A New Method for Noninvasive Quantification of Valvular Regurgitation Based on Conservation of Momentum

The noninvasive Doppler assessment of regurgitant volume from jet size is limited by the fundamental inequality of jet volume and regurgitant volume and by the dependence of jet dimensions on driving pressure and instrument settings for a given flow volume. Therefore, this study addresses the hypothesis that an equation could be derived from basic physical principles to quantify regurgitant volume with velocities that can be directly measured by Doppler echocardiography. The principle of conservation of momentum for free turbulent jets resembling many cardiac lesions yields an equation for regurgitant volume as a function of maximum jet velocity, a distal centerline velocity, and the intervening distance. This theory was tested throughout a range of physiologic flow rates and pressures (orifice velocities) in steady flow for 0.008-0.40 cm2 circular orifices and a noncircular orifice and in physiologic pulsatile flow for 0.08 and 0.20 cm2 circular orifices. Plots of centerline velocities versus axial distance coincided with those expected for such jets. Calculated and actual volumetric flows agreed well by linear regression in the turbulent jet: for steady flow rates,y=0.98x+0.09 (r=0.99, SEE=0.14 1/min), with similar correlations for circular and noncircular orifices; for pulsatile flow, y= 1.02x+0.03 for peak flow rate (r=0.98, SEE=0.18 I/min) and y=1.02x+0.58 for total regurgitant volume (r=0.95, SEE=0.81 ml). There was no significant effect of orifice size or location of velocity measurement within the turbulent jet. Therefore, for free jets resembling many clinical lesions, regurgitant flow rate and volume can be calculated noninvasively from Doppler velocities without planimetry of jet area. Because the required information is intrinsic to the jet, this method should apply regardless of associated valvular lesions. It should also apply to orifices of variable shape because turbulent eddies obliterate the details of flow at the orifice. The special case of jets impinging on walls must be considered separately for both this technique and flow mapping. (Circulation 1989;79:1343-1353)