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Catheterization and Cardiovascular Diagnosis 12:317-323 (1986)

Intravascular Blood Velocity in Simulated Coronary Artery Stenoses

David Kilpatrick, MD, and Stephen 6. Webber, 6 Med sci (Hons)

The profiles of blood velocity within arterial stenoses have been measured using fiber optic laser Doppler anemometry (FOLDA). The arterial stenoses were created in arteries and tubes of similar size to human coronary arteries and were perfused in vitro at pressures and flows typical of those in the human circulation.

At very low flow rates, flow and peak velocity are linearly related, and thus peak velocity measurement can predict internal cross-sectional areas accurately. With higher flow rates, the intravascular velocities are not linearly related to flow and cannot be used to measure internal cross-sectional area. This is due to flattening of the velocity profile at both more severe stenoses and higher flow rates.

Key words: velocity profile, laser Doppler anemometry, fluid dynamics, assessment of stenosis severity

IN T RO D U CTlO N

In assessing coronary artery disease, the angiographic appearance of a stenosed artery in a single plane is widely used. The severity of the stenosis is usually assessed from the plane that shows the greatest degree of narrow- ing and has been shown to be inaccurate in some patients [I ,2]. A potential method for increasing the accuracy with which stenosis severity can be calculated is to measure the mean intravascular velocity before and within the stenosis and to then use the principle of conservation of flow to calculate the ratio of cross-sectional areas. The ratio of the cross-sectional areas of a stenosed region and a normal region is the inverse of the ratio of the respec- tive mean velocities.

To examine the potential of this method of stenosis assessment, we have used the technique of fiber optic laser Doppler anemonietry (FOLDA) [3,4] to construct velocity profiles through stenoses in in vitro arteries. In addition, we have examined the relationship of mean velocity to measured peak velocity in a series of experiments to determine if FOLDA can be used to calculate the cross-sectional area of a coronary artery stenosis.

METHODS The in vitro system for the measurement of pressure,

flow, and velocity across narrowings in vessels is shown in Figure 1. For flow at a constant perfusion pressure, a reservoir of adjustable height was used. The pressure height was stabilized within the closed reservoir by an air inlet pipe set at a level below that of the blood. This sets the perfusion height at the level of the base of the inlet pipe and produces constant perfusion pressure for different levels of blood within the reservoir.

For constant-flow experiments where only low flow rates were needed. a syringe pump (Braun 871104) was used. This pump and the reservoir were connected through a versatile tap system using wide-bore tubing (minimum bore 3.5 mm) to the test section of artery, which was established 10 cm downstream from a tap. This distance was sufficient to allow reformation of the parabolic profie of laminar flow with velocities of up to 1 m/sec. The pressure gradient was measured by a fluid- filled differential manometer also made from wide-bore tubing. Flow rates were measured by timing the collec- tion of a volume of blood. An electromagnetic flow meter (NARC0 RT500) with cannulating flow probe was also used in some experiments. Only steady flow has been used in these experiments. All measurements were made at equilibrium, when the prescure differences were steady for at least 5 sec. Any changes in the pressure difference during the period of timing were considered to invalidate that run, and the run was repeated. These changes in pressure typically occurred when a clot formed within a severe stenosis or the reservoir emptied during the run.

From the University of Tasmania, Hobart, Australia.

Received October 20, 1985; revision accepted May 12, 1986

This work was supported by a grant from the N . H . and M.R.C. of Australia. D. Kilpatrick was supported in part by a grant from the Eileen Andrew Foundation. S . Webber was supported by an N.H. and M.R.C. student grant and an AMSA-Lilley vacation rescarch fellowship.

Address reprint requests to D. Kilpatrick, Department of Medicine, University o€ Tasmania, 43 Collins Street, Hobart, Auslralia, 7000.

C3 1986 Alan R. Liss. Inc.

318 Kilpatrick and Webber

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Fig. 1. A block diagram of the experimental system as set up for a single stenosis.

All experiments were performed using whole human blood from the Blood Bank. Blood was collected in anticoagulant citrate phosphate dextrose solution. (TUTA Laboratories) and stored at 4°C. All experiments were performed at room temperature (23"C), and the blood was allowed to equilibrate to this temperature before experiments were commenced. In addition, the blood was continuously stirred by a magnetic stirring device (Scientific Equipment Manufacturers).

Blood velocity was measured within the artery and in the stenosis using fiber optic laser Doppler anemometry [3,4]. Both the position of the test region and the position of the fiber were under the control of three-dimensional micromanipulators (Prior Laboratories, UK). This enables the construction of both radial and axial velocity profiles. The fiber optic technique uses a fiber (core of 50 p and external diameter of 125 p) that can be inserted into the vessel. The light is transmitted along the fiber, through the tip of the fiber and is then reflected off particles within the fluid and collected by the same fiber. The penetrance of the laser into the fluid is a function of the geometry of the fiber termination and the density of the particles within the fluid. For these experiments, the fiber was terminated by fracturing the tip, with the result that the termination was not always absolutely perpendic- ular to the fiber. In most instances, a maximum pene-

trance in blood of 1 mm giving a volume of measurement of 200,000 p was obtained. The exact distance that the light penetrated the blood was not tested for each run in this publication but is the subject of continuing research. A recent theoretical treatment of the fiber optic technique discusses fully the penetrance of the laser technique in relation to fiber parameters [5]. An avalanche photodiode detection system (TIEF 83 [Texas Instruments] Ava- lanche Photodiode and LH0082 [National] transconduct- ance amplifier) was used with the fiber optic anemometer to give a band width of 6 mega-Hz, equivalent to a velocity of 1.4 m/sec with blood. Spectral analysis was performed on a Spectral Dynamics SD350 and SD351 fast Fourier transform analyser.

Both plastic tubing (polyethylene and polyvinyl) and freshly dissected sheep carotid arteries (3-4 mm diameter) have been used in these studies. Pressure flow studies are comparable for both arteries and plastic tubes. The arteries used in these experiments were dissected from sheep during a different series of experiments and were undisturbed before their dissection. They were kept in normal saline at 4°C and used as soon as possible after they had been collected. Side branches were tied and the arteries stretched so that severe buckling was not observed on perfusion. At the time of perfusion experiments, no arteries were observed to show independent

Blood Velocity in Coronary Artery Stenoses 319

0 vasomotor activity, and they were not exposed to vaso- active medications. All experiments were conducted with steady-state flow.

The stenoses in the arteries were induced by constrict- ing the artery by a matrix band occluder (a dental device used for paclung amalgum) using a 5-mm wide strip of metal foil.

The machined brass stenoses are abrupt, with both leading and trailing internal edges smoothed.

Velocity profiles at a stenosis were constructed by shifting the position of the fiber optic probe within the stenosis in steps of 0.1 mm both horizontally and verti- cally. These profiles were constructed at 1-mm intervals along the stenosis. Axial profiles have been Constructed by advancing the fiber optic probe through the stenosis and adjusting the horizontal and vertical positions to obtain the maximum velocity for each position along the axis of the vessel. Velocity profiles were measured on 10 stenoses, but each experimental run was under different conditions, so that the presented results are of a typical post-stenotic profile. In the experiments that determine the maximum velocities at which flow profiles remain parabolic, the results presented are selected from a series of experiments through a range of different conditions. The peak velocity in the stenosis was measured at varying rates of flow and compared with velocity calculated from the flow rate and the area of the stenosis (assuming parabolic flow).

RESULTS Calibration of FOLDA

Figure 2 shows a calibration curve for the fiber optic laser Doppler anemometer for blood flowing in an unobstructed glass tube 5 mm in diameter at velocities typical of velocities in human coronary arteries. The velocity measured is the peak velocity obtained by racking across the vessel in two dimensions. When these data were fitted to a straight line, a regression analysis indicated that 99.8% of velocity variation was associated with the variation in flow rate. The slope of this line is proportional to the cross-sectional area of the glass tube.

Velocity Profiles at an Arterial Stenosis

1. Cross-sectional profiles. Figure 3 represents a typical cross-sectional profile drawn at a stenosis in a sheep carotid artery. The profiles start at the distal end of the stenosis and illustrate the region downstream from the stenosis. In this example, the stenosis was provided by the matrix band occluder. The FOLDA technique as used here does not differentiate forward from reverse flow, and it is possible that the circumferential flow towards the periphery is reversed. This figure demonstrates the potential of this technique to fully measure intravascular profiles.

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Fig. 2. Calibration curve of fiber optic laser Doppler anemometer. Peak velocity in a 5-mm diameter glass tube is compared to flow rate. 1 mlsec velocity is represented by 4.1-MHz Dop- pler shift. Statistically, these data were fitted to a straight line; regression analysis indicated that 99.8% of velocity variation is associated with variation in the flow rate.

2. The maintenance of a parabolic profile in laminar flow. The velocity flow curves for two stenoses are plotted in Figure 4. The stenoses are machined brass .5 cm long and 0.97 mm and 1.57 mm diameter, respec- tively, in a 3-mm diameter polyethylene vessel. The predicted parabola based on laminar flow is plotted for each set. In each curve, predicted velocity and measured velocity were identical at low rates of flow, but the measured velocity deviated from the predicted velocity increasingly as the flow increased. Figure 5 shows the velocity profiles at points on each curve recorded at low rates of flow. Multiple profdes are measured from different axial positions along the stenosis. (The nonzero measurements on the vessel wall are typical measurements of velocity at a boundary using this technique and probably represent an artifact.)

3. Axial profiles. Axial profiles constructed through an abrupt machined stenosis are outlined in Figure 6. The stenosis in Figure 6 was produced by a machined


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Fig. 3. Velocity profiles beyond an 82.2% area stenosis in a sheep carotid artery. Each profile is constructed by FOLDA velocity measurements at 0.1 mm intervals in the cross-sectional plane. This representation is plotted with perspective.

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Fig. 4. Calculated and measured velocities are compared for two stenoses, 91% and 60%. The straight lines represent predicted velocity based on a parabolic velocity profile within the stenoses. The velocity points (measured by FOLDA) represent the actual peak velocities recorded.

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DISCUSSION

One potential method of improving the evaluation of coronary artery severity in patients is to record intracor- onary velocities and to calculate from these the relative changes of internal cross-sectional area. For this technique to be successful, both a method of intravascular velocity measurement must be developed and the relationship of the measured velocity to the mean velocity known. The technique of FOLDA enables velocity measurements within the vessels. The results presented in this paper both show the potential of the FOLDA technique and establish the conditions required to relate FOLDA velocity measurements to mean velocity.

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Fig. 5. Profiles of velocity through the stenoses in Figure 4. For each stenosis, a calculated parabolic profile is constructed. The calculated profile is shown in open squares for each set of curves. The curves drawn with other symbols represent FOLDA measurements at intervals through the stenosis. Both of these sets of curves are constructed using very low rates of flow and are taken from the curves (Fig. 4) at the appropriate velocity point.

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At typical flows in human coronary arteries, the velocity profiles flatten into the stenosis, and thus the parabolic profile of laminar flow in a straight tube is no longer applicable. This flattening of the velocity profile has been demonstrated in Figures 4 and 5 . As the velocity increases, the measured curve deviates further from the predicted curve. This deviation both is greater with more severe stenoses and occurs at lower flow rates. At the velocities and dimensions used, this deviation represents the flattening of flow profiles predicted by Lee and Fung [8]. It is possible to have deviations of flow if instabilities occur; however, these instabilities were not seen in the measured profiles and would not be predicted at the velocities and with the dimensions of the vessels used in these experiments. In our experiments, the tube lengths were chosen to allow complete reformation of laminar flow before any stenosis. The stenoses were chosen to be of typical size for human coronary artery stenoses. Fully formed parabolic flow within a stenosis would not be expected with a stenosis length much less than 10 tube diameters.

Deshpande et a1 [9] derived solutions for steady flow at an axisymmetric stenosis; and these, although not including eddies or local instabilities, predict our experimental observations satisfactorily.

These data are important because they demonstrate that the peak velocity of flow within a stenosis cannot be used to calculate the cross-sectional area of the stenosis in vivo unless the exact velocity profile is known. A comparison of the mean velocity prior to and within a stenosis will enable the calculation of the cross-sectional area of a stenosis, but the technique of measurement of mean velocity is difficult. Fiber optic Doppler anemometry mea- sures a small, pinpoint velocity and cannot be used to predict mean velocity unless the exact profile is known.

Parabolic flow does occur within stenoses at very slow rates of flow. When the flow rate is very slow, the velocity to flow rate relationship is linear, with a slope of 2. This is illustrated at the beginning of the curves in Figure 4. This principle has been used to measure the cross-sectional area of applied stenoses such as those applied by the matrix band occluder. When using this technique, the assumption that the velocity profile is parabolic can be tested by doubling the flow rate. If on doubling the flow rate, the velocity does not double, then the peak velocity is no longer twice the mean velocity, and as a corollary of this, the velocity profiles within the stenosis are no longer parabolic. By measuring the spatial peak velocity at very slow rates with FOLDA, accurate measurements of diameter can be made.

Providing these conditions are met, the FOLDA technique is satisfactory for measuring the cross-sectional area of a stenosis. For severe stenoses, up to 98%, flow rates as low as .003 ml/sec were required for maintenance of the parabolic profile. The problems associated

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Fig. 6. An axial velocity profile proximal to a fixed machined stenosis. Blood flow is from left to right. The inset diagram is in the correct position on the horizontal axis and represents the internal structure of the applied stenosis. The velocity is represented by the closed circles and increases 2 mm before the actual stenosis is reached.

FOLDA

The technique of fiber optic laser Doppler anemometry allows the reconstruction of velocity profiles within small vessels. From reconstructions such as in Figure 3, it is possible to describe the pattern of flow. In this case, the curves demonstrate the maintenance of laminar flow within moderate stenoses. Outside the central stream of flow, some minor asymmetries were recorded, repre- senting flow patterns within the region of separation. This particular technique does not differentiate the direction of flow except in a complex change of spectral shape. Other FOLDA systems [6] can detect changes in flow direction. At the edge of the artery, the velocities are nonzero. This is probably an artifact related to the interaction between the probe and the boundary layers.

Velocity Profiles

The velocities demonstrated in Figure 3 are measured from a system with pressure gradients sufficient to pro- duce an average velocity in the order of 15 cmhec in a straight tube, slightly slower than the maximum phasic velocity in an unobstructed coronary artery. At higher rates of flow (with average velocities in a nonstenosed tube of 40 cm/sec), the peak velocity rapidly exceeded 1.4 m/sec, which is the limit of the spectrum analyser, and thus a quantitative analysis of flow at all points within the profile was not possible. Mates et al [7] constructed profiles within a large-scale model that are qualitatively similar to these profiles. The fiber optic technique enables the construction of profiles within small vessels without the need for modeling. These profiles are also similar to those derived from theoretical solutions [8].


with this measurement are mainly related to the position of the fiber tip within the vessel. Our system of moving the fiber across the vessel to pick the peak velocity is not directly applicable to in vivo use.

In the printed velocity profiles (Figs. 3 and 5 ) , the velocities at the wall are nonzero. This effect is assumed to be an interaction between the vessel wall and the probe. The degree of variability in the profiles at different points in the stenosis is as recorded and could be due to second-by-second variation in the flow rate, which occurs when whole blood is used as the perfusing fluid. Experimentally, the constant-pressure perfusion system we have used gives a much more steady flow than other perfusion systems tried, such as syringe pumps, which may show marked variability; (the advance of the plunger within the syringe barrel is never smooth).

Steady or Pulsatile Flow

The accuracy of FOLDA and its frequency response (3 msec/transform, approximately 300 Hz) is sufficient to document pulsatile flow. We have not studied pulsatile flow in this series of experiments; however, Young and Tsai [ 10,l I] have suggested that pulsatile flow is probably more stable than steady-state flow. Our reasons for studying the simplest form of flow are related to the greater accuracy with which one can establish the profiles when the potential variability of pulsatile flow is avoided. We thought it important to test and report the simplest case first.

Streaming of Flow The axial profile shown in Figure 6 demonstrates that

the velocity increases prior to the stenosis. This streaming of flow before the stenosis must leave a layer of relative stasis at the wall of the vessel proximal to the stenosis. These experiments have not demonstrated the streaming effect continuing into the stenosis because the blunting of the profiles tends to reduce the observed velocity. This would tend to cancel any effect of further physiological streaming within the stenosis, which would result in a physiological orifice with a smaller area than the anatomical orifice. Theoretical predictions of the degree of blunting for a known stenosis would enable a comparison of the predicted with measured velocities; however, the data required to characterize the stenosis sufficiently well to predict the flattening of the profile are only available in models.

Similar eddy regions are found downstream from the stenosis; however, these have been recognized before, and several authors have treated the problems of separation of flow mathematically [7,9-121.

Turbulence

The techniques of velocity measurement described are

methods are used. The first involves the measurement of peak velocity in a system with constant perfusion pressure and increasing the degree of stenosis. If turbulence occurs, then the velocity will suddenly fall from the laminar profile to a turbulent profile where, if turbulence is fully developed, the measured velocity is approximately 1.06 times the average velocity. This method tests the physiological situation because it reproduces the typical Reynolds numbers from the coronary arteries accurately. In our experiments, using the diameter of the stenotic region as the dimension, the Reynolds numbers were less than 200. The second method of detecting turbulence is to measure the velocity flow curves with increasing flow rates. This technique is not physiologic; however, providing flow rates do not exceed those seen for that degree of stenosis at typical perfusion pressures, then the technique is valid; and experimentally, it is easier to increase flow rates than to increase the severity of a stenosis. If turbulence were to be seen, the velocity-flow curve would show an incontinuity. This has not been observed in experiments to date. It is impossible to be exclusive with these experiments and predict that turbulence never occurs in a stenosed coronary artery. These results are consistent with those of Mates et a1 [7] and Young and Tsai [10,11] using scale models and also with the theoretical predictions of Forrester and Young [ 12,131 and Lee and Fung [8].

ACKNOWLEDGMENTS

We wish to thank Glenn McPherson for his statistical help, Stephen Walker for the extension to FOLDA, San- dra Petrie and David Lees for secretarial and artwork assistance. We are grateful to Graham Boyd, Julian Hoff- man, and John Tyberg for encouragement and advice.

REFERENCES

1. Grondin CM, Dydra I, Pasternac A, Campeau L, Bourassa MG, Lesperance J : Discrepancies between cineangiographic and post mortem findings in patients with coronary artery disease and recent myocardial revascularization. Circulation 49:703-708, 1974.

2. Hutchins BM, Bulkley BH, Ridolfi RL, Griffin LSC, Lohr FT, Piasio MA: Correlation of coronary arteriograms and left ventri- culograms with post mortem studies. Circulation 56:32-37, 1977.

3. Kilpatrick D: Laser fiber optic Doppler anemometry in the measurement of blood velocities in vivo. In “Computers in Cardiol- ogy.” New York, IEEE, 1980, pp 467-470.

4. Kilpatrick D, Tyberg JV, Parmley WW: Blood velocity measurement by fiber optic laser Doppler anemometry. IEEE Trans Biomed Eng 29: 142-145, 1982.

5 . Stern MD: Laser Doppler velocimetry in blood and multiply scattering fluids: Theory. Applied Optics 24: 1968-1986, 1985.

6. Kajiya F, Hoki N, Tomonaga G, Nishihara H: A laser-Doppler- velocimeter using an optical fiber and its application to local velocity measurement in the coronary artery. Experientia

suitable to detect turbulence even in small vessels. Two 37:1171-1173, 1981.

7. Mates RE, Gupta RL, Bell AC, Klocke FJ: Fluid dynamics of coronary artery stenosis. Circ Res 42: 152-162, 1978.

8. Lee JS and Fung YC: Flow in locally constricted tubes at low Reynold’s numbers. J Appl Mech 37:9-16, 1970.

9. Deshpande MD, Giddens DP, Mabon RF: Steady laminar flow through modelled vascular stenoses. J Biomechanics 9: 165-174, 1976.

10. Young DF and Tsai FY: Flow characteristics in models of arterial stenoses. (1) Steady flow. J Biomechanics 6:395-410, 1973.


1 I . Young DF and Tsai FY: Flow characteristics in models of arterial stenoses. (2) Unsteady flow. J Biomechanics 6547-559, 1973.

12. Forrester JH and Young DF: Flow through a converging-diverg- ing tube and its implications in occlusive vascular disease. 1 . Theoretical development. J Biomechanics 3:297-305, 1970.

13. Forrester JH and Young DF: Flow through a converging-diverg- ing tube and its implications in occlusive vascular disease. 2. Theoretical and experimental results and their implications. J Biomechanics 3:307-3 16, 1970.