An estimated shape function for drift in a platelet-transport model.

Prior work has shown that concentration profiles of platelets in flowing whole blood and of platelet-sized beads in flowing blood suspensions can include near-wall excesses. A model to describe this phenomenon was built about a single-component convective diffusion equation. To incorporate redistribution to preferred sites by shear flows of red cell suspensions, the model used a drift shape function (in addition to the commonly used augmented diffusion coefficient). This paper reports experiments that provide an average concentration profile from which the shape function for that model is calculated; the experiments and shape function are for the particular conditions of 40% hematocrit, platelet-sized latex beads (2.5 microns diameter), tube ID of 217 microns, and a wall shear rate of 555 s-1. Less precise estimates of the shape function obtained from data of previous studies indicate that the shape function is similar for the hematocrit of 15%.     

Detection of red cell aggregation by low shear rate viscometry in whole blood with elevated plasma viscosity

The viscosity of whole blood measured at low shear rates is determined partly by shear resistance of the red cell aggregates present, stronger aggregation increasing the viscosity in the absence of other changes. Effects of cell deformability can confound interpretation and comparison in terms of aggregation, however, particularly when the plasma viscosity is high. We illustrate the problem with a comparison of hematocrit-adjusted blood from type 1 diabetes patients and controls in which it is found the apparent and relative viscosities at a true shear rate of 0.20 s-1 are lower in the patient samples than age matched controls, in spite of reports that aggregation is increased in such populations. Because the plasma viscosities of the patients were higher on average than controls, we performed a series of experiments to examine the effect of plasma protein concentration and viscosity on normal blood viscosity. Dilution or concentration by ultrafiltration of autologous plasma and viscosity measurements at low shear on constant hematocrit red cell suspensions showed (a) suspension viscosity at 0.25 and 3 s-1 increased monotonically with plasma protein concentration and viscosity but (b) the relative viscosity increased, in concert with the microscopic aggregation grade, up to a viscosity of approximately 1.25 mPa-s but above this the value the relative viscosity no longer increased as the degree of aggregation increased in concentrated plasmas. It is suggested that in order to reduce cell deformation effects in hyperviscous pathological plasmas, patient and control plasmas should be systematically diluted before hematocrit is adjusted and rheological measurements are made. True shear rates should be calculated. Comparison of relative viscosities at low true shear rates appears to allow the effects of red cell aggregation to be distinguished by variable shear rate viscometry in clinical blood samples.     

The bulk rheology of close-packed red blood cells in shear flow

A theoretical analysis is made of the dynamical behavior and bulk rheology of close-packed red blood cell suspensions subjected to simple shear flow. The model for the polyhedral cell shapes and tank-treading membrane motion developed in the companion paper (1) is used. The flow in the thin lubricating plasma layers between cells is analyzed taking into account the mechanical properties of the membrane at the corner regions of sharp membrane curvature. This leads to predictions for the apparent viscosity as a function of hematocrit and shear rate. Good agreement with experimental results is obtained at moderate and high shear rates (above 20 s-1). At lower shear rates, a rapid rise in apparent viscosity has been found experimentally, and the mechanisms leading to this behavior are examined.     

Elevated capillary tube hematocrit reflects degradation of endothelial cell glycocalyx by oxidized LDL

Proteoglycans and plasma proteins bound to the endothelial cell glycocalyx are essential for vascular function, but at the same time, they lower capillary tube hematocrit by reducing capillary volume available to flowing blood. Because oxidized low-density lipoproteins (oxLDL) reduce the effective thickness of the glycocalyx (Vink H, Constantinescu AA, and Spaan JAE. Circulation 101: 1500-1502, 2000), we designed the present study to determine whether this is caused by pathological degradation of glycocalyx constituents or increased glycocalyx deformation by elevated shear forces of flowing blood. Capillaries from the right cremaster muscle of 24 hamsters were examined by using intravital microscopy after systemic administration of normal LDL (n = 4), moderate oxLDL (6-h oxidation with CuSO(4), n = 7), severe oxLDL (18-h oxidation, n = 5), and moderate oxLDL plus superoxide dismutase (SOD) and catalase (n = 8). Capillary tube hematocrit increased from 0.16 +/- 0.03 to 0.37 +/- 0.05 and from 0.15 +/- 0.01 to 0.31 +/- 0.03 after moderate oxLDL and severe oxLDL, respectively. These changes were paralleled by increases in red blood cell flux from 8.7 +/- 1.9 to 13.8 +/- 3 and from 10.7 +/- 2.1 to 16.3 +/- 3.2 cells/s after moderate oxLDL and severe oxLDL, respectively, in the absence of changes in anatomic capillary diameter. Red blood cell velocity, as a measure for the shear forces on the glycocalyx, was not affected by oxLDL, whereas tissue pretreatment with SOD and catalase completely abolished the effects of oxLDL on glycocalyx thickness, capillary hematocrit, and red blood cell flux. We conclude that elevation of capillary tube hematocrit by oxLDL reflects degradation of the endothelial glycocalyx by oxygen-derived free radicals.     

Effects of flowing RBCs on adhesion of a circulating tumor cell in microvessels

Adhesion of circulating tumor cells (CTCs) to the microvessel wall largely depends on the blood hydrodynamic conditions, one of which is the blood viscosity. Since blood is a non-Newtonian fluid, whose viscosity increases with hematocrit, in the microvessels at low shear rate. In this study, the effects of hematocrit, vessel size, flow rate and red blood cell (RBC) aggregation on adhesion of a CTC in the microvessels were numerically investigated using dissipative particle dynamics. The membrane of cells was represented by a spring-based network connected by elastic springs to characterize its deformation. RBC aggregation was modeled by a Morse potential function based on depletion-mediated assumption, and the adhesion of the CTC to the vessel wall was achieved by the interactions between receptors and ligands at the CTC and those at the endothelial cells forming the vessel wall. The results demonstrated that in the microvessel of \(15\,\upmu \hbox {m}\) diameter, the CTC has an increasing probability of adhesion with the hematocrit due to a growing wall-directed force, resulting in a larger number of receptor–ligand bonds formed on the cell surface. However, with the increase in microvessel size, an enhanced lift force at higher hematocrit detaches the initial adherent CTC quickly. If the microvessel is comparable to the CTC in diameter, CTC adhesion is independent of Hct. In addition, the velocity of CTC is larger than the average blood flow velocity in smaller microvessels and the relative velocity of CTC decreases with the increase in microvessel size. An increased blood flow resistance in the presence of CTC was also found. Moreover, it was found that the large deformation induced by high flow rate and the presence of aggregation promote the adhesion of CTC.     

Dynamics of blood flow: modeling of Fåhraeus and Fåhraeus–Lindqvist effects using a shear-induced red blood cell migration model

Blood flow in micro capillaries of diameter approximately 15–500 μm is accompanied with a lower tube hematocrit level and lower apparent viscosity as the diameter decreases. These effects are termed the Fåhraeus and Fåhraeus–Lindqvist effects, respectively. Both effects are linked to axial accumulation of red blood cells. In the present investigation, we extend previous works using a shear-induced model for the migration of red blood cells and adopt a model for blood viscosity that accounts for the suspending medium viscosity and local hematocrit level. For fully developed hematocrit profiles (i.e., independent of axial location), the diffusion fluxes due to particle collision frequency and viscosity gradients are of equal magnitude and opposite directions. The ratio of the diffusion coefficients for the two fluxes affects both the Fåhraeus and Fåhraeus–Lindqvist effects and is found related to the capillary diameter and discharge hematocrit using a well-known data-fit correlation for apparent blood viscosity. The velocity and hematocrit profiles were determined numerically as functions of radial coordinate, tube diameter, and discharge hematocrit. The velocity profile determined numerically is consistent with the derived analytical expression and the results are in good agreement with published numerical results and experimental data for hematocrit ratio and hematocrit and velocity profiles.     

Volume flow and wall shear stress quantification in the human conjunctival capillaries and post-capillary venules in vivo

Understanding the mathematical relationships of volume blood flow and wall shear stress with respect to microvessel diameter is necessary for the study of vascular design. Here, for the first time, volume flow and wall shear stress were quantified from axial red blood cell velocity measurements in 104 conjunctival microvessels of 17 normal human volunteers. Measurements were taken with a slit lamp based imaging system from the post capillary side of the bulbar conjunctiva in microvessel diameters ranging from 4 to 24 micrometers. The variation of the velocity profile with diameter was taken into account by using a profile factor function. Volume flow ranged from 5 to 462 pl/s with a mean value of 102 pl/s and gave a second power law best fitting line (r=0.97) deviating significantly from the third power law relation with diameter. The estimated wall shear stress declined hyperbolically (r=0.93) from a maximum of 9.55 N/m(2) at the smallest capillaries, down to a minimum of 0.28 N/m(2) at the higher diameter post capillary venules. The mean wall shear stress value for all microvessels was 1.54 N/m(2).     

Effect of nonaxisymmetric hematocrit distribution on non-Newtonian blood flow in small tubes

Hematocrit distribution and red blood cell aggregation are the major determinants of blood flow in narrow tubes at low flow rates. It has been observed experimentally that in microcirculation the hematocrit distribution is not uniform. This nonuniformity may result from plasma skimming and cell screening effects and also from red cell sedimentation. The goal of the present study is to understand the effect of nonaxisymmetric hematocrit distribution on the flow of human and cat blood in small blood vessels of the microcirculation. Blood vessels are modeled as circular cylindrical tubes. Human blood is described by Quemada's rheological model, in which local viscosity is a function of both the local hematocrit and a structural parameter that is related to the size of red blood cell aggregates. Cat blood is described by Casson's model. Eccentric hematocrit distribution is considered such that the axis of the cylindrical core region of red cell suspension is parallel to the axis of the blood vessel but not coincident. The problem is solved numerically by using finite element method. The calculations predict nonaxisymmetric distribution of velocity and shear stress in the blood vessel and the increase of apparent viscosity with increasing eccentricity of the core.     

Investigation of platelet margination phenomena at elevated shear stress

Thrombosis is a common complication following the surgical implantation of blood contacting artificial organs. Platelet transport, which is an important process of thrombosis and strongly modulated by flow dynamics, has not been investigated under the shear stress level associated with these devices, which may range from tens to several hundred Pascal.The current research investigated platelet transport within blood under supra-physiological shear stress conditions through a micro flow visualization approach. Images of platelet-sized fluorescent particles in the blood flow were recorded within microchannels (2 cm x 100 microm x 100 microm). The results successfully demonstrated the occurrence of platelet-sized particle margination under shear stresses up to 193 Pa, revealing a platelet near-wall excess up to 8.7 near the wall (within 15 microm) at the highest shear stress. The concentration of red blood cells was found to influence the stream-wise development of platelet margination which was clearly observed in the 20% Ht sample but not the 40% Ht sample. Shear stress had a less dramatic effect on the margination phenomenon than did hematocrit. The results imply that cell-cell collision is an important factor for platelet transport under supra-physiologic shear stress conditions. It is anticipated that these results will contribute to the future design and optimization of artificial organs.     

The failure of hydrodynamic analysis to define pore size in cell membranes

The equivalent pore theory predicts that the size of water transporting pores can be calculated from the ratio of osmotic (Pf, cm . s-1) to diffusive (Pd, cm . s-1) water permeability. Determinations of Pf and Pd in human red cells within the last thirty years have increased the ratio of Pf to Pd. According to the equivalent pore theory the pore diameter has increased from 9 A to 25 A. A pore diameter of 25 A is not compatible with the permeability characteristics of the red cell membrane. We conclude that the equivalent pore theory fails to determine pore size in red blood cells. We suggest that water transporting pores in human red cells transport water molecules in a single file fashion.     

Microhemodynamics of blood flow in narrow glass capillaries of 9 to 20 micrometers; the Fahraeus effect

Velocities of the red blood cell (RBC) and the suspending medium in glass capillaries of 9 to 20 micron were measured under microscopic observation. The effects of physical factors such as driving pressure, capillary diameter, hematocrits and RBC deformability on flow velocities were studied using freshly drawn blood of the rat resuspended in phosphate buffered saline solution in the hematocrit range between 5 and 12.5%. These RBC suspensions were made to flow through the test glass capillaries under known negative driving pressures. Ratios of capillary hematocrit to feed hematocrit taken as measures of the Fahraeus effect showed almost constant value of about 0.74. While, ratios of capillary hematocrit to discharge hematocrit showed a characteristic dependence on capillary diameter, showing minimal values at about 13 micron in capillary diameter. The same hematocrit ratios were found to be well correlated with values of wall shear rates estimated from the relative RBC velocities.     

Transient lateral transport of platelet-sized particles in flowing blood suspensions.

Concentration profiles of 2.5 microns latex beads were measured to demonstrate lateral transport of platelet-sized objects in flows of blood suspensions; the flows had equivalent Poiseuille wall shear rates (WSRs) from 250 to 1220 s-1. Each experimental trial began with a steady flow of suspension without beads in a thin-walled capillary tube (219 microns ID; 10.2 microns SD). The tube entrance was then switched to a reservoir containing suspension of equal hematocrit, but with beads, for a short interval of flow at the same WSR. This process established a paraboloidal tongue of labeled suspension with a transient concentration gradient at its surface. The tube and contents were rapidly frozen to fix the suspended particles in flow-determined locations. Segments of frozen tube were collected at distances from the entrance corresponding to 13%, 39%, and 65% of the axial extent of the ideal paraboloidal tongue. Concentration profiles were estimated from distances measured on fluorescence microscope images of cross-cut tube segments. Experiments used tubes either 40 or 50 cm long, suspension hematocrits of 0, 15, or 40%, and bead concentrations in the range of 1.5-2.2 x 10(5)/mm3. Profiles for 0% hematocrit suspension, a dilute, single-component suspension, had features expected in normal diffusive mixing in a flow. Distinctly different profiles and more lateral transport occurred when the suspensions contained red cells; then, all profiles for 13% extent had regions of excess bead concentration near the wall. Suspension flows with 40% hematocrit exhibited the largest amount of lateral transport. A case is made that, to a first approximation, the rate of lateral transport grew linearly with WSR; however, statistical analysis showed that for 40% hematocrit, less lateral transport occurred when the WSR was 250 s-1 or 1220 s-1 than 560 s-1, thus indicating that the rate behavior is more complex.     

The kinetics of thrombin- and SFLLRN-induced aggregation of human platelets in flow through tubes

The kinetics of aggregation of human platelets activated by alpha-thrombin (0.17-0.35 nM) and the hexapeptide SFLLRN (2-10 microM) was studied in plasma-free washed cell suspensions undergoing Poiseuille flow at 37 degrees C using a previously described double infusion technique. Platelet-rich Tyrodes, prepared from venous blood by multiple centrifugation, and agonist were rapidly mixed in a small chamber and the suspension flowed through various lengths of 1.19 and 0.76 mm diameter polyethylene tubing at mean transit times t from 0.2 to 43 s and mean tube shear rates = 41.9, 335, and 1335 s-1. Effluent was collected in 0.5% glutaraldehyde and single cells and aggregates in the volume range 1-10(5) micron 3 counted and sized using an aperture impedance counter. The rate and extent of aggregation with thrombin increased with increasing [thrombin] and , and although characterized by a small initial lag time, exhibited a very rapid growth of aggregates to macroscopic size, > 10(5) micron 3, at low and moderate shear rates. With SFLLRN, the initial lag times were appreciably longer, but subsequently aggregates also rapidly grew to macroscopic size. We hypothesize that the initial lag time is due to the time required for sufficient secretion and surface organization of ligands such as vWF (known to be released by the platelet) to occur, in order for cross-bridging of the GPIIb-IIIa receptors on adjacent platelets to take place. It appears that thrombin, which, at the low concentrations used, primarily activates the platelet via binding to the GPIb alpha receptor, can more rapidly facilitate secretion of the ligand than SFLLRN, which activates the cell via binding to the seven transmembrane domain receptor.     

Aggregation and disaggregation kinetics of human blood platelets: Part II. Shear-induced platelet aggregation.

A population balance equation (PBE) mathematical model for analyzing platelet aggregation kinetics was developed in Part I (Huang, P. Y., and J. D. Hellums. 1993. Biophys. J. 65: 334-343) of a set of three papers. In this paper, Part II, platelet aggregation and related reactions are studied in the uniform, known shear stress field of a rotational viscometer, and interpreted by means of the model. Experimental determinations are made of the platelet-aggregate particle size distributions as they evolve in time under the aggregating influence of shear stress. The PBE model is shown to give good agreement with experimental determinations when either a reversible (aggregation and disaggregation) or an irreversible (no disaggregation) form of the model is used. This finding suggests that for the experimental conditions studied disaggregation processes are of only secondary importance. During shear-induced platelet aggregation, only a small fraction of platelet collisions result in the binding together of the involved platelets. The modified collision efficiency is approximately zero for shear rates below 3000 s-1. It increases with shear rates above 3000 s-1 to about 0.01 for a shear rate of 8000 s-1. Addition of platelet chemical agonists yields order of magnitude increases in collision efficiency. The collision efficiency for shear-induced platelet aggregation is about an order of magnitude less at 37 degrees C than at 24 degrees C. The PBE model gives a much more accurate representation of aggregation kinetics than an earlier model based on a monodispersed particle size distribution.     

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.     

Blood low shear rate rheometry: influence of fibrinogen level and hematocrit on slip and migrational effects.

Red blood cell (RBC) aggregation is of prime importance in vivo and in vitro for low flow rates. It may be estimated by rheometrical measurements at low shear rates, but these are perturbed by slip and migrational effects which have already been highlighted in the past. These effects lead to a torque decay with time so that the true value of the stress at low shear rates may be greatly underestimated. Elevated aggregation being associated with different diseases, pathological blood samples show more pronounced perturbing effects and a strong time dependency in low shear rate rheometry. To test the dependence of slip and migrational effects on RBC aggregation, and particularly to determine the way in which they depend upon fibrinogen concentration ([Fb]), a home-made measuring system with roughened internal and external walls (170 microns roughness) was used to study low shear rate rheometry for RBC suspensions in PBS buffer containing albumin (at 50 g/l) and fibrinogen at various concentrations. The influences of hematocrit, shear rate, and fibrinogen concentration were investigated. Particular attention was paid to data acquisition at low shear rates (10(-3) s-1 to 3 x 10(-2) s-1). The combined influence of hematocrit and fibrinogen was investigated by adjusting hematocrit to 44 or 57% and fibrinogen concentration ([Fb]) to 3.0-4.5-6.5 g/l. Microscopic observations of the blood samples at rest were performed. They showed that different structures were formed according to fibrinogen concentration. The rheometrical measurements indicated that torque decay with shearing duration was strongly dependent on fibrinogen concentration and on shear rate at fixed hematocrit. Migrational and slip effects were more pronounced as shear rate decreased, fibrinogen concentration was raised, and hematocrit was lowered. The results have been explained on the basis of the expected microstructure of flowing blood in relation to the microscopic observations at rest.     

Passive mechanical behavior of human neutrophils: power-law fluid.

The mechanical behavior of the neutrophil plays an important role in both the microcirculation and the immune system. Several laboratories in the past have developed mechanical models to describe different aspects of neutrophil deformability. In this study, the passive mechanical properties of normal human neutrophils have been further characterized. The cellular mechanical properties were assessed by single cell micropipette aspiration at fixed aspiration pressures. A numerical simulation was developed to interpret the experiments in terms of cell mechanical properties based on the Newtonian liquid drop model (Yeung and Evans, Biophys. J., 56: 139-149, 1989). The cytoplasmic viscosity was determined as a function of the ratio of the initial cell size to the pipette radius, the cortical tension, aspiration pressure, and the whole cell aspiration time. The cortical tension of passive neutrophils was measured to be about 2.7 x 10(-5) N/m. The apparent viscosity of neutrophil cytoplasm was found to depend on aspiration pressure, and ranged from approximately 500 Pa.s at an aspiration pressure of 98 Pa (1.0 cm H2O) to approximately 50 Pa.s at 882 Pa (9.0 cm H2O) when tested with a 4.0-micron pipette. These data provide the first documentation that the neutrophil cytoplasm exhibits non-Newtonian behavior. To further characterize the non-Newtonian behavior of human neutrophils, a mean shear rate gamma m was estimated based on the numerical simulation. The apparent cytoplasmic viscosity appears to decrease as the mean shear rate increases. The dependence of cytoplasmic viscosity on the mean shear rate can be approximated as a power-law relationship described by mu = mu c(gamma m/gamma c)-b, where mu is the cytoplasmic viscosity, gamma m is the mean shear rate, mu c is the characteristic viscosity at characteristic shear rate gamma c, and b is a material coefficient. When gamma c was set to 1 s-1, the material coefficients for passive neutrophils were determined to be mu c = 130 +/- 23 Pa.s and b = 0.52 +/- 0.09 for normal neutrophils. The power-law approximation has a remarkable ability to reconcile discrepancies among published values of the cytoplasmic viscosity measured using different techniques, even though these values differ by nearly two orders of magnitude. Thus, the power-law fluid model is a promising candidate for describing the passive mechanical behavior of human neutrophils in large deformation. It can also account for some discrepancies between cellular behavior in single-cell micromechanical experiments and predictions based on the assumption that the cytoplasm is a simple Newtonian fluid.     

Glycoprotein (GP) Ib-IX-transfected cells roll on a von Willebrand factor matrix under flow. Importance of the GPib/actin-binding protein (ABP-280) interaction in maintaining adhesion under high shear

Adhesion of platelets to sites of vascular injury is critical for hemostasis and thrombosis and is dependent on the binding of the vascular adhesive protein von Willebrand factor (vWf) to the glycoprotein (GP) Ib-V-IX complex on the platelet surface. A unique but poorly defined characteristic of this receptor/ligand interaction is its ability to support platelet adhesion under conditions of high shear stress. To examine the structural domains of the GPIb-V-IX complex involved in mediating cell adhesion under flow, we have expressed partial (GPIb-IX), complete (GPIb-V-IX), and mutant (GPIbalpha cytoplasmic tail mutants) receptor complexes on the surface of Chinese hamster ovary (CHO) cells and examined their ability to adhere to a vWf matrix in flow-based adhesion assays. Our studies demonstrate that the partial receptor complex (GPIb-IX) supports CHO cell tethering and rolling on a bovine or human vWf matrix under flow. The adhesion was specifically inhibited by an anti-GPIbalpha blocking antibody (AK2) and was not observed with CHO cells expressing GPIbbeta and GPIX alone. The velocity of rolling was dependent on the level of shear stress, receptor density, and matrix concentration and was not altered by the presence of GPV. In contrast to selectins, which mediate cell rolling under conditions of low shear (20-200 s-1), GPIb-IX was able to support cell rolling at both venous (150 s-1) and arterial (1500-10,500 s-1) shear rates. Studies with a mutant GPIbalpha receptor subunit lacking the binding domain for actin-binding protein demonstrated that the association of the receptor complex with the membrane skeleton is not essential for cell tethering or rolling under low shear conditions, but is critical for maintaining adhesion at high shear rates (3000-6000 s-1). These studies demonstrate that the GPIb-IX complex is sufficient to mediate cell rolling on a vWf matrix at both venous and arterial levels of shear independent of other platelet adhesion receptors. Furthermore, our results suggest that the association between GPIbalpha and actin-binding protein plays an important role in enabling cells to remain tethered to a vWf matrix under conditions of high shear stress.