DeGroff C G, Shandas R, Valdes-Cruz L
University of Colorado Health Sciences Center, The Children's Hospital, Denver 80218, USA.
Circulation. 1998 Apr 28;97(16):1597-605. doi: 10.1161/01.cir.97.16.1597.
Flow-rate dependencies of the Doppler continuity equation are addressed in this study.
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.
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.
本研究探讨了多普勒连续性方程的流量依赖性。
通过使用带有湍流模型的计算流体动力学（CFD）软件，创建了圆形狭窄孔口的三维轴对称模型。针对各种孔口面积大小（0.785、1.13、1.76和3.14平方厘米）和流量（0.37至25.0升/分钟）进行了流动模拟。雷诺数范围为100至8000。每次模拟获得充分收敛后，确定缩窄处的位置。对于每次运行，将缩窄处横截面上的最大速度和平均速度制成表格，并确定缩窄处横截面积（有效孔口面积）。缩窄处的最大速度与平均速度之间的差异在高流量状态下最小，在低流量状态下差异更大。在较低流量状态下，缩窄处的速度矢量分布呈抛物线形，而在高流量状态下，分布变得更加扁平。此外，有效孔口面积（缩窄处横截面积）随流量而变化。在中等流量状态下，有效孔口面积达到最小值，并在低流量和高流量状态下扩大，在高流量状态下保持相对恒定。
我们已经表明，在低流量时，缩窄处的最大速度与平均速度之间存在显著差异。对此的一个可能解释是粘性效应在低流量时导致缩窄处边缘的速度较低，从而形成抛物线形分布。在较高流量状态下，惯性力克服粘性阻力，导致分布更扁平。有效孔口面积本身也随流量而变化，在中等流量状态下面积最小。这些与流量相关的因素导致多普勒连续性方程中出现与流量相关的误差。我们的结果与在不同心输出量条件下使用多普勒连续性方程对狭窄瓣膜面积进行临床测量密切相关。
