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.     

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.     

The equilibrium size distribution of rouleaux.

Rouleaux are formed by the aggregation of red blood cells in the presence of macromolecules that bridge the membranes of adherent erythrocytes. We compute the size and degree of branching of rouleaux for macroscopic systems in thermal equilibrium in the absence of fluid flow. Using techniques from statistical mechanics, analytical expressions are derived for (a) the average number of rouleaux consisting of n cells and having m branch points; (b) the average number of cells per rouleau; (c) the average number of branch points per rouleau; and (d) the number of rouleaux with n cells, n = 1, 2, ..., in a system containing a total of N cells. We also present the results of numerical evaluations to establish the validity of asymptotic expressions that simplify our formal analytic results.     

Kinetics of rouleau formation. II. Reversible reactions.

Red blood cells aggregate face-to-face to form long, cylindrical, straight chains and sometimes branched structures called rouleaux. Here we extend a kinetic model developed by R. W. Samsel and A. S. Perelson (1982, Biophys. J. 37:493-514) to include both the formation and dissociation of rouleaux. We examine thermodynamic constraints on the rate constants of the model imposed by the principle of detailed balance. Incorporation of reverse reactions allows us to compute mean sizes of rouleaux and straight chain segments within rouleaux, as functions of time and at equilibrium. Using the Flory - Stockmayer method from polymer chemistry, we obtain a closed-form solution for the size distribution of straight chain segments within rouleaux at any point in the evolution of the reaction. The predictions of our theory compare favorably with data collected by D. Kernick , A.W.L. Jay , S. Rowlands , and L. Skibo (1973, Can. J. Physiol. Pharmacol. 51:690-699) on the kinetics of rouleau formation. When rouleaux grow large, they may contain rings or loops and take on the appearance of a network. We demonstrate the importance of including the kinetics of ring closure in the development of realistic models of rouleaux formation.     

Kinetics of rouleau formation. I. A mass action approach with geometric features.

In the presence of certain macromolecules, such as fibrinogen, immunoglobulin, dextran, and polylysine, erythrocytes tend to aggregate and form cylindrical clusters called "rouleaux" in which cells resemble coins in a stack. The aggregates may remain cylindrical or they may branch, forming tree, and networklike structures. Using the law of mass action and notions from polymer chemistry, we derive expressions describing the kinetics of the early phase of aggregation. Our models generalize work initiated by Ponder in 1927 who used the Smoluchowski equation to predict the concentration of rouleaux of different sizes. There are two novel features to our generalization. First, we allow erythrocytes that collide near the end of a stack of cells to move to the end of the cylinder and elongate it. Second, we incorporate geometric information into our models and describe the kinetics of branched rouleau formation. From our models we can predict the concentration of rouleaux with n cells and b branches, the mean number of cells per rouleau, the mean number of branches per rouleau, and the average length of a branch. Comparisons are made with the available experimental data.     

Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method

In this paper we develop a lattice Boltzmann algorithm to simulate red blood cell (RBC) behavior in shear flows. The immersed boundary method is employed to incorporate the fluid-membrane interaction between the flow field and deformable cells. The cell membrane is treated as a neo-Hookean viscoelastic material and a Morse potential is adopted to model the intercellular interaction. Utilizing the available mechanical properties of RBCs, multiple cells have been studied in shear flows using a two-dimensional approximation. These cells aggregate and form a rouleau under the action of intercellular interaction. The equilibrium configuration is related to the interaction strength. The end cells exhibit concave shapes under weak interaction and convex shapes under strong interaction. In shear flows, such a rouleau-like aggregate will rotate or be separated, depending on the relative strengths of the intercellular interaction and hydrodynamic viscous forces. These behaviors are qualitatively similar to experimental observations and show the potential of this numerical scheme for future studies of blood flow in microvessels.     

Aggregation and disaggregation of red blood cells

The aggregation of red blood cells may be analyzed as an interaction of an adhesive surface energy and the elastic stored energy which results from deformation of the cell. The adhesive surface energy is the work required to separate a unit adhered area and is the resultant of adhesive forces due to the bridging molecules that bind the cells together and the electrostatic repulsion due to surface charge. The elastic strain energy in the case of the red blood is associated with the membrane elasticity only since the interior of the cell is liquid. The membrane elasticity is due both to bending stiffness and shear. The area expansion is small and may be neglected. These assumptions allow realistic computation of red cell shapes in rouleaux. The disaggregation of rouleaux requires an external force which must overcome the adhesive energy and also supply additional elastic energy of deformation. Depending on the geometry, the initial effect of elastic energy may tend to aid disaggregation. In a shear flow, the stresses on a suspended rouleau alternately tend to compress and to disaggregate the cells if they are free to rotate. This introduces a time dependence so that viscous effects due to the viscosity of the cell membrane, the cell cytoplasm and the external fluid may play a role in determining whether disaggregation proceeds to completion or not.     

The dynamics of shear disaggregation of red blood cells in a flow channel

Red blood cell (RBC) rouleaux were formed in a flow channel in the presence of 2 g/dl dextran (molecular weight 76,000). The partial separation of RBC rouleau doublets adhering to the floor of the flow channel in response to small oscillatory shear stresses was observed experimentally. Theoretical analyses on displacement and drag force were performed to determine whether the motion of the cell involves membrane rotation (i.e., rolling) or sliding. From the experimental data and the results of theoretical analyses, it is concluded that, under the conditions of the experiments, the RBCs in a doublet separate from each other by rolling, rather than sliding of the sheared cell.     

Kinetics of linear rouleaux formation studied by visual monitoring of red cell dynamic organization

Red blood cells (RBCs) in the presence of plasma proteins or other macromolecules may form aggregates, normally in rouleaux formations, which are dispersed with increasing blood flow. Experimental observations have suggested that the spontaneous aggregation process involves the formation of linear rouleaux (FLR) followed by formation of branched rouleaux networks. Theoretical models for the spontaneous rouleaux formation were formulated, taking into consideration that FLR may involve both "polymerization," i.e., interaction between two single RBCs (e + e) and the addition of a single RBC to the end of an existing rouleau (e + r), as well as "condensation" between two rouleaux by end-to-end addition (r + r). The present study was undertaken to experimentally examine the theoretical models and their assumptions, by visual monitoring of the spontaneous FLR (from singly dispersed RBC) in plasma, in a narrow gap flow chamber. The results validate the theoretical model, showing that FLR involves both polymerization and condensation, and that the kinetic constants for the above three types of intercellular interactions are the same, i.e., k(ee) = k(er) = k(rr) = k, and for all tested hematocrits (0.625-6%) k < 0.13 +/- 0.03 s(-1).     

Segregation into separate rouleaux of erythrocytes from different species. Evidence against the agglomerin hypothesis of rouleaux formation.

Erythrocytes from one species were labelled with fluorescein isothiocyanate and mixed with unlabelled erythrocytes from another species. Albumin polymers were added to generate rouleaux. The species of origin of erythrocytes in rouleaux was determined by fluorescence microscopy. Erythrocytes from different species segregated into independent rouleaux. However, fluorescent and non-fluorescent erythrocytes from one individual were mixed randomly in rouleaux. These results confirm, using a novel experimental approach, previous observations of Sewchand & Canham [(1976) Can. J. Physiol. Pharmacol. 54, 437-442]. Since rouleaugenic agents are not species-specific, under the 'agglomerin' hypothesis of rouleau formation they would be expected to form bridges between cells from different species. It follows that either the agglomerin hypothesis is incorrect, or additional species-specific surface components are involved in the aggregation of agglomerin-cross-bridged cells.     

Fibrinogen-induced erythrocyte aggregation: erythrocyte-binding site in the fibrinogen molecule

The effect of fibrinogen and fibrinogen-derived products on the velocity of rouleau formation of human erythrocytes was quantitatively examined with a rheoscope combined with a video-camera, an image analyzer and a computer. (i) The velocity of rouleau formation by naturally occurring low-molecular-weight fibrinogen of 305 kDa and by desialylated fibrinogen was the same as that by native fibrinogen of 340 kDa. (ii) Concerning fibrinogen degradation products by plasmin, the velocity of rouleau formation decreased upon going from fibrinogen greater than fragment X greater than fragment Y (the ratio of molar concentration of fibrinogen, fragment X and fragment Y for giving a certain velocity of rouleau formation was approx. 1:2:5). The effect of fragments X and Y on the fibrinogen-induced rouleau formation was additive. (iii) Fragments D and E could not induce rouleau formation and did not affect the fibrinogen-, fragment X- and fragment Y-induced rouleau formation. (iv) Fibrinopeptides A and B and artificial tetrapeptides (Gly-Pro-Arg-Pro and Gly-His-Arg-Pro) did not affect the fibrinogen-induced rouleau formation. (v) The possible erythrocyte-binding site in fibrinogen molecule for leading to rouleaux was proposed to be in A alpha-chain (probably, around residues No. 207-303) near the terminal domain of the trinodular structure of fibrinogen.     

Rheological behaviors of bovine blood forming artificial rouleaux

A purpose of the present study is to make an artificial rouleau of bovine red blood cells which is not capable of rouleau formation under physiological condition. Rheological behaviors of bovine blood forming artificial rouleaux were examined. The modification of cell surface by enzyme trypsin induced rouleau formation, whereas the modification of cell surface by neuraminidase did not cause any aggregate formation. The drastic elevation of the fibrinogen content in bovine red blood cells suspension also brought about the formation of rouleau. The value of dynamic rigidity modulus G' of bovine red blood cells in saline solution containing high concentration of fibrinogen is somewhat smaller than that of trypsin treated bovine red blood cells in plasma. The value of G' of trypsin treated bovine red blood cells in plasma first increased to a maximum value and then decreased with the time. It is supposed that the removal of macro-molecules from the cell surface facilitates the mutual approach of cells and causes the formation of rouleau which seems to be the same as that of human and horse bloods.     

Dielectric approach to investigation of erythrocyte aggregation. II. Kinetics of erythrocyte aggregation-disaggregation in quiescent and flowing blood

A method based on dielectric properties of dispersed systems was applied to investigate the kinetics of RBC aggregation and the break-up of the aggregates. Experimentally, this method consists of measuring the capacitance at a frequency in the beginning of the beta-dispersion. Two experimental protocols were used to investigate the aggregation process. In the first case, blood samples were fully dispersed and then the flow was decreased or stopped to promote RBC aggregation. It was found that the initial phases of RBC aggregation are not affected by the shear rate. This finding indicates that RBC aggregation is a slow coagulation process. In the second case, RBCs aggregated under flow conditions at different shear rates and after the capacitance reached plateau levels, the flow was ceased. The steady-state capacitance of the quiescent blood and the kinetics of RBC aggregation after stoppage of shearing depend on the prior shear rate. To clarify the reasons for this effect, the kinetics of the disaggregation process was studied. In these experiments, time courses of the capacitance were recorded under different flow conditions and then a higher shear stress was applied to break up RBC aggregates. It was found that the kinetics of the disaggregation process depend on both the prior and current shear stresses. Results obtained in this study and their analysis show that the kinetics of RBC aggregation in stasis consists of two consecutive phases: At the onset, red blood cells interact face-to-face to form linear aggregates and then, after an accumulation of an appropriate concentration of these aggregates, branched rouleaux are formed via reactions of ends of the linear rouleaux with sides of other rouleaux (face-to-side interactions). Branching points are broken by low shear stresses whereas dispersion of the linear rouleaux requires significantly higher energy.     

The superposition of steady on oscillatory shear and its effect on the viscoelasticity of human blood and a blood-like model fluid

To understand the pulsatility of human blood flow in vivo, it is necessary to separately investigate (1) steady shear and oscillatory flow, and (2) the superposition of steady shear flow on oscillatory flow performed under in vitro conditions. In this study a variable steady shear rate was superimposed in parallel on oscillatory shear at a constant frequency (0.5 Hz) for human blood (45% hematocrit), and an aqueous polyacrylamide polymer solution (AP 30E, concentration 300 ppm). The effect of superposition of the above two shear flows on the viscoelasticity of blood was more pronounced for the elastic (η′') than for the viscous (η′) component of viscoelasticity. With increasing superimposed shear rate, both η′ and η′' decreased, especially at the low shear region. This behavior can be explained by the viscoelastic properties of blood and the phenomena of blood aggregation and disaggregation. Quantitatively, the dependence of the viscous component of complex viscosity on superimposed shear for both blood and polymer solution is described by a modified Carreau equation. The elastic component of complex viscosity decreased exponentially with increasing superimposed shear, and it is described by an exponential model. © 1997 Elsevier Science Ltd     

Effects of shear flow on photosynthesis in a dilute suspension of microalgae

This study investigates the effects of shear stress on photosynthesis in dilute suspensions of Spirulina platensis and Chlorella by measuring the oxygen production rate using a coaxial, double-rotating-cylinder apparatus that generates Couette shear flow. Our device enables up to 0.6 Pa shear stress to be applied, which has the hydrodynamic effect of generating the algal motion and acutely augmenting the oxygen production rate of Spirulina, primarily because the surface area of algae exposed to illumination is increased. However, there is shear-flow limitation on any increase in oxygen production, and the shear stress at maximum oxygen production rate tends to decrease with increasing temperature. The comparative study with Chlorella showed the reverse relationship between oxygen production and shear stress, and the cause of this difference is discussed in terms of several factors such as size, shape, hydrodynamic stress capacity and others.     

Inhibition and acceleration of erythrocyte aggregation induced by small macromolecules

The aggregation (especially the 'rouleau' formation) of human erythrocytes induced by polysaccharide and polyglutamic acid was quantitatively examined by using a low-shear rheoscope combined with a television image analyzer and a computer. (1) The morphological characteristics of rouleaux induced by these macromolecules are presented. (2) Polysaccharides with high molecular weights of 70 400 and 494 000 and poly(glutamic acids) with weights of 50 000 and 66 000 formed the rouleaux (then the three-dimensional aggregates). But polysaccharides with the low molecular weights of 10 300 and 42 500 and poly(glutamic acids) with weights of 8000 and 20 000 did not. The dependences of the velocity of rouleau formation on the macromolecule concentration and on the shear rate are shown. (3) The erythrocyte aggregation induced by high-molecular-weight polysaccharides was inhibited by low-molecular-weight polysaccharides and glucose, but was not affected by low-molecular-weight poly(glutamic acids). (4) The aggregation induced by high-molecular-weight poly(glutamic acids) was inhibited by poly(glutamic acid) with a molecular weight of 8000, but was accelerated by that of 20 000. The poly(glutamic acid)-induced aggregation was not affected by low-molecular-weight polysaccharides. (5) The stereochemical structure-dependent interaction (or the mode of bridging) of macromolecules with erythrocytes was stressed for the mechanism of erythrocyte aggregation.     

Modes of rouleaux formation of human red blood cells in polyvinylpyrrolidone and dextran solutions

The mechanics by which normal human erythrocytes join on a plastic cover slip into two cell doublets and larger aggregates of rouleaux were studied microscopically. Polyvinylpyrrolidone (PVP-360) or dextran (DX-70 or DX-110) were used as the rouleau agents. The minimum concentration of the rouleau-inducing agents required to form doublets was 1 g/L for PVP-360 and 5 g/L for the DXs. Three modes of interaction were observed in Ringer's solution with PVP or DX, cresting and flipping (involving no intercellular sliding) and a sliding mode of doublet formation (involving less gravitational work and less cellular deformation). The sliding mechanism occurred in suspensions with the lower concentrations of the rouleau agent but was also observed when geometric constraints prevented the nonsliding interaction of larger groups of cells in the higher concentrations of the rouleau agent. The technique provides a sensitive index for studying the combined effect of cellular flexibility and intercellular adhesion. Significant changes were observed for reduced membrane surface charge or reduced ionic calcium.     

The forward rate of binding of surface-tethered reactants: effect of relative motion between two surfaces

The reaction of molecules confined to two dimensions is of interest in cell adhesion, specifically for the reaction between cell surface receptors and substrate-bound ligand. We have developed a model to describe the overall rate of reaction of species that are bound to surfaces under relative motion, such that the Peclet number is order one or greater. The encounter rate between reactive species is calculated from solution of the two-dimensional convection-diffusion equation. The probability that each encounter will lead to binding depends on the intrinsic rate of reaction and the encounter duration. The encounter duration is obtained from the theory of first passage times. We find that the binding rate increases with relative velocity between the two surfaces, then reaches a plateau. This plateau indicates that the increase in the encounter rate is counterbalanced by the decrease in the encounter duration as the relative velocity increases. The binding rate is fully described by two dimensionless parameters, the Peclet number and the Damk?hler number. We use this model to explain data from the cell adhesion literature by incorporating these rate laws into "adhesive dynamics" simulations to model the binding of a cell to a surface under flow. Leukocytes are known to display a "shear threshold effect" when binding selectin-coated surfaces under shear flow, defined as an increase in bind rate with shear; this effect, as calculated here, is due to an increase in collisions between receptor and ligand with increasing shear. The model can be used to explain other published data on the effect of wall shear rate on the binding of cells to surfaces, specifically the mild decrease in binding within a fixed area with increasing shear rate.     

Shear breakage of nylon membrane microcapsules in a turbine reactor

The breakage of nylon membrane microcapsules is proposed as a new method to study and quantify shear effects in biological systems. A critique of this method shows that a narrower particle size distribution may be an important improvement in the breakage study as well as breakage control in many bioreactor and biotechnological applications. In a turbine reactor, it was shown that the primary process which determines the microcapsule breakage is the shear effect. The breakage kinetics are first order with regard to the microcapsule concentration. The breakage kinetic constant was ob served to be dependent on the temperature and the particle size, and proportional to the average shear rate and the third power of the turbine angular velocity. Decrease of the breakage kinetic constant with temperature can be explained by a decrease of fluid viscosity and a change in nylon membrane properties. An increase in the breakage kinetic constant with the microcapsule diameter can be due to a lowering of internal pressure and a reduction of the membrane resistance with size. Proportionality between the breakage kinetic constant and the shear rate shows that shear is the main process which leads to microcapsule breakage. The additional intervention in the shear rate expression of the turbine angular speed in the form of the turbine and particle velocities, results in the dependence of the breakage kinetic constant on the third power of the angular velocity.