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16. Fridovich I: Quantitative aspects of the production ofsuperox-ide anion radical by milk xanthine oxidase. J Biol Chem 245:4053^*057, 1970

17. McCord JM, Keale BB, Fridovich I: An enzyme-based theoryof obligate anaerobiosis. The physiological function of superox-ide dismutase. Proc Natl Acad Sci (USA) 68: 1024-1027, 1971

18. Gregory EM, Fridovich I: Induction of superoxide dismutaseby molecular oxygen. J Bacteriol 114: 543-548, 1193-1197,1973

19. McCord JM, Fridovich I: Superoxide dismutase: an enzymicfunction for erythrocuprein (Hemocuprein). J Biol Chem 244:6049-6055, 1969

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22. Player TJ, Mills DJ, Horton A A: Age dependent changes in ratliver microsomal and mitochondrial- NADPH dependent lipidperoxidation. Biochem Biophys Res Commun 78: 1397-1402,1977

23. Masugi F, Nakamura T: Effect of vitamin E deficiency on thelevel of superoxide dismutase, glutathione peroxidase, catalaseand lipid peroxide in rat liver. Internat J Vit Nutr Res 46:187-191, 1976

24. Chow CK: Glutathione peroxidase, catalase and superoxide dis-mutase in rat blood. Internat J Vit Nutr Res 47: 268-273, 1977

Quantitation of Carotid Stenosis with Continuous-Wave(C-W) Doppler Ultrasound

MERRILL P. SPENCER, M.D. AND JOHN M. REID, PH.D.

SUMMARY Two methods for determining the degree of stenoses developing on the origin of the internalcarotid were tested using non-invasive Doppler ultrasonic imaging (DOPSCAN) of the carotid bifurcations.Spectral analysis of Doppler audio recordings was utilized in determining the maximum frequencies foundwithin the stenosis, as well as the ratio of the frequency downstream to the stenosis, to the frequency within thestenosis. The theoretical relationships between blood flow, velocity, and pressure drop are defined for all gradesof stenosis and they predict that carotid flow will not be reduced unless the lumen diameter is less than 1.5 mm.At critical diameter reductions, below 1 mm, the frequencies in human carotids do not exceed 16 KHzbecause turbulence limits peak velocities. If the maximum systolic frequency exceeds 5 KHz, when 5 MHzprobes are directed at a 30° angle from the body axis, there is always present stenosis up to diameters of lessthan 3.5 mm by x-ray angiographic measurements. Frequency ratio studies confirm that plaque growth is notsymmetrical but they did not improve x-ray angiography correlations because of the limitations of x-ray inmeasuring cross sectional areas from projection films and limitations of the spot size of x-ray tubes.

Stroke Vol 10, No 3, 1979

THE ADVERSE CLINICAL EFFECTS of ather-osclerotic plaques on the carotid artery are manifest inthe patient's eye and brain through reduction of bloodperfusion following stenosis of the channel or by em-bolization from the site of the plaque. It is generallyagreed that more than one-third of strokes result fromcervical arterial disease and primarily from plaquesoccurring on the origin of the internal carotid artery.For stroke prevention the identification of carotidplaques and quantitation of stenosis is of primary im-portance.

Non-invasive diagnostic methods are needed toevaluate patients with symptoms of cerebrovascularinsufficiency because of the inherent dangers and costsof the alternative, x-ray contrast angiography. In ad-dition, they are needed for medical or surgical followup in the study of the natural history of the athero-sclerotic plaque. With the general availability of non-invasive Doppler ultrasound, which provides bloodvelocity signals from the carotid arteries, it is impor-tant to fully utilize this information to evaluate the

degree of stenosis and the attendant collateral circula-tion. This paper presents a system for determining thedegree of stenosis using the increased Doppler audiofrequencies within the stenotic segment.

Methods

Carotid blood velocity was measured with 5 MHzcontinuous-wave (C-W) directional Doppler ultra-sonic equipment designed and built in the Bioengineer-ing Center of this Institute.1 The ultrasonic probe con-sists of a dual-crystal lens-focusing transducermounted on a position sensing arm and directedtoward the carotid arteries at a 60° angle from thebody axis. With this equipment and procedure, a 1KHz Doppler frequency shift represents a bloodvelocity of 30 cm/sec. The probe is placed against theneck with intervening coupling jelly and the Dopplershifted frequencies are recorded. A Doppler image ofthe carotid bifurcation (DOPSCAN),* including thecommon carotid and its external and internal

From the Institute of Applied Physiology and Medicine, 701 Six-teenth Ave., Seattle, WA 98122

•Obtainable from Carolina Medical Electronics, King, NorthCarolina.

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DOPSCAN FOR CAROTID STENOSIS/Spwicer and Reid 'ill

SYSTOLICI mo i

The mean velocity (v) was calculated from the follow-ing equation:

v =

N O R M A L I N T E R N A L C A R O T I D

FIGURE I. Doppler spectrum of frequencies (velocities) inthe normal internal carotid.

branches, is developed.2"4 Magnetic tape recordingsare made of selected audio signals for later spectralanalysis. Diameters calculated from Doppler findingswere compared with the minimal diametermeasurements found on x-ray contrast angiographicfilms.

Three methods were tested to determine the lumencross section at the origin of the internal carotidartery. All methods used spectral analysis! of Dopplersignals to determine the maximum systolic frequency(fm«i), (fig. 1). Though the mean frequency (f) ispreferable because it represents the mean velocity (v),fmai is substituted because it can be more accuratelydetermined than f which must be derived from the zerocrossing meter. Though zero crossing meters_ areavailable, their accuracy in determining f isquestionable.6

The first method tried, and the simplest to perform,utilized only the greatest frequency found at the site ofthe stenosis, flmai. The other 2 methods utilized thefrequency ratio between the internal carotid signalsfound at the angle of the jaw f^a*. downstream to theorigin, and fln?ax (fig. 2).

The theoretical basis for our first method was theconcept that a decreasing cross sectional area within astenotic segment would produce an increase invelocities and corresponding Doppler shifted frequen-cies. Theoretical model predictions were carried out todetermine the maximum range of Doppler frequenciesthat might be expected with internal carotid stenosis.We assumed a linear relationship between resistance(R) and blood flow (F).* R was calculated in dyne-centimeter-seconds from the following equation:

Rdy.c

Where i) represents the viscosity of the blood (nominalvalue of 0.04 Poise), L represents the length of thestenotic segment (nominal value of 0.2 cm) and rrepresents artery radius. R is converted to clinicalterms of mm Hg/ml/min by dividing by 79,380, andflow for any given stenosis was calculated from:

F = AP/R

tKay Elemetrics Corp, Off-line Spectral Analyzer, Pine Brook,New Jersey.

F/60irr*

The calculations considered a network model (fig. 3)in which the origin of the internal carotid artery wasrepresented by a linear resistance R,.

We also compared both the relationship of the ratiofi/fi and the Vft/U to the minimum x-ray diameterusing the principle of continuity of flow in the un-branching internal carotid artery (fig. 4). The rationalefor using fs/f,, without a square root function, is basedon the concept of plaque development on one side ofthe artery lumen and growing across the artery lumen.The differences expected from symmetric andasymmetric stenosis are illustrated in figure 5. Inorder to test which of these assumptions was most cor-rect the x-ray angiographic diameter at the origin ofthe internal carotid was compared with each frequen-cy ratio method.

X-ray contrast angiographic films were analyzedand compared with Doppler frequencies from 95 inter-nal carotid arteries from 64 patients, representing allusable studies by both methods in 2 Seattle vascularlaboratories during one calendar year. The minimumdiameter found at the origin of the internal carotidwas measured with a micrometer utilizing all availablefilms. If no stenosis was present the diameter wasmeasured at a distance of 0.5 cm from the bifurcationto represent Di. D2 was measured 5-6 cmdownstream.

From the best available films the minimum D!could not be measured with certainty within 0.5 mm,and greater uncertainty was often present. The leastmeasureable x-ray diameter was found, using phan-tom wires, to be 0.8 mm and probably representedlimitations caused by cathode spot size. Themagnification ratio of the x-ray projections was foundto vary, from 1.2 to 1.4 but adjustments were notmade for this error in correlation considerations.

Results

Model Predictions

Figure 6 represents the theoretical relationshipsbetween F, v, and lumen diameter (D) as well as theexpected mean Doppler frequency in KHz. Controlflow was set at 300 ml/min, Pt at 100 mm/Hg andbrain resistance (R2) and resistance of the collateralchannels (R,) were assumed to be equal at 0.333PRU's. It is apparent, from the model data, that in-creasing degrees of axisymmetric stenosis will notdiminish the blood flow through the artery below 10%of its control value until the diameter within thestenosis is less than 1.5 mm. During this early phase,termed Grade I stenosis, blood velocity and corre-sponding Doppler frequencies progressively increasein an exponential manner proportional to the inversesquare of the diameter. Below a diameter of 1 mm acritical phase is reached when a small decrease in

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128 S T R O K E V O L 10, N o 3, M A Y - J U N E 1979

1 L Jk, k

L J•ii . n

i

D O P S C A N S P E C T R A A N G I O G R A M

FIGURE 2. DOPSCAN image of the carotid bifurcation in a patient with a "tight" stenosis ofthe internal carotid. Frequencies within the stenosis (fj are elevated while down-stream fre-quencies (fj) are decreased below normal.

CAROTID BRAIN

3 COLLATERALS R4FIGURE 3. Resistive model for internal carotid circulationto the brain. Normal flow through J?, is also primarilythrough R, with a small amount through R4.

Since : f1A1 -

FIGURE 4. Rationale for calculating arterial stenosisfrom Doppler signals. D,, represents the diameter at theorigin of the internal; D, represents the downstream diam-eter; f represents the mean Doppler frequency found withinthe stenotic segment on the origin of the internal carotid;and ft represents the mean Doppler frequency downstreamto the origin.

lumen diameter produces a great decrease in bloodflow. This critical phase is termed Grade III stenosis.In Grade III stenosis, velocity reaches its greatestvalues but variations in collateral resistance aroundthe stenosis greatly affects F and v. In Grades IV andV, velocities decrease again through the frequencyrange of Grades I and II and flow is greatlydiminished to zero at occlusion.

AXISYMMETRIC

STENOSIS

0 1 2 3 4 5

DIAMETER (mm)FIGURE 5. The difference in relationship between diameterand cross sectional area for asymmetric and axisymmetricstenosis.

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DOPSCAN FOR CAROTID STENOSIS /Spencer and Reid 329

* * A/(Decrease In Crosseclional

Area

LUMEN DIAMETER* (mm)

FIGURE 6. Theoretical relationships between bloodvelocity and flow in graded stenosis calculated from themodel of Figure 4. Stenosis geometry is assumed to besmooth and axisymmetric. The effects of turbulent flow inabrupt stenosis is not considered. Settings for collateral andbrain vascular resistance are in the normal range forhumans.

FIGURE 7. Maximum systolic frequencies found inpatients with normal and stenotic carotid diameters. Thetheoretical relationship expected in smooth (non-abrupt)stenosis, re-plotted from figure 6, is also shown. Thedifference in highest frequencies attainable may be due toturbulence in patient arteries causing loss of head pressureand reducing velocities.

Carotid Diameters and Doppler Frequencies

The spectral distribution of frequencies represent-ing blood velocities in the internal carotid arteries of ahealthy subject, age 21, are seen in figure 1, where aconcentration of energy near the maximum frequencyedge (fmax) of the spectrum provides the normal"smooth" or "breezy" quality to the audio signal.

Figure 7 illustrates the relationship between fmax

and the x-ray minimal diameter in each of 95 humaninternal arteries. The horizontal lines representgreater than usual uncertainty of the x-raymeasurements. For 77 diameters greater than 1.5 mm,D, = 8.77 f"0-67 with a coefficient of correlation of 0.74.The close correspondence of fmax and D! to the inversesquare relationship is apparent. Progressive deviationfrom the theoretical relationship develops progres-sively but becomes severe when the diameter de-creases below 2 mm. No stenoses less than 0.5 mmwere found on the films as predicted from the phan-tom measurements. The highest Doppler frequenciesmeasured were 15-16 KHz and occurred in the diam-eter range of 0.75 to 2 mm.

Frequency Ratios

Figure 8 illustrates the first results obtained whenwe utilized the square root of the frequency ratio

In this method, the downstream diameter D2

is assumed to be 5 mm because a series of x-ray filmmeasurements determined that this figure representedthe median diameter of the internal carotid at the

X-RAV DIAMETER

FIGURE 8. Relationship between x-ray angiographicdiameters and Doppler diameters calculated from the squareroot of the Doppler frequency ratio. This analysis assumesaxisymmetric stenosis and the failure of fit is shown.

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330 STROKE VOL 10, No 3, MAY-JUNE 1979

ocUJ

•

DO

PP

l)S

IS

zLU

0

20

40

60

80

. 20 .40

Di/Dj

• • • . •

-

• • • /

/ " • . •

/ • 1 • j

.60 .80 1.00I I I

/ '

I I 1

1.20I /

-

i

f,

1.40

1.20

1.00

.80

.60

.40

_ .20

100 80 60 40 20 0

% STENOSIS X-RAYFIGURE 9. Relationship between Doppler frequency ratios/2//, and x-ray diameter ratios Dt/D2 in normal and stenoticinternal carotid arteries. The use off2/fi assuming stenosesare asymmetric without a square root function improves thefit between x-ray and Doppler data. Horizontal bars repre-sent unusual uncertainty in measuring the x-ray diameter.

The most important problem with x-rayresolvability of stenotic lesions is its inability to repre-sent the cross sectional area of a stenotic segment.Because plaques do develop on one side of the arteryand expand asymmetrically toward the axis, becausethe number of x-ray projections are limited andresolvability appears greater than 0.8 mm, the truecross sectional area of the lumen cannot be measured.The Doppler frequency, which is related to velocity, is,however, closely related to the cross sectional area aswell as to volumetric flow. The differences betweenDoppler and x-ray may be expected on the basis of x-ray inaccuracies alone, and the final test of Dopplerawaits a better standard for comparison.

Precision in measurement of carotid stenosis isprobably only needed for the higher degrees ofstenosis where blood velocities are low, resulting indangers of large thromboembolisms. In this situa-tion, Doppler may find its greatest role in strokeprevention measures. For stenoses greater than 70%(diameter 1.5 mm or less), predicted by a Dopplersystolic frequency of 10 KHz or greater, Dopplerprovides a 63% sensitivity, 85% specificity, and anoverall accuracy of 95%.

angle of the jaw. The best fit regression line projectedan intercept of the Doppler diameter axis causing anunderestimation of the x-ray diameter in higherdegrees of stenosis.

Results using fj/^ without the square root functionare shown in figure 9. The positive intercept iseliminated leaving only the random variations. A testfor closeness of fit to the line of identity gave the figureof 0.70, allowing an accuracy ± 20% in 80% of thecases. For diameter ratios greater than 1.4, where anunusually large bulb occurs at the origin of the inter-nal carotid, a complete loss of correlation occurred. Inthese situations, of course, stenosis is not present.

Discussion

The findings that the Doppler frequency ratio,rather than its square root, provides a better predic-tion of the least x-ray diameter, confirms the obser-vations of both pathologists and radiographers thatplaque development is, in fact, asymmetric. Thoughfigure 5 illustrates the relationship between the crosssectional area and the least diameter in only one typeof asymmetric stenosis, many variations in the form ofasymmetry produce a similar effect and all differ fromthe axisymmetric case by lying closer to a linear rela-tion than does the axisymmetric case.

Acknowledgment

This research was supported by the National Institutes of Health,Grant #HL 19341. We thank the Departments of Radiology at theProvidence Medical Center and Northwest Hospital in Seattle fortheir cooperation. The skill of clinical physiology technicians,Sheryl Clark, Lou Granado, Dave Moseley, John O'Brien, andKarmann Titland is acknowledged. The special encouragement ofDrs. Edwin C. Brockenbrough and George I. Thomas has greatlyenhanced the quality of this study.

References

1. Reid J, Spencer M: Ultrasonic Doppler technique for imagingblood vessels. Science 176: 1235-1236, 1972

2. Spencer M, Reid J, David D, Paulson P: Cervical carotid imag-ing with a continuous-wave Doppler flowmeter. Stroke 5:145-154, 1974

3. Spencer M, Brockenbrough E, Davis D, Reid J: Cerebrovascularevaluation using Doppler C-W ultrasound. In White D, Brown R(eds) Ultrasound in Medicine. New York, Plenum, 1976

4. Thomas G, Spencer M, Jones T, Edmark K, Stavney L: Non-invasive carotid bifurcation mapping — its relation to carotidsurgery. Am J Surg 128: 129-314, Feb 1974

5. Reneman R, Spencer M: Difficulties in processing of ananalogue Doppler flow signal; with special reference to zero-crossing meters and quantification. Cardiovascular applicationsof ultrasound. In Reneman R (ed) Chap. 3, 32 Amsterdam-London, North-Holland Publishing Company, 1973

6. Spencer M, Denison A: Pulsatile blood flow in the vascularsystem. In Hamilton (ed) Handbook of Physiology, AmericanPhysiology Society, 1963

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M P Spencer and J M ReidQuantitation of carotid stenosis with continuous-wave (C-W) Doppler ultrasound.

Print ISSN: 0039-2499. Online ISSN: 1524-4628 Copyright © 1979 American Heart Association, Inc. All rights reserved.

is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231Stroke doi: 10.1161/01.STR.10.3.326

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