= Regurgitant fraction
{title2=$\mathrm{RF}=V_R/V_T$}
The \b[<regurgitant fraction>] is the proportion of a valve-related total ejected <blood> volume that returns through the leaking valve. For the left ventricular balance used to assess <mitral regurgitation>, let $V_T$ be total ventricular <stroke volume>, $V_F$ the matched forward aortic volume and $V_R$ the <regurgitant volume>. With no other abnormal communication or confounding valve leak,
$$
V_T=V_F+V_R,\qquad \mathrm{RF}=\frac{V_R}{V_T}=1-\frac{V_F}{V_T}.
$$
The imaging recommendations use complementary volume and flow measurements to quantify these quantities.<Recommendations for Noninvasive Evaluation of Native Valvular Regurgitation by William A. Zoghbi and others>[Section II.B.6, volumetric methods; Figure 8, p.316]{ref}
An original example takes $V_T=100$ mL and $V_F=70$ mL. Then $V_R=30$ mL and RF is 30%. The quotient $30/70\approx42.9\%$ instead expresses leakage relative to forward delivery; it is not the same fraction. The denominator is part of the definition.
Equal fractions also need not indicate equal transported amounts. A 30 mL leak out of 100 mL and a 60 mL leak out of 200 mL both have RF 30%. Conversely, an unchanged 30 mL <regurgitant volume> gives RF 50% if total ejection falls to 60 mL. These stipulated cases isolate the normalization rather than assigning a clinical severity category.
The two measurements in a derived RF may share errors. For $r=1-F/T$, first-order propagation gives
$$
u^2(r)\simeq\frac{u^2(F)}{T^2}+\frac{F^2u^2(T)}{T^4}
-\frac{2F}{T^3}\operatorname{Cov}(F,T).
$$
The <covariance> term should follow the actual acquisition and data reduction, rather than assuming independence because forward and total volume have different names.<Guide to the expression of uncertainty in measurement by JCGM>[§5.2.2, equation 13]{ref}
RF is therefore a normalized transport quantity. A peak jet <velocity>, a valve image and <ejection fraction> provide other information; none supplies RF without the matching flow or volume model. Specify the valve, flow convention and acquisition interval when comparing measurements.
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