Determination the Appropriate Velocity Threshold...

1699

Determination of the Most Appropriate VelocityThreshold for Applying Hemispheric Flow

Convergence Equations to Calculate Flow Rate:Selected According to the

Transorifice Pressure GradientDigital Computer Analysis of the Doppler Color

Flow Convergence RegionYou-Bin Deng, MD; Takahiro Shiota, MD; Robin Shandas, PhD;

Jun Zhang, MD; David J. Sahn, MD

Background. While flow convergence methods have been promising for calculating volume flows fromcolor Doppler images, it appears that the velocity threshold used and the transorifice pressure gradientdramatically influence the accuracy of application of the simple hemispheric flow convergence equationfor calculation of flow rate. The present in vitro study was performed to determine whether the value ofvelocity threshold at which the shape of proximal isovelocity surface best fits given shape assumptionswith different orifice sizes and flow rates is predictable as a function independent of orifice size fromclinically measurable peak velocity or transorifice pressure gradient information.Methods and Results. In an in vitro model built to facilitate ultrasound imaging, steady flow was driven

through circular discrete orifices with diameters of 3.8, 5.5, and 10 mm. Flow rates ranged from 2.88 to8.28 1min with corresponding driving pressure gradients from 14 to 263 mm Hg. At each flow rate,Doppler color-encoded M-mode images through the center of the flow convergence region were obtainedand transferred into the microcomputer (Macintoshilci) in their original digital format. Then, thecontinuous wave Doppler traces of maximal velocity through the orifice were derived for the calculationof driving pressure gradient. Direct numerical spatial velocity measurements were obtained from thedigital color encoded M-mode velocities with computer software. For each flow rate, we could calculateflow volume from any number of velocity distance combinations with a number of assumptions and use theresults to assess expected flow convergence shape based on a priori knowledge of the progression fromoblate hemispheroid to hemisphere to prolate hemispheroid changes observed previously. Our resultsshowed that for a given ratio of calculated flow rate to actual flow rate (0.7 and 1), the velocity thresholdthat could be used for the calculation of flow rate with a hemispheric flow convergence equation correlatedwell with the pressure gradient for a given orifice size, and the differences in velocity threshold that couldbe used this way among different orifice sizes once they were adjusted for the covariate pressure gradientswere not statistically significant (P=.79 for ratio=0.7, and P=.81 for ratio=1).

Conclusions. Our present study provides an orifice size-independent quantitative method that canbe

used to select the most suitable velocity threshold for applying a simple hemispheric flow convergence

equation based on clinically predictable pressure gradients ranging from 40 to 200 mm Hg, and it offersa correction factor that can be applied to the hemispheric flow convergence equation when the pressure

gradient is less than 40 mm Hg. (Circulation. 1993;88[part 11:1699-1708.)KEY WORDs * flow * echocardiography

C olor Doppler mapping of the flow convergence accelerating flow field imaged using color Doppler byregion proximal to a regurgitant or stenotic the aliasing velocity at that surface. Because of an

orifice has recently been proposed as a new inability for direct measurement of the proximal isove-method for noninvasive quantitation of flow rate be- locity surface area by color Doppler due to spatialtween cardiac chambers.1-8 The theories behind this errors, slow sampling rates, and angle dependence ofmethod state that the flow rate can be obtained by Doppler velocity measurements, simplified methods tomultiplying the proximal isovelocity surface area in an

Reprint requests to Dr David J. Sahn, Director, The ClinicalReceived October 27, 1992; revision accepted June 8, 1993. Care Center for Congenital Heart Disease, Oregon Health Sci-From the Clinical Care Center for Congenital Heart Disease, ences University, 3181 SW Sam Jackson Park Rd-UHN60,

Oregon Health Sciences University. Portland, OR 97201.

by guest on June 26, 2018http://circ.ahajournals.org/

Dow

nloaded from

http://circ.ahajournals.org/

1700 Circulation Vol 88, No 4, Part 1 October 1993

FIG 1. This page and facing page. Digital color-encoded flow convergence region images for an orifice diameter of 5.5 mm andflow rate of 5.88 Llmin at the velocity thresholds of 30 cm/s (A), 38 cm/s (B), 48 cm/s (C), and 55 cm/s (D) with correspondingcalculated flow to actual flow ratios of 1.20, 1.14, 1.00, and 0.86. A square portion of the derived color M-mode image panel (E,upper color panel, white rectangle) was selected and transferred directly into digital velocity determinations (E, lower panel) forfurther analysis.

calculate the proximal isovelocity surface area havebeen proposed that use the center radius of the flowconvergence region in a direction parallel to Dopplersampling by assuming a hemispheric geometric shape.1Although both in vitro and animal studies have dem-onstrated good correlations between actual and calcu-lated flow rate using this assumption, calculated flowrate commonly underestimates or overestimates actualflow rate depending on the different color Doppleraliasing velocities used with different actual flow ratesand varying orifice sizes.3,5,9-11 It is now clear that thegeometric shape of proximal isovelocity surfacechanges with flow rate and orifice size, although apriori knowledge to guide proper choice of thesevariables is not available in clinical application ofthese methods.1,3,910,12-17A recent study from our laboratory17 has shown that

the shape of proximal flow convergence isovelocityregion is a function of transorifice pressure gradientand aliasing velocity and that it can assume any shapefrom flat "pan-shaped" ellipse to hemispheroidalshapes depending on the value of aliasing velocity (Fig1A through D) and pressure gradient. Hence, applyingthe simple hemispheric flow convergence equation to

these images will obviously result in different calcu-lated flow rates for different aliasing velocities chosenin the acceleration field even though actual flow rateremains constant. The progression from overestima-tion to underestimation we observed when using mag-netic resonance imaging (MRI) angle-independentvelocimetry and calculating hemisphere-based flowrates14,15 suggested a systematic change that was tosome extent velocity related and led to our askingwhether continuous wave Doppler velocity could beused to suggest the portion of the zone of accelerationwherein the hemispheric assumption, the simplest toimplement, might be applied to calculate flow volume(Fig 2). The present study was designed to allowdigital acquisition of centerline acceleration of veloc-ities to allow calculations of the whole range velocitiesby unwrapping aliasing and to allow tests of the fit ofa number of geometric flow convergence models overa range of flows, orifice sizes, and driving velocities inan in vitro model. We had hoped to use these data tolook for methods of predicting where within the flowconvergence zone and when clinically hemisphericflow convergence geometry assumptions could be usedto estimate volume flow rate.


Dow

nloaded from


Deng et al Computer Analysis of Flow Convergence 1701

7 s Y~~~~~~~~~~~~~~~~~~~~~~~ _>0^^>tf....f..r................. . ................................. _......| .......66 0 .1-0213 0 1 -0 - 0.24 - 0.24

............................... ............. .... ................................. ........ ......... ................ .. ... ... .. .... .. ..

17 0 023027 0.24: 0267' -0.26717 .-.0. .j.-.0. ............. .. -026.

18 0.93 -0.293- 0.293, 0.293 0.267 -0.2931 9 - 0.32 - 0.32 - 0.32 - 0.32. - 0.293. - 0.293.20 0.347 -0.347 0 .347 0.32. - 0.32 -0.3221 0347.- -0.373- 0.347 0.373. 0.373 -0.34722 -_04 -0.4 -0.4 -0 - 0.373: -0.373

.. ... .........6 .. ... .: ...........................23 0.48 0.48 - 0.453 - 0.427 - 0.427 -0.45324 0.453 .453 0.427 0.453 0.48 0.48... .. .1. .. .. ..... ...... ....................,........... .. .. .. .. .. .. ..

25 0.4 0.4. 0.373 0.373: 0.4 0.42726 0.32 0.32: 0.267 0.32 0.293: 0.4............. .................................. ..................... ................ .... ............................0.24:

0.241

0.1 87. 0. 60.08. 0.0267.

0.267:-1 - -..- W. c-.W 1 0.267: 0.347i0.213. 0.187T

MethodsExperimental Design

For generating a steady acceleration field, steady flowwas driven through circular discrete orifices mounted ina dual-chamber model. Planar circular orifices withdiameters of 3.8, 5.5, and 10 mm were used. Flow was

driven into the top chamber of a circular plastic tube(diameter, 12.4 cm; length, 24 cm) through the orificemounted in-between the top chamber and bottomchamber, into the bottom chamber, and back out to a

OVERESTIMATION

ORIFICE

FIG 2. Schema of multiple aliasing boundaries of flowconvergence proximal to an orifice. This demonstrates a

general tendency for use of low Nyquist velocities (upperarrow), especially when acceleration is rapid to overestimateactual flow rate, because the true isovelocity shape is prolatehemispheroid (solid line) not hemispheric (dashed line) andfor a high aliasing velocity (lower arrow) to underestimateactual flow rate when the hemispheric (dashed line) assump-

tion is used because the actual isovelocity surface is flattened(solid line).

recirculating pump. In this model, even for the largestorifice, the rounded walls were infinitely large related tothe dimensions of the orifice and flow convergence. Asolution of water mixed with 1% by weight cornstarchwas used as the fluid medium. Actual flow rate wasmeasured in the model using a rotameter, and flow rateswere cross-checked by draining the model into a grad-uated cylinder and timing the collection with a stop-watch. Flow rate ranged from 2.88 to 8.28 L/min. Themodel has previously been described.17

Doppler Color Flow Mapping and Image TransferDoppler color flow mapping was performed using a

Vingmed CFM 750 ultrasound imaging system(Vingmed Sound, A/S, Norway) with a transducerfrequency of 5 MHz and aliasing velocity of 50 cm/s.The color Doppler high-pass filter was complex but hasa rolloff to minimize flow velocities <8 cm/s (medium).This system is equipped with a digital output port thatpermits us to transfer two-dimensional and colorM-mode Doppler velocity assignments in their originaldigital format from the digital scan converter in thesystem directly into a microcomputer before color as-signment and without having to convert the signal intoanalog format. Doppler flow map data are thus trans-ferred as digital velocity assignments.18'19 For scanning,the transducer was placed and fixed on a speciallyconstructed window in the model to image flow goingaway from the transducer. All other imaging settings,

28........................ ....................... .... .. 1: ...................

27 I.


Dow

nloaded from



including gain and depth, were optimized and keptconstant throughout the study. Color M-mode flowconvergence images were acquired by placing theM-mode cursor line through the center of the two-dimensional imaged flow convergence region aimedtowards the orifice.For every flow state (every discrete combination of

orifice size and flow rate), a sequence of 10 to 20two-dimensional Doppler color flow frames and Dopp-ler color-encoded M-mode images through the center offlow convergence region were acquired on the ultra-sound scanner digital cineloop and transferred into themicrocomputer (Macintosh IIci) in original digital for-mat for subsequent offline computer analysis. Also ateach setting, the continuous wave Doppler traces ofmaximal velocity through the orifice were obtained andused for the calculation of driving pressure gradientusing a simplified Bernoulli assumption.

Measurements and Data AnalysisDoppler color-encoded M-mode images through the

center of the flow convergence region were analyzed (Fig1E). The velocity information could be averaged as afunction of time on the M-mode tracings because of thesteady flow setup used (Fig 1E). Care was taken to alwayshave the bottom of the region of interest at the sameposition at the orifice and the upper zone of the M-modeline proximal to the beginning of the flow convergenceregion.

Direct numerical spatial velocity measurements wereaccomplished using digital values for color pixel inten-sity obtained with computer software provided byVingmed (Vingmed Sound, A/S, Norway) with a sam-pling gate increment of 0.4 mm starting from the orificeposition to a point proximal to the beginning of flowconvergence region.18.19 Because flow was imaged goingaway from the transducer and displayed as blue, thevelocities measured by computer were represented bynegative numbers. If velocity exceeded the Nyquistvelocity, the color became red (alias), and the velocitieswere shown as positive numbers. The velocities mea-sured at the alias region were reassigned and recalcu-lated into true velocities according to the aliasing veloc-ity and the number of times aliasing occurred. Flow ratewas calculated with the hemispheric flow equation:

CFR=2- W. V. 60/1000where CFR is calculated flow rate (L/min), R is radius(cm) from the orifice, and V is velocity (cm/s) at theradius R. Then, the individual velocity thresholds usedfor the calculation of flow rate were plotted versus radiias well as the ratios of calculated flow rate to actual flowrate. Since a hemispheric flow convergence equationwas used to calculate flow rates, the value of thecalculated to actual flow ratio contains informationabout the expected isovelocity surface shape at anygiven velocity threshold, ie, a value of 1 would beconsistent with a hemispheric shape; a value of morethan 1 would indicate elongation of shape toward aprolate hemispheroidal configuration, the larger theratio, the more asymmetric the shape; and values of lessthan 1 would indicate flattening toward a pan-shapedellipse configuration, the lower the ratio, the moreflattened the shape (Figs 1 and 2). Because the velocity

thresholds available for use in the calculation of flowrate actually represent the serial different velocities onthe color bar used in color Doppler imaging system, theresulting curves allow us to determine the thresholdvelocity at which the shape of the proximal isovelocitysurface is best fit for a given shape assumption and whatkind of correction factors should be introduced for thecalculation of flow rate with the hemispheric flowconvergence equation at different flow rates and orificesizes or pressure gradients. In digital processing of thedata transfer for the Vingmed 750 system, any velocitylimit could be chosen during data analysis, yielding awhole stream of velocity-distance data. Differencesamong velocity threshold for a given ratio of calculatedto actual flow rate at different transorifice pressuregradients were determined from actual measurementsand expressed in absolute numbers.The pressure gradient for every discrete combination of

flow rate and orifice size was calculated using the simpli-fied Bernoulli equation PG=4* V2,20,21 where PG is pres-sure gradient (mm Hg) and V is maximal velocity (m/s) atthe orifice measured with continuous wave Doppler. Pres-sure gradients were plotted versus velocity threshold atwhich the ratios of calculated to actual flow rate wereeither 0.7 or 1, respectively, to determine whether thesevelocities (thresholds) were related to the potentiallyclinically measurable pressure gradients using simple lin-ear regression analysis. The differences among the linearregression lines for different orifice sizes were determinedwith an analysis of covariance.

ResultsThe direct numerical velocity measures were ob-

tained for the regions containing a single alias. Becauseof the multialiasing and difficulty of determining pre-cisely how many times aliasing occurred near the orifice,the true velocities were not measurable in these regionsclose to the orifice.

Relationship of Velocity to RadiusFig 3 shows the relationship of velocities to the radial

distance at which they occurred for different flow rates atdifferent orifice sizes and shows how the velocities in-crease when approaching the orifices. An increase in flowrate resulted in a right and upward shift to these curves.This suggests that for the whole velocity range, the isove-locity surface radius is larger with higher flow rates.

Fig 4 shows the relationship between velocities andradii for two different orifice sizes at two flow rates.Note that the curve has shifted upward and the slopehas become steeper in the mid- and high-velocity rangewhen the orifice diameter decreased from 5.5 to 3.8 mm,indicating that velocity acceleration profile of the flowconvergence region for different sized orifices changeseven though the flow rates are matched.

Relationship of Ratios of Calculated Flow Rate toActual Flow Rate to the Velocity Thresholds

Fig 5 shows the relationship of the ratio of calculatedflow rate using a hemispheric flow convergence equationto actual flow rate to the varying velocity thresholds alongthe center line at different actual flow rates and orificesizes. It demonstrates that the shape of isovelocity surfaceis not constant and changes with the velocity thresholdused for the calculation of flow rates for a given flow rate


Dow

nloaded from



C7

E

t

B

5,

E

Tl

1.0D = 3.8 mm

0.8 U FR = 5.88 Vmin

* FR = 4.68V/mn* FR = 3.48 Vmdn

0.6 M FR = 2.88 Vmin

0.4

0.2 -

0.00.0 0.2 0.4 0.6 0.8 1.0 1.

Distance (cm)

1.0

D = 5.5 mm

0.8 * FR = 6.48 Vmin

* FR = 5.28 lmin* FR 4.08Vmin

0.6 - FR = 3.48 Vmin* FR = 2.88 /min

0.4-

0.2-

0.00.0

A

Co

E

Z->

-T

0

.2

B

51

E

t0411

0.2 0.4 0.6 0.8 1.0 1.2

Distance (cm)

FIG 3. Radial distancefrom the orifice is shown plotted withrespect to velocity showing the relationship for different flowrates at two orifice sizes. FR indicates flow rate; and D,diameter.

and orifice size or pressure gradient. As such, the hemi-spheric flow convergence equation will obviously result indifferent calculated flow rates for different aliasing veloc-ities with progressive underestimation near the orifice andprogressive overestimation far from the orifice eventhough actual flow rate remains constant.The position of the curve shifted upward and the slope

became flatter with increases in flow rates or pressuregradients for a constant orifice size. This means that forthe whole range of ratios of calculated flow rates to theactual flow rates, ie, the given shape of the isovelocitysurface and thus the velocity threshold that can be usedfor the calculation of flow rate using hemispheric flowconvergence equation increases with flow rates or pressuregradients for any given orifice size. This relationship wassensitive to variation in transorifice pressure gradient. Forexample (Fig 5B), increases in transorifice pressure gradi-ent of 15 to 41 mm Hg for the curves resulted in changesin velocity threshold of 7 and 16 cm/s for ratio of 1 andfrom 4 to 18 cm/s for a ratio of 0.7, suggesting that for thecalculation of flow rate, velocity threshold can be adjustedto make the aliasing pattern fit for the given shape ofisovelocity surface selected for flow rate or pressuregradient. It also demonstrates that the shape of isovelocitysurface for a given velocity threshold changes with the flowrate or pressure gradients for a given orifice size.From the curves, it was also found that the shape of

isovelocity surface was still flattened and calculated flowrates still underestimated actual flow rates even at the

FR = 3.48 I1min0.8

0.6- E D=3.8mm* D=5.Smm

0.4

0.2-

0.00.0 0.2 0.4 0.6 0.8 1.0 1.2

Distance (cm)

1.0

FR = 5.88 Ilmin0.8

0.6 D*0=3.8mm0.6- Ah X * D=5.Smm

0.4-

0.2-

0.00.2 0.4 0.6 0.8 1.0 1.2

Distance (cm)

FIG 4. Radial distancefrom the orifice plotted versus veloc-ity showing the relationship for different orifice sizes at twoequal flow rates. It shows that the position of velocity profilesbetween different orifice size differs even when flow rate is thesame. FR indicates flow rate; and D, diameter.

low-velocity range (as low as 20 cm/s) for the largestorifices and lowest flow rates (Fig 5D and E) that werecorresponding to the pressure gradient of less than 40mm Hg, and the shape was still prolate hemispheroidaland calculated flow rates still overestimated actual flowrates even at the high-velocity range (more than 80cm/s) for the smallest orifice and high flow rates (Fig5A) that were corresponding to the pressure gradientsof more than 200 mm Hg. This suggests that beyondthese ranges we could not select isovelocity contourranges that behaved hemispherically but that differentcorrections would need to be applied in addition tovelocity selection for the calculation of flow rates withthe hemispheric flow convergence equation for condi-tions of both very-low- and very-high-pressuregradients.

Relationship of Velocity Threshold for a Given Shapeof Isovelocity Surface at Different Flow Rates andOrifice Sizes to the Pressure GradientsFor a given ratio of calculated flow rate to actual flow

rate (0.7 and 1 in the present study), the velocitythresholds that were usable for the calculation of flowrate with the hemispheric flow convergence equationwere correlated well with the pressure gradient acrossthe orifice for a given orifice size (Figs 6 and 7),


Dow

nloaded from



A

1.8-

D=3.8imm1.61.4

1.2

1.0

0.6

0.6* FR=5.88 Urm (263 mrnHg)

0.4 4 FR=5.28 Urm (196 mmHg)* FPR=4.68 1rm (160 mmHg)

0.2 * FR=4.08 Urm (139 mmHg)

0.00.0 0.2 0.4 0.6 0.8 1.C

Velocity Threshold (misec)

1.8-D=5.Smm

1.6- * FR=6.48 Vm (181 mmHg)

. FR=5.88 Urm (114 mmHg)1.4 - + FR=5.28 Urm (97 mmHg)

1.2 -_F R =4~~~FR-.68 11m (82 mmHg)1.2

1.0

0.6-

0.2- . . . . . . . .

0.00.0 0.2 0.4 0.6 0.8 1.0

Velocity Threshold (mslec)

1.8

1.6 D=1Omm

1.4-

1.2 X FR=8.28 Urm (38 mmHg)FR-7.68 1rm (29 mmHg)

1.0 FR=7.08 Urm (24 mmHg)U FR=5.88 Urm (14 mrnHg)

0.6_

0.2 0.4 0.6 0.8

Velocity Threshold (mince)

ai:

0

-)--

2

.2


D

e

3:

-i.E.9

2

a

w2

J1

'S.2

or

D=5.5 mm1.6 * FR=4.68 Um (82 mmHg)

, FR=4.08 UM (60 mmHg)1.4 -

a FR=3.48 VUM (48 mmHg)1.2 apt * FRi2.88 Vm (27 mmHg)

1.0

0.8

0.6

0.4-

0.2

0.0 A

0.0 0.22 0.4 0.6 0.8


1.0

FIG 5. Graphic display ofvelocity threshold with relationship tothe ratio of calculated flow rate (FR) (calculated with thatvelocity threshold using a hemispheric flow convergence equa-

tion) expressed as a ratio to actual FR for different FRs andpressure gradients for the three different orifice sizes. Numbers inbrackets indicate the corresponding transorifice pressure gradi-ents. A and B, Higher and lower rates for the 3.8-mm orifice, Cand Dfor the 5.5-mm orifice, and Efor the 10-mm orifice. Theratio increases at lower velocity thresholdsfor any orifice size andincreases with increasing FR (pressure gradient) for any givenvelocity threshold and orifice size. For the whole range of ratios,the velocity threshold requiredfor the hemispheric calculation ofFR is higher with higherFRs (or higherpressure gradients) at anyorifice size. Note that the ratio is still less than 1 at lowflow rates(D) and large orifices (E) with correspondingpressure gradientsof less than 40 mm Hg even at lower velocities (as low as 20cmls), and the ratio is still larger than 1 at high FRs and smallorifice sizes (A) with corresponding pressure gradients of morethan 200mm Hg even at the higher velocities (up to 80 cmls). Dindicates diameter.

indicating that the velocity threshold used for thecalculation of flow rate using the hemispheric flowconvergence equation for a given shape of isovelocitysurface and a given orifice size was predictable frompressure gradients. All linear regression lines for thecalculated to actual flow rate ratios of 0.7 and 1 betweenthe different orifice sizes appeared to have similar slope,and the differences in velocity thresholds among thedifferent orifice sizes adjusted for the covariate pressure

gradients were not statistically significantly different(Figs 6A and 7A, P=.79 for ratio=0.7 and P=.81 forratio=1). This suggests that for a given ratio of calcu-lated to actual flow rate, ie, for a given shape ofisovelocity surface, the velocity thresholds (selectedusing pressure gradient as an index parameter) thatcould be used for the accurate calculation of flow rate bya hemispheric formula over a wide range of pressuregradients was independent of orifice size.

B

.C

0-i

Uo.9

2

.23

.1A:'S2cc1

c

L.

-i

30

.2

cj1

0

S

or

0

0.0 1.0


Dow

nloaded from



A

70 a

60

50s

40

30

20 - ,

Pressure Gradient (mmHg)

B

Three Orifice Sizes Together

60 80 100 120 140 160 180 2


BTwo Orifice Sizes Together

20 40 60 80 100 120 140 160 180


FIG 6. Linear regression analysis between pressure gradientand the velocity threshold at which the ratio of calculated toactual (CAL/ACT) flow rate (FR) is 0. 7for the orifices withdiameters (D) of 3.8, 5.5, and 10 mm (A) and for all orificesizes together (B). The differences in velocity thresholdsamong three orifice sizes adjusted for the covariate pressure

gradients are not statistically different (P=. 79), indicating thatthe relationship between the velocity threshold and the pres-

sure gradients is independent of orifice size (see text fordetail). Note that the calculated FRs should be corrected by

dividing them by 0.7 when the velocity thresholds shown in this

graph are selected and used for the hemispheric flow conver-

gence equation.

DiscussionEffects of Selected Aliasing Velocities on the Shape ofIsovelocity SurfaceThe quantitation of flow rates through a regurgitant

or stenotic orifice using the proximal flow convergencemethod is based on the continuity equation. The as-

sumptions in the method predict that the flow rate canbe obtained by multiplying proximal isovelocity surfacearea by color Doppler aliasing velocity. Because thedirect measurement of the true proximal isovelocitysurface area cannot be made by color Doppler from anyplane of information because of angle dependency ofDoppler, the simplest usual method to calculate theproximal isovelocity surface area is from the centerradius of the flow convergence region by assuming a

hemispheric geometry. Several investigators have used


FIG 7. Linear regression analysis between pressure gradientand the velocity threshold at which the ratio of calculated toactual (CAL/ACT) flow rate (FR) is 1 for the orifices withdiameters (D) of 3.8 and 5.5 mm (A) and for the two orificesizes together (B). Again, the differences in velocity thresholdsbetween the two orifice sizes adjusted for the covariatepressure gradients are not statistically different (P=.81), as inFig 6 showing a relationship independent of orifice size.

this method to calculate the regurgitant flow rates invitro and in animal studies and obtained good correla-tion between calculated and actual flow rates.1,3-8 How-ever, calculated flow rates have sometimes either un-derestimated or overestimated actual flow rates with thehemispheric flow convergence equation in differentconditions of flow rate, orifice size, and chosen aliasingvelocity, with a general tendency for use of low aliasingvelocities in high-flow rate studies and small orifice sizesto overestimate actual flow rate and for high chosenaliasing velocities in low-flow rate studies and with largeorifice sizes to underestimate actual flow rate (Refer-ences 1, 3, 5, and 9-13; Fig 2). Our present studydemonstrated that the shape of the expected isovelocitysurface was not constant but changed with the velocitythresholds for any given flow rate and orifice size (Fig1A through D) and also changed with the flow rate or

pressure gradients for a given velocity threshold. Thiswould explain the overestimation or underestimation ofactual flow rates reported previously depending on thedifferent flow rates assessed or the aliasing velocities

A

5,

E

0

b-

c'

To

* D=5.5 mn,,y-0.24x+16.56,r=0.95E D=8 mnr~y*0.28x+13.5,r=0.98

a


Dow

nloaded from



selected for use with a hemispheric flow convergenceequation. In the present study, the shape of isovelocitysurface was determined by the ratio of calculated toactual flow rate. Our findings are in agreement withprevious observations that the shape of isovelocitysurface determined by (1) directly viewing the flowconvergence region on color Doppler after color anglecorrection for the lateral dimensions, (2) when flowconvergence was imaged by direct optical visualizationof particle tracking, or (3) when it was imaged by phasevelocity encoded MR115 showed that an aliasing regioncould assume any shape from flat pan-shaped ellipse tohemispheric to prolate hemispheroid depending on thevalue of the velocity threshold selected.15

Proximal Velocity Profile of FlowConvergence Region

In the present study, the velocities along the centerline of flow convergence region were acquired as esti-mated flow velocity using computer software with adepth increment of 0.4 mm from the orifice positionfrom images that were directly transferred into themicrocomputer from the digital scan converter in theultrasound imaging system. This digital computer tech-nique has proven to be very accurate for extractingspatial velocity data and has been validated previous-ly.18,19 Our findings are generally consistent with previ-ous reports in which the velocity acceleration profilewas obtained by measuring the axial radius of flowconvergence region at varying aliasing velocities.22

Since it was very difficult to identify the actual shapeof isovelocity surface when planning blind application ofhemispheric flow convergence equation due to thedependence of color aliasing pattern on flow rate andorifice size, some investigators22 have analyzed thevelocity profile of flow convergence region instead ofthe calculation of a single isovelocity surface area to tryto assess the flow rate by comparing the position ofmeasured velocity profile curves with a nomogram to apreviously determined family of velocity-distance pro-files of flow convergence regions at different flow rates.Although they developed a nomogram for estimatingflow rates independent of orifice size,22 our resultsindicated that the position of velocity profile curvesvaried not only with flow rate for a constant orifice sizebut also with the orifice size even for a constant flowrate, suggesting that the method to analyze the velocityprofile to assess flow rate was influenced by orifice size,an unknown in potential in clinical applications suchthat overestimation and underestimation could occur.

Correction Procedure for Using the SimpleHemispheric Flow EquationAs indicated in the present and previous stud-

ies,3,12,17,23 the theoretical assumption that the proximalflow convergence region consists of a series of hemi-spheric surfaces does not fit for the practical situationwhere the shape of the isovelocity surfaces changesbased on the flow rate, orifice size, and aliasing velocity,changing from flattened to hemispherical to hemisphe-roidal shapes such that applying the simple hemisphericflow convergence equation to calculate flow rates willobviously overestimate or underestimate actual flowrates (Fig 2). Several investigators3,9,12,24 have attemptedto provide modified methods as enhancements to the

simple flow convergence technique. In an in vitro study,Utsunomiya et a13 assumed the shape of isovelocitysurface as hemiellipsoid rather than hemispheric andchanged the flow convergence equation into one wherethe area became the surface area of a hemiellipsoid.The surface area was calculated by measuring thelong-axis aliasing radius, short-axis aliasing radius, and90° short-axis radius from two orthogonal scanningplanes. They found that although aliasing radius de-creased with increasing aliasing velocities, calculatedvolume flow rate was constant with the percent differ-ence between calculated and actual flow rates rangingfrom -9.2% to 4.3% for the four aliasing velocityconditions. However, in the clinical setting, the flowconvergence method using a hemielliptic assumption tocalculate flow rates is limited by the requirement thattwo orthogonal, a longitudinal, and a 900 short-axis viewmust be recorded. The short-axis image can almostnever be obtained clinically. Another simple and appli-cable correction method was to measure the axial radiusand transverse one of flow convergence region on onlyone two-dimensional color Doppler scanning plane inthe hemispheroidal surface area calculation instead ofthree radii on two orthogonal scanning planes, and asatisfactory result was reported using this method toestimate the cardiac output in an animal experiment.24Even though two- and four-chamber orthogonal viewsare available clinically, it should be kept in mind thatbecause of angle dependence,9 the transverse radiusmeasured by abovementioned method does not repre-sent the true transverse measurement of the flow con-vergence region.Our present in vitro study demonstrated that the most

appropriate velocity thresholds for applying the hemi-spheric flow convergence equation increased markedlyand had a linear relationship with pressure gradientsranging from 40 to 200 mm Hg, and this relationship wasindependent of orifice size (Fig 7). For pressure gradi-ents of 40 to 200 mm Hg, the most suitable velocitythresholds varied from 20 to 80 cm/s, which are withinthe obtainable limits of the currently used color Dopp-ler system. Those findings are supported by previousqualitative observation of effects of pressure gradienton the proximal flow convergence region using theparticle tracking technique where dramatic changesoccurred in streamline angle as the pressure gradientvaried.17 The present study provided an alternative wayof correcting overestimation or underestimation of ac-tual flow rate in view of the uncertainty of determiningtrue color aliasing shape just by allowing selection of thevelocity threshold using the pressure gradient yieldingan isovelocity surface that fit for the hemispheric as-sumption to obtain better estimation of actual flow rate.For largest orifices and low-flow rates that were corre-sponding to pressure gradients of less than 40 mm Hg inthe present study, the actual flow rate was still under-estimated even using low velocity (velocity threshold) of10 to 20 cm/s when a simple hemispheric flow conver-gence equation was used. Under this condition, the flowrate can be calculated with a hemispheric flow conver-gence equation by selecting the pressure gradient de-pendent velocity threshold at which the color aliasingpattern is best fit for the shape of isovelocity surfacewith ratio of calculated flow rate to actual flow rate to be


Dow

nloaded from



0.7 and can be corrected by dividing the calculated flowrate by 0.7 (Fig 6).

For the lower pressure gradient applications thataccount for the low flow rates and large orifice sizessuch as mitral stenosis, some investigators26 have pro-posed a correction procedure to make the aliasingvelocity pattern a better fit for the hemispheric flowconvergence equation by decreasing the aliasing veloc-ity as low as 10 to 20 cm/s. Our findings show that forsuch low aliasing velocities (even quite far from theorifice), surface geometry is still flattened because ofslow axial acceleration when gradients are low. Inaddition, the use of very low velocity thresholds islimited by our findings that the velocity profile curvesoverlapped in the portion of low velocity range betweenthe varying flow rates. Previous studies22'24 also demon-strated that the low aliasing velocity patterns wereuncertain and subject to frame-to-frame variability,slow frame rates, and deformation by and fusion withneighboring flow phenomena.

Clinical ImplicationsThe flow convergence method has already been used

in patients with native and prosthetic mitral regurgita-tion,27-29 mitral stenosis,2426 ventricular septal defect,2,30and aortic coarctation.31 It therefore promises to be-come a useful method for quantifying flow rates. How-ever, there are several problems such as instrumentlimitations (slow sampling speeds, angle dependence,and poor spatial resolution) and physiological factorsthat hinder the application of this simple flow hemi-spheric equation to clinical cases.17 Of the physiologicalfactors, the most important one might be the flowpulsatility and varying hemodynamic conditions in theheart. Both the previous studies1'3'9'10'12'13 and our pre-sent one demonstrate that the shape of the isovelocitysurface of flow convergence region changes with theflow rate and orifice size and the former will certainlycompound application in pulsatile flow. Since the in-stantaneous regurgitant flow rate and regurgitant orificesize change32'33 and therefore the color aliasing patternalso changes for a given aliasing velocity with differenthemodynamic conditions within a cardiac cycle, it is easyto understand why the overestimation or underestima-tion occurs frequently when the simple hemispheric flowconvergence equation is used blindly to quantify theflow rate using only one aliasing velocity under differenthemodynamic conditions within the whole cardiac cycle.Our present study provides an orifice size-independentrelationship between the most suitable velocity thresh-old for applying the hemispheric flow convergenceequation and pressure gradients ranging from 40 to 200mm Hg that are estimated clinically and analogous tomany of the clinical situations, certainly at peak systole,for example. It also offers a method for correcting theunderestimation of flow rate calculated with hemi-spheric flow convergence equation at a low pressuregradient of less than 40 mm Hg by dividing the calcu-lated flow rate by 0.7 (Fig 6B). One way of quantifyingthe flow rate in potential clinical application using theinformation provided in the present study is to adjustthe aliasing velocity according to the estimated peakpressure gradient to calculate the maximal instanta-neous regurgitant flow rate from the color Dopplerimage showing a maximal flow convergence region. The

other way is to calculate the total regurgitant flowvolume by integrating multiple instantaneous flow rateover time calculated with a simple hemispheric flowconvergence equation from the color M-mode tracing offlow convergence region by adjusting the aliasing veloc-ity to make the color aliasing pattern fit for the hemi-spheric shape according to the instantaneous pressuregradient obtained from the continuous wave Dopplertracing across the regurgitant orifice. This might beintegrated with an automatic computer calculation soft-ware method5 and might provide the most accuratemethod for quantifying flow rates clinically.

Study LimitationsThe present study to demonstrate the relationship

between the most appropriate velocity threshold for ap-plying the simple hemispheric flow convergence equationand the pressure gradients is limited to the planar circularorifice. However, this is not always the clinical situation.Although our findings showed this relationship was inde-pendent of orifice size, we did not determine the effects oforifice shape (triangle, oval, or rectangular) and the archi-tecture of orifice plane on this relationship. Further stud-ies are needed to determine the influence of orifice shapeand architecture on the relationship between velocitythreshold and pressure gradients and what kind of correc-tion should be introduced under nonplanar and noncircu-lar orifice conditions.We did not provide a correction factor for the hemi-

spheric flow convergence equation for hemodynamiccondition with pressure gradients of more than 200mm Hg under which conditions the flow rate calculatedwith hemispheric flow convergence equation would stilloverestimate the actual flow rate, even using very highvelocity thresholds (more than 80 cm/s). However,hemodynamic condition with pressure gradients ofmore than 200 mm Hg is rare in clinical situations.Therefore, this limitation should not affect the clinicalapplication of the method provided by the present studyfor selecting velocity thresholds according to the pres-sure gradient.

ConclusionsThe shape of isovelocity surface changes with velocity

threshold for a given orifice size and flow rate orpressure gradient and also changes with pressure gradi-ents for a given velocity threshold. Our present studyprovides an orifice size-independent quantitativemethod for selecting the most suitable velocity thresh-old for applying the simple hemispheric flow conver-gence equation according to clinically estimated pres-sure gradients ranging from 40 to 200 mm Hg and offersa correcting factor to the hemispheric flow convergenceequation when the pressure gradient is less than 40mm Hg.

AcknowledgmentsDr Deng is a research fellow from Union Hospital, Tongji

Medical University, Wuhan 430022, People's Republic ofChina. This work was partially supported by National Heart,Lung, and Blood Institute grant R01-HL-36472.

References1. Recusani F, Bargiggia GS, Yoganathan AP, Raisaro A,

Valdes-Cruz LM, Sung H-V, Bertucci C, Gallati M, Moises UA,


Dow

nloaded from



Simpson IA, Tronconi L, Sahn DJ. A new method for quantifi-cation of regurgitant flow rate using color Doppler flow imaging ofthe flow convergence region proximal to a discrete orifice: an invitro study. Circulation. 1991;83:594-640.

2. Sahn DJ, Simpson IA, Murillo A, Valdes-Cruz LM. Observation ofacceleration proximal to restrictive orifices in congenital heartdisease: important clues for the interpretation of Doppler colorflow maps. Circulation. 1988;789(suppl II):II-649. Abstract.

3. Utsunomiya T, Ogawa T, Doshi R, Patel D, Quan M, Henry WL,Gardin JM. Doppler color flow 'proximal isovelocity surface area'method for estimating volume flow rate: effects of orifice shape andmachine factors. JAm Coll Cardiol. 1991;17:1103-1111.

4. Utsunomiya T, Mehta K, Nguyen D, Patel D, Doshi R, Gardin JM.Accuracy of flow rate calculation in funnel orifices by colorDoppler zero-shift 'proximal isovelocity surface area' method.JAm Coll Cardiol. 1991;17(suppl A):148A. Abstract.

5. Shandas R, Golebiovski P, Valdes-Cruz LM, Jones M, Murillo A,Yamada I, Sahn DJ. A new automatic computer method for mea-suring mean flow convergence radius from color MQ modesprovides more accurate flow rate estimates: in vitro and animalstudies of mitral regurgitation. JAm Coil Cardiol. 1991;17(supplA):149A. Abstract.

6. Utsunomiya T, Beck J, Eisenman D, Doshi D, Gardin JM. Calcu-lation of regurgitant volume and regurgitant fraction using thecolor Doppler 'proximal isovelocity surface area' method. J AmCoil Cardiol. 1991;17(suppl A):358A. Abstract.

7. Levine RA, Rodriguez L, Cape EG, Vesier C, Thomas JD,Weyman AE, Cagniot A, Yoganthan AD. The proximal flow con-vergence method for calculating orifice flow rate requires cor-rection for surrounding leaflet geometry. JAm Coll Cardiol. 1991;17(suppl A):359A. Abstract.

8. Rodriguez L, Vlahakes GJ, Yoganathan AP, Guerrero JL, LevineRA. Quantification of regurgitant flow rate using the proximal flowconvergence method: in vivo validation. Circulation. 1989;80(supplII):II-571. Abstract.

9. Rodriguez L, Anconina J, Flachskampf FA, Weyman AE, LevineRA, Thomas JD. Impact of finite orifice size on proximal flowconvergence: implication for Doppler quantification of valvularregurgitation. Circ Res. 1992;70:923-930.

10. Utsunomiya T, Quan M, Doshi R, Patel D, Gardin JM. Effect offlow rate, orifice size and aliasing velocity on volume calculationusing Doppler color proximal isovelocity surface area method.JAm Coll Cardiol. 1990;15(suppl A):89A. Abstract.

11. Valdes-Cruz LM, Recusani F, Shandas R, Murillo A, Jones M,Cape E, Moises V, Yoganthan A, Sahn DJ. Accuracy of flowconvergence methods for calculating mitral regurgitant flow: vali-dation studies in an animal model. J Am Coil Cardiol. 1990;15(suppl A):11OA. Abstract.

12. Shandas R, Lee Y, Golebiovski P, Mrosko B, Sahn DJ. Flowconvergence calculation of flow rate through non or minimallyrestrictive orifices: in vitro studies. J Am Coll Cardiol. 1991;17(suppl A):359A. Abstract.

13. Moises V, Chao K, Shandas R, Murillo A, Belot J-P, Valdes-CruzL, Sahn DJ. Effects of orifice size and shape on flow rate estimatedfrom flow convergence region imaged by color Doppler flowmapping proximal to restrictive orifices: an in vitro study. JAm CollCardiol. 1990;15(suppl A):109A. Abstract.

14. Cranney G, Shandas R, Liepmann D, Weintraub R, Zhang J,Walker P, Pohost G, Yoganathan A, Sahn D. Phase velocity NMRquantification of the proximal flow convergence region: in vitrostudies using physiological orifices and pulsatile flow. Circulation.1991;84(suppl II):II-203. Abstract.

15. Weintraub R, Shandas R, Cranney G, Walker P, Yoganathan A,Sahn DJ. Comparison of flow convergence (FC) calculations usingcolor Doppler flow mapping (CD) and phase velocity encodedMRI: an in vitro study. Circulation. 1991;84(suppl II):II-636.Abstract.

16. Zhang J, Jones M, Shandas R, Valdes-Cruz LM, Murillo A,Yamada I, Kang SU, Weintraub RG, Shiota T, Sahn DJ. Accuracyof flow convergence estimates of mitral regurgitant flow by use of

multiple color flow Doppler M-mode aliasing boundaries: anexperimental animal study. Am Heart J. 1993;125(Pt 1):449-458.

17. Shandas R, Gharib M, Liepmann D, Shiota T, Sahn DJ. Experi-mental studies to define the geometry of the flow convergenceregion: laser Doppler particle tracking and color Doppler imaging.Echocardiography. 1992;9:43-50.

18. Shandas R, Belt JP, Cali G, Moises V, Sahn DJ. Comparison ofanalog and digital methods of transferring color Doppler imagedata for off-line analysis. JAm Coll Cardiol. 1990;15:88A. Abstract.

19. Simpson IA, Sneddon JF, Smith G, McKenna WJ. Quantitation ofspatial velocity characteristics in hypertrophic cardiomyopathy:on-line digital analysis of color Doppler flow map imagings. Circu-lation. 1991;84(suppl II):II-636. Abstract.

20. Hatle L, Angelsen BA, Tromsdal A. Noninvasive assessment ofaortic stenosis by Doppler ultrasound. BrHeart J. 1980;43:284-292.

21. Yoganathan AP, Cape EG, Sung HW, Williams FP, Jimoh A.Review of hydrodynamic principle for cardiologist: application tothe study of blood flow and jets by imaging techniques. JAm CoilCardiol. 1988;12:1344-1353.

22. Giesler MO, Stauch M. Color Doppler determination of regur-gitant flow: from proximal isovelocity surface areas to proximalvelocity profiles: an in vitro study. Echocardiography. 1992;9:51-62.

23. Barclay SA, Changsheng X, Loyd D, Andersson G, Ask P, WranneB. The flow convergence region proximal to a regurgitant orificehas a non-hemispherical velocity field. Circulation. 1991;84(supplII):II-105. Abstract.

24. Shiota T, Valdes-Cruz LM, Sahn DJ, Shandas R, Murillo A, JonesM, Yamada I, Weintraub RG, Kang SU, Zhang J. Estimation ofcardiac output and mitral orifice area using new proximal flowconvergence method: validation in animal model of chronic mitralstenosis. JAm Coll Cardiol. 1992. In press. Abstract.

25. Sahn DJ. Instrumentation and physical factors related to visual-ization of stenotic and regurgitant jets by Doppler color flowmapping. JAm Coll CardioL 1988;12:1354-1365.

26. Rodriguez L, Monterroso V, Mueller L, Harrigan P, Thomas JD,Weyman AE, Levine RA. Validation of a new method for valvearea calculation using the proximal isovelocity surface area inpatients with mitral stenosis. J Am Coll Cardiol. 1990;15(supplA):109A. Abstract.

27. Bargiggia GS, Tronconi L, Sahn DJ, Recusani F, Raisaro A,DeServi S, Valdes-Cruz LM, Montemartini C. A new method forquantitation of mitral regurgitation based on color Doppler flowimaging of flow convergence proximal to regurgitant orifice. Circu-lation. 1991;84:1481-1489.

28. Chen C, Koschyk D, Mehl C, Klarhofer M, Kupper W, Bleifeld W.Comparison of quantifying mitral regurgitation using colorDoppler proximal isovelocity surface area and angiography. Circu-lation. 1991;84(suppl II):II-637. Abstract.

29. Bargiggia GS, Tronconi L, Rasaro A, Recusani F, Ragni T,Valdes-Cruz LM, Sahn DJ, Montemartini C. Color Dopplerdiagnosis of mechanical prosthetic mitral regurgitation: usefulnessof the flow convergence region proximal to the regurgitant orifice.Am Heart J. 1990;120:1137-1142.

30. Moises VA, Maciel BC, Hornberger LK, Murillo-Olivas A,Valdes-Cruz LM, Sahn DJ, Weintraub RG. A new method fornoninvasive estimation of ventricular septal defect shunt flow byDoppler color flow mapping: imaging of the laminar flow con-vergence region on the left septal surface. J Am Coil Cardiol.1991;18:824-832.

31. Simpson IA, Sahn DJ, Valdes-Cruz L, Chung KJ, Sherman FS,Swensson RE. Color Doppler flow mapping in patients with coarc-tation of the aorta: new observations and improved evaluation withcolor flow diameter and proximal acceleration as predictors ofseverity. Circulation. 1988;77:736-744.

32. Yoran C, Yellin EL, Becker RM, Gabbay S, Frater RWM, Son-nenblick EH. Dynamic aspects of acute mitral regurgitation: effectsof ventricular volume, pressure and contractility on the effectiveregurgitant orifice area. Circulation. 1979;60:170-179.

33. Yellin EL, Yoran C, Sonnenblick EH, Gabbay S, Frater RWM.Dynamic changes in the canine mitral regurgitant orifice areaduring ventricular ejection. Circ Res. 1979;45:677-683.


Dow

nloaded from


Y B Deng, T Shiota, R Shandas, J Zhang and D J Sahngradient. Digital computer analysis of the Doppler color flow convergence region.

convergence equations to calculate flow rate: selected according to the transorifice pressure Determination of the most appropriate velocity threshold for applying hemispheric flow

Print ISSN: 0009-7322. Online ISSN: 1524-4539 Copyright © 1993 American Heart Association, Inc. All rights reserved.

is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231Circulation doi: 10.1161/01.CIR.88.4.1699

1993;88:1699-1708Circulation.

http://circ.ahajournals.org/content/88/4/1699World Wide Web at:

The online version of this article, along with updated information and services, is located on the

http://circ.ahajournals.org//subscriptions/

is online at: Circulation Information about subscribing to Subscriptions:

http://www.lww.com/reprints Information about reprints can be found online at: Reprints:

document. Permissions and Rights Question and Answer available in the

Permissions in the middle column of the Web page under Services. Further information about this process isOnce the online version of the published article for which permission is being requested is located, click Request

can be obtained via RightsLink, a service of the Copyright Clearance Center, not the Editorial Office.Circulation Requests for permissions to reproduce figures, tables, or portions of articles originally published inPermissions:


Dow

nloaded from

http://circ.ahajournals.org/content/88/4/1699

http://www.ahajournals.org/site/rights/

http://www.lww.com/reprints

http://circ.ahajournals.org//subscriptions/


Determination the Appropriate Velocity Threshold...

Documents

Transcript of Determination the Appropriate Velocity Threshold...