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.     

Effect of zymosan-activated plasma on the deformability of rabbit polymorphonuclear leukocytes.

Intravascular infusion of inflammatory mediators causes a sudden neutropenia due to the sequestration of polymorphonuclear leukocytes (PMN) within the microvasculature of the lung and other organs. This sequestration could be due to a decrease in the ability of PMN to deform and pass through the narrow capillary bed. The purpose of this study was to determine if the complement fragments present in zymosan-activated plasma (ZAP) caused a rapid stiffening of PMN. The PMN deformability was determined by measuring the pressure required to pass PMN through a polycarbonate filter containing 5-micron pores at a constant flow rate as well as the extraction of PMN compared with red blood cells and 125I-labeled albumin by the filter. The role of the cytoskeleton in PMN deformation was examined in studies where F-actin formation was inhibited using cytochalasin B or microtubule assembly was inhibited using colchicine. The results showed that treatment with ZAP induced a rapid decrease in PMN deformability. Inhibiting the formation of F-actin made the unstimulated PMN more deformable and reduced the stiffening induced by ZAP. In contrast, inhibition of microtubule reassembly did not alter either normal deformability or the ZAP-induced decrease in deformability. In vivo, colchicine increased normal PMN margination but did not inhibit the rapid sequestration of PMN induced by infusion of ZAP. These studies indicate that ZAP induces a rapid decrease in PMN deformability that is mediated through the cytoskeleton. They suggest that this decrease is due to the polymerization of F-actin.     

A continuum theory of blood cells filtration at low flow rates

Blood cells filtration with decreasing pressure under gravity was studied for evaluation of the cell fluidity or deformability at a low shear state. A continuum approach was made to the flow and pressure in the filter at the low flow state to relate macro- and micro-scopic quantities. The mass conservation law of each species provided a set of differential equations with respect to the pore fraction and filter resistance. The numerical calculation was made for various values of hematocrit and leukocrit. It was shown that the filter resistance might be increased with decreasing pressure, resulting from both red and white cells. The leukocrit, more than 0.05% white cells, may influence the filtration, depending upon the cell deformation. Even in the absence of the white cell, a decrease in pressure increased the filter resistance markedly. The present result indicates that single red cell shows a nonlinear behavior of flow in pores at the low pressure level.     

Decreased membrane deformability in Melanesian ovalocytes from Papua New Guinea

We examined the ability of Melanesian ovalocytes from Papua New Guinea to be deformed in order to probe the resistance of these cells to invasion by several species of malaria parasite. We found ovalocytes were refractile to drug-induced endocytosis, that they formed abnormal rouleaux, showed reduced deformability when aspirated into 0.6-micron diameter pores in polycarbonate sieves, and failed to crenate when mounted under a glass coverslip. No substantial differences were found between normocytes and ovalocytes in their initial rate of filtration through 4.5-micron pore polycarbonate sieves, their membrane fluidity as measured by the rate of depolarization of fluorescent probes or the rate of extraction of cytoskeletal proteins in low ionic strength buffers. We conclude that the resistance of ovalocytes to undergo localized deformation might be significant in explaining the resistance of these cells to invasion by malarial merozoites.     

Field diagnosis of urinary schistosomiasis by multiple use of nuclepore urine filters

It has been recognized recently that the standard field technique for the diagnosis of urinary schistosomiasis, urine filtration using reusable polyamide mesh filters, may give false-positive findings because filters cannot be washed adequately in all circumstances. In this study the alternative filtration method using polycarbonate membrane filters was tested, and the same problem existed. A variety of more vigorous washing procedures was field tested with the conclusion that polycarbonate filters can be washed adequately for reuse by a simple procedure that includes boiling for 5 min in tap water prior to washing with detergent.     

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.     

Separation and characterization of red blood cells with different membrane deformability using steric field-flow fractionation

Human red blood cells were treated in different ways to alter their membrane deformability, and the hydrodynamic behavior of these altered cells was studied using the steric field-flow fractionation (FFF) technique. The relationships between cell retention in the FFF channel, flow-rate of the carrier fluid and the applied field strength were studied for normal and glutaraldehyde-fixed human red cells, and separation conditions were optimized. The effect of flow-induced hydrodynamic lift forces on red cell retention in the steric FFF channel was studied, and the results suggest that the membrane deformability of the red cell is an important factor contributing to the lift force, besides other previously described effects due to density and flow velocity. Using steric FFF, a mixture of normal and glutaraldehyde-fixed human red cells was completely separated with a resolution twice that found in published d ata from gel permeation, another hydrodynamic separation technique. Partial loss of membrane deformability, induced by different degrees of glutaraldehyde-fixation, by diamide, or by a thermal treatment, has also been studied. Steric FFF is thus shown to have potential for rapid separation and differentiation of red cells with different density and membrane deformability, conditions known to be associated with, e.g., cell senescence and certain hematological diseases.     

Regulation of red blood cell filterability by Ca2+ influx and cAMP-mediated signaling pathways

To investigate the mechanism of theregulation of human red blood cell deformability, we examined thedeformability under mechanical stress. Washed human red blood cellswere rapidly injected through a fine needle, and their filterabilitywas measured using a nickel mesh filter. The decrease in filterabilityshowed a V-shaped curve depending on the extracellularCa²⁺ concentration; the maximumdecrease was achieved at ~50 µM. The decreased filterability wasaccompanied by no change in cell morphology and cell volume, indicatingthat the decrease in filterability can be ascribed to alterations ofthe membrane properties. Ca²⁺entry blockers (nifedipine and felodipine) inhibited the impairment offilterability under mechanical stress. ProstaglandinsE₁ and E₂, epinephrine, andpentoxifylline, which are thought to modulate the intracellularadenosine 3',5'-cyclic monophosphate (cAMP) level of redblood cells, improved or worsened the impaired filterability accordingto their expected actions on the cAMP level of the cells. These resultsstrongly suggest that the membrane properties regulating red blood celldeformability are affected by the signal transduction system, includingCa²⁺-dependent and cAMP-mediatedsignaling pathways.

     

Experimental study on filtrability of polymorphonuclear leukocyte suspensions

Filtrability of a suspension of polymorphonuclear leukocytes (PMNs) was examined in a Nuclepore membrane filtration system utilizing a gradually reduced pressure difference with or without an additional negative pressure. The filtration process was continuously recorded using a TV-video system for data analysis. The PMN content in the filtrate was directly measured. The pressure-flow relation was analyzed in terms of the relative resistance of the PMN suspension to that of the suspending medium. The relative resistance of the PMN suspension increased with an increase in the filtered volume until it approached infinity at the level of low pressure difference (2.8 - 0 cmH2O). The remarkable increase in flow resistance was closely associated with the plugging of PMNs in the membrane pores. At high pressure differences (12.8 - 10 cmH2O, 7.8 - 5 cmH2O), the relative resistance increased up to finite values, as the filtered volume increased. The variation in the relative resistance was greatly dependent upon the pressure difference or the flow condition. The amount of filtered cell fraction increased with an increase of additional pressure, indicating that the relative resistance was changed according to the rate of PMN plugging and dislodging in the pores of the membrane.     

Flow characteristics of red cell containing fluids through pores. The effect of filter plugging, a mathematical model

A mathematical model was developed that describes the effects of filter plugging on flow through 3 micron pore polycarbonate filters as a function of time, pressure, and cell concentration, both under stirring and nonstirring conditions. The mathematical constants for the model were derived from experimental data generated with a filtration apparatus, and were tested by using various concentrations of cells that are able to plug filter pores. A computer simulation program was written to test the model over a wide range of nonfilterable cell concentrations.     

Effect of temperature on the deformability of a lamprey, Entosphenus japonicus, and Pacific salmon, Oncorhynchus keta, red blood cells, studied using a modified filtration method

The rates of filtration through Nuclepore filters (5 or 8 μm) of blood from lampreys and Pacific salmon have been studied using a method which visualizes the flow pattern. From these measurements, passage times for single red blood cells have been calculated and serve as an index of their deformability. The deformability increases as temperature is raised in vitro , but even at 5°C the passage time of lamprey blood is relatively rapid. The increase in deformability with a rise in temperature is small relative to that found in other fish such as yellowtail and carp.
The distribution of red cell volumes has shown the presence of a secondary peak for salmon blood taken during surgery which is reduced following recovery, the main peak being at a lower volume.     

Impact of blood manufacturing and donor characteristics on membrane water permeability and in vitro quality parameters during hypothermic storage of red blood cells

Several factors have been proposed to influence the red blood cell storage lesion including storage duration, blood component manufacturing methodology, and donor characteristics [1,18]. The objectives of this study were to determine the impact of manufacturing method and donor characteristics on water permeability and membrane quality parameters.Red blood cell units were obtained from volunteer blood donors and grouped according to the manufacturing method and donor characteristics of sex and age. Membrane water permeability and membrane quality parameters, including deformability, hemolysis, osmotic fragility, hematologic indices, supernatant potassium, and supernatant sodium, were determined on day 5 ± 2, day 21, and day 42. Regression analysis was applied to evaluate the contribution of storage duration, manufacturing method, and donor characteristics on storage lesion.This study found that units processed using a whole blood filtration manufacturing method exhibited significantly higher membrane water permeability throughout storage compared to units manufactured using red cell filtration. Additionally, significant differences in hemolysis, supernatant potassium, and supernatant sodium were seen between manufacturing methods, however there were no significance differences between donor age and sex groups.Findings of this study suggest that the membrane-related storage lesion is initiated prior to the first day of storage with contributions by both blood manufacturing process and donor variability. The findings of this work highlight the importance of characterizing membrane water permeability during storage as it can be a predictor of the biophysical and chemical changes that affect the quality of stored red blood cells during hypothermic storage.     

Physico-chemical factors of erythrocyte deformability

The aim of this study is to assess the role of different physico-chemical factors on the deformability measurements by using the initial filtration flow rate method, and to differentiate between the membrane or internal origin of some rigidity changes. The deformability is maximum for the physiological pH value and it decreases sharply for hypotonic and hypertonic buffer. For normal RBC, the deformability is independent of the pO2 level and a small decrease is observed for increasing pCO2 values (with constant pH). A theoretical model of filtration for the "Hemorheometre" will be also developed.     

Reduced erythrocyte deformability associated with calcium accumulation

Erythrocytes exposed to subhemolytic shear stress in vitro exhibit decreased deformability as determined by a filtration method. Intracellular calcium content of these cells has been measured by atomic absorption spectroscopy and found to be 35 and 55% higher than controls (0.0157 μmol/ml packed red blood cells) after shear stress levels of 100 and 130 N/cm², respectively. These alterations occur without significant changes in ATP level, intracellular magnesium content, cell volume, or morphology, and without large associated sodium and potassium fluxes. Results indicate that calcium may be responsible for or associated with changes in the viscoelastic properties of the red cell membrane caused by sublytic mechanical trauma.     

Developments in red cell rheology at the Institut de Pathologie Cellulaire

The present day rheological approximation, which has been used successfully to quantitate the deformability properties of red cells, is based on the view that the cell has a liquid interior encapsulated by a viscoelastic solid membrane shell. A review of historical developments in this field shows that determination of intrinsic red cell membrane properties has not come from simple mathematical analysis of experiments. On the contrary, considerable insight has been required to bring together physical and biological methods to rationalize the unique deformability characteristics of the red blood cell. Key developments at the Institut de Pathologie Cellulaire (IPC) in the early 1970s played a role in our improved understanding of red cell rheology. In this article, we describe the material concepts of the red cell membrane held before 1970, discuss the seminal developments at Bicetre, and, finally, outline the contemporary view of red cell deformability.     

The effects of temperature on the filtration of diluted blood through 3 μm and 5 μm filters

The effect of temperature on the flow of diluted blood [Hct = 0.21], through 5 μm Nuclepore filters, is described by the Arrhenius equation with an energy of activation of 27.7 kJ/mol. Plasma, diluted with PBS, is almost three times less sensitive to temperature, with an energy of activation of 9.8 kJ/mol, while red cells are of intermediate sensitivity, with an energy of activation of 14.7 kJ/mol. The most sensitive elements to changes in temperature are leukocytes, with energies of activation of 31 kJ/mol and 35 kJ/mol for fast-flowing leukocytes (granulocytes and lymphocytes) and slow-flowing leukocytes (monocytes) respectively. Hence, the major determinants of the decline in filterability of blood through micropore filters are the leukocytes. This effect is compounded when blood is kept for 10 minutes or more at 10° C due to activation of granulocytes, which leads to permanent pore blocking when the affected blood is filtered at room temperature. The combination of increased passage time of leukocytes through peripheral areas at abnormally low temperatures and subsequent activation might influence the flow of blood in non-affected tissues. The effect of temperature on the filterability of red blood cells through 3 μm filters is not described by the Arrhenius equation and the deviations are seen as a gradual change of slope rather than a sharp break between two straight lines. The data are consistent with a gradual shift in rate limiting step away from the entry event into pores, which dominates at low temperature but becomes progressively less important at elevated temperatures. The changing parameter is probably the volume of the red cell, which is less important when flow is measured through 5 μm pores.     

Effect of some nickel compounds on red blood cell characteristics

The effect of certain inorganic and coordinated nickel compounds on the resistance to different destructive substances, rheological properties, and functional activity of healthy human red blood cells (RBC), was investigated. It is shown that nickel compounds affect the erythrocyte membrane lipid bilayer, as well as membrane proteins to various extents, depending on the type of compounds used. In general, the acceleration of erythrocyte aging was observed to be more pronounced in young erythrocytes. The observed results suggest that nickel compounds decrease water permeability across erythrocyte membranes. Almost all the investigated nickel compounds decrease erythrocyte thermostability, deformability, and the rate of O₂ release by erythrocytes.     

Validation and application of an automated rheoscope for measuring red blood cell deformability distributions in different species

BACKGROUND: The deformability of red blood cells (RBCs) is of great importance for the conservation of oxygen delivery in the microcirculation. Even a small fraction of rigid cells is considered to harm the exchange of respiratory gases. Techniques that measure RBC deformability often provide an indication of the mean deformability. It may not be possible, however, to assess whether this mean value is reduced by the presence of a small rigid cell fraction or by a slight overall reduction in RBC deformability. A technique that provides a deformability distribution would be of great value to study diseases that are marked by subpopulations with a reduced deformability. METHODS: This paper describes a rheoscope system that uses advanced image analysis techniques to quickly quantify the deformability of many individual cells in shear flow, in order to find the RBC-deformability distribution. Since variations in the shear stress are responsible for variations in cell elongation, and hence introduce an additional spread in the cell deformability distribution, we first determined the spread caused by instrumental error. We then utilized the technique to investigate the relation between cell deformability and cell size of single blood samples of different species (human, pig, rat and rabbit). RESULTS: The spread caused by instrumental error was small compared to the actual RBC-deformability spread in blood samples. The deformability distribution of human and pig cells are alike although their cell sizes are different. Rat and rabbit cells show comparable deformability and size distributions. With this technique no correlation was found between cell deformability and cell size in animal RBCs. In the human sample a minor correlation was found between cell deformability and cell size. CONCLUSIONS: The automated rheoscope enables us to study the mechanical properties of RBCs more thoroughly by their deformability distribution. These deformability distributions are hardly influenced by the technique or by cell size.     

Effect of hypoxia on erythrocyte deformability in different species

The contribution of erythrocyte deformability to the pulmonary vascular resistance during hypoxia in different animal species has not been examined. We hypothesized that the increase in pulmonary vascular resistance during hypoxia was partially due to erythrocytes (RBC's) becoming less deformable during hypoxia, and therefore their transit in the capillaries becomes restricted. To test this, we measured an index of deformability of RBC's from six animal species (dog, pig, cat, rabbit, hamster, rat) during normoxic and hypoxic condition, and compared the changes in deformability with the pulmonary hypoxic pressor response (HPR) which has been reported in the same species. Deformability was indexed as the resistance that a Hemafil polycarbonate membrane (Nucleopore filter, 4.7 micron pores) offers to a 10% suspension of RBC's. The RBC suspension was either normoxic (PO2 = 150 torr) or hypoxic (PO2 = 50 torr). We found that hypoxia decreased RBC deformability; the largest decrease occurred in rat RBC's, a small but significant decrease was observed in the RBC's of cats, rabbits and hamsters, but no change was detected in RBC's of dogs or pigs. In general, such changes in deformability do not correlate well with the HPR in intact or in isolated lungs, for example the pig, had the largest HPR but the smallest change in RBC deformability. In some species, however, there was a positive correlation between RBC deformability and HPR, for example rats, rabbits and cats are usually better responders than dogs and hamsters, similarly the deformability of RBC's in rats, rabbits and cats were also more influenced by hypoxia than RBC's from dogs. The limiting factors in this relationship are the artificial conditions which were used to measure deformability and HPR, both may be different than in the intact conditions. Nevertheless the present data show that erythrocytes of some species can become less flexible during hypoxia, and hence may impede the transit in the capillaries. Therefore we propose that the hypoxic pressor response in the pulmonary vasculature may be partly due to smooth muscle contraction (vasoconstriction) and partly due to a decrease in erythrocyte deformability (capillary obstruction). Both components are likely to be species dependent.