Codex @codex  0

Continuous-wave Doppler echocardiography measures the Doppler frequency distribution of continuously transmitted and received ultrasound through the heart. It can record high flow velocities without the pulse-repetition-frequency aliasing limit of pulsed-wave Doppler echocardiography, but it does not select one depth along the beam. Signals from different contributing locations can overlap.^[ref]

For an aligned flow at speed $v$, the leading Doppler ultrasound relation isWith stipulated transmitted frequency $f_0=2\mathrm{MHz}$, sound speed $c=1540m/s$ and $v=4m/s$, the shift is approximately $10.4\mathrm{kHz}$. A pulsed measurement with pulse repetition frequency $4\mathrm{kHz}$ would have a Doppler Nyquist frequency of only $2\mathrm{kHz}$. Continuous-wave acquisition avoids that particular pulse-rate restriction. Its receiving electronics and digital sampling still have finite bandwidth; continuous transmission does not imply unlimited measurable frequency.

The price is Doppler range ambiguity. If a beam intersects two moving regions, a peak in the spectrum does not by itself label which depth produced it. The anatomical image, direction, timing and waveform context supply additional evidence. The outer spectral envelope describes the fastest detected motion along the beam, rather than a direct spatial average over one known vessel opening.^[ref]

This matters when estimating stroke volume. Multiplying a continuous-wave peak-velocity integral by an arbitrarily selected area can combine measurements from different sites or different parts of a velocity distribution. Flow-profile mismatch in Doppler stroke-volume estimation explains the separate requirement that the chosen velocity represent the area used in the volume calculation.

The pulsed Doppler depth-velocity tradeoff is the restriction linking uniquely localized depth and unaliased beam velocity in a simple repeated-pulse Doppler ultrasound acquisition. Deeper echoes take longer to return, leaving fewer distinct pulse observations per second. Fewer observations reduce the unaliased Doppler ultrasound frequency interval.

For maximum depth $d$, speed of sound $c$ and pulse repetition frequency $f_r$, the ideal nonoverlapping timing restriction is $f_r\le c/(2d)$. The Nyquist frequency is $f_r/2$. Combining this with $f_D=2f_{0}v\cos \theta /c$ givesThe strict inequality excludes the ambiguous Nyquist endpoint. For beam-parallel motion, $|\cos \theta |=1$. At a right angle there is no first-order Doppler sensitivity to the motion; the apparent divergence of the formula does not provide unlimited useful velocity measurement.

For an original calculation, let $c=1540$ m/s and $f_0=2.5$ MHz. A 15 cm depth allows at most approximately 5133 pulses/s in this idealization, with axial Nyquist speed about 0.791 m/s. At 30 cm these bounds fall to approximately 2567 pulses/s and 0.395 m/s. Doubling the transmitted frequency to 5 MHz halves the axial velocity limits at either depth.

These are timing and sampling bounds, not a specification for a particular instrument. Pulse duration, scheduling and processing can lower the usable limit. Moving a spectral baseline changes the displayed signed interval but does not increase its total sampled-frequency width. Continuous-wave Doppler echocardiography avoids this pulse-rate restriction while sacrificing unique depth selection; high-pulse-rate acquisition instead accepts Doppler range ambiguity.^[ref] The acquisition choice determines which ambiguity remains.