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％。     

What can we learn from Einstein and Arrhenius about the optimal flow of our blood?

Background

The oxygen flow in humans and other higher animals depends on the erythrocyte-to-blood volume ratio, the hematocrit. Since it is physiologically favourable when the flow of oxygen transport is maximum it can be assumed that this situation has been achieved during evolution. If the hematocrit was too low, too few erythrocytes could transport oxygen. If it was too high, the blood would be very viscous, so that oxygen supply would again be reduced.

Methods

The theoretical optimal hematocrit can be calculated by considering the dependence of blood viscosity on the hematocrit. Different approaches to expressing this dependence have been proposed in the literature. Here, we discuss early approaches in hydrodynamics proposed by Einstein and Arrhenius and show that especially the Arrhenius equation is very appropriate for this purpose.

Results & conclusions

We show that despite considerable simplifications such as neglecting the deformation, orientation and aggregation of erythrocytes, realistic hematocrit values of about 40% can be derived based on optimality considerations. Also the prediction that the ratio between the viscosities of the blood and blood plasma at high shear rates nearly equals Euler's constant (2.718) is in good agreement with observed values. Finally, we discuss possible extensions of the theory. For example, we derive the theoretical optimal hematocrit for persevering divers among marine mammals to be 65%, in excellent agreement with the values observed in several species.

General significance

These considerations are very important for human and animal physiology since oxygen transport is an important factor for medicine and physical performance.     

Theoretical comparison of wall-derived and erythrocyte-derived mechanisms for metabolic flow regulation in heterogeneous microvascular networks

The objective of this study is to compare the effectiveness of metabolic signals derived from erythrocytes and derived from the vessel wall for regulating blood flow in heterogeneous microvascular networks. A theoretical model is used to simulate blood flow, mass transport, and vascular responses. The model accounts for myogenic, shear-dependent, and metabolic flow regulation. Metabolic signals are assumed to be propagated upstream along vessel walls via a conducted response. Arteriolar tone is assumed to depend on the conducted metabolic signal as well as local wall shear stress and wall tension, and arteriolar diameters are calculated based on vascular smooth muscle mechanics. The model shows that under certain conditions metabolic regulation based on wall-derived signals can be more effective in matching perfusion to local oxygen demand relative to regulation based on erythrocyte-derived signals, resulting in higher extraction and lower oxygen deficit. The lower effectiveness of the erythrocyte-derived signal is shown to result in part from the unequal partition of hematocrit at diverging bifurcations, such that low-flow vessels tend to receive a reduced hematocrit and thereby experience a reduced erythrocyte-derived metabolic signal. The model simulations predict that metabolic signals independent of erythrocytes may play an important role in local metabolic regulation of vascular tone and flow distribution in heterogeneous microvessel networks.     

Influence of temperature on the optimal hematocrit of the bullfrog (Rana catesbeiana)

Summary The influence of temperature on blood viscosity and consequently on the potential for oxygen transport by blood was determined using a controlled flow, variable pressure tube viscometer, and blood from adult bullfrogs. Blood viscosity was determined as a function of hematocrit and temperature, and oxygen capacity was determined as a function of hematocrit. These data were used to describe 1) the potential for oxygen transport in the tube viscometer, and 2) the relation between the optimal hematocrit, the hematocrit which provided the greates oxygen transport, and temperature. The optimal hematocrit increased at a rate of 0.237% per °C increase in temperature. This value is close to the rate of change inin vivo hematocrit of 0.246 and 0.240% per °C increase in body temperature (T_b) observed in winter bullforgs acclimated to 5 and 20°C, respectively. During the summer the hematocrit ratio showed no consistent relation to T_b. These results suggest that in bullfrogs the cardiovascular adjustments to change in T_b involve the optimal hematocrit in winter, but not in summer.     

Red blood cells under flow show maximal ATP release for specific hematocrit

ATP release by red blood cells (RBCs) under shear stress (SS) plays a pivotal role in endothelial biochemical signaling cascades. The aim of this study is to investigate through numerical simulation how RBC spatiotemporal organization depends on flow and geometrical conditions to generate ATP patterns. Numerical simulations were conducted in a straight channel by considering both plasma and explicit presence of RBCs, their shape deformation and cell-cell interaction, and ATP release by RBCs. Two ATP release pathways through cell membrane are taken into account: pannexin 1 channel, sensitive to SS, and cystic fibrosis transmembrane conductance regulator, which responds to cell deformation. Several flow and hematocrit conditions are explored. The problem is solved by the lattice Boltzmann method. Application of SS to the RBC suspension triggers a nontrivial spatial RBC organization and ATP patterns. ATP localizes preferentially in the vicinity of the cell-free layer close to channel wall. Conditions for maximal ATP release per cell are identified, which depend on vessel size and hematocrit Ht. Increasing further Ht beyond optimum enhances the total ATP release but should degrade oxygen transport capacity, a compromise between an efficient ATP release and minimal blood dissipation. Moreover, ATP is boosted in capillaries, suggesting a vasomotor activity coordination throughout the resistance network.     

Comparison of various approaches to calculating the optimal hematocrit in vertebrates

An interesting problem in hemorheology is to calculate that volume fraction of erythrocytes (hematocrit) that is optimal for transporting a maximum amount of oxygen. If the hematocrit is too low, too few erythrocytes are present to transport oxygen. If it is too high, the blood is very viscous and cannot flow quickly, so that oxygen supply to the tissues is again reduced. These considerations are very important, since oxygen transport is an important factor for physical performance. Here, we derive theoretical optimal values of hematocrit in vertebrates and collect, from the literature, experimentally observed values for 57 animal species. It is an interesting question whether optimal hematocrit theory allows one to calculate hematocrit values that are in agreement with the observed values in various vertebrate species. For this, we first briefly review previous approaches in that theory. Then we check which empirical or theoretically derived formulas describing the dependence of viscosity on concentration in a suspension lead to the best agreement between the theoretical and observed values. We consider both spatially homogeneous and heterogeneous distributions of erythrocytes in the blood and also possible extensions, like the influence of defective erythrocytes and cases where some substances are transported in the plasma. By discussing the results, we critically assess the power and limitations of optimal hematocrit theory. One of our goals is to provide a systematic overview of different approaches in optimal hematocrit theory.     

PEG-albumin supraplasma expansion is due to increased vessel wall shear stress induced by blood viscosity shear thinning

We studied the extreme hemodilution to a hematocrit of 11% induced by three plasma expanders: polyethylene glycol (PEG)-conjugated albumin (PEG-Alb), 6% 70-kDa dextran, and 6% 500-kDa dextran. The experimental component of our study relied on microelectrodes and cardiac output to measure both the rheological properties of plasma-expander blood mixtures and nitric oxide (NO) bioavailability in vessel walls. The modeling component consisted of an analysis of the distribution of wall shear stress (WSS) in the microvessels. Our experiments demonstrated that plasma expansion with PEG-Alb caused a state of supraperfusion with cardiac output 40% above baseline, significantly increased NO vessel wall bioavailability, and lowered peripheral vascular resistance. We attributed this behavior to the shear thinning nature of blood and PEG-Alb mixtures. To substantiate this hypothesis, we developed a mathematical model of non-Newtonian blood flow in a vessel. Our model used the Quemada rheological constitutive relationship to express blood viscosity in terms of both hematocrit and shear rate. The model revealed that the net effect of the hemodilution induced by relatively low-viscosity shear thinning PEG-Alb plasma expanders is to reduce overall blood viscosity and to increase the WSS, thus intensifying endothelial NO production. These changes act synergistically, significantly increasing cardiac output and perfusion due to lowered overall peripheral vascular resistance.     

Vascular remodeling of the mouse yolk sac requires hemodynamic force

The embryonic heart and vessels are dynamic and form and remodel while functional. Much has been learned about the genetic mechanisms underlying the development of the cardiovascular system, but we are just beginning to understand how changes in heart and vessel structure are influenced by hemodynamic forces such as shear stress. Recent work has shown that vessel remodeling in the mouse yolk sac is secondarily effected when cardiac function is reduced or absent. These findings indicate that proper circulation is required for vessel remodeling, but have not defined whether the role of circulation is to provide mechanical cues, to deliver oxygen or to circulate signaling molecules. Here, we used time-lapse confocal microscopy to determine the role of fluid-derived forces in vessel remodeling in the developing murine yolk sac. Novel methods were used to characterize flows in normal embryos and in embryos with impaired contractility (Mlc2a(-/-)). We found abnormal plasma and erythroblast circulation in these embryos, which led us to hypothesize that the entry of erythroblasts into circulation is a key event in triggering vessel remodeling. We tested this by sequestering erythroblasts in the blood islands, thereby lowering the hematocrit and reducing shear stress, and found that vessel remodeling and the expression of eNOS (Nos3) depends on erythroblast flow. Further, we rescued remodeling defects and eNOS expression in low-hematocrit embryos by restoring the viscosity of the blood. These data show that hemodynamic force is necessary and sufficient to induce vessel remodeling in the mammalian yolk sac.     

Optimal hematocrit theory during activity in the bullfrog (Rana catesbeiana).

1. There is an exponential relationship between blood viscosity (cP) and hematocrit (%) for the bullfrog; eta = 1.81 e0.033Hct. The in vitro optimal hematocrit calculated for blood flow through tubes, from this relationship for bullfrog blood, is 30%. 2. Amphibian blood is a non-Newtonian fluid with viscosity dependent on shear rate. It has a finite yield shear stress of about 1.5 dynes cm-2. 3. Hematocrit of bullfrogs was increased from 27% (control) to 57% by isovolemic erythrocythemia (constant volume blood-doping). There was a slight increase in systolic, diastolic and venous blood pressure with elevated hematocrit. 4. Systemic arch blood flow rate was inversely related to blood viscosity for erythrocythemic bullfrogs. The decrease in systemic arch blood flow at high hematocrits was due primarily to reduced pulse volume rather than reduced heart rate. 5. Systemic arch blood flow, when standardised between individuals, was inversely related to blood viscosity; Qbl = 0.185 + 3.73 eta -1. This relationship was significantly different from that predicted by the Poiseuille-Hagen flow formula. The in vivo optimal hematocrit calculated from this relationship was 41%. 6. Optimal hematocrit theory appears to be generally applicable for Rana catesbeiana in vitro and in vivo. Most individuals had an in vivo optimal hematocrit, but the absence of a clear optimal hematocrit for some individuals could reflect methodological variability, or in vivo physiological compensation for the increased blood viscosity at high hematocrit.     

Osmotic and Ionic Regulation of North American Zebra Mussels (Dreissena polymorpha)

SYNOPSIS. Unlike other freshwater bivalves that survive formonths in deionized water, Dreissena polymorpha requires minimalconcentrations of Na, K, Mg, and Cl in the bathing medium forlong-term survival. Although ion transport rates are higherin D. polymorpha compared to other freshwater bivalves, theytend to have lower blood solute concentrations. D. polymorphahas an unusually "leaky" epithelium with a high paracellularpermeability to solutes. Thus, even with high transport rates,it may not be possible for zebra mussels to retain higher bloodsolutes because of the extensive passive loss of ions. Undera hyperosmotic stress, D. polymorpha will rapidly osmoconform(about 12 hr) due primarily to the diffusion of solutes andpartially to the osmotic loss of water. D. polymorpha is notcapable of surviving an imbalance of Na/K in the external medium.In the absence of K the cells will tend to lose volume to achieveisosmotic balance with the blood, but the animals usually diewithin a few days. If D. polymorpha is exposed to excess K inthe environment (1 mM), they will accumulate K in the blood.If the K enters the cells, cellular volume would expand dueto increase in osmolyte concentration, yet, if K remains inthe blood, there will be an electrochemical imbalance. In eithercase, the animal cannot survive much longer than a day. WhenNa and K are present in the medium in a balanced combinationapproximated by artificial seawater (ASW), D. polymorpha willsurvive an acute transfer to 100 mosm ASW indefinitely (months).Our preliminary studies have shown that D. polymorpha will toleratestep-wise acclimation to solutions >250 mosm provided thechanges in salinity do not exceed 50–100 mosm. Freshwaterbivalves, unlike the marine bivalves, have limited free aminoacids in their body fluids and must rely on inorganic ions forosmotic regulation. The free amino acids serve as an importantosmolyte buffer for volume regulation when an animal experiencesan environment of changing salinity. The inability of Dreissena,and perhaps other freshwater bivalves, to tolerate hyperosmoticallyinduced dehydration may be due, in part, to the inability toaccumulate or retain sufficient intracellular K to facilitateregulatory volume adjustments.     

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.     

Pulsatile flow in a coronary artery using multiphase kinetic theory

Pulsatile flow in a model of a right coronary artery (RCA) was previously modeled as a single-phase fluid and as a two-phase fluid using experimental rheological data for blood as a function of hematocrit and shear rate. Here we present a multiphase kinetic theory model which has been shown to compute correctly the viscosity of red blood cells (RBCs) and their migration away from vessel walls: the Fahraeus–Lindqvist effect. The computed RBC viscosity decreases with shear rate and vessel size, consistent with measurements. The pulsatile computations were performed using a typical cardiac waveform until a limit cycle was well established. The RBC volume fractions, shear stresses, shear stress gradients, granular temperatures, viscosities, and phase velocities varied with time and position during each cardiac cycle. Steady-state computations were also performed and were found to compare well with time-averaged transient results. The wall shear stress and wall shear stress gradients (both spatial and temporal) were found to be highest on the inside area of maximum curvature. Potential atherosclerosis sites are identified using these computational results.     

Dunaliella salina: A model System for Studying the Response of Plant Cells to Stress

This review focuses on the biochemical and physiological responseof the halotolerant green alga, Dunaliella salina, to conditionsof stress. It is now well established that in response to stress,cells of Dunaliella salina var. bardawil show increased glycerolproduction, massive ßcarotene accumulation and enhancedabscisic acid metabolism. In this respect, cellular responsesare regulatory and seem to depend on a diversity of mechanismswhich may be linked to a modification of the abscisic acid balance.Dunaliella lacks a rigid cell wall and the cellular contentsare enclosed by an elastic plasma membrane that permits rapidcell volume changes in response to extracellular changes inosmolarity. Based on the ‘stretch activated ion channelsmodel’ reviewed recently by Kirst (1990) we propose thefollowing cascade of responses: volume change/distortion ofplasmalemma     

Elevated plasma viscosity in extreme hemodilution increases perivascular nitric oxide concentration and microvascular perfusion

We tested the hypothesis that high-viscosity (HV) plasma in extreme hemodilution causes wall shear stress to be greater than low-viscosity (LV) plasma, leading to enhanced production of nitric oxide (NO). The perivascular concentration of NO was measured in arterioles and venules and the tissue of the hamster chamber window model, subjected to acute extreme hemodilution, with a hematocrit (Hct) of 11% using Dextran 500 (n = 6) or Dextran 70 (n = 5) with final plasma viscosities of 1.99 +/- 0.11 and 1.33 +/- 0.04 cp, respectively. HV plasma significantly increased the periarteriolar, perivenular, and tissue NO concentration by 2.0, 1.9, and 1.4 times the control (n = 7). The NO concentration with LV plasma was not statistically different from control. Arteriolar shear stress was significantly increased in HV plasma relative to LV plasma in arterioles but not in venules. Aortic endothelial NO synthase (eNOS) protein expression was increased with HV plasma but not with LV plasma. There was a weak correlation between perivascular NO concentration and the locally calculated shear stress induced by the procedures, when blood viscosity was corrected according to Hct values previously determined in studies of microvascular Hct distribution. The finding that the periarteriolar and venular NO concentration in HV plasma was the same although arteriolar shear stress was significantly greater than venular shear stress maybe be due to differences in vessel wall metabolism between arterioles and venules and the presence of NO transport through the blood stream in the microcirculation. Results support the concept that in extreme hemodilution HV plasma maintains functional capillary density through a NO-mediated vasodilatation.     

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.     

Regulation of oxygen delivery during induced polycythemia in exercising dogs

Previous studies have concluded that polycythemia decreases oxygen delivery primarily because of a large fall in cardiac output associated with a rise in systemic vascular resistance that has been attributed to increased blood viscosity. However, because other studies have shown that polycythemia may not reduce oxygen delivery, an alternative hypothesis is that cardiac output falls in response to a rising oxygen content, thereby maintaining oxygen delivery constant. To determine whether oxygen content participates in the regulation of cardiac output during polycythemia, we studied eight chronically instrumented dogs trained to exercise on a treadmill. The dogs underwent exchange transfusion with packed red blood cells containing methemoglobin, which caused an increase in hematocrit from 35 +/- 1 to 50 +/- 1% and in viscosity, with little change in oxygen content. The expected fall in exercise cardiac output failed to occur after exchange transfusion with red blood cells containing methemoglobin (7.5 +/- 4 vs. 6.8 +/- 0.5 l/min; P = not significant), and there was no rise in systemic vascular resistance. Methylene blue was then administered intravenously to facilitate conversion of methemoglobin to oxyhemoglobin, which increased oxygen content (12.8 +/- 0.9 vs. 18.4 +/- 0.9 vol%; P < 0.01) with no change in hematocrit or viscosity. Resting cardiac output did not change significantly, but there was a significant decrease in exercise output (6.8 +/- 0.5 vs. 5.8 +/- 0.4 l/min; P < 0.05). Thus we conclude that the fall in cardiac output seen in acute polycythemia results in part from the regulation of oxygen delivery and is not due solely to increased blood viscosity.     

Effects of cold exposure and shear stress on endothelial nitric oxide synthase activation

Endothelial nitric oxide synthase (eNOS) is the primary enzyme that produces nitric oxide (NO), which plays an important role in blood vessel relaxation. eNOS activation is stimulated by various mechanical forces, such as shear stress. Several studies have shown that local cooling of the human finger causes strong vasoconstriction, followed after several minutes by cold-induced vasodilation (CIVD). However, the role played by endothelial cells (ECs) in blood vessel regulation in respond to cold temperatures is not fully understood. In this study, we found that low temperature alone does not significantly increase or decrease eNOS activation in ECs. We further found that the combination of shear stress with temperature change leads to a significant increase in eNOS activation at 37 °C and 28 °C, and a decrease at 4 °C. These results show that ECs play an important role in blood vessel regulation under shear stress and low temperature.     

Plug Effect of Erythrocytes in Capillary Blood Vessels

As an idealized problem of the motion of blood in small capillary blood vessels, the low Reynolds number flow of plasma (a newtonian fluid) in a circular cylindrical tube involving a series of circular disks is studied. It is assumed in this study that the suspended disks are equally spaced along the axis of the tube, and that their centers remain on the axis of the tube and that their faces are perpendicular to the tube axis. The inertial force of the fluid due to the convective acceleration is neglected on the basis of the smallness of the Reynolds number. The solution of the problem is derived for a quasi-steady flow involving infinitesimally thin disks. The numerical calculation is carried out for a set of different combinations of the interdisk distance and the ratio of the disk radius to the tube radius. The ratio of the velocity of the disk to the average velocity of the fluid is calculated. The different rates of transport of red blood cells and of plasma in capillary blood vessels are discussed. The average pressure gradient along the axis of the tube is computed, and the dependence of the effective viscosity of the blood on the hematocrit and the diameter of the capillary vessel is discussed.     

Blood flow in the capillary bed

From arteries to veins, the blood has to go through the ‘capillary’ blood vessels. These blood vessels are so small that often their diameter is smaller than that of the red blood cells. Intimate interactions occur, therefore, between the blood cells and the blood vessels.

A general survey of recent works on capillary blood flow is given in this article. Some details are presented for two problems: the problem of deformation of the flexible red blood cells, their motion in the capillary blood vessels, and the pressure drop due to the red cell blood vessel interaction; and the problem of the flow of plasma ‘bolus’ between neighboring red cells.

The solution supplies many details about the microcirculation phenomenon. Taken together, a method is offered for the calculation of pressure drop in the capillary as a function of various physical parameters: the red cell volume per unit blood volume, (hematocrit), the ratio of the cell diameter to the blood vessel diameter, the ratio of the length of the blood vessel to its length, the volume of individual red cells, and a parameter relating the cell membrane elasticity, plasma viscosity and the cell velocity.     

A new method for measuring the yield stress in thin layers of sedimenting blood.

A new method is presented to describe the low shear rate behavior of blood. We observed the response of a thin layer of sedimenting blood to a graded shear stress in a wedge-shaped chamber. The method allows quantitation of the degree of phase separation between red cells and plasma, and extracts the yield stress of the cell phase as a function of hematocrit. Our studies showed that the behavior of normal human blood underwent a transition from a solid-like gel to a Casson fluid. This transition began at the Casson predicted yield stress. The viscoelastic properties of blood were examined at shear stresses below the yield stress. The measured Young's elastic moduli were in good agreement with published data. The yield stress of blood showed a linear dependence on hematocrit up to 60%, and increased more rapidly at higher hematocrit.