Holen J, Waag R C, Gramiak R
Ultrasound Med Biol. 1987 Jun;13(6):321-8. doi: 10.1016/0301-5629(87)90165-7.
Torricelli's equation expresses a simple relationship between fluid velocity and pressure gradient in orifice flow and is currently used in conjunction with noninvasive Doppler ultrasound to determine gradients in mitral stenosis, and aortic stenosis, as well as other cardiovascular orifices. In theory, however, the Torricelli equation overestimates the gradient in aortic stenosis and the Borda equation should be more applicable. A brief tutorial derivation of the Borda and Torricelli equations is presented. The applicability of Torricelli's equation in aortic stenosis was studied experimentally with a rigid wall, pulsatile flow analogue. Doppler ultrasound and manometric data were collected simultaneously. Percent stenosis, peak flow rate and fluid viscosity were varied. The results demonstrated that the Torricelli equation consistently overestimated the pressure gradient. At 61% area stenosis, the overestimation exceeded 100%. In vivo studies are required to determine the relevance of the observations to clinical situations.
托里拆利方程表达了孔口流中流体速度与压力梯度之间的简单关系，目前它与无创多普勒超声结合使用，以确定二尖瓣狭窄、主动脉瓣狭窄以及其他心血管孔口处的压力梯度。然而，从理论上讲，托里拆利方程高估了主动脉瓣狭窄时的压力梯度，而博尔达方程应该更适用。本文给出了博尔达方程和托里拆利方程的简要推导教程。使用刚性壁、脉动流模拟实验研究了托里拆利方程在主动脉瓣狭窄中的适用性。同时收集了多普勒超声和压力测量数据。改变狭窄百分比、峰值流速和流体粘度。结果表明，托里拆利方程一直高估压力梯度。在面积狭窄61%时，高估超过100%。需要进行体内研究以确定这些观察结果与临床情况的相关性。
