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.     

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.     

Effects of sedimentation of small red blood cell aggregates on blood flow in narrow horizontal tubes

The flow properties of aggregating red cell suspensions flowing at low flow rates through horizontal tubes are analyzed using a theoretical model. The effects of sedimentation of small aggregates, which will be formed at comparatively high flow rates, on the relative apparent viscosity are considered. In the case in which a large number of small aggregates are formed in a suspension flowing through a horizontal tube, it seems that red cells are transported as a concentrated suspension through the bottom part of the tube because of sedimentation of aggregates. A two-layer flow model is used for the distribution of red cells. It consists of plasma in the upper part and a concentrated red cell suspension in the bottom part of the tube divided by a smooth and horizontal interface. It is assumed that the suspension is a Newtonian fluid whose viscosity increases exponentially with hematocrit. The velocity distribution, the relative apparent viscosity and the flux of red cells are calculated as functions of width of plasma layer for a different discharge hematocrit. The theoretical results are compared with the results obtained from experimental data. The relative apparent viscosity increases rapidly with an increasing degree of sedimentation over a wide range of plasma layer widths.     

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.     

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.     

Hemorheological implications of perfluorocarbon based oxygen carrier interaction with colloid plasma expanders and blood

Perfluorocarbon (PFC) emulsions used as artificial oxygen carriers lack colloid osmotic pressure (COP) and must be administered with colloid‐based plasma expanders (PEs). Although PFC emulsions have been widely studied, there is limited information about PFC emulsion interaction with PEs and blood. Their interaction forms aggregates due to electrostatic and rheological phenomena, and change blood rheology and blood flow. This study analyzes the effects of the interaction between PFC emulsions with blood in the presence of clinically‐used PEs. The rheological behavior of the mixtures was analyzed in vitro in parallel with in vivo analysis of blood flow in the microcirculation using intravital microscopy, when PEs were administered in a clinically relevant scenario. The interaction between the PFC emulsion and PE with blood produced PFC droplets and red blood cell (RBCs) aggregation and increased blood viscosity in a shear dependent fashion. The PFC droplets formed aggregates when mixed with PEs containing electrolytes, and the aggregation increased with the electrolyte concentration. Mixtures of PFC with PEs that produced PFC aggregates also induced RCBs aggregation when mixed with blood, increasing blood viscosity at low shear rates. The more viscous suspension at low shear rates produced a blunted blood flow velocity profile in vivo compared to nonaggregating mixtures of PFC and PEs. For the PEs evaluated, human serum albumin produced minimal to undetectable aggregation. PFC and PEs interaction with blood can affect sections of the microcirculation with low shear rates (e.g., arterioles, venules, and pulmonary circulation) when used in a clinical setting, because persistent aggregates could cause capillary occlusion, decreased perfusion, pulmonary emboli or focal ischemia. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29:796–807, 2013     

Effect of aggregation and shear rate on the dispersion of red blood cells flowing in venules

Previous in vitro studies of blood flow in small glass tubes have shown that red blood cells exhibit significant erratic deviations in the radial position in the laminar flow regime. The purpose of the present study was to assess the magnitude of this variability and that of velocity in vivo and the effect of red blood cell aggregation and shear rate upon them. With the use of a gated image intensifier and fluorescently labeled red blood cells in tracer quantities, we obtained multiple measurements of red blood cell radial and longitudinal positions at time intervals as short as 5 ms within single venous microvessels (diameter range 45-75 microm) of the rat spinotrapezius muscle. For nonaggregating red blood cells in the velocity range of 0.3-14 mm/s, the mean coefficient of variation of velocity was 16.9 +/- 10.5% and the SD of the radial position was 1.98 +/- 0.98 microm. Both quantities were inversely related to shear rate, and the former was significantly lowered on induction of red blood cell aggregation by the addition of Dextran 500 to the blood. The shear-induced random movements observed in this study may increase the radial transport of particles and solutes within the bloodstream by orders of magnitude.     

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.     

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.     

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.     

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.     

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.     

Effect of erythrocyte aggregation on velocity profiles in venules

A recent whole organ study in cat skeletal muscle showed that the increase in venous resistance seen at reduced arterial pressures is nearly abolished when the muscle is perfused with a nonaggregating red blood cell suspension. To explore a possible underlying mechanism, we tested the hypothesis that red blood cell aggregation alters flow patterns in vivo and leads to blunted red blood cell velocity profiles at reduced shear rates. With the use of fluorescently labeled red blood cells in tracer quantities and a video system equipped with a gated image intensifier, we obtained velocity profiles in venous microvessels (45-75 microm) of rat spinotrapezius muscle at centerline velocities between 0.3 and 14 mm/s (pseudoshear rates 3-120 s(-1)) under normal (nonaggregating) conditions and after induction of red blood cell aggregation with Dextran 500. Profiles are nearly parabolic (Poiseuille flow) over this flow rate range in the absence of aggregation. When aggregation is present, profiles are parabolic at high shear rates and become significantly blunted at pseudoshear rates of 40 s(-1) and below. These results indicate a possible mechanism for increased venous resistance at reduced flows.     

Effect of microrheology of blood on the apparent flow instability in a rotational viscometer

Flow instability (formation of vortices and a concurrent increase in the apparent viscosity) was studied in the rotational rhombospheroid viscometer of 3 degrees, 5 degrees and 10 degrees gaps over a range of speeds from 10 to 300 r.p.m.. Comparisons between different blood systems were carried out mainly at 250 r.p.m. Experiments were carried out on blood samples obtained directly from human subjects, or from the Blood Bank, or from horses. Reconstituted suspensions of red cells in albumin or dextran were also used. Apparent flow instability was found to be not solely a function of blood viscosity, but a multiple function of many viscosity factors or blood subphases, including instability-decreasing factors such as haematocrit and aggregation of red cells; and instability-increasing factors such as rigidity of red cells; and thus specific to and characteristic of individual blood samples. Apparent instability can be described by multiple regressions as a function, Z, of red cell rigidity, Tk, blood viscosity, napp, and aggregation of red cells, AG; for example: Z = -28.29 + 26.24 Tk + 0.109 napp (r = 0.816; P less than 0.001), or Z = 5.90 - 0.0165 AG - 0.752 napp (r = 0.573; P less than 0.05). The apparent instability can be seen only in one-third of blood samples obtained from horses, and in more than half of blood samples obtained from human donors; majority of human donors shows apparent instability below 3 per cent.     

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.     

3-D computational modeling of media flow through scaffolds in a perfusion bioreactor

Media perfusion bioreactor systems have been developed to improve mass transport throughout three-dimensional (3-D) tissue-engineered constructs cultured in vitro. In addition to enhancing the exchange of nutrients and wastes, these systems simultaneously deliver flow-mediated shear stresses to cells seeded within the constructs. Local shear stresses are a function of media flow rate and dynamic viscosity, bioreactor configuration, and porous scaffold microarchitecture. We have used the Lattice-Boltzmann method to simulate the flow conditions within perfused cell-seeded cylindrical scaffolds. Microcomputed tomography imaging was used to define the scaffold microarchitecture for the simulations, which produce a 3-D fluid velocity field throughout the scaffold porosity. Shear stresses were estimated at various media flow rates by multiplying the symmetric part of the gradient of the velocity field by the dynamic viscosity of the cell culture media. The shear stress algorithm was validated by modeling flow between infinite parallel plates and comparing the calculated shear stress distribution to the analytical solution. Relating the simulation results to perfusion experiments, an average surface shear stress of 5x10(-5)Pa was found to correspond to increased cell proliferation, while higher shear stresses were associated with upregulation of bone marker genes. This modeling approach can be used to compare results obtained for different perfusion bioreactor systems or different scaffold microarchitectures and may allow specific shear stresses to be determined that optimize the amount, type, or distribution of in vitro tissue growth.     

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.     

A dynamical study of the mechanical stimuli and tissue differentiation within a CaP scaffold based on micro-CT finite element models

The control of the mechanical stimuli transmitted to the cells is critical for the design of functional scaffolds for tissue engineering. The objective of this study was to investigate the dynamics of the mechanical stimuli transmitted to the cells during tissue differentiation in an irregular morphology scaffold under compressive load and perfusion flow. A calcium phosphate-based glass porous scaffold was used. The solid phase and the fluid flow within the pores were modeled as linear elastic solid material and Newtonian fluid, respectively. In the fluid model, different levels of viscosity were used to simulate tissue differentiation. Compressive strain of 0.5% and fluid flow with constant inlet velocity of 10 μm/s or constant inlet pressure of 3 Pa were applied. Octahedral shear strain and fluid shear stress were used as mechano-regulatory stimuli. For constant inlet velocity, stimuli equivalent to bone were predicted in 80% of pore volume for the case of low tissue viscosity. For the cases of high viscosity, fluctuations between stimuli equivalent to tissue formation and cell death were predicted due to the increase in the fluid shear stress when tissue started to fill pores. When constant pressure was applied, stimuli equivalent to bone were predicted in 62% of pore volume when low tissue viscosity was used and 42% when high tissue viscosity was used. This study predicted critical variations of fluid shear stress when cells differentiated. If these variations are not controlled in vitro, they can impede the formation of new matured tissue.     

Viscoelasticity of Human Blood

Measurements made for oscillatory flow of blood in circular tubes show that blood possesses elastic properties which make consideration of its viscous properties alone inadequate. Results are for a frequency of 10 Hz while varying the amplitude of the velocity gradient for red blood cells in plasma at concentrations ranging from 0 to 100% apparent hematocrit. For velocity gradients less than 1-2 sec^-1 both the viscous and elastic components of the shearing stress are linearly related to the gradient. For hematocrits above 20% the elastic component of the complex coefficient of viscosity increases with hematocrit approximately to the third power while the viscous component increases exponentially. Oscillatory flow measurements at very low hematocrits, when extrapolated to zero cell concentration, give the intrinsic viscosity of the average individual isolated red cell. The viscous part of this is found to be 1.7 which is compared with theoretical values from the rigid ellipsoid model for which the minimum possible value is 2.5. This difference is attributed to cell deformability. With increasing velocity gradient nonlinear properties develop. The viscous component of the complex viscosity becomes of the order of the steady flow viscosity at high gradients while the elastic component tends to decrease in inverse proportion to the gradient. Thus, the elastic component of the oscillatory stress tends to saturate, this tendency appearing at the approximate level of the yield stress.     

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.