Theory of non-Newtonian viscosity of red blood cell suspension: effect of red cell deformation

The effects of the deformation of red blood cells on non-Newtonian viscosity of a concentrated red cell suspension are investigated theoretically. To simplify the problem an elastic spherical shell filled with an incompressible Newtonian fluid is considered as a model of a normal red cell. The equation of the surface of the shell suspended in a steady simple shear flow is calculated on the assumption that the deformation from a spherical shape is very small. The relative viscosity of a concentrated suspension of such particles is obtained based on the "free surface cell" method proposed by Happel. It is shown that the relative viscosity decreases as the shear rate increases.     

Wall shear stress in backward-facing step flow of a red blood cell suspension.

An experimental investigation of the wall shear stress distribution downstream of a backward-facing step is carried out. The wall shear stress distribution was determined by measuring the deformation of a gel layer, attached to the wall downstream of the step. Speckle pattern interferometry was applied to measure the deformation of the gel layer. The measured deformation, combined with the properties of the gel layer, served as an input for a finite element solid mechanics computation to determine the stress distribution in the gel layer. The wall shear stress, required to generate the measured deformation of the gel layer, was determined from these computations. A Newtonian buffer solution and a non-Newtonian red blood cell suspension were used as measuring fluids. The deformation of the gel layer was determined for a Newtonian buffer solution to evaluate the method and to obtain the properties of the gel layer. Subsequently, the wall shear stress distribution for the non-Newtonian red blood cell suspension was determined for three different flow rates. The inelastic non-Newtonian Carreau-Yasuda model served as constitutive model for the red blood cell suspension. Using this model, the velocity and wall shear stress distribution were computed by means of a finite element fluid mechanics computation. From the comparison between the numerical and the experimental results, it can be concluded that wall shear stresses, induced by the red blood cell suspension, can be modeled accurately by employing a Carreau-Yasuda model.     

Polyamines--sickling red blood cell interaction.

The binding of polyamine as a function of concentration to normal and sickling rcc'. blood cells is analyzed by Langmuir type binding isotherms, based on the Gouy-Chapman model for an electrical double Iayer, where the zeta potential is a function of only the normal distance coordinate. For normal erythrocytes, the apparent exotropic binding constants are found to be 103, 110, and 130 dl/g at normal distance coordinates of 4, 5, and 6 Å, iezpectively. The esotropic binding constant is determined to be 420 dl/g at a distance of 7 Å. For sickling red blood cells, the apparent exotropic binding constants are 3.3, 3.8, 4.6, and 6-7 dl/g at a distance of 4 to 7 Å. The esotropic binding constant at a distance of 8 Å is found to be 12-9 dl/g. The apparent binding affinity of polyamines to the normal red blood cell. therefore, is approximately 30 times greater than to the sickling erythrocyte.The Praxis pulse nuclear magnetic resonance spectrometer is used to determine the spin-lattice relaxation time (T₁) for water in the presence of normal and sickling red blood cells. The spin-lattice relaxation time is found to be 540 ms for normal erythrocytes and 445 ms for sickling red blood cells in the oxy state. Differences in the spin-spin relaxation time (T₂) for the two types of erythrocyte are negligible, being within the range of normal experimental error.     

Thermoelasticity of red blood cell membrane.

The elastic properties of the human red blood cell membrane have been measured as functions of temperature. The area compressibility modulus and the elastic shear modulus, which together characterize the surface elastic behavior of the membrane, have been measured over the temperature range of 2-50 degrees C with micropipette aspiration of flaccid and osmotically swollen red cells. In addition, the fractional increase in membrane surface area from 2-50 degrees C has been measured to give a value for the thermal area expansivity. The value of the elastic shear modulus at 25 degrees C was measured to be 6.6 X 10(-3) dyne/cm. The change in the elastic shear modulus with temperature was -6 X 10(-5) dyne/cm degrees C. Fractional forces were shown to be only on the order of 10-15%. The area compressibility modulus at 25 degrees C was measured to be 450 dyne/cm. The change in the area compressibility modulus with temperature was -6 dyne/cm degrees C. The thermal area expansivity for red cell membrane was measured to be 1.2 X 10(-3)/degrees C. With this data and thermoelastic relations the heat of expansion is determined to be 110-200 ergs/cm2; the heat of extension is 2 X 10(-2) ergs/cm2 for unit extension of the red cell membrane. The heat of expansion is of the order anticipated for a lipid bilayer idealized as twice the behavior of a monolayer at an oil-water interface. The observation that the heat of extension is positive demonstrates that the entropy of the material increases with extension, and that the dominant mechanism of elastic energy storage is energetic. Assuming that the red cell membrane shear rigidity is associated with "spectrin," unit extension of the membrane increases the configurational entropy of spectrin by 500 cal/mol.     

Theoretical and experimental study of the time dependent flow of red blood cell suspension through narrow pores

The Hemorheometer has been adapted to allow the recording of the flow rate during the filtration process. For newtonian fluids, the flow rate variation versus time through the pores is well approximated by Poiseuille's law. For dilute red blood cell suspensions, the same analysis can be applied by introducing the concept of "apparent filtration viscosity" which is higher than the usual viscosity measured by Couette viscometry. The apparent filtration viscosity parameter is related to the deformations undergone by red blood cells as they pass through the narrow pores. Apparent filtration viscosity can be used to obtain a precise determination of the erythrocyte deformability. Measurements performed, for a given blood sample, with pores of different diameters (5 microns, 8 microns and 12 microns) show that the error on the value of apparent filtration viscosity is less than 3%. As a result, the sensitivity of the filtration method allows to discriminate among normal blood samples. High concentrations of erythrocytes or leucocytes are found to modify the apparent filtration viscosity. These factors are apparent in the recorded filtration curves. Their effects on filtration measurements can be easily estimated.     

Redox metabolism of glutathione in the red blood cell.

A theoretical study of the biochemical and clinical aspects of the reduction-oxidation metabolism of glutathione in the mature red blood cell is presented. A summarizing survey of the literature data has led to the formulation of a mathematical model which comprises the kinetic properties of the enzymes partaking in the hexose monophosphate pathway (HMP) and the oxidation of NADPH and GSH. The model takes the form of a system of differential equations describing the motion of metabolites in one cell. The interactions between metabolites ane enzymes, in particular between glutathione and the SH-dependent enzymes of glucose phosphorylation and HMP have been included into the model...     

The stress-free shape of the red blood cell membrane.

The two main proposals found in the literature for the stress-free shape of the red cell membrane are (a) the bioconcave shape and (b) the sphere of the same surface area. These possibilities are evaluated in this paper using theoretical modeling of equilibrium membrane shapes according to Zarda et al. (1977. J. Biomech. 10:211-221) and by comparison to experiments on red cells whose membrane shear modulus has been increased by treatment with diamide. Neither proposal is found to be compatible with all the experimental behaviour of native red cells. Neither proposal is found to be compatible with all the experimental behaviour of native red cells. To account for this discrepancy we propose that either the shear modulus of the native membrane is dependent on the membrane strain or that the bending stiffness is higher than estimated by Evans (1980. Biophys. J. 30:265-286). These studies suggest that the bioconcave disk is the more likely possibility for the stress-free shape.     

Viscoelasticity of the human red blood cell

We report here the first measurements of the complex modulus of the isolated red blood cell (RBC). Because the RBC is often larger than capillary diameter, important determinants of microcirculatory function are RBC deformability and its changes with pathologies, such as sickle cell disease and malaria. A functionalized ferrimagnetic microbead was attached to the membrane of healthy RBC and then subjected to an oscillatory magnetic field. The resulting torque caused cell deformation. From the oscillatory forcing and resulting bead motions, which were tracked optically, we computed elastic and frictional moduli, g' and g', respectively, from 0.1 to 100 Hz. The g' was nearly frequency independent and dominated the response at all but the highest frequencies measured. Over three frequency decades, g' increased as a power law with an exponent of 0.64, a result not predicted by any simple model. These data suggest that RBC relaxation times that have been reported previously, and any models that rest upon them, are artifactual; the artifact, we suggest, arises from forcing to an exponential fit data of limited temporal duration. A linear range of response was observed, but, as forcing amplitude increased, nonlinearities became clearly apparent. A finite element model suggests that membrane bending was localized to the vicinity of the bead and dominated membrane shear. While the mechanisms accounting for these RBC dynamics remain unclear, methods described here establish new avenues for the exploration of connections among the mechanical, chemical, and biological characteristics of the RBC in health and disease. storage modulus; loss modulus; magnetic twisting cytometry; erythrocyte; viscoelasticity; rheology     

Conductometric study of shear-dependent processes in red cell suspensions. I. Effect of red blood cell aggregate morphology on blood conductance

The conductance and capacitance of flowing and quiescent red blood cell (RBC) suspensions were measured at a frequency of 0.2 MHz. The results demonstrate that the time-dependent changes in the conductance recorded during the aggregation process differ in nature for suspensions of short linear rouleaux, branched aggregates and RBC networks. It is shown that the conductance of RBC suspensions measured during the aggregation and disaggregation processes follows the morphological transformations of the RBC aggregates. Thus, this method enables characterization of the morphology of RBC aggregates formed in whole blood and in suspensions with physiological hematocrits both under flow conditions and in stasis. These results in combination with previous ones suggest that this technique can be used for studies of dynamic RBC aggregation and probably for diagnostic use.     

On the structure of agglutinated sheep red blood cell membranes.

Specimens of isolated sheep red blood cell membranes are prepared by an agglutination technique in which membranes are stacked in regular arrays. X-ray diffraction patterns are recorded from such specimens which show meridional and equatorial diffraction phenomena. The meridional reflections correspond to single lamellar repeat periods of 160-186 A. It is concluded that two asymmetric membranes are contained in the elementary period. Lipid phases with preferentially oriented hydrocarbon chains are part of the membrane structure. The stacking of the membranes is also demonstrated in the electron microscope. The X-ray scattering curve of intracellular hemoglobin of intact sheep red blood cells is recorded to a spacing of about 8 A-1. The broad diffraction rings of this scattering curve are replaced by a series of rather sharp rings, when the red blood cells are agglutinated and placed in a hypertonic medium. Both the presence of a functioning membrane and the agglutination appear to be essential for the full expression of this phenomenon.     

The aging of the red blood cell. A multifactor process

Red blood cell (rbc) senescence is associated with loss of surface sialic acid, which is the principal carrier of surface negative charge and determines the electrokinetic behavior of old rbcs. Loss of sialic acid in an old rbc is demonstrated in its decreased electric mobility and lower negative charge density, determined topographically with cationic particle labeling. Surface sialic acid determines also the mutual attraction--repulsion forces, as demonstrated in enhanced aggluinability with cationic molecules, lectins, and blood group antibodies. Loss of sialic acid accompanies ATP-depletion in vitro; thus, a T-antigen site is unmasked. Macrophages have specific receptors to the site as to newly exposed galactose and N-acetyl galactosamine sugars. Furthermore, the involvement of complement molecules in the recognition of old RBCs by macrophages has been shown. This is possibly due to loss of sialic acid or at least a regrouping--relocation of surface anionic sites due to cell shape changes from discocytes to crenated forms, which accompany both in vivo and in vitro rbc aging. In turn, shape changes are apparently controlled by the cytoskeletal network underlying the rbc membrane, which undergoes structural alteration with physiologic aging in changing the dimensions of oligomeric spectrin and the thickness of the spectrin-actin cytoskeletal assembly.     

Rabbit red blood cell hexokinase

Summary Rabbit hexokinase (EC 2.7.1.1) has been shown to exist in reticulocytes as two distinct molecular forms, designated hexokinase Ia and Ib, but only one of these was consistently present in mature red cells. In vivo, hexokinase la and Ib show a decay rate of 3 and 8% a day, respectively, while in vitro they show a similar stability.The possibility that the proteolytic activities of the reticulocyte could be responsible for the fast decay of hexokinase was investigated. No differences were found in the decay rates of hexokinase la and Ib during in vitro reticulocyte maturation in presence or absence of proteolytic inhibitors. Contrariwise, many findings indicate the ATP-dependent proteolytic system of the reticulocyte as a possible mechanism. In fact, the decay of hexokinase and the degradation of 3H-globins are both stimulated by ATP and ubiquitin; they show similar kinetic properties and both disappear during reticulocyte maturation.The cellular localization of hexokinase la and Ib was shown to be responsible for the differences found between their decay rates.Abbreviations PMSF phenylmethylsulfonyl fluoride - TPCK 1-1-tosylamide-2-phenylethyl-chloromethyl ketone - TLCK N -p-tosyl-L-lysine chloromethyl ketone