CT Scanning

Spec mapping: OCR H556 Module 6.5 — Medical Imaging (computed tomography: rotating X-ray source and detector array; acquisition of many 1-D projections from different angles; computer reconstruction of a 2-D cross-section by filtered back-projection or iterative methods; stacking 2-D slices into a 3-D volume; the Hounsfield scale; trade-off between higher dose and 3-D diagnostic information). Refer to the official OCR H556 specification document for exact wording.

A conventional X-ray radiograph is a two-dimensional shadow projection of a three-dimensional body. All the structures lying along a single ray from source to detector are superimposed onto a single image point. If a tumour sits directly behind a rib, the rib's attenuation can completely mask it. If two soft-tissue organs overlap, their boundaries are impossible to separate. These limitations restricted X-ray imaging for decades, and were only overcome in 1971 when the British engineer Godfrey Hounsfield, working at EMI, built the first computed tomography (CT) scanner. Within a few years Hounsfield's device had revolutionised diagnostic radiology, and he shared the 1979 Nobel Prize in Physiology or Medicine for the achievement.

CT imaging is now one of the commonest diagnostic tools in any major hospital. A modern scanner can image an entire human body in a few seconds at millimetre resolution, revealing bones, organs, tumours and blood vessels in three dimensions. This lesson covers the principle of CT, the image-reconstruction process at A-Level depth, the Hounsfield scale, and the compromises involved in clinical use — all part of Module 6.5 — Medical Imaging of the OCR A-Level Physics A specification (H556).

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The Basic Idea

A CT scanner acquires many X-ray images of the same slice of the patient's body from different angles, then uses a computer to reconstruct a cross-sectional image of the slice from the collection of projections. The word tomography comes from the Greek tomos ("slice") and graphein ("to write") — literally, "slice drawing".

Crucially, the computer does more than just average or overlay the images. It uses the information encoded in the many projections to solve for the X-ray attenuation at every point in the slice. The classical pedagogical algorithm is filtered back-projection, a computational technique that A-Level students need to describe in qualitative terms but not derive. The result is a two-dimensional map of attenuation coefficients across the slice. By stacking many such slices in sequence, a three-dimensional volume of the patient is built up, ready for inspection from any direction.

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How a CT Scanner Works

A modern CT scanner consists of:

• An X-ray source and a detector array mounted on a rotating gantry, on diametrically opposite sides of the patient.
• A patient table (couch) that slides through the gantry, moving the patient incrementally through the imaging plane.
• A high-power computer that reconstructs images from the raw projection data in near-real time.

The source–detector pair rotates around the patient through 360°, collecting a one-dimensional line image at each of many different angles (typically several hundred to a few thousand). Each 1-D image represents the total attenuation along a set of parallel rays through the slice at that angle. After a complete rotation — taking less than a second in modern scanners — the couch moves forward slightly and a new slice is imaged. In helical (spiral) CT the couch moves continuously while the gantry rotates, so the source traces out a helical path through the patient and the whole body can be scanned in a few breaths.

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Reconstruction: From Projections to Image

The computational problem at the heart of CT is this: given the total attenuation $-\ln(I/I_0)$−ln(I/I0​) along each of many rays through the slice, reconstruct the local attenuation coefficient $\mu(x,y)$μ(x,y) at every point $(x,y)$(x,y) in the slice.

A simple, almost pictorial way to picture the algorithm is filtered back-projection:

• Each one-dimensional projection is swept back across the image plane at the angle it was taken, "laying down" the measured attenuation along the direction of the ray.
• Many such back-projections from different angles are superimposed.
• Where real structure exists, contributions from many rays reinforce; where there is no structure, the streaks from individual back-projections wash out.
• A mathematical filter is applied to each projection before back-projection, which removes the blurring inherent in raw back-projection. In the limit of infinitely many projections the reconstruction becomes exact.

flowchart TB
    Start["X-ray source emits<br/>fan-beam across patient"]
    Det["Detector array records<br/>1-D projection at this angle"]
    Rot["Gantry rotates by<br/>small angle Δθ"]
    Mult["Loop: repeat for<br/>many angles (~1000)"]
    Filt["Apply ramp filter<br/>to each projection"]
    Recon["Back-project all<br/>filtered projections<br/>onto image plane"]
    Slice["2-D slice in HU"]
    Stack["Couch advances;<br/>next slice"]
    Vol["3-D volume image"]
    Start --> Det
    Det --> Rot
    Rot --> Mult
    Mult --> Filt
    Filt --> Recon
    Recon --> Slice
    Slice --> Stack
    Stack --> Vol

Modern scanners use iterative reconstruction in addition to (or instead of) filtered back-projection: they start with a guess for $\mu(x,y)$μ(x,y), forward-project it to predict what the projections would be, compare with the measured projections, and update the image to reduce the discrepancy. Iterative methods are more computationally intensive but produce cleaner images at lower dose.

For A-Level purposes you must be able to explain three things:

• Why multiple angles are necessary. A single projection cannot distinguish between a small dense object and a diffuse weakly-attenuating one along the same line of sight. More projections break this degeneracy.
• What the computer does. It reconstructs a 2-D map of attenuation coefficients $\mu(x,y)$μ(x,y) from the set of 1-D projections.
• Why the result is 3-D. Stacking many adjacent 2-D slices produces a 3-D volume that can be sliced and visualised in any plane.

You do not need to know the mathematics of the Radon transform or its inverse.

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The Hounsfield Scale

CT images are displayed in grey-scale, with each pixel representing an attenuation coefficient. To make images comparable across different scanners and different patients, the attenuation is expressed relative to water on the Hounsfield scale:

$\text{HU} = 1000 \times \dfrac{\mu_\text{tissue} - \mu_\text{water}}{\mu_\text{water}}.$HU=1000×μwater​μtissue​−μwater​​.

HU ("Hounsfield units") is dimensionless. By definition:

• Water has HU = 0.
• Air has HU $\approx -1000$≈−1000.
• Fat has HU $\approx -100$≈−100.
• Soft tissue has HU $\approx 10$≈10–$80$80 (typically 30–50).
• Fresh blood has HU $\approx 30$≈30–$45$45; clotted blood appears denser ($\sim 70$∼70–$80$80).
• Dense cortical bone has HU $\approx +1000$≈+1000 to $+2000$+2000.
• Metallic implants have HU $> 3000$>3000.

The huge range — from $-1000$−1000 (air) to several thousand (metal) — means that no single grey-scale display can show all tissues at once. Radiologists use windowing: selecting a limited range of HU values to map to the full grey-scale. A "lung window" might run from $-1000$−1000 to $-500$−500, showing lung tissue clearly. A "bone window" might run from 0 to $+1500$+1500, optimising display of bones and fractures. Several different windows are produced from the same raw projection data without re-scanning.

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Worked Example 1: HU of a soft tissue

A CT pixel shows an attenuation coefficient of $\mu_\text{tissue} = 0.21$μtissue​=0.21 cm$^{-1}$−1; water at the same effective beam energy has $\mu_\text{water} = 0.19$μwater​=0.19 cm$^{-1}$−1. Find the Hounsfield value of the pixel.

Solution.

$$\begin{aligned} \text{HU} &= 1000 \times \dfrac{0.21 - 0.19}{0.19} \\ &= 1000 \times \dfrac{0.02}{0.19} \\ &\approx 105. \end{aligned}$$HU​=1000×0.190.21−0.19​=1000×0.190.02​≈105.​

A value of $\approx 105$≈105 HU is consistent with soft tissue containing a small amount of contrast agent, or with dense bone marrow. Pure soft tissue without contrast would be closer to $40$40 HU.

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Worked Example 2: Why many angles?

Why is it impossible to reconstruct a 2-D image from a single X-ray projection, no matter how high the resolution of the detector?

Solution. A single projection gives only the total attenuation along each ray through the slice, $\int \mu(x,y)\,\mathrm{d}s$∫μ(x,y)ds along the ray. It cannot distinguish between different distributions of attenuation along the same ray. For example, a small dense object positioned at any depth along the ray would produce the same total attenuation. To localise the object in two dimensions you need at least a second projection from a different angle.

More generally, reconstructing a full 2-D attenuation map $\mu(x,y)$μ(x,y) requires projections from many angles — enough to sample the Radon transform of $\mu$μ with sufficient angular density to permit the inverse transformation. In practice modern scanners take of order $10^3$103 projections per slice.

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Worked Example 3: HU of a contrast-enhanced vessel

A blood vessel filled with iodinated contrast medium has $\mu = 0.50$μ=0.50 cm$^{-1}$−1 at the effective beam energy, against water at $\mu_\text{water} = 0.20$μwater​=0.20 cm$^{-1}$−1. Find the HU value. What windowing setting would optimally display this vessel against surrounding soft tissue at $\sim 50$∼50 HU?

Solution.

$$\begin{aligned} \text{HU} &= 1000 \times \dfrac{0.50 - 0.20}{0.20} \\ &= 1000 \times 1.50 = +1500. \end{aligned}$$HU​=1000×0.200.50−0.20​=1000×1.50=+1500.​

The vessel is at $+1500$+1500 HU. To display it clearly against $+50$+50-HU soft tissue, a "contrast window" with centre $\sim +800$∼+800 and width $\sim 2000$∼2000 would map the surrounding tissue to mid-grey and the iodine-filled vessel to bright white — the standard angiographic display preset.

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CT vs Plain X-Ray

The advantages of CT over plain radiography are profound:

• Cross-sectional (2-D) imaging. CT shows precise location of internal structures in a slice plane, whereas a plain X-ray gives only a 2-D shadow projection of a 3-D body.
• 3-D volume. Stacked slices give a full volumetric data set that can be re-sliced in any plane.
• Soft-tissue contrast. CT distinguishes attenuation differences of a fraction of one percent, making it possible to see organs, tumours, blood clots and brain haemorrhages that are invisible on plain X-ray.
• No structural overlap. Two objects at different depths are cleanly separated; no more hiding behind ribs.
• Quantitative. Hounsfield units give a reproducible, quantitative measure of tissue attenuation.

Disadvantages and limitations:

• Higher dose. A head CT delivers $\sim 2$∼2 mSv, an abdominal CT $\sim 10$∼10 mSv — much higher than plain radiography (chest X-ray $\sim 0.02$∼0.02 mSv).
• Cost. A CT scanner costs millions of pounds and needs a large shielded room; plain X-ray machines are a fraction of the cost.
• Motion artefacts. Patient movement during the scan blurs the reconstruction or produces streak artefacts.
• Beam-hardening artefacts. Because the X-ray beam is not monoenergetic, lower energies are preferentially attenuated and the beam "hardens" (shifts to higher mean energy) as it traverses dense structures. This produces systematic errors in the reconstructed HU values near bones.
• Metal artefacts. Metal implants (dental fillings, prosthetic joints) cause severe streaks across the image because their attenuation is so high that the logarithm in the reconstruction equation becomes unreliable.

Despite these drawbacks, CT has transformed clinical practice. It is the front-line imaging technique for trauma, stroke, cancer staging, and countless other applications.

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Where Does CT Fit Among the Imaging Modalities?

CT is one of four major imaging modalities in the Module 6.5 syllabus, and it is useful to see how the choice between them is made:

flowchart TB
    Q["Clinical question:<br/>structure or function?"]
    A["Anatomy / structure"]
    F["Function / metabolism"]
    Z["Ionising?"]
    Z2["Ionising acceptable?"]
    XR["Plain X-ray<br/>(2-D, low dose)"]
    CT["CT<br/>(3-D, higher dose)"]
    US["Ultrasound<br/>(non-ionising, soft tissue, foetal-safe)"]
    PET["PET / PET-CT<br/>(functional, higher dose)"]
    Q --> A
    Q --> F
    A --> Z
    Z --> XR
    Z --> CT
    A --> US
    F --> Z2
    Z2 --> PET

The split is clean: X-ray and CT for bone and dense-structure anatomy at the cost of ionising-radiation dose; ultrasound for soft-tissue and foetal anatomy without any ionising radiation; PET for metabolic function. Where structural information is also needed alongside function, PET is combined with CT (PET-CT) in a single instrument.

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Radiation Dose and Patient Safety

CT delivers significantly higher radiation dose than plain radiography. A single head CT gives about 2 mSv — about a year of natural background — and a full abdominal CT about 10 mSv. CT scans are only ordered when clinically justified, and scanner manufacturers have worked for decades to reduce dose through better detectors, iterative reconstruction algorithms, and dose-modulation techniques that adjust the X-ray beam to the local body thickness.

Children are particularly sensitive to ionising radiation because their tissues are still developing and they have many years ahead in which a radiation-induced cancer could arise. Paediatric CT protocols therefore use lower tube currents, faster acquisition, and more aggressive iterative reconstruction.

The ALARA principle (As Low As Reasonably Achievable) of plain-X-ray operator protection extends to CT in the form of dose-tracking software that records and audits every patient exposure.

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