THROMBOSIS RESEARCH Printed in the United

Suppl. II, vol. 8, 1976 Pergamon Press, Inc.

States

SECTION

VISCOSITY

AND

THIXOTROPIC

VISCOELASTICITY

PARAMETERS

C.R. Department New

I

Huang

OF BLOOD

OF WHOLE

and

W.

HUMAN

SYSTEMS

BLOOD

Fabisiak

of Chemical Engineering and Chemistry Jersey Institute of Technology Newark, N.J. O7lO2, U.S.A.

ABSTRACT The rheological property of 8 samples of whole blood from healthy adult human subjects was studied with a Weissenberg Pheogoniometer, modified with a continuously variable speed drive. Experimental data showed a hysteresis loop in the shear stress versus the shear rate plot .and a torque-decay in the shear stress versus the shearing time plot which is under a constant shear rate. With these characteristics, whole human blood is under the classification of thixotropic fluid with its viscosity being timedependent and shear rate-dependent. A rheological equation with 5 parameters was employed to represent experimental data of each blood sample. Thus the 5 thixotropic parameters of each blood sample can be used to characterize the rheological property of the blood sample. The results pertaining to these parameters will be discussed.

INTRODUCTION The rheological behavior of the blood is a basic physical property which is essential in studying intravascular flow. It has its physiological significance because it controls the circulation of blood as it affects all organs. The flow of,blood in vivo can be considerably altered, impaired or hindered if the rheo logical behavior does not conform with the normal values. Because of the complexity of blood from the viewpoint of physiology, Che1

xistry and rheology, a simple question ";4hatis the normal range of' viscosities of blood from a.healthy human subject?" has no simple answer.

One of the reasons is that the viscosity of blood is a shear rate dependent and time dependent quantity. This quantity

is not well-defined. Xemorheology, a term first introduced in 1951 by Copley (11, has advanced ver:r rapidly in recent years.

Researchers who study

the rheology of human blood soon learn the significant difference of the rheological behavior of blood between normal healthy subjects and patients with certain pathological conditions. Dintenfass observed by accident in 1961 that the blood viscosity at low shear rate is 4 to lo-fold higher in patients suffering from myocardial infarction or arterial thrombosis than in healthy subjects (2,3). His futher work on blood viscosity in normals and patients is summarized in his book (4). In more recent communications in the last few years, Aronson et al studied blood viscosity of 47 young healthy women before and during the administration of oral contraceptives (5). Clinical signs of thrombophlebitis developed in one patient who had shown the sharpest and highest rise in blood viscosity. They suggested that hemoglobin electrophoresis in conjunction with a blood viscosity test is an effective means of scre( ~4,” ef) disease and ening patients between hemoglobin I.lemphis/s classical sickle cell anemia with hemoglobins .S(dpe:). They found that both Xemyhis/S red blood cell and hemoglobin SS red blood cell have a similar degree of sickling.

However, the viscosoty of

Uemphis/S red blood cell is much less than that of hemoglobin SS red blood cell, suggesting that the sickled cells of Memphis/S are less rigid than those of hemoglobin SS. Stormer et al investigated blood viscosity in patients with peripheral vascular diseases at low shear rate (7). They found that at the shear rate of 0.0 1 set-I-,the statistical average blood viscosity among 40 patients is 28$ higher than the corresponding average of 45 healthy persons. - At the shear rate of 4.6 set-l, it is 14% higher respectively. Abnormal plasma protein concentrations - low albumin, high o(,,d, , 6 and y globulins and high fibrinogen - were observed among patients in this study. Currently, the most widely used method to study the rheological behavior of blood is to obtain the blood viscosity at diffe-

Suppl.

II

THIXOTROPY

OF HUMAN

rent shear rates in steady shear flow.

BLOOD

3

There are two main draw-

backs in using a set of values of viscosity at different sheer rates to represent the rheological behavior of blood. They are as follows:

I.

Even a number of values of viscosity of blood

at different shear rates are obtained, this information is still not sufficient to represent the rheological behavior of the blood sample.

One rheological characteristic of blood, the thixotropy,

which has been found to be of special potential significance is not included (10). Thixotropy is a time-dependent and shear rate dependent rheological behavior observed in blood and other concentrated supension systems. II. The values of viscosity at low shear rates have lost their original physical meaning because they are calculated from Newton's law of viscosity. It is especially true when the shear rates are near or below the shear rate corresponding to the yield stress of blood. In order to give complete representation of the thixotropy of blood, a rheological equation is needed to define the viscosity of blood. This equation can be used to represent quantitatively the rheograms of blood and can be used to calculate blood viscosity at a given shear rate and a given time of shearing. Therefore, the thixotropic parameters of the equation can be used to characterize the complete rheological behavior of blood, and they should be employed to compare rheological behavior among blood samples. RESULTS AND DISCUSSION A rheological equation of state by Huang is proposed to represent the thixotropy of whole human blood (8). The equation was developed from a model based on the isothermal structure change in blood induced by shearing. In a previous communication, it was proposed that the progressive breakdown and formation of structure among rouleaux cause of the thixotropic has been demonstrated to characteristic rheograms

and individual erythrocytes is the major behavior of blood (9). This equation be successful in representing the two of blood samples (lo), in the hysteresis

loop end the torque-decay curve. The following is the equation with five thixotropic parameters: -"t: - .20 =

/cc3 + GAP"

@Pa

4

HUANG

where z

is the

sllezl-

AND

FABISIAK

Suppl.

stress; $, the shear rate; t,

the

121

time of

shearing; Cl, the kinetic rate constant of the structural breakdown among rouleaux and individual erythrocytes induced by shearing;n, the order of the structural breakdown reaction; A, the equilibrium value of structural arrangement parameter;fi, the Newtonian contribution of the viscosity and?,, the yield stress. Blood samples, anticoagulated with powdered EDTA, from eight donors were studied.

All the donors are apparently healthy males

with age ranging between 20 to 35 years

old.

For each sample,

two characteristic rheograms, the hysteresis loop and the torquedecajrcurve, were measured by a modified $Jeissenberg Rheogonimeter attached with a X-Y recorded.

From these experimental

obtained rheograms, the thixotropic parameters for each blood sample were calculated by the method of non-linear parameter estimation via a digital computer. Table 1 is a summary of these thixotropic parameters of eight blood donors. Column 2 gives the yield stress,7*, of the blood samples.

This finding verifies our postulate i-na previous

communication (9) that there is a yield stress of whole human blood. When it is sheared at shear rates approximately below 0.01 set-l, the bulk of blood sample behaves similarly to a solid. Knowing that there is a yield stress of blood, it would be improper to use riewton's law of viscosity to calculate the viscosity especially in the low shear rate region. Dintenfass claimed that the viscosity of normal healthy human subjects at shear rate of 0.01 see-1 -Acnges from 10 to 60 poises (4), Copley and King found that the viscosity is approximately 1 poise at the same shear rate (11) . From the viewpoint of fluid dynamics, it is hard to believe that the viscosity of blood from normal healthy human subjects can fluctuate ten or more time from one to the other. It is even more difficult to believe that for the same person the blood viscosity at low shear rate (0.01 set-1) can be a thousand times of its value at a shear rate of 40 set-l as shown by Dintenfass (4). From Column 2, we found that the average yield stress is about 0.08 Column 3 is dr"'kW?with a flunctuation of about + 0.03 d!P'\&,?, the Newtonian contribution of viscosity. The values show that there is very small fluctuation among blood samples except for

Suppl.

THIXOTROPY

II

3lood Sample No. 3.

OF HUMAN

BLOOD

The Newtonian contribution of viscosity

might be contributed by water, inorganic salts and low molecular weight organic chemicals in the serum. The rate constant of structural breakdown induced by a shearing force is listed It averages about 0.2 with a fluctuation around in Column 4. + 253. Column 5 gives the equilibrium constant of the structural arrangement parameter. A large value of A indicates a large degree of inter-rouleaux linkage caused by surface active molecules such as fibrinogen - fibrin complex or macroglobulin. It is worth noting that the average value of A is around 0.27 + 0.03 but with two exceptions, Blood Sample No. 3 has a very low value of 0.14 and Blood Sample No. 8 has a rather high value of 0.38. The last column of Table 1 is the values of the order of the structural breakdown reaction. It averages to about 1.2 with a fluctuation of + 0.27 among samples, except Blood Sample No. 3 has a unusually high value of 2.23.

It should be mentioned that the blood samples were obtained from the New Jersey College of Uedicine and Dentistry without the identity and medical history of their donors.

It

was a great surprise for us to learn from the medical college that the donor of Blood Sample No. 3 has a mild case of pernicious anemia and the donor of Blood Sample No. 8 has a mild Because their cases were so mild, both donors were being considered as apparently healthy human subjects. From our findings of thixotropic parameters, it is case of ulceration colitis.

evident that the abnormality of the donor of Blood Sample NO. shows in the following parameters,p, A andn. 3 Comparing with the average values discussed below, the blood of this donor is thin in its Newtonian contribution of viscosity, 101~ in the

degree

of

inter-rouleaux linkage and easy to breakdown

the linking due to a higher order of breakdown reaction. For the donor of Blood Sample No. 8, we can also spot the abnormality in parameter A. The high value of A of the donor shows a large degree of linking among rouleaux, thus increasing his blood viscosity.

HUANC AND FABISIAK

Suppl. II

TABLX 1 Summary of Thixotropic Parameters Blood Sample f\Io. TU

3 4

0.084 0.113 0.051 0.076

5 6 7 8

0.097 0.055 0.109 0.069

1 2

/cc 0.062

0.064 0.049 0.066 0.067 0.060 0.071 0.067

Cl

A

0.19

0.26

0.28

0.24

0.21

0.14 0.34 0.27

0.15 0.21

0.25 0.16 0.21

0.28

0.30 0.38

n

1.37 1.06 2.23 0.95 1.37 1.07 1.50 1.00

As illustrated earlier in this communication, researchers study the rheological property of blood in conjunction with different pathological conditions for the purpose of investigation, correlation, or for -thedevelopment of a clinical test. He have demonstrated that the representation of the rheological behavior of blood by thixotropic parameters is better than the representation given by viscosities at different shear rates. Knowing the thixotropic parameters of a blood sample, one can calculate the viscosity of the sample at any shear rate and at any time of shearing from the rheological equation.

Also the use of thixotropic parameters will eliminate the uncertainty of the viscosity at the low shear rate region measured by different investigators. From this limited study of eight blood samples, it is unfair to draw any conclusions from a statistical point of view. However, it cannot be considered accidental that mild cases of ulceration clotitis and pernicious anemia were spotted as abnormalities in thixotropic parameters among so called "apparently healthy human subjects." The pernicious anemia case exhibited definite abnormalities in three of five thixotropic parameters. It was quite reasonable as this pathological condition has a direct bearing on blood. It was interesting to observe that the ulceration clotitis case would also exhibit

Suppl. II

THIXOTROPY

OF HUMAN

BLOOD

abnormality in one of the thixotropic parameters. We believe that the thixotropy test of blood, in cooperation with other clinical test, may prove to be significant in detecting and predicting the degree of seriousness of cardiovascular diseases in future years. Further work is being done at our institute. ACKNOWLEDGEMENTS This work is supported by a grant from the National Science Foundation, Grant No. GK-37206. We are indebted to Dr. E. Washington of New Jersey College of Medicine and Dentistry who supplied us with the blood samples.

REFERENCES 1.

Copley, A.L., J. Colloid Sci.: 7, 323, 1952.

2.

Dintenfass, L., Thixotropy of Blood at Very low rates of shear, Kolloid zeit s&rift: 180, 160, 1962.

3.

Dintenfass, L., Thixotropy of blood and proneness to thrombus formation, Circulation Res.: 11, 233, 1962.

4.

Dintenfass, L. Blood Microtheology, Butterworths, London, 1971.

5*

Aronson, H.B., Magora, F. and Schenker, J.G., Effect of oral contraceptives on blood viscosity, Am. J. Obst. and a.: 110, 997, 1971.

6.

Cooper, M.R., Kraus, A.P., Felts J.H. and Myers R., A Third Case of hemoglobin Memphis/Sickle cell disease, Am. J. Med. 155, 535, 1973.

7.

Stormez, B., Horsch, R., Kleinschmidt, F., Loose, D., Bruster, H. and Kre,mer, K., Blood viscosity in patients with peripheral vascular diseases in the area of low shear rates, J. Cardiovascular Surger~:~, 577, 1974.

8.

Huang, C.R., A Thermodynamic approach to generalized rheological equations of state for time-dependent and time independent Newtonian fluids, Chem. Ena. J.: 3, 100, 1971.

9.

Huang, C.R., King, R.B. and Copley, A.L., Rheogoniometric studies of whole human blood at shear rates down to 0.0009 set-1 Part II- mathematical interpretation, Biorheology: 10, 23, 1973.

7

HUANG AND FABISIAK

Suppl. I1

10. Huang, C.R., Siskovic, ii.,Robertson, R.Y.J., Fabisiak, rj., Smithberg, E.H. and Copley, A.L., Quantitative Characterization of Thixotropy of Whole Human Blood, presented at II International Congress of Ziorheology, Rehovot, Israel,

1974-1975s 11. Copley, A.L. and King, R.G. Zxperientia: 26, 904, 1970.

Thixotropic parameters of whole human blood.

THROMBOSIS RESEARCH Printed in the United Suppl. II, vol. 8, 1976 Pergamon Press, Inc. States SECTION VISCOSITY AND THIXOTROPIC VISCOELASTICITY...
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