Impact of finite orifice size on proximal flow convergence: Implications for Doppler quantification of valvular regurgitation

Analysis of velocity acceleration proximal to a regurgitant valve has been proposed as a method to quantify the regurgitant flow rate (Q(o)). Previous work has assumed inviscid flow through an infinitesimal orifice, predicting hemispheric isovelocity shells, with calculated flow rate given by Q(c)=2πr(N)²V(N), where V(N) is user-selected velocity of interest and r(N) is the distance from that velocity to the orifice. To validate this approach more rigorously and investigate the impact of finite orifice size on the assumption of hemispheric symmetry, numerical and in vitro modeling was used. Finite-difference modeling demonstrated hemispheric shape for contours more than two orifice diameters from the orifice. More proximal than this (where the measured velocity V(N) exceeded 3% of the orifice velocity V(o)), flow was progressively underestimated, with a proportional error ΔQ/Q(o) nearly identical to the ratio of contour velocity to orifice velocity, V(N)/V(o). For the in vitro investigations, flow rates from 4.3 to 150 cm³/sec through 0.3 and 1.0 cm² circular orifices were imaged with color Doppler with aliasing velocities from 19 to 36 cm/sec. Overall, the calculated flow (assuming hemispheric symmetry) correlated well with the true flow, Q(c)=0.88Q(o)-7.82 (r=0.945, SD=12.2 cm³/sec, p<0.0001, n=48), but progressively underestimated flow when the V(N) approached the orifice velocity V(o). Applying a correction factor predicted by the numerical modeling, ΔQ was improved from -13.81±13.01 cm³/sec (mean±SD) to +1.54±5.67 cm³/sec. These data indicate that flow can be accurately calculated using the hemispheric assumption as Q(c)=2πr(N)²V(N) when V(N)<<V(o). For larger V(N), flow is systematically underestimated, but a more accurate estimate may be obtained by multiplying Q(c) by V(o)/(V(o)- V(N)). These observations lend additional support for the clinical use of the proximal acceleration concept and suggest a simple correction factor to make a more accurate estimation of valvular regurgitation.