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Viscosity of the packed red and white blood cells
EXPERIMENTAL
ARD
Viscosity
MOLECULAR
PATHOLOGY
of the
4,
Packed
597-605
Red
(1965)
and
White
Blood
Cells’
LEOPOLD DINTENFASS Department
of Medicine,
University
Received
of Sydney,
October
Sydney,
Australia
16, 1964
The fluidity of the packed red blood cells is well known to hematologists and physiologists alike and is taken for granted by them. Physicists and rheologists, accustomedto an exponential increasein the viscosity of suspensionsof rigid particles with an increase in the concentration of the dispersed phase, have observed and acknowledged this most unusual behavior of the blood only in the most recent times (Dintenfass, 1962; Haynes, 1963; Erslev and Atwater, 1963; and Rand, 1964). Formerly to this, there had existed (among physicists) a tacit assumption that the red cell may be treated as a rigid, or nearly rigid. body and that the internal viscosity of the red cell is of no consequence. It is the intention of this communication to show not only that the red cell behaves as a fluid drop, but also that the red cells originating from different individuals exhibit different viscosity, although the hemoglobin in all the casesis normal. It will be shown that packed blood cells rich in the white cells exhibit increasedviscosity. METHODS The packed red cells have been obtained by centrifugation of the anticoagulated (EDTA) human blood, collected by venipuncture from healthy donors and from a seriesof patients. Some sampleswere centrifuged directly from plasma, while others were washed repeatedly with isotonic saline and centrifuged at 15000 X g for a period of 12 minutes. Subsequentto this the last drops of supernatant were removed. The hematocrit value was checked by high-speed microhematocrit methods and was found, in all samples,to be not less than 98 per cent. The packed blood cells enriched in the white cells have been obtained in the following manner: Blood obtained from leukaemia patients was centrifuged, the buffy coat was aspirated and diluted with isotonic saline, and centrifuged again; the resulting buffy coat was aspirated again, diluted again, centrifuged again, and so forth. Depending on the number of operations, materials of different content of white (leukaemic) cells have been prepared. The viscosity of packed cells has been determined using a rotational ring-in-ring viscometer. This is a modification of a previously described cone-in-cone viscometer (Dintenfass, 1963, 1964). The ring-in-ring viscometer is better suited for studies at relatively higher rates of shear. The basic part of the viscometer consistsof a Teflon ring, suspendedon a torsion strip, and a brass annulus, rotated by meansof a beltdrive. The Teflon ring is 15 mm high, has an internal diameter of 24.7 mm; the width of the annulus, accommodating,the ring is 1.9 mm; the internal gap between the inner 1 Supported by grants from the National Heart
Foundation 597
of Australia
598
LEOPOLD
DINTENFASS
wall of the annulus and the inner surface of the ring is 0.58 mm, is 0.64 mm. The rate of shear evolved in the annulus is equal to RPM = revolutions per minute), the velocity gradient across annulus (outer and inner) being identical and homogeneous. The ring-in-ring adapter are illustrated by Figs. 1 and 2.
while the outer gap 2.1 X RPM (where both parts of the viscometer and the
FIG. 1. The ring-in-ring viscometer. Center: the viscometer. Left: a spotlight, scale, and a tachometer. Right: in the foreground is the “Zeromax” stepless drive a secondary gearbox (reduction lOO:l), while in the background is a thermostat mercury-contact thermometer.
a semi-circular and motor, and equipped with a
The torsion strips used were “Mallory 73” beryllium copper strips of cross-sections 0.008 X 0.025, 0.008 X 0.075, and 0.016 X 0.075 inches. The viscometer was calibrated using standard oils obtained from the National Standards Laboratories, C.S.I.R.O., Sydney. The temperature was controlled by means of a mercury-contact thermometer and relay. Actual measurement of viscosity. The fluid tested was poured into the gap between the Teflon ring and the brass annulus. The drive was started and the positions of the
VISCOSITY
OF
THE
PACKED
BLOOD
CELLS
599
lightspot on the semi-circular scale were noted. The deflections of the lightspot indicated a twist in the torsion strip, the lightspot being reflected from a tiny mirror attached to the strip. The number of revolutions was progressively increased. When the scale could not accommodate further deflections of the lightspot, a heavier torsion strip was used. It was necessary to remove a surface film (formed probably of denaturated proteins) which occurred in some samples, especially at higher temperatures.
FIG. 2. Teflon ring and two annufi. The annulus (left) is made of brass while the other (right) is made of Teflon. The Teflon ring is fastened to a brass holder through an universal joint, a small mirror being secured onto this holder. This mirror deflects a lightspot onto the scale and permits. therefore, measurement of the deflections of the torsion strip,
Rheological nomenclature The “rate of shear” or the “velocity gradient” is a function of the relative velocity of the fluid laminae or of the surfaces surrounding the fluid and of the geometry of these surfaces. In the simplest case of two parallel surfaces, spaced by a gap d, and moving at a relative velocity I/, the velocity gradient between these surfaces is equal to V/d; the units of velocity, cm/set, are divided by the units of distance, cm, in order to yield the units of the rate of shear,set-l. The term “thixotropic” describesa system in which viscosity depends on the time and the rate of shear, decreasing with the increasing rate of shear. A thixotropic system is reversible, the thixotropic recovery time ranging from a microsecond to a number of hours, depending on the instrument and the method of testing, and on the
600
LEOPOLD
DINTENFASS
intrinsic properties of the material tested. The presence of thixotropy in suspensions or emulsions indicates aggregation (flocculation) of the suspended particles. The fundamental unit of (dynamic) viscosity is a “poise” which is equal to 100 centipoises (cp) . One centipoise is equal to the viscosity of water at 20°C. RESULTS
AND
DISCUSSION
The experimental data are plotted as viscosity, in poises, against the rate of shear, in reciprocal seconds, on a log-log scale. As may be observed from Figs. 3 and 4, the %
700 600 500
0
123456 OOOdb.
0
400 1 300 c 200
t
: kf Y 100 0 90 SO 70 1 601
I
1101111 0.4 0.6
0.6
!
2
3
4
567
7) ) potses FIG. 3. Flow curves of the packed blood cells. Viscosity of the red blood cells, packed at ISOOO x g, is determined by means of a ring-in-ring viscometer. Hematocrit values are not less than 98 per cent. Experimental points are plotted on coordinates of viscosity, in poises, and of rates of shear, in reciprocal seconds, on a log-log scale. Cells from six normal adults were used. (1) Red cells packed from saline and tested at 20°C. (2) Red cells packed from plasma and tested at 20°C. (3) Red cells packed from plasma and tested at 37°C. (4) Red cells packed from plasma and tested at 37°C. (5) Red cells packed from plasma and tested at 37°C. (6) Red cells pack from plasma and tested at 37°C.
viscosity of the packed red cells depends on three obvious parameters: the velocity gradient, the temperature, and the origin of the cells. An increase of the rate of shear, for instance from 20 reciprocal seconds to 200 reciprocal seconds, causes a decrease in viscosity by 30 to 80 per cent. This decrease is reversible, that is, it is recovered when the rate of shear decreases. An increase in temperature also causes a decrease in the viscosity of packed cells. A decrease of temperature from 42’C to 37°C is accompanied by viscosity increase of l&20 per cent. There is no great difference in flow properties between the packed cells centrifuged from plasma or from saline. Although the actual numerical value of viscosity may differ, the principal pattern and range of flow properties remains unaltered. Variations in viscosity were found to exist between the packed cells obtained from various normal donors and from patients. However, it is not intended here to suggest
VISCOSITY
OF
THE
PACKED
BLOOD
CELLS
601
or imply that the data obtained are representative of blood elements in health or disease. It is intended only to show that, notwithstanding the origin of the red cells, the viscosity of the packed cells ranges from 0.4 to 3 poises (at rates of shear higher than 20 set-l), although the packed cells obtained from leukaemia patients may exhibit higher viscosities (Fig. 5). It is important to realize that the centrifuged rigid particles of suspensions of clays, inorganic oxides, microscopic glass or plastic spheres, etc. would show a consistency nearly that of pitch or concrete. At concentrations of 55-70 per cent, suspensions of 300
c
*
60
c 0.4
b
42'C 0.6
0.6 !
2
3
4
5 678910
FIG. 4. Viscosity of the red blood cells, packed from saline at 15000 x g, as determined by means of a rotational viscometer. Hematocrit values are not less than 98 per cent. A, red cells from an afibrogenaemia patient; B, red cells from a normal adult; C, red cells from a hemophilia patient; D, blood cells from a myeloblastic leukaemia patient (white cell count 100,000) ; E, blood cells from a lymphocytic leukaemia patient (white cell count 540,000). System A, B, and C contain only negligible amount of the white cells. Please note that hemoglobin was normal in all the cases studied. Determinations were carried out at 37°C unless otherwise indicated. The results are plotted as viscosity, in poises, against the rate of shear, in reciprocal seconds, on a log-log scale.
the rigid particles would show viscosity a thousands times larger than the viscosity of packed red cells at a hematocrit of 98 per cent (Dintenfass, 1962). The only feasible explanation for the low viscosity of the packed red cells is that the cells behave as fluid drops of rather low internal viscosity. It is known from the theoretical works of Taylor (1932) and Oldroyd (1953, 1955), as also from the experimental studies of Mason and his collaborators (Rumscheidt and Mason, 1961; Karnis et al., 1963), that emulsions in which the viscosity of disperse phase is about SO-fold larger than that of the continuous phase behave as suspensions of rigid particles. It would be reasonable to deduce that the internal viscosity of the red cell in flow cannot be more than 50 X viscosity of saline, that is, no more than about 30 centipoises, and likely only 10 to 20 centipoises. As the viscosity of the packed cells is shear-dependent, it should be also reasonable to expect that the internal viscosity of the red cell is shear-dependent.
602
LEOPOLD
DINTENFASS
If the internal viscosity of the red cell is as low as suggested, then there should be a visible change in the relative viscosity of the packed cells (that is, the viscosity of the packed cells divided by the viscosity of plasma) as a function of variations in the ratio of the internal viscosity of the red cell to the viscosity of plasma (so-called Taylor’s p). In order to test this point, the following experiment was carried out. The red cells obtained from a polycythaemia patient were centrifuged, twice washed with isotonic saline, resuspended in plasmas prepared by mixing the native plasma with certain amounts of macroglobulins, and centrifuged again at 15000 X R. The now 250
-
200 150 100
7 b: "7 d
-
80 70 60 50. 40 30 20 -
10 e710
I-
I
20
30
40 50
IIS,,
70
100
200
300 4oc
7'
of the packed red cells prepared by centrifugation from plasmas of various FIG. 5. Viscosity viscosities. Results obtained are plotted as the relative viscosity, nr (that is, the ratio of the viscosity of suspension to the viscosity of the respective plasma), against the rate of shear, in reciprocal seconds. Log-log scale is used. Plasmas viscosities: A = 1 centipoise, B = 2.1 centipoises, C = 7.0 centipoises. Please note that the packed cells obtained from the highest viscosity plasma show the lowest relative viscosity.
separated plasmas were tested, their viscosities being 1 cp, 2.1 cp, and 7.0 cp, respectively. The viscosities of the packed cells in these plasmas are illustrated by Fig. 5. It may be observed that the packed cells in ‘the highest viscosity plasma show the lowest relative viscosity. This phenomenon may be explained on the basis of Taylor’s theory; that is, that the viscosity of the packed cells depends on the ratio of the internal viscosity of the cell and of the viscosity of the continous phase, and that the relative viscosity of the packed cells is less when this ratio is lowest. Consequently, it would appear that the numerical value of the internal viscosity of the red cells tested is above 7 cp. When discussing the numerical values for the internal viscosity of the red cell, we should remember that these values are not true values of the viscosity of the interior, but values magnified by the effect of the red cell membrane. The evidence on the low internal viscosity of the red cell is augmented by direct microscopic observations. The red cell in flow is known to undergo rapid deformations (Bloch, 1961)) and when caught in a narrow capillary segment it may perform
VISCOSITY
OF
THE
PACKED
BLOOD
603
CELLS
periodic protruding movements alike that of a fluid-filled bag (Branemark and Lindstrom, 1963). Palmer (1959) observed that the red cells in flow assume a teardrop shape, and that they are indented in collisions with leucocytes. Branemark and Lindstrom (1963) noted that the red cell may stretch to a narrow “film” while slipping past the white cell. The latter reports directed my attention to the study of rigidity and fluidity of the white cells. Advantage was taken of the white cells available from leukaemia patients, some of whom were undergoing an exchange blood transfusion. Packed cells enriched 400 300 200
100 80 -i 60 u) ; 40
20
10 8
is I NIIII 0.4
06 0.8 I
2
3 4 5 670910
20
30
3
m ) pOlSe*
FIG. 6. Viscosity of the human packed blood cells. The unlabeled curve (left) illustrates the packed red cells obtained from a polycythaemia patient. All other curves show the packed cells enriched in the white cells by in vitro preparations. Concentration of the white cells: Curve ZA, 1.75 per cent; Curve ZB, 3.5 per cent; Curve lA, 17 per cent; Curve IB, 80 per cent. White cells used in these preparations have been obtained from a myeloid leukaemia case. All packed cells systems have been prepared by centrifugation at 15000 X g. Data are plotted as viscosity, in poises, against the rate of shear, in reciprocal seconds.
in the white cells were obtained by separation of the buffy coat, as described in Methods. Systems containing white cells were always tested within four hours of blood extraction. Viscometric results are contained in Fig. 6, Curve 1A illustrating a system containing 17 per cent of the white cells and 82 per cent of the red cells, and Curve IB illustrating a system containing 80 per cent of the white cells and 19 per cent of the red cells, Curves 2A and 2B illustrate systemsof packed cells of lower content of the white cells, but prepared from the blood of a different leukaemia patient. It may be seenthat as the concentration of the white cells increases,the viscosity and the shear-dependenceof the packed cells also increase. The flow curves, plotted as viscosity against the rate of shear on a log-log scale, indicate a pronounced thixotropy. This is due neither to the minute quantity of plasma present (systems were packed at 15000 >: g) nor to the network-type aggregation of the cells (at close packing such free aggregation cannot take place). A decreaseof the resistanceto flow with an increase of the linear velocity and of the velocity gradient, while simultane-
604
LEOPOLD
DINTENFASS
ously the whole body of cells exists under homogeneous velocity gradient, indicates that the phenomena observed are due to the rheological structure of the cells themselves. The effects of these rheological structures could be, however, subdivided into the effects due to the actual cell interior, and the effects due to the cell membrane. With the present technique such differentiation is not easy. It is known, however, from the most recent studies of Rand (1964) that the membrane of the red cell is viscoelastic. It could be assumed that the viscoelasticity of the white cell membrane is not greater than that of the red cell membrane; if such assumption is correct, the difference in bulk viscosities could be attributed mainly to the differences of the cells interiors. That is, the internal viscosity and the internal molecular and colloidal structures differ. It would appear that the internal viscosity of the white cell is greater than that of the red cell; also, that the thixotropy of the former is much more pronounced. If a comparison can be made between the protoplasm of the white cell and that of the tissue cells, it could be noted that Rieser (1949) found the viscosity of protoplasm in muscle fiber to be 14-45 cp, while Seifriz (1938, 1952) observed values ranging from 2.5 to 2500 cp. Seifriz realized that protoplasm is thixotropic and that, consequently, the viscosity of protoplasm will change accordingly to external mechanical conditions. More recently, Yagi (1961) related the rate of amoeboid movement to the apparent internal viscosity of the amoeba of proteus type. The rate of movement was found to increase as the internal viscosity decreased. CONCLUSIONS The red cells, of normal hemoglobin content, packed at 15000 X g, exhibit viscosities ranging from 0.4 to 3 poises (at about 100 set-l), depending on the particular individual from which these cells have been obtained. The packed blood cells obtained from leukaemic patients are characterized by higher viscosity. Packed blood cells, enriched in the white cells, show greatly increased viscosities. As the viscosity of blood has been found related to thrombotic states and circulatory deficiency (Dintenfass, 1964), an elevation of blood viscosity because of the presence of the white cells, in excessive amounts, in patients suffering from leukaemia may be of interest. It does appear that in humans the ratio of viscosities of the packed white cells and the packed red cells may vary from 5 to 100, depending on the rate of shear. The interior of the white cell appears to be more viscous and more shear-dependent (thixotropic) than that of the red cell. Further application of rheological techniques to the study of structure (molecular and colloidal) and flow behavior of the blood cells is hoped to give some insight into microcirculation in both normal and pathological cases. SUMMARY
viscosity of the packed blood cells, prepared by centrifugation at 15000 X g, has been determined by means of a rotational viscometer. The packed cells exhibit high fluidity if compared to any known suspensions of solid particles. This fluidity is attributed to the low internal viscosity of the cell interior. Systems containing the white cells, obtained from leukaemia patients, exhibit slightly higher viscosity than the packed celIs of normal blood cells. It is concluded that the internal viscosity of
VISCOSITY
OF
THE
PACKED
BLOOD
605
CELLS
the white cell is higher and more shear-depending (thixotropic) than the internal viscosity of the normal red cell. The packed red cells, all containing normal hemoglobin, differ in viscosity depending on their origin. ACKNOWLEDGMENT I am indebted
to the National
Heart
Foundation
of Australia
for support
of this study.
REFERENCES BLOCH, 5.
E. H.
(1961).
The
rheology
BRANEMARK,
P. I., and LINDSTROM,
139-143. DINTENFASS, 48-68.
L. (1959).
A study
of blood J. (1963).
in thixotropy
in the living
microvascular
Shape of circulating of concentrated
blood
pigment
system. corpuscles. suspensions.
Rheol.
BUZZ. 20,
Biorheology Kolloid-Z.
1, 182,
L. (1962). Considerations of the internal viscosity of red cells and its effect on the of whole blood. Angiology 8, 333-344. DINTENFASS, L. (1963). An application of a cone-in-cone viscometer to the study of viscosity, thixotropy and clotting of whole blood. Biorheology 1, 91-99. DINTENFASS, L. (1964). Viscosity and clotting of blood in venous thrombosis and coronary occlusion. Circulation Res. 14, l-16. DINTENFASS, L. (1965). A ring-in-ring adapter for the cone-in-cone rotational viscometer. Biorheology 2, 221. ERSLEV, A. J., and ATWATER, J. (1963). Effect of MCHC on viscosity. J. Lab. CZin. Med. 62, 401. HAYNES, R. H. (1963). Physical aspects of the mammalian circulatory system. Trans. Sot. Rheology 7, 19. KARNIS, A., GOLDSMITH, H. L., and MASON, S. G. (1963). Axial migration of particles in Poiseuille flow. Nature 200, 159. OLDROYD, J. G. (1953). The elastic and viscous properties of emulsions and suspensions. Proc. Roy. Sm. Ser. A 218, 122-132. OLDROYD, J. G. (1955). The effect of interfacial stabilizing film on the elastic and viscous properties of emulsions. Proc. Roy. Sot. Ser. A 232, 567-577. PALMER, A. A. (1959). A study of blood flow in minute vessels of the pancreatic region of the rat with reference to intermittent corpuscular flow in individual capillaries. Quart. J. Exptl. Physiol. 44, 149-159. RAND, R. P. (1964). Mechanical properties of the red cell membrane. II. Viscoelastic breakdown of the membrane. Biophys. J. 4, 303-316. RIESER, P. (1964). The protoplasmic viscosity of muscle. Protoplasma 39, 95. RUMSCHEIDT, F. D., and MASON, S. G. (1961). Particle motions in sheared suspentions. XI. Internal circulation in fluid drops. J. CoZZoid Sci. 16, 210-237. SEIFRIZ, W. (1938). Recent contributions to the theory of protoplasmic structure. Science 88, 21. SEIFRIZ, W. (1952). The rheological properties of protoplasm. In “Deformation and Flow in Biological Systems” (A. Frey-Wyssling, ed.) P. 3. North Holland, Amsterdam. TAYLOR, G. I. (1932). The viscosity of fluid containing small drops of another fluid. Proc. Roy. Sot. Ser. A 138, 4148. YAGI, K. (1961). The mechanical and colloidal properties of Amoeba protoplasm and their relations to the mechanism of amoeboid movement. Comp. Biochem. Physiol. 3, 73-91. DINTFZNFASS,
viscosity
ARD
Viscosity
MOLECULAR
PATHOLOGY
of the
4,
Packed
597-605
Red
(1965)
and
White
Blood
Cells’
LEOPOLD DINTENFASS Department
of Medicine,
University
Received
of Sydney,
October
Sydney,
Australia
16, 1964
The fluidity of the packed red blood cells is well known to hematologists and physiologists alike and is taken for granted by them. Physicists and rheologists, accustomedto an exponential increasein the viscosity of suspensionsof rigid particles with an increase in the concentration of the dispersed phase, have observed and acknowledged this most unusual behavior of the blood only in the most recent times (Dintenfass, 1962; Haynes, 1963; Erslev and Atwater, 1963; and Rand, 1964). Formerly to this, there had existed (among physicists) a tacit assumption that the red cell may be treated as a rigid, or nearly rigid. body and that the internal viscosity of the red cell is of no consequence. It is the intention of this communication to show not only that the red cell behaves as a fluid drop, but also that the red cells originating from different individuals exhibit different viscosity, although the hemoglobin in all the casesis normal. It will be shown that packed blood cells rich in the white cells exhibit increasedviscosity. METHODS The packed red cells have been obtained by centrifugation of the anticoagulated (EDTA) human blood, collected by venipuncture from healthy donors and from a seriesof patients. Some sampleswere centrifuged directly from plasma, while others were washed repeatedly with isotonic saline and centrifuged at 15000 X g for a period of 12 minutes. Subsequentto this the last drops of supernatant were removed. The hematocrit value was checked by high-speed microhematocrit methods and was found, in all samples,to be not less than 98 per cent. The packed blood cells enriched in the white cells have been obtained in the following manner: Blood obtained from leukaemia patients was centrifuged, the buffy coat was aspirated and diluted with isotonic saline, and centrifuged again; the resulting buffy coat was aspirated again, diluted again, centrifuged again, and so forth. Depending on the number of operations, materials of different content of white (leukaemic) cells have been prepared. The viscosity of packed cells has been determined using a rotational ring-in-ring viscometer. This is a modification of a previously described cone-in-cone viscometer (Dintenfass, 1963, 1964). The ring-in-ring viscometer is better suited for studies at relatively higher rates of shear. The basic part of the viscometer consistsof a Teflon ring, suspendedon a torsion strip, and a brass annulus, rotated by meansof a beltdrive. The Teflon ring is 15 mm high, has an internal diameter of 24.7 mm; the width of the annulus, accommodating,the ring is 1.9 mm; the internal gap between the inner 1 Supported by grants from the National Heart
Foundation 597
of Australia
598
LEOPOLD
DINTENFASS
wall of the annulus and the inner surface of the ring is 0.58 mm, is 0.64 mm. The rate of shear evolved in the annulus is equal to RPM = revolutions per minute), the velocity gradient across annulus (outer and inner) being identical and homogeneous. The ring-in-ring adapter are illustrated by Figs. 1 and 2.
while the outer gap 2.1 X RPM (where both parts of the viscometer and the
FIG. 1. The ring-in-ring viscometer. Center: the viscometer. Left: a spotlight, scale, and a tachometer. Right: in the foreground is the “Zeromax” stepless drive a secondary gearbox (reduction lOO:l), while in the background is a thermostat mercury-contact thermometer.
a semi-circular and motor, and equipped with a
The torsion strips used were “Mallory 73” beryllium copper strips of cross-sections 0.008 X 0.025, 0.008 X 0.075, and 0.016 X 0.075 inches. The viscometer was calibrated using standard oils obtained from the National Standards Laboratories, C.S.I.R.O., Sydney. The temperature was controlled by means of a mercury-contact thermometer and relay. Actual measurement of viscosity. The fluid tested was poured into the gap between the Teflon ring and the brass annulus. The drive was started and the positions of the
VISCOSITY
OF
THE
PACKED
BLOOD
CELLS
599
lightspot on the semi-circular scale were noted. The deflections of the lightspot indicated a twist in the torsion strip, the lightspot being reflected from a tiny mirror attached to the strip. The number of revolutions was progressively increased. When the scale could not accommodate further deflections of the lightspot, a heavier torsion strip was used. It was necessary to remove a surface film (formed probably of denaturated proteins) which occurred in some samples, especially at higher temperatures.
FIG. 2. Teflon ring and two annufi. The annulus (left) is made of brass while the other (right) is made of Teflon. The Teflon ring is fastened to a brass holder through an universal joint, a small mirror being secured onto this holder. This mirror deflects a lightspot onto the scale and permits. therefore, measurement of the deflections of the torsion strip,
Rheological nomenclature The “rate of shear” or the “velocity gradient” is a function of the relative velocity of the fluid laminae or of the surfaces surrounding the fluid and of the geometry of these surfaces. In the simplest case of two parallel surfaces, spaced by a gap d, and moving at a relative velocity I/, the velocity gradient between these surfaces is equal to V/d; the units of velocity, cm/set, are divided by the units of distance, cm, in order to yield the units of the rate of shear,set-l. The term “thixotropic” describesa system in which viscosity depends on the time and the rate of shear, decreasing with the increasing rate of shear. A thixotropic system is reversible, the thixotropic recovery time ranging from a microsecond to a number of hours, depending on the instrument and the method of testing, and on the
600
LEOPOLD
DINTENFASS
intrinsic properties of the material tested. The presence of thixotropy in suspensions or emulsions indicates aggregation (flocculation) of the suspended particles. The fundamental unit of (dynamic) viscosity is a “poise” which is equal to 100 centipoises (cp) . One centipoise is equal to the viscosity of water at 20°C. RESULTS
AND
DISCUSSION
The experimental data are plotted as viscosity, in poises, against the rate of shear, in reciprocal seconds, on a log-log scale. As may be observed from Figs. 3 and 4, the %
700 600 500
0
123456 OOOdb.
0
400 1 300 c 200
t
: kf Y 100 0 90 SO 70 1 601
I
1101111 0.4 0.6
0.6
!
2
3
4
567
7) ) potses FIG. 3. Flow curves of the packed blood cells. Viscosity of the red blood cells, packed at ISOOO x g, is determined by means of a ring-in-ring viscometer. Hematocrit values are not less than 98 per cent. Experimental points are plotted on coordinates of viscosity, in poises, and of rates of shear, in reciprocal seconds, on a log-log scale. Cells from six normal adults were used. (1) Red cells packed from saline and tested at 20°C. (2) Red cells packed from plasma and tested at 20°C. (3) Red cells packed from plasma and tested at 37°C. (4) Red cells packed from plasma and tested at 37°C. (5) Red cells packed from plasma and tested at 37°C. (6) Red cells pack from plasma and tested at 37°C.
viscosity of the packed red cells depends on three obvious parameters: the velocity gradient, the temperature, and the origin of the cells. An increase of the rate of shear, for instance from 20 reciprocal seconds to 200 reciprocal seconds, causes a decrease in viscosity by 30 to 80 per cent. This decrease is reversible, that is, it is recovered when the rate of shear decreases. An increase in temperature also causes a decrease in the viscosity of packed cells. A decrease of temperature from 42’C to 37°C is accompanied by viscosity increase of l&20 per cent. There is no great difference in flow properties between the packed cells centrifuged from plasma or from saline. Although the actual numerical value of viscosity may differ, the principal pattern and range of flow properties remains unaltered. Variations in viscosity were found to exist between the packed cells obtained from various normal donors and from patients. However, it is not intended here to suggest
VISCOSITY
OF
THE
PACKED
BLOOD
CELLS
601
or imply that the data obtained are representative of blood elements in health or disease. It is intended only to show that, notwithstanding the origin of the red cells, the viscosity of the packed cells ranges from 0.4 to 3 poises (at rates of shear higher than 20 set-l), although the packed cells obtained from leukaemia patients may exhibit higher viscosities (Fig. 5). It is important to realize that the centrifuged rigid particles of suspensions of clays, inorganic oxides, microscopic glass or plastic spheres, etc. would show a consistency nearly that of pitch or concrete. At concentrations of 55-70 per cent, suspensions of 300
c
*
60
c 0.4
b
42'C 0.6
0.6 !
2
3
4
5 678910
FIG. 4. Viscosity of the red blood cells, packed from saline at 15000 x g, as determined by means of a rotational viscometer. Hematocrit values are not less than 98 per cent. A, red cells from an afibrogenaemia patient; B, red cells from a normal adult; C, red cells from a hemophilia patient; D, blood cells from a myeloblastic leukaemia patient (white cell count 100,000) ; E, blood cells from a lymphocytic leukaemia patient (white cell count 540,000). System A, B, and C contain only negligible amount of the white cells. Please note that hemoglobin was normal in all the cases studied. Determinations were carried out at 37°C unless otherwise indicated. The results are plotted as viscosity, in poises, against the rate of shear, in reciprocal seconds, on a log-log scale.
the rigid particles would show viscosity a thousands times larger than the viscosity of packed red cells at a hematocrit of 98 per cent (Dintenfass, 1962). The only feasible explanation for the low viscosity of the packed red cells is that the cells behave as fluid drops of rather low internal viscosity. It is known from the theoretical works of Taylor (1932) and Oldroyd (1953, 1955), as also from the experimental studies of Mason and his collaborators (Rumscheidt and Mason, 1961; Karnis et al., 1963), that emulsions in which the viscosity of disperse phase is about SO-fold larger than that of the continuous phase behave as suspensions of rigid particles. It would be reasonable to deduce that the internal viscosity of the red cell in flow cannot be more than 50 X viscosity of saline, that is, no more than about 30 centipoises, and likely only 10 to 20 centipoises. As the viscosity of the packed cells is shear-dependent, it should be also reasonable to expect that the internal viscosity of the red cell is shear-dependent.
602
LEOPOLD
DINTENFASS
If the internal viscosity of the red cell is as low as suggested, then there should be a visible change in the relative viscosity of the packed cells (that is, the viscosity of the packed cells divided by the viscosity of plasma) as a function of variations in the ratio of the internal viscosity of the red cell to the viscosity of plasma (so-called Taylor’s p). In order to test this point, the following experiment was carried out. The red cells obtained from a polycythaemia patient were centrifuged, twice washed with isotonic saline, resuspended in plasmas prepared by mixing the native plasma with certain amounts of macroglobulins, and centrifuged again at 15000 X R. The now 250
-
200 150 100
7 b: "7 d
-
80 70 60 50. 40 30 20 -
10 e710
I-
I
20
30
40 50
IIS,,
70
100
200
300 4oc
7'
of the packed red cells prepared by centrifugation from plasmas of various FIG. 5. Viscosity viscosities. Results obtained are plotted as the relative viscosity, nr (that is, the ratio of the viscosity of suspension to the viscosity of the respective plasma), against the rate of shear, in reciprocal seconds. Log-log scale is used. Plasmas viscosities: A = 1 centipoise, B = 2.1 centipoises, C = 7.0 centipoises. Please note that the packed cells obtained from the highest viscosity plasma show the lowest relative viscosity.
separated plasmas were tested, their viscosities being 1 cp, 2.1 cp, and 7.0 cp, respectively. The viscosities of the packed cells in these plasmas are illustrated by Fig. 5. It may be observed that the packed cells in ‘the highest viscosity plasma show the lowest relative viscosity. This phenomenon may be explained on the basis of Taylor’s theory; that is, that the viscosity of the packed cells depends on the ratio of the internal viscosity of the cell and of the viscosity of the continous phase, and that the relative viscosity of the packed cells is less when this ratio is lowest. Consequently, it would appear that the numerical value of the internal viscosity of the red cells tested is above 7 cp. When discussing the numerical values for the internal viscosity of the red cell, we should remember that these values are not true values of the viscosity of the interior, but values magnified by the effect of the red cell membrane. The evidence on the low internal viscosity of the red cell is augmented by direct microscopic observations. The red cell in flow is known to undergo rapid deformations (Bloch, 1961)) and when caught in a narrow capillary segment it may perform
VISCOSITY
OF
THE
PACKED
BLOOD
603
CELLS
periodic protruding movements alike that of a fluid-filled bag (Branemark and Lindstrom, 1963). Palmer (1959) observed that the red cells in flow assume a teardrop shape, and that they are indented in collisions with leucocytes. Branemark and Lindstrom (1963) noted that the red cell may stretch to a narrow “film” while slipping past the white cell. The latter reports directed my attention to the study of rigidity and fluidity of the white cells. Advantage was taken of the white cells available from leukaemia patients, some of whom were undergoing an exchange blood transfusion. Packed cells enriched 400 300 200
100 80 -i 60 u) ; 40
20
10 8
is I NIIII 0.4
06 0.8 I
2
3 4 5 670910
20
30
3
m ) pOlSe*
FIG. 6. Viscosity of the human packed blood cells. The unlabeled curve (left) illustrates the packed red cells obtained from a polycythaemia patient. All other curves show the packed cells enriched in the white cells by in vitro preparations. Concentration of the white cells: Curve ZA, 1.75 per cent; Curve ZB, 3.5 per cent; Curve lA, 17 per cent; Curve IB, 80 per cent. White cells used in these preparations have been obtained from a myeloid leukaemia case. All packed cells systems have been prepared by centrifugation at 15000 X g. Data are plotted as viscosity, in poises, against the rate of shear, in reciprocal seconds.
in the white cells were obtained by separation of the buffy coat, as described in Methods. Systems containing white cells were always tested within four hours of blood extraction. Viscometric results are contained in Fig. 6, Curve 1A illustrating a system containing 17 per cent of the white cells and 82 per cent of the red cells, and Curve IB illustrating a system containing 80 per cent of the white cells and 19 per cent of the red cells, Curves 2A and 2B illustrate systemsof packed cells of lower content of the white cells, but prepared from the blood of a different leukaemia patient. It may be seenthat as the concentration of the white cells increases,the viscosity and the shear-dependenceof the packed cells also increase. The flow curves, plotted as viscosity against the rate of shear on a log-log scale, indicate a pronounced thixotropy. This is due neither to the minute quantity of plasma present (systems were packed at 15000 >: g) nor to the network-type aggregation of the cells (at close packing such free aggregation cannot take place). A decreaseof the resistanceto flow with an increase of the linear velocity and of the velocity gradient, while simultane-
604
LEOPOLD
DINTENFASS
ously the whole body of cells exists under homogeneous velocity gradient, indicates that the phenomena observed are due to the rheological structure of the cells themselves. The effects of these rheological structures could be, however, subdivided into the effects due to the actual cell interior, and the effects due to the cell membrane. With the present technique such differentiation is not easy. It is known, however, from the most recent studies of Rand (1964) that the membrane of the red cell is viscoelastic. It could be assumed that the viscoelasticity of the white cell membrane is not greater than that of the red cell membrane; if such assumption is correct, the difference in bulk viscosities could be attributed mainly to the differences of the cells interiors. That is, the internal viscosity and the internal molecular and colloidal structures differ. It would appear that the internal viscosity of the white cell is greater than that of the red cell; also, that the thixotropy of the former is much more pronounced. If a comparison can be made between the protoplasm of the white cell and that of the tissue cells, it could be noted that Rieser (1949) found the viscosity of protoplasm in muscle fiber to be 14-45 cp, while Seifriz (1938, 1952) observed values ranging from 2.5 to 2500 cp. Seifriz realized that protoplasm is thixotropic and that, consequently, the viscosity of protoplasm will change accordingly to external mechanical conditions. More recently, Yagi (1961) related the rate of amoeboid movement to the apparent internal viscosity of the amoeba of proteus type. The rate of movement was found to increase as the internal viscosity decreased. CONCLUSIONS The red cells, of normal hemoglobin content, packed at 15000 X g, exhibit viscosities ranging from 0.4 to 3 poises (at about 100 set-l), depending on the particular individual from which these cells have been obtained. The packed blood cells obtained from leukaemic patients are characterized by higher viscosity. Packed blood cells, enriched in the white cells, show greatly increased viscosities. As the viscosity of blood has been found related to thrombotic states and circulatory deficiency (Dintenfass, 1964), an elevation of blood viscosity because of the presence of the white cells, in excessive amounts, in patients suffering from leukaemia may be of interest. It does appear that in humans the ratio of viscosities of the packed white cells and the packed red cells may vary from 5 to 100, depending on the rate of shear. The interior of the white cell appears to be more viscous and more shear-dependent (thixotropic) than that of the red cell. Further application of rheological techniques to the study of structure (molecular and colloidal) and flow behavior of the blood cells is hoped to give some insight into microcirculation in both normal and pathological cases. SUMMARY
viscosity of the packed blood cells, prepared by centrifugation at 15000 X g, has been determined by means of a rotational viscometer. The packed cells exhibit high fluidity if compared to any known suspensions of solid particles. This fluidity is attributed to the low internal viscosity of the cell interior. Systems containing the white cells, obtained from leukaemia patients, exhibit slightly higher viscosity than the packed celIs of normal blood cells. It is concluded that the internal viscosity of
VISCOSITY
OF
THE
PACKED
BLOOD
605
CELLS
the white cell is higher and more shear-depending (thixotropic) than the internal viscosity of the normal red cell. The packed red cells, all containing normal hemoglobin, differ in viscosity depending on their origin. ACKNOWLEDGMENT I am indebted
to the National
Heart
Foundation
of Australia
for support
of this study.
REFERENCES BLOCH, 5.
E. H.
(1961).
The
rheology
BRANEMARK,
P. I., and LINDSTROM,
139-143. DINTENFASS, 48-68.
L. (1959).
A study
of blood J. (1963).
in thixotropy
in the living
microvascular
Shape of circulating of concentrated
blood
pigment
system. corpuscles. suspensions.
Rheol.
BUZZ. 20,
Biorheology Kolloid-Z.
1, 182,
L. (1962). Considerations of the internal viscosity of red cells and its effect on the of whole blood. Angiology 8, 333-344. DINTENFASS, L. (1963). An application of a cone-in-cone viscometer to the study of viscosity, thixotropy and clotting of whole blood. Biorheology 1, 91-99. DINTENFASS, L. (1964). Viscosity and clotting of blood in venous thrombosis and coronary occlusion. Circulation Res. 14, l-16. DINTENFASS, L. (1965). A ring-in-ring adapter for the cone-in-cone rotational viscometer. Biorheology 2, 221. ERSLEV, A. J., and ATWATER, J. (1963). Effect of MCHC on viscosity. J. Lab. CZin. Med. 62, 401. HAYNES, R. H. (1963). Physical aspects of the mammalian circulatory system. Trans. Sot. Rheology 7, 19. KARNIS, A., GOLDSMITH, H. L., and MASON, S. G. (1963). Axial migration of particles in Poiseuille flow. Nature 200, 159. OLDROYD, J. G. (1953). The elastic and viscous properties of emulsions and suspensions. Proc. Roy. Sm. Ser. A 218, 122-132. OLDROYD, J. G. (1955). The effect of interfacial stabilizing film on the elastic and viscous properties of emulsions. Proc. Roy. Sot. Ser. A 232, 567-577. PALMER, A. A. (1959). A study of blood flow in minute vessels of the pancreatic region of the rat with reference to intermittent corpuscular flow in individual capillaries. Quart. J. Exptl. Physiol. 44, 149-159. RAND, R. P. (1964). Mechanical properties of the red cell membrane. II. Viscoelastic breakdown of the membrane. Biophys. J. 4, 303-316. RIESER, P. (1964). The protoplasmic viscosity of muscle. Protoplasma 39, 95. RUMSCHEIDT, F. D., and MASON, S. G. (1961). Particle motions in sheared suspentions. XI. Internal circulation in fluid drops. J. CoZZoid Sci. 16, 210-237. SEIFRIZ, W. (1938). Recent contributions to the theory of protoplasmic structure. Science 88, 21. SEIFRIZ, W. (1952). The rheological properties of protoplasm. In “Deformation and Flow in Biological Systems” (A. Frey-Wyssling, ed.) P. 3. North Holland, Amsterdam. TAYLOR, G. I. (1932). The viscosity of fluid containing small drops of another fluid. Proc. Roy. Sot. Ser. A 138, 4148. YAGI, K. (1961). The mechanical and colloidal properties of Amoeba protoplasm and their relations to the mechanism of amoeboid movement. Comp. Biochem. Physiol. 3, 73-91. DINTFZNFASS,
viscosity