Theoretical and experimental analysis of the sedimentation kinetics of concentrated red cell suspensions in a centrifugal field: determination of the aggregation and deformation of RBC by flux density and viscosity functions

The flow properties of blood are mostly determined using various viscometric approaches, and described in terms of a shear rate or shear stress dependent apparent viscosity. The interpretation of results are rather difficult, especially at low shear rates when particle sedimentation and migration within the viscometer gap are significant. By contrast, analysing the separation process in concentrated RBC suspensions in a centrifugal field also yields information about the viscosity function, including particle-particle interaction and deformation parameters. In this paper, the sedimentation process is approached by means of the theory of kinematic waves and theoretically described by solving the corresponding one-dimensional quasi-linear partial differential equation based on viscosity/flow function as a function of volume concentration. The sedimentation kinetics of rigid spherical RBC suspended in saline and normal RBC suspended in Dx-saline solutions were investigated by means of a separation analyser (LUMiFuge 114). The instrument detects the light transmission over the total length of the cell containing the suspension. During centrifugation the analyser automatically determines the position of the particle free fluid/suspension interface or the sediment by means of a special algorithm. The data obtained with sedimentation of rigid spherical RBC at different volume concentrations demonstrate that, in the case of suspensions rotated in containers of constant cross section, there is good agreement between the theory of kinematic waves developed by Anestis and Schneider (1983) and the results of the experiments. Such good agreement was obtained even though a restrictive one-dimensional model was used to obtain the theoretically derived sedimentation time course. In addition, we describe an algorithm enabling the experimental determination of the viscosity and related flux density function to be made for any suspension. Through this approach, we investigated in detail the rheological behavior of suspended rigid spheres at low Reynolds numbers ranging from 10(-6) to 10(-3). The method here introduced also enabled us to investigate RBC suspensions with respect to the deformability and interactions of the cells by means of the separation analysis. Normal, rigid as well as aggregating RBC exhibited marked differences in the sedimentation kinetics, which were quantified by means of the flux and viscosity functions based on the theory of kinematic waves.     

Role of hydrogen bonding in red cell aggregation.

The role of hydrogen bonding in red cell aggregation induced by dextran was studied with the use of urea, an inhibitor for hydrogen bonding. In order to avoid hemolysis of red cells by the high concentration of urea, the studies were performed on human red cells hardened in glutaraldehyde. The degree of red cell aggregation at Hct = 45% was estimated by the use of a coaxial cylinder viscometer. The viscometric aggregation index (VAI) was calculated from viscosity values at shear rates of 52 sec-1 (eta H) and 0.05 sec-1 (eta L); VAI = (eta L - eta H)/eta H. Red cells with surface charge intact and with charge removal by neuraminidase treatment were studied. Urea at high concentrations, e.g., 6 M, significantly inhibited red cell aggregation induced by dextran. These findings indicate that hydrogen bonding plays an important role in dextran-induced red cell aggregation. An understanding of the nature of the forces involved in red cell aggregation serves to establish the physicochemical principles of cell-to-cell interactions induced by macromolecules.     

Effect of high osmotic media on blood viscosity and red blood cell deformability

Effects of high osmotic media on the shape and deformability of RBC were examined for determining increasing factors of blood viscosity. Dog blood and Urographin (a hypertonic contrast medium) were used; the plasma osmolality was changed by Urografin suspended in blood. The viscosity was measured for normal RBC and glutaraldehyde-treated RBC suspensions with a cell volume concentration. The RBC deformability was evaluated from the difference in viscosity between the two suspensions. It was shown that normal RBC suspension increased the viscosity with increase in osmolality at high shear rate; hardened RBC suspension decreased the viscosity with increase in osmolality. It was concluded that the RBC deformability decreased with increasing osmolality.     

Graded alterations of RBC aggregation influence in vivo blood flow resistance

Although the effects of red blood cell (RBC) aggregation on low-shear rate blood viscosity are well known, the effects on in vivo flow resistance are still not fully resolved. The present study was designed to explore the in vivo effects of RBC aggregation on flow resistance using a novel technique to enhance aggregation: cells are covalently coated with a block copolymer (Pluronic F-98) and then suspended in unaltered plasma. RBC aggregation was increased in graded steps by varying the Pluronic concentration during cell coating and was verified by microscopy and erythrocyte sedimentation rate (ESR), which increased by 200% at the highest Pluronic level. RBC suspensions were perfused through an isolated in situ guinea pig hindlimb preparation while the arterial perfusion pressure was held constant at 100 mmHg via a pressure servo-controlled pump. No significant effects of enhanced RBC aggregation were observed when studies were conducted in preparations with intact vascular control mechanisms. However, after inhibition of smooth muscle tone (using 10(-4) M papaverin), a significant change in flow resistance was observed in a RBC suspension with a 97% increase of ESR. Additional enhancements of RBC aggregation (i.e., 136 and 162% increases of ESR) decreased flow resistance almost to control values. This was followed by another significant increase in flow resistance during perfusion with RBC suspensions with a 200% increase of ESR. This triphasic effect of graded increases of RBC aggregation is most likely explained by an interplay of several hemodynamic mechanisms that are triggered by enhanced RBC aggregation.     

Blood modeling using polystyrene microspheres

The steady flow viscosity at shear rates 0 to 120 sec-1 and dynamic viscoelasticity at frequencies 0.02 to 0.8 Hz were determined for aqueous suspensions of uniform polystyrene microspheres of 1.0 micron diameter. Rheological properties of the microsphere suspensions were Newtonian for particle concentrations up to 32%. By introducing dextran and calcium chloride into the particle suspensions, non-Newtonian behavior was produced similar to that observed for human blood. The cooperative effects of dextran and calcium ions promoted aggregation of particles at a concentration as low as 12%. Thus, a suspension of uniform sized spherical polystyrene particles in aqueous solution of dextran may be made to mimic blood by controlling the surface charge on the polystyrene spheres using addition of calcium ions to the medium.     

Effects of cellular morphology on the viscoelastic behavior of high hematocrit RBC suspensions

Using a constant-amplitude (+/- 1 degree) oscillatory Couette viscometer (f = 0.01-1.0 Hz), we have measured the viscous (eta') and elastic (eta") components of the complex viscosity at 25 degrees C for shape-transformed human RBC suspended in isotonic buffer at 80% hematocrit. Morphology-altering drugs employed were: ECHINOCYTIC AGENT 2,4-dinitrophenol (DNP, 0.1-5 mM); STOMATOCYTIC AGENT chlorpromazine hydrochloride (CPZ, 0.01-0.1 mM). All suspensions exhibited decreasing eta' and eta" with increasing frequency. Compared to biconcave, control RBC suspensions, salient effects of shape transformation included: 1) for DNP, a dose-related elevation of both eta' and eta", with a 850% increase in eta' and a 2500% increase in eta" at 5 mM and the lowest frequency; 2) for CPZ, a dose-related elevation of both eta' and eta", with a 170% increase in eta' and a 280% increase in eta" at 0.1 mM and the lowest frequency; 3) for both DNP and CPZ, the elevations of eta' and eta" were inversely related to frequency. Using 2 mM DNP and various concentrations of CPZ, both eta' and eta" could be returned to control with 0.08 mM CPZ; further increases of CPZ at constant DNP led to elevations of both components. Comparisons of eta' and eta" to steady shear viscometric data indicated that neither a nominal shear rate approach nor a RMS complex viscosity technique was able to completely reconcile these data; a modified Kelvin-Voigt model proved useful in evaluating cellular versus membrane contributions to eta". These results indicate that RBC morphology is an important determinant of the oscillatory behavior of RBC suspensions and suggest the usefulness of the technique for studies of drug-membrane interactions.     

Effect of enhanced red blood cell aggregation on blood flow resistance in an isolated-perfused guinea pig heart preparation

The role of red blood cell (RBC) aggregation as a determinant of in vivo blood flow is still unclear. This study was designed to investigate the influence of a well-controlled enhancement of RBC aggregation on blood flow resistance in an isolated-perfused heart preparation. Guinea pig hearts were perfused through a catheter inserted into the root of the aorta using a pressure servo-controlled pump system that maintained perfusion pressures of 30 to 100 mmHg. The hearts were beating at their intrinsic rates and pumping against the perfusion pressure. RBC aggregation was increased by Pluronic (F98) coating of RBC at a concentration 0.025 mg/ml, corresponding to about a 100% increment in RBC aggregation as measured by erythrocyte sedimentation rate. Isolated heart preparations were perfused with 0.40 l/l hematocrit unmodified guinea pig blood and with Pluronic-coated RBC suspensions in autologous plasma. At high perfusion pressures there were no significant differences between the flow resistance values for the two perfusates, with differences in flow resistance only becoming significant at lower perfusion pressures. These results can be interpreted to reflect the shear dependence of RBC aggregation: higher shear forces associated with higher perfusion pressures should have dispersed RBC aggregates resulting in blood flow resistances similar to control values. Experiments repeated in preparations in which the smooth muscle tone was inhibited by pre-treatment with papaverine indicated that significant effects of enhanced RBC aggregation could be detected at higher perfusion pressures, underlining the compensatory role of vasomotor control mechanisms.     

Red cell aggregation and viscoelasticity of blood from seals, swine and man

RBC aggregation and viscoelasticity parameters were determined for 40% suspensions of washed cells in autologous plasma from elephant seals (ES), Mirounga angustirostris, ringed seals (RS), Phoca hispida, and swine, (SS), Sus scrofa. Interspecific comparisons including human (HS) blood data revealed unusual rheological properties of seal blood relative to that from pigs or man: 1) RBC aggregation extent, rate and sedimentation were lower for seals (AI = 0, ZSR = .40, ESR = 0 for RS blood) relative to humans; 2) Viscous (n') and elastic (n") components of complex viscosity (OCRD) were lower for both seal species relative to SS blood, but only at shear rates less than or equal to 10 sec-1 (P less than 0.05), while n"/n' ratios for RS blood were lower than HS blood at all shear rates (P less than 0.01); 3) Blood viscosity measurements for RS and SS blood from rotational viscometry (Contraves) were consistent with OCRD data; 4) Seal plasma fibrinogen levels were low compared to pigs or humans (RS fibrinogen = -43% v. HS and -57% v. SS; ES fibrinogen = -58% v. HS and -69% v. SS). Electrophoretic mobility of RS red cells was +25% relative to those of humans. These results demonstrate differences in hemorheological indices among mammalian species and suggest the value of comparative rheologic studies.     

The mechanism of erythrocyte sedimentation in Westergren's examination.

The authors deduced the equation that describes the sedimentation of erythrocytes as the function of time, hematocrit, hemoglobin and some plasma protein concentrations and the citrate viscosity and density. This values served to describe plasma and erythrocyte density, plasma viscosity, erythrocyte aggregation and the influence of suspension concentration on the erythrocyte sedimentation rate. The influence of citrate on blood dilution (the reduction of hematocrit and plasma protein concentrations) was also considered. A good agreement between the observed and predicted values was obtained.     

肠淋巴液引流对失血性休克大鼠红细胞流变性的影响

目的:观察肠淋巴液引流对失血性休克大鼠红细胞流变性指标以及血液黏度的作用。方法:Wistar雄性大鼠均分为假休克组、休克组(复制失血性休克模型)、引流组(复制失血性休克模型,自低血压1 h引流休克肠淋巴液)。在低血压3 h或相应时间,经腹主动脉取血,检测红细胞参数、红细胞电泳、红细胞沉降率(ESR)以及血液黏度,计算红细胞聚集指数、红细胞变形指数。结果:与假休克组比较,休克组红细胞数量、红细胞比积(HCT)、血红蛋白(Hb)、平均红细胞血红蛋白浓度(MCHC)、红细胞电泳率与迁移率、红细胞变形指数、全血黏度、全血低切与高切相对黏度和还原黏度显著降低,休克组平均红细胞体积、红细胞电泳时间、ESR、血沉方程K值与校正K值、红细胞聚集性指数、血浆黏度显著升高;引流组MCHC、红细胞电泳率与迁移率、全血黏度、全血低切与高切还原黏度均显著降低,引流组红细胞体积分布宽度(RDW-SD)显著增加。同时,引流组HCT、RDW-SD、红细胞变形指数、全血黏度、全血低切与高切相对黏度显著高于休克组;ESR、血沉方程K值与校正K值、红细胞聚集性指数、血浆黏度显著低于休克组。结论:休克肠淋巴液引流可改善失血性休克大鼠红细胞流变行为,从而改善血液流变性。     

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.     

Red blood cell orientation in orbit C = 0.

Two modes of behavior of single human red cells in a shear field have been described. It is known that in low viscosity media and at shear rates less than 20 s-1, the cells rotate with a periodically varying angular velocity, in accord with the theory of Jeffery (1922) for oblate spheroids. In media of viscosity greater than approximately 5 mPa s and sufficiently high shear rates, the cells align themselves at a constant angle to the direction of flow with the membrane undergoing tank-tread motion. Also, in low viscosity media, as the shear rate is increased, more and more cells lie in the plane of shear, undergoing spin with their axes of symmetry aligned with the vorticity axis of the shear field in an orbit "C = 0" (Goldsmith and Marlow, 1972). We have explored this latter phenomenon using two experimental methods. First, the erythrocytes were observed in the rheoscope and their diameters measured. Forward light scattering patterns were correlated with the red cell orientation mode. Light flux variations after flow onset or stop were measured, and the characteristic times of erythrocyte orientation and disorientation were assessed. The characteristic time of erythrocyte orientation in Orbit C = 0 is proportional to the inverse of the shear rate. The corresponding coefficient of proportionality depends on the suspending medium viscosity eta o. The disorientation time tau D, after flow has been stopped, is such that the ratio tau D/eta o is independent of the initial applied shear stress. However, tau D is much shorter than one would expect if pure Brownian motion were involved. The proportion of erythrocytes in orbit C = 0 was also measured. It was found that this proportion is a function of both the shear rate and eta o. At low values of eta o, the proportion increases with increasing shear rate and then reaches a plateau. For higher values of eta o (5 to 10 mPa s), the proportion of RBC in orbit C = 0 is a decreasing function of the shear stress. A critical transition between orbit C = 0 and parallel alignment was observed at high values of eta o, when the shear stress is on the order of 1 N/m2. Finally, the effect of altering membrane viscoelastic properties (by heat or diamide treatment) was tested. The proportion of oriented cells is a steep decreasing function of red cell rigidity.     

Experimental investigation of the rheological activation of blood platelets

In order to define various aspects of platelet rheological activation, samples of whole blood and platelet-rich plasma (PRP) from the same donors were subjected for 5 min to shear rates increasing from 10 to 10000 sec-1 (shear stresses from 10(-2) to 30 Pa approximatively) in a Couette type viscometer. The following parameters were measured: erythrocyte hemolysis; lactic dehydrogenase activity; plasma B-Thromboglobulin (B-TG); adenine nucleotides, and platelet photometric aggregation. The experimental results reveal that: In whole blood, hemolysis only reached at maximum 2% of the total hemolysis. Plasma LDH activity increased regularly beyond 500 sec-1, in close correlation with B-TG plasma concentration. In contrast, ADP and ATP levels remained stable up to 1000 sec-1 then increased slowly. In PRP, the LDH, ADP and ATP levels remain practically stable up to shear rates around 5000 sec-1. In contrast, B-TG appeared to be released in plasma at shear rate values of 3000 sec-1 and its progression is only correlated with the other parameters, when the platelet lysis occurred. Finally, a rapid and complete inhibition of platelet aggregation to ADP was observed from 5000 sec-1.     

Relationships between hemorheology, erythrocyte metabolism, and von willebrand factor in athletes and patients with peripheral arterial disease

The relationship between hemorheology, erythrocyte ATP and 2,3-diphosphoglycerate (2,3-DPG) concentrations, and von Willebrand factor antigen was studied in athletes and peripheral arterial disease patients. Lower blood viscosity, mainly due to a higher erythrocyte deformability, was found in athletes compared to control subjects. Higher 2,3-DPG/Ht levels in athletes were correlated with blood viscosity, erythrocyte deformability, the rigidity index, and erythrocyte suspension viscosity at low shear stress. It is suggested that these relationships might be determined by the predominance of immature erythrocytes in the blood circulation of the athletes. In the group of patients, a decrease in ATP/Ht was related to increased erythrocyte aggregation and a higher erythrocyte suspension viscosity. Moreover, the concentration of von Willebrand factor was positively correlated with the erythrocyte aggregation index, erythrocyte suspension viscosity, and plasma viscosity. The results show that alterations in erythrocyte and plasma rheology may be involved in the modification of the functional state of the vascular endothelium and the development of atherosclerosis.     

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.     

Rheological properties of mammalian cell culture suspensions: Hybridoma and HeLa cell lines

Data on viscous (eta') and elastic (eta') components of the complex viscosity versus oscillatory angular frequency (0.01 to 4.0 rad/s) with increasing strains were obtained for hybridoma cell (62'D3) and HeLa cell (S3) suspensions in PBS at 0.9 (mL/mL) cell volume fraction using a Weissenberg rheogoniometer equipped with two parallel plate geometry at ambient temperature. Both cell suspensions exhibited shear thinning behavior. From the measured viscoelastic properties, the yield stress was calculated. Hybridoma cell suspension (15 mum as the mean diameter of cells) showed the yield stress at 550 dyne/cm(2) that was 1.8 times higher than the value of HeLa cell suspension (22 mum mean diameter) as measured at the oscillatory angular frequency, 4.0 rad/s. The apparent viscosities of HeLa cell suspension at four concentrations and varying steady shear rate were also determined using the Brookfield rotational viscometer. The yield stress to steady shear test was about 130 dyne/cm(2) for HeLa cell suspension at 0.9 (mL/mL) cell volume fraction. The apparent viscosity was in the range about 1 approximately 1000 Poise depending on the cell concentration and shear rate applied. A modified semiempirical Mooney equation, \documentclass{article}\pagestyle{empty}\begin{document}$ \eta = \eta _0 \exp [K\dot \gamma ;{ - \beta } \phi /(1 - K'\sigma \phi _c /D)] $\end{document} was derived based on the cell concentration, the cell morphology, and the steady shear rate. The beta, shear rate index, was estimated as 0.159 in the range of shear rate, 0.16 to 22.1 s(-1), for the cell volume fractions from 0.6 to 0.9 (mL/mL). In this study, the methods of determining the shear sensitivity and the viscous and the elastic components of mammalian cell suspensions are described under the steady shear field. (c) 1993 John Wiley & Sons, Inc.     

Aggregation of red blood cells studied by ultrasound backscattering

The erythrocyte aggregation phenomenon is an important factor in capillary circulation. This phenomenon can be evaluated by a number of methods (microscopic observations, viscometry, light measurements) which cannot be applied simply to in vivo measurements. In contrast, ultrasound which propagates through soft tissues allows measurement of the mechanical properties of red blood cell (RBC) suspensions which depend on the aggregation phenomenon. We devised an apparatus in order to measure in vitro the ultrasonic backscattering intensity of RBC suspensions. First, with latex particles of different sizes, the ultrasonic backscattering coefficient has been measured in order to evaluate the apparatus response. Then, the ultrasonic backscattering coefficient of different aggregated erythrocyte suspensions has been measured and correlated with the erythrocyte sedimentation rate. Finally, the size of RBC aggregates of different suspensions has been evaluated.     

Oscillating viscometer--evaluation of a new bedside test

A viscometer for bedside blood measurements was developed, consisting of an oscillating resonator probe mounted directly into a disposable vacutainer tube for blood withdrawal. It was tested in vitro on blood samples with variable hematocrits (20-60%), increasing fibrinogen concentrations (0-20 g/l), increasing concentrations of an admixed radiographic contrast medium and erythrocyte suspensions in dextran 40 and dextran 70. Results were compared with those obtained with a conventional Couette viscometer. Oscillating viscometry yielded generally higher values than Couette viscometry, and had a good sensitivity for changes in hematocrit with a good correlation between the two methods (r=0.96, p<0.0001). Oscillating viscosity depended on the resonator frequency, it was higher at 3900 Hz than at 215 Hz, suggesting a viscoelastic behavior of blood. Erythrocyte aggregation, induced by increasing fibrinogen concentrations or dextran 70, affected oscillating viscometry. At a high frequency, i.e. a smaller penetration depth of the shear wave, oscillating viscosity tended to decrease, which suggests a depletion of the boundary layer from erythrocytes when they aggregate. At low frequency with a deeper shear wave penetration (about 50 microm), erythrocyte aggregation increased oscillating viscosity. Bedside tests in 17 patients with coronary heart disease and 10 controls confirmed the easy practicability of the test and showed lower oscillating viscosity in these patients despite higher fibrinogen concentrations presumably due to increased erythrocyte aggregation. We conclude that oscillating viscometry is an interesting bedside test, which is capable of providing new information on the biorheology of the erythrocyte-poor boundary layer near the vessel wall.     

Measurements of viscosity of synthetic erythrocyte suspensions

Measurements were made of the viscosity of suspensions of synthetic erythrocytes composed of hemoglobin solutions encapsulated in liposomes, as a function of shear rate, temperature, suspension concentration, lipid membrane composition, and the viscosity of the suspending medium. It was found that the viscous behavior of the synthetic erythrocyte suspensions was non-Newtonian and nearly the same as that of suspensions of natural erythrocytes prepared similarly, with the major difference being that synthetic erythrocyte suspensions are somewhat more viscous. Suspensions of Fluosol FC-43 prepared similarly were found to be essentially Newtonian fluids, and substantially different and more viscous than either erythrocyte suspension. The higher viscosity of synthetic erythrocyte suspensions probably accounts for the ability of these suspensions to maintain normal systemic vascular resistance in transfusion experiments, in spite of the fact that synthetic erythrocytes are smaller than natural erythrocytes.     

Effects of aggregation on the flow properties of red blood cell suspensions in narrow vertical tubes

The flow properties of aggregating red cell suspensions flowing at low rates through vertical tubes with diameters from 30 microns to 150 microns are analyzed using a theoretical model. Unidirectional flow is assumed, and the distributions of velocity and red cell concentration are assumed to be axisymmetric. A three-layer approximation is used for the distribution of red cells, with a cylindrical central core of aggregated red cells moving with uniform velocity, a cell-free marginal layer near the tube wall, and an annular region located between the core and the marginal layer containing suspended non-aggregating red cells. This suspension is assumed to behave approximately as a Newtonian fluid whose viscosity increases exponentially with red cell concentration. Physical arguments concerning the mechanics of red cell attachment to, and detachment from the aggregated core lead to a kinetic equation for core formation. From this kinetic equation and the equation for conservation of red cell volume flux, a relationship between core radius and pressure gradient is obtained. Then the relative viscosity is calculated as a function of pseudo-shear rate. At low flow rates, it is shown that the relative viscosity decreases with decreasing flow and that the dependence of relative viscosity on shear rates is more pronounced in larger tubes. It is also found that the relative viscosity decreases with increasing aggregation tendency of suspension. These theoretical predictions are in good qualitative and quantitative agreement with experimental results.