{title2=$A_{\rm eff}$}

The \b[<effective regurgitant orifice area>] is a flow-equivalent area for a leaking <heart valve>: the instantaneous backward volume flow rate $Q_R(t)$ divided by the corresponding jet speed $u_j(t)$,
$$
A_{\rm eff}(t)=\frac{Q_R(t)}{u_j(t)}.
$$
It characterizes the effective stream passing through the leak. It need not equal the anatomical opening traced on an image, because flow contracts and its <velocity> is not uniform across every geometric surface. The <vena contracta> and the upstream convergence pattern provide complementary flow information.<Recommendations for Noninvasive Evaluation of Native Valvular Regurgitation by William A. Zoghbi and others>[Sections II.B.3.b–c and II.B.6, pp. 309–313]{ref}

The <proximal isovelocity surface area method> illustrates how an area can be inferred without drawing the hole itself. <Color Doppler> identifies an upstream surface at a selected aliasing speed $v_a$. In an ideal hemispherical convergence model of radius $r$, <conservation of mass> gives
$$
Q_R\simeq2\pi r^2v_a,\qquad A_{\rm eff}\simeq\frac{2\pi r^2v_a}{u_j}.
$$
Continuous-wave <Doppler echocardiography> supplies the jet speed. The convergence radius and jet speed must refer to matching times. The hemisphere is an assumption about flow geometry, not a property guaranteed by the instrument.<Recommendations for Noninvasive Evaluation of Native Valvular Regurgitation by William A. Zoghbi and others>[Section II.B.6.c, p. 312; timing and shape qualifications, pp. 312–313]{ref}

For an original model calculation, let $r=0.8$ cm, $v_a=30$ cm/s and $u_j=500$ cm/s. Then $Q_R\simeq120.64$ mL/s and $A_{\rm eff}\simeq0.2413\,\mathrm{cm^2}$. At otherwise fixed inputs a ten-percent radius overestimate multiplies the inferred area by $1.1^2=1.21$. The radius-squared dependence explains why a small geometric measurement error can matter substantially.

An instantaneous effective area and an integrated <regurgitant volume> answer different questions:
$$
V_R=\int A_{\rm eff}(t)u_j(t)\,dt.
$$
If the effective area is constant, this becomes $V_R=A_{\rm eff}\,\mathrm{VTI}$ using the <velocity-time integral>. A stipulated VTI of 150 cm with the calculated constant area gives 36.19 mL. A single peak area generally cannot be pulled outside the integral when the leak changes during <systole>. Alternatively, $V_R/\mathrm{VTI}$ defines a velocity-weighted mean effective area over that interval. The technical report explicitly distinguishes instantaneous convergence measurements from temporally varying regurgitation.<Recommendations for Noninvasive Evaluation of Native Valvular Regurgitation by William A. Zoghbi and others>[Section II.B.6.c, timing and duration of regurgitation, pp. 312–313]{ref}


 Effective regurgitant orifice area (source code)