= Ejection fraction
{title2=$\mathrm{EF}$}
\b[Ejection fraction] is the fraction of a ventricle's <end-diastolic volume> lost from its cavity during ejection:
$$
\mathrm{EF}=\frac{V_{\rm ED}-V_{\rm ES}}{V_{\rm ED}}
=1-\frac{V_{\rm ES}}{V_{\rm ED}}.
$$
The numerator is volumetric <stroke volume>; $V_{\rm ES}$ is <end-systolic volume>. The chamber must be specified: <right ventricular ejection fraction> concerns the <right ventricle>, whereas a calculation for the <left ventricle> concerns its own pair of volumes.
Time-resolved <magnetic resonance imaging> can estimate the two volumes from a consistently defined cavity. A primary right-ventricular study used cine images and three-dimensional modelling in 120 subjects.<Reference right ventricular systolic and diastolic function normalized to age, gender and body surface area from steady-state free precession cardiovascular magnetic resonance by Alicia M. Maceira and others>[Abstract, Methods and results]{ref} The <ejection fraction> is a derived quantity, not an additional independent volume observation.
An original example illustrates its scale dependence. Volumes of 120 and 60 mL give $\mathrm{EF}=50\%$ and <stroke volume> 60 mL. Volumes of 240 and 120 mL give the same <ejection fraction> but twice the <stroke volume>. Consequently, <ejection fraction> alone does not determine <cardiac output>; <heart rate> and an appropriate forward-flow interpretation are also needed.
Its response to shared measurement errors is instructive. Multiplying both measured volumes by the same positive scale $k$ leaves the <ejection fraction> unchanged. Adding the same offset $b$ does not:
$$
\widehat{\mathrm{EF}}=1-\frac{kV_{\rm ES}+b}{kV_{\rm ED}+b}
=\frac{k(V_{\rm ED}-V_{\rm ES})}{kV_{\rm ED}+b}.
$$
For the 120/60 mL example, $k=1$ and $b=20$ mL change the calculated fraction from $0.5$ to $60/140\approx0.429$, even though the volume difference remains 60 mL. This is an error-model example, not a universal correction for <image segmentation>. Likewise, cavity volume loss can include backward flow through a <heart valve>; the formula alone does not establish net useful delivery.
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