Red cell and ghost viscoelasticity. Effects of hemoglobin concentration and in vivo aging.

To assess the influence of intracellular hemoglobin concentration on red cell viscoelasticity and to better understand changes related to in vivo aging, membrane shear elastic moduli (mu) and time constants for cell shape recovery (tc) were measured for age-fractionated human erythrocytes and derived ghosts. Time constants were also measured for osmotically shrunk cell fractions. Young and old cells had equal mu, but tc was longer for older cells. When young cells were shrunk to equal the volume (and hence hemoglobin concentration and internal viscosity) of old cells, tc increased only slightly. Thus membrane viscosity (eta = mu . tc) increases during aging, regardless of increased internal viscosity. However, further shrinkage of young cells, or slight shrinkage of old cells, caused a sharp increase in tc. Because this increased tc is not explainable by elevated internal viscosity, eta increased, possibly due to a concentration-dependent hemoglobin-membrane interaction. Ghosts had a greater mu than intact cells, with proportionally faster tc; their membrane viscosity was therefore similar to intact cells. However, the ratio of old/young membrane viscosity was less for ghosts than for intact cells, indicating that differences between young and old cell eta may be partly explained by altered hemoglobin-membrane interaction during aging. It is postulated that these changes in viscoelastic behavior influence in vivo survival of senescent cells.     

Red blood cell orientation in orbit C = 0.

Two modes of behavior of single human red cells in a shear field have been described. It is known that in low viscosity media and at shear rates less than 20 s-1, the cells rotate with a periodically varying angular velocity, in accord with the theory of Jeffery (1922) for oblate spheroids. In media of viscosity greater than approximately 5 mPa s and sufficiently high shear rates, the cells align themselves at a constant angle to the direction of flow with the membrane undergoing tank-tread motion. Also, in low viscosity media, as the shear rate is increased, more and more cells lie in the plane of shear, undergoing spin with their axes of symmetry aligned with the vorticity axis of the shear field in an orbit "C = 0" (Goldsmith and Marlow, 1972). We have explored this latter phenomenon using two experimental methods. First, the erythrocytes were observed in the rheoscope and their diameters measured. Forward light scattering patterns were correlated with the red cell orientation mode. Light flux variations after flow onset or stop were measured, and the characteristic times of erythrocyte orientation and disorientation were assessed. The characteristic time of erythrocyte orientation in Orbit C = 0 is proportional to the inverse of the shear rate. The corresponding coefficient of proportionality depends on the suspending medium viscosity eta o. The disorientation time tau D, after flow has been stopped, is such that the ratio tau D/eta o is independent of the initial applied shear stress. However, tau D is much shorter than one would expect if pure Brownian motion were involved. The proportion of erythrocytes in orbit C = 0 was also measured. It was found that this proportion is a function of both the shear rate and eta o. At low values of eta o, the proportion increases with increasing shear rate and then reaches a plateau. For higher values of eta o (5 to 10 mPa s), the proportion of RBC in orbit C = 0 is a decreasing function of the shear stress. A critical transition between orbit C = 0 and parallel alignment was observed at high values of eta o, when the shear stress is on the order of 1 N/m2. Finally, the effect of altering membrane viscoelastic properties (by heat or diamide treatment) was tested. The proportion of oriented cells is a steep decreasing function of red cell rigidity.     

Ektacytometric analysis of factors regulating red cell deformability

Photometric analysis of laser diffraction patterns has been used to obtain quantitative measurements of deformability of specifically modified normal red cells. Variation of deformability with suspending medium osmolality and with applied shear stress was used to distinguish between changes in internal viscosity, surface area-to-volume ratio, and viscoelastic properties of the membrane in their influence on whole cell deformability.     

Tank-tread frequency of the red cell membrane: dependence on the viscosity of the suspending medium

Single human red cells were suspended in media with viscosities ranging from 12.9 to 109 mPa s and subjected to shear flow ranging from 1/s to 290/s in a rheoscope. This is a transparent cone-plate chamber adapted to a microscope. The motion of the membrane around red cells oriented in a steady-state fashion in the shear field (tank-tread motion) was videotaped. The projected length and width of the cells as well as the frequency of tank-tread motion were measured. One-thousand eight-hundred seventy-three cells of three blood donors were evaluated. The frequency increased with the mean shear rate in an almost linear fashion. The slope of this dependence increased weakly with the viscosity of the suspending medium. No correlation was found between the frequency and four morphological red cell parameters: the projected length and width of the cells as well as the ratio and the square root of the product of these quantities. The energy dissipation within the red cell membrane was estimated based on the measured parameters and compared to the energy dissipation in the undisturbed shear flow. At constant mean shear rate the rise of the energy dissipation with viscosity is slower whereas at constant viscosity the rise with the shear rate is steeper than in the undisturbed shear flow. A fit of the data collected in this work to a theoretical red cell model might allow one to determine intrinsic mechanical constants in the low deformation regime.     

Spin-label studies of erythrocyte deformability. IV. Relation of electron spin resonance spectral change with deformation and orientation of erythrocytes in shear flow.

Electron spin resonance (ESR) spectra of spin-labeled human erythrocytes in shear flow are simulated to derive semi-empirical relations of the ESR spectral change with deformation and orientation of the cells by using a modified theoretical model developed for deformation and orientation of liquid drops. The six observed spectra at different shear stress values were simultaneously simulated by adjusting only two parameters. One parameter can be related to the ratio of the internal to the external viscosity, and the other to the elastic property of the cell membrane. From these results we have derived a semi-empirical relationship between the average deformation index or the orientation angle with a spectral measure, which characterizes the spectral shape change induced by shear stress. Thus, it becomes possible to obtain improved quantitative information on the rheological behavior of red blood cells by using the spin-label ESR method.     

Osmolality- and hematocrit-mediated flow behavior of RBC suspensions in 33 micrometer ID tubes

The effects of suspending medium osmolality (166 to 736 mosm/kg) on relative viscosity (eta r) and tube hematocrit (HT) measured in 33 microns diameter tubes were studied for 40, 47 and 57% feed hematocrit (HF) suspensions of human RBC in buffer. At all feed hematocrits, eta r increased sharply for the hypertonic media, but was essentially insensitive to hypotonicity. HT/HF was less affected by osmolality (13% change over the entire range of osmolality and feed hematocrit). Viscosities could not be calculated from the experimental HT values. However, eta r could be predicted from RBC number concentration and the tube diameter/RBC volume ratio via a semi-empirical model. RBC transport efficiency depended on both feed hematocrit and osmolality, and was maximal at or near isotonic conditions. Our results appear applicable to non-isotonic regions of the microcirculation, and to estimation of flow resistance for RBC with abnormal cellular mechanical properties.     

Bioelectrorheological model of the cell. 2. Analysis of creep and its experimental verification

The electrorheological model of the cell proposed in Part 1 of this work was used to analyze changes in time of the shape of a cell acted on by a constant-amplitude external alternating electric field, with lossiness of the media taken into account. Shear stress in the cell membrane was determined. This model was then subjected to preliminary experimental verification using Neurospora crassa (slime) spheroplasts subjected to an external alternating electric field of constant frequency (3 MHz) and varying magnitude for different periods of time. Reversible viscoelastic cell deformation and fatigue (stiffening) of the material were observed. A satisfactory fit of the experimental data to Burgers' rheological model was found, and the values of the elastic moduli E1 = 9 X 10(2) N/m2, E2 = 2 X 10(2) N/m2 and viscosities eta 1 = 8 X 10(4) Ns/m2; eta 2 = 7 X 10(3) Ns/m2 were evaluated.     

The effects of suspending medium viscosity on erythrocyte deformation and haemolysis in vitro

Fresh adult human erythrocytes were suspended in isotonic pH adjusted solutions containing various concentrations of Dextran T.500. The cells were subjected to uniform hydrodynamic shear stress in a Ferranti Shirley Cone and Plate Viscosimeter. The amount of lysis incurred at any given combination of explosure parameters was markedly affected by the viscosity of the suspending medium. Optical diffraction patterns obtained whilst the cells were undergoing shear demonstrated that cellular deformation was also a function of viscosity. Consequently, the distorted shape of the stressed cell must play a crucial role in the haemolytic process.     

Effects of shear rate and suspending viscosity on deformation and frequency of red blood cells tank-treading in shear flows

The tank-treading rotation of red blood cells (RBCs) in shear flows has been studied extensively with experimental, analytical, and numerical methods. Even for this relatively simple system, complicated motion and deformation behaviors have been observed, and some of the underlying mechanisms are still not well understood. In this study, we attempt to advance our knowledge of the relationship among cell motion, deformation, and flow situations with a numerical model. Our simulation results agree well with experimental data, and confirm the experimental finding of the decrease in frequency/shear-rate ratio with shear rate and the increase of frequency with suspending viscosity. Moreover, based on the detailed information from our simulations, we are able to interpret the frequency dependency on shear rate and suspending viscosity using a simple two-fluid shear model. The information obtained in this study thus is useful for understanding experimental observations of RBCs in shear and other flow situations; the good agreement to experimental measurements also shows the potential usefulness of our model for providing reliable results for microscopic blood flows.     

Motion and deformation of a red blood cell in a shear flow: a two-dimensional simulation of the wall effect

The motion and deformation of a single red blood cell in a simple shear flow between two parallel walls is studied theoretically. A two-dimensional deformable microcapsule is adopted as a model for the cell, which has a thin moving membrane, like a tank-tread, around the interior and is deformed into an elliptical shape with a constant area. Applying the finite element method to the Stokes equations, the tank-tread motion and deformation is determined in a stationary motion, under fluid dynamic interaction between the cell and the walls. It is shown that the motion and deformation of the microcapsule crucially depends on the channel width between the two walls. As the width decreases, the microcapsule is more elongated and the frequency of tank-tread motion decreases at a constant shear rate. In addition, the angle of inclination decreases at the low range of the viscosity ratio of internal to external fluids and increases at the high range. The results obtained are compared with experimental observations and applied to the behavior of cells under mutual interaction.     

Computation of the average shear-induced deformation of red blood cells as a function of osmolality

A model was developed for computing the average deformation of red cells as a function of suspending medium osmolality. It assumes a population of red cells characterized by a single value for surface area and for isotonic volume, but having a Gaussian distribution in mean intracellular hemoglobin concentration (MCHC). The ability of cells of a given hemoglobin concentration to deform is assumed to be limited by either the amount of redundant surface area available or the intracellular viscosity, determined by the intracellular hemoglobin concentration. The surface area limitation is calculated by finding the dimensions of a prolate ellipsoid having the volume and surface area of the red cell. The viscosity limitation is incorporated in two ways. First, the ratio of intracellular to extracellular viscosity must lie below a certain threshold to permit deformation, and second, its magnitude determines the extent of cell elongation. This model gave a reasonable fit to experimental data for a threshold viscosity ratio close to 1. Extension to cell populations for which either mean cell hemoglobin concentration or surface area had been modified also provided a close reproduction of the experimental curves.     

The growth response of cells in medium made hyperosmolal with electrolytes or mannitol.

A comparison of the growth rates of established human lymphoid and tumor cell lines was performed in nutrient medium made hyperosmolal with mannitol, NaCl, or mixtures of NaCl and KCl at a constant Na/K ratio. It was found that considerably higher osmolalities were attained with mannitol than electrolytes before a reduction in the growth rate of the culture was observed. This suggests that mannitol and electrolytes affected the growth rate through different mechanisms. Mannitol uptake was studied with two of the cell lines and both cell lines were found to be permeable to mannitol. This eventually would have eliminated the osmolality gradient between the interior of the cell and the medium, and could explain why higher osmolalities were obtained with mannitol before the growth rate was effected. In addition, initial experiments showed that these cell lines may also be able to metabolize mannitol.     

Mechanical and chemical injury to thylakoid membranes during freezing in vitro

The relative contributions of membrane rupture due to osmotic stress and of chemical membrane damage due to the accumulation of cryotoxic solutes to cryoinjury was investigated using thylakoid membranes as a model system. When thylakoid suspensions were subjected to a freeze-thaw cycle in the presence of different molar ratios of NaCl as the cryotoxic solute and sucrose as the cryoprotective solute, membrane survival first increased linearly with the osmolality of the solutions used to suspend the membranes, regardless of the molar ratio of salt to sucrose. It subsequently decreased when the ratio of sucrose to salt was not sufficiently high for complete cryopreservation by sucrose. There was an optimum of cryopreservation at intermediate osmolalities (approx. 0.1 osmol/kg). This optimum of cryopreservation at a given sucrose concentration could be shifted to lower solute concentration, if mixtures of NaCl and NaBr were used instead of NaCl alone. At suboptimal initial osmolalities, damage is attributed mainly to membrane rupture. Under these conditions, cryopreservation is not influenced by the chaotropicity of the suspending medium. At supraoptimal initial solute concentrations, solute (i.e., chemical) effects determine membrane survival. Under these conditions, increased ratios of sugar to salt increased cryoprotection. In mixtures of NaCl and NaBr at constant molar ratios of salt to sucrose, chemical membrane damage was quantitatively related to the lyotropic properties of the ions used. The degree of chemical damage becomes more pronounced with rising osmolalities of the suspending media. With NaF as the cryotoxic solute, damage was more severe than should be expected from its lyotropic properties. This may reflect a specific interaction of fluoride with the membranes. Protein release from the membranes during freezing in the presence of different anions was qualitatively comparable at identical ratios of sugar to salt. However, the total amount of protein released was correlated linearly with membrane inactivation, even when different anions acted on the membranes. Gel electrophoretic analysis of proteins released from thylakoid membranes during freezing revealed discrete bands indicative of mechanical and chemical damage, respectively.     

Analysis of red blood cell motion through cylindrical micropores: effects of cell properties.

Filtration through micropores is frequently used to assess red blood cell deformability, but the dependence of pore transit time on cell properties is not well understood. A theoretical model is used to simulate red cell motion through cylindrical micropores with diameters of 3.6, 5, and 6.3 microns, and 11-microns length, at driving pressures of 100-1000 dyn/cm2. Cells are assumed to have axial symmetry and to conserve surface area during deformation. Effects of membrane shear viscosity and elasticity are included, but bending resistance is neglected. A time-dependent lubrication equation describing the motion of the suspending fluid is solved, together with the equations for membrane equilibrium, using a finite difference method. Predicted transit times are consistent with previous experimental observations. Time taken for cells to enter pores represents more than one-half of the transit time. Predicted transit time increases with increasing membrane viscosity and with increasing cell volume. It is relatively insensitive to changes in internal viscosity and to changes in membrane elasticity except in the narrowest pores at low driving pressures. Elevating suspending medium viscosity does not increase sensitivity of transit time to membrane properties. Thus filterability of red cells is sensitively dependent on their resistance to transient deformations, which may be a key determinant of resistance to blood flow in the microcirculation.     

On the measurement of shear elastic moduli and viscosities of erythrocyte plasma membranes by transient deformation in high frequency electric fields.

We present a new method to measure the shear elastic moduli and viscosities of erythrocyte membranes which is based on the fixation and transient deformation of cells in a high-frequency electric field. A frequency domain of constant force (arising by Maxwell Wagner polarization) is selected to minimize dissipative effects. The electric force is thus calculated by electrostatic principles by considering the cell as a conducting body in a dielectric fluid and neglecting membrane polarization effects. The elongation A of the cells perpendicular to their rotational axis exhibits a linear regime (A proportional to Maxwell tension or to square of the electric field E2) at small, and a nonlinear regime (A proportional to square root of Maxwell tension or to the electric field E) at large extensions with a cross-over at A approximately 0.5 micron. The nonlinearity leads to amplitude-dependent response times and to differences of the viscoelastic response and relaxation functions. The cells exhibit pronounced yet completely reversible tip formations at large extensions. Absolute values of the shear elastic modulus, mu, and membrane viscosity, eta, are determined by assuming that field-induced stretching of the biconcave cell may be approximately described in terms of a sphere to ellipsoid deformation. The (nonlinear) elongation-vs.-force relationship calculated by the elastic theory of shells agress well with the experimentally observed curves and the values of mu = 6.1 x 10(-6) N/m and eta = 3.4 x 10(-7) Ns/m are in good agreement with the micropipette results of Evans and co-workers. The effect of physical, biochemical, and disease-induced structural changes on the viscoelastic parameters is studied. The variability of mu and eta of a cell population of a healthy donor is +/- 45%, which is mainly due to differences in the cell age. The average mu value of cells of different healthy donors scatters by +/- 18%. Osmotic deflation of the cells leads to a fivefold increase of mu and 10-fold increase of eta at 500 mosm. The shear modulus mu increases with temperature showing that the cytoskeleton does not behave as a network of entropy elastic springs. Elliptic cells of patients suffering from elliptocytosis of the Leach phenotype exhibit a threefold larger value of mu than normal discocytes of control donors. Cross-linking of the spectrin by the divalent S-H agents diamide (1 mM, 15 min incubation) leads to an eightfold increase of mu whereas eta is essentially constant. The effect of diamide is reversed after treatment with S-S bond splitting agents.     

Cat Heart Muscle in Vitro : IX. Cell ion and water contents in anisosmolal solutions

Cell contents of water, K, Na, and Cl have been determined in cat right ventricular papillary muscles immersed in solutions with and without NaCl when the external osmolality was varied with sucrose. The plot of cell water/kilogram dry weight (corrected for sucrose content) vs. (external osmolality)^-1 suggests that not less than 82% of water present in cells at physiological external osmolality is free to move across the cell membrane in response to an imposed osmotic gradient. Cells fail to increase their water content in very hypotonic solutions. For osmolalities greater than 5 times isosmolal, at which the mannitol space and the Cl³⁶ space are both equal to 100% of muscle water, rather large amounts of univalent cation appear to remain "bound" to the tissue.     

Red cell extensional recovery and the determination of membrane viscosity.

A theory of membrane viscoelasticity developed by Evans and Hochmuth in 1976 is used to analyze the time-dependent recovery of an elongated cell. Before release, the elongated cell is the static equilibrium where external forces are balanced by membrane elastic force resultants. Upon release, the cell recovers its initial shape with a time-dependent exponential behavior characteristic of the viscoelastic solid model. It is shown that the model describes the time-dependent recovery process very well for a time constant in the range of 0.1-0.13 s. The time constant is the ratio membrane surface viscosity eta:membrane surface elasticity mu. Measurements for the shear modulus mu of 0.006 dyne/cm give a value for the surface viscosity of red cell membrane as a viscoelastic solid material of eta = mu tc = (6-8) X 10(-4) poise . cm.     

Rheological properties of mammalian cell culture suspensions: Hybridoma and HeLa cell lines

Data on viscous (eta') and elastic (eta') components of the complex viscosity versus oscillatory angular frequency (0.01 to 4.0 rad/s) with increasing strains were obtained for hybridoma cell (62'D3) and HeLa cell (S3) suspensions in PBS at 0.9 (mL/mL) cell volume fraction using a Weissenberg rheogoniometer equipped with two parallel plate geometry at ambient temperature. Both cell suspensions exhibited shear thinning behavior. From the measured viscoelastic properties, the yield stress was calculated. Hybridoma cell suspension (15 mum as the mean diameter of cells) showed the yield stress at 550 dyne/cm(2) that was 1.8 times higher than the value of HeLa cell suspension (22 mum mean diameter) as measured at the oscillatory angular frequency, 4.0 rad/s. The apparent viscosities of HeLa cell suspension at four concentrations and varying steady shear rate were also determined using the Brookfield rotational viscometer. The yield stress to steady shear test was about 130 dyne/cm(2) for HeLa cell suspension at 0.9 (mL/mL) cell volume fraction. The apparent viscosity was in the range about 1 approximately 1000 Poise depending on the cell concentration and shear rate applied. A modified semiempirical Mooney equation, \documentclass{article}\pagestyle{empty}\begin{document}$ \eta = \eta _0 \exp [K\dot \gamma ;{ - \beta } \phi /(1 - K'\sigma \phi _c /D)] $\end{document} was derived based on the cell concentration, the cell morphology, and the steady shear rate. The beta, shear rate index, was estimated as 0.159 in the range of shear rate, 0.16 to 22.1 s(-1), for the cell volume fractions from 0.6 to 0.9 (mL/mL). In this study, the methods of determining the shear sensitivity and the viscous and the elastic components of mammalian cell suspensions are described under the steady shear field. (c) 1993 John Wiley & Sons, Inc.     

Detection of red cell aggregation by low shear rate viscometry in whole blood with elevated plasma viscosity

The viscosity of whole blood measured at low shear rates is determined partly by shear resistance of the red cell aggregates present, stronger aggregation increasing the viscosity in the absence of other changes. Effects of cell deformability can confound interpretation and comparison in terms of aggregation, however, particularly when the plasma viscosity is high. We illustrate the problem with a comparison of hematocrit-adjusted blood from type 1 diabetes patients and controls in which it is found the apparent and relative viscosities at a true shear rate of 0.20 s-1 are lower in the patient samples than age matched controls, in spite of reports that aggregation is increased in such populations. Because the plasma viscosities of the patients were higher on average than controls, we performed a series of experiments to examine the effect of plasma protein concentration and viscosity on normal blood viscosity. Dilution or concentration by ultrafiltration of autologous plasma and viscosity measurements at low shear on constant hematocrit red cell suspensions showed (a) suspension viscosity at 0.25 and 3 s-1 increased monotonically with plasma protein concentration and viscosity but (b) the relative viscosity increased, in concert with the microscopic aggregation grade, up to a viscosity of approximately 1.25 mPa-s but above this the value the relative viscosity no longer increased as the degree of aggregation increased in concentrated plasmas. It is suggested that in order to reduce cell deformation effects in hyperviscous pathological plasmas, patient and control plasmas should be systematically diluted before hematocrit is adjusted and rheological measurements are made. True shear rates should be calculated. Comparison of relative viscosities at low true shear rates appears to allow the effects of red cell aggregation to be distinguished by variable shear rate viscometry in clinical blood samples.     

Effects of gender and age on thixotropic properties of whole blood from healthy adult subjects

The thixotropic parameters of whole blood from 314 healthy subjects (154 women, 160 men) were measured with our modified method by Low shear 30 Rheometer and calculated according Huang's equation. This communication offered the reference range of thixotropic parameters from man and woman group. The results demonstrated that no significant differences existed in the plasma viscosity and fibrinogen between man and woman group. Man group had statistically higher values in HCT, yield stress (tau 0), Newtonian contribution of viscosity (mu), non-Newtonian contribution of viscosity (eta s--mu), apparent viscosity at 2.37 sec-1 (eta s), the equilibrium value of the structural parameter (A) and apparent kinetic rate constant of rouleaux breakdown (ARC) than those in woman group. The man and woman groups could be separately divided into five subgroups in terms of age. It was found that the levels of fibrinogen and plasma viscosity had a tendency of increasing with aging. In the old subgroup (greater than 60 years) of men and women HCT, tau v, mu, eta s, (eta s--mu) and A had significant lower values than those in young and middle-age subgroups. However, it was very interested that there were differences of ARC versus age between man group and woman group, i.e. ARC in the man subgroup II, IV had lower and the woman subgroup II, III, IV had higher values than their respective older subgroup did.