The sedimentation coefficient of red blood cell suspensions as a measure of deformability: continuous monitoring of centrifugal sedimentation

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Chemical Enoineerin O Science, Vol. 52, No. 6, pp. 1059 -1064, 1997 Copyright © 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0009-2509/97 S17.00 + 0.00

S0009-2509(96)00455-1

The sedimentation coefficient of red blood cell suspensions as a measure of deformability: continuous monitoring of centrifugal sedimentation (Received 26 May 1996; accepted in revised form 2 October 1996)

INTRODUCTION Normal circulation of red blood cells (RBCs) depends on their ability to deform (Mohandas et al., 1983; Chien, 1987). This ability ensures passage of normal RBCs through narrow capillaries, and reduces the viscosity of blood when flowing in larger vessels. Abnormal (reduced) deformability is manifested in hemolytic states, and leads to shortening of RBC survival time. Thus, measurement of the deformability of RBCs is an important tool in assessing their function. A few methods exist for measuring RBC deformability: filtration through small pores (Chien, 1981; Leblond and Coulombe, 1981), viscometry of cell suspensions (Meiselman, 1981; More and Thurston, 1987), aspiration of cells through micropipettes (Evans, 1980), and deformation under shear stress of either individual cells (rheoscopy) (Meiselman, 1981; Sehmid-Schonbein et al., 1984) or a population of cells (ektacytometry) (Bessis et al., 1980; Mohandas, 1988). The existence of such a variety of tests indicates that the fundamental understanding of this important property of RBCs is yet incomplete. In the absence of a complete theory, the definition of deformability is essentially empirical and methoddependent. Moreover, each method may be differently sensitive to the cellular and external factors which determine the deformability (Mohandas et al., 1983). Therefore, it is important to obtain additional information by developing new methods for the measurement of deformability of RBCs. These methods should be as simple and convenient as possible with regard to their performance as well as their interpretation. Recently, a centrifugal sedimentation approach has been tested for assessing RBC deformability (Albalak et al., 1996). Some attempts in this direction had previously been reported. However, in one case the experiments were performed under very low g-values and in a centrifuge of impractically large dimensions (Braasch and Roghauseh, 1971); in the other case, whole blood was employed rather than washed RBCs (Sirs, 1970), therefore the effect of plasma proteins on the sedimentation of RBCs was also included. The hypothesis underlying the centrifugal sedimentation approach is that the centrifugal field deforms the RBCs because it exerts a different force at each point of the cell membrane, according to its radial distance from the center of rotation. This deformation should be manifested by a change in the rate of sedimentation of the RBCs. Thus, the centrifugal field is expected to play a double role: to cause the sedimentation of RBCs while simultaneously deforming them. For a given centrifugal field, then, the sedimentation coeiticient should be a measure of deformability. This principle has indeed been demonstrated (Alalak et al., 1996). However, the experimental system does not allow continuous monitoring of the sedimentation process;

therefore the performance of the experiments is inconvenient. In the present paper, a system with continuous monitoring is presented. Due to the added convenience and accuracy of this system, the centrifugal sedimentation behavior of RBCs has been studied much more in depth than with the previous system. In particular, interesting and unexpected effects of the rotation speed and the size of the tube containing the suspension have been revealed. For comparison, sedimentation under gravity has also been studied. EXPERIMENTAL Sample preparation Blood was withdrawn from healthy donors and mixed with EDTA (1.5 _ 0.25 mg/ml blood) as anticoagulant. The RBCs were separated by centrifugation (Serofuge, ClayAdams, Inc., NY) for 3 min at 3000 rpm. The RBCs were then washed three times with physiological solution (0.89 wt % NaC1). The volume fraction of RBCs was measured using a capillary and a centrifuge designed for this purpose (Bio-Dynamics Inc., IN, U.S.A., Model 617). The reported result is the percentage of the volume of the packed RBCs at the end of the centrifugation, to be referred to in the following as PCV (packed cell volume, %). Three types of treatments of RBCs were employed in this study in order to modify artificially their deformability: partial fixation with glutaraldehyde, treatment with diamide (diazine dicarboxylic acid bis[N,N-dimethylamide]), and suspension in hypotonie or hypertonic solutions. Partial fixation with glutaraldehyde was achieved by incubating the washed RBCs for 15 min at room temperature in a physiological solution which contained either 0.025 or 0.05% of glutaraldehyde. After 15 min the cells were washed three times in order to remove the excessive glutaraldehyde, then suspended in physiological solution to obtain the desired PCV. Treatment with diamide was done in a similar manner, with either a 5 or a 10 mM solution of diamide. Incubation was performed for 15 min at 25°C. Hypotonic or hypertonic solutions were prepared by dissolving the required amount of NaC1 in distilled water. Performance of the experiments The experimental system is shown in Fig. 1. It consists of a horizontally rotating plate, an electrical motor, a control unit and a flash. The plate (25.6 crn in diameter) is made of transparent perspex and its top surface is painted black. These circular grooves are engraved in the top surface, at a distance of 2.2 mm from each other. A groove for holding a glass tube is located radially, so that the end of the tube, which is nearest to the center of rotation, is at a distance of 6.5 cm

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from this center. A flash is located below the plate and is fired once in each rotation. This setup makes the glass tube appear stationary. Because of the black paint on the top surface of the plate, only the grooves are transparent to the light of the flash. The rotation speed is controlled and measured by a digital tachometer. The plate and motor are enclosed in an aluminium box with a transparent plastic cover. The glass tubes are 6.5 cm in length and internal diameters varying between 0.4 to 4.2 mm. At the beginning of an experiment, the RBC suspension to he tested was well mixed, then a glass tube was dipped into the suspension until it was completely filled. One side of the glass tube was sealed with putty, and it was placed in the groove on the rotating plate with the sealed side facing away from the center. The time for the boundary between the suspension and the clear liquid to cross the circular grooves in the plate was recorded about 6 to 7 times during sedimentation through a distance of about 15 ram. Each experiment was repeated three times. For each set of experiments, in which the effect of variations in a parameter were studied, the RBCs were taken from the same blood sample. Sedimentation under gravity was studied simply by using vertical glass tubes, and following the height of the suspension with time.

RESULTS AND DISCUSSION The sedimentation rate of a single particle is conveniently characterized by using the sedimentation coefficient, s, defined as the ratio of the velocity of the particle to the driving force acting on it per unit mass. Under conditions for which the sedimentation coefficient is constant, a simple equation can be developed for the position of the particle vs time. For sedimentation under gravity the distance traveled down by the particle, Ah, is given by

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where g is the gravitational acceleration, and t is the time. For sedimentation in a centrifugal field, the radial distance of the particle from the center of rotation, r, is given by (Aris and Amundson, 1973) In t ~ o ) = s c o 2 t

(2)

where r0 is the initial value of r, and co is the angular velocity of rotation. The sedimentation coefficient depends on the size, shape, density, and orientation of the particle, and on the density and viscosity of the liquid. Analogously, the rate of sedimentation of a suspension, defined as the rate of motion of the boundary between the suspension and the clear liquid, can also be characterized by a sedimentation coefficient. In addition to the above-mentioned parameters which determine s for a single particle, the sedimentation coefficient for a suspension depends on the particle volume fraction (Aris and Amundson, 1973). Since the conditions within the suspension may change during the sedimentation process, it is not a priori clear that the sedimentation coefficient remains constant and that the above equations hold for a concentrated suspension. However, Figs 2 and 3, which present typical data for gravitational and centrifugal sedimentation, respectively, show that eqs (1) and (2) hold very well for sedimentation of RBC suspensions of high concentration. These experiments were performed at a rotation speed of 1500 rpm, with a suspension of PCV of 15% in a glass tube of 1 mm internal diameter. The correlation coefficients for all the centrifugal sedimentation experiments performed were higher than 0.99, and for the gravitational sedimentation experiments higher than 0.98. The following discussion presents two complementary lines of investigation. First, the effects of the parameters defining the system on the sedimentation coefficient of normal RBCs are demonstrated and discussed. Then, results for RBCs which are modified by various methods are presented. The dependence of the sedimentation coefficient on the applied centrifugal force is the central hypothesis which motivated the present study. It is assumed that the centrifugal field deforms the RBCs, thus changing their sedimentation coefficient. Figure 4 shows the dependence of the sedimentation coefficient on the rotation speed of the centrifuge, for various PCVs. The values shown are normalized to the sedimentation coefficient at 1500 rpm, for the same PCV.

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Fig. 5. The dependence of the sedimentation coefficient on the PCV. The normalization is with respect to PCV of 0.15: (©) centrifugal sedimentation at 1500 rpm; (Fq) gravitational sedimentation. The internal diameter of the glass tube is 1 mm.

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Fig. 3. Typical data for centrifugal sedimentation of RBCs. PCV = 15%; speed of rotation = 1500 rpm, internal diameter of the glass tube is 1 mm.

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Fig. 4. The dependence of the normalized sedimentation coefficient on the speed of rotation. The normalization is with respect to Slsoo, the sedimentation coefficient for 1500 rpm, for the same PCV. PCV values are: 10% (C)), 15% (Fq), 25% (A), 35% (V). The value indicated on the vertical axis is the sedimentation coefficient for gravitation sedimentation, also normalized with respect to S15o0.

For comparison, the normalized sedimentation coefficient for gravitational sedimentation is indicated on the vertical axis (it is also normalized to the value of the centrifugal sedimentation coefficient at 1500 rpm). Two important observations can be made on the basis of the data shown in Fig. 4. First, the sedimentation coefficient for centrifugal sedimentation is higher than for gravitational sedimentation. This observation implies that deformation of

the cells by the centrifugal field indeed enhances sedimentation, thereby supporting the hypothesis underlying this study. The other observation which is based on Fig. 4 is the striking dependence of the sedimentation coefficient on the rotation speed at relatively low speeds: s is very strongly decreasing with o9 for rotation speeds between roughly 400 and 600 rpm. This behavior is common to all PCVs studied, and the normalized sedimentation coefficient is almost independent of the PCV. It is very difficult to explain this strong dependence of s on o9. One possible explanation might have been the formation of aggregates of RBCs, for which the effective size and consequently the sedimentation coefficient is much larger than for single RBCs. This process should have been quite sensitive to the PCV; however, as Fig. 4 shows, this is not the case. Thus, the insensitivity of the normalized sedimentation coefficient to the PCV casts doubt on this explanation. Above about 600rpm, the sedimentation coefficient mildly increases with the rotation speed. Therefore, for practical purposes of assessing the deformability of RBCs, a rotation speed has to be chosen within this range of mild dependence. All further experiments were performed with the centrifuge rotating at 1500 rpm, which was found convenient for accurate performance of the experiments. As already mentioned, the sedimentation coefficient of a suspension depends on the particle volume fraction. This is shown for suspensions of RBCs in Fig. 5. Experience indicated that a convenient PCV to work with was 15%; therefore, the results shown in Fig. 5 are normalized to the value obtained for this PCV. It can be seen that, in general, the sedimentation coefficient decreases with PCV, as expected. It is interesting to note that the functional dependence of the normalized sedimentation coefficient on the PCV is the same for gravitational and centrifugal sedimentation. The sensitivity of the sedimentation coefficient to the PCV is quite high for the whole range. Therefore, it is important to measure accurately the PCV. Although the radii of the tubes used for the sedimentation experiments are large compared with a single RBC, the high PCV of the ceils may lead to strong interactions with the tube wall. This possibility was studied in a series of

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Fig. 6. The dependence of the normalized sedimentation coefficient on the internal diameter of the tube. The normalization is with respect to sl, the sedimentation coefficient for a 1 mm tube, for the same PCV: (Full symbols) gravitational sedimentation; (empty symbols) centrifugal sedimentation. PCV values are: 15% (A), 25% (r-q), 35% (O), 15% (v and O), 20% (O), and 25% (O).

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Fig. 7. The normalized sedimentation coefficient of aged RBCs (standard experimental conditions). The normalization was done with respect to the first measurement.

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experiments with tubes varying in internal diameter from 0.4 to 4.2 mm. The results are summarized in Fig. 6 for centrifugal as well as gravitational sedimentation. The values of the sedimentation coefficient are normalized to the value obtained in a 1 mm tube for the same PCV. It can be seen that for tube diameters smaller than a certain 'critical' value, the sedimentation coefficient decreases with an increase in the tube internal diameter. Above the 'critical' diameter, the sedimentation coefficient remains approximately constant. In centrifugal sedimentation, the 'critical' diameter is about 1 mm. Therefore, a tube of 1 mm in internal diameter was chosen as the standard tube for the experiments. For gravitational sedimentation, the 'critical' diameter is about 2 ram. The mechanism responsible for this dependence of the sedimentation coefficient on the tube diameter is unknown. It may be speculated that aggregates of RBCs are formed in the smaller tubes. However, as in the case of the dependence on the rotation speed, the results shown in Fig. 6 are not very dependent on the PCV. Thus, it remains questionable whether the formation of aggregates is responsible for the effect of the tube diameter. After establishing the standard conditions for performing the experiments (1500 rpm, internal diameter of 1 mm, and PCV of 15%), RBC samples from 200 healthy donors were tested. The experiments were always performed within 24 h of blood withdrawal, which, as will be shown below, is an acceptable time delay. Usually, however, they were performed within only a few hours. The sedimentation coefficients were in the range 0.81 x 10 -7 to 1.1 x 10 -7 s. In order to demonstrate further that the sedimentation coefficient of RBCs depends on their deformability, suspensions of modified RBCs were studied. Figure 7 shows normalized sedimentation coefficients for physiologically modified RBCs, which were kept (after the washing process) in a refrigerator at 5°C for various periods of time. The normalization was done with respect to the first measurement. It is dearly seen that the sedimentation coefficient decreases with time. Within 24 h it varies only by a few percent, within the experimental error. However, a consider-

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Fig. 8. The effects of glutaraldehyde (C)) and diamide ([:]) on the normalized sedimentation coefficient (standard experimental conditions). The normalization is with respect So, the sedimentation coefficient for untreated RBCs.

able decrease in the sedimentation coefficient is observed after more than one day of delay. This observation is consistent with previously known information (Rice-Evans and Dunn, 1982) regarding the increase of the membrane rigidity with time, due to changes in membrane proteins that follow loss of ATP from RBCs. Thus, an increase in the membrane rigidity leads to a decrease in the sedimentation coefficient. Fixation with glutaraldehyde and treatment with diamide are also known to increase the rigidity of RBCs (Chien et al., 1968; Fischer et al., 1978). Figure 8 shows that the sedimentation coefficient decreases as the concentration of the

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In addition, interesting but yet unexplained phenomena are presented regarding the effects of the rotation speed and the internal diameter of the tube on the sedimentation coefficient. These observations may not be essential for assessing the deforming of RBCs; however, they are interesting and intriguing from a hydrodynamic point of view.

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Department of Chemical Engineering Technion- Israel Institute of Technology 32000 Haifa, Israel

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Department of Hematoloqy Rambam Medical Center Haifa, Israel i

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treating agent increases. Thus, the higher the rigidity of the RBC membrane, the lower the sedimentation coefficient. These results are consistent with the data shown in Fig. 7 on the effect of in vitro aging on the sedimentation coefficient, in the sense that both experiments show that the sedimentation coefficient decreases with increased rigidity. These results are also in agreement with previous data measured with a different centrifugal system (Albalak et al., 1996). The deformability of RBCs may also be affected by physical means, such as the osmotic pressure of the suspending solution. As shown in Fig. 9, the sedimentation coefficient is highest for an isotonic solution. This implies that the RBC is most deformable under isotonic conditions. The sedimentation coefficient appreciably decreases when the osmotic pressure is either reduced or increased. The results reported here on the effect of hypertonic solutions are consistent with results measured by other methods for dehydrated RBCs (Mohandas et al., 1980; Reinhart and Chien, 1986).

SUMMARY AND CONCLUSIONS A simple experimental system was developed for measuring the centrifugal sedimentation coefficient of RBC suspensions. The hypothesis underlying these measurements is that the centrifugal field deforms the RBCs, thus changing their sedimentation coefficient. The extent to which it changes should depend on the deformability of the RBCs; therefore, the sedimentation coefficient should serve as a measure of deformability. As a point of reference, the sedimentation coefficient was also measured under the effect of gravity. The basic hypothesis is supported by the results presented in this paper. It is shown that when the RBCs are less deformed (as in the case of sedimentation under gravity) or less deformable (due to treatment, aging or hypertonic environment) the sedimentation coefficient decreases. Thus, the sedimentation coefficient may serve as a measure of deformability. The present results confirm and add to previous data obtained in a centrifugal system without continuous monitoring (Albalak et al., 1996). The present study also established a range of normal values for the sedimentation coefficient of healthy donors.

ABRAHAM MARMUR* Department of Chemical Engineerinq Technion-lsrael Institute of Technology 32000 Haifa, Israel REFERENCES

Albalak, A., Streichman, S. and Marmur, A. (1996) Chem. Enqng Comm. 152-153, 5-15. Aris, R. and Amunsdon, N. R. (1973) Mathematical Methods in Chemical Engineering: First Order Partial Differential Equations with Applications, Vol. 2, pp. 232-249. PrenticeHall, Englewood Cliffs, N J, U.S.A. Bessis, M., Mohandas, N. and Feo, C. (1980) Automated ektacytometry: a new method of measuring red cell deformability and red cells indices. Blood Cells 6, 315-327. Braasch, D. and Rogausch, H. (1971) Deformability and migration speed of red cells centrifuged at low q-values. Pflugers Arch. 323, 34-40. Chien, S. (1981) Determinants of blood viscosity and red cell deformability. Scand. J. Clin. Lab. Invest. 41 (suppl. 156), 7-12. Chien, S. (1987) Red cell deformability and its relevance to blood flow. Ann. Rev. Physiol. 49, 177-192. Chien, S., Dellenback, R. J., Usami, S., Seaman, G. V. F. and Gregersen, M. I. (1968) Centrifugal packing of suspensions of erythrocytes hardened with acetaldehyde. Proc. Soc. Exp. Biol. Med. 127, 982-985. Evans, E. A. (1980) Minimum energy analysis of membrane deformation applied to pipet aspiration and surface adhesion of red blood cells. Biophys. J. 30, 265-284. Fischer, T. M., Haest, C. W. M., Stor, M., Kamp, D. and Deuticke, B. (1978) Selective alteration of erythrocyte deformability by SH-reagents. Evidence for an involvement of spectrin in membrane shear elasticity. Biochim. Biophys. Acta 510, 270-282. Leblond, P. F. and Coulombe, L (1981) Evaluation of a simplified filtration technique for the routine measurement of erythrocyte deformability. Scand. J. Clin. Lab. Invest. 41, (suppl. 156), 35-40. Meiselman, H. J. (1981) Morphological determinants of blood cell deformability. Scand. J. Clin. Lab. Invest. 41 (suppl. 156), 27-34. Mohandas, N. (1988) Measurements of cellular deformability and membrane material properties of red cells by ektacytometer. Methods Hematol. 19, 299-320. Mohandas, N., Chasis, J. A. and Shohet, S. B. (1983) The influence of membrane skeleton on red cell deformability, membrane material properties, and shape. Seminars Hematol. 20, 225-242.

*Corresponding author. Fax: 972-4-8293088; E-mail: [email protected].

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Mohandas, N., Clark, M. R., Jacbos, M. S. and Shohet, S. B. (1980) Analysis of factors regulating erythrocyte deformability. J. Clin. Invest. 66, 563-573. More, R. B. and Thurston, G. B. (1987) Intrinsic viscoelasticity of blood cell suspensions: effects of erythrocyte deformability. Biorheology, 24, 297-309. Reinhart, W. H. and Chien, S. (1986) Red cell rheology in stomatocyte--echinocyte transformation: roles of cell geometry and cell shape. Blood 67, 1110--1118.

Rice-Evans, C. A. and Dunn, M. J. (1982) Erythrocyte deformability and disease. TIBS 282-286. Schmid-Schonbein, G. W., Gaehtgens, P., Fischer, T. and Stohr, L. M. (1984) Biology of red cells: non-nucleated erythrocytes as fluid drop-like cell fragments. Int. J. Microcirc. Clin. Exp. 3, 161-196. Sirs, J. A. (1970) Automatic recording of the rate of packing of erythrocytes in blood by a centrifuge. Phys. Med. Biol. 15, 9-14.