08 Ultrasound

Depth from round-trip time

13 µs/cm rule in soft tissue (c = 1540 m/s).

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Simulation

Depth from round-trip time — 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.

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Formula

d = \frac{c t}{2}

Variables

t · Round-trip timeµsc · Speed of soundm/s

Results

d
Depth
8.008cm
d
Depth
80.08mm
t/d
Time per cm
12.99µs/cm

Explanation

d = \frac{c t}{2}

What it means

Pulse-echo ranging: depth = c t / 2. In soft tissue c = 1540 m/s so t/d ≈ 13 µs per cm of depth. The scanner assumes this c; if the true speed differs, distances are wrong (a classic fat or silicone pitfall). 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 round-trip time in µs. 104 µs → 8 cm. The time-per-cm output should sit near 13 if c is 1540. Change one input and watch the curve and the simulation follow.

Symbols

tRound-trip time104 µs
cSpeed of sound1,540 m/s

Worked example

A typical case from the default values: t = 104 µs (Round-trip time); c = 1,540 m/s (Speed of sound). Substituting into the relation gives d = 8.008 cm; d = 80.08 mm; t/d = 12.99 µs/cm. These are teaching numbers — align them with your machine.

Typical values give

d = 8.008cm
d = 80.08mm
t/d = 12.99µs/cm

Where it comes from

The displayed formula is the working relation. 13 µs/cm rule in soft tissue (c = 1540 m/s). Usual reference: Edelman / Bushberg. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Edelman / Bushberg

Assumptions & limits

Constant speed, straight ray, no refraction. Beam path through mixed fat/muscle is not 1540 everywhere — spatial calipers can be biased.

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. Constant speed, straight ray, no refraction. Beam path through mixed fat/muscle is not 1540 everywhere — spatial calipers can be biased.

Keep this

Gel, angle, and assumed speed of sound — get those three right before you trust a centimetre. Constant speed, straight ray, no refraction. Beam path through mixed fat/muscle is not 1540 everywhere — spatial calipers can be biased.

In this specialty

Ultrasound