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.     

Linear and nonlinear analyses of pulsatile blood flow in a cylindrical tube

A non-Newtonian shear-thinning constitutive relation is proposed to study pulsatile flow of whole blood in a cylindrical tube. The constitutive relation, which satisfies the principle of material frame indifference, is derived from viscometric data obtained from whole blood over a range of hematocrits. Assuming axisymmetric flow in a rigid cylindrical tube of constant diameter, a second-order, nonlinear partial differential equation governing the axial velocity component is obtained. Imposing a periodic pressure gradient, the governing equation was solved numerically using finite difference methods over a range of Stokes values and hematocrits. For a forcing frequency of 1 Hz, results are presented over tube diameters ranging between 0.1 and 2 cm and over hematocrits ranging between 10 and 80%. For a given hematocrit, velocity profiles predicted for the non-Newtonian model under sinusoidal forcing reveal attenuated volume flow rate and enhanced vorticity transport over the tube cross-section relative to a Newtonian fluid having a viscosity corresponding to the high shear-rate limit. For moderate to high Stokes numbers, consistent with flow in large arteries, our results revealed a viscosity distribution that was nearly time invariant. An analytic solution was obtained for a fluid having arbitrarily prescribed radially varying, temporally invariant viscosity and density distributions under arbitrary periodic pressure forcing. Close agreement was observed between our numerical and analytical results when the imposed viscosity distribution was chosen to approximate the time-averaged viscosity distribution predicted by the shear-thinning non-Newtonian model. For St > or approximately= 100, the disparity between our results and those of a Newtonian fluid of constant viscosity grows with a decreasing ratio of the DC to AC components of the pressure-gradient amplitude below 50%. In particular, for any purely oscillatory pressure-gradient (vanishing DC component), the Womersley solution is a particularly poor predictor of the amplitude and phase of wall shear rate for over half of the flow cycle. Under such circumstances, the analytical models presented here provide a simple and accurate means of estimating instantaneous wall shear rate, knowing only the pressure gradient and hematocrit.     

On the relative importance of rheology for image-based CFD models of the carotid bifurcation

BACKGROUND: Patient-specific computational fluid dynamics (CFD) models derived from medical images often require simplifying assumptions to render the simulations conceptually or computationally tractable. In this study, we investigated the sensitivity of image-based CFD models of the carotid bifurcation to assumptions regarding the blood rheology. METHOD OF APPROACH: CFD simulations of three different patient-specific models were carried out assuming: a reference high-shear Newtonian viscosity, two different non-Newtonian (shear-thinning) rheology models, and Newtonian viscosities based on characteristic shear rates or, equivalently, assumed hematocrits. Sensitivity of wall shear stress (WSS) and oscillatory shear index (OSI) were contextualized with respect to the reproducibility of the reconstructed geometry, and to assumptions regarding the inlet boundary conditions. RESULTS: Sensitivity of WSS to the various rheological assumptions was roughly 1.0 dyn/cm(2) or 8%, nearly seven times less than that due to geometric uncertainty (6.7 dyn/cm(2) or 47%), and on the order of that due to inlet boundary condition assumptions. Similar trends were observed regarding OSI sensitivity. Rescaling the Newtonian viscosity based on time-averaged inlet shear rate served to approximate reasonably, if overestimate slightly, non-Newtonian behavior. CONCLUSIONS: For image-based CFD simulations of the normal carotid bifurcation, the assumption of constant viscosity at a nominal hematocrit is reasonable in light of currently available levels of geometric precision, thus serving to obviate the need to acquire patient-specific rheological data.     

Effects of hematocrit on thixotropic properties of human blood

The rheological properties of whole human blood exhibit thixotropic behavior at low shear rates up to about ten reciprocal seconds (1). The accepted cause of this shear rate-dependent and time-dependent behavior is the progressive breakdown of rouleaux into individual red cells. Huang developed a rheological equation which incorporates the kinetics of rouleau breakdown in his models (2). This five-parameter equation was used successfully to represent the hysteresis loop and the torque-decay curve of whole human blood. Numerical values of these five thixotropic parameters, which characterize the rheological behavior of the blood from apparently healthy human subjects, were established (3). In this communication, we examined the effect of hematocrit on each of the above mentioned parameters. The results show that the following parameters will increase their values with an increase in hematocrit: the yield stress, Newtonian contribution of viscosity, non-Newtonian contribution of viscosity, apparent viscosity and the equilibrium value of the structural parameter which indicates the relative amount of rouleaux in blood. Mathematical equations were developed to give the relationship between parameters and hematocrit. Two other thixotropic parameters, viz. the kinetic rate constant of rouleaux breakdown into individual red cells and the order of the breakdown reaction, were found to be independent of the hematocrit. It is consistent with reaction kinetic theory that the rate constant and the order of reaction are independent of the concentration of reactants.     

In silico biophysics and hemorheology of blood hyperviscosity syndrome

Hyperviscosity syndrome (HVS) is characterized by an increase of the blood viscosity by up to seven times the normal blood viscosity, resulting in disturbances to the circulation in the vasculature system. HVS is commonly associated with an increase of large plasma proteins and abnormalities in the properties of red blood cells, such as cell interactions, cell stiffness, and increased hematocrit. Here, we perform a systematic study of the effect of each biophysical factor on the viscosity of blood by employing the dissipative particle dynamic method. Our in silico platform enables manipulation of each parameter in isolation, providing a unique scheme to quantify and accurately investigate the role of each factor in increasing the blood viscosity. To study the effect of these four factors independently, each factor was elevated more than its values for a healthy blood while the other factors remained constant, and viscosity measurement was performed for different hematocrits and flow rates. Although all four factors were found to increase the overall blood viscosity, these increases were highly dependent on the hematocrit and the flow rates imposed. The effect of cell aggregation and cell concentration on blood viscosity were predominantly observed at low shear rates, in contrast to the more magnified role of cell rigidity and plasma viscosity at high shear rates. Additionally, cell-related factors increase the whole blood viscosity at high hematocrits compared with the relative role of plasma-related factors at lower hematocrits. Our results, mapped onto the flow rates and hematocrits along the circulatory system, provide a correlation to underpinning mechanisms for HVS findings in different blood vessels.     

Effect of hematocrit on wall shear rate in oscillatory flow: do the elastic properties of blood play a role?

Porcine blood was used to examine the relationship between hematocrit levels and wall shear rate patterns in straight and curved artery models under fixed oscillatory flow conditions characteristic of larger arteries. It is demonstrated that porcine blood models both the viscous and elastic components of the 2 Hz complex viscosity of human blood quite accurately over a broad range of shear rates (1-1000 s-1) and hematocrits (20%-80%). For a fixed oscillatory flow waveform (Poiseuille peak shear rate = 168 s-1; mean shear rate 84 s-1), increases in hematocrit produced a decrease in the peak wall shear rate in both the straight and curved artery models and a corresponding decrease in wall shear rate reversal on the inside wall of the curved artery model. The same trends were also observed for oscillatory flows of aqueous glycerin solutions of increasing viscosity in the range of viscosity of the blood samples tested. Aqueous glycerin solutions produced wall shear rate waveforms of the same magnitude and shape as the porcine blood. This indicates that variations in the shear rate, and therefore the shear stress, were caused primarily by changes in the viscous and not the elastic properties of blood. The results suggest that simple Newtonian fluids may be sufficient for in vitro determination of the first order effects to be expected of human blood flow in large vessels having complex geometries and shear rates in or above the range of the present study.     

Numerical simulation of non-Newtonian blood flow dynamics in human thoracic aorta

Three non-Newtonian blood viscosity models plus the Newtonian one are analysed for a patient-specific thoracic aorta anatomical model under steady-state flow conditions via wall shear stress (WSS) distribution, non-Newtonian importance factors, blood viscosity and shear rate. All blood viscosity models yield a consistent WSS distribution pattern. The WSS magnitude, however, is influenced by the model used. WSS is found to be the lowest in the vicinity of the three arch branches and along the distal walls of the branches themselves. In this region, the local non-Newtonian importance factor and the blood viscosity are elevated, and the shear rate is low. The present study revealed that the Newtonian assumption is a good approximation at mid-and-high flow velocities, as the greater the blood flow, the higher the shear rate near the arterial wall. Furthermore, the capabilities of the applied non-Newtonian models appeared at low-flow velocities. It is concluded that, while the non-Newtonian power-law model approximates the blood viscosity and WSS calculations in a more satisfactory way than the other non-Newtonian models at low shear rates, a cautious approach is given in the use of this blood viscosity model. Finally, some preliminary transient results are presented.     

Viscoelasticity of Human Blood

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

Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: Steady flows

Effects of the non-Newtonian viscosity of blood on a flow in a coronary arterial casting of man were studied numerically using a finite element method. Various constitutive models were examined to model the non-Newtonian viscosity of blood and their model constants were summarized. A method to incorporate the non-Newtonian viscosity of blood was introduced so that the viscosity could be calculated locally. The pressure drop, wall shear stress and velocity profiles for the case of blood viscosity were compared for the case of Newtonian viscosity (0.0345 poise). The effect of the non-Newtonian viscosity of blood on the overall pressure drop across the arterial casting was found to be significant at a flow of the Reynolds number of 100 or less. Also in the region of flow separation or recirculation, the non-Newtonian viscosity of blood yields larger wall shear stress than the Newtonian case. The origin of the non-Newtonian viscosity of blood was discussed in relation to the viscoelasticity and yield stress of blood.     

Critical Transitions in Early Embryonic Aortic Arch Patterning and Hemodynamics

Transformation from the bilaterally symmetric embryonic aortic arches to the mature great vessels is a complex morphogenetic process, requiring both vasculogenic and angiogenic mechanisms. Early aortic arch development occurs simultaneously with rapid changes in pulsatile blood flow, ventricular function, and downstream impedance in both invertebrate and vertebrate species. These dynamic biomechanical environmental landscapes provide critical epigenetic cues for vascular growth and remodeling. In our previous work, we examined hemodynamic loading and aortic arch growth in the chick embryo at Hamburger-Hamilton stages 18 and 24. We provided the first quantitative correlation between wall shear stress (WSS) and aortic arch diameter in the developing embryo, and observed that these two stages contained different aortic arch patterns with no inter-embryo variation. In the present study, we investigate these biomechanical events in the intermediate stage 21 to determine insights into this critical transition. We performed fluorescent dye microinjections to identify aortic arch patterns and measured diameters using both injection recordings and high-resolution optical coherence tomography. Flow and WSS were quantified with 3D computational fluid dynamics (CFD). Dye injections revealed that the transition in aortic arch pattern is not a uniform process and multiple configurations were documented at stage 21. CFD analysis showed that WSS is substantially elevated compared to both the previous (stage 18) and subsequent (stage 24) developmental time-points. These results demonstrate that acute increases in WSS are followed by a period of vascular remodeling to restore normative hemodynamic loading. Fluctuations in blood flow are one possible mechanism that impacts the timing of events such as aortic arch regression and generation, leading to the variable configurations at stage 21. Aortic arch variations noted during normal rapid vascular remodeling at stage 21 identify a temporal window of increased vulnerability to aberrant aortic arch morphogenesis with the potential for profound effects on subsequent cardiovascular morphogenesis.     

Blood viscosity and optimal hematocrit in narrow tubes

Blood viscosity in normal adults was measured in glass tubes with diameters of 50, 100 and 500 microns for a wide range of adjusted feed hematocrits (15-70%). Blood viscosity decreased at each of the adjusted feed hematocrits when going from a 500-micron tube to a 50-micron tube. The viscosity reduction increased with increasing hematocrit. The steepness in the hematocrit-viscosity curves decreased with decreasing tube diameter. Erythrocyte transport efficiency (hematocrit/blood viscosity) was calculated to estimate the optimal hematocrit for oxygen transport. Optimal hematocrit averaged 38% in 500-micron tubes, 44% in 100-micron tubes and 51% in 50-micron tubes. Our results suggest that the strong F?hraeus-Lindqvist effect at high hematocrits may help to maintain oxygen transport in polycythemic patients as long as the driving pressure is sufficient.     

Model-independent relationships between hematocrit,blood viscosity,and yield stress derived from Couette viscometry data

This paper describes a procedure, based on Tikhonov regularization, for obtaining the shear rate function or equivalently the viscosity function of blood from Couette viscometry data. For data sets that include points where the sample in the annulus is partially sheared the yield stress of blood will also be obtained. For data sets that do not contain partially sheared points, provided the shear stress is sufficiently low, a different method of estimating the yield stress is proposed. Both the shear rate function and yield stress obtained in this investigation are independent of any rheological model of blood. This procedure is applied to a large set of Couette viscometer data taken from the literature. Results in the form of shear rate and viscosity functions and yield stress are presented for a wide range of hematocrits and are compared against those reported by the originators of the data and against independently measured shear properties of blood.     

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.     

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.     

The pressure-flow relation in resting rat skeletal muscle perfused with pure erythrocyte suspensions

In spite of numerous investigations of erythrocyte rheology, there is limited information about the influence of erythrocyte suspensions on whole organ pressure-flow relationships. In this study, we present whole organ pressure-flow curves for resting vasodilated gracilis muscle of the rat, in which the microanatomy and vessel properties have been determined previously. For pure erythrocyte suspensions from donor rats, the organ resistance increases only mildly with perfusion time (less than a 5% shift over a one-hour perfusion time), while in contrast, erythrocyte suspensions containing leukocytes show an increases of resistance near 100% over a period of 25 min. Variation in pressure-flow curves in the muscle at the same arterial hematocrit between different rats is less than 15%. The pressure-flow relation for pure erythrocyte suspensions depends on hematocrit. Shear thinning is exhibited at high hematocrits, while Newtonian behavior is approached at arterial hematocrits below 15%. The whole organ apparent viscosity for pure erythrocyte suspensions (normalized by cell-free plasma resistance) is a non-linear function of hematocrit; at physiological pressures, it reaches values comparable to those of apparent viscosities measured in rotational viscometers or in in vitro tube flow (diameters greater than 0.8 mm). The apparent viscosities estimated from the whole organ experiments tend to be higher than those measured in straight tubes under in vitro conditions. The pressure-flow curves for pure erythrocyte suspensions are shifted towards lower pressures than the curves for mixed suspensions of erythrocytes at the same hematocrit and with leukocytes at physiological cell counts. These acute experiments show that pure erythrocyte suspensions yield highly reproducible resistances in the skeletal muscle microcirculation with dilated arterioles. Relative apparent viscosities measured in vivo are higher than those measured in straight glass tubes of comparable dimesions.     

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.     

Non-Newtonian blood flow in human right coronary arteries: steady state simulations

This study looks at blood flow through four different right coronary arteries, which have been reconstructed from bi-plane angiograms. Five non-Newtonian blood models, as well as the usual Newtonian model of blood viscosity, are used to study the wall shear stress in each of these arteries at a particular point in the cardiac cycle. It was found that in the case of steady flow in a given artery, the pattern of wall shear stress is consistent across all models. The magnitude of wall shear stress, however, is influenced by the model used and correlates with graphs of shear stress versus strain for each model. For mid-range velocities of around 0.2 m s(-1) the models are virtually indistinguishable. Local and global non-Newtonian importance factors are introduced, in an attempt to quantify the types of flows where non-Newtonian behaviour is significant. It is concluded that, while the Newtonian model of blood viscosity is a good approximation in regions of mid-range to high shear, it is advisable to use the Generalised Power Law model (which tends to the Newtonian model in those shear ranges in any case) in order to achieve better approximation of wall shear stress at low shear.     

一种改进型体液表观粘度函数测量仪

本文介绍一种性能较好的体液表观粘度函数快测系统,它是在较严密的流变学理论基础上通过较精细的硬、软件设计而研究成功的.其前身为L-1型粘度计,但作了重要改进.它的最大特点是能在一次测量过程完后得到不同切变率下的表观粘度;同时能在通常认为困难却十分重要的“低剪切”段令人满意地工作.     

Rheology of synovial fluid

After a discussion of the role of synovial fluid as a joint lubricant, rheological measurements are described with both normal (healthy) synovial fluids and pathological ones. Shear stress and first normal stress difference are measured as a function of shear gradient to calculate the apparent shear viscosity eta 1 and the apparent normal viscosity psi 7 as well as an apparent shear modulus G'. It is found, that in case of diseased synoviae all rheological parameters deteriorate. Most significant changes are observed with the zero shear viscosity eta 0, the shear modulus G', and a characteristic time theta 1, which is the reciprocal of the critical shear rate Dc which determines the onset of shear thinning. The rheological deterioration of synovial fluids is explained in terms of solute structure, whereby a molecular mass of the backbone hyaluronic acid of at least 10(7) g.mol-1 is required for satisfactory function. A theory of the rheological performance of normal synovial fluid as well as its pathological deterioration is proposed.