Analysis of the Effect of Flow Rate on the Doppler Continuity Equation for Stenotic Orifice Area Calculations

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Abstract
Background —Flow-rate dependencies of the Doppler continuity equation are addressed in this study. Methods and Results —By use of computational fluid dynamic (CFD) software with turbulence modeling, three-dimensional axisymmetric models of round stenotic orifices were created. Flow simulations were run for various orifice area sizes (0.785, 1.13, 1.76, and 3.14 cm 2 ) and flow rates (0.37 to 25.0 L/min). Reynolds numbers ranged from 100 to 8000. Once adequate convergence was obtained with each simulation, the location of the vena contracta was determined. For each run, maximum and average velocities across the cross section of the vena contracta were tabulated and vena contracta cross-sectional area (effective orifice area) determined. The difference between the maximum velocity and the average velocity at the vena contracta was smallest at high-flow states, with more of a difference at low-flow states. At lower-flow states, the velocity vector profile at the vena contracta was parabolic, whereas at high-flow states, the profile became more flattened. Also, the effective orifice area (vena contracta cross-sectional area) varied with flow rate. At moderate-flow states, the effective orifice area reached a minimum and expanded at low- and high-flow states, remaining relatively constant at high-flow states. Conclusions —We have shown that significant differences exist between the maximum velocity and the average velocity at the vena contracta at low flow rates. A likely explanation for this is that viscous effects cause lower velocities at the edges of the vena contracta at low flow rates, resulting in a parabolic profile. At higher-flow states, inertial forces overcome viscous drag, causing a flatter profile. Effective orifice area itself varies with flow rate as well, with the smallest areas seen at moderate-flow states. These flow-dependent factors lead to flow rate–dependent errors in the Doppler continuity equation. Our results have strong relevance to clinical measurements of stenotic valve areas by use of the Doppler continuity equation under varying cardiac output conditions.