Physica

02 Imaging

Hounsfield unit

CT number from linear attenuation relative to water.

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Simulation

Hounsfield unit — Change the numbers; the scene follows.

Where it works

CT scanner

CT scanner

Gantry

Inside the rotating gantry: tube, bowtie, and detectors that define CTDI and HU.

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Formula

HU=1000μμwμw\mathrm{HU}=1000\frac{\mu-\mu_w}{\mu_w}

Typical values

Variables

Results

  • HU

    Hounsfield unit

    19.4HU

  • μ(HU)

    Check μ

    0.21cm⁻¹

Explanation

HU=1000μμwμw\mathrm{HU}=1000\frac{\mu-\mu_w}{\mu_w}

What it means

The Hounsfield unit rescales linear attenuation so water is 0 and air is −1000: HU = 1000 (μ−μ_w)/μ_w. Fat is negative (~ −80 to −100), soft tissue ~0–50, contrast-enhanced vessels hundreds, cortical bone hundreds to 1000+. This is a working relation in Diagnostic imaging.

Where it is used

Clinically it sits on the CT scanner — Gantry. Inside the rotating gantry: tube, bowtie, and detectors that define CTDI and HU. Diagnostic equations live on the tube, the detector, and the patient: magnification, air kerma, CTDI, and why bone lights up at 70 kV. They turn a technique chart into physics you can defend.

CT scanner · Open this machine

How to use it

Invert the formula to get μ from a measured HU if you need it for a dose or PET-AC calculation. Water μ depends on beam energy (typically ~0.20 cm⁻¹ at an effective ~60–70 keV). Change one input and watch the curve and the simulation follow.

Symbols

  • μMaterial attenuation0.21 cm⁻¹
  • μ_wWater attenuation0.206 cm⁻¹

Worked example

A typical case from the default values: μ = 0.21 cm⁻¹ (Material attenuation); μ_w = 0.206 cm⁻¹ (Water attenuation). Substituting into the relation gives HU = 19.4 HU; μ(HU) = 0.21 cm⁻¹. These are teaching numbers — align them with your machine.

Typical values give

  • HU = 19.4HU
  • μ(HU) = 0.21cm⁻¹

Where it comes from

The displayed formula is the working relation. CT number from linear attenuation relative to water. Usual reference: Bushberg. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Bushberg

Assumptions & limits

Defined for the scanner’s effective energy and reconstruction kernel. Beam hardening, contrast, and metal make HU non-linear. Not a density meter without calibration.

Pitfalls

kVp is not the same as effective energy. CTDI is not patient dose — SSDE and organ dose come after. Do not quote DLP as if it were effective dose without a k-factor. Defined for the scanner’s effective energy and reconstruction kernel. Beam hardening, contrast, and metal make HU non-linear. Not a density meter without calibration.

Keep this

Technique is physics: kV sets contrast, mAs sets noise, filtration sets the spectrum. Defined for the scanner’s effective energy and reconstruction kernel. Beam hardening, contrast, and metal make HU non-linear. Not a density meter without calibration.

In this specialty

Diagnostic imaging