A study of non-Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases

Blood flow through a stenosed artery has been investigated in this paper. Blood has been represented by a non-Newtonian fluid obeying Herschel-Bulkley equation. This model has been used to study the influence of the fluid behaviour index n, shear-dependent nonlinear viscosity K and the yield stress tau H in blood flow through stenosed arteries. The variation of the wall shear stress and the flow resistance with n, K and tau H has been shown graphically. It is observed that the wall shear stress and the flow resistance increase in Herschel-Bulkley fluid in comparison with corresponding Newtonian fluid. It is of interest to note that, in the present model, the thickness of the plug core varies with the axial distance z in the stenotic region. Finally, some biological implications of the present model for some arterial diseases have been briefly discussed.     

Velocities and stress levels of axisymmetric, azimuthal flow within the toroidal rotary seal of the IBM 2997 continuous flow cell separator and the implications

Continuous flow blood fraction separators are used to facilitate the removal of specific blood components for donation or for certain medical procedures. Problems with one such device, the IBM 2997 Blood Processor, have been noted in a number of independent investigations. A key feature of this particular unit is a ceramic rotary seal that allows the continuous separation by centrifugation to take place. The equation of motion for flow inside a split toroid cavity within the rotary seal has been solved numerically; velocities and shear stresses found numerically compare favorably with limiting case, analytical solutions. Predicted torque values as a function of rotation rate and fluid viscosity also served as an experimental check on the validity of the mathematical findings. Comparison of calculated shear stress levels and exposure times with known thresholds for cell damage shows that platelet and leukocyte losses may indeed be caused by the seal. Suggestions are made to improve performance of the IBM Blood Processor.     

Biomechanics of cell rolling: shear flow, cell-surface adhesion, and cell deformability

The mechanics of leukocyte (white blood cell; WBC) deformation and adhesion to endothelial cells (EC) has been investigated using a novel in vitro side-view flow assay. HL-60 cell rolling adhesion to surface-immobilized P-selectin was used to model the WBC-EC adhesion process. Changes in flow shear stress, cell deformability, or substrate ligand strength resulted in significant changes in the characteristic adhesion binding time, cell-surface contact and cell rolling velocity. A 2-D model indicated that cell-substrate contact area under a high wall shear stress (20 dyn/cm2) could be nearly twice of that under a low stress (0.5 dyn/cm2) due to shear flow-induced cell deformation. An increase in contact area resulted in more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy that inputs to a cell decreased due to a flattened cell shape. The model also predicted a plateau of WBC rolling velocity as flow shear stresses further increased. Both experimental and computational studies have described how WBC deformation influences the WBC-EC adhesion process in shear flow.     

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.     

Epinephrine causes a reduction in lymph node cell output in sheep

The lymphatic system has a critical role in the return of fluids, proteins, and cells to the circulatory system. However, the effects of stress, including exercise, on this system have not been adequately studied. We investigated the effect of a physiological dose (1 mg) of epinephrine (Epi) on lymph flow, cell concentration, and lymphocyte subsets in efferent subcutaneous lymph in sheep. Blood leukocyte numbers, differential, lymphocyte subsets, and blood and lymph pools of lymphocytes were determined simultaneously. A significant acute increase in lymph flow was followed by a post-injection decrease in flow and cellular output. No changes in lymphocyte subsets or pools of lymphocytes were seen in either blood or lymph. The timing of elevated plasma and lymph concentrations of Epi and norepinephrine (NE) corresponded with the increased lymph flow. In conclusion, Epi injection caused no change in lymphocyte subset distribution, leukocyte concentration, or pools of lymphocytes. A decrease in lymph flow and cellularity was documented post-injection, indicating that lymphatic tissue has no role in the leukocytosis seen after Epi injection. Lymphocyte retention by lymph nodes, however, may contribute to post-injection lymphopenia.     

Flow cytometric studies of platelet responses to shear stress in whole blood

The objective of this work was to evaluate quantitatively the effects of flow on platelet reactions using a flow cytometric technique. Whole blood was exposed to well defined, laminar shear stress in a cone-and-plate viscometer in the absence of added agonists. Blood specimens were fixed with formaldehyde and incubated with two monoclonal antibodies. Antibody 6D1, specific for platelet membrane glycoprotein Ib (GPIb), was used to identify and enumerate platelets and platelet aggregates on the basis of their characteristic forward scatter and 6D1-FITC fluorescence profiles. Anti-CD62 antibody, specific for the granule membrane protein-140 (GMP-140), was used to measure platelet activation. Results showed platelet aggregation increasing with increasing shear stress with marked increase in this response for a pathophysiological stress level of 140 dyn/cm² and higher. This stress level also was the apparent threshold for formation of large platelet aggregates (“large” refers to particles larger than 10 μm in equivalent sphere diameter). These platelet responses to shear stress were insensitive to aspirin, but strongly inhibited by agents that elevate platelet cyclic adenosine monophosphate (cAMP) levels. Moreover, pre-incubation of whole blood with monoclonal antibodies that inhibit von Willebrand factor binding to GPIb or von Willebrand factor and fibrinogen binding to GPIIb/IIIa inhibited platelet aggregation. Aggregation induced by shear at 37° C was less in extent than at 23° C. At physiological shear stresses, whole blood was more susceptible to shear-induced platelet aggregation than platelet-rich plasma. This study reaffirms that flow cytometric methods have several important advantages in studies of shear effects on platelets, and extends the methodology to whole blood unaltered by cell separation methods.     

Advances in endothelial shear stress proteomics

The vascular endothelium lining the luminal surface of all blood vessels is constantly exposed to shear stress exerted by the flowing blood. Blood flow with high laminar shear stress confers protection by activation of antiatherogenic, antithrombotic and anti-inflammatory proteins, whereas low or oscillatory shear stress may promote endothelial dysfunction, thereby contributing to cardiovascular disease. Despite the usefulness of proteomic techniques in medical research, however, there are relatively few reports on proteome analysis of cultured vascular endothelial cells employing conditions that mimic in vivo shear stress attributes. This review focuses on the proteome studies that have utilized cultured endothelial cells to identify molecular mediators of shear stress and the roles they play in the regulation of endothelial function, and their ensuing effect on vascular function in general. It provides an overview on current strategies in shear stress-related proteomics and the key proteins mediating its effects which have been characterized so far.     

Molecular basis of the effects of shear stress on vascular endothelial cells

Blood vessels are constantly exposed to hemodynamic forces in the form of cyclic stretch and shear stress due to the pulsatile nature of blood pressure and flow. Endothelial cells (ECs) are subjected to the shear stress resulting from blood flow and are able to convert mechanical stimuli into intracellular signals that affect cellular functions, e.g., proliferation, apoptosis, migration, permeability, and remodeling, as well as gene expression. The ECs use multiple sensing mechanisms to detect changes in mechanical forces, leading to the activation of signaling networks. The cytoskeleton provides a structural framework for the EC to transmit mechanical forces between its luminal, abluminal and junctional surfaces and its interior, including the cytoplasm, the nucleus, and focal adhesion sites. Endothelial cells also respond differently to different modes of shear forces, e.g., laminar, disturbed, or oscillatory flows. In vitro studies on cultured ECs in flow channels have been conducted to investigate the molecular mechanisms by which cells convert the mechanical input into biochemical events, which eventually lead to functional responses. The knowledge gained on mechano-transduction, with verifications under in vivo conditions, will advance our understanding of the physiological and pathological processes in vascular remodeling and adaptation in health and disease.     

Analysis of temporal shear stress gradients during the onset phase of flow over a backward-facing step

Endothelial cells in blood vessels are exposed to bloodflow and thus fluid shear stress. In arterial bifurcations and stenoses, disturbed flow causes zones of recirculation and stagnation, which are associated with both spatial and temporal gradients of shear stress. Such gradients have been linked to the generation of atherosclerotic plaques. For in-vitro studies of endothelial cell responses, the sudden-expansion flow chamber has been widely used and described. A two-dimensional numerical simulation of the onset phase of flow through the chamber was performed. The wall shear stress action on the bottom plate was computed as a function of time and distance from the sudden expansion. The results showed that depending on the time for the flow to be established, significant temporal gradients occurred close to the second stagnation point of flow. Slowly ramping the flow over 15 s instead of 200 ms reduces the temporal gradients by a factor of 300, while spatial gradients are reduced by 23 percent. Thus, the effects of spatial and temporal gradients can be observed separately. In experiments on endothelial cells, disturbed flow stimulated cell proliferation only when flow onset was sudden. The spatial patterns of proliferation rate match the exposure to temporal gradients. This study provides information on the dynamics of spatial and temporal gradients to which the cells are exposed in a sudden-expansion flow chamber and relates them to changes in the onset phase of flow.     

Numerical investigation of mass transport through patient-specific deformed aortae

Blood flow in human arteries has been investigated using computational fluid dynamics tools. This paper considers flow modeling through three aorta models reconstructed from cross-sectional magnetic resonance scans of female patients. One has the normal control configuration, the second has elongation of the transverse aorta, and the third has tortuosity of the aorta with stenosis. The objective of this study is to determine the impact of aortic abnormal geometries on the wall shear stress (WSS), luminal surface low-density lipoproteins (LDLs) concentration, and oxygen flux along the arterial wall. The results show that the curvature of the aortic arch and the stenosis have significant effects on the blood flow, and in turn, the mass transport. The location of hypoxia areas can be predicted well by ignoring the effect of hemoglobin on the oxygen transport. However, this simplification indeed alters the absolute value of Sherwood number on the wall.     

Two-layered blood flow in stenosed tubes for different diseases

A two-fluid model for blood flow through a stenosed tube has been developed. The model consists of a core (suspension of RBCs) and peripheral plasma layer. The core is assumed to be represented by a polar fluid and the plasma layer by a Newtonian fluid. The flow is assumed to be steady and laminar, and the fluids incompressible. The flow variables are computed for normal blood and for the cases of polycythemia, plasma cell dyscrasias and for Hb SS diseases. Resistance to flow has been computed for different stenosis length and for different stenosis height. Shear stress distribution along the axial distance has been computed for different stenosis height. The impact of size effects (particle size to tube diameter) on blood diseases is discussed.     

Numerical Simulation of Blood Flow Through Microvascular Capillary Networks

A numerical method is implemented for computing blood flow through a branching microvascular capillary network. The simulations follow the motion of individual red blood cells as they enter the network from an arterial entrance point with a specified tube hematocrit, while simultaneously updating the nodal capillary pressures. Poiseuille’s law is used to describe flow in the capillary segments with an effective viscosity that depends on the number of cells residing inside each segment. The relative apparent viscosity is available from previous computational studies of individual red blood cell motion. Simulations are performed for a tree-like capillary network consisting of bifurcating segments. The results reveal that the probability of directional cell motion at a bifurcation (phase separation) may have an important effect on the statistical measures of the cell residence time and scattering of the tube hematocrit across the network. Blood cells act as regulators of the flow rate through the network branches by increasing the effective viscosity when the flow rate is high and decreasing the effective viscosity when the flow rate is low. Comparison with simulations based on conventional models of blood flow regarded as a continuum indicates that the latter underestimates the variance of the hematocrit across the vascular tree.     

Influence of storage and buffer composition on the mechanical behavior of flowing red blood cells

On-chip study of blood flow has emerged as a powerful tool to assess the contribution of each component of blood to its overall function. Blood has indeed many functions, from gas and nutrient transport to immune response and thermal regulation. Red blood cells play a central role therein, in particular through their specific mechanical properties, which directly influence pressure regulation, oxygen perfusion, or platelet and white cell segregation toward endothelial walls. As the bloom of in-vitro studies has led to the apparition of various storage and sample preparation protocols, we address the question of the robustness of the results involving cell mechanical behavior against this diversity. The effects of three conservation media (EDTA, citrate, and glucose-albumin-sodium-phosphate) and storage time on the red blood cell mechanical behavior are assessed under different flow conditions: cell deformability by ektacytometry, shape recovery of cells flowing out of a microfluidic constriction, and cell-flipping dynamics under shear flow. The impact of buffer solutions (phosphate-buffered saline and density-matched suspension using iodixanol/Optiprep) are also studied by investigating individual cell-flipping dynamics, relative viscosity of cell suspensions, and cell structuration under Poiseuille flow. Our results reveal that storing blood samples up to 7 days after withdrawal and suspending them in adequate density-matched buffer solutions has, in most experiments, a moderate effect on the overall mechanical response, with a possible rapid evolution in the first 3 days after sample collection.     

不仅是"益母"草:益母草的心脏保护作用

益母草作为一种传统的妇科中药,近年来的研究表明其作用是多方面的。在心血管方面,益母草能改善心肌缺血、增加冠状动脉血流、提高心功能,其机制主要是在氧化应激状态下通过清除氧自由基、抑制活性氧簇生成发挥抗氧化作用。益母草心脏保护作用的另一机制是促进血管发生。临床试验也表明,益母草能抑制冠心病人的血小板聚集,起抗凝、抗血栓形成作用,从而改善血流变学参数。本文根据目前研究进展,对益母草的心脏保护作用简要综述。     

Rheology of embryonic avian blood

Shear stress, a mechanical force created by blood flow, is known to affect the developing cardiovascular system. Shear stress is a function of both shear rate and viscosity. While established techniques for measuring shear rate in embryos have been developed, the viscosity of embryonic blood has never been known but always assumed to be like adult blood. Blood is a non-Newtonian fluid, where the relationship between shear rate and shear stress is nonlinear. In this work, we analyzed the non-Newtonian behavior of embryonic chicken blood using a microviscometer and present the apparent viscosity at different hematocrits, different shear rates, and at different stages during development from 4 days (Hamburger-Hamilton stage 22) to 8 days (about Hamburger-Hamilton stage 34) of incubation. We chose the chicken embryo since it has become a common animal model for studying hemodynamics in the developing cardiovascular system. We found that the hematocrit increases with the stage of development. The viscosity of embryonic avian blood in all developmental stages studied was shear rate dependent and behaved in a non-Newtonian manner similar to that of adult blood. The range of shear rates and hematocrits at which non-Newtonian behavior was observed is, however, outside the physiological range for the larger vessels of the embryo. Under low shear stress conditions, the spherical nucleated blood cells that make up embryonic blood formed into small aggregates of cells. We found that the apparent blood viscosity decreases at a given hematocrit during embryonic development, not due to changes in protein composition of the plasma but possibly due to the changes in cellular composition of embryonic blood. This decrease in apparent viscosity was only visible at high hematocrit. At physiological values of hematocrit, embryonic blood viscosity did not change significantly with the stage of development.     

Wall shear stress fixed points in cardiovascular fluid mechanics

Complex blood flow in large arteries creates rich wall shear stress (WSS) vectorial features. WSS acts as a link between blood flow dynamics and the biology of various cardiovascular diseases. WSS has been of great interest in a wide range of studies and has been the most popular measure to correlate blood flow to cardiovascular disease. Recent studies have emphasized different vectorial features of WSS. However, fixed points in the WSS vector field have not received much attention. A WSS fixed point is a point on the vessel wall where the WSS vector vanishes. In this article, WSS fixed points are classified and the aspects by which they could influence cardiovascular disease are reviewed. First, the connection between WSS fixed points and the flow topology away from the vessel wall is discussed. Second, the potential role of time-averaged WSS fixed points in biochemical mass transport is demonstrated using the recent concept of Lagrangian WSS structures. Finally, simple measures are proposed to quantify the exposure of the endothelial cells to WSS fixed points. Examples from various arterial flow applications are demonstrated.     

Blood flow in tapered tubes with biorheological applications

A steady laminar flow of blood in a uniform tapered tube has been examined. Blood rheology is assumed to be described by a polar fluid. The analytical expressions for velocities (both axial and radial), total angular velocity, wall shear and pressure drop have been obtained. In literature, the parameters N (coupling number) and L (length ratio) have been chosen independently. But, in the present analysis, it is found that they are interrelated. Variation of the flow variables with suspension concentration and tapered angle have been investigated. Some of the theoretical models for the flow through tapered tubes have been critically examined. The pressure-flow relationship has been studied numerically over the flow rate range 0.01-0.1 cc/sec and compared with experimental results. It has been shown that the existing experimental results are for the tapered tubes of larger diameter which correspond to the flow under Newtonian conditions. Finally, some biological implications and future developments of this theory have been indicated.     

Pulsatile flow of Casson's fluid through stenosed arteries with applications to blood flow

The effects of non-Newtonian nature of blood and pulsatility on flow through a stenosed tube have been investigated. A perturbation method is used to analyse the flow. It is of interest to note that the thickness of the viscous flow region is non-uniform (changing with axial distance). An analytic relation between viscous flow region thickness and red cell concentration has been obtained. It is important to mention that some researchers have obtained an approximate solution for the flow rate-pressure gradient equation (assuming the ratio between the yield stress and the wall shear to be very small in comparison to unity); in the present analysis, we have obtained an exact solution for this non-linear equation without making that assumption. The approximate and exact solutions compare well with one of the exact solutions. Another important result is that the mean and steady flow rates decrease as the yield stress theta increases. For the low values of the yield stress, the mean flow rate is higher than the steady flow rate, but for high values of the yield stress, the mean flow rate behaviour is of opposite nature. The critical value of the yield stress at which the flow rate behaviour changes from one type to another has been determined. Further, it seems that there exists a value of the yield stress at which flow stops for both the flows (steady and pulsatile). It is observed that the flow stop yield value for pulsatile flow is lower than the steady flow. The most notable result of pulsatility is the phase lag between the pressure gradient and flow rate, which is further influenced by the yield stress and stenosis. Another important result of pulsatility is the mean resistance to flow is greater than its steady flow value, whereas the mean value of the wall shear for pulsatile flow is equal to steady wall shear. Many standard results regarding Casson and Newtonian fluids flow, uniform tube flow and steady flow can be obtained as the special cases of the present analysis. Finally, some applications of this theoretical analysis have been cited.     

Assessment of human left ventricle flow using statistical shape modelling and computational fluid dynamics

Blood flow patterns in the human left ventricle (LV) have shown relation to cardiac health. However, most studies in the literature are limited to a few patients and results are hard to generalize. This study aims to provide a new framework to generate more generalized insights into LV blood flow as a function of changes in anatomy and wall motion. In this framework, we studied the four-dimensional blood flow in LV via computational fluid dynamics (CFD) in conjunction with a statistical shape model (SSM), built from segmented LV shapes of 150 subjects. We validated results in an in-vitro dynamic phantom via time-resolved optical particle image velocimetry (PIV) measurements. This combination of CFD and the SSM may be useful for systematically assessing blood flow patterns in the LV as a function of varying anatomy and has the potential to provide valuable data for diagnosis of LV functionality.     

Effect of vaginal distension on blood flow and hypoxia of urogenital organs of the female rat.

Vaginal delivery of children causes traumatic injury to tissues of the pelvic floor and is correlated with stress urinary incontinence; however, the exact mechanism of organ and tissue injury leading to incontinence development is unknown. The purpose of this project was to test the hypothesis that vaginal distension results in decreased blood flow to, and hypoxia of, the urogenital organs responsible for continence, which would suggest an ischemic and/or reperfusion mechanism of injury. Thirteen female rats underwent vaginal distension for 1 h. Thirteen age-matched rats were sham-distended controls. Blood flow to the bladder, urethra, and vagina were determined using a microsphere technique. Hypoxia of these organs was determined by immunohistochemistry. Blood flow to all three organs was significantly decreased just before release of vaginal distension. Bladder blood flow decreased further immediately after release of vaginal distension and continued to be significantly decreased 15 min after the release. Blood flow to both the urethra and vagina tripled immediately after release, inducing a rapid return to normal values. Vaginal distension resulted in extensive smooth muscle hypoxia of the bladder, as well as extensive hypoxia of the vaginal epithelium and urethral hypoxia. Bladders from sham-distended rats demonstrated urothelial hypoxia as well as focal hypoxic areas of the detrusor muscle. We have clearly demonstrated that vaginal distension results in decreased blood flow to, and hypoxia of, the bladder, urethra, and vagina, supportive of hypoxic injury as a possible mechanism of injury leading to stress urinary incontinence.