A model based on dimensional analysis for non-invasive quantification of valvular regurgitation under confined and impinging conditions

Abstract

The most descriptive measure of valvular insufficiency is the regurgitant volume. Current techniques for measuring it, however, are invasive and semi-quantitative at best. Cape and colleagues have recently developed a non-invasive technique for the quantitation of regurgitant flows corresponding to free jets cases. This technique is, unfortunately, not applicable to cases of jets constrained and/or impinging on the atrial walls as observed in many cases of mitral regurgitation. The purpose of this paper was therefore to develop an equation based on dimensional analysis, for calculating peak regurgitant flow rates from quantities than can be measured by Doppler ultrasound/echocardiography. The result is an equation for flow rate, Q o, as a function of orifice velocity, U o, a downstream centerline velocity, U m, at a distance, x, from the orifice, the diameter of the receiving chamber, D c, and the impingement height, H: Q 0 =(π U 0/4 )[a( U 0/U m )H cD d c x e] [2/c+d+e)] where a, c, d and e can be found by multiple linear regressions on pulsed Doppler jet centerline velocity data. The assumptions made in the derivation are such that they should be physiologically applicable. The advantage of this method compared to the previous one is its theoretical justification and ability to quantify accurately peak regurgitant flow rate, and total regurgitant volume.