IMG-31

Ultrasound round-trip attenuation

A_dB = 2 α f z. Soft-tissue α ≈ 0.5 dB cm⁻¹ MHz⁻¹.

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UltrasoundUS attenuation

Governing equation

A_{\mathrm{dB}}=2\alpha f z

$z \in \left[0.5, 20\right]$

where

\alpha: Attenuation α (dB/cm/MHz)
f: Frequency (MHz)
z: Depth (cm)
A: Round-trip loss (dB)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

A_{\mathrm{dB}}=2\alpha f z

$z \in \left[0.5, 20\right]$

$z = 0.5$ $A = 2.5$

Along the curve

②

Domain of the variable — blue

z_{\min} = 0.5,\quad z_{\max} = 20

$z \in \left[0.5, 20\right]$

$z = 0.5$ $z = 0.5$

Along the curve

③

Response curve — green

A_{\mathrm{dB}}=2\alpha f z

$z \in \left[0.5, 20\right]$

$z = 0.5$ $A = 2.5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}A}{\mathrm{d}z}

$z \in \left[0.5, 20\right]$

$z = 0.623$ $A^{\prime} = 5$

Along the curve

Lecture brief

Historical brief

Larmor precession, CT Beer projections, SNR and Nyquist sampling are why MRI and CT images exist as numbers. The lab computes frequency, dose and resolution limits. This sheet (IMG-31 — Ultrasound round-trip attenuation) is the form associated with US attenuation. Working symbols: $\alpha$ , $f$ , $z$ $\rightarrow$ $A$ . TGC restores the depth-dependent loss. Bone and air stop the beam (α huge, Z mismatch).

Purpose

Purpose: compute

A

from

\alpha

f

z

in Medical imaging via

A_{\mathrm{dB}}=2\alpha f z

A_dB = 2 α f z. Soft-tissue α ≈ 0.5 dB cm⁻¹ MHz⁻¹. Use it when a real medical imaging question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\alpha = 0.500\,\mathrm{dB/cm/MHz}

f = 5.000\,\mathrm{MHz}

z = 6.000\,\mathrm{cm}

, the governing relation

A_{\mathrm{dB}}=2\alpha f z

yields

A = 30.00\,\mathrm{dB}

. A fading echo from deeper tissue. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Attenuation α \alpha0.5 dB/cm/MHzFrequency f5 MHzDepth z6 cm

Outputs

Round-trip loss A30.00 dB

Reading speed

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Narration of this film

A fading echo from deeper tissue.

TGC restores the depth-dependent loss. Bone and air stop the beam (α huge, Z mismatch).

Reading speed

Watch on YouTube