Radial displacement of red blood cells during hemodilution and the effect on arteriolar oxygen profile

In this study, we assessed the magnitude of the erratic deviations in the radial position of red blood cells (RBCs) in the laminar flow regime of arterioles in a hamster window preparation and the intraluminal Po(2) profile to determine whether this variability affects the intraluminal distribution of oxygen in conditions of normal hematocrit and hemodilution. A gated image intensifier was used to visualize fluorescently labeled RBCs in tracer quantities and obtain multiple measurements of RBC radial and longitudinal positions at time intervals on the order of 5 ms within single arterioles (diameter range 40-95 microm). RBCs in the velocity range of 0.3-14 mm/s exhibit a mean coefficient of variation of velocity of 16.9 +/- 10.5% and a SD of the radial position of 1.98 +/- 0.98 microm. Both quantities were inversely related to hematocrit, and the former was significantly lowered by hemodilution. Our experimental results presented very similar values and shape compared with the intraluminal oxygen profile derived theoretically for normal hematocrit, suggesting that shear-augmented diffusion due to the measured radial displacement of RBCs did not significantly affect oxygen diffusion from blood into the arteriolar vessel wall. Po(2) profiles in the arterioles assumed an increasingly parabolic configuration with increasing levels of hemodilution.     

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.     

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.     

Relationship between erythrocyte aggregate size and flow rate in skeletal muscle venules

In previous studies we showed that intravenous infusion of Dextran 500 in the rat causes blunting of the velocity profile of red blood cells in venules at low shear rates. To determine whether this blunting is associated with the formation of red blood cell aggregates, we measured the length and width of particles in the venular flow stream at systemic hematocrits up to 20% with a high-speed video camera and a new image analysis technique. Data were obtained at various shear rates under normal (nonaggregating) conditions as well as after infusion of Dextran 500. Under normal conditions, particle length (parallel to the vessel axis) was 6.5 +/- 2.7 microm and width (perpendicular to the axis) was 6.1 +/- 1.7 microm, in agreement with published dimensions of individual red blood cells for this species. After Dextran 500 infusion, particle length and width increased significantly to 8.7 +/- 5.1 and 10.4 +/- 4.4 microm, respectively. Particle dimensions were greater in the central region of the flow stream for both normal and dextran-treated blood and increased at low flow rates with dextran-treated blood. This study provides direct confirmation of aggregate formation at low shear in venules with high-molecular-weight dextran as well as an estimate of aggregate size and range.     

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.     

Determination of microvascular flow pattern formation in vivo

Blood flow in microvessels differs significantly from that of red blood cells (RBC) flowing through long, straight glass tubes in vitro. The in vivo situation is characterized by the presence of plasma favoring aggregation, by the irregular geometry of vessel segments, and by frequent branching points. Here, a method is presented to characterize flow patterns in microvascular blood flow during intravital microscopy based on Fourier analysis of recorded light intensity patterns. The interpretation of the resulting power spectra in terms of pattern size distribution was validated by model experiments employing artificial textures and by reverse transformation of idealized spectra. The determined size of RBC flow patterns in microvessels ranged from approximately 8 microm in capillaries to approximately 14 microm in vessels of >30 microm. With increasing shear rate above approximately 100 s(-1) pattern size increased, possibly reflecting formation of short-lived flow clusters. Below approximately 100 s(-1) an increase of pattern size with decreasing shear rate was found in experiments using local occlusion and treatment with high-molecular-weight dextran, suggesting the formation of aggregates. The dynamic process of generation and destruction of RBC flow patterns could well contribute to flow resistance in vivo in peripheral vascular beds.     

Rheological properties of the blood influencing selectin-mediated adhesion of flowing leukocytes

We studied how the rheological properties of blood influenced capture and rolling adhesion of leukocytes as well as their margination in the bloodstream. When citrated, fluorescently labeled blood was perfused through glass capillaries coated with P-selectin, leukocytes formed numerous rolling attachments. The number of attached leukocytes increased as the hematocrit was increased between 10% and 30% and was essentially constant from 30% to 50%. In EDTA-treated blood, adhesion was absent, and the flux of marginated cells varied little with increasing hematocrit. However, the velocity of marginated leukocytes increased monotonically, whereas the volumetric flow rate was constant, implying that the flow velocity profile became blunted and wall shear rate increased. Thus increasing hematocrit promoted attachment for a given total flow rate, without increasing margination, even though wall shear rate and blood viscosity increased. Blood was diluted to 20% hematocrit with plasma, 40-kDa dextran (to reduce red blood cell aggregation), or 500-kDa dextran (to enhance aggregation). Increasing aggregation correlated with increasing leukocyte adhesion and with more slow-flowing leukocytes near the wall. Thus flowing erythrocytes promote leukocyte adhesion, either by causing margination of leukocytes or by initiating and stabilizing attachments that follow.     

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.     

Cell-free layer and wall shear stress variation in microvessels

In this study, we simulated multiple red blood cells flowing through straight microvessels with the immersed-boundary lattice-Boltzmann model to examine the shear stress variation on the microvessel surface and its relation to the properties of cell-free layer. Significant variation in shear stress has been observed due to the irregular configuration of blood cells flowing near the microvessel wall. A low shear stress is typically found at locations where there is a cell flowing close to the wall, and a large shear stress at locations with a relatively wide gap between cell and wall. This relationship between the shear stress magnitude and the distance between cell and wall has been attributed to the reverse pressure difference developed between the front and rear sides of a cell flowing near the vessel wall. We further studied the effects of several hemodynamic factors on the variation of shear stress, including the cell deformability, the flow rate, and the aggregation among red blood cells. These simulations show that the shear stress variation is less profound in situations with wider cell-free layers, since the reverse pressure difference around the edge cells is less evident, and the influence of this pressure difference on wall shear stress becomes weaker. This study also demonstrates the complexity of the flow field in the gap between cell and wall. More precise experimental techniques are required accurately measure such shear stress variation in microcirculation.     

Velocity pulse advances pressure pulse by close to 45 degrees in the rat pial arterioles

In order to clarify the phase relationship between velocity pulse and pressure pulse propagating along microvessels, the red cell velocity and intravascular pressure were simultaneously measured in the rat pial arterioles of 41-53 microm in diameter with a high temporal resolution by a laser-Doppler anemometer and a servo-null micropressure system. It was found that the velocity pulse preceded the pressure pulse in all the measured arterioles by 18.7-35.6 ms. The corresponding phase difference was 43.6+/-6.9 degrees (mean +/- SD), which is not statistically different from 45 degrees. The value is consistent with the phase difference predicted for the blood flow in microvessels with a small reflection coefficient at frequencies as low as the heart rate of the rats. The present results suggest that the upstream changes in blood flow are transmitted by the velocity pulse faster than by the pressure pulse in the microvasculature.     

Tank-tread frequency of the red cell membrane: dependence on the viscosity of the suspending medium

Single human red cells were suspended in media with viscosities ranging from 12.9 to 109 mPa s and subjected to shear flow ranging from 1/s to 290/s in a rheoscope. This is a transparent cone-plate chamber adapted to a microscope. The motion of the membrane around red cells oriented in a steady-state fashion in the shear field (tank-tread motion) was videotaped. The projected length and width of the cells as well as the frequency of tank-tread motion were measured. One-thousand eight-hundred seventy-three cells of three blood donors were evaluated. The frequency increased with the mean shear rate in an almost linear fashion. The slope of this dependence increased weakly with the viscosity of the suspending medium. No correlation was found between the frequency and four morphological red cell parameters: the projected length and width of the cells as well as the ratio and the square root of the product of these quantities. The energy dissipation within the red cell membrane was estimated based on the measured parameters and compared to the energy dissipation in the undisturbed shear flow. At constant mean shear rate the rise of the energy dissipation with viscosity is slower whereas at constant viscosity the rise with the shear rate is steeper than in the undisturbed shear flow. A fit of the data collected in this work to a theoretical red cell model might allow one to determine intrinsic mechanical constants in the low deformation regime.     

A reevaluation and discussion on the threshold limit for hemolysis in a turbulent shear flow

One major factor of red blood cell damage induced by artificial heart valves is the magnitude of turbulent shear stresses in the flow field. An often-cited threshold for hemolysis is 400 N/m(2) (Sallam and Hwang, Biorheology 21 (1984) 783). This value, however, was measured with a one-component laser Doppler anemometer and was not calculated from the major principal Reynolds shear stress, therefore underestimating the threshold. This study performed flow field measurements under similar conditions, using a two-component laser Doppler anemometer and determining major principal Reynolds shear stress, to reevaluate the hemolytic threshold as 800 N/m(2) with an exposure time of 1 ms. The Kolmogorov length scales, approximately 9 microm, are capable of inflicting direct damage to the red blood cells. These results will serve as a more accurate reference in future heart valve design and testing.     

Shear‐induced diffusion of red blood cells measured with dynamic light scattering‐optical coherence tomography

Quantitative measurements of intravascular microscopic dynamics, such as absolute blood flow velocity, shear stress and the diffusion coefficient of red blood cells (RBCs), are fundamental in understanding the blood flow behavior within the microcirculation, and for understanding why diffuse correlation spectroscopy (DCS) measurements of blood flow are dominantly sensitive to the diffusive motion of RBCs. Dynamic light scattering‐optical coherence tomography (DLS‐OCT) takes the advantages of using DLS to measure particle flow and diffusion within an OCT resolution‐constrained three‐dimensional volume, enabling the simultaneous measurements of absolute RBC velocity and diffusion coefficient with high spatial resolution. In this work, we applied DLS‐OCT to measure both RBC velocity and the shear‐induced diffusion coefficient within penetrating venules of the somatosensory cortex of anesthetized mice. Blood flow laminar profile measurements indicate a blunted laminar flow profile and the degree of blunting decreases with increasing vessel diameter. The measured shear‐induced diffusion coefficient was proportional to the flow shear rate with a magnitude of ~0.1 to 0.5 × 10^?6 mm². These results provide important experimental support for the recent theoretical explanation for why DCS is dominantly sensitive to RBC diffusive motion.      

Effect of Dextran 500 on Radial Migration of Erythrocytes in Postcapillary Venules at Low Flow Rates

Recently, we reported that collision efficiency (fraction of total collisions that result in the formation of aggregates) between red blood cells was an important factor in the formation of aggregates in postcapillary venules. In the present study, we focus on how high molecular weight dextran influences the overall radial migration trend of red blood cells in the postcapillary venule along a longitudinal distance of 50 μm from the bifurcation which would in turn affect collision behavior of these cells. A radial migration index, which defines the extent of radial migration of individual cells relative to the vessel center, was found to have a larger magnitude after infusion of dextran (1.9 ± 2.73) compared to that before dextran infusion (1.48 ± 3.89). This implied that dextran-induced aggregation might provide an external force to actively move cells towards the centerline of the vessel, which could contribute to the greater number of red blood cells participating in collision (16% increase) and aggregate formation. Further analysis of the collision behavior of individual red blood cells revealed that collision frequencies of individual cells decreased from a wide range (1 to 14) to a narrow range (1 to 5) after dextran treatment, indicating the alteration of collision behavior of red blood cells by the presence of aggregates along the flow stream.     

Effect of erythrocyte aggregation at normal human levels on functional capillary density in rat spinotrapezius muscle

Previous studies have shown that functional capillary density (FCD) is substantially reduced by erythrocyte aggregation. However, only supranormal levels of aggregability were studied. To investigate the effect of erythrocyte aggregability at the level seen in healthy humans, the FCD of selected capillary fields in rat spinotrapezius muscle was determined with high-speed video microscopy under normal (nonaggregating) conditions and after induction of erythrocyte aggregation with Dextran 500 (200 mg/kg). To examine shear rate dependence, the effect was studied both at normal and reduced arterial pressures (50 and 25 mmHg), the latter achieved by short periods of hemorrhage. In a separate study, volume flow was determined in arterioles (52.1 +/- 3.7 microm) under the same conditions. Before Dextran 500 infusion, FCD fell to 91% and 76% of control values, respectively, when arterial pressure was reduced to 50 and 25 mmHg. After Dextran 500 infusion, FCD was 96% at normal arterial pressure and fell to 79% and 37% of normal control values at 50 and 25 mmHg. All FCD values were significantly lower after dextran infusion. FCD reduction after lowering arterial pressure or dextran infusion appeared to be due to plasma skimming rather than capillary plugging. Reduction of FCD by dextran at reduced pressure was compensated by increased red blood cell flux in capillaries with red blood cell flow. We conclude that the level of aggregability seen in healthy humans is an important determinant of FCD only at reduced arterial pressure.     

Temporal and spatial variations of cell-free layer width in arterioles

Separation of red blood cells and plasma in microcirculatory vessels produces a cell-free layer at the wall. This layer may be an important determinant of blood viscosity and wall shear stress in arterioles, where most of the hydraulic pressure loss in the circulatory system occurs and flow regulatory mechanisms are prominent. With the use of a newly developed method, the width of the cell-free layer was rapidly and repeatedly determined in arterioles (10- to 50-microm inner diameter) in the rat cremaster muscle at normal arterial pressure. The temporal variation of the cell-free layer width was non-Gaussian, but calculated mean and median values differed by <0.2 microm. The correlation length of the temporal variations downstream (an indication of mixing) was approximately 30 microm and was independent of pseudoshear rate (ratio of mean velocity to vessel diameter) and of vessel diameter. The cell-free layer width was significantly different on opposite sides of the vessel and inversely related. Increasing red blood cell aggregability reduced this inverse relation but had no effect on correlation length. In the diameter range studied, the mean width of the cell-free layer increased from 0.8 to 3.1 microm and temporal variations increased from 30% to 70% of the mean width. Increased aggregability did not alter either relationship. In summary, the cell-free layer width in arterioles is diameter dependent and shows substantial non-Gaussian temporal variations. The temporal variations increase as diameter increases and are inversely related on opposite sides of the vessel.     

Diameter changes in skeletal muscle venules during arterial pressure reduction

Previous studies in skeletal muscle have shown a substantial (>100%) increase in venous vascular resistance with arterial pressure reduction to 40 mmHg, but a microcirculatory study showed no significant venular diameter changes in the horizontal direction during this procedure. To examine the possibility of venular collapse in the vertical direction, a microscope was placed horizontally to view a vertically mounted rat spinotrapezius muscle preparation. We monitored the diameters of venules (mean diameter 73. 8 +/- 37.0 microm, range 13-185 microm) oriented horizontally and vertically with a video system during acute arterial pressure reduction by hemorrhage. Our analysis showed small but significant (P < 0.0001) diameter reductions of 1.0 +/- 2.5 microm and 1.8 +/- 3. 1 microm in horizontally and vertically oriented venules, respectively, upon reduction of arterial pressure from 115.0 +/- 26. 3 to 39.8 +/- 12.3 mmHg. The venular responses were not different after red blood cell aggregation was induced by Dextran 500 infusion. We conclude that diameter changes in venules over this range of arterial pressure reduction are isotropic and would likely increase venous resistance by <10%.     

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.     

Effect of secondary flow on biological experiments in the cone-plate viscometer: methods for estimating collision frequency, wall shear stress and inter-particle interactions in non-linear flow.

We present a theoretical analysis of fluid flow and particle interactions in the cone-plate viscometer under conditions typically applied in biological studies. The analysis demonstrates that at higher shear rates, besides linear primary flow in the rotational direction, prominent non-linear secondary flow causes additional fluid circulation in the radial direction. Two parameters, the cone angle and Reynolds number, characterize flow in the viscometer over all ranges of shear rate. Our results indicate that secondary flow causes positional variations in: (i) the velocity gradient, (ii) the direction and magnitude of the wall shear stress at the plate surface, (iii) inter-particle collision frequency, (iv) magnitude and periodicity of normal and shear forces applied during particle-particle interactions, and (v) inter-particle attachment times. Thus, secondary flow may significantly influence cellular aggregation, platelet activation and endothelial cell mechanotransduction measurements. Besides cone-plate viscometers, this analysis methodology can also be extended to other experimental systems with complex non-linear flows.     

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.