 Flow-profile mismatch in Doppler stroke-volume estimation

Flow-profile mismatch in Doppler stroke-volume estimation occurs when the velocity used in a stroke volume calculation does not represent the spatial average over the measured opening. The exact instantaneous volumetric flow rate isfor fixed area $A$. Consequently $\mathrm{SV}=A\int \bar{v}(t)dt$. Replacing $\bar{v}$ by a centerline velocity or fastest spectral envelope requires an additional profile assumption. The ASE report distinguishes the modal part of a pulsed Doppler spectrum from the outer continuous-wave envelope representing the fastest detected cells.^[ref]

An original family of axisymmetric profiles makes the missing factor explicit. Within a circular opening of radius $R$, supposeHere $u(t)$ is the centerline velocity. Integrating concentric annuli givesThe Doppler profile correction factor is therefore $\alpha =n/(n+2)$ for this stipulated family. A parabolic profile $n=2$ has $\alpha =1/2$; a blunter profile $n=8$ has $\alpha =0.8$. Both have the same centerline velocity and vanish at the wall. These shapes are examples, not fitted cardiac profiles.

For $R=1\mathrm{cm}$ and a centerline velocity-time integral of $20\mathrm{cm}$, uncorrected multiplication by $A=\pi \mathrm{c}{\mathrm{m}}^2$ gives $62.8\mathrm{mL}$. The two model profiles instead transport approximately $31.4$ and $50.3\mathrm{mL}$. Identical peak data can therefore support different transported volumes when the profile differs.

Real Doppler measurements also involve beam direction, sample-volume extent and signal processing. Their spectral envelope need not coincide with the literal centerline trace used in this example. The illustration isolates the averaging issue; it is not a universal factor-of-two correction for clinical measurements. The sampling site and anatomical area must be matched as well.^[ref]