From the University of Colorado Health Sciences Center, The
Children's Hospital, Denver, Colo.
Correspondence to Curt G. DeGroff, MD, Cardiovascular Flow Dynamics Laboratory, University of Colorado Health Science Center, The Children's Hospital, 1056 E 19th Ave, B-100, Denver, CO 80218. E-mail degroff.curt{at}tchden.org
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 cm2 ) 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.
© 1998 American Heart Association, Inc.
Clinical Investigation and Reports
Analysis of the Effect of Flow Rate on the Doppler Continuity Equation for Stenotic Orifice Area Calculations
A Numerical Study
Key Words: echocardiography • stenosis • blood flow
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