     

Tube flow of human blood at near zero shear

Pressure-velocity relations were obtained in vertical and horizontal glass tubes (I.D. 26 to 83 micron) perfused with normal human blood at feed hematocrits between 0.25 and 0.65. Perfusion pressures used corresponded to wall shear stresses up to 0.27 dyn cm-2. Red cell velocity measurements were made both immediately following implementation of perfusion pressure (with red cells still disaggregated) and in a steady state situation (with red cells aggregated). Analysis of the slopes of the linear relations between perfusion pressure and velocity showed apparent viscosity to decrease with the manifestation of red cell aggregation. In horizontal tubes, sedimentation and aggregation occurred simultaneously, and apparent viscosity increased due to axial asymmetry of cell concentration. Evidence for a yield shear stress (flow stagnation at positive driving pressure) was not observed.     

Shear modulation of intercellular contact area between two deformable cells colliding under flow

Shear rate has been shown to critically affect the kinetics and receptor specificity of cell-cell interactions. In this study, the collision process between two modeled cells interacting in a linear shear flow is numerically investigated. The two identical biological or artificial cells are modeled as deformable capsules composed of an elastic membrane. The cell deformation and trajectories are computed using the immersed boundary method (IBM) for shear rates of 100-400s(-1). As the two cells collide under hydrodynamic shear, large local cell deformations develop. The effective contact area between the two cells is modulated by the shear rate, and reaches a maximum value at intermediate levels of shear. At relatively low shear rate, the contact area is an enclosed region. As the shear rate increases, dimples form on the membrane surface, and the contact region becomes annular. The nonmonotonic increase of the contact area with the increase of shear rate from computational results implies that there is a maximum effective receptor-ligand binding area for cell adhesion. This finding suggests the existence of possible hydrodynamic mechanism that could be used to interpret the observed maximum leukocyte aggregation in shear flow. The critical shear rate for maximum intercellular contact area is shown to vary with cell properties such as radius and membrane elastic modulus.     

The clinical significance of whole blood viscosity in (cardio)vascular medicine

Whole blood is a non-Newtonian fluid, which means that its viscosity depends on shear rate. At low shear, blood cells aggregate, which induces a sharp increase in viscosity, whereas at higher shear blood cells disaggregate, deform and align in the direction of flow. Other important determinants of blood viscosity are the haematocrit, the presence of macro-molecules in the medium, temperature and, especially at high shear, the deformability of red blood cells. At the sites of severe atherosclerotic obstructions or at vasospastic locations, when change of vessel diameter is limited, blood viscosity contributes to stenotic resistance thereby jeopardising tissue perfusion. However, blood viscosity plays its most important role in the microcirculation where it contributes significantly to peripheral resistance and may cause sludging in the postcapillary venules. Apart from the direct haemodynamic significance, an increase in blood viscosity at low shear by red blood cell aggregation is also associated with increased thrombotic risk, as has been demonstrated in atrial fibrillation. Furthermore, as increased red blood cell aggregation is a reflection of inflammation, hyperviscosity has been shown to be a marker of inflammatory activity. Thus, because of its potential role in haemodynamics, thrombosis and inflammation, determination of whole blood viscosity could provide useful information for diagnostics and therapy of (cardio)vascular disease.