08 Ultrasound

Maximum PRF and aliasing

PRF_max = c/(2d). Nyquist velocity v_max = c PRF / (4 f₀ cos θ).

Play lecture Cast to TV

Listen

Listen · English

Simulation

Maximum PRF and aliasing — 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

\mathrm{PRF}_{max}=c/(2d),\quad v_{max}=c\,\mathrm{PRF}/(4 f_0\cos\theta)

Variables

d · Depthcmc · Speed of soundm/sf₀ · Probe frequencyMHzθ · Doppler angle°PRF · PRF usedkHz

Results

PRF_max
Max PRF for depth
7.7kHz
v_max
Nyquist velocity
30.8cm/s

Explanation

\mathrm{PRF}_{max}=c/(2d),\quad v_{max}=c\,\mathrm{PRF}/(4 f_0\cos\theta)

What it means

The next pulse cannot leave until the previous echo from depth d has returned: PRF_max = c/(2d). Nyquist velocity in Doppler is c PRF / (4 f₀ cosθ). High-flow, deep vessels force a compromise or a shift to CW / high-PRF. 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

10 cm depth → PRF_max ≈ 7.7 kHz. At 5 MHz, 0°, v_max ≈ 60 cm/s at that PRF. Scale, baseline shift and steering change the usable limit. Change one input and watch the curve and the simulation follow.

Symbols

dDepth10 cm
cSpeed of sound1,540 m/s
f₀Probe frequency5 MHz
θDoppler angle0 °
PRFPRF used4 kHz

Worked example

A typical case from the default values: d = 10 cm (Depth); c = 1,540 m/s (Speed of sound); f₀ = 5 MHz (Probe frequency); θ = 0 ° (Doppler angle); PRF = 4 kHz (PRF used). Substituting into the relation gives PRF_max = 7.7 kHz; v_max = 30.8 cm/s. These are teaching numbers — align them with your machine.

Typical values give

PRF_max = 7.7kHz
v_max = 30.8cm/s

Where it comes from

The displayed formula is the working relation. PRF_max = c/(2d). Nyquist velocity v_max = c PRF / (4 f₀ cos θ). Usual reference: Bushberg / Edelman. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Bushberg / Edelman

Assumptions & limits

Single-gate, no packet overhead. Colour Doppler uses several pulses per line so the usable frame-limited PRF is lower than this range-only limit.

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, no packet overhead. Colour Doppler uses several pulses per line so the usable frame-limited PRF is lower than this range-only limit.

Keep this

Gel, angle, and assumed speed of sound — get those three right before you trust a centimetre. Single-gate, no packet overhead. Colour Doppler uses several pulses per line so the usable frame-limited PRF is lower than this range-only limit.

In this specialty

Ultrasound