= Doppler profile correction factor
{c}
A \b[Doppler profile correction factor] converts a specified sampled <velocity> into the area-mean normal <velocity> needed to calculate <volumetric flow rate>. For a fixed opening of <cross-sectional area> $A$ and nonzero sampled trace $u_s(t)$, define
$$
\alpha(t)=\frac{\bar v(t)}{u_s(t)},\qquad
Q(t)=A\alpha(t)u_s(t),\qquad
V=A\int\alpha(t)u_s(t)\,dt.
$$
The definition depends on both the spatial flow profile and what the instrument's sampled trace represents. A centerline trace, spectral mode and fastest detected envelope need not have the same correction. The primary ASE report distinguishes these spectral quantities and requires matched locations for <velocity> and <area> measurements.<Recommendations for Quantification of Doppler Echocardiography by Miguel A. Quiñones and others>[PW Doppler and CW Doppler, printed pp. 168–169]{ref}
Even if each instantaneous correction is known, the appropriate correction for a whole <velocity-time integral> is generally not its ordinary time average. Provided the denominator is nonzero,
$$
\alpha_{\rm eff}=\frac{\int\alpha(t)u_s(t)\,dt}{\int u_s(t)\,dt},\qquad
V=A\alpha_{\rm eff}\,\mathrm{VTI}_s.
$$
This <velocity-weighted Doppler profile correction> gives greater influence to intervals carrying more of the sampled <velocity-time integral>.
In an original two-interval calculation, each interval lasts one second. Let sampled <velocities> be 10 and 30 cm/s and instantaneous corrections 0.5 and 1.0. The sampled <velocity-time integral> is 40 cm, while its corrected counterpart is $0.5\times10+1\times30=35$ cm. Thus $\alpha_{\rm eff}=0.875$, whereas the ordinary average correction is 0.75. For $A=1\,\mathrm{cm^2}$, the latter would predict 30 mL instead of the model's 35 mL.
When the sampled <velocity> is nonnegative, this is a weighted mean and lies between the instantaneous corrections. Reversing <fluid flow> can create cancellation in the denominator, so that conclusion need not hold. A factor measured in a steady tube also cannot be assigned to a changing cardiac profile without evidence. The calculation explains an averaging requirement; it supplies no universal clinical correction.
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