IMG-24

Hounsfield unit

HU = 1000 (μ − μw)/μw. Water is 0, air is −1000.

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CTHounsfield

Governing equation

\mathrm{HU}=1000(\mu-\mu_w)/\mu_w

$\mu \in \left[0, 0.8\right]$

where

\mu: Attenuation μ (1/cm)
\mu_w: Water μ (1/cm)
HU: Hounsfield unit (HU)

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

\mathrm{HU}=1000(\mu-\mu_w)/\mu_w

$\mu \in \left[0, 0.8\right]$

$\mu = 0$ $HU = -1000$

Along the curve

②

Domain of the variable — blue

\mu_{\min} = 0,\quad \mu_{\max} = 0.8

$\mu \in \left[0, 0.8\right]$

$\mu = 0$ $\mu = 0$

Along the curve

③

Response curve — green

\mathrm{HU}=1000(\mu-\mu_w)/\mu_w

$\mu \in \left[0, 0.8\right]$

$\mu = 0$ $HU = -1000$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}HU}{\mathrm{d}\mu}

$\mu \in \left[0, 0.8\right]$

$\mu = 0.005$ $HU^{\prime} = 5000$

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-24 — Hounsfield unit) is the form associated with Hounsfield. Working symbols: $\mu$ , $\mu_w$ $\rightarrow$ $HU$ . Bone ~ +400 to +1000, fat ~ −50 to −100. kV and reconstruction kernel shift HU slightly.

Purpose

Purpose: compute

HU

from

\mu

\mu_w

in Medical imaging via

\mathrm{HU}=1000(\mu-\mu_w)/\mu_w

HU = 1000 (μ − μw)/μw. Water is 0, air is −1000. 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

\mu = 0.220\,\mathrm{1/cm}

\mu_w = 0.200\,\mathrm{1/cm}

, the governing relation

\mathrm{HU}=1000(\mu-\mu_w)/\mu_w

yields

HU = 100\,\mathrm{HU}

. A grey scale anchored at water and air. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Attenuation μ \mu0.22 1/cmWater μ \mu_w0.2 1/cm

Outputs

Hounsfield unit HU100 HU

Reading speed

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Narration of this film

A grey scale anchored at water and air.

Bone ~ +400 to +1000, fat ~ −50 to −100. kV and reconstruction kernel shift HU slightly.

Reading speed

Watch on YouTube