RHEOLOGICAL PROPERTIES OF BLOOD
Rheology is a specialized part of fluid mechanics and is concerned principally with non-Newtonian and viscoelastic substances.
A Newtonian liquid is one in which the viscosity, at fixed temperature and pressure, is independent of the shear stress. Thus, a non-Newtonian liquid is one in which the viscosity depends on shear stress. Water and honey are Newtonian, but many aqueous suspensions of fine particulate matter such as water-base paint, plaster, and oil emulsions are non-Newtonian. The distinction is qualitatively obvious if one imagines two spoons, one in a pot of honey (Newtonian) and the other in a pot of mayonnaise (non-Newtonian emulsion). The honey is harder to stir (has a higher viscosity) than the mayonnaise, but when the spoons are removed and held above the pots, the honey continues to drizzle off its spoon, whereas the mayonnaise coating the other spoon clings indefinitely to it without flow, thus exhibiting “infinite” viscosity.
Viscoelastic substances are those that show a capacity to recover original shape after a briefly applied stress, but flow after long periods of stress. Examples are rubber adhesives for joining paper, “bouncing putty,” chewing gum, food- stuffs (bread dough), and all natural and synthetic rubber prior to vulcanization.
To a very slight extent blood displays viscoelasticity, but from the rheological point of view, its non-Newtonian quality is far more significant.
To visualize the physics underlying viscosity, consider a freshly shuffled clean deck of cards placed on a table. If the top of the deck were gently pushed horizontally, the cards would tend to slide over each other more or less uniformly,
“lubricated” by a thin film of air between each pair of card surfaces. If the cards were coated with a thin film of honey, it would require much more “push,” horizontally applied, to make the deck slide apart.
ny two adjacent playing cards form an elementary device for measuring viscosity. Between the cards one could fix the film thickness Ay (cm) of the “lubricant” layer, whatever the composition might be; one could measure the force F (dynes) applied horizontally to the upper card causing it to move over the lower card; and one could determine the linear displacement AX (cm) of one card relative to the other in a time interval At (set), thus obtaining the rate of displacement i (cm/set).
For Newtonian fluids (including all gases), the value of
House paint is an industrial liquid specifically designed to have yield stress, without which the applied wet film would sag and drool, like varnish, unless brushed out thinly. The yield stress of house paint prevents its flow vertically downward under gravitational stress. The existence of yield stress means that, in equation 4, q can go to infinity since 7 remains finite as the strain rate goes to zero. Conceptually, this is misleading (27) and it is more meaningful either to describe the non-Newtonian viscosity of blood in terms of a relationship of stress to strain rate or to cite the value of yield stress of blood and the limiting (minimum) viscosity attained at sufficiently high shear stress and shear rate, as discussed below.
In summary, the phrase blood rheology implies that blood exhibits a variable viscosity depending on how rapidly it is forced to flow under shear. Viscosity is defined as a ratio of shear stress to strain rate. An easily visualized, though some- what impractical, means for quantitatively measuring these parameters has been suggested, and the meaning of yield stress has been considered. Because of its experimental simplicity, the capillary viscometer was first to come into general use and is still preferred for measuring the viscosity of a Newtonian fluid. The French physician Poiseuille (34) was the first to relate the viscosity of the liquid flowing in the capillary to what is measured experimentally; his motivation was understanding the circulation of blood. His attempts to carry out the capillary experiment on blood were thwarted for a variety of reasons, principally thrombogenesis, and he was forced to study simple liquids instead, such as saline solution. In any case, he set forth the relation bearing his name for steady laminar flow of a fluid through a straight cylindrical tube.
Thus, Poiseuille’s law (eq. 6) predicts, all other parameters being held constant, that: I) the flow rate will be halved if viscosity is doubled; 2) the flow rate will be augmented 16-fold if the radius is doubled; and 3) the pressure drop will be doubled if the length is doubled.
Measurements of the viscous properties of non-Newtonian fluids at low rates of strain (low stresses) are better accomplished in viscometers derived from the concept of the sliding playing cards in which the fluid is contained between two radially symmetrical coaxial elements, one of which rotates relative to the other. The basic parameters measured are torque and rotational speed. The most common types are: I) coaxial cylinder (Couette) viscometer, 2) cone-in-cone viscometer, and 3) cone-on-plate viscometer. For reasons shown subsequently, the coaxial cylinder arrangement is preferred for blood rheology, provided that: I) the annular gap between cylinders is of the order of
Since Poiseuille’s time, blood rheology has proved not only experimentally difficult but indeed peculiarly beset with artifacts. The artifacts in turn have led to inaccurate interpretations or to downright misleading conclusions. To understand how the artifacts enter the picture, it is fruitful to “synthesize” blood *starting with water, adding successively microions, proteins, lipids, and then the formed elements. At each step the artifacts reported or presumed are considered.
Physiological Saline, Ringer Solution The addition of microionic electrolytes (NaCl, CaC12, bicarbonate, phosphate, etc.) to water in the concentration relevant to blood greatly improves the precision with which the Couette viscometer, properly designed, can be read, owing to dissipation of electrostatic charge that may form on the cylindrical surfaces. The absolute ,viscosities of such solutions are always Newtonian, lie a few percent above the viscosity of pure water at the same temperature, and are well documented. Thus such solutions make excellent reference standards for Couette and cone-on-plate viscometers. Because electrolytic solutions also make excellent corrosion media, choice of metals becomes important. Usually the stainless steels are adequate. Tantalum is the best of all materials in respect to anticorrosion properties but is difficult to machine. It is obvious that if a particular Couette or cone-on-plate viscometer indicates the saline solution to be non-Newtonian the viscometric reading is at fault. An apparent increase of viscosity with increase in rotational speed often indicates development of secondary flows (indicating that a more narrow gap is required); the converse may indicate bearing friction or some related mechanical problem. Any bubbles adherent to either surface of a coaxial (rotational) viscometer in general invalidate the reading. The electrical conductivity of ,physiological saline and similar solutions does nothing to help the several end-effect problems of capillary viscometers that operate by drainage under hydrostatic pressure.
C. Saline Solutions of Fractionated Plasma Proteins Inasmuch as the plasma proteins are capable of denaturation at interfaces between their solution and a gas or a containing wall, two artifacts can arise in gravity-draining capillary viscometers, viz., decrease of effective capillary radius by sorption of the protein (cf. eq. 6) and change of shape of the menisci above and below the capillary; hence, change of the driving pressure gradient and of the kinetic energy corrections. However, solutions of a single protein (e.g., albumin and saline, y-globulin in saline) may be relatively stable over a short period of time so that a viscometric determination can be accomplished.
D. Plasma and Serum
Anticoagulated or native plasma, especially, and serum usually present some form of experimental artifact in viscometry, attributable to a tendency toward rigid or semirigid surface films (14). In capillary viscometers the surface film is often sufficient to prevent, or grossly delay, passage of the liquid. In rotational viscometers the effect becomes particularly important in measurements conducted at low rates of strain (7, 14). Nevertheless, when the rotational viscometer is operated with a guard ring (which eliminates the interface) or when a capillary viscometer is operated such that flow rate is the imposed parameter (23) and pressure gradient (measured by transducer in a gas-free circuit) is the observed response, plasma and serum are Newtonian, down to zero strain rate and up to at least several thousand inverse seconds of strain rate.
Precisely which chemical species in plasma or serum are responsible for these effects at the plasma-gas interface have not yet been documented, but free lipids (e.g., fatty acid) and lipoproteins are suspected. The effects are not confined to gas-liquid (e.g., air-liquid) interfaces. Hydrophobic surfaces, like silicone rubber, after contact with plasma rapidly become wettable by aqueous solutions (contact angle approaches zero) and are found to possess a film of bound protein (18).
Blood oxygenators in which there is direct contact between air and blood produce a sludge having a high content of lipid and protein. Plasma obtained by clean venopuncture followed by immediate centrifugation in siliconized tubes has been shown to possess a much more striking tendency to form a rigid film at a gas interface than anticoagulated plasma. It is not evident what processes are involved that account for the diminished, though still pronounced, ability of stored anticoagulated blood (heparin, ACD, EDTA) to form rigid surface films.
E. Formed Elements and Physiological Saline or Equivalent
Usually the red cells so dorninatc rheological proccsscs by reason of their volume concentration that the leukocytes and platelets are without observable effect. Furthermore, in many studies blood is centrifuged and the buffy coat (leukocytes and platelets) is removed prior to experimentation with the red cells. When the red cells are washed to rcmovc the plasma protein and then suspcnded in Ringer solution or physiological saline, at normal hcmatocrit levels (35-45), one obtains a rheologically simple, easily handled fluid, slow settling. Unfortunately, as will bc shown, it bears little relation to the rheology of blood.
The principal artifact involved is that of the “Vand” (43) cffcct. In brief, according to this reasoning, there must be a layer next to the boundary surface in which the local concentration of suspcnclcd rnattcr (cells or whatcvcr) is lower than in the nlain body of the fluid because the centers of particles cannot physically be at the wall.
Visualize as the extreme limiting cast a glass pipe 1 .OOl cm in diameter filled with glass marbles each
When the capillary diameter of a Poiseuillian viscometer approaches the diameter of a red cell (viz., 8 p) one may expect the various complications of nonuniform concentration to ensue, but this is rarely the case in any rotational viscometer, except at the apex of a cone-on-plate viscometer.
What corrections are to be made in that case are not apparent. Models such as that of Vand are concerned with rigid, suspended bodies, whereas the red cell
is easily deformed and distorted, so that its center of mass can approach the boundary wall more closely than would be predicted from the model of a rigid, biconcave disc. The effect is easily noted in cinephotomicrography.
The “wall-effect” problem is not to be dismissed lightly, for the microcirculatory vessels (arterioles, capillaries, venules) involve these geometrical considerations. The capillary in particular is a special problem in the fluid mechanical sense, since its lumen is the same or less than the diameter of the red cell. Passage of red cells through living capillaries of the microcirculation has only the most indirect connection with blood rheology. Strictly speaking, it is a microrheological problem: a process governed by membrane deformability and by surface chemistry (red cell/wall). Iany case, except for the wall effect, the rheology of suspensions of red cells in physiological saline or equivalent solutions presents no grave problems of artifacts.
F. Whole Blood and Suspensions of Red Cells in Plasma The measurement of the rheological properties of whole blood, or of red cells suspended in plasma, is complicated by the surface film effects of plasma by itself and by the wall effect of suspensions of red cells in saline. These effects are insignificant compared with those resulting from the interaction of plasma fibrinogen (not activated, i.e., not fibrin) with red cells.
Artifacts that derive from effects produced by fibrinogen and red cells are: I) inconveniently rapid sedimentation of red cells, 2) syneresis of plasma next to any boundary surface, and 3) densification of the red cell core (increase in actual hexnatocrit).
Because of sedimentation, the cone-on-plate or cone-in-cone viscometer, when operated at low rotational speeds, is likely to be in error because of the existence of a plasma layer next to the upper coaxial surface (Fig. 1) regardless of whether it is on the upper or lower surface that the torque measurement is made. Since the fluid under shear is no longer homogenous, and since the plasma layer acts as a lubricant for the cell-rich fluid, the measured torque is substantially, but to an indefinite degree, less than it should be.
Typical torque-time curves (32) are shown in Figure 3 for blood in a coaxial cylinder viscometer suddenly exposed to various steady values of strain ‘rate (0.1, 0.2, 0.4, 1.0, and 30 se&). The decreasing torque in the first four curves corresponds to the’ progressive formation of plasma-rich, red cell,-poor layer next to a surface, even though the surface is roughened. The effect is much more severe if the surface is smooth.
It is interesting to note that different investigators using identical Couette viscometers have come to contradictory conclusions about their experimental data; the origin of the contradiction lies principally in how the time-dependent variation of torque is interpreted.
In capillary viscometers operated under relatively high wall stresses (flow rates), blood remains sufficiently homogeneous to yield replicable measurement of its viscous properties provided that one does not attempt to operate the capillary as a falling meniscus viscometer (which entails the artifact of the rigid surface film). Even the best designed capillary viscometer is likely to yield nonreplicable data if blood is allowed to stand in the capillary for more than a few seconds and if then flow is gradually reestablished such that the reduced velocity5 p is less than about 1 see-i. These conditions, well documented by cinephotomicrography, (3 1) bring about a gross layer of plasma next to the wall surrounding a core of red cells that, mutually adhering, flow as a plug (Fig. 4~). It is easy to misinterpret this extreme case of two-phase flow as evidence that blood is a Newtonian and relatively low- viscosity fluid near and at zero rate of strain.
Another aspect of capillary viscometry of blood often overlooked is the effect of sedimentation rate. One knows from the standard vertical tube tests (e.g., Westergren, Wintrobe) that the sedimentation rate is of the order of a few millimeters per hour (49). For ease of visualization, assume 3.6 mm/hr = 3600 p/hr = lp/sec. If we now consider a horizontal hollow fiber of 120-p inside diameter carrying blood and stop the flow, the above figure would suggest that within 1 min the red cell interface should have settled down to about the midplane of the fiber. This is found to be approximately the case (31). On restarting the flow of blood thus settled, a gross flow of plasma above the settled pack of red cells is first noted, followed sooner or later by remixing of cells.
In summary, therefore, viscometry of blood plasma is usually attended by surface film effects that can lead to gross errors. When the artifacts are removed, plasma is found to be Newtonian. Rheological measurements of whole blood at high strain rates is relatively simple inasmuch as it behaves as a homogeneous and Newtonian liquid. At low rates of strain sedimentation and formation of a clear plasma phase may easily nullify the intended measurement or produce entirely wrong results. For this reason, speed of execution of the experiment becomes important, with a well-mixed sample.
IV. RHEOLOGY OF
A ship of sample of normal human blood drawn into ACD solution shear stress to shear strain rate of which Figure 5 is typical shows a relati (hematocrit, .on- 40; fibrinogen concentration, 260 mg %; temperature
The existence of the yield shear stress has been disputed but has been confirmed experimentally bY direct measurement in both Couette (7) and in capillary viscometers (23). As noted in section III, its measurement is attended by experi mental difficulties, notable syneresis of plasma, formation of a plasma layer next to the boundary surface, and sedimentation, so that speed of measurement is essential. By proper execution, the yield shear stress as well as all other rheological properties can be replicated.
It has long been recognized that the viscosity of blood increases with hematocrit? Data cited in most medical texts (i.e., 11) refer to high shear strain rate data, thus the range of applicability of equation 15, with the constant TN of that equation ranging from about 0.03 poise at hematocrit of 40 to 0.10 at hematocrit 65. Furthermore, at least over the range of O-50 hematocrit, the value of qN in equation 1.5 can be reasonably related to the hematocrit H by an equation attributable to Vand (42) for suspensions of rigid spheres, viz.
In the non-Newtonian regime, the effect of hematocrit is totally different. he yield stress for blood hematocrit 40 is typically 0.04 dynes/cm2.
Fibrinogen
The non-Newtonian rheology of blood is dominated by the interaction of fibrinogen (native, not activated, not fibrin) with red cells. At normal hematocrit levels, no other plasma protein in the absence of fibrinogen seems capable of producing a yield shear stress in red cells,7 although P-lipoprotein has been implicated as having a synergistic effect \with fibrinogen.
Temperature
In normal blood, at levels of shear rate such that equation 1.5 is applicable, i.e., Newtonian flow, it has been shown that the temperature coefficient of viscosity is identical with that for water over the range of lo-
In the non-Newtonian regime and at zero shear, the rheological properties of normal blood are less affected by temperature. The yield stress is found to be independent of temperature at least over the range of 37-
If the yield stress is not dependent on temperature, at least for the majority of human subjects, the -activation energy for fibrinogen adsorption on red cells (the origin of the ‘Cstructure” of blood) must be close to zero.
A. Polycythemia, Anemia
When the hematocrit exceeds 50 or thereabouts, blood shows various rheological abnormalities difficult to quantify. Equations 17 and 18 do not necessarily apply, even crudely. The sedimentation rate, for example, usually goes to zero, even in the presence of fibrinogen, as a result of crowding of red cells. In fact, at hematocrit levels exceeding about 65, the dominant process underlying blood flow must be deformation of red cells. Any model suspension consisting of rigid biconcave discs of uniform size at a volume concentration of 65 % is either already a solid or a dilatentg paste. Blood is therefore unusual in its ability to “flow” even at high red cell concentrations. A representative rheological diagram for polycythemic blood is given in Figure 7, the fibrinogen concentration being normal.
One notes a yield stress four times the normal value, which corresponds to A of equation 18 equal to 1.1 X KP (assuming A$ to be 4); and the ultimate New- tonian viscosity VN is 0.066, corresponding to a relative viscosity of 7.7. Equation 17 predicts a relative viscosity of 5.1. The agreement is reasonable in view of neglect of terms beyond the second power.
n general, anemic blood (hematocrit less than 30) displays nearly Newtonian behavior and the ultimate viscosity is reasonably well correlated by equation 17. Usually the yield stress is negligibly small. Only with hyperfibrinogemia is there likely to be a significant departure from Newtonian flow.
B. Ajbrinogenemia, Hyperjbrinogenemia
The rarely noted blood abnormality afibrinogenemia has been studied rheologically (24) with the finding that the sample having a normal hematocrit showed substantially no yield stress and an almost constant viscosity. This result is in accord with experiments on suspensions of red cells in saline and in serum.
Hyperfibrinogenemia produces elevations in yield stress (cf. eq. 19) and, as is well known, a high sedimentation rate at usual levels of hematocrit. The high sedimentation rate complicates rheological determinations.The relationship between shear
stress and shear strain rate is markedly curved below an abscissa value of 2.5 seP12. (Thus, eq. 14 is not obeyed). The Newtonian relation given by equation 15 is not attained at a value of shear strain rate of 300 set-l (abscissa value 17.7), although presumably it would be found at a higher value of shear strain rate. Further, there is a twofold difference in the extrapolated values of yield stress at
C. Diabetes Mellitus
Merrill (unpublished results) in collaboration with the
D. Hyperlipemias
Despite an early publication (28) suggesting that high levels of triglycerides in plasma produce a substantial negative temperature coefficient of yield stress (low temperature: high yield stress), it has been impossible to substantiate this by other experiments. It seems likely that, in most cases of hyperlipemia, the rheological properties of blood are not significantly different from those of normal blood and that, when the negative temperature coefficient of yield stress is noted, it signifies some special micellar organization of the lipid and, most probably, a specific interaction of lipids and protein or lipids and lipoproteins.
Plasma Protein Abnormalities Other Than Fibrinogen
I) Lipoproteins. It is extremely difficult to gain clear-cut evidence on the effect of lipoproteins. One report (29) on artificial suspensions of red cells in various protein fractions suggests that &lipoprotein has a significant synergistic effect in enhancing yield stress, but only in the presence of fibrinogen and cannot produce a yield stress in the absence of fibrinogen.
2) Hyperproteinemia. A weak trend toward increase of yield stress (at constant hematocrit and fibrinogen concentration) with increase in total plasma protein concentration is reported (24), based oormal blood donor samples over the range of concentrations 5.2-
3) CryogZobuZinemia. As expected, cryoglobulinemia leads to drastic increase of yield stress as temperature is decreased below
Macroglobuhmnia. Wells reports significant increase of yield stress and non-Newtonian behavior in the low-shear regimen of samples drawn from patients suffering from macroglobulinemia, as compared with controls at equal hematocrit and fibrinogen level. One can postulate, while awaiting further experimental evidences, that: a) the macroglobulins are directly adsorbed ;on the red cell surface and are capable of sticking two surfaces together via some sort of bridge, like fibrinogen; or b) the macroglobulins bind to fibrinogen already adsorbed on the surface and enhance the bridging already possible with fibrinogen.
F. Blood After Extracorporeal Circulation
In this type of circulation (17), including heart-lung machines, such a wide range of rheological abnormality has been reported that it is difficult to offer a useful generalization. There are at least three common factors to consider: 1) free hemoglobin in the plasma, 2) erythrocyte ghosts, and 3) fragments of denatured plasma protein/lipid films resulting from direct contact with air or oxygen. ( The rheological effect of free hemoglobin, within clinically relevant limits, is not impressive. There is a small trend toward increase of the yield stress with increasing free hemoglobin concentration (6).
The rheological properties of suspensions of lysed red cells (ghosts) prepared by osmotic lysis as compared with intact cells suggest that fibrinogen continues to be effective in forming (under stasis) network aggregates of ghosts, as in the case with whole blood. There is no evidence to suggest that in actual mixtures containing mostly intact red cells and a small percentage of ghosts, as produced in the extracorporeal circulation, there is a significant rheological change on this account.
By far the most important rheological alteration is produced by the denatured protein-lipid film, probably acting on the red cell membrane. Several effects are well known: that the rate of hemolysis is ra-pidly increased by an fluid mechanical pattern in the presence of air bubbles (46) as compared with the identical pattern without bubbles; that in disc oxygenators a sludge is produced that by analysis is found to contain high concentrations of proteins and lipids; and that the blood usually has an abnormally high sedimentation rate. All these factors point to aggre- gation of red’cells by the denatured material, over and above the effect (reversible) of fibrinogen.
Direct rheological tests on blood oxygenated by direct contact with air (as in a heart-lung’ machine) usually show: 1) elevated yield stress; 2) poor replicabil ityS probably, the result of sedimentation; and 3) poor correlation by the linearization of the Casson equation (6).
VI. EFFECT OF ADDITIVES ON BLOOD RHEOLOGY
A. Anticoagulants
It is extremely difficult to devise an in vitro test for the rheological properties of blood without the use of an anticoagulant and thus to make a comparison between the properties of blood in the circulation and after addition of anticoagulants. Cokelet (6) studies in a Couette viscometer blood freshly drawn from a donor next to the instrument (before clotting occurred) and, after making allowance for dilution of plasma proteins when an aqueous solution of anticoagulant was used, concluded that none of the following anticoagulants used in any reasonable concentrations produced any significant change of the rheological properties compared with the control : heparin, sodium citrate, ACD, EDTA (ethylenediaminetetra- acetate-sodium salt), sodium oxalate.
From these observations it is concluded that the level of free ionic calcium in the plasma, which would be drastically diminished by all of the listed anticoagulants except heparin, does not play a role of any observable significance in the fibrinogen-red cell structure.
B. Saline Solution
In the limited circumstances in which it might be feasible to dilute whole blood with isotonic saline solution, the only effect is to reduce the yield stress by diminution of hematocrit, more or less following equation 18 and concomitantly, by diminution of fibrinogen concentration, equation 19, wheras the ultimate Newtonian viscosity is reduced approximately according to equation
pressure are negligible in the range compatible with life, namely 303 zt 5 millios- moles/liter. The yield stress at a constant volume fraction of packed cells (hematocrit) is slightly increased as the plasma becomes hypotonic (< 303 milliosmoles/ liter), perhaps because a loss of biconcavity in the red cell as it expands thus permits a greater contact between the cell faces and thus a more effective bridging of cells by fibrinogen.
C. Plasma Expanders, Substitute Plasma
As is well known, simple saline solutions are of little clinical value because they lack the colloid osmotic pressures whereby they may be retained in the circu lation. Among the clinical alternatives are albumin solutions or other plasma protein preparations free of fibrinogen and saline solutions of miscellaneous random-coiling macromolecules, whether of biological or synthetic origin.
Colloid osmotic pressure is dictated by number-average molecular weight whereas solution viscosity is governed in a complicated manner by weight-average molecular weight plus a host of other considerations; the net result is that saline solutions of the plasma proteins at a given level of concentration and of molecular weight altvays show a considerably lower viscosity than solutions of random-coiling macromolecules. Table 1 compares the relative viscosity of albumin in saline to the relative viscosity of dextrans at equal concentration (3 g/dl), (dextrans representing random-coiling macromolecules), as well as the “ideal” colloid osmotic pressure (neglecting second-order and higher terms in the virial expansionlo).
I) Albumin solutions. To decrease blood viscosity in vivo by dilution, albumin solutions at a concentration of 3-
2) Dextrans. Dextrans, all factors considered, are probably next best after albumin solutions. It is true that, at equal hematocrit and fibrinogen concentra tions, the dextrans exceeding 40,000 wt-avg mol wt increase the yield stress compared with the control, and indeed experimental types exceeding 120,000 mol powerfully flocculate red cells.
Per unit concentration in blood, dextran of lowest molecular weight affords both the highest colloid osmotic pressure and the least tendency either to increase plasma viscosity or, more importantly, red cell adhesion. On the other hand, if the number-average molecular weight is much less than 60,000 (compared with albumin at 67,000) the dextran will be rapidly excreted through the kidney. Thus, narrow practical limits are placed on the molecular weight of the dextran employed clinically.
VII. MAMMALIAN BLOOD OTHER THAN HUMAN
Dog blood (37) has been investigated in the low-shear regime (less than 100 set-l shear rate) over which human blood displays its non-Newtonian properties with substantially the same findings, viz., that the non-Newtonian properties are the same in kind, and virtually in degree, and reflect the reversible structuring ascribable to the interaction of fibrinogen with red cells. In dog blood the median fibrinogen concentration is higher and consequently the median yield stress is higher than in human blood.
It is difficult to perform accurate rheological studies on the blood of rodents because of the small volumes of blood that may be withdrawn without sacrificing the animals. The blood of the golden hamster may be representative of rodent blood. Its rheological properties were studied by Berman et al. (1) and were found to be qualitatively similar to other mammalian blood: yield stress varies with fibrinogen concentration and with hematocrit; at normal levels of either in the hamster, the yield stress is around 0.02-0.04 dynes/cm2.
Hamster blood has been particularly interesting to study rheologically because one can, in the cheek pouch, study flow patterns” in the microcirculation by cinephotomicrography (1, 2, 10) and correlate qualitatively the flows observed with the rheological characteristics measured; the unequivocal result is that as yield stress increases for whatever reason, venular flow appears slower and stasis is more frequent.
