Evaluation of the Valve Area Underestimation by the Continuity Equation

Abstract

During the last years, noninvasive determination of the aortic valve area by Doppler echocardiography using the continuity equation became popular. However, a systematic valve area underestimation of about 15 % compared to invasive measurements using the Gorlin formula has been reported. The cause therefore is unknown. The purpose of this study was to evaluate whether the valve area underestimation by the Doppler method might be due to differences in the hydrodynamic background of both methods. This comparison is facilitated by the fact that the Gorlin formula is based on the continuity equation. Compared to the continuity equation, there are four changes within the Gorlin formula: (1) the additional use of a discharge coefficient, which leads to valve area overestimation by the factor 1.17; (2) neglect of the prestenotic velocity, causing further overestimation by the factor 1.036 (in mild stenosis this factor may be 1.18 and more); (3) the wrong calculation of the mean pressure drop, which leads to a mean change by the factor 0.95, and (4) the incorrect substitution of the height by the pressure drop in the derivation of the Gorlin formula causes underestimation by the factor 0.97. Combining these four factors results in valve area overestimation of the Gorlin formula compared to the continuity equation by the factor 1.12. This explains to a large extent the valve area underestimation by the continuity equation.

Demonstration of left ventricular outflow tract eccentricity by 64-slice multi-detector CT

“…A trend towards underestimation of AVA was seen, when diameter derived estimations of ALVOT were used compared to direct AVA planimetry (0.89 ± 0.38 cm 2 vs. 1.00 ± 0.4 cm 2 ). It has long been observed that echo derived estimates of AVA are often smaller than those estimated using invasive techniques [10][11][12][13]. Our findings that ALVOT is frequently underestimated when diameter-derived calculation is used, may account for some of the observed discrepancy between echo and invasively determined AVA measurement.…”

Demonstration of Left Ventricular Outflow Tract Eccentricity by Real Time 3D Echocardiography: Implications for the Determination of Aortic Valve Area

“…Using 2D echocardiography (2DE), the aortic valve area (AVA) is usually calculated with the continuity equation. The continuity equation (CE) has shown concordance with invasive techniques but with consistent underestimation 1–3 . The commonly used formulation of the continuity equation relies on assumptions about both the geometry of the left ventricular outflow tract (LVOT) and the applied imaging planes.…”

“…Two‐Dimensional Echocardiography Two‐dimensional measurement of the left ventricular outflow tract diameter (DLVOT‐2D) was performed immediately underneath the aortic valve from trailing to leading edge during peak systole when the aortic cusps were maximally separated. Images were viewed on a digital review station (Medcon, Tel Aviv, Israel) and the approximated cross‐sectional area of the left ventricular outflow tract (ALVOT‐2D) was calculated using π× radius 2 . The images were analyzed by two readers (DM and BK) who were blinded to each other's findings.…”

“…The diameter of LVOT on this idealized view was then measured (DLVOT‐3D). Using this diameter a second estimate of the outflow tract area (ALVOT‐3Dplax) was calculated by π× radius 2 . A second plane, the “LVOT plane” was then aligned parallel to and bisecting the aortic root and LVOT (Fig.…”

Dynamics of the Left Ventricular Outflow Tract during the Cardiac Cycle Assessed (with) Via Tridimensional Echocardiography

“…This method would also allow modifying the continuity formula regularly used in the estimation of the aortic valve area (AVA). It is usually considered that AVA measurement using continuity equation over-estimates the severity of the aortic stenosis [9][10][11]. This could be partly because the area is estimated and not directly measured, underestimating the numerator factor of the equation.…”