08 Ultrasound

PW Doppler aliasing limit

Nyquist velocity = PRF × c / (4 f₀ cosθ). Raise PRF, drop f₀, or switch to CW to un-alias.

Play lecture Cast to TV

Listen

Listen · English

Simulation

PW Doppler aliasing limit — Change the numbers; the scene follows.

Where it works

Ultrasound

Console

On the console — depth (13 µs/cm), PRF, frame rate, dynamic range, aliasing limit.

Open this machine

Formula

v_{\mathrm{Nyq}}=\frac{\mathrm{PRF}\cdot c}{4 f_0\cos\theta}

Variables

PRF · Pulse repetition frequencykHzf_0 · Transducer frequencyMHzθ · Doppler angle°c · Speed of soundm/s

Results

v_Nyq
Nyquist velocity
1.155m/s
v_Nyq
Nyquist velocity
115.5cm/s
PRF/2
Max Doppler shift
3,000Hz

Curve

Explanation

v_{\mathrm{Nyq}}=\frac{\mathrm{PRF}\cdot c}{4 f_0\cos\theta}

What it means

Pulsed Doppler samples the RF at PRF, so the Doppler shift aliases above PRF/2. Translating f_D = 2 v f₀ cosθ / c gives a maximum unambiguous velocity PRF c / (4 f₀ cosθ). Deep sample volume forces a low PRF (wait for the echo) and is exactly when the jet aliases — the reason we keep a CW probe on the echo cart. Baseline shift buys you almost 2× in one direction at the cost of the other. This is a working relation in Ultrasound.

Where it is used

Clinically it sits on the Ultrasound — Console. On the console — depth (13 µs/cm), PRF, frame rate, dynamic range, aliasing limit. Ultrasound equations sit on the probe face and along the beam: impedance, Snell, Doppler, MI and TI. They explain why gel matters, why aliasing appears, and why a mechanical index is on the screen.

Ultrasound · Open this machine

How to use it

Enter PRF (kHz), centre frequency (MHz), angle (0 = aligned) and c (1540 m/s). 6 kHz, 2 MHz, 0° → v_Nyq ≈ 1.16 m/s. A 4 m/s AS jet will alias — use CW. Change one input and watch the curve and the simulation follow.

Symbols

PRFPulse repetition frequency6 kHz
f_0Transducer frequency2 MHz
θDoppler angle0 °
cSpeed of sound1,540 m/s

Worked example

A typical case from the default values: PRF = 6 kHz (Pulse repetition frequency); f_0 = 2 MHz (Transducer frequency); θ = 0 ° (Doppler angle); c = 1,540 m/s (Speed of sound). Substituting into the relation gives v_Nyq = 1.155 m/s; v_Nyq = 115.5 cm/s; PRF/2 = 3,000 Hz. These are teaching numbers — align them with your machine.

Typical values give

v_Nyq = 1.155m/s
v_Nyq = 115.5cm/s
PRF/2 = 3,000Hz

Where it comes from

The displayed formula is the working relation. Nyquist velocity = PRF × c / (4 f₀ cosθ). Raise PRF, drop f₀, or switch to CW to un-alias. Usual reference: Edelman / Kremkau. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Edelman / Kremkau

Assumptions & limits

Single-gate PW, constant PRF, no HPRF (multi-gate) mode. Angle in the denominator: 60° already halves the Nyquist velocity, which is why we stay < 20° in vascular work when we can.

Pitfalls

Soft-tissue 1540 m/s is an assumption — not a measurement in that patient. Doppler angle 90° gives no shift. MI and TI are on-screen estimates, not absorbed dose. Single-gate PW, constant PRF, no HPRF (multi-gate) mode. Angle in the denominator: 60° already halves the Nyquist velocity, which is why we stay < 20° in vascular work when we can.

Keep this

Gel, angle, and assumed speed of sound — get those three right before you trust a centimetre. Single-gate PW, constant PRF, no HPRF (multi-gate) mode. Angle in the denominator: 60° already halves the Nyquist velocity, which is why we stay < 20° in vascular work when we can.

In this specialty

Ultrasound