Hemodynamic effects of red blood cell aggregation

The influence of red blood cell (RBC) aggregation on blood flow in vivo has been under debate since early 1900's, yet a full understanding has still has not been reached. Enhanced RBC aggregation is well known to increase blood viscosity measured in rotational viscometers. However, it has been demonstrated that RBC aggregation may decrease flow resistance in cylindrical tubes, due to the formation of a cell-poor zone near the tube wall which results from the enhanced central accumulation of RBC. There is also extensive discussion regarding the effects of RBC aggregation on in vivo blood flow resistance. Several groups have reported increased microcirculatory flow resistance with enhanced RBC aggregation in experiments that utilized intravital microscopy. Alternatively, whole organ studies revealed that flow resistance may be significantly decreased if RBC aggregation is enhanced. Recently, new techniques have been developed to achieve well-controlled, graded alterations in RBC aggregation without influencing suspending phase properties. Studies using this technique revealed that the effects of RBC aggregation are determined by the degree of aggregation changes, and that this relationship can be explained by different hemodynamic mechanisms.     

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.     

Determination of erythrocyte transit times through micropores. II-- Influence of experimental and physicochemical factors

A new red blood cell filtration system, termed the Cell Transit Time Analyzer (CTTA), has been developed in order to measure the individual transit times of a large number of cells through cylindrical micropores in special "oligopore" filters: the system operates on the electrical conductometric principle and employs special computer software to provide several measures of the resulting transit time histogram. Using this system with filters having pore diameters of 4.5 or 5.0 cm and length to diameter ratios of 3.0 to 4.7, we have evaluated the effects of several experimental factors on the flow behavior of normal and modified human RBC. Our results indicate : 1) linear PBC pressure - flow behavior over a driving pressure range of 2 to 10.5 cm H2O with zero velocity intercepts at delta P = 0, thus suggesting the Poiseuille - like nature of the flow; 2) resistance to flow or "apparent viscosities" for normal RBC which are between 3.1 to 3.9 cPoise and are independent of driving pressure and pore geometry; 3) increased flow resistance (i.e., increased transit times) for old versus young RBC and for RBC made less deformable by DNP-induced crenation or by heat treatment at 48 degrees C; 4) increased mean transit time and poorer reproducibility when using EDTA rather than heparin as the anticoagulant agent. Further, using mixtures of heat-treated and normal RBC and various percentile values of the transit time histogram. We have been able to demonstrate the presence of sub-populations of rigid cells and thus the value of measurements which allow statistical analyses of RBC populations.     

Two-dimensional lattice Boltzmann study of red blood cell motion through microvascular bifurcation: cell deformability and suspending viscosity effects

Red blood cell (RBC) motion and trajectories in bifurcated microvessels are simulated using a two-dimensional immersed boundary-lattice Boltzmann method (IB-LBM). A RBC is modeled as a capsule with viscous interior fluid enclosed by a flexible membrane. For the symmetric bifurcation model employed, the critical offset position in the mother branch, which separates the RBC flux toward the two branches, has been calculated. The RBC flux and the hematocrit partitioning between the two daughter branches have also been studied. Effects of the flow-rate ratio, cell deformability and suspending viscosity have been examined. Simulation results indicate that increased cell rigidity and suspending viscosity have counter effects on cell trajectory through a bifurcation: the cell trajectory shifts toward the low flow-rate branch for less deformable cells, and toward the high flow-rate branch for more viscous plasma. These results imply that a higher cell rigidity would reduce the regular phase separation of hematocrit and plasma skimming processes in microcirculation, while an increased viscosity has the opposite effect. This has implications for relevant studies in fundamental biology and biomedical applications.     

Determination of erythrocyte transit times through micropores. II. Influence of experimental and physicochemical factors

A new red blood cell filtration system, termed the Cell Transit Time Analyzer (CTTA), has been developed in order to measure the individual transit times of a large number of cells through cylindrical micropores in special "oligopore" filters; the system operates on the electrical conductometric principle and employs special computer software to provide several measures of the resulting transit time histogram. Using this system with filters having pore diameters of 4.5 or 5.0 microns and length to diameter ratios of 3.0 to 4.7, we have evaluated the effects of several experimental factors on the flow behavior of normal and modified human RBC. Our results indicate: 1) linear RBC pressure-flow behavior over a driving pressure range of 2 to 10.5 cm H2O with zero velocity intercepts at delta P = 0, thus suggesting the Poiseuille-like nature of the flow; 2) resistance to flow or "apparent viscosities" for normal RBC which are between 3.1 to 3.9 cPoise and are independent of driving pressure and pore geometry; 3) increased flow resistance (i.e., increased transit times) for old versus young RBC and for RBC made less deformable by DNP-induced crenation or by heat treatment at 48 degrees C; 4) increased mean transit time and poorer reproducibility when using EDTA rather than heparin as the anticoagulant agent. Further, using mixtures of heat-treated and normal RBC and various percentile values of the transit time histogram, we have been able to demonstrate the presence of sub-populations of rigid cells and thus the value of measurements which allow statistical analyses of RBC populations.     

Tank treading of optically trapped red blood cells in shear flow

Tank-treading (TT) motion is established in optically trapped, live red blood cells (RBCs) held in shear flow and is systematically investigated under varying shear rates, temperature (affecting membrane viscosity), osmolarity (resulting in changes in RBC shape and cytoplasmic viscosity), and viscosity of the suspending medium. TT frequency is measured as a function of membrane and cytoplasmic viscosity, the former being four times more effective in altering TT frequency. TT frequency increases as membrane viscosity decreases, by as much as 10% over temperature changes of only 4°C at a shear rate of ∼43 s⁻¹. A threshold shear rate (1.5 ± 0.3 s⁻¹) is observed below which the TT frequency drops to zero. TT motion is also observed in shape-engineered (spherical) RBCs and those with cholesterol-depleted membranes. The TT threshold is less evident in both cases but the TT frequency increases in the latter cells. Our findings indicate that TT motion is pervasive even in folded and deformed erythrocytes, conditions that occur when such erythrocytes flow through narrow capillaries.     

Erythrocyte filtrability measurement by the initial flow rate method

A new filtration technique, based on the initial filtration rate of a diluted RBC suspension through 5 mu Nucleopore filter is described. As only a few hundreds RBCs traverse each pore and as the measurement are made in a few seconds, the method is by large insensitive to filter plugging and to sedimentation effects. The results are given as a filtration index IF which is, as a first order approximation, independent of the filter conductance and of the suspending medium viscosity. The filtration times are measured electronically. The filters are re-used many times. The influence on the results reproducibility of RBC washing, of the anticoagulant, of the blood sample and the suspension storage times are considered. With our technical procedure, the relative incertitude on the measurement of I.F. is about +/- 10%. The filtration index is shown to be an intrinsic RBC filterability property.     

Analysis of red blood cell motion through cylindrical micropores: effects of cell properties.

Filtration through micropores is frequently used to assess red blood cell deformability, but the dependence of pore transit time on cell properties is not well understood. A theoretical model is used to simulate red cell motion through cylindrical micropores with diameters of 3.6, 5, and 6.3 microns, and 11-microns length, at driving pressures of 100-1000 dyn/cm2. Cells are assumed to have axial symmetry and to conserve surface area during deformation. Effects of membrane shear viscosity and elasticity are included, but bending resistance is neglected. A time-dependent lubrication equation describing the motion of the suspending fluid is solved, together with the equations for membrane equilibrium, using a finite difference method. Predicted transit times are consistent with previous experimental observations. Time taken for cells to enter pores represents more than one-half of the transit time. Predicted transit time increases with increasing membrane viscosity and with increasing cell volume. It is relatively insensitive to changes in internal viscosity and to changes in membrane elasticity except in the narrowest pores at low driving pressures. Elevating suspending medium viscosity does not increase sensitivity of transit time to membrane properties. Thus filterability of red cells is sensitively dependent on their resistance to transient deformations, which may be a key determinant of resistance to blood flow in the microcirculation.     

Action of hydroxyethyl starch on the flow properties of human erythrocyte suspensions

Hydroxyethyl starch (HES) has often been used as a plasma expander, but questions still remain concerning the mechanisms by which it produces changes in the rheological properties of blood and erythrocyte (RBC) suspensions under various flow conditions. The present investigation has shown that the dynamic viscosity of HES (232,000 and 565,000 daltons) solutions rises in a nonlinear fashion with increasing HES concentration, and for a given concentration of HES exhibits Newtonian behavior at shear rates between 0.15 to 124 sec-1. At low (less than 0.9 sec-1) shear rates the apparent viscosity of a 40% RBC suspension increases with lower concentrations of HES because of RBC aggregation. At higher concentrations of HES, increases in suspension viscosity are due to an increase in the viscosity of the continuous phase since the RBC are largely disaggregated. At high (greater than 36 sec-1) shear rates the relative viscosity (eta/eta O) of RBC suspensions slowly decreases with increasing HES concentration. At low shear rates eta/eta O increases and then decreases with increasing HES concentration. Evidence of the concentration-dependent effects of HES on RBC aggregation is provided not only by the viscometric analysis but also from measurements of erythrocyte sedimentation rate (ESR) and the zeta sedimentation ratio (ZSR). HES is a more potent aggregating agent in phosphate buffered saline (PBS) than it is in plasma. Polymer size has only a slight effect on the extent of RBC aggregation produced, but does have a significant effect on the concentration of polymer at which maximum aggregation occurs. The viscosity-corrected electrophoretic mobility of RBC in HES rises monotonically with the concentration of HES in the suspending medium. Decreases in the extent of RBC aggregation with increasing polymer concentrations probably result from an increase in the electrostatic repulsive forces between the cells.     

Osmolality- and hematocrit-mediated flow behavior of RBC suspensions in 33 micrometer ID tubes

The effects of suspending medium osmolality (166 to 736 mosm/kg) on relative viscosity (eta r) and tube hematocrit (HT) measured in 33 microns diameter tubes were studied for 40, 47 and 57% feed hematocrit (HF) suspensions of human RBC in buffer. At all feed hematocrits, eta r increased sharply for the hypertonic media, but was essentially insensitive to hypotonicity. HT/HF was less affected by osmolality (13% change over the entire range of osmolality and feed hematocrit). Viscosities could not be calculated from the experimental HT values. However, eta r could be predicted from RBC number concentration and the tube diameter/RBC volume ratio via a semi-empirical model. RBC transport efficiency depended on both feed hematocrit and osmolality, and was maximal at or near isotonic conditions. Our results appear applicable to non-isotonic regions of the microcirculation, and to estimation of flow resistance for RBC with abnormal cellular mechanical properties.     

Cellular determinants of low-shear blood viscosity

Low-shear viscometry is one of the methods commonly used to estimate the degree of red blood cell (RBC) aggregation in various bloods and RBC suspensions. However, it has been previously shown that alterations in RBC morphology and mechanical behavior can affect the low-shear apparent viscosity of RBC suspensions; RBC aggregation is also sensitive to these cellular factors. This study used heat treatment (48°C, 5 min), glutaraldehyde (0.005–0.02%) and hydrogen peroxide (1 mM) to modify cell geometry and deformability. Red blood cell aggregation was assessed via a Myrenne Aggregometer (“M” and “Ml” indexes), RBC suspension viscosity was measured using a Contraves LS-30 viscometer, and RBC shape response to fluid shear stresses (i.e., deformability) was determined by ektacytometry (LORCA system). Our results indicate that low-shear apparent viscosity and related indexes may not always reflect changes of RBC aggregation if cellular properties are altered: for situations where RBC aggregation has been only moderately affected, cellular mechanical factors may be the major determinant of low-shear viscosity. These findings thus imply that in situations which may be associated alterations of RBC geometry and/or deformability, low-shear viscometry should not be the sole measurement technique used to assess RBC aggregation.     

Alteration of Blood Flow in a Venular Network by Infusion of Dextran 500: Evaluation with a Laser Speckle Contrast Imaging System

This study examined the effect of dextran-induced RBC aggregation on the venular flow in microvasculature. We utilized the laser speckle contrast imaging (LSCI) as a wide-field imaging technique to visualize the flow distribution in venules influenced by abnormally elevated levels of RBC aggregation at a network-scale level, which was unprecedented in previous studies. RBC aggregation in rats was induced by infusing Dextran 500. To elucidate the impact of RBC aggregation on microvascular perfusion, blood flow in the venular network of a rat cremaster muscle was analyzed with a stepwise reduction of the arterial pressure (100 → 30 mmHg). The LSCI analysis revealed a substantial decrease in the functional vascular density after the infusion of dextran. The relative decrease in flow velocity after dextran infusion was notably pronounced at low arterial pressures. Whole blood viscosity measurements implied that the reduction in venular flow with dextran infusion could be due to the elevation of medium viscosity in high shear conditions (> 45 s^-1). In contrast, further augmentation to the flow reduction at low arterial pressures could be attributed to the formation of RBC aggregates (< 45 s^-1). This study confirmed that RBC aggregation could play a dominant role in modulating microvascular perfusion, particularly in the venular networks.     

Influence of cell-specific factors on red blood cell aggregation

The reversible aggregation of red blood cells (RBC) into linear and three-dimensional structures continues to be of basic science and clinical interest: RBC aggregation affects low shear blood viscosity and microvascular flow dynamics, and can be markedly enhanced in several clinical states. Until fairly recently, most research efforts were focused on relations between suspending medium composition (i.e., protein levels, polymer type and concentration) and aggregate formation. However, there is now an increasing amount of experimental evidence indicating that RBC cellular properties can markedly affect aggregation, with the term "RBC aggregability" coined to describe the cell's intrinsic tendency to aggregate. Variations of aggregability can be large, with some changes of aggregation substantially greater than those resulting from pathologic states. The present review provides a brief overview of this topic, and includes such areas as donor-to-donor variations, polymer-plasma correlations, effects of RBC age, effects of enzymatic treatment, and current developments related to the mechanisms involved in RBC aggregation.     

Red blood cell shape transitions and dynamics in time-dependent capillary flows

The dynamics of single red blood cells (RBCs) determine microvascular blood flow by adapting their shape to the flow conditions in the narrow vessels. In this study, we explore the dynamics and shape transitions of RBCs on the cellular scale under confined and unsteady flow conditions using a combination of microfluidic experiments and numerical simulations. Tracking RBCs in a comoving frame in time-dependent flows reveals that the mean transition time from the symmetric croissant to the off-centered, nonsymmetric slipper shape is significantly faster than the opposite shape transition, which exhibits pronounced cell rotations. Complementary simulations indicate that these dynamics depend on the orientation of the RBC membrane in the channel during the time-dependent flow. Moreover, we show how the tank-treading movement of slipper-shaped RBCs in combination with the narrow channel leads to oscillations of the cell's center of mass. The frequency of these oscillations depends on the cell velocity, the viscosity of the surrounding fluid, and the cytosol viscosity. These results provide a potential framework to identify and study pathological changes in RBC properties.     

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.     

RBC aggregation: laboratory data and models

The reversible aggregation of red blood cells (RBC) into linear and three-dimensional structures continues to be of basic science and clinical interest: RBC aggregation affects low shear blood viscosity and microvascular flow dynamics, and can be markedly enhanced in several clinical states. Until fairly recently, most research efforts were focused on relations between suspending medium composition (i.e., protein levels, polymer type and concentration) and aggregate formation. However, there is now an increasing amount of experimental evidence indicating that RBC cellular properties can markedly affect aggregation, with the term "RBC aggregability" coined to describe the cell's intrinsic tendency to aggregate. Variations of aggregability can be large, with some changes of aggregation substantially greater than those resulting from pathologic states. The present review provides a brief overview of this topic, and includes such areas as donor-to-donor variations, polymer-plasma correlations, effects of RBC age, effects of enzymatic treatment, and current developments related to the mechanisms involved in RBC aggregation.     

Temperature-dependent threshold shear stress of red blood cell aggregation

Red blood cell (RBC) aggregation is becoming an important hemorheological parameter, which exhibits a unique temperature dependence. However, further investigation is still required for understanding the temperature-dependent characteristics of hemorheology that includes RBC aggregation. In the present study, blood samples were examined at 3, 10, 20, 30, and 37 °C. When the temperature decreases, the whole-blood and plasma viscosities increase, whereas the aggregation indices (AI, M, and b) yield contrary results. Since these contradictory results are known to arise from an increase in the plasma viscosity as the temperature decreases, aggregation indices that were corrected for plasma viscosity were examined. The corrected indices showed mixed results with the variation of the temperature. However, the threshold shear rate and the threshold shear stress increased as the temperature decreased, which is a trend that agrees with that of the blood viscosity. As the temperature decreases, RBC aggregates become more resistant to hydrodynamic dispersion and the corresponding threshold shear stress increases as does the blood viscosity. Therefore, the threshold shear stress may help to better clarify the mechanics of RBC aggregation under both physiological and pathological conditions.     

Theoretical modeling of filtration of blood cell suspensions

A theoretical model of filtration of suspensions containing red blood cells (RBCs) and white blood cells (WBCs) has been developed. Equations are written for the pressure drop, the filtration flow and the fractions of filter pores containing RBCs (alpha) and WBCs (alpha*). Because the relative resistances (ratios of resistance of cell to resistance of suspending fluid) of RBCs (beta) and WBCs (beta*) through the filter pore are greater than one, the transit of these cells (especially WBCs) through the filter is slower than that of suspending fluid; this leads to values of alpha and alpha* higher than those simply expected from the hematocrit and leukocrit, respectively, in the entering and exiting suspensions. In the absence of pore plugging by the cells (steady flow), the pressure drop can be computed from alpha, alpha*, beta and beta*. In order to model unsteady flow, differential equations are written to include pore plugging and the subsequent unplugging by the rising filtration pressure at a constant flow. By specifying the fractions of entering RBCs (epsilon) and WBCs (epsilon*) which would plug the pores and the rate at which the plugged pores would unplug in response to pressure rise (epsilon u), as well as the fractions of entering RBCs (epsilon p) and WBCs (epsilon p*) that would plug the pores permanently, theoretical pressure-time curves can be generated by numerical integration, and the results fit the experimental data well. From such fitting of theoretical curve to experimental data, information can be deduced for epsilon, epsilon*, epsilon u, epsilon p and epsilon* p.     

Modulation of red blood cell aggregation and blood viscosity by the covalent attachment of Pluronic copolymers

Despite many years of research, the physiologic or possible pathologic significance of RBC aggregation remains to be clearly determined. As a new approach to address an old question, we have recently developed a technique to vary the aggregation tendency of RBCs in a predictable and reproducible fashion by the covalent attachment of nonionic polymers to the RBC membrane. A reactive derivative of each polymer of interest is prepared by substitution of the terminal hydroxyl group with a reactive moiety, dichlorotriazine (DT), which covalently bonds the polymer molecule to membrane proteins. Pluronics are block copolymers of particular interest as these copolymers can enhance or inhibit RBC aggregation. Pluronics exhibit a critical micellization temperature (CMT): a phase transition from predominantly single, fully hydrated copolymer chains to micelle-like structures. The CMT is a function of both copolymer molecular mass and concentration. This micellization property of Pluronics has been utilized to enhance or inhibit RBC aggregation and hence to vary low-shear blood viscosity. Pluronic-coated RBCs were prepared using reactive DT derivatives of a range of Pluronics (F68, F88, F98 and F108) and resuspended in autologous plasma at 40% hematocrit. Blood viscosity was measured at a range of shear rates (0.1-94.5 s(-1)) and at 25 and 37 degrees C using a Contraves LS-30 couette low shear viscometer. RBC aggregation and whole blood viscosity was modified in a predictable manner depending upon the CMT of the attached Pluronic and the measurement temperature: below the CMT, RBC aggregation was diminished; above the CMT it was enhanced. This technique provides a novel tool to probe some basic research questions. While certainly of value for in vitro mechanistic studies, perhaps the most interesting application may be for in vivo studies: typically, intravital experiments designed to examine the role of RBC aggregation in microvascular flow require perturbation of the suspending plasma to promote or reduce aggregation (e.g., by the addition of dextran). By binding specific Pluronics to the surface, we can produce RBCs that intrinsically have any desired degree of increased or decreased aggregation when suspended in normal plasma, thereby eliminating many potential artifacts for in vivo studies. The copolymer coating technique is simple and reproducible, and we believe it will prove to be a useful tool to help address some of the longstanding questions in the field of hemorheology.     

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.