Calculation of aortic valve area by Doppler echocardiography : a direct application of the continuity equation KENT

The continuity equation suggests that a ratio of velocities at two different cardiac valves is inversely proportional to the ratio of cross-sectional areas of the valves. To determine whether a ratio of mitral/aortic valve orifice velocities is useful in determining aortic valve area in patients with aortic stenosis, 10 control subjects and 22 patients with predominant aortic stenosis were examined by Doppler echocardiography. The ratio of (mean diastolic mitral velocity)/(mean systolic aortic velocity), (Vm)/(Va), and the ratio of (mitral diastolic velocity-time integral)/(aortic systolic velocity-time integral), (VTm)/(VTa), were determined from Doppler spectral recordings. Aortic valve area determined at catheterization by the Gorlin equation was the standard of reference. High-quality Doppler recordings were obtained in 30 of 32 subjects (94%). Catheterization documented valve areas of 0.5 to 2.6 (mean 1.1) cm2. There was good correlation between Doppler-determined (Vm)/(Va) and Gorlin valve area (r = .90, SEE = 0.23 cm2); a better correlation was noted between (VTm)/(VTa) and Gorlin valve area (r = .93, SEE = 0.18 cm2). The data demonstrate the usefulness of Doppler alone in the determination of aortic valve area in adults with absent or mild aortic or mitral regurgitation and no mitral stenosis. Although the use of mean velocity and velocity-time integral ratios requires accurate measurement of mitral and aortic velocities, it does not require squaring of these velocities or measurement of the cross-sectional area of flow. Circulation 73, No. 5, 964-969, 1986. IDENTIFICATION and quantification of aortic stenosis remains a significant problem in adults with systolic murmurs. Cardiac catheterization is frequently required to identify patients with significant aortic stenosis and to quantitate its severity by determining mean systolic pressure gradient and valve area. Doppler echocardiography has proved to be accurate in the identification of patients with aortic stenosis by detecting high velocity's or turbulence-7 in the aorta downstream from the stenotic valve during systole. Doppler determination of the peak systolic velocity allows calculation of the peak instantaneous pressure gradient by means of the simplified Bernoulli equation. 12, 8-l Mean systolic gradient can also be calculated from Doppler velocity recordings by determining the averFrom the Division of Cardiology, Department of Medicine, University of Texas Health Science Center and Veterans Administration Hospital, San Antonio. Supported in part by a grant from the Veterans Administration. Address for correspondence: Kent L. Richards, M.D., Division of Cardiology, Veterans Administration Hospital, San Antonio, TX 78284. Received Aug. 5, 1985; revision accepted Feb. 13, 1986. 964 age of multiple systolic instantaneous gradients" -'2 or by calculating turbulence variables.'-'-5 Because pressure gradient is flow dependent, it may be very high in patients in whom aortic valve flow is high and stenosis is only moderate; likewise low gradients may be noted if flow is low despite the presence of severe stenosis. For this reason, aortic valve area is usually estimated from catheterization pressure and flow data by means of the Gorlin equation; the calculated Gorlin valve area is used clinically to judge the severity of valvular stenosis. Aortic valve area can also be calculated noninvasively by combining two-dimensional imaging and Doppler echocardiography. 16 Doppler is used to determine the high velocities from the stenotic valve from which the pressure gradient is calculated, as well as to determine the velocities from a normal valve at which cardiac output is measured. Echocardiographic imaging is used to estimate the normal valve cross-sectional area, which is combined with velocity at that site to calculate cardiac output.'7 Alternatively, noninvasive Doppler pressure gradient and invasive cardiac output can be used to estimate CIRCULATION by gest on A ril 3, 2017 http://ciajournals.org/ D ow nladed from DIAGNOSTIC METHODS-DOPPLER ECHOCARDIOGRAPHY valve area. 18 Echocardiographic imaging alone has not proved to be reliable for estimating aortic valve area. 19 The continuity equation provides a simple alternative by which Doppler alone can be used to calculate aortic valve area. The concept is illustrated in figure 1, in which blood flows steadily from left to right through a cylinder with a cross-sectional area of (Al) at its left end and a cross-sectional area of (A2) where it narrows. The rate at which blood flows through the large section of the tube can be calculated by multiplying the cross-sectional area of the tube (Al) by the mean velocity of blood at that site (V1). Likewise, the rate of flow across the narrowed segment of the tube can be calculated as the product of cross-sectional area (A2) times mean velocity (V2) within the narrowed segment. The rate at which blood flows into the tube (Q1) is the same as the rate at which blood flows out of the tube (Q2) because there are no branches in the tube and because flow occurs from left to right only. Mathematically, if (Q1) (A1)(V1) and (Q2) (A2)(V2), and Q1 = Q2, then: QI = (AI)(V1) = (A2)(V2) Q2 (1) If the equation is rearranged, a ratio of cross-sectional areas (A2)/(A 1) is shown to be proportional to the inverse ratio of velocities (VI)/(V2): (A2)/(A1) = (VI)/(V2) (2) This model of the circulation can be applied to the heart if we conceptualize the tube as beginning at the normal mitral valve and ending at a stenotic aortic valve. If aortic and mitral valve regurgitation are absent and intracardiac shunts are not present, the volume flow rate through aortic and mitral valves will be equal. If the velocities and cross-sectional areas are relabeled to represent the valve of origin (aortic = a, mitral = m), then equation 2 becomes: (Aa)/(Am) = (Vm)/(Va) (3)