Doppler ultrasound in aortic stenosis: in vitro studies of pressure gradient determination

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.