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.     

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.     

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

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

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.     

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.     

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.     

Effect of the endothelial surface layer on transmission of fluid shear stress to endothelial cells

Responses of vascular endothelial cells to mechanical shear stresses resulting from blood flow are involved in regulation of blood flow, in structural adaptation of vessels, and in vascular disease. Interior surfaces of blood vessels are lined with a layer of bound or adsorbed macromolecules, known as the endothelial surface layer (ESL). In vivo investigations have shown that this layer has a width of order 1 microm, that it substantially impedes plasma flow, and that it excludes flowing red blood cells. Here, the effect of the ESL on transmission of shear stress to endothelial cells is examined using a theoretical model. The layer is assumed to consist of a matrix of molecular chains extending from the surface, held in tension by a slight increase in colloid osmotic pressure relative to that in free-flowing plasma. It is shown that, under physiological conditions, shear stress is transmitted to the endothelial surface almost entirely by the matrix, and fluid shear stresses on endothelial cell membranes are very small. Rapid fluctuations in shear stress are strongly attenuated by the layer. The ESL may therefore play an important role in sensing of shear stress by endothelial cells.     

Micro-PTV Measurement of the Fluid Shear Stress Acting on Adherent Leukocytes In Vivo

Leukocyte adhesion is determined by the balance between molecular adhesive forces and convective dispersive forces. A key parameter influencing leukocyte adhesion is the shear stress acting on the leukocyte. This measure is indispensable for determining the molecular bond forces and estimating cell deformation. To experimentally determine this shear stress, we used microparticle tracking velocimetry analyzing more than 24,000 images of 0.5 μm fluorescent microbeads flowing within mildly inflamed postcapillary venules of the cremaster muscle in vivo. Green fluorescent protein, expressed under the lysozyme-M promoter, made leukocytes visible. After applying stringent quality criteria, 3 of 69 recordings were fully analyzed. We show that endothelial cells, but not leukocytes, are covered by a significant surface layer. The wall shear rate is nearly zero near the adherent arc of each leukocyte and reaches a maximum at the apex. This peak shear rate is 2-6-fold higher than the wall shear rate in the absence of a leukocyte. Microbead trajectories show a systematic deviation toward and away from the microvessel axis upstream and downstream from the leukocyte, respectively. The flow field around adherent leukocytes in vivo allows more accurate estimates of bond forces in rolling and adherent leukocytes and improved modeling studies.     

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.     

Numerical simulation of two-phase non-Newtonian blood flow with fluid-structure interaction in aortic dissection

The behavior of blood cells and vessel compliance significantly influence hemodynamic parameters, which are closely related to the development of aortic dissection. Here the two-phase non-Newtonian model and the fluid-structure interaction (FSI) method are coupled to simulate blood flow in a patient-specific dissected aorta. Moreover, three-element Windkessel model is applied to reproduce physiological pressure waves. Important hemodynamic indicators, such as the spatial distribution of red blood cells (RBCs) and vessel wall displacement, which greatly influence the hemodynamic characteristics are analyzed. Results show that the proximal false lumen near the entry tear appears to be a vortex zone with a relatively lower volume fraction of RBCs, a low time-averaged wall shear stress (TAWSS) and a high oscillatory shear index (OSI), providing a suitable physical environment for the formation of atherosclerosis. The highest TAWSS is located in the narrow area of the distal true lumen which might cause further dilation. TAWSS distributions in the FSI model and the rigid wall model show similar trend, while there is a significant difference for the OSI distributions. We suggest that an integrated model is essential to simulate blood flow in a more realistic physiological environment with the ultimate aim of guiding clinical treatment.     

Wall shear stress in backward-facing step flow of a red blood cell suspension.

An experimental investigation of the wall shear stress distribution downstream of a backward-facing step is carried out. The wall shear stress distribution was determined by measuring the deformation of a gel layer, attached to the wall downstream of the step. Speckle pattern interferometry was applied to measure the deformation of the gel layer. The measured deformation, combined with the properties of the gel layer, served as an input for a finite element solid mechanics computation to determine the stress distribution in the gel layer. The wall shear stress, required to generate the measured deformation of the gel layer, was determined from these computations. A Newtonian buffer solution and a non-Newtonian red blood cell suspension were used as measuring fluids. The deformation of the gel layer was determined for a Newtonian buffer solution to evaluate the method and to obtain the properties of the gel layer. Subsequently, the wall shear stress distribution for the non-Newtonian red blood cell suspension was determined for three different flow rates. The inelastic non-Newtonian Carreau-Yasuda model served as constitutive model for the red blood cell suspension. Using this model, the velocity and wall shear stress distribution were computed by means of a finite element fluid mechanics computation. From the comparison between the numerical and the experimental results, it can be concluded that wall shear stresses, induced by the red blood cell suspension, can be modeled accurately by employing a Carreau-Yasuda model.     

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.     

The fluid shear stress distribution on the membrane of leukocytes in the microcirculation

Recent in-vivo and in-vitro evidence indicates that fluid shear stress on the membrane of leukocytes has a powerful control over several aspects of their cell function. This evidence raises a question about the magnitude of the fluid shear stress on leukocytes in the circulation. The flow of plasma on the surface of a leukocyte at a very low Reynolds number is governed by the Stokes equation for the motion of a Newtonian fluid. We numerically estimated the distribution of fluid shear stress on a leukocyte membrane in a microvessel for the cases when the leukocyte is freely suspended, as well as rolling along or attached to a microvessel wall. The results indicate that the fluid shear stress distribution on the leukocyte membrane is nonuniform with a sharp increase when the leukocyte makes membrane attachment to the microvessel wall. In a microvessel (10 microns diameter), the fluid shear stress on the membrane of a freely suspended leukocyte (8 microns diameter) is estimated to be several times larger than the wall shear stress exerted by the undisturbed Poiseuille flow, and increases on an adherent leukocyte up to ten times. High temporal stress gradients are present in freely suspended leukocytes in shear flow due to cell rotation, which are proportional to the local shear rate. In comparison, the temporal stress gradients are reduced on the membrane of leukocytes that are rolling or firmly adhered to the endothelium. High temporal gradients of shear stress are also present on the endothelial wall. At a plasma viscosity of 1 cPoise, the peak shear stresses for suspended and adherent leukocytes are of the order of 10 dyn/cm2 and 100 dyn/cm2, respectively.     

血浆层对血管壁剪应力和剪应力梯度的影响

在细小血管中,由于血细胞明显的趋轴效应,管中的血液分为两个不同的区域,即具有血细胞的核心区和邻近管壁和血浆层。应用两相分层流模型,研究在相同的流量和管径下,当核心区中的血液分别为牛顿流体和Casson流体时,不同的血浆层厚度对细小血管壁剪应力和剪应力梯度的影响。结果表明,血浆层的存在对壁剪应力和壁剪应力梯度有较大影响,当血浆层厚度仅为血管半径的1％和3％时,壁剪应力梯度分别下降约10％和20％。     

FLUID SHEAR-STIMULATED DINOFLAGELLATE BIOLUMINESCENCE

Bioluminescence studies provide insight into the properties of water motion that are stimulatory to flow-sensitive organisms such as dinoflagellates, the most common sources of near-surface oceanic bioluminescence. Previous laboratory studies employing steady flows have characterized the luminescent response of dinoflagellates in terms of shear stress. In the present study, computational and experimental approaches were used to investigate the contributions of shear and acceleration to cells responding in a laminar converging flow field, where regions of high acceleration and shear are spatially separated. Flow-stimulated flashes by the dinoflagellates Lingulodinium polyedrum and Ceratocorys horrida were used as a near-instantaneous monitor of cell response. By combining video analysis of flash trajectories with computational methods, the location of each stimulated cell was determined and flow parameters at that location were calculated. Based on several criteria, shear stress was considered the flow parameter most stimulatory to cells. For both dinoflagellates species and for all flow rates, essentially all cells responded downstream near the wall where shear stress levels were maximal, and levels of acceleration and extensional stress were as much as two orders of magnitude less than locations away from the wall. Minimum shear stress levels at the cell positions were consistent with response thresholds based on previous studies. Bioluminescence is an excellent tool for examining how organisms respond to flow at the small temporal and spatial scales relevant to planktonic organisms.     

Non-Newtonian Blood Flow in Left Coronary Arteries with Varying Stenosis: A Comparative Study

This paper presents Computational fluid dynamic (CFD) analysis of blood flow in three different 3-D models of left coronary artery (LCA). A comparative study of flow parameters (pressure distribution, velocity distribution and wall shear stress) in each of the models is done for a non-Newtonian (Carreau) as well as the Newtonian nature of blood viscosity over a complete cardiac cycle. The difference between these two types of behavior of blood is studied for both transient and steady states of flow. Additionally, flow parameters are compared for steady and transient boundary conditions considering blood as non-Newtonian fluid. The study shows that the highest wall shear stress (WSS), velocity and pressure are found in artery having stenosis in all the three branches of LCA. The use of Newtonian blood model is a good approximation for steady as well as transient blood flow boundary conditions if shear rate is above 100 s-1. However, the assumption of steady blood flow results in underestimating the values of flow parameters such as wall shear stress, pressure and velocity.     

Geometrical focusing of cells in a microfluidic device: an approach to separate blood plasma

It is well known that when a suspension of cells flows in small vessels (arterioles or venules), there exists a cell-free layer of a few microns adjacent to the vascular walls. Using an in vitro model, we show experimentally that for a fixed flow rate a geometrical constriction in the flow can artificially enhance the cell-free layer. Also, we show that rapid variation of the geometry coupled to the deformability of the cells can dramatically modify their spatial distribution in the channel. The effects of the constriction geometry, flow rate, suspending fluid viscosity, cell concentration, and cell deformability are studied and the results are interpreted in terms of a model of the hydrodynamic drift of an ellipsoidal cell in a shear flow. We propose a microfluidic application of this focusing effect for separation of the red blood cells from the suspending plasma.     

Introducing shear stress in the study of bacterial adhesion

During bacterial infections a sequence of interactions occur between the pathogen and its host. Bacterial adhesion to the host cell surface is often the initial and determining step of the pathogenesis. Although experimentally adhesion is mostly studied in static conditions adhesion actually takes place in the presence of flowing liquid. First encounters between bacteria and their host often occur at the mucosal level, mouth, lung, gut, eye, etc. where mucus flows along the surface of epithelial cells. Later in infection, pathogens occasionally access the blood circulation causing life-threatening illnesses such as septicemia, sepsis and meningitis. A defining feature of these infections is the ability of these pathogens to interact with endothelial cells in presence of circulating blood. The presence of flowing liquid, mucus or blood for instance, determines adhesion because it generates a mechanical force on the pathogen. To characterize the effect of flowing liquid one usually refers to the notion of shear stress, which is the tangential force exerted per unit area by a fluid moving near a stationary wall, expressed in dynes/cm(2). Intensities of shear stress vary widely according to the different vessels type, size, organ, location etc. (0-100 dynes/cm(2)). Circulation in capillaries can reach very low shear stress values and even temporarily stop during periods ranging between a few seconds to several minutes (1). On the other end of the spectrum shear stress in arterioles can reach 100 dynes/cm(2)(2). The impact of shear stress on different biological processes has been clearly demonstrated as for instance during the interaction of leukocytes with the endothelium (3). To take into account this mechanical parameter in the process of bacterial adhesion we took advantage of an experimental procedure based on the use of a disposable flow chamber (4). Host cells are grown in the flow chamber and fluorescent bacteria are introduced in the flow controlled by a syringe pump. We initially focused our investigations on the bacterial pathogen Neisseria meningitidis, a Gram-negative bacterium responsible for septicemia and meningitis. The procedure described here allowed us to study the impact of shear stress on the ability of the bacteria to: adhere to cells (1), to proliferate on the cell surface (5)and to detach to colonize new sites (6) (Figure 1). Complementary technical information can be found in reference 7. Shear stress values presented here were chosen based on our previous experience(1) and to represent values found in the literature. The protocol should be applicable to a wide range of pathogens with specific adjustments depending on the objectives of the study.     

In?Vitro Measurement of Particle Margination in the Microchannel Flow: Effect of Varying Hematocrit

It has long been known that platelets undergo margination when flowing in blood vessels, such that there is an excess concentration near the vessel wall. We conduct experiments and three-dimensional boundary integral simulations of platelet-sized spherical particles in a microchannel 30 μm in height to measure the particle-concentration distribution profile and observe its margination at 10%, 20%, and 30% red blood cell hematocrit. The experiments involved adding 2.15-μm-diameter spheres into a solution of red blood cells, plasma, and water and flowing this mixture down a microfluidic channel at a wall shear rate of 1000 s⁻¹. Fluorescence imaging was used to determine the height and velocity of particles in the channel. Experimental results indicate that margination has largely occurred before particles travel 1 cm downstream and that hematocrit plays a role in the degree of margination. With simulations, we can track the trajectories of the particles with higher resolution. These simulations also confirm that margination from an initially uniform distribution of spheres and red blood cells occurs over the length scale of O(1 cm), with higher hematocrit showing faster margination. The results presented here, from both experiments and 3D simulations, may help explain the relationship between bleeding time in vessel trauma and red blood cell hematocrit as platelets move to a vessel wall.     

Flow around cells adhered to a microvessel wall. I. Fluid stresses and forces acting on the cells

To evaluate the fluid forces acting on cells adhered to a microvessel wall, we numerically studied the flow field around adherent cells and the distribution of the stresses on their surfaces. For simplicity, the cells were modeled as rigid particles attached to a wall of a circular cylindrical tube regularly in the flow direction, in a row or two rows. It was found that not the detailed shape of the model cells but their height from the vessel wall is a key determinant of the fluid forces and torque acting on them. In both arrangements of one row and two rows, the axial spacing between neighboring adherent cells significantly affects the distributions of the stresses on them, which results in drastic variations of the fluid forces with the axial spacing and the relative positions with respect to their neighboring cells. The drag force acting on an adherent cell in the vessel was evaluated to be larger than the value in the 2D chamber flow at the same wall shear stress, mainly due to much larger variations of the pressure distribution on the cell surface in the vessel flow.