= Proximal isovelocity surface area method
The \b[<proximal isovelocity surface area method>] estimates instantaneous flow towards a leaking <heart valve> from the upstream convergence field. <Color Doppler> supplies a contour at a chosen aliasing speed $v_a$. If that contour represents a hemisphere of radius $r$, flow approximately normal to it gives
$$
Q_R\simeq2\pi r^2v_a,\qquad A_{\rm eff}\simeq\frac{Q_R}{u_j},
$$
where the matched jet speed $u_j$ comes from <continuous-wave Doppler echocardiography>. The inferred <effective regurgitant orifice area> is a flow-equivalent area, not the area of the colored region or necessarily the anatomical hole.<Recommendations for Noninvasive Evaluation of Native Valvular Regurgitation by William A. Zoghbi and others>[Section II.B.6.c, p. 312, flow-convergence equations]{ref}
The physical idea is <conservation of mass>. More generally, $Q=\int_S\boldsymbol u\cdot\boldsymbol n\,dS$. Replacing that integral by one speed times a surface area requires an appropriate velocity component and geometry. <Doppler ultrasound> measures a component along the beam, so an apparent constant-color contour is not automatically a measured three-dimensional surface of constant normal speed.
For an original hemispherical example, let $r=0.6$ cm and $v_a=40$ cm/s. The modeled backward flow is $90.48$ mL/s. With matched $u_j=500$ cm/s, the effective area is $0.1810\,\mathrm{cm^2}$. If this area remains constant and the <velocity-time integral> is 140 cm, the modeled <regurgitant volume> is 25.33 mL. These are stipulated inputs, not severity thresholds.
Geometry and timing can each change that inference. In an ideal radial model restricted to a known <solid angle> $\Omega$, $Q=\Omega r^2v_a$; a hemisphere uses $\Omega=2\pi$. Thus a stipulated $\Omega=\pi$ gives half the flow at the same radius and speed. This illustrates <flow-convergence angle correction>; a real nonhemispherical or confined flow needs a justified geometric model rather than an arbitrary numerical adjustment.
Likewise, a radius observed at one instant must be paired with the jet speed at that instant. A peak effective area multiplied by a full-cycle velocity integral can overstate transported volume when the leak occupies only part of <systole>. The technical report explicitly discusses matching times, nonplanar convergence and changing regurgitant duration.<Recommendations for Noninvasive Evaluation of Native Valvular Regurgitation by William A. Zoghbi and others>[Section II.B.6.c, pp. 312–313, timing, duration and shape qualifications]{ref} The apparatus observes an aliased velocity pattern and a jet spectrum; the flow and area are derived through the stated model.
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