You are viewing a free preview of this lesson.
Subscribe to unlock all 14 lessons in this course and every other course on LearningBro.
A conventional X-ray radiograph is a two-dimensional 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 may 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. 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 — which covers section 6.5.2 of the OCR A-Level Physics A specification (H556) — describes the principle of CT, the image reconstruction process, the Hounsfield scale, and the compromises involved in clinical use.
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 from the collection. 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 attenuation at every point in the slice. The mathematical technique is called the inverse Radon transform — a generalisation of the simpler back-projection method — and was worked out by the Austrian mathematician Johann Radon in 1917, decades before anyone thought of applying it to medicine.
The result is a two-dimensional map of attenuation coefficients across the slice. By stacking many such slices, a three-dimensional volume is built up.
A modern CT scanner consists of:
flowchart TB
S["X-ray source<br/>(rotating)"]
P["Patient<br/>(on sliding couch)"]
D["Detector array<br/>(opposite source, rotates with it)"]
G["Gantry<br/>rotates 360° around patient"]
C["Computer<br/>reconstructs image"]
V["Volume image<br/>3D"]
S --> P
P --> D
S --> G
D --> G
D --> C
C --> V
The source-detector pair rotates around the patient through 360°, collecting a 1-D line image at many different angles (typically hundreds or thousands). Each 1-D image represents the total attenuation along a set of parallel rays through the slice at that particular 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, tracing out a helical path through the patient and allowing very rapid whole-body scans.
The computational problem at the heart of CT is this: given the total attenuation -\ln(I/I_0) along each of many rays through the slice, reconstruct the attenuation coefficient \mu(x,y) at every point (x,y) in the slice.
A simple but illustrative way to picture the reconstruction is filtered back-projection. Imagine sweeping each 1-D projection back across the image plane at the angle it was taken, laying down the measured attenuation along the direction of the ray. If many such back-projections from different angles are superimposed, high-attenuation features (where real structure exists) are reinforced, while the "streaks" from individual rays wash out. With a suitable mathematical filter applied to each projection before back-projection, the reconstruction becomes exact in the limit of infinitely many projections.
In practice, modern scanners use iterative reconstruction techniques that are more computationally intensive but produce cleaner images at lower doses.
For A-Level purposes you need to understand:
You do not need to know the mathematics of back-projection or Radon inversion.
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:
HU = 1000 × (μ_tissue - μ_water) / μ_water
where HU ("Hounsfield units") gives a dimensionless value. By definition:
The huge range — from -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 to -500, showing lung tissue clearly. A "bone window" might run from 0 to +1500, showing bones and fractures. Multiple windows are produced from the same raw data.
A CT scan pixel shows an attenuation coefficient of \mu_{\text{tissue}} = 0.21 cm⁻¹. If water has \mu_{\text{water}} = 0.19 cm⁻¹, what is the HU value?
Solution.
HU = 1000 × (0.21 - 0.19) / 0.19
= 1000 × 0.02/0.19
≈ 105
This is consistent with soft tissue containing a small amount of contrast agent, or with bone marrow. A pure soft-tissue value without contrast would be closer to 40.
The advantages of CT over plain radiography are profound:
Subscribe to continue reading
Get full access to this lesson and all 14 lessons in this course.