Effects of temperature and haematocrit on the relationships between blood flow velocity and blood flow in a vessel of fixed diameter

O. Paut* and B. Bissonnette

Department of Anaesthesia, The Hospital for Sick Children and University of Toronto, 555 University Avenue, Toronto, Ontario, Canada, M5G 1X8*Corresponding author: Department of Pediatric Anesthesia and Intensive care Medicine, La Timone Children’s hospital, 365 Bd Jean Moulin, F-13385 Marseille cedex 5, France

Accepted for publication: September 24, 2001


    Abstract
 Top
 Abstract
 Introduction
 Methods and results
 Comments
 References
 
Background. To determine whether temperature and haematocrit (Hct) alter the relationship between blood flow (BF) and blood flow velocity (BFV).

Methods. Using a transcranial Doppler apparatus, we measured the peak velocity of whole blood cells pumped by a cardiopulmonary bypass (CPB) circuit, through a 0.15-cm internal diameter segment of rigid tubing. BF and BFV relationships were obtained at temperatures of 19, 28, and 37°C and at Hct of 0.05, 0.22, 0.39, and 0.54, by altering CPB flow over a range from 10 to 100 cc/min. Linear regression analysis was performed.

Results. The relationship between velocity and flow for the pooled Hct data was y=(0.43)x+0.86, r2=0.998 and 95% CI (0.999–1) whereas the association for the temperature data was y=(0.42)x+0.02, r2=0.9998 and 95% CI (0.999–0.9997). Changes of blood viscosity had no effect on velocity at a given flow rate. The combined effect of Hct and temperature on velocity for the relationship with flow is expressed by: y=1.3+2.4x.

Conclusion. In fixed diameter vessels with laminar flow, the linear relationship between flow and velocity is not affected by changes in temperature and Hct in clinical ranges. These results are explained by the Fahraeus–Lindquist effect. They support the use of transcranial Doppler sonography to estimate cerebral blood flow in infants who may have large variations of Hct and/or temperature during bypass.

Br J Anaesth 2002; 88: 277–9

Keywords: anaesthesia, paediatric; equipment: transcranial Doppler apparatus; blood, haemodilution; complications, hypothermia


    Introduction
 Top
 Abstract
 Introduction
 Methods and results
 Comments
 References
 
Transcranial Doppler sonography (TCD) is used to measure cerebral perfusion. It is non-invasive, has a high temporal resolution, and allows continuous monitoring. The major limitation is that it measures blood flow velocity (BFV) rather than blood flow (BF). Clinical and animal studies have found a good correlation between changes in BFV in the basal cerebral arteries and BF during physiological changes such as PaCO2 and temperature.1 Blood temperature and haematocrit (Hct) can influence blood viscosity,2 and might change the relationship between BF and BFV. This study was designed to determine whether temperature and Hct alter BFV, in a model, simulating a small basal cerebral artery in infants.


    Methods and results
 Top
 Abstract
 Introduction
 Methods and results
 Comments
 References
 
A cardiopulmonary bypass (CPB) circuit primed with human whole blood was connected to a 0.15-cm internal diameter segment of rigid tubing. The CPB flow rates were adjusted between 10 and 100 cc min–1 with increments of 10 cc min–1. Calibration of this system was by timed collection of all effluent blood from the circuit into a graduated cylinder. Peak velocity through this tubing was determined by TCD using a 4 MHz continuous wave Doppler probe (Medasonics, Fremont, CA, USA). This segment of tubing passed through a glass box containing mock cerebrospinal fluid. The TCD probe was fastened to the box through a hole created on the box side, which was subsequently sealed with epoxy glue (Fig. 1). The TCD probe was 30 mm distant from the tube, allowing for blood velocity recordings. The angle of insonation was set at 5°. Flow-velocity data were obtained at temperatures of 19, 28 and 37°C using outdated human packed red blood cells (PRBC) reconstituted with outdated plasma to give a Hct of 0.39. The velocity was also recorded at Hct of 0.05, 0.22, 0.39, and 0.54 using reconstituted whole blood at a temperature of 37°C. Five velocity values were recorded at each interval and averaged. Linear regression analysis and the coefficient of correlation (r2) were performed and calculated using GraphPad InStat version 3.00 for Windows 95 (GraphPad Software, San Diego, CA, USA). P<0.05 was considered statistically significant.



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Fig 1 Experimental system used.

 
There was a strong linear relationship between blood flow and blood velocity at each set of conditions (r2>0.99). The velocity varied directly with flows at all Hct (Fig. 2). The relationship between flow and velocity for the pooled Hct data was y=(0.43)x+0.86, r2=0.998 and 95% CI (0.999–1). Similarly, temperatures from 19 to 37°C did not affect the relationships between flow and velocity (y=(0.42)x+0.02, r2=0.9998 and 95% CI (0.999–0.9997)). The combined effect of temperature and Hct changes on velocity was y (BFV)=1.3+2.4x (BF).



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Fig 2 (A) Effect of Hct changes on blood velocity. (B) Effect of temperature variations on blood flow velocity.

 

    Comments
 Top
 Abstract
 Introduction
 Methods and results
 Comments
 References
 
We found a linear relationship between blood flow and peak blood flow velocity, in fixed diameter vessels with laminar flow. This relationship is not altered by changes in temperature and haematocrit within clinical ranges. Variations of blood viscosity which are affected by Hct and temperature do not affect the peak velocity in a small fixed diameter vessel, as peak velocity for a given flow rate was similar whatever the temperature or Hct.

In experimental and clinical settings, many physiologic factors affect cerebral blood flow velocity. Among them, Hct and core temperature have been widely studied. In adults, normovolaemic haemodilution with a decrease of Hct from 38 to 30% was associated with an average 16% increase in cerebral blood flow velocity.3 In children, an inverse relationship between cerebral blood flow velocity and Hct has been demonstrated during deep hypothermic cardiopulmonary bypass.4 During deep hypothermia, cerebral blood flow was reduced by 40%.5 The cerebral blood flow velocity was also correlated with cerebral blood flow. In eight children undergoing cardiac surgery with deep hypothermia, the authors demonstrated that cerebral blood flow velocity was reduced to 33% of the control value, whereas oxygen consumption was decreased to 20% of control.1

The effects of Hct and temperature on cerebral blood flow velocity can be related either to their effect on blood viscosity, on cerebral blood flow adaptation to cerebral metabolic rate for oxygen, or both. Changes in Hct can change blood viscosity. Moderate haemodilution (Hct 22%) decreases blood viscosity by 30–50% at a low blood temperature2 whereas an increase in Hct increased blood viscosity and decreased CBF.6 Blood viscosity increases when blood temperature decreases; however, the increase in viscosity is observed mostly at temperature below 15°C.2 The cerebral blood flow adapts with metabolic demand. It is reduced during hypothermia when oxygen consumption is decreased.1 During polycythaemia, there is an increase in arterial oxygen content and a decrease in cerebral blood flow velocity.6 In animals, a nitroprusside infusion administered to normalize the arterial oxygen content in polycythaemia allowed cerebral blood flow velocity to return to baseline values.6

In cerebral resistance blood vessels, the pressure-flow relationships are given by Poiseuille’s law (equation 1):

Q = {pi}Pr4/8l{eta}(1)

where Q is blood flow, P is the pressure gradient across the vessel, r is the vessel radius, {eta} is blood viscosity and l is the vessel length. Given that cerebral blood flow velocity (CBFV) is expressed by equation 2

CBFV=Q/{pi}r2(2)

We can replace Q in equation 2 to obtain equation 3

CBFV=Pr2/8l{eta}(3)

In this equation, if P, r2 and the vessel length are constant, cerebral blood flow velocity is inversely proportional to viscosity. In animals a decrease in Hct was associated with only a small 4.4% change in basilar artery diameter,7 whereas the pial arterioles constricted as Hct decreased.8 These results are consistent with the finding that the hyperaemia accompanying haemodilution is the result of a decrease in blood viscosity and/or an adaptive phenomenon to variations in cerebral metabolism.7 9

As tube length, vessel radius, and pressure are maintained constant, one would expect cerebral blood flow velocity, at a given flow, to vary proportionally with blood viscosity. In the present study, the blood flow velocity varied directly with blood flow, independently of Hct and temperature, hence independently of viscosity. Several general properties about biomechanics of blood explain these observations. The Fahraeus–Lindquist effect confirms that the apparent viscosity of whole blood varies with the Hct. Normally, plasma viscosity is 1.2–1.3 times that of water, whereas the blood viscosity is 2.4 times that of plasma. Furthermore, the effect of viscosity of whole blood depends critically on the size of the vessel through which it flows. When blood is flowing through vessels narrower than 2 mm in internal diameter, the apparent viscosity tends toward that of plasma.10 This explains the present observation and confirms that, in a 1.5-mm internal diameter tube intended to simulate the diameter of an infant’s mean cerebral artery, viscosity does not affect blood flow velocity recordings.

In conclusion, we found that in a small vessel of fixed diameter, wide variations of temperature, Hct and viscosity did not affect the relationships between blood flow velocity and blood flow. It supports the clinical usefulness of TCD to assess cerebral blood flow in infants who have large changes of Hct or temperature which can occur during cardiopulmonary bypass.


    Acknowledgement
 
The authors thank Patrice Aubin, for his help in reviewing the manuscript.


    References
 Top
 Abstract
 Introduction
 Methods and results
 Comments
 References
 
1 van der Linden J, Priddy R, Ekroth R, et al. Cerebral perfusion and metabolism during profound hypothermia in children. A study of middle cerebral artery ultrasonic variables and cerebral extraction of oxygen. J Thorac Cardiovasc Surg 1991; 102: 103–14[Abstract]

2 Eckmann D, Bowers S, Stecker M, Cheung A. Hematocrit, volume expander, temperature and shear rate effects on blood viscosity. Anesth Analg 2000; 91: 539–45[Abstract/Free Full Text]

3 Bruder N, Cohen B, Pellissier D, Francois G. The effect of hemodilution on cerebral blood flow velocity in anesthetized patients. Anesth Analg 1998; 86: 320–4[Abstract]

4 Gruber EM, Jonas RA, Newburger JW, et al. The effect of hematocrit on cerebral blood flow velocity in neonates and infants undergoing deep hypothermic cardiopulmonary bypass. Anesth Analg 1999; 89: 322–7[Abstract/Free Full Text]

5 Linden JVD, Wesslen O, Ekroth R, Tyden H, Ahn HV. Transcranial Doppler-estimated versus thermodilution-estimated cerebral flow during cardiac operations. J Thorac Cardiovasc Surg 1991; 102: 95–102[Abstract]

6 Rosenkrantz T, Stonestreet B, Hansen N, Nowicki P, Oh W. Cerebral blood flow in the newborn lamb with polycythemia and hyperviscosity. J Pediatr 1984; 104: 276–80[ISI][Medline]

7 Muizelaar J, Bouma G, Levasseur J, Kontos H. Effect of hematocrit variations on cerebral blood flow and basilar artery diameter in vivo. Am J Physiol 1992; 242: H949–54

8 Hudak M, Jones M, Popel A, et al. Hemodilution causes size-dependent constriction of pial arterioles in the cat. Am J Physiol 1989; 257: H912–H7[Abstract/Free Full Text]

9 Hurn P, Traystman R, Shoukas A, Jones M. Pial microvascular hemodynamics in anemia. Am J Physiol 1993; 264: H2131–5.[Abstract/Free Full Text]

10 Henry J, Meehan J. General properties of the circulation. In: Henry J, Meehan J, eds. The Circulation. Chicago: Year book Medical Publishers, Inc.; 1971; 15–23