Graph that demonstrates that volume flow will decrease during a Grade II & III stenosis (75% occlusion), as flow velocity first spikes before dropping during a Graft IV stenosis (90% occlusion).
Spencer P, Reid, J.M., Quantification of Carotid Stenosis with Continuous-Wave (C-W) Doppler Ultrasound, Stroke 1979;10:326-330.
3
Jongyeol Kim MD
A2V2V1A1
Rule of Continuity
A1V1 = A2V2
Jongyeol Kim MD
Flow Velocity
Blood Volume
600
500
400
300
200
100
% Decrease in Crossectional Area
LUMEN DIAMETER (mm)
% Decrease in Diameter80 4060 30 20
1 2 3 3.5 4 5
BLOOD FLOW
DO
PP
LE
R F
RE
QU
EN
CY
(K
Hz)
(ml/
min
) a
nd
(c
m/s
ec
)
Normal Diameter
Grade IGrade II
III
IV
V
18
20
14
16
10
12
6
8
2
4
0
36648496
00
Waveforms
Jongyeol Kim MD Jongyeol Kim MD
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Jongyeol Kim MD Jongyeol Kim MD
Jongyeol Kim MD Jongyeol Kim MD
Direct Effect1. Acute elevation of blood flow velocities
2. Flow disturbances
3. Decreased blood flow
Jongyeol Kim MD
upstream downstream
Direct effect
Jongyeol Kim MD
Indirect effect Downstream Flow disturbances
Damping waves
Low flow acceleration
Upstream Decreased velocity
Increased pulsatility
5
Jongyeol Kim MD Jongyeol Kim MD
Jongyeol Kim MD
DDx between ICA and ECA
ICA ECA
Wave form Low resistance High resistance
Caliber Larger Smaller
Branch No Yes
Temporal pulsation No response Response
Jongyeol Kim MDSchulz UGR, Rothwell PM, Major variation in carotid bifurcation anatomy. 2001;32:2522-2529
Jongyeol Kim MD
Principles of Doppler ultrasound
θ
V = (Fd C)/(2ft cos θ)
Fr Ft
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Ancillary
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326 STROKE VOL 10, No 3, MAY-JUNE 1979
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
19. McCord JM, Fridovich I: Superoxide dismutase: an enzymicfunction for erythrocuprein (Hemocuprein). J Biol Chem 244:6049-6055, 1969
20. Noguchi T, Cantor AH, Scott ML: Biochemical andhistochemical studies of the selenium-deficient pancreas in
chicks. J Nutr 103: 1502-1511, 197321. Sharma OP: Age related changes in lipid peroxidation in rat
brain and liver. Biochem Biophys Res Commun 78: 469-475,1977
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.
MethodsCarotid blood velocity was measured with 5 MHz
continuous-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.
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 DFIGURE 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.
ResultsModel 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
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 MFIGURE 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.
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 fmaxand 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 RatiosFigure 8 illustrates the first results obtained when
we utilized the square root of the frequency ratio
In this method, the downstream diameter D2is 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./
% 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.
DiscussionThe 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.
AcknowledgmentThis 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.
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
The Spencer’s Curve: ClinicalImplications of a ClassicHemodynamic Model
Andrei V. Alexandrov, MD
A B S T R A C T
Merrill P Spencer and John M Reid applied the Hagen-Poiseuillelaw, continuity principle, and cerebrovascular resistance to de-scribe a theoretical model of the relationship between theflow velocity, flow volume, and decreasing size of the resid-ual vessel lumen. The model was plotted in a graph that be-came widely known as the Spencer’s curve. Although derivedfor a smooth and axis-symmetric arterial stenosis of a shortlength in a segment with no bifurcations being perfused at sta-ble arterial pressures and viscosity, this model represents amilestone in understanding cerebral hemodynamics with long-lasting practical and research implications. This review summa-rizes several hemodynamic principles that determine velocityand flow volume changes, explains how the model aids inter-pretation of cerebrovascular ultrasound studies, and describesits impact on clinical practice and research.
of a classic hemodynamic model.J Neuroimaging 2007;17:6-10.
DOI: 10.1111/j.1552-6569.2006.00083.x
Received September 20, 2006, and in revised formSeptember 20, 2006. Accepted for publication Septem-ber 29, 2006.
From the Stroke Research and Neurosonology Program,Barrow Neurological Institute, Phoenix, Arizona.
Address correspondence to Andrei V. Alexandrov,MD, Stroke Research and Neurosonology Program,Barrow Neurological Institute, Suite 300 Neurology,500 West Thomas Road, Phoenix, AZ 85013. E-mail:[email protected].
“A theory is a good theory if it satisfies two requirements:It must accurately describe a large class of observations on thebasis of a model that contains a few arbitrary elements, and itmust make definite predictions about the results of future obser-vations.”Stephen W. HawkingA Brief History of Time
Introduction
Merrill P Spencer and John M Reid applied the Hagen-Poiseuille law, continuity principle, and cerebrovascu-lar resistance to build a hypothetical flow model with aview to illustrate the relationship between arterial bloodflow velocities, flow volume, and decreasing size of theresidual lumen as it applies to the internal carotid artery(ICA).1 In 1979, they published a simple and clear graph(shown here in Fig 1) that has since been reproducedin many textbooks, including major textbooks on cere-brovascular ultrasound.2,3 This model has since beenwidely used for interpretation of cerebrovascular ultra-sound studies as means of explaining the velocity behav-ior with various degrees of the ICA and, most recently,intracranial arterial stenoses.4
This model, now known as the Spencer’s curve, rep-resents a milestone in understanding cerebral hemo-dynamics that has long-lasting practical and researchimplications. This review summarizes several hemody-namic principles that determine velocity and flow vol-ume changes, explains how the model aids interpretationof cerebrovascular ultrasound studies, and describes itsimpact on clinical practice and research.
Key Principles of Hemodynamics
Reflected in the Curve
The Spencer’s curve is a polynomial curve of the third or-der since the predicted arterial blood flow velocity showsboth linear and nonlinear components in its rise with asubsequent decrease to the zero level.5 This means that
Copyright ◦C 2007 by the American Society of Neuroimaging 6
Fig 1. The Spencer’s curve (reproduced with permis-sion from Spencer MP, Reid JM. Quantitation of carotidstenosis with continuous wave Doppler ultrasound. Stroke1979;10:326-330).
the peak systolic velocity (PSV) is inversely proportion-ate to several functions of the residual lumen diameter(d ):
PSV ∼ 1d + d 2 + d 3 . . .
.
An explanation how the first and second powers of vesseldiameter influence the velocity behavior is provided be-low. The fourth power of the vessel diameter [d 4 = (2r)4,where r is the vessel radius], is also likely to play a role asit directly influences flow volume and resistance to flowas it will be shown below. However, it is the cubic func-tion (d 3) that really explains the turn of the curve fromthe upslope down to the downslope with the most severevessel narrowing. Higher powers of radius may also playa role but their contribution in construction of the modelis practically negligible.
Spencer and Reid used a vessel with straight walls andno bifurcations in their model of an axis-symmetric andsmooth-surface arterial stenosis. In this situation, the flowvelocity and cross-sectional areas (A) are linked in theso-called continuity principle2:
A1 x PSV1 = A2 x PSV2
PSV2
A2
PSV1
A1
Fig 2. A correlation of the ICA peak systolic velocity andpercent stenosis on arteriography in the NASCET trial (mod-ified from Eliasziw M, et al Stroke 1995;26:1747-1752). (A)Nearly all nonstandardized measurements of ICA PSV fit un-der the area of a hypothetical Spencer’s curve; (B) A com-bination of hypothetical Spencer curves that reflect individualperformance of participating laboratories in the NASCET trial.
Since fluid is noncompressible and since the applied pres-sure remained the same in the Spencer and Reid model,the maximum stenotic (PSV2) velocity increases by theamount inversely proportionate to the squared functionof the residual vessel diameter:
PSV2 = A1PSV1
A2, or PSV ∼ 1
�r 2 , or1d2 .
Hence, the prestenotic (PSV1) velocity is not shown inthe graph (Fig 1), but the graph contains the initial ve-locity value with 0 degree stenosis, or normal vessel pa-tency. This could be used as a reference point (or range)in subsequent estimations of disease severity by the ve-locity changes. As discussed below, subsequent researchshowed that velocity ratios could complement absolutemeasurements of the maximum velocity despite the pres-ence of bifurcations.
Flow acceleration begins at the stenosis entrancewhere the pressure energy of flow (ie, blood pressure) is
Alexandrov: Clinical Implications of a Classic Hemodynamic Model 7
converted into the kinetic energy of flow with increasedvelocities. This conversion of energy is described by theBernoulli effect:
P1 − P 2 − �P = 1/2� (V 2
1 − V 22 ),
where � is the density of the fluid that has not beencommented on but presumably remained stable in theSpencer and Reid model.1 The velocity changes are there-fore mainly driven by the arterial pressure (P ) gradientand the size of the residual lumen. Assuming that arterialblood pressure remained constant across various degreesof the carotid stenosis, the model showed that the initialPSV increase compensated for the flow volume throughthe residual lumen (Fig 1), yet velocity should not beequated with flow volume even though both are drivenby the pressure gradient. Further PSV increase with se-vere stenoses becomes insufficient, and the flow volumestarts to decrease particularly with ≥80% stenosis (Fig 1).Hence, the commonly used term “hemodynamically sig-nificant” stenosis refers to a significant pressure or flowvolume drop across the stenosis that prompts recruitmentof collateral flow to compensate for this arterial lesion.
This flow volume decrease will occur particularly if thecerebrovascular resistance also does not decrease distalto a severe stenosis, as it was assumed for simplicity ofthe model. Notably, the flow volume per unit of timedirectly depends on the pressure difference described inthe Hagen-Poiseuille law:
Flow volume = �(P1 − P2)r8�L
4
where P 1 is the pressure at the beginning and P 2 is thepressure at the end of the flow system, r is the radius ofthe lumen, � is a constant, � is the fluid viscosity, and Lis the length or distance that flow has to travel betweenthe pressure points.
In the Spencer and Reid model, no compensatory post-stenotic vasodilation was introduced and the fluid viscos-ity as well as the length of the arterial stenosis also re-mained stable. Thus, an axis-symmetric, smooth-surface,presumably short-length and circular arterial narrowingproduced, not surprisingly, a perfect correlation betweenthe arterial flow velocity, flow volume, and increasingdegree of the carotid stenosis under these controlled andideal circumstances. The model, based on a few elements,was proposed to predict the arterial flow velocity behav-ior across the entire spectrum of carotid stenosis, and toderive diagnostic criteria for spectral Doppler ultrasoundfor grading the stenosis.1
Interpretation of Cerebrovascular Ultrasound
Studies
Application of hemodynamic principles to interpreta-tion of vascular ultrasound studies is a complex taskthat requires careful clinical and pathophysiological con-siderations. In reality, most arterial stenoses are axis-asymmetric with irregular surface, and have variable le-sion length and compliance of the vessel wall. The bloodviscosity, pressure, and distal resistance also vary betweenpatients and within an individual over time. Therefore,the Spencer’s curve could best serve as a guide rather thana source of actual velocity values for grading an arterialstenosis. In fact, Spencer and Reid applied this model intheir own exploration of the predictive value of spectralDoppler measurements in 64 patients against cerebral an-giography to identify the size of the residual lumen andpercent arterial stenosis. They achieved good results forultrasound prediction of the severe ICA disease in theirlaboratory.1 However, the actual frequency parametersfound in their study and the proposed grades of an ar-terial stenosis were not directly adopted into practice atother laboratories since direct and angle-corrected ultra-sound imaging methods were introduced6 and the needfor further intralaboratory validation was emphasized(www.icavl.org). Many subsequent independent valida-tion studies have been performed in this important clini-cal field laying foundation for the 2003 multidisciplinaryconsensus criteria.7,8
However, the model reflected the general directionof hemodynamic changes with carotid disease and, as itwill be shown below, it did survive the test of time as abasis to explain individual hemodynamic changes and tounderstand the results of clinical research.
To interpret any given blood flow velocity value, onemust consider whether this velocity was found on theupslope or on the downslope, or “the other side” of theSpencer’s curve. For example, an abnormally elevatedflow velocity is most likely to be found on the upslope ofthe Spencer’s curve, ie, within the 50% to 90% ICA diam-eter reduction range. How can one decide if a given veloc-ity is abnormal? If there is a reference velocity value suchas an unobstructed ICA before the stenosis or on the con-tralateral side, an arterial stenosis of about 50% diameterreduction will double the velocity value assumed normalfor a particular patient. Since the ICA has a bulb that nor-mally has low velocities and could be affected by an axis-asymmetric plaque, the common carotid artery (CCA) ve-locity and the ICA/CCA PSV ratios were introduced tocompensate for this clinical uncertainty.9 Despite wide in-terindividual variations,10 the PSV itself remains the sin-gle best predictor of the stenosis11 since when it exceeds
8 Journal of Neuroimaging Vol 17 No 1 January 2007
125 cm/sec, one can say with a great degree of certaintythat this patient with an atheroma, free of abnormal sys-temic hemodynamic changes, has ≥50% ICA stenosis.8,11
Remarkably, these interindividual PSV variations8 gen-erally follow the shape of the Spencer’s curve (see Graphin the 2003 Consensus criteria, ref. 8). The 2003 Consen-sus criteria identify ICA PSV, ICA/CCA PSV ratio, andICA EDV as useful velocity parameters that should beused together with gray scale and color flow imaging find-ings to interpret carotid ultrasound studies.8 Additionalfactors that affect velocity measurements include anglecorrection and interlaboratory equipment/protocol dif-ferences.8
However, elevated, “normal,” and decreased veloci-ties can also be found on the “other side” of the Spencer’scurve, ie, with the so-called angiographic “string” signs ornear-occlusions indicating most severe arterial stenoses.The differential diagnosis includes the use of the ve-locity ratios between the prestenotic and stenotic seg-ments, ie, the ICA/CCA PSV ratios, velocity asymme-try between homologous segments on bilateral examina-tions, and spectral waveform analysis. For example, theICA/CCA ratio of <4 identifies the range of <70% ICAstenoses that most often present with the PSV of <230cm/sec.11 The same relatively low velocities can be foundwith evidence of a significant impedance to flow such asICA/CCA ratio greater than 4, the poststenotic bluntingof arterial waveforms and signs of flow diversion or collat-eralization.4 The latter will likely show higher contralat-eral velocities and lower ratios implying compensatoryflow. Flow velocities must be interpreted in the contextof waveform appearance, flow velocity ratios, and pu-tative determinants of flow velocity, if available to theinterpreter.
In clinical practice, this helps to identify hemodynami-cally significant stenoses that may have variable velocitiesbut are likely to be on the “other side” of the Spencer’scurve. The multidisciplinary consensus criteria identifythese very severe lesions as having variable velocities,8
and application of the Spencer’s curve principle in con-junction with other hemodynamic and imaging consider-ations helps to sort out these changes.
The Spencer’s Curve and Research Studies
Application of a nonstandardized ultrasound screening ina large scale multicenter clinical trial led to one of the mostfrustrating observations13 fortunately overshadowed byother rigorously designed and successful studies.10-12,14-16
Nevertheless, if one expects a suboptimal performance ofultrasound screening for carotid stenosis, plotting veloc-ities vs. percent stenosis should result in somewhat ran-
dom scatter. During the North American SymptomaticCarotid Endarterectomy Trial (NASCET), nonstandard-ized PSV values from over 1100 patients seen at almost 50centers were plotted against percent diameter reductionof the ICA on catheter angiography.13 Figure 2A showsthis scatter-plot that remarkably reveals a nonrandom be-havior of the PSV. Almost all measurements fit underthe area under a hypothetical Spencer’s curve! This hap-pened because different sonographers used different ma-chines at the study centers. Each lab has its own diagnosticcriteria with variable local velocity cutoffs leading to in-dividual Spencer’s curves of different amplitude (Fig 2B).But when these individual measurements were summedup together, the resulting scatter clearly followed the basichemodynamic model. Since this is a post hoc interpreta-tion, NASCET data set offers only indirect support to theSpencer’s curve. Remarkably, this information presentin the scatter-plot escaped attention of the NASCET co-ordinating center investigators. An editorial that accom-panied their report identified other significant flaws andbiases.17
This observation,13 along with critical analysis of thevelocity behavior by Grant et al,10 pointed out that a sin-gle velocity parameter may not perform equally well be-tween patients or laboratories, and that a local valida-tion study is required at any given laboratory to use anyselected diagnostic criteria with any confidence in theirperformance.
To enable clinical researchers to reliably screen fora significant carotid artery disease, the AsymptomaticCarotid Atherosclerosis Study trialists successfully em-ployed a prospective multicenter standardization strat-egy.14 Their experience revealed that despite large in-terlaboratory variations, standardization and optimizednoninvasive screening using various ultrasound methodsand cutoffs is possible.14 Evaluation of the on-site perfor-mance was done using locally validated diagnostic criteriathat take into account both the hemodynamic predictionand specific instruments that produce flow velocity mea-surements.
The Clinical Impact
Self-validation of locally adopted diagnostic criteria spe-cific to laboratory personnel and particular equipment,continuing education, and quality control (as laboratoryperformance can change over time) are paramount com-ponents of successful practice of cerebrovascular ultra-sound (www.icavl.org). The Spencer’s curve, whether itis being called that or not during any specific lecture,became an excellent teaching tool for both the begin-ners and advanced ultrasound users. This hemodynamic
Alexandrov: Clinical Implications of a Classic Hemodynamic Model 9
model is evoked in one aspect or another to interpret in-dividual results in everyday practice, and to understandthe laboratory performance through self-validation stud-ies. Implications of this model are now being discussed intranscranial Doppler studies of intracranial vessels, withparticular emphasis on grading intracranial stenosis in-cluding diffuse lesions.4,18 It is difficult to understate itsimportance as it should be an integral part of any text-book, educational course, or quality assessment when-ever we deal with applied principles of hemodynamics.
References
1. Spencer MP, Reid JM. Quantitation of carotid stenosis withcontinuous wave Doppler ultrasound. Stroke 1979;10:326-330.
2. von Reutern GM, Budingen HJ. Ultrasound Diagnosis ofCerebrovascular Disease. Stuttgart: Georg Thieme Verlag,1993:64.
4. Alexandrov AV. Cerebrovascular Ultrasound in Stroke Preven-tion and Treatment . New York: Futura/Blackwell Publishing,2003.
5. Alexandrov AV, Brodie DS, McLean A, Murphy J, Hamil-ton P, Burns PN. Correlation of peak systolic velocity andangiographic measurement of carotid stenosis revisited.Stroke 1997;28:339-342.
6. Comerota AJ, Cranley JJ, Cook SE. Real-time B-modecarotid imaging in diagnosis of cerebrovascular disease.Surgery 1981;89:718-729.
7. deBray JM, Glatt B. Quantitation of atheromatous stenosisin the extracranial internal carotid artery. Cerebrovasc Dis1995;5:414-426.
8. Grant EG, Benson CB, Moneta GL, et al. Carotid arterystenosis: gray-scale and Doppler US diagnosis—Society ofRadiologists in Ultrasound Consensus Conference. Radiol-ogy 2003;229:340-346.
BL, Strandness DE. Carotid artery velocity patterns in nor-mal and stenotic vessels. Stroke 1980;11:67-71.
10. Grant EG, Duerinckx AJ, El Saden SM, et al. Ability to useduplex US to quantify internal carotid arterial stenoses: factor fiction? Radiology 2000;214:247-252.
11. Hunink MG, Polak JF, Barlan MM, O’Leary DH. Detec-tion and quantification of carotid artery stenosis: efficacyof various Doppler velocity parameters. Am J Roentgenol1993;160:619-625.
12. Moneta GL, Edwards JM, Chitwood RW, Taylor LM,Lee RW, Cummings CA, Porter JM. Correlation ofNorth American Symptomatic Carotid EndarterectomyTrial (NASCET) angiographic defintion of 70-99% inter-nal carotid stenosis with duplex scanning. J Vasc Surg1993;17:152-157.
13. Eliasziw M, Rankin RN, Fox AJ, Haynes RB, Bar-nett HJ. Accuracy and prognostic consequences of ul-trasonography in identifying severe carotid artery steno-sis. North American Symptomatic Carotid EndarterectomyTrial (NASCET) Group. Stroke 1995;26:1747-1752.
14. Howard G, Baker WH, Chambless LE, Howard VJ, JonesAM, Toole JF. An approach for the use of Doppler ul-trasound as a screening tool for hemodynamically signif-icant stenosis (despite heterogeneity of Doppler perfor-mance). A multicenter experience. Asymptomatic CarotidAtherosclerosis Study Investigators. Stroke 1996;27:1951-1957.
15. Bray JM, Galland F, Lhoste P, Nicolau S, Dubas F, EmileJ, Pillet J. Colour Doppler and duplex sonography and an-giography of the carotid bifurcations. Prospective, double-blind study. Neuroradiology 1995;37:219-224.
16. Steinke W, Reis S, Artemius N, Schwartz A, Hennerici M.Power Doppler imaging of carotid stenosis. Comparisonwith color Doppler flow imaging and angiography. Stroke1997;28:1981-1987.
17. Ringelstein EB. Skepticism towards carotid ultrasonog-raphy: a virtue, an attitude, or fanaticism? Stroke1995;26:1743-1746.
18. Sharma VK, Lao A, Malkoff MD, Frey JL, Alexandrov AV.Diffuse intracranial disease: the other side of the Spencer’scurve. Cerebrovasc Dis 2006;20(suppl 3):132 [abstract].
10 Journal of Neuroimaging Vol 17 No 1 January 2007
