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.     

Development of a rheological analogue to periprosthetic fluid

The purpose of this work is to design a rheological analogue to periprosthetic fluid, for potential use in wear testing of orthopaedic implants. Polymer solutions of sodium carboxymethyl cellulose (CMC), xanthan and mixtures thereof were prepared, and the experimentally determined viscosity-shear rate dependence was analyzed using the three-parameter modified Cross model. A mixture containing 0.185 wt% CMC and 0.075 wt% xanthan was identified as being the closest rheological match for periprosthetic fluid in both steady shear and oscillatory modes of deformation.     

Thixotropic properties of whole blood from healthy human subjects

The steady state non-Newtonian viscosity of whole human blood has been widely studied as a function of the shear rate; and used to characterize the blood in various pathological disorders. In our previous studies, we demonstrated that blood is a thixotropic fluid. Its time-dependency and shear rate dependency of rheological behavior can be represented by an equation developed by Huang. Parameters of the equation can be used for the characterization of an individual's blood. They provide information, such as the kinetic rate constant of breakdown of RBC rouleaux to individual erythrocytes and the relative amount of rouleau formation in the dynamic equilibrium between rouleaux and individual erythrocytes. In this communication, the thixotropic parameters from blood samples of fifteen apparently healthy human subjects were investigated. When compared to the use of apparent viscosity values for the correlation with a pathological disorder, thixotropic parameters are preferable. The mean values of thixotropic parameters obtained from apparently healthy human subjects provide a base for comparison with the same parameters as obtained from blood samples of patients with certain pathological disorders involving the circulation.     

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.     

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.     

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.     

Obtaining the shear stress versus shear rate relationship and yield stress of blood from capillary viscometry data by Tikhonov regularization

This paper describes a procedure, based on Tikhonov regularization, for extracting the shear stress versus shear rate relationship and yield stress of blood from capillary viscometry data. The relevant equations and the mathematical nature of the problem are briefly described. The procedure is then applied to three sets of capillary viscometry data of blood taken from the literature. From each data set the procedure computes the complete shear stress versus shear rate relationship and the yield stress. Since the procedure does not rely on any assumed constitutive equation, the computed rheological properties are therefore model-independent. These properties are compared against one another and against independent measurements. They are found to be in good agreement for shear stress greater than 0.1 Pa but show significant deviations for shear stress below this level. A possible way of improving this situation is discussed.     

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.     

Non-Newtonian rheology of leukemic blood and plasma: are n and k parameters of power law model diagnostic?

When discussing the rheological properties of normal and leukemic blood it must be considered that blood is a suspension of cells in aqueous solution which is also known as plasma. Whole blood viscosity and plasma viscosity were determined by Rheometer LS30 which allows measuring whole blood and plasma viscosity in the middle and low shear rate ranges. The measurements of the viscosity showed that whole blood and plasma behave as non-Newtonian power law fluid. The values of n (non-Newtonian index) and k (consistency index) of power law fluid were calculated for both leukemic blood and plasma samples. The importance of this phenomenon for the micro-circulation is discussed.     

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.     

An instrument to evaluate the time dependent flow properties of blood at moderate shear rates

The rheology of blood is characterized by shear thinning, viscoelasticity, and thixotropy. Its rheological evaluation is usually accomplished using a torque balance technique during rotational viscometry. Because a stable torque balance does not develop instantly, studies of thixotropy and viscoelasticity of blood have usually been carried out only at low shear rate where their development is slow enough to be monitored accurately. The torque balance technique may be converted from static to dynamic by incorporating the rate of change of sensing system angular momentum. We have modified our Couette viscometer, adding a computer-controlled stepping motor and a second digital voltmeter. The latter is used to determine the angular position of the sensing system every 25 or 50 msec. The new approach allows rapid observation of the development and disappearance of shear stress, enabling us to examine the transient behavior of blood at moderate shear rate (1 to 100 inverse seconds). The transient flow behavior of blood at moderate shear rate is most easily compared directly with the behavior of Newtonian fluids. We present information about the response of our system using a torque balance observation rate of 20 per second. Blood's viscoelasticity is observed to fall substantially as shear rate rises, while its thixotropic transient excess stress rises steadily with increasing shear rate.     

Comparison between a generalized Newtonian model and a network-type multiscale model for hemodynamic behavior in the aortic arch: Validation with 4D MRI data for a case study

Blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties. Thus, an appropriate non-Newtonian model is advisable; and we choose a Modified version of the rheological model of Phan-Thien and Tanner (MPTT). The different parameters of this model, derived from the rheology of polymers, allow characterization of the non-Newtonian nature of blood, taking into account the behavior of red blood cells in plasma. Using the MPTT model that we implemented in the open access software OpenFOAM, numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient. We started from a patient-specific model which was constructed from medical images. Exiting flow boundary conditions have been developped, based on a 3-element Windkessel model to approximate physiological conditions. The parameters of the Windkessel model were calibrated with in vivo measurements of flow rate and pressure. The influence of the selected viscosity of red blood cells on the flow and wall shear stress (WSS) was investigated. Results obtained from this model were compared to those of the Newtonian model, and to those of a generalized Newtonian model, as well as to in vivo dynamic data from 4D MRI during a cardiac cycle. Upon evaluating the results, the MPTT model shows better agreement with the MRI data during the systolic and diastolic phases than the Newtonian or generalized Newtonian model, which confirms our interest in using a complex viscoelastic model.     

Measurement of erythrocyte orientation in flow by spin labeling III--erythrocyte orientation and rheological conditions

The measurements of erythrocyte orientation, obtained through a spin labeling technique, are compared with a phenomenological model. Several rheological conditions are varied: hematocrit, suspending medium viscosity, blood age, artificial reversible aggregation. We found that the onset of orientation is very sensitive to any variation of these conditions, and that its measurement would be a good method to assess erythrocyte deformability. A critical shear rate for the orientation process is then determined and compared to the corresponding parameter obtained from viscosity measurements of identical suspensions. A close qualitative relationship is found between the two sets of values of the critical shear rate.     

Rheological characterization of a fungal fermentation for the production of pneumocandins

The filamentous fungus Glarea lozoyensis produces a novel, pharmaceutically important pneumocandin (B₀) that is used to synthesize a polypeptide, which demonstrates fungicidal activity against clinically relevant pathogens. The scale-up of the pneumocandin fermentation requires an understanding of the rheological properties of the broth and the factors that influence flow behavior. A systematic approach for characterizing the rheological properties using a standard methodology is presented here. An appropriate rheometer was chosen and the effects of shear rate ramping, broth handling, creep and yield testing were examined. The fed-batch fermentation used a soluble production medium that allowed the relationship between biomass and rheological properties to be studied up to the 19-m³ scale. The morphologically heterogeneous broth demonstrated time-dependent shear thinning behavior with thixotropy and a yield stress. The flow curves were described by the power law model, with flow behavior of 0.35-0.4 and consistency index up to 10 Pa.sⁿ. The use of a cup and bob rheometer was preferable to alternative techniques, including turbine and spindle systems defined by Mitschka's technique. The consistency index and flow behavior were shown to have a non-linear relationship with biomass concentrations up to 140 g/L. The consistency index continually increased with biomass during the fermentation, while the flow behavior initially decreased rapidly and then remained at low values for the remainder of the batch cultivation. The consistency index and yield stress were influenced by temperature, osmotic pressure, and pH, while the flow behavior remained independent of these factors.     

Numerical simulation and comparative analysis of flow field in axial blood pumps

The objective study was to estimate the rheological properties and physiological compatibility of the blood pump by simulating the internal flow field of the blood pump. In this study we use computational fluid dynamics method to simulate and analyse two models of axial blood pumps with a three-blade diffuser and a six-blade diffuser, named pump I and pump II, respectively, and to compare the flow patterns of these two kinds of blood pumps while both of them satisfy the conditions of the normal human blood differential pressure and blood flow. Results indicate that (i) the high shear force occurs between the diffuser and the rotor in which the crucial place leads to haemolysis and (ii) under the condition of 100 mmHg pressure head and 5 l/min flow rate, the difference between the two kinds of blood pumps, as far as the haemolytic performance is concerned, is notable. The haemolysis index of the two pumps is 0.32% and 0.2%. In conclusion, the performance of the blood pump is influenced by the diffusers' blade number. Pump II performed better than pump I, which can be the basic model for blood pump option.     

Study of rheological properties of açai berry pulp: an analysis of its time-dependent behavior and the effect of temperature

The industry of açai-based products has been growing in the last few years. Knowledge about the physical properties of açai pulp, including its rheology, is essential to the optimization of industrial processes. This work presents the rheological behavior of açai berry pulp in relation to the effects of shear rate, temperature, and time of shearing. The entire study was carried out in the temperature range of 10–70 °C. Açai pulp showed a non-Newtonian, pseudoplastic, and time-dependent behavior. Four upward and backward shear rate cycles were evaluated, resulting in complex hysteresis loops, in which thixotropy and anti-thixotropy zones were observed. Downward flow curves could be satisfactorily represented by the Power-Law rheological model. The stress profiles as a function of shear rate obtained in the first upward curves suggest a breakdown of the initial fluid structure at low shear rates. Tests were also carried out at a constant shear rate of 20 s^?1 and, in this case, the Weltman model of thixotropy satisfactorily fit the experimental data. The activation energy, which was calculated by the Arrhenius equation, was 29.0 kJ/mol. The achievements of this work may be useful to further studies about açai pulp rheology and may contribute to process design in the açai industry.     

Human blood oscillating axially in a tube

Experiments were performed to study the rheological response of human blood at hematocrit ratios of 0 to 0.45 in axial oscillatory flow in a tube of uniform bore. Three principal regimes of flow were identified, depending on the amplitude of oscillation. At the highest amplitudes (and therefore the largest range of shear rates in the blood) there was turbulent motion and the friction coefficient increased in proportion to the square of the hematocrit. At small amplitudes the friction decreased with increase in amplitude, the rate of decrease increasing with hematocrit. At intermediate amplitudes the friction increased in proportion to the square of the hematocrit. Glutaraldehyde fixation of the red cells caused increase in the friction, and reduced the rate of decrease of friction with amplitude at small amplitudes. With a stenosis of very modest degree and span the friction in normal blood increased disproportionately, and a small blind hole in the lumen of the stenosis caused additional and disproportionate increase in friction.     

Competitive role between fibrinogen and albumin on thixotropy of red cell suspensions

Plasmatic proteins, namely fibrinogen and globulins, play a major role in red blood cell (RBC) aggregation which is accountable for the three-dimensional structure of blood. Consequently, blood rheological properties linked to this structure must be modified when the protein plasma content changes. This paper gives results and related comments on thixotropic properties of RBC suspensions (0.45 hematocrit) in isotonic solutions containing various amount of fibrinogen to which albumin is added. Thixotropic behavior of these RBC suspensions is studied with a low inertia coaxial cylinders viscometer at a shear rate step of Y = 1 s-1. Rheograms are interpreted in term of thixotropy coefficient. The main conclusion is that albumin improves RBC disaggregability of whole blood, resulting probably from a competitive effect between fibrinogen and albumin in the RBC aggregation process.     

Multiple equilibrium states in a micro-vascular network

We use a simple model of micro-vascular blood flow to explore conditions that give rise to multiple equilibrium states in a three-node micro-vascular network. The model accounts for two primary rheological effects: the Fåhræus-Lindqvist effect, which describes the apparent viscosity of blood in a vessel, and the plasma skimming effect, which governs the separation of red blood cells at diverging nodes. We show that multiple equilibrium states are possible, and we use our analytical and computational tools to design an experiment for validation.     

Measurement of the erythrocyte orientation in a flow by spin labeling

When a suspension of erythrocytes labeled in their membrane with a fatty acid paramagnetic molecule is allowed to flow in a flat quartz sample cell, the recorded electron paramagnetic spectra change as a function of the orientation of the cell in the magnetic field. This indicates that the red cells are themselves oriented in the flow. Such spectral variations have been reproduced by a numerical simulation procedure, which allowed us to quantify the proportion of oriented red blood cells by measuring the amplitude of some characteristic lines on the experimental spectra. Orientation rates were then measured as a function of various rheological parameters, such as shear rate, hematocrit and viscosity of the suspending medium. The kinetics of the disorientation process was determined by stopping the flow.