Biorheology, 1975, Vol. 12, pp. 341-346. Pergamon Press. Printed in Great Britain.

VISCOELASTIC PROPERTIES OF HUMAN BLOOD

AND RED CELL SUSPENSIONS* S, CHIEN, R. G. KING, R. SKALAK, S. USAMI and A. L. COPLEY Laboratory of Hemorheology, College of Physicians and Surgeons, Columbia University, New York, N.Y. 10032, Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, N.Y. 10027; Laboratory of Biorheology, Polytechnic Institute of New York, Brooklyn, N.Y. 11201, and New York Medial College, New York, N.Y, 10029, U.S.A. (Received 3 March 1975)

INTRODUCTION

Macrorheological and microrheological studies on blood and red cell suspensions have suggested the presence of viscoelastic properties in these systems [1-5]. These rheological properties, especially the elastic component, are conveniently measured by oscillatory tests in which the phase and amplitude relations between stress and strain are determined. In contrast to the large number of rheological investigations on blood under steady shears, there have been relatively few oscillatory studies [6-9]. The purpose of the present investigation is to characterize the viscoelastic behavior of blood and red cell suspensions over wide ranges of cell concentrations and frequencies of oscillation and to correlate these macrorheological findings with the microrheological observations reported by Copley et al. [10] and by U sami et al. [11] at this Congress. METHODS

Fresh blood samples were drawn from normal human subjects, with EDTA as the anticoagulant. After centrifugation, the buffy coat was removed from the blood samples and two types of suspensions were prepared. In one group of experiments, the red blood cells (RBC) were resuspended in the autologous plasma to yield cell concentrations varying from 45 to 95%. In another group of experiments, the red cells were washed three times in a Ringer-albumin solution (A-Ringer), which was buffered with tris to pH 7·4 and contained 0·5 per cent human serum albumin to prevent RBC crenation. The washed RBC were then suspended in the A-Ringer solution to yield RBC concentrations varying from 45 to 95%. The suspensions of RBC in A-Ringer solution provided a system in which RBC aggregation did not occur. Previous studies have shown that RBC aggregation occurs in plasma at low shear conditions [2,4]; due to the aggregating effects of fibrinogen and globulins. The apparatus used for the oscillatory test is the Weissenberg Rheogoniometer[12-14]. The instrument (manufactured by Sangamo Weston Controls Ltd., Sussex, England) was modified in the present study to provide a cone-and-plate geometry requiring only 4 ml of blood sample and a water jacket for temperature control [15]. All studies were performed at a temperature of 37°C. The lower plate of the cone-and-plate assembly is driven by an oscillatory motor and the upper cone is attached to a torque sensing element. The cone angle is one half degree and the diameter of the cone-plate system is 11 cm. The frequency of oscillation was varied from 6·0 x 10-4 to 6·0 X 10 1 Hz and the amplitude of oscillation at the perimeter was 500 ILm, corresponding to an angular displacement of 0'26°. The oscillatory motion of the plate and the resultant displacement of the cone are amplified and recorded on an u.v. recorder (Honeywell, Westfield, N.J.). From the phase shift and the amplitude ratio between the input and the output, the viscous component (7) ') and elastic component (7) //) of the complex viscosity were calculated according to the procedure of Maude and Walters [16, 17]. 7)//= G/27Tn in which n is the frequency and G is the elastic modulus. *The abstract of the paper appears in Biorheology 12,81,1975. The paper was given at the 2nd International Congress of Biorheology, by R. Skalak. 341

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RESULTS

For Newtonian standard oils, the 1/" value was essentially zero over the frequency range studied. The computed 1/' value for these oils agreed well with the nominal values supplied by the manufacturer and showed no frequency dependence.

Results on 1/' Figure 1(A) shows the variation of 1/' with frequency for suspensions of RBC in plasma at four hematocrit levels. At each hematocrit, 1/' decreases with increasing frequency. The 1/' -frequency curve becomes progressively higher with increasing hematocrit. Figure 1(B) shows the relation between 1/' and frequency for suspensions of RBC in A-Ringer solution. At 95% hematocrit, the curve for RBC in A-Ringer is similar to that for RBC in plasma. At \ lower hematocrits, however, the 1/' curve for RBC in A-Ringer was considerably lower and showed less frequency dependence. A comparison between RBC in A-Ringer and RBC in plasma can be made at a given frequency. In Fig. 2, 1/' at a frequency of 0·1 Hz is plotted against the hematocrit. At each hematocrit, the curve for RBC in plasma is higher than that for RBC in A-Ringer. The ratio of the 1/' values is approximately 5: 1 at a hematocrit of 45%. With increasing hematocrit, the two I

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curves tend to converge and the ratio decreases toward a constant value of approximately 1·7: 1, which is the ratio of the viscosities of the two suspending media.

Results on 1/" At the high hematocrit values of 95 and 80%, 1/" for RBC in plasma increased progressively with a decrease in frequency (Fig. 3A). At 60 and 45%, however, 1/" for RBC in plasma tended to level off at frequencies below 0·1 Hz. At 95% hematocrit, the 1/"-frequency curve for RBC in A-Ringer (Fig. 3B) is almost identical to that for RBC in plasma. At 45% hematocrit, however, the 1/" curve for RBC in A-Ringer is markedly lower than that for RBC in plasma, and the values obtained at the frequencies tested remain constant. A comparison between RBC in plasma and RBC in A-Ringer can be made at a given frequency, e.g. 0·1 Hz, as shown in Fig. 4. The TJ" data are essentially the same for the two types of suspensions at hematocrit values above 80%, but the TJ" curve for RBC in plasma becomes significantly higher at lower hematocrits. At a hematocrit value of 45%, the ratio of TJ" values for the two types of suspensions is approximately 6: 1. DISCUSSION

Thurston [7, 8] investigated the viscoelastic properties of human blood with the use of oscillatory tests in tube flow, covering a frequency range of 0,1-100 Hz. He also studied the effect of superimposition of mean shear rates on the oscillatory shear. The present study was performed over a lower frequency range in a cone-and-plate geometry and no steady shear was superimposed on the oscillatory test. The present investigation includes studies on highly concentrated cell suspensions, with hematocrit raised to 95%. When experimental conditions (i.e. frequency, cell concentration, etc.) are comparable between the two studies, the results on viscosity and elasticity are in very good agreement. Our findings indicate that, at high hematocrits, the viscoelastic behaviors of RBC in plasma and in A-Ringer are essentially the same and the 1/" value gives an indication of the elastic modulus of the cells, presumably that of the cell membrane [18-21]. At the lower hematocrits, e.g. 45%, the monodispersed suspension of RBC in A-Ringer shows a rather low 1/" value. The six-fold increase in TJ" for RBC in plasma most likely represents the elastic behavior of the rouleaux [4] formed by red cells in the presence of the aggregating plasma proteins. The above conclusion on 45% RBC suspensions is supported by the microrheological observations reported by Copley et a/. [10] and U sami et al. [11] on the same instrument setup. At low frequencies of oscillation, e.g. 0·01 Hz, suspensions of 45% RBC in plasma showed extensive rouleau formation with time, and these large rouleaux undergo cyclic elastic distortion at the

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imposed frequency. At these low frequencies, rheogoniometric tests showed a considerable elastic component, as indicated by the T/" value (Fig. 3A). With an increase in the frequency of oscillation above 0·1 Hz, rouleau size becomes progressively smaller, and the value of T/" also decreases. As the frequency is raised to 1 Hz or higher, suspensions of 45% RBC in plasma become essentially monodispersed, and the T/" value indeed decreases to the low value found for the monodispersed suspension of 45% RBC in A-Ringer (Figs. 3A and B). Therefore, the present investigations offer direct evidence in support of the concept that the elastic component of the rheological behavior of blood from healthy human subjects stems from the storage and dissipation of energy due to the elastic distortion of RBC aggregates [22]. The elastic component of the rheological behavior of very concentrated RBC suspensions, however, reflects largely the elastic contribution from the deformation of single erythrocytes. Thus, the results of oscillatory tests have confirmed and extended the contention by Chien et a/. based on steady shear experiments that RBC aggregation and RBC deformation are two major mechanisms in affecting the rheological behavior of blood [23,24]. Our studies confirm the earlier observations by Lessner et al. [6] and by Thurston [7,8], who

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employed different geometries than the one we used. Our findings also show that, although normal forces were not found by Copley and King [25] for blood of healthy human subjects with hematocrits at and above 44%, an elastic component can be measured with the Weissenberg Rheogoniometer. DISCUSSION REMARKS

Question (G. M. Odell). Do you have any data on the behavior of suspensions of red cell ghosts? Answer (R. Skalak). No. Question (G. M. Odell). But you would conjecture that, if cell membrane elasticity is responsible for the elastic properties of the suspension, then ghost suspensions should behave almost exactly like whole blood except for effects of rouleau per se? Answer (R. Skalak). Yes, ghost cell suspensions should be expected to behave in a similar way, if they are intact. There will be some effect, primarly on the apparent viscosity, if the fluid inside the ghosts is not of the same viscosity as hemoglobin. Question (H. L. Goldsmith). Would Dr. Skalak comment on the differences in the elasticity obtained in ringers and in plasma suspensions of red cells? Answer (R. Skalak). The differences are due to the more rapid and extensive formation of rouleau in plasma as compared to suspensions of red cells in Ringer solution. The differences in the elasticity parallel the differences in rouleau formation shown in the microphotograms presented by Dr. Copley and the motion pictures presented by Dr. Usami at the earlier sessions of this congress. Question 1 (A. Silberberg). Have you made any systematic analysis of the effect of varying cell membrane properties? Question 2 (A. Silberberg). Have you measured the frequency dependence of the dynamic viscosity or rigidity and can you say something about the value of the main relaxation time? This should be related to the shape-relaxation time of the cell. Answer 1 (R. Skalak). No systematic variations of the cell membrane properties have been attempted as yet. BRY VOL. 12 NO. 6-B

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Answer 2 (R. Skalak). We have not interpreted our results in terms of relaxation times, but will try to do so. Inasmuch as rouleau formation affects the present results, the relaxation times involved may be larger and show a wider range of distribution than the relaxation times of a single cell. Acknowledgements-This investigation was supported by U.S.P.H.S. Research Grants HL 06139 and HL 16851 and Office of Naval Research Contract NOOOI4-67-A-0449-0002 and NOOOI4-75-C-0222. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

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