= Pulsed-wave Doppler echocardiography
= PW Doppler echocardiography
{c}
{synonym}
\b[Pulsed-wave Doppler echocardiography] uses timed <ultrasound> transmissions and returns to measure motion within a selected sampling region of the <heart> or nearby vessels. An echo's round-trip delay provides depth information, so a time window can select a location. The resulting Doppler spectrum describes a finite sample volume rather than an exact point.<Recommendations for Quantification of Doppler Echocardiography by Miguel A. Quiñones and others>[General Principles, p.167; PW Doppler, pp.168–169]{ref}
For sound speed $c$ and round-trip delay $t$, the ideal depth is $d=ct/2$. Avoiding ambiguity between successive pulses in a simple single-depth system requires waiting at least $2d/c$ before the next pulse. If $f_r$ is the <pulse repetition frequency>, this gives
$$
f_r\le\frac{c}{2d}.
$$
The Doppler signal is sampled once per pulse, so unaliased shifts obey $|\Delta f|<f_r/2$. For aligned flow and transmitted frequency $f_0$,
$$
|v|<\frac{cf_r}{4f_0}\le\frac{c^2}{8f_0d}.
$$
This is the <pulsed Doppler depth-velocity tradeoff> in the stated idealization. With $c=1540\,\mathrm{m/s}$, $f_0=2.5\,\mathrm{MHz}$ and $d=0.10\,\mathrm m$, the highest ideal pulse rate is $7700\,\mathrm{Hz}$ and the corresponding speed limit is about $1.19\,\mathrm{m/s}$. Doubling the depth halves both limits. Practical timing margins can reduce them further.
<Aliasing> is an ambiguity of the sampled signal, not proof that blood reverses direction. For example, sinusoidal Doppler shifts of $5000\,\mathrm{Hz}$ and $1000\,\mathrm{Hz}$ have identical complex samples at a $4000\,\mathrm{Hz}$ pulse rate, because their frequencies differ by exactly one sampling rate. The example concerns the Doppler signal, not direct sampling of the megahertz acoustic carrier.
High-pulse-rate variants can trade unique range localization for a larger velocity range. <Continuous-wave Doppler echocardiography> instead transmits and receives continuously, accepting depth ambiguity. The choice of acquisition method therefore changes what information the measured spectrum contains.<Recommendations for Quantification of Doppler Echocardiography by Miguel A. Quiñones and others>[General Principles and high-PRF discussion, pp.167–168]{ref}
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