BritishJourtral of Haematology, 1976, 34, 347.
Annotation PLASMA AND WHOLE BLOOD VISCOSITY In 1687 Isaac Newton wrote in his Principia ‘the resistance which arises from the lack of slipperiness of the parts of a liquid, other things being equal, is proportional to the velocity with which the parts of a liquid are separated from one another’. The ‘lack of slipperiness’ we now call ‘viscosity’. According to Scott Blair (1969) viscosity is an old word originally meaning ‘stickiness’ and derives from the Latin word for mistletoe. The concept of viscosity is simple; it is the resistance offered by a liquid to attempts to change its shape. Its mathematical expression depends on a knowledge of the laws of elasticity and fluid flow. In practice viscosity may be defined as the ratio of shear stress to shear rate. The rate of shear is the tangential force exerted across a unit area between two parallel planes of the fluid under consideration, unit distance apart, one plane being fixed whilst the other moves at unit velocity. If the planes are distance x apart and move at relative velocity v then the velocity gradient is v/x. This velocity gradient is called the shear rate. If tr is measured in cm/s and x in cm then v / x is expressed in reciprocal seconds, s - l . The force per unit area which produces this rate of shear is the shear stress. If the ratio of shear stress to shear rate is constant then a liquid is said to be ‘Newtonian’ in character-i.e. if the flow rate is to be doubled twice the force will be required to bring this about. The unit of viscosity is the Poise named after Poiseuille (1846), a physician, who formulated the relationship between the variables determining the rate of flow of fluids through narrow tubes. This relationship may be expressed as n A P r4 rate of flow = - x- x -
g
l
r
where: A P / l = pressure gradient where 1 = tube length; q = viscosity; r = radius of tube. In his Hunterian Lecture, Dormandy (1970) noted the discrepancy between the amount of attention paid to the importance of driving pressure and vessel calibre compared with the study of the physiology and pathology of blood viscosity. This is due partly to the fact that whole blood does not behave in a Newtonian fashion, as the ratio of shear stress to shear rate is not constant. Plasma is believed to be Newtonian in behaviour although doubts have been expressed, perhaps based on inadequate techniques, that this is so. Whereas Copley & Staimby (1960) and Wells & Merrill(1961) presented data which showed plasma to be apparently non-Newtonian, Joly (1962) attributed the apparent non-Newtonian character to the effect of a molecular arrangement, of great strength, at the liquid-air interface of their particular measuring instruments. The breakdown of the surface film by the introduction of a guard ring produced data which supports the claim that plasma behaves in a truly Newtonian manner. The rheology of whole blood is far more complex than that of plasma. Whole blood may be considered as a concentrated suspension of red cells in a continuous Newtonian medium. Correspondence:Dr M. J. Phillips, Department of Haematology, Taunton and Somerset Hospital, Musgrove Park, Taunton, Somerset.
3 47
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Annotation
The suspension of red cells in plasma and other supporting media results in non-Newtonian behaviour (Whitmore, 1963; Charm & Kurland, 1972, 1974). The dependence of whole blood viscosity on shear rate is well established, non-Newtonian behaviour becoming more pronounced at low rates of shear. Dintenfass (1962) drew attention to the fact that the viscosity of blood is not only dependent on the rate of shear but also the time over which the shear is applied. Fluids which show a time-dependent viscosity are said to be thixotropic. Paints which ‘thin’ on repeated mixing or brushing are an every-day example of thixotropic fluids.
Measurement of Viscosity Capillary tube viscounetry. The principle behind all capillary tube viscometers is the measurement of the time taken for a standard volume of the test fluid to flow through a capillary tube of standard length and diameter under a standard force at standard temperature. In the classical Ostwald ‘U’-tube instrument the driving force is the standard height of the test fluid itself. The head of pressure varies with the specific gravity of the test fluid and the viscosity measured is termed ‘kinematic viscosity’. Other capillary instruments have an independent driving force and produce ‘absolute viscosity’ or ‘dynamic viscosity’ (Absolute viscosity = kinematic viscosity x density). These instruments have the advantage of requiring only small volumes of test fluid and show a relatively high degree of accuracy. There are two disadvantages. Firstly, they usually operate at high rates of shear which precludes their use in detecting the non-Newtonian influence of cells in whole blood; plasma viscosity measurements are not affected, The second disadvantage arises from the non-uniform flow in the capillary which is slowest at the periphery and fastest at the centre. If flow is imagined as occurring in a series of concentric cylinders, the rate of shear varies across the tube and mathematical analysis of this phenomenon is complex. Capillary viscometers are suitable for the measurement of plasma viscosity. The normal range using the Harkness-designed instrument (Harkness, 1963) at 25°C on plasma separated from blood anticoagulated with EDTA is I .SO-I .72 centipoise; levels for normal individuals are remarkably constant within this range when measured over a period of years. The measurement of plasma viscosity has replaced estimation of erythrocyte sedimentation rate (ESR) in the authors’ hospital. It is a particularly useful index of the severity of hyperproteinaemic states and also of the response to treatment of myeloma and macroglobulinaemia. A comparison of plasma viscosity and ESR in various disease states has been reviewed by Harkness (1971).In addition to the clinical usefulness there are definite technical advantages. Estimations are performed on small samples (0.3-0.5 ml) in less than I min; batch testing can be done rapidly, and samples can, if necessary, be tested several days after collection with no loss of accuracy. Rotational viscornetry. In principle the test liquid is introduced either between a flat plate and the wide-angled base of a suspended bob, or between a cup and a suspended cylindrical bob. Viscosity is calculated from the measured torque on the suspending wires when the plate or cup is rotated at a variety of speeds. The rate of shear depends upon the speed of rotation. Such instruments carry the advantages that viscosity can be measured over a wide range of shear rate. The Wells-Brookfield microviscometer has been used extensively in
Annotation
349
whole blood viscosity measurement but is not reliable at shear rates below 23 s-'. Recent introduction of the Contraves low shear viscometer allows measurement at shear rates as low as 0.07 s-'. The non-Newtonian behaviour of whole blood must be taken into account if measurement of viscosity is to have clinical significance. For example, what are the shear rates which apply in vim? The cardiac cycle must produce velocity changes which differ from blood vessel to blood vessel because of differences in diameter and flow rate. It is known that the lowest shear rate and, hence, the highest viscosity occurs in the large veins; the highest shear rate probably occurs in capillaries. Factors Ie$uencieg Whole Blood Viscosity Hmnatocrit. There have been many conflicting reports of the relationship between viscosity and haematocrit. Hess (I~II), Kunitz (1926)and Whittaker & Winton (1933)described a curvilinear relation based on measurements with a capillary viscometer ; Nyggard et a1 (1935) and Burch & de Pasquale (1963)using a similar technique described a linear relationship. Virgilio et al (1964,also using a capillary instrument, showed that the logarithm of blood viscosity was related to haematocrit in a linear fashion and this was confirmed both by Gregerson et a1 (1965)and by other workers (Begg & Hearns, 1966;Dormandy, 1970; Dormandy & Edelman, 1973; Dormandy et al, 1973)who used rotational viscometers. The clinical importance of the relationship is not established. A change in haematocrit from 40% to 45% raises viscosity by 12% at a shear rate of 230 s - l but by 25% at a shear rate of 5.75 s - l . Rapid administration of intravenous fluids provides haemodilution with a rapid lowering of blood viscosity. This is the rationale behind the use of various intravenous solutions, including low molecular weight dextran, in the treatment of conditions giving rise to haemoconcentration. Dormandy (1970)showed that a reduction of haematocrit from 50% to 45%, producing a 12% fall in viscosity, reduced haemoglobin by 10%. This fall in oxygencarrying capacity was compensated for by an increase in blood flow of between 20 and 30%. Nevertheless the viscosity-haematocrit relation must take into account the degree of red cell aggregation, especially at low rates of shear. The introduction of more accurate and convenient low shear rate viscometers may assist in further elucidation of the clinical significance of the haematocrit-viscosity relationship. Red cell aggregation. At rest red cells form three-dimensional continuous networks of rouleaux (Charm & Kurland, 1972).When stress is applied, the continuous network is broken down into smaller rouleaux which gradually shorten until, at sufficiently high shear stress, the rouleaux disperse into discrete cells. Aggregation of red cells at low rates of shear has long been considered of great importance in accounting for the high viscosities encountered under these conditions. Low shear rate-viscosity relationships in many pathological states have been exhaustively described (Dintenfass, 1971).However, a recent report by Copley ct a1 (1975)using a specially modified rotary viscometer throws some doubt on these findings. Blood was subjected to an initial high rate of shear sufficient to make the cells discrete; rotation was stopped and then restarted at a variety of speeds. At very low rates of shear (0.01-10s-') aggregation of the cells had begun after as little as 30 s and increased thereafter. This suggests that much previously published data from experiments in which unknown degrees of red cell aggregation must have been present should be reassessed.
3 50
Annotation
Plasma jibrinogen. Plasma fibrinogen levels have been shown to influence whole blood viscosity (Mcrrill et a!, 1963a; Weaver et al, 1969). The effect is increasingly pronounced at lower shear rates and is at least partly responsible for the non-Newtonian behaviour of whole blood (Dormandy et al, 1973). The latter group of workers have shown in a study of a large series of claudicants that the high blood viscosity obtained in such patients was associated with abnormally raised plasma fibrinogen; when this was lowered with Clofibrate the viscosity fell to normal levels with symptomatic and objective improvement (Dormandy & Edelman, 1973 ; Dormandy ct a!, 1973, 1974). A study of diabetics with retinopathy showed raised viscosity levels but no evidence that retinopathy was associated with raised fibrinogen levels (Hoare et a!, 1976). Red cell interiial viscosity. At near zero flow velocities human blood may exhibit viscosities of 100-10 ooo times that of water; at high flow velocities it is only 2-10 times that of water (Dintenfass, 1965, 1966). If red cells were replaced by rigid spheres of corresponding dimensions, the resultant fluid would have the consistency of brick at a haematocrit of 65%. Blood remains fluid at a haematocrit of 95%. This difference could only be accounted for by a low red cell internal viscosity (Dintenfass, 1968). It has been shown that solutions ofhaemoglobin are Newtonian and that they have a lower viscosity than blood at the same concentration of haemoglobin (Cokelet & Meiselman, 1968). One of the problems involved in the measurement of intcrnal viscosity is that invasive techniques would destroy thc internal environment and inter-molecular relationships. Dintenfass (1968) derived a mathematical expression based on a study of red cell suspensions in fluids of different viscosities. He determined that the internal viscosity was remarkably low (1-6 cP). Red cellJEexibility or deformability. It would seem logical that the ability of red cells to deform readily, particularly in the micro-circulation, is essential to the maintenance of blood fluidity. Rcd cell flexibility can be measured by a centrifugation technique (Sirs, 1970) and by a filtration technique using membranes with pores of standard diameter (Reid et al, 1975, 1976). Thc latter workers demonstrated a gross reduction in red cell deformability in patients with ischaemic disease of the legs. Dintenfass & Lake (1976) have reported that flexibility and viscosity are altered by beta blocking agents. Mayer (1976) has shown that oral anticoagulants lower viscosity both in healthy subjects and in patients with coronary artery diseasc.
Concltisioris This annotation has attempted to provide a broad view of the physical aspects of viscosity. The clinical applications are, as yet, not clearly discernible. The measurement of plasma viscosity affords a useful non-specific index of disease which some believe to be superior to that provided by the ESR. Many would question the need for any non-specific index of discase although it is difficult to envisage the management of a disorder such as temporal arteritis without such an index, fundamentally unsatisfactory though it may be. Measurement of whole blood viscosity, and the factors which influence it, does seem to have specific clinical implications. Studies of red cell flexibility and internal viscosity are directly relcvant to any understanding of blood flow through small vessels. Such studies may throw more light on the behaviour of sickle cells and other deformed or damaged erythrocytes in the micro-circulation. The interactions of red cell aggregation, low shear rate and fibrinogen or fibrinogen degradation product concentrations must be considered in any
Annotation
351
observation on the pathogenesis of venous thrombosis. Viscosity changes in peripheral arterial disease are already being studied in some depth. More importantly, perhaps, the manufacture and marketing of drugs which purport to lower blood viscosity and increase red cell flexibility indicates that therapeutic manipulation of the physical properties of blood is becoming both a reality and an objective. Recent reports that commonly,used drugs such as beta-blockers and oral anticoagulants affect whole blood viscosity may stimulate research into the viscosity effects of other drugs. It is possible to foresee that measurement of blood viscosity will become a responsibility of haematology departments.
Departments of Haematology and Clinical Chemistry, Taunton and Somerset Hospital, Tatinton, Somerset
M. J. PHILLIPS J. HARKNESS
REFERENCES BEGG,T.B. & HEARNS, J.B. (1966) Components in blood viscosity. The relative contribution of haematocrit, plasma fibrinogen and other proteins. Clinical Science, 31, 87. BURCH,C.E. & DE PASQUALE, N.P. (1963) Phlebotomy. Use in patients with erythrocytosis and ischaemic heart disease. Archives of Internal Medicinr, 111,
687.
CHARM,S.E. & KURLAND, G.S. (1972) Cardiovascular Fluid Dynamics, Vol. 2, chap. IS. Academic Press, New York. CHARM, S.E. & KURLAND, G.S. (1974) Blood Flow and Microcirculation, p 28. Wiley, New York. H.J. (1968) Rheological COKELET, G.R. & MEISELMAN, coniparison of haemoglobin solutions and erythrocyte suspensions. Science, 162, 275. COPLEY, A.L. & STAINSBY, C. (1960) Flow Properties of Blood, p 97. Pergamon Press, Oxford. COPLEY,A.L., KING, R.G., CHIFS, S . , USAMI,S., SKALAK, R. & HUANG,C.R. (1975) Microscopic observations of viscoelasticity of human blood in steady and oscillatory shear. Biorheology, 12, 257. DINTENFASS, L. (1962) Thixotropy of blood at very low rates of shear. Kolloidzeitschrift, 180, 160. DINTENFASS, L. (1965) Viscosity of the packed red and white blood cells. Experimental Molecular Pathology, 4. 597-
DINTENFASS, L. (1966) Viscoinetry of human blood for shear rates of 0-~,ooo,ooosec-’. Nature, 211,632. DINTENFASS, L. (1968) Internal viscosity of the red cell and a blood viscosity equation. Natrm, 219,956. DINTENFASS, L. (1971) Blood Microrheology. Viscosity factors in bloodjloiv, ischaeruia and thrombosis. Butterworths, London. DINTENFASS, L. & LAKE,B. (1976) Beta-blockers and blood viscosity. Lancet, i, 1026. DORMANDY, J.A. (1970) Clinical significance of blood viscosity. Annals of the Royal College of Snrgeons of England, 47, 21 I.
DORMANDY, J.A. & EDELMAN, J. (1973) A new aetiological factor in deep venous thrombosis. BritishJonrnal of Surgery, 60, 187. DORMANDY, J.A., HOARE,E.M., COLLEY, J., ARROWSMITH,D.E. & DORMANDY, T.L. (1973) Clinical, haemodynamic, rheological and biocheniical findings in 126 patients with intermittent claudication. British Medical Journal, iv, 576. DORMANDY, J.A., HOARE,E.M. & DORMANDY, T.L. (1974) Effect of Clofibrate on blood viscosity in intermittent claudication. British Medical Journal, iv, 259.
GRBGERSON, MI.,PERIC,B., CHIEN,S., SINCLAIR, D., CHANG, C. & TAYLOR, H. (1965) Viscosity of blood at low shear rates; observations on its relation to volume concentration and size of the red cells. Proceedings 4th International Congress of Rheology (ed. by A. L. Copley), Part 4, p 613. Interscience, New York. HARKNESS, J. (1963) A new instrument for the measurement of plasma viscosity. Lancet, ii, 280. HARKNESS, J. (1971) The viscosity of human blood plasma; its measurement in health and disease. Biorheology, 8, 171. HESS,W. (191I) Blutviscositat und Blutkorpherchen. A r c h i v j h die Cesamle Physiologic, 140, 354. HOARE,E.M., BARNES, A.J. & DORMANDY, J.A. (1976) Abnormal blood viscosity in diabetes mellitus and retinopathy. Biorheology, 13, 21. JOLY, M. (1962) Dispositif pour la viscosiinktrie prtcise de systhes contenant des proteines. Biorheology, I, I 5 . KUNITZ,M. (1926) An empirical formula for the relation between viscosity of solution and volume of solute.Journal of General Physiology, 9, 715 . MAYER,G.A. (1976) Blood viscosity and oral anticoagulant therapy. American ]ournal of Clinical Pathology, 65, 402. MERRILL, E.W., COKELET, G.C., BRITTEN, A. &WELLS,
3 52
Annotation
R.E. (1963a) Non-Newtonian rheology of human blood-4ects of fibrinogen deduced by subtraction. Circulation Research, 13, 48. NYCCARD, K.K., WILDER, M. & BERKSON, J. (1935) The relation betwecn viscosity of the blood and the relative volume of erythrocytes. AmericanJournal .f Physiatogy, 114,128. POISEUILLE, J.L.M. (1846) Recherches expkrimentales sur le mouvement des liquides dans les tubes de trts petits diamttres. Paris, M h . Sauans &rang. 9, 433. J.A., BARNES,A.J., LOCK, REID,H.L., DORMANDY, P.J. & DORMANDY, T.L. (197s) Impaired red cell deformability in peripheral vascular disease. Lancet, i, 666. REID,H.L., BARNES, A.J., LOCK,P.J., DORMANDY, J.A. K DORMANDY, T.L. (1976) A simple method for measuring erythrocyte deformability. Journal sf CIinicul Pathology (in press). SCOTT BLAIR,G.W. (1969) Elementary Rheology, p 12. Academic Press, New York.
SIRS,J.A. (1970) Automatic recording of the rate of packing of erythrocytes in blood by centrifuge. Physics in Medicine and Biology, 15, 9. VIRGILIO,R.W., LONG,D.M., MUNDTH,E.D. & MCCLENATHAN, J.E. (1964) The effect of temperature and haematocrit on the viscosity of blood. Surgery, 55, 825. WEAVER, J.P.A., EVANS,A. 81 WALDER, D.N. (1969) The effect of increased fibrinogen content on the viscosity of blood. Clinical Science, 36, I. WELLS, R.E. & MERRILL, E.W. (1961) Shear rate dependence of viscosity of human blood and blood plasma. Rheology Bulletin, 30, (2),6. R.S. (1963) Rheology of the Circulation, WHITMORE, p 5 8 . Pergamon Press, Oxford. WHITTAKBR,S.R.F. & WINTON, F.R. (1933) The apparent viscosity of blood flowing in the isolated hind-limb of the dog, and its variation with corpuscular concentration. Journal of’ Physiology, 78, 339.
Annotation PLASMA AND WHOLE BLOOD VISCOSITY In 1687 Isaac Newton wrote in his Principia ‘the resistance which arises from the lack of slipperiness of the parts of a liquid, other things being equal, is proportional to the velocity with which the parts of a liquid are separated from one another’. The ‘lack of slipperiness’ we now call ‘viscosity’. According to Scott Blair (1969) viscosity is an old word originally meaning ‘stickiness’ and derives from the Latin word for mistletoe. The concept of viscosity is simple; it is the resistance offered by a liquid to attempts to change its shape. Its mathematical expression depends on a knowledge of the laws of elasticity and fluid flow. In practice viscosity may be defined as the ratio of shear stress to shear rate. The rate of shear is the tangential force exerted across a unit area between two parallel planes of the fluid under consideration, unit distance apart, one plane being fixed whilst the other moves at unit velocity. If the planes are distance x apart and move at relative velocity v then the velocity gradient is v/x. This velocity gradient is called the shear rate. If tr is measured in cm/s and x in cm then v / x is expressed in reciprocal seconds, s - l . The force per unit area which produces this rate of shear is the shear stress. If the ratio of shear stress to shear rate is constant then a liquid is said to be ‘Newtonian’ in character-i.e. if the flow rate is to be doubled twice the force will be required to bring this about. The unit of viscosity is the Poise named after Poiseuille (1846), a physician, who formulated the relationship between the variables determining the rate of flow of fluids through narrow tubes. This relationship may be expressed as n A P r4 rate of flow = - x- x -
g
l
r
where: A P / l = pressure gradient where 1 = tube length; q = viscosity; r = radius of tube. In his Hunterian Lecture, Dormandy (1970) noted the discrepancy between the amount of attention paid to the importance of driving pressure and vessel calibre compared with the study of the physiology and pathology of blood viscosity. This is due partly to the fact that whole blood does not behave in a Newtonian fashion, as the ratio of shear stress to shear rate is not constant. Plasma is believed to be Newtonian in behaviour although doubts have been expressed, perhaps based on inadequate techniques, that this is so. Whereas Copley & Staimby (1960) and Wells & Merrill(1961) presented data which showed plasma to be apparently non-Newtonian, Joly (1962) attributed the apparent non-Newtonian character to the effect of a molecular arrangement, of great strength, at the liquid-air interface of their particular measuring instruments. The breakdown of the surface film by the introduction of a guard ring produced data which supports the claim that plasma behaves in a truly Newtonian manner. The rheology of whole blood is far more complex than that of plasma. Whole blood may be considered as a concentrated suspension of red cells in a continuous Newtonian medium. Correspondence:Dr M. J. Phillips, Department of Haematology, Taunton and Somerset Hospital, Musgrove Park, Taunton, Somerset.
3 47
348
Annotation
The suspension of red cells in plasma and other supporting media results in non-Newtonian behaviour (Whitmore, 1963; Charm & Kurland, 1972, 1974). The dependence of whole blood viscosity on shear rate is well established, non-Newtonian behaviour becoming more pronounced at low rates of shear. Dintenfass (1962) drew attention to the fact that the viscosity of blood is not only dependent on the rate of shear but also the time over which the shear is applied. Fluids which show a time-dependent viscosity are said to be thixotropic. Paints which ‘thin’ on repeated mixing or brushing are an every-day example of thixotropic fluids.
Measurement of Viscosity Capillary tube viscounetry. The principle behind all capillary tube viscometers is the measurement of the time taken for a standard volume of the test fluid to flow through a capillary tube of standard length and diameter under a standard force at standard temperature. In the classical Ostwald ‘U’-tube instrument the driving force is the standard height of the test fluid itself. The head of pressure varies with the specific gravity of the test fluid and the viscosity measured is termed ‘kinematic viscosity’. Other capillary instruments have an independent driving force and produce ‘absolute viscosity’ or ‘dynamic viscosity’ (Absolute viscosity = kinematic viscosity x density). These instruments have the advantage of requiring only small volumes of test fluid and show a relatively high degree of accuracy. There are two disadvantages. Firstly, they usually operate at high rates of shear which precludes their use in detecting the non-Newtonian influence of cells in whole blood; plasma viscosity measurements are not affected, The second disadvantage arises from the non-uniform flow in the capillary which is slowest at the periphery and fastest at the centre. If flow is imagined as occurring in a series of concentric cylinders, the rate of shear varies across the tube and mathematical analysis of this phenomenon is complex. Capillary viscometers are suitable for the measurement of plasma viscosity. The normal range using the Harkness-designed instrument (Harkness, 1963) at 25°C on plasma separated from blood anticoagulated with EDTA is I .SO-I .72 centipoise; levels for normal individuals are remarkably constant within this range when measured over a period of years. The measurement of plasma viscosity has replaced estimation of erythrocyte sedimentation rate (ESR) in the authors’ hospital. It is a particularly useful index of the severity of hyperproteinaemic states and also of the response to treatment of myeloma and macroglobulinaemia. A comparison of plasma viscosity and ESR in various disease states has been reviewed by Harkness (1971).In addition to the clinical usefulness there are definite technical advantages. Estimations are performed on small samples (0.3-0.5 ml) in less than I min; batch testing can be done rapidly, and samples can, if necessary, be tested several days after collection with no loss of accuracy. Rotational viscornetry. In principle the test liquid is introduced either between a flat plate and the wide-angled base of a suspended bob, or between a cup and a suspended cylindrical bob. Viscosity is calculated from the measured torque on the suspending wires when the plate or cup is rotated at a variety of speeds. The rate of shear depends upon the speed of rotation. Such instruments carry the advantages that viscosity can be measured over a wide range of shear rate. The Wells-Brookfield microviscometer has been used extensively in
Annotation
349
whole blood viscosity measurement but is not reliable at shear rates below 23 s-'. Recent introduction of the Contraves low shear viscometer allows measurement at shear rates as low as 0.07 s-'. The non-Newtonian behaviour of whole blood must be taken into account if measurement of viscosity is to have clinical significance. For example, what are the shear rates which apply in vim? The cardiac cycle must produce velocity changes which differ from blood vessel to blood vessel because of differences in diameter and flow rate. It is known that the lowest shear rate and, hence, the highest viscosity occurs in the large veins; the highest shear rate probably occurs in capillaries. Factors Ie$uencieg Whole Blood Viscosity Hmnatocrit. There have been many conflicting reports of the relationship between viscosity and haematocrit. Hess (I~II), Kunitz (1926)and Whittaker & Winton (1933)described a curvilinear relation based on measurements with a capillary viscometer ; Nyggard et a1 (1935) and Burch & de Pasquale (1963)using a similar technique described a linear relationship. Virgilio et al (1964,also using a capillary instrument, showed that the logarithm of blood viscosity was related to haematocrit in a linear fashion and this was confirmed both by Gregerson et a1 (1965)and by other workers (Begg & Hearns, 1966;Dormandy, 1970; Dormandy & Edelman, 1973; Dormandy et al, 1973)who used rotational viscometers. The clinical importance of the relationship is not established. A change in haematocrit from 40% to 45% raises viscosity by 12% at a shear rate of 230 s - l but by 25% at a shear rate of 5.75 s - l . Rapid administration of intravenous fluids provides haemodilution with a rapid lowering of blood viscosity. This is the rationale behind the use of various intravenous solutions, including low molecular weight dextran, in the treatment of conditions giving rise to haemoconcentration. Dormandy (1970)showed that a reduction of haematocrit from 50% to 45%, producing a 12% fall in viscosity, reduced haemoglobin by 10%. This fall in oxygencarrying capacity was compensated for by an increase in blood flow of between 20 and 30%. Nevertheless the viscosity-haematocrit relation must take into account the degree of red cell aggregation, especially at low rates of shear. The introduction of more accurate and convenient low shear rate viscometers may assist in further elucidation of the clinical significance of the haematocrit-viscosity relationship. Red cell aggregation. At rest red cells form three-dimensional continuous networks of rouleaux (Charm & Kurland, 1972).When stress is applied, the continuous network is broken down into smaller rouleaux which gradually shorten until, at sufficiently high shear stress, the rouleaux disperse into discrete cells. Aggregation of red cells at low rates of shear has long been considered of great importance in accounting for the high viscosities encountered under these conditions. Low shear rate-viscosity relationships in many pathological states have been exhaustively described (Dintenfass, 1971).However, a recent report by Copley ct a1 (1975)using a specially modified rotary viscometer throws some doubt on these findings. Blood was subjected to an initial high rate of shear sufficient to make the cells discrete; rotation was stopped and then restarted at a variety of speeds. At very low rates of shear (0.01-10s-') aggregation of the cells had begun after as little as 30 s and increased thereafter. This suggests that much previously published data from experiments in which unknown degrees of red cell aggregation must have been present should be reassessed.
3 50
Annotation
Plasma jibrinogen. Plasma fibrinogen levels have been shown to influence whole blood viscosity (Mcrrill et a!, 1963a; Weaver et al, 1969). The effect is increasingly pronounced at lower shear rates and is at least partly responsible for the non-Newtonian behaviour of whole blood (Dormandy et al, 1973). The latter group of workers have shown in a study of a large series of claudicants that the high blood viscosity obtained in such patients was associated with abnormally raised plasma fibrinogen; when this was lowered with Clofibrate the viscosity fell to normal levels with symptomatic and objective improvement (Dormandy & Edelman, 1973 ; Dormandy ct a!, 1973, 1974). A study of diabetics with retinopathy showed raised viscosity levels but no evidence that retinopathy was associated with raised fibrinogen levels (Hoare et a!, 1976). Red cell interiial viscosity. At near zero flow velocities human blood may exhibit viscosities of 100-10 ooo times that of water; at high flow velocities it is only 2-10 times that of water (Dintenfass, 1965, 1966). If red cells were replaced by rigid spheres of corresponding dimensions, the resultant fluid would have the consistency of brick at a haematocrit of 65%. Blood remains fluid at a haematocrit of 95%. This difference could only be accounted for by a low red cell internal viscosity (Dintenfass, 1968). It has been shown that solutions ofhaemoglobin are Newtonian and that they have a lower viscosity than blood at the same concentration of haemoglobin (Cokelet & Meiselman, 1968). One of the problems involved in the measurement of intcrnal viscosity is that invasive techniques would destroy thc internal environment and inter-molecular relationships. Dintenfass (1968) derived a mathematical expression based on a study of red cell suspensions in fluids of different viscosities. He determined that the internal viscosity was remarkably low (1-6 cP). Red cellJEexibility or deformability. It would seem logical that the ability of red cells to deform readily, particularly in the micro-circulation, is essential to the maintenance of blood fluidity. Rcd cell flexibility can be measured by a centrifugation technique (Sirs, 1970) and by a filtration technique using membranes with pores of standard diameter (Reid et al, 1975, 1976). Thc latter workers demonstrated a gross reduction in red cell deformability in patients with ischaemic disease of the legs. Dintenfass & Lake (1976) have reported that flexibility and viscosity are altered by beta blocking agents. Mayer (1976) has shown that oral anticoagulants lower viscosity both in healthy subjects and in patients with coronary artery diseasc.
Concltisioris This annotation has attempted to provide a broad view of the physical aspects of viscosity. The clinical applications are, as yet, not clearly discernible. The measurement of plasma viscosity affords a useful non-specific index of disease which some believe to be superior to that provided by the ESR. Many would question the need for any non-specific index of discase although it is difficult to envisage the management of a disorder such as temporal arteritis without such an index, fundamentally unsatisfactory though it may be. Measurement of whole blood viscosity, and the factors which influence it, does seem to have specific clinical implications. Studies of red cell flexibility and internal viscosity are directly relcvant to any understanding of blood flow through small vessels. Such studies may throw more light on the behaviour of sickle cells and other deformed or damaged erythrocytes in the micro-circulation. The interactions of red cell aggregation, low shear rate and fibrinogen or fibrinogen degradation product concentrations must be considered in any
Annotation
351
observation on the pathogenesis of venous thrombosis. Viscosity changes in peripheral arterial disease are already being studied in some depth. More importantly, perhaps, the manufacture and marketing of drugs which purport to lower blood viscosity and increase red cell flexibility indicates that therapeutic manipulation of the physical properties of blood is becoming both a reality and an objective. Recent reports that commonly,used drugs such as beta-blockers and oral anticoagulants affect whole blood viscosity may stimulate research into the viscosity effects of other drugs. It is possible to foresee that measurement of blood viscosity will become a responsibility of haematology departments.
Departments of Haematology and Clinical Chemistry, Taunton and Somerset Hospital, Tatinton, Somerset
M. J. PHILLIPS J. HARKNESS
REFERENCES BEGG,T.B. & HEARNS, J.B. (1966) Components in blood viscosity. The relative contribution of haematocrit, plasma fibrinogen and other proteins. Clinical Science, 31, 87. BURCH,C.E. & DE PASQUALE, N.P. (1963) Phlebotomy. Use in patients with erythrocytosis and ischaemic heart disease. Archives of Internal Medicinr, 111,
687.
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