= Doppler echocardiography
\b[Doppler echocardiography] combines <echocardiography> with <Doppler ultrasound> to examine motion, particularly <blood flow>, in and around the <heart>. The image locates anatomical structures, while frequency shifts in returning <ultrasound> provide information about motion along the beam. It supplies a velocity measurement rather than a direct measurement of <cardiac output>.
For a moving scatterer with speed $v$, beam-to-flow angle $\theta$, transmitted frequency $f_0$ and sound speed $c$, the leading approximation is
$$
\Delta f\simeq\frac{2f_0v\cos\theta}{c}.
$$
The two-way factor arises because the outgoing and returning wave both interact with the moving scatterer. For stipulated $f_0=2.5\,\mathrm{MHz}$, $v=1.0\,\mathrm{m/s}$, $c=1540\,\mathrm{m/s}$ and $\theta=0$, the shift is about $3.25\,\mathrm{kHz}$. At $60^\circ$ the same flow gives half that shift. Interpreting the latter as perfectly aligned flow would underestimate the speed by a factor of two.
<Pulsed-wave Doppler echocardiography> uses timing to select a sampling region, whereas <continuous-wave Doppler echocardiography> receives signals continuously along the beam. The acquired velocity spectrum and the selected anatomical region must therefore be interpreted together. A moving tissue signal and a blood-flow signal are different observations even if both produce a <Doppler effect>.
A motivating primary validation by <Halfdan Ihlen> and colleagues compared Doppler-derived <cardiac output> with independent thermodilution and Fick measurements. The protocol included changes in flow during dobutamine infusion, testing correspondence over changing conditions rather than only one resting observation.<Determination of cardiac output by Doppler echocardiography by Halfdan Ihlen and others>[Abstract: ten thermodilution comparisons and eleven Fick-method comparisons]{ref}
Turning a velocity record into transported volume additionally requires an appropriate flow area and representative velocity distribution. The <velocity-time integral> makes that connection explicit. A large peak velocity alone neither determines the volume moved per beat nor identifies a unique <clinical diagnosis>.
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