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The effect of pressure pulsations on the Fahraeus-Lindqvist effect
MICROVASCULAR
RESEARCH
l&245-249
(1978)
BRIEF COMMUNICATIONS The Effect of Pressure
Pulsations on the Fahraeus-Lindqvist Eff ectl
C. K. KRISHNAKUMAR,* ALLEN A. ROVICK,~ AND ZALMAN LAVAN* * Illinois Institute of Technology, MMAE Department, Chicago, Illinois 60616, and f Department of Physiology, College of the Health Services, Rush University, Chicago, Illinois 60612 Received March 28,1977
The effect of superposition of pressure pulses on the steady flow of blood through narrow tubes with diameters in the Fahraeus-Lindqvist range was studied experimentally to determine whether pulsations modify the diameter-dependent viscosity reduction of blood in these rigid tubes. Glass tubes 65 and 78 m in internal diameter were perfused with steady pressures and sinusoidally oscillating pressures (50% amplitude at frequencies of 1 and 2 Hz) with the same mean values. It was observed that introduction of pulsations did not affect the mean flow rate of blood through the test segments.
In order to model the flow of blood in tissue blood vessels in an earlier study (Krishnakumar et al., 1976), we compared the flow in rigid tubes under pulsatile and steady pressure perfusion. These studies showed that superimposedpressure pulses do not affect the flow resistance of Newtonian fluids in the laminar regime. However, the model tubes used were considerably larger than arterioles where the rheological properties of blood become significant. Therefore, the previous study was extended to tubes with diameters in the Fahraeus-Lindqvist range (Fahraeus and Lindqvist, 193I), smaller than 300 armin internal diameter (i.d.). Several theories have been advanced to explain the decreasein the apparent viscosity of blood with tube diameter in steady flow. All center around the nonuniform distribution of cells across the tube radius (Goldsmith and Mason, 1967; Barbee and Cokelet, 1971). The question naturally arises as to whether the red cell distribution and hence the apparent viscosity of blood are modified by pulsation. Physiologically this might be very important since changesin blood viscosity in the arterioles would alter the flow resistance of this important vascular sector, and changes in the radial red cell distribution in the arterioles would influence the uniformity of red cell concentration among their branches. METHODS Segments of glass tubes 65 and 78 m in i.d. were perfused with whole blood of hematocrit 43 at a temperature of 37O. The mean Reynolds numbers (Re) employed ranged between 0.44 and 3.75, bracketing the Re values that occur in arterioles. The perfusion system was essentially the same as the one used in our earlier work (Krishnakumar et al., 1976) except that the oscillatory pressure was applied directly to i This work was supported by a grant-in-aid from the Chicago Heart Association. 0026.2862/78/0152-0245SO2.00/0 245 Copyright 01978 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
BRIEF COhlhWNICATIONS
246
the air spaceat the top of the supply reservoir and the second reservoir was eliminated. A Plexiglas module (Fig. 1) was fabricated to hold the tube test sections.The throughflow channel and the channel perpendicular to it were about 1 mm in diameter. Filtered, heparinized (5 U/ml) human bank blood was continuously circulated in the throughflow channel to prevent RBC settling. Whenever different blood sampleswere mixed, they were tested for compatibility. One end of the perpendicular channel was connected to a Statham P-23 pressuretransducer and the other end led to the test section. TOP VIEW OF MODULE ASSEMBLY TO PRESSURE TRANSDUCER AND POLYGRAPH Y-l FII- TFR -.
--b
I
I 1 I
I
I I ----
’ L----
1 L-_
THROUGHFLOW
FIG. 1. Diagram of the test section module showing the through-flow channel. The perpendicular channel connects the test section to the pressuretransducer. The test section is sealed with O-rings and the efRuentis measuredin a pipet.
Volume flow rates were determined by timing the meniscus movement in relatively large, horizonal pipets with bores between 850 and 900 pm. The pipet flow resistance was negligible compared with that of the test segments.The lowest acceptedflow rate was determinedby the first sign of cell settling in the collection pipet. RESULTS Figures 2 and 3 show the relationship between flow rate and pressure drop for the tubes used in this study. The least-squaresregressionlines for steady pressureperfusion are shown in the figures. The vertical brackets represent 95% confidence limits for
BRIEF COMMUNICATIONS
)k 0
APmmHg FIG. 2. Blood flow vs pressure drop in a test section. The lower line is the relationship that would be present if the flow were fully developed and the blood had the same viscosity as in a large-bore tube. The upper line is the linear regression line for steady perfusion of the test section. The vertical bars are the 95% confidencelimits of this line. Sixteen to twenty-four points obtained during pulsatile perfusion fall into each shaded area. 775~
Tube,b=zo(upper
curve)
AhnmHg FIG. 3. Blood flow vs pressure drop in two test sections. Each line is equivalent to the upper line of Fig.
2.
248
BRIEF COMhfUNICATIONS
steady pressure perfusion. In Fig. 2, the lower line shows the pressure dropflow rate relations that would obtain in that tube, if the blood exhibited the viscosity that it had in a large-bore tube. Hence, it illustrates the reduction in apparent viscosity produced by the Fahraeus-Lindqvist effect. Pulse amplitudes of 50% (peak to peak) of the mean pressure at the tube entrance, at frequencies of 1 and 2 Hz, were superimposedon the mean pressure gradients. The flow values obtained during the pulsatile perfusion are enclosed in the shaded areas (Figs. 2 and 3). Each of these areas is composedof 16 to 24 experimental points. It is clear that the flow rates under pulsatile perfusion are the same as those under steady perfusion at the samemean pressurevalue. DISCUSSION Arterial pressure pulsations modify tissue blood flow, often in a complex manner (Rovick and Robertson 1964; Yonce et al., 1972; Scearceand Yonce, 1976). Although the causeof this effect is far from clear, it has usually been assumedto result exclusively from an action of the pulsations on the vascular smooth muscle contractile activity. In support of this assumption, pulsation has been shown to have a significant effect on the autoregulatory responsivenessof skeletal muscle resistance vessels (Mellander and Arvidsson, 1974; Lalone et al., 1975). However, the vascular wall passive properties, the actions of the pressure pulse on the pattern of fluid flow, and the coupling of the vascular wall and fluid motions could all contribute to the relationship of pulse and tissue blood flow. In our previous study (Krishnakumar et al., 1976) we demonstrated that superimposedpressure pulses do not affect the flow resistanceof Newtonian fluids either in the fully developed or in the developing laminar regime. The present study demonstratesthat the blood flow through tubes of the size of arterioles is also unaffected by the pulsatile character of the flow, and that the diameter-dependentreduction in the apparent viscosity of blood in the Fahraeus-Lindqvist range is unaffected. It can now be concluded that the hydrodynamic factors and the non-Newtonian behavior of blood alone do not play a significant role in pulse-induced changesof tissue blood flow. Such changes must be solely due to one or some combination of: the distensibility characteristics of vessel walls, the reactive properties of the vascular smooth muscle,and the interactions of the wall and fluid motions. ACKNOWLEDGMENTS The authors gratefully acknowledge the technical assistanceof J. S. Rovick. REFERENCES BARBEE,J. H., ANDCOKELET,G. R. (197 I). The Fahraeus effect. Mlcrouasc. Res. 3,6-16. FAHRAEUS,R., AND L~NDQVIST, T. (193 I). Viscosity of blood in capillary tubes. Amer. J. Physfol. %,562568 GOLDSMITH,H. L., AND MASON,S. G. (1967). The microrheology of dispersions. In “Rheology” (F. R. Eirich, ed.), Vol. 4, Chap. 2. Academic Press,New York. KIUSHNAKUMAR,C. K., ROVICK,A. A., AND LAVAN, Z. (1976). The effect of pressure pulsations on time mean flow rate. h4icrovasc. Res. 11.4 l-49.
BRIEF COMhRJNICATIONS
249
LALONE, B., SCHWINGHAMMER, J., AND MAJOR,T. (1975). Autoregulation of skeletal muscle blood flow
during pulsatile and non-pulsatile perfusion. Fed. Proc. 34, 848. MELLANDER, S., AND ARVIDSSON, S. (1974). Possible dynamic component in the myogenic vascular
responserelated to pulse pressure distension.Actu Physiol. Band. 90,283-285. ROVICK, A. A., AND ROBERTSON, P. A. (1964). Interaction of mean and pulse pressuresin the circulation
of the isolated dog tongue. Circ. Res. 15208-2 15. SCEARCE, R. W. JR., AND YONCE, L. R. (1976). Pulsatile pressure-flow dynamics in resting skeletal
muscle. Physiologist 19,355. YONCE, L. R., MCGEE, J. W., SANDERSON, J. R., AND BEER, G. (1972). Vasodilator response to
epinephrine in denervated muscle: Role of pulse pressure.Amer. J. Physiol. 223,407-414.
RESEARCH
l&245-249
(1978)
BRIEF COMMUNICATIONS The Effect of Pressure
Pulsations on the Fahraeus-Lindqvist Eff ectl
C. K. KRISHNAKUMAR,* ALLEN A. ROVICK,~ AND ZALMAN LAVAN* * Illinois Institute of Technology, MMAE Department, Chicago, Illinois 60616, and f Department of Physiology, College of the Health Services, Rush University, Chicago, Illinois 60612 Received March 28,1977
The effect of superposition of pressure pulses on the steady flow of blood through narrow tubes with diameters in the Fahraeus-Lindqvist range was studied experimentally to determine whether pulsations modify the diameter-dependent viscosity reduction of blood in these rigid tubes. Glass tubes 65 and 78 m in internal diameter were perfused with steady pressures and sinusoidally oscillating pressures (50% amplitude at frequencies of 1 and 2 Hz) with the same mean values. It was observed that introduction of pulsations did not affect the mean flow rate of blood through the test segments.
In order to model the flow of blood in tissue blood vessels in an earlier study (Krishnakumar et al., 1976), we compared the flow in rigid tubes under pulsatile and steady pressure perfusion. These studies showed that superimposedpressure pulses do not affect the flow resistance of Newtonian fluids in the laminar regime. However, the model tubes used were considerably larger than arterioles where the rheological properties of blood become significant. Therefore, the previous study was extended to tubes with diameters in the Fahraeus-Lindqvist range (Fahraeus and Lindqvist, 193I), smaller than 300 armin internal diameter (i.d.). Several theories have been advanced to explain the decreasein the apparent viscosity of blood with tube diameter in steady flow. All center around the nonuniform distribution of cells across the tube radius (Goldsmith and Mason, 1967; Barbee and Cokelet, 1971). The question naturally arises as to whether the red cell distribution and hence the apparent viscosity of blood are modified by pulsation. Physiologically this might be very important since changesin blood viscosity in the arterioles would alter the flow resistance of this important vascular sector, and changes in the radial red cell distribution in the arterioles would influence the uniformity of red cell concentration among their branches. METHODS Segments of glass tubes 65 and 78 m in i.d. were perfused with whole blood of hematocrit 43 at a temperature of 37O. The mean Reynolds numbers (Re) employed ranged between 0.44 and 3.75, bracketing the Re values that occur in arterioles. The perfusion system was essentially the same as the one used in our earlier work (Krishnakumar et al., 1976) except that the oscillatory pressure was applied directly to i This work was supported by a grant-in-aid from the Chicago Heart Association. 0026.2862/78/0152-0245SO2.00/0 245 Copyright 01978 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
BRIEF COhlhWNICATIONS
246
the air spaceat the top of the supply reservoir and the second reservoir was eliminated. A Plexiglas module (Fig. 1) was fabricated to hold the tube test sections.The throughflow channel and the channel perpendicular to it were about 1 mm in diameter. Filtered, heparinized (5 U/ml) human bank blood was continuously circulated in the throughflow channel to prevent RBC settling. Whenever different blood sampleswere mixed, they were tested for compatibility. One end of the perpendicular channel was connected to a Statham P-23 pressuretransducer and the other end led to the test section. TOP VIEW OF MODULE ASSEMBLY TO PRESSURE TRANSDUCER AND POLYGRAPH Y-l FII- TFR -.
--b
I
I 1 I
I
I I ----
’ L----
1 L-_
THROUGHFLOW
FIG. 1. Diagram of the test section module showing the through-flow channel. The perpendicular channel connects the test section to the pressuretransducer. The test section is sealed with O-rings and the efRuentis measuredin a pipet.
Volume flow rates were determined by timing the meniscus movement in relatively large, horizonal pipets with bores between 850 and 900 pm. The pipet flow resistance was negligible compared with that of the test segments.The lowest acceptedflow rate was determinedby the first sign of cell settling in the collection pipet. RESULTS Figures 2 and 3 show the relationship between flow rate and pressure drop for the tubes used in this study. The least-squaresregressionlines for steady pressureperfusion are shown in the figures. The vertical brackets represent 95% confidence limits for
BRIEF COMMUNICATIONS
)k 0
APmmHg FIG. 2. Blood flow vs pressure drop in a test section. The lower line is the relationship that would be present if the flow were fully developed and the blood had the same viscosity as in a large-bore tube. The upper line is the linear regression line for steady perfusion of the test section. The vertical bars are the 95% confidencelimits of this line. Sixteen to twenty-four points obtained during pulsatile perfusion fall into each shaded area. 775~
Tube,b=zo(upper
curve)
AhnmHg FIG. 3. Blood flow vs pressure drop in two test sections. Each line is equivalent to the upper line of Fig.
2.
248
BRIEF COMhfUNICATIONS
steady pressure perfusion. In Fig. 2, the lower line shows the pressure dropflow rate relations that would obtain in that tube, if the blood exhibited the viscosity that it had in a large-bore tube. Hence, it illustrates the reduction in apparent viscosity produced by the Fahraeus-Lindqvist effect. Pulse amplitudes of 50% (peak to peak) of the mean pressure at the tube entrance, at frequencies of 1 and 2 Hz, were superimposedon the mean pressure gradients. The flow values obtained during the pulsatile perfusion are enclosed in the shaded areas (Figs. 2 and 3). Each of these areas is composedof 16 to 24 experimental points. It is clear that the flow rates under pulsatile perfusion are the same as those under steady perfusion at the samemean pressurevalue. DISCUSSION Arterial pressure pulsations modify tissue blood flow, often in a complex manner (Rovick and Robertson 1964; Yonce et al., 1972; Scearceand Yonce, 1976). Although the causeof this effect is far from clear, it has usually been assumedto result exclusively from an action of the pulsations on the vascular smooth muscle contractile activity. In support of this assumption, pulsation has been shown to have a significant effect on the autoregulatory responsivenessof skeletal muscle resistance vessels (Mellander and Arvidsson, 1974; Lalone et al., 1975). However, the vascular wall passive properties, the actions of the pressure pulse on the pattern of fluid flow, and the coupling of the vascular wall and fluid motions could all contribute to the relationship of pulse and tissue blood flow. In our previous study (Krishnakumar et al., 1976) we demonstrated that superimposedpressure pulses do not affect the flow resistanceof Newtonian fluids either in the fully developed or in the developing laminar regime. The present study demonstratesthat the blood flow through tubes of the size of arterioles is also unaffected by the pulsatile character of the flow, and that the diameter-dependentreduction in the apparent viscosity of blood in the Fahraeus-Lindqvist range is unaffected. It can now be concluded that the hydrodynamic factors and the non-Newtonian behavior of blood alone do not play a significant role in pulse-induced changesof tissue blood flow. Such changes must be solely due to one or some combination of: the distensibility characteristics of vessel walls, the reactive properties of the vascular smooth muscle,and the interactions of the wall and fluid motions. ACKNOWLEDGMENTS The authors gratefully acknowledge the technical assistanceof J. S. Rovick. REFERENCES BARBEE,J. H., ANDCOKELET,G. R. (197 I). The Fahraeus effect. Mlcrouasc. Res. 3,6-16. FAHRAEUS,R., AND L~NDQVIST, T. (193 I). Viscosity of blood in capillary tubes. Amer. J. Physfol. %,562568 GOLDSMITH,H. L., AND MASON,S. G. (1967). The microrheology of dispersions. In “Rheology” (F. R. Eirich, ed.), Vol. 4, Chap. 2. Academic Press,New York. KIUSHNAKUMAR,C. K., ROVICK,A. A., AND LAVAN, Z. (1976). The effect of pressure pulsations on time mean flow rate. h4icrovasc. Res. 11.4 l-49.
BRIEF COMhRJNICATIONS
249
LALONE, B., SCHWINGHAMMER, J., AND MAJOR,T. (1975). Autoregulation of skeletal muscle blood flow
during pulsatile and non-pulsatile perfusion. Fed. Proc. 34, 848. MELLANDER, S., AND ARVIDSSON, S. (1974). Possible dynamic component in the myogenic vascular
responserelated to pulse pressure distension.Actu Physiol. Band. 90,283-285. ROVICK, A. A., AND ROBERTSON, P. A. (1964). Interaction of mean and pulse pressuresin the circulation
of the isolated dog tongue. Circ. Res. 15208-2 15. SCEARCE, R. W. JR., AND YONCE, L. R. (1976). Pulsatile pressure-flow dynamics in resting skeletal
muscle. Physiologist 19,355. YONCE, L. R., MCGEE, J. W., SANDERSON, J. R., AND BEER, G. (1972). Vasodilator response to
epinephrine in denervated muscle: Role of pulse pressure.Amer. J. Physiol. 223,407-414.