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Simplification of the Doppler Continuity Equation for Calculating Stenotic Aortic

Valve Area Catherine M. Otto, MD, Alan S. Pearlman, MD, Carolyn L. Gardner, RDCS,

Carol D. Kraft, RDCS, and Michelle C. Fujioka, RDCS, Seattle, Wash.

Determination of aortic valve area by the continuity equation is feasible and accurate but requires planimetry. Because the ratio of maximum velocities in the left ventricular outflow tract (LVOT) to aortic jet is quite similar to the ratio of velocity-time integrals at these sites, the continuity equation can be simplified by substituting maximum velocities for velocity-time. integrals. Agreement with invasively determined aortic valve areas is similar with the conventional and simplified forms of the continuity equation. However, substitution of the average or sex-specific LVOT diameter for measured LVOT diameter in individual patients leads to less accurate aortic valve area determination. We conclude that simplification of the continuity equation, with measured LVOT diameter and maximum velocity and aortic jet maximum velocity, allows noninvasive calculation of the aortic valve area in a way that is simple and accurate. (JAM Soc EcHo 1988;1:155-7.)

Several groups have demonstrated that stenotic aor­tic valve areas can be determined noninvasively by the continuity equation with Doppler and two­dimensional echocardiography. 1·3 Because this re­quires determin;1tion ofvelocity-time integrals, which can be time-consuming and tedious, we evaluated potential ways to simplify this process.

METHODS

Doppler continuity equation valve areas were com­pared with Godin formula valve areas determined at catheterization in 10~ adults with suspected aortic stenosis. Doppler studies were performed immedi­ately after catheterization. Patients ranged in age from 33 to 87 years, with a mean age of 69 years. There were 67 men and 36 women. This study was approved by our institutional Human Subjects Com­mittee, and informed consent was obtained for the echocardiographic evaluation. Coexisting aortic in­sufficiency was present on pulsed Doppler echocar­diography in 88 patients (85%) and was graded 1 +

From the Division of Cardiology, Department ofMedicine, Uni­versity of Washington. Reprint requests: Catherine M. Otto, MD, University of Wash­ington, Division of Cardiology, RG-22, Seattle, WA 98195.

in 25, 2 + in 48, and 3 + in 15 patients. O¢er data from some of these patients have been reported elsewhere.2

Midsystolic left ventricular outflow tract (LVOT) diameter (D) was averaged from five to 10 para­sternal long axis two-dimensional images and cir­cular cross-sectional areas (CSA) calculated [CSALvoT = 1T (D/2?]. The LVOT velocity curve was recorded from an apical approach with pulsed Doppler echocardiography (9 mm sample volume length), and both the velocity-time integral (VTI) and maximum velocity ( V) were averaged from 3 to 5 beats. Because the aortic (Ao) jet may be

· eccentric, the window (apical, right parasternal, or suprasternal) that showed the highest velocity signal with continuous wave Doppler was recorded, and 3 to 5 beats were averaged for maximum velocity and velocity-time integral.

Conventional Continuity Equation.

From these data aortic valve area (AVA) was cal­culated with the conventional continuity equation as follows:

Method 1 AVA= (VTILvOT/VTIAo) X CSALvoT

Potential Simplifications

Because the systolic ejection periods and the shape of the velocity time curves are similar in the L VOT

155

156 Otto et al.

1.0

0.8

~ 0.6 a: ~ E >

0.4

n~ 103 r~ 0.96 y ~ 0.94x + 0.0010.2

/ 0+-----~------.-----~------,-----,

0 0.2 0.4 0.6 0.8 1.0

VTI Ratio

Figure 1 LVOT:Ao velocity-time integral ratio (x axis) vs maximum velocities ratio (y axis).

5.0

4.0

.. 1.0

2.0 3.00 1.0

Journal of the American Society of

Echocardiography

n~ 103 r~ 0.87 y~ 0.94x + 0.19cm2

SEE~ 0.35 cm2

4.0 5.0

AVA by Cath (cm2)

Figure 2 Catheterization Godin formula aortic valve areas (x axis) vs Doppler continuity equation valve areas determined with ratio of maximum velocities instead of velocity-time integrals (y axis).

Table 1 Potential modifications of the Doppler continuity equation

Continuity equation r Regression equation

Conventional (VTI) 0.87 DOP = 0.92 CATH + 0.16 cm2

Simplified (V=) 0.87 DOP = 0.94 CATH + 0.19 cm2

Mean LVOT-D 0.81 DOP = 0.67 CATH + 0.41 cm2

Sex-specific LVOT-D 0.84 DOP = 0.81 CATH + 0.31 cm2

SEE, Standard error of the estimate; Vfl, velocity-time integral ratio; DOP, Doppler; CATH, catheterization; V muo

maximum velocity ratio; LVOT-D, left ventricular outflow tract diameter.

and aortic jets, the ratio ofLVOT to aortic-jet max­imwn velocities is nearly identical to the ratio of velocity-timeintegrals(r = 0.96,y = 0.94x + 0.01, standard error ofthe estimate [SEE] = 0.35; Figure 1). The correlation is unchanged if the 5 data points with a velocity-time integral ratio over 0.50 are ex­cluded (r = 0.94, y = 0.99x + 0.18, SEE = 0.31). Therefore the continuity equation was modified by substituting maximum velocities for velocity-time in­tegral as follows:

Method 2 AVA= (VLvoT/VAo) X CSALvoT

The group mean LVOT diameter was 2.3 em. There was no relationship between LVOT diameter and age, body surface area, or the degree ofcoexisting aortic insufficiency; however, diameter was signifi­cantly smaller in women than men (2.0 vs 2.5 em, p < 0.01). Thus two other potential modifications of the continuity equation were evaluated by substi­tuting as follows for each patient in the continuity equation:

SEE (cm2)

0.34 0.35 0.31 0.33

left ventricular outflow tract to aortic jet

Method 3 Group mean L VOT diameter Method 4 Sex-specific mean LVOT diameter

Doppler echocardiography and catheterization valve areas were determined by independent observ­ers. Catheterization valve areas were calculated by the Godin formula with angiographic stroke volume for transaortic valve flow ifcoexisting aortic insufficiency was present. Comparisons were made with linear regressiOn.

RESULTS

Aortic valve areas determined by the simplified con­tinuity equation agreed well with catheterization valve areas (Figure 2). With catheterization valve areas as the standard of reference, the conventional continuity equation (method 1) and the simplified continuity equation (method 2) yielded nearly iden­tical data (Table 1). Doppler valve areas calculated

Volume l Number 2 March-April 1988

with the group mean (method 3) or sex-specific mean LVOT diameter (method 4) correlated less well with catheterization valve areas, and the regression lines deviated more markedly from the line of identity (Table 1).

DISCUSSION

These data indicate that the Doppler continuity equa­tion can be simplified by substituting the LVOT: Ao maximum velocity ratio for the ratio of velocity-time integrals without significantly altering the accuracy of this method as compared with catheterization valve areas, as has been suggested by other groups. 1•3

As with the conventional continuity equation, a care­ful search must be made from multiple windows and transducer angulations to record the highest aortic jet velocity. Although LVOT velocity invariably is recorded from an apical approach (because the pre­stenotic flow tends to parallel the long axis of the outflow tract), careful positioning of the sample vol­ume just below the region of acceleration into the aortic jet is required.

Although one may argue that maximum velocities

Simplification of Doppler continuity equation 157

in the LVOT and aortic jet do not occur simulta­neously and that substitution of velocities for velocity-time integrals should require simultaneous instantaneous velocities, in fact the ratio ofmaximum velocities is nearly identical to the ratio of velocity­time integrals. Thus use of the maximum velocity ratio in the continuity equation, albeit imperfect, works and is practical. However, LVOT diameter does vary substantially from patient to patient, and it should be measured directly in each patient for accurate valve area determination.

REFERENCES

l. Skjaerpe T, Hegrenaes L, Harle L. Non-invasive estimation of valve area in patients witll aortic stenosis by Doppler ultra­sound and two-dimensional echocardiography. Circulation 1985;72:810-8.

2. Otto CM, Pearlman AS, Comess KA, Reamer RP, Janko CL, Huntsman LL. Determination of me stenotic aortic valve area in adults using Doppler echocardiography. J Am Coli Cardiol 1986;7:509-17.

3. Zoghbi W A, Farmer KL, Soto JG, Nelson JG, Quinones MA. Accurate non-invasive quantification of stenotic aortic valve area by Doppler echocardiography. Circulation 1986;73: 452-9.