Hematocrit, Viscosity and Coronary Blood Flow*

DISEASES of the CHEST SEPTEMBER, 1965

Volume 48

Number 3

Hematocrit, Viscosity and Coronary Blood Flow* G. E.

n

N. P. DEPASQUALE, New Orleans, Louisiana

BURCH, M.D., F.C.C.P. AND

ALTHOUGH PHYSIOLOGISTS

FOR MORE

than a century ha,·e been aware of the fact that blood flow is influenced by viscosity, for purposes of simplification viscosity has usually been neglected in experimental and theoretic considerations of blood flow. The widely employed relationship-flow is equal to pressure divided hy resistance (F=P /R )- -assumes that flow is steady and that the fluid in motion is homogeneous and has Newtonian characteristics. These assumptions ignore viscosity in considerations of hlood flow, pressure and resistance. As early as 1912, Hes.c;l demonstrated that viscosity of blood was dependent upon the velocity of hlood flow, a fact which has been amply confinned hy recent studies.! Furthennore, tee h nologic advancements have made it possible to meac;ure pulsatile flow. In considerations of pulsatile flow of a non-Newtonian fluid, it is not pennissible to ignore viscosity. The purpose of the present paper is to describe the resultc; of studies of the relationship between blood viscositv and hematocrit and to relate these studies to coronary blood flow. On the hasis of these considerations, we hope to provide a rationale for phlebotomy in patients with coronary heart disease and erythrocytosis. ·Supported by grants from the U.S. Public Health Sen,ice. Presented at the 30th Annual Meeting, American College of Chest Physicians, San Francisco. June 18-22. 1964. ··From the Department of Medicine. Tulane Univenity School of Medicine and the Charity Hospital of Louisiana.

M.D.**

The "A nomalous" V iscosit)' of Blood: \Vhen a simple fluid such as water or a low molecular weight organic solvent is caused to flow through a tube, the apparent viscosity of the fluid remains constant (as long as flow is laminar) at all rates of flow. As the fluid undergoes laminar flow, the molecules slip by each other in planes. If one plane moves faster than another, it is said to be "sheared" from the other. If the rate of shearing is independent upon the rate of flow of the liquid, i.e., if the viscosity of a fluid is independent of shear rate (and thus of flow rate), it is known as a Newtonian fluid. On the other hand, when a sample of blood is caused to flow through a tube (greater than 1.0 mm. in diameter),3 the apparent viscosity of the blood progressively decreac;es as the linear rate of flow is increased until an asymptomatic value is reached. A fluid whose apparent viscosity is shear rate dependent is known ac; a non-Newtonian fluid. Relationship of Hematocrit to Viscos;t)': The non-Ne\\10nian characteristics of blood cannot be appreciated in ordinary capillary viscometers because only one point on a viscosity-shear rate curve is ohtained l1'o:ingsuch an instrument. In addition, because of the small bore of the capillary of such viscometers, the shear rate is extremely high. \Vells and ~1erriW estimated the shear rate in a representative capillary viscosimeter to be about 2000 sec: t • Such a shear rate is conliiderably beyond the physiologic range for large \"es.~ls when it is considered that the shear rate at the wall of the aorta at

Copyright, 1965, by the American College of Chest Physicians

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226

Diseases of the ChNt

BURCH AND DE PASQUALE

rest is estimated to be between 100 and 300 sec. -I. Yet the classic cun'es relating viscosity to hematocrit have been derived from capillary viscometers. These curves show the viscosity-hematocrit relationship to be curvilinear. The slope of the cun'e is such that viscosity increases very gradually between a hematocrit of 0 per cent and 50 per cent, after which the curve becomes steeper. Although many textbooks of physiology show such curves, they are physiologically meaningles.~. The relationship between viscosity and hematocrit is properly represented by a curve which relates the viscosity of a sample of blood of known hematocrit to various shear rates within the physiologic range. Until recently, such measurements were difficult to make. However, modification of a commercial cone plate viscometer ha~ made it possible to measure the viscosity of small samples of blood at various shear rates. The characteristic.~ of this instrument have been fully described by Wells and Merrill. 1 Figure I shows the relationship between viscosity and shear rate for a sample of blood with a hematocrit of 46 per cent. The shear rates shown vary between 23

and 230 sec:). It can be seen from this figure that viscosity decreases as shear rate increases. Figure 2 shows the relationship between \'iscosity and shear rate for samples of blood from five subjects with various hematocrits. Again there is an inverse relationship between viscosity and shear rate. However, with increasing hematocrit, the influence of shear rate on the magnitude of apparent viscosity increases. The greater influence of shear rate on viscosity a~ hematocrit increases may be better appreciated from the regression lines shown in Figure 3. As shear rate decreases, the line of regression relating viscosity to hematocrit becomes steeper. Relationship Between Viscosity and Coronary Blood Flow: In spite of a great deal of work, relatively little is known concerning coronary blood flow, particularly in man. However, certain facts are obvious according to well-established hemodynamic principles. Coronary blood flow is equal to the pres.~ure difference between the root of the aorta and the right atrium divided by the sum of the various resistances in the coronary vascular bed. The two most important resistances in the coronary vascular

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FIGURE 1: Relationship of apparent viscosity of whole blood with a hematocrit of 46 per cent to shear rate. Shear rate dependence of viscosity is demonstrated by the fact that as the shear rate decreases from 230 to 23 sec: 1 apparent viscosity increases. (From Arch. Int. Med.• III :687, 1963).

Volume -l8, No.

Scptem~r 196~

~

HEMATOCRIT, VISCOSITY AND

bed are the caliber of the blood vessels and the manifest viscosity of the blood. Although blood viscosity in the coronary vascular bed has not been measured in vivo, using certain assumptions, it is possible to estimate the viscosity in a given segment of the coronary arterial circulation. The pulsatile variations in coronary blood flow ha\'e been described by GreggS and are represented in Fig. 4. Isometric contraction of the left ventricle is associated with a sudden decrease in left coronary artery flow. However, during left ventricular ejection left coronary inflow increases, but declines again at the end of systole. \Vith the onset of isometric relaxation, coronary flow increases to reach a peak in early diastole after which flow declines gradually, but is ne\'ertheles.<; maintained at relatively high levels (Fig. 4). Right coronary artery inflow. on the other hand, is not associated with such sharp fluctuations (Fig. 4). The most notable differ-

CORO~ARY

227

BLOOD FLOW

ence between left and right coronary artery inflow is the absence of an abrupt decrease in right coronary inflow during is0metric contraction. Figure 5 illustrates variations in the linear rate of left and right coronary blood flow for a segment of coronary artery 1.0 nun. in radius derived from the rates of volume inflow shown in Fig. 4. The time course of the apparent viscosity of two samples of blood with hematocrits of 58 and 40 per cent respectively was detennined with the cone-in-plate viscosimeter for the calculated shear rates. It can be seen that the apparent viscosity of the sample of blood with the hematocrit of 58 per cent is higher than that of the sample with a hematocrit of 40 per cent. In addition, the increase in viscosity which occurs during isometric contraction is considerably greater for the sample with the 58 per cent hematocrit than for the sample with the 40 per cent hematocrit. Furthermore, the abrupt increase in apparent viscosity

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from five subjects greater the shear in a considerably with a hematocrit

228

Diseue5 of the Chm

BURCH AND DE PASQUALE

which occurs during isometric contraction is of considerably greater magnitude in the left than in the right coronary artery. Although the approximations shown in Fig. 5 are crude, they may wen be representative of the true rheologic state. However, it must be stated that Taylor,7 on the basis of a theoretic analysis of phasic flow which took into account shear-dependence, concluded that use of a~ymptomatic value of the viscosity coefficient resulted in only a sman error in the calculation of flow for larger arteries. [,'en if the shear dependence of viscosity is ignored, the fact remains that for a given shear stres." the higher the hematocrit the lower the rate of flow. The diagrams shown in Fig. 5 may provide some insight into clinical problems related to coronary heart disease. It is well known that 60 to 70 per cent of myocardial infarct~ are in the distribution of the left coronary artery. This finding may be related, at least in part, to the abrupt decrease in shear rate and increac;e in apparent viscosity which occurs in the left, but not in the right coronary artery during

isometric contraction. Obviously, the greater the rise in viscosity, the more energy required to reinstitute forward flow during the ejection phase of systole. Another point which deserves consideration is the fact that proximal to an area of coronary arterial narrowing, the linear rate of blood flow is decreased. The decreased blood flow would accentuate the phasic variations shown in Fig. 5 and shear rates may reach extremely low levels. The magnitude of the increase in apparent viscosity as linear rate of flow and shear rate decrease is directly proportional to the hematocrit. In patient~ with markedly elevated hematocrit", it is conceivable that apparent viscosity may increase to such high levels that the diseased myocardium may be unable to produce sufficient energy during the ejection phase of systole to reverse the decrease in blood flow which occurs durin~ isometric contraction. 1\ferrin et al.' have shown that static human blood possesses a distinctive yield stres.~ and that the cube root of the yield stress value varies linearly with hematocrit. Thus, the energy required to reinstitute forward flow in the left coronary artery following the marked decrease

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FIGURE 3: Lines of regression obtained by plotting hematocrit against apparent viscosity for the shear rates shown for blood obtained from 25 .subjects with different hematocrits. The lower the shear rate the greater the rate of regression. For example, an increase in hematocrit from 40 to 50 per cent results in a greater increase in viscosity at the lower shear rate of 23 sec:1 than at the higher shear rate of 230 sec:l •

Volum~ 48, No.3 September 196'

HEMATOCRIT. VISCOSITY AND CORONARY BLOOD FLOW

in the linear rate of flow and in the shear rate which occurs during isometric contraction would be proportional to the hematocrit. It must be remembered that shear rate may decline almost to zero during isometric contraction. These facts are consistent with the clinical finding that myocardial infarction may occur in the absence of demonstrable coronary artery occlusion. In such instances, there may be a "rheologic obstruction" rather than an anatomic obstruction of the coronary artery. Reduction in hematocrit would be a,;sociated with improvement in all rheologic parameters, i.e., a given shear stress would result in a greater flow and a given decrease in shear rate would be associated with a less marked rise in apparent viscosity. In addition, as the hematocrit is lowered, the yield stres." value would also decrease. Phlebotomy in Patients with Angina Pectoris: As previously reported:· 10 many patients with coronary heart disease and myocardial infarction have high levels of hematocrit. Although a statistical study of the hematocrit in patients with angina pectoris without myocardial infarction has not been conducted, we have observed a large number of patients with angina pectoris with high hematocrit values. It has been our practice in such patients to reduce the hematocrit to at least between 45 and 47 per cent by repeated small phlebotomies. 40

SYSTOLE

229

Phlebotomy has usually been associated with a decrease in the frequency of anginal attacks. l l In addition, many patients report a general feeling of improvement in well being after phlebotomy which may be due to an increase in coronary artery blood flow, a decrease in myocardial work or both as the blood viscosity is lowered. We have found that repeated small phlebotomies (200 to 300 ml.) are more effective in maintaining a reduction in hematocrit than phlebotomies of larger volume. No untoward reactions have been observed during or after these small phlebotomies. It is difficult to evaluate the effectiveness of procedures or drugs in relieving pain. This is particularly true for angina pectoris which may be associated with strong emotional overlay. Electrocardiographic tests of effort tolerance would be of limited value in attempting to remove the subjective factor since many patients have an abnormal resting electrocardiograph. It should be pointed out that erythrocytosis in the majority of our patients with coronary heart disease is not of a compensatory nature, but probably reflects a response to psychic stress probably in part due to the coronary heart disease. Because the increased red blood cell mass is not compensatory, there is no reason to hesitate to lower the hematocrit. The increased hematocrit does not serve in any way to improve oxygenation of

DIASTOLE

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4: The time course of coronary blood flow during a single cardiac cycle replotted from data obtained from Gregg.- Consult for details.

FIGURE

Di~as~s of th~ Ch~\t

BURCH AND DE PASQUALE

the tissues and may, in fact, decrease oxygenation on the basis of the rheologic factors described earlier in this paper. Even when erythrocytosis is compensatory, it may be more efficient to have a normal hematocrit and good blood flow than a high hematocrit and low blood flow. In patients with tetralogy of Fallot and marked polyqthemia, phlebotomy is often associated with an increase in oxygen saturation. However, because of the extremely low pulmonary blood flow, some degree of polyqthemia is essential. Normal hematocrits in patients with severe tetralogy of

Fallot may be associated with "air-hunger." However, these considerations are not applicable to patients with coronary heart disease. It would be interesting to know the hematocrit level beyond which no further improvement in tissue (myocardium in particular) oxygenation occurs. Nature has provided the organism with a surplus of virtually all tissues. Man is endowed with more nephrons, myocardial fibers, alveoli and so forth than needed to maintain good health. Undoubtedly the red blood cells are also subject to nature's extravagance. Of course, nature is "wise"

RELATIONSHIP BETWEEN CORONARY BLOOD FLOW, SHEAR RATE AND VISCOSITY

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FIGURE 5: Time course of linear rates of blood Aow during a single cardiac cycle (upper curves) in a segment of the left and right coronary arteries of l.0 mm. radius calculated from the rates of coronary flow shown in Figure 4. Time course of shear rate for a single cardiac cycle (middle curves) calculated from the linear rates of flow by dividing four times the velocity by the radius. Time course of the variations in apparent viscosity during the cardiac cycle (lower curves) for a hematocrit of 40 and 58 per cent derived from data obtained with the cone plate viscometer.

Volum~ 48. No.3 ~pt~mber 196';

HEMATOCRIT. VISCOSITY AND CORONARY BLOOD FLOW

and the excess of functional tissue provides a margin of safety in the event of destruction of tissue or unusual demands in time of stress. Reduction of the hematocrit to levels beyond which no improvement in tissue oxygenation would occur would remove the margin of safety. In such an event, sudden blood loss may result in difficulty. Thus, it is best to make some compromise such as reduction of the hematocrit to 45 per cent rather than to 40 per cent. However, in severe angina pectoris, it may be worthwhile to forego the luxury of a margin of safety and reduce the hematocrit to 40 per cent. Certainly, many women of menstruating age tolerate hematocrits of 35 to 40 per cent with no difficulty. GENERAL DISCUSSION

Many patients with myocardial infarction and/or angina pectoris have elevated hematocrit values.,·IO.11 \Vhen the hematocrit is elevated in such patients, the increase is usually moderate, rarely exceeding 58 per cent. The el")throc)tosis is probably due to stress as is evidenced by the fact that simply placing the patients in bed may result in a reduction in hematocrit. Also following myocardial infarction with rest and therapy, there may be a fall in the hematocrit. Reduction of only moderately elevated hematocrits in patients with coronary heart disease and erythrocytosis may result in marked improvement in exercise tolerance and a decrease in the frequency of anginal attacks. It should be empha~ized that as far a~ is known, erythroc)tosis plays no role in the development of coronal")' arteriosclerosis. The point to be made, however, is that in patients with coronary arteriosclerosis, an elevated hematocrit may predispose to angina pectoris and/or myocardial infarction. Recently, Conley et al.,13 compared the hematocrit values in 200 patients with myocardial infarct with those of normal healthy medical students and found no significant difference between the hematocrits of the two groups. This is in contrast to our

own previously reported findings.'·lo The most important difference between our study and that of Conley et ai., was the significantlv lower hematocrit values of our controls' than those of Conley et al. The basis for these differences is unknown. However, neither the series of Conley and associates nor our own should be accepted as representative of the true situation. Many more studies involving a large number of patients must be obtained before the problem of the epidemiologic relationship between hematocrit and myocardial infarction is solved. In regard to phlebotomy, there is no doubt that patients with angina pectoris and erythroqtosis are improved clinically by phle botom y. In addition, el)throcytosis serves no useful function in such patients. Although a few physicians may have an emotional aversion to phlebotomy because it recalls a medically "unscientific era," there is abundant modem rheologic data which provides a theoretic basis for this practice in patients with elevated hematocrit and ischemic heart disease. It appears to us to be more difficult to justify allowing a patient with angina pectoris to maintain a hematocrit of 55 per cent or more than to justify reducing the hematocrit to 45 per cent by repeated carefully performed, small phlebotomies. SUMMARY

Patients with ischemic heart disease and erythrocytosis may experience a decrease in the frequency of anginal attacks and an increase in effort tolerance following reduction of the hematocrit by phlebotomy. The clinical improvement following phlebotomy was related to modem rheologic principles based upon the shear dependance of blood viscosity. No attempt was made to establish an epidemiologic re 1a t ion ship between increa~d hematocrit and angina pectoris. However, it was emphasized that patients with ischemic heart disease and erythrocytosis are improved clinically by reduction of the hematocrit to between 45 and 47 per cent.

BURCH AND DE PASQUALE RESUMEN

Los sujetos con isquemia del miocardio y eritrocitosis pueden experimentar un aumento de la tolerancia al esfuerzo y una menor frecuencia de las crisis anginosas mediante la reduccion hematocritica consecutiva a la flebotomia. Estos resultados c1inicos parecen relacionados con los principios reologicos modemos basados en la dependencia absoluta de la viscosidad sanguinea. No hemos intentado establecer relacion epidemiologica entre el aumento hematocritico y la gravedad del estado anginoso, sin embargo, se· ha puesto de relieve el hecho de que los pacientes con isquemia del miocardio y eritrocitosis mejoran con la reduceion de la cifra hematocritica a entre 45 y 47 por ciento.

2 COPLEY, A. L. AND STAINSBY, G.: Flow Prop3 4

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ZUSAMMENFASSUNG

Patienten mit ischamischer Herzkrankheit und Erythrocytose konnen eine Herabsetzung in der Haufigkeit von pectanginosen Anfallen erfahren sowie ein Anstieg in der Vertriiglichkeit von Belastungen im Anschluj3 an eine Verringerung des Haematocrits durch Phlebotomie. Die klinische Besserung nach der Phlebotomie stand in Beziehung zu den modernen rheologischen Prinzipien und basiert auf der Abweichung der Blutviscositat. Es wurden keinerlei Versuche unternommen. urn eine epidemiologische Beziehung zwischen erhohtem Haematocritwert und Angina pectoris zu errechnen. Es wurde aber hervorgehoben. daJ3 Patienten mit ischamischen Herzkrankheiten und Erythrocytose klinisch gebessert werden durch Verringerung des Haemocrit bis zwischen 45 und 47%. REFERENCES HESS, W. R.: "Der Stromungswidentand des Blutes gegenuber kleinen Druckwerten," Arch. Physiol. (Leipzig), 1912, p. 137.

Diseues of the Chest

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erties 01 Blood, Pergamon Press, New York, 1960. FAHRAEUS, R. AND UNDQVlST, T.: ''Viscosity of Blood in Narrow Capillary Tubes," Am. J. Physiol., 96:562, 1931. WELLS, R. E. AND MERRILL, E. W.: "Influence of Flow Properties of Blood Upon Viscosity. Hematocrit Relationships," J. Clin. Invest., 41: 1591, 1962. WELLS, R. E., DENTON, R. AND MERRILL, E. W.: "Measurement of Viscosity of Biologic Fluids by Cone Plate Viscometer," J. Lab. and Clin. Med., 57:646, 1961. GREGO, D. E.: Coronary Circulation in Health and Disease, Lea and Febiger, Philadelphia, 1950. TAYLOR, M. G.: "Influence of the Anomalous Viscosity of Blood upon Its Oscillatory Flow," Phys. Med. Bioi., 3:273, 1959. MERRILL, E. W., GILLILAND, E. R., COKELET, G., SHIN, H., BRITTEN, A. AND WELLS, R. E.: "Rheology of Human Blood Near and at Zero Flow," Biophysical J., 3: 199, 1963. BURCH, G. E. AND DEPASQUALE, N. P.: ''The Hematocrit in Patients with Myocardial Infarction," JAMA, 180:63 1962. DEPASQUALE, N. P. AND BURCH, G. E.: "Hematocrit in Women with Myocardial Infarction," JAMA, 183: 142, 1963. BURCH, G. E. AND DEPASQUALE, N. P. "Phlebotomy-Use in Patients with Erythrocytosis and Ischemic Heart Disease," Arch. Int. Med., 111:687, 1963. BURCH, G. E. AND DEPASQUALE, N. P.: "Erythrocytosis and Ischemic Myocardial Disease (Annotation)," Am. Heart J., 62:139, 1961. CONLEY, C. L., RUSSELL, R. P., THOMAS, C. B. AND TUMULTY, P. A.: "Hematocrit Values in Coronary Artery Disease," Arch. Int. Med., 113: 170, 1964.

For reprints, please write: Dr. Burch, 1430 Tulane Avenue, New Orleans.

BRONCHOGRAPHY BY MEANS OF SPRAY teristlcs of this spray method. when compared with new method for bronchography was devised so the fonner methods are as follows: It Is a safer as to avoid respiratory dlmcultles. A flexible single method. not accompanied by respiratory disturbcatheter Is used. The various formerly employed conances: the whole procedure Is simple and easy: finer trast media were scrutinized In every way and procontours are obtained: smaller amounts of contrast pyllodone BaSO,-NaCI solution was found the most medium Is reqUired: the elimination proceeds suitable for this spraying method. Bronchography smoothly. was performed In the lateral position with the atrected side down. Four ways were employed as the HlaoTA. S. rt III.: "Bronchography by Means of a Spray routes of spray of the contrast medium. I.e.• pharyngeal. tracheal. bronchial and selective. The characMethod," /"''''uu /. Tho~. S.~g .• 18:26, 1%). A