What X-rays are, how the machine makes them, and why bone stops more of them than muscle.
CT scanners,
from first principles
You lie on a table at the centre of a ring. The ring hums. A voice says “Breathe in… hold… breathe normally.” What does the machine do in those seconds? This document starts with light and shadows. It ends with how the scanner measures you, how a computer rebuilds you as slices, and what the scan costs your body.
TopicThe CT scanner
Main questionHow do X-rays from a ring become a picture of a slice of you?
You needLight · shadows · percentages
Key parts03 Getting through · 05 Rebuilding · 10 Dose
Chapters13 + glossary
Reading timeAbout 45 minutes
FP-00
Start here
What you will understand, and the path to it.
CT stands for computed tomography. “Tomography” means “drawing slices”. “Computed” means that a computer calculates each slice. No camera inside the machine ever sees the slice directly. This document explains how that is possible.
You will understand
You will understand
Why one measurement gives only a total along a line, and how many lines from many angles are enough to rebuild a slice.
You will understand
Why you hold your breath, why some scans use dye and others do not, and why metal must come off.
You will understand
What the radiation dose of a CT scan is, how experts estimate its risk, and how large that risk is.
The path
Each chapter uses only the chapters before it. Amber chapters are the key parts.
- X-rays
- The tube
- Getting through
- The machine
- Rebuilding a slice
- Numbers to greys
- Breath-hold
- The dye
- Metal
- Dose and risk
- Other risks
- Together
- Limits
How to read the boxes
KEY POINT
The idea of the section in one sentence.
ANALOGY
A picture from daily life, and where it stops working.
COMMON MISTAKE
A wrong idea that many people have.
NOTE
A simplification or an assumption.
NOTE
This document explains the physics and published averages. It is not medical advice about your own scans. The hospital records the dose of each scan, and your radiographer or doctor can tell you about yours.
FP-01
X-rays: light you cannot see
What goes through you, and why it can do harm.
Why we need this. To see inside you, the machine needs something that goes through skin and muscle, but not through everything equally.
Light travels in very small packets of energy. We call one packet a photon. Physicists measure the energy of one photon in a small unit, the electronvolt (eV). 1 keV is 1,000 eV.
A photon of visible light has about 2 eV. An X-ray is light with much more energy in each photon. The photons in a CT beam have about 20 to 120 keV. That is tens of thousands of times more than visible light.
This large energy has two results:
- X-rays go through soft parts of your body. Visible light stops at your skin. Most X-ray photons pass through a hand without hitting anything.
- An X-ray photon that does hit an atom can knock an electron out of it. We call this ionisation. The free electron moves fast and ionises more molecules on its path. One 60 keV photon can cause roughly 2,000 ionisations in this way.
KEY POINT
X-rays are photons with enough energy to pass through soft tissue and to ionise atoms. The first property makes CT possible. The second property is the source of its risk (chapter 10).
The problem with a normal X-ray picture
A normal X-ray picture is a shadow. X-rays go through you onto a flat detector. Places behind dense parts get fewer X-rays, so they look different. But the picture is flat. Everything along the path of the beam lands on the same spot.
Diagram · a flat X-ray loses depth
CheckWhy does visible light stop at your skin, but most X-rays go through your hand?
Each X-ray photon carries tens of thousands of times more energy than a photon of visible light. Most X-ray photons pass between and through the atoms of soft tissue without being stopped. Visible light photons are absorbed or scattered in the first millimetres of skin.
FP-02
Making X-rays: the tube
How the machine turns electricity into X-rays, and stops them at once.
Why we need this. The scanner needs a strong, steady beam of X-rays that it can turn on and off in a fraction of a second.
The source is an X-ray tube. It works in four steps:
- A thin wire, the filament, gets very hot, like the wire in an old light bulb. Hot metal releases electrons.
- A very high voltage pulls these electrons across a vacuum towards a metal target, usually tungsten. We call this the tube voltage. It is given in kilovolts (kV). A common setting is 120 kV, which is 120,000 volts.
- The electrons hit the target at about 59% of the speed of light. They stop suddenly. Some of their energy comes out as X-ray photons.
- About 99% of the energy becomes heat, not X-rays. So the target is a disc that spins fast. This spreads the heat over a large ring of metal. Oil around the tube carries the heat away.
At 120 kV, each electron arrives with 120 keV of energy. So no photon can have more than 120 keV. Most photons have much less, with an average of roughly 60 to 70 keV. A thin metal filter at the exit removes the weakest photons. Those photons would stop in your skin, add dose and give no information.
Diagram · inside the X-ray tube
KEY POINT
An X-ray tube makes X-rays only while the high voltage is on. When the voltage turns off, the X-rays stop at once, like the light from a switched-off lamp.
COMMON MISTAKE
“After a CT scan, I am a little radioactive.” This is wrong. The X-rays are light. They stop when the tube turns off, and nothing in you gives off radiation afterwards. Some other scans (for example PET scans) inject a radioactive substance. CT does not.
CheckThe radiographer sets the tube voltage to 80 kV instead of 120 kV. What is the highest photon energy now?
80 keV. Each electron gets 80 keV of energy from 80 kV, so no photon can have more. Lower-energy photons are stopped more easily (chapter 03). So 80 kV suits thin patients and children, but not large patients.
FP-03
How much gets through
The one thing the scanner measures, and what that number means.
Why we need this. The scanner measures only one thing: how many photons reach each detector. To rebuild a picture, we must know how that number depends on what is in the path.
Each layer removes the same fraction
Send 1,000,000 X-ray photons into water. After 3.6 cm, about half of them are left. After the next 3.6 cm, half of those are left: one quarter of the start. Each equal layer removes the same fraction, not the same number.
Diagram · halving in each 3.6 cm of water
We call this loss of X-rays attenuation. The thickness that removes half is the half-value thickness. For water and the typical energy of a CT beam, it is about 3.6 cm.
Each material has its own rate
Different materials remove X-rays at different rates. We give each material one number for this rate: its attenuation coefficient. Its symbol is μ, the Greek letter “mu”. The unit is “per cm”. A large μ means the material stops X-rays quickly.
| Material | μ per cm (about) | Half-value thickness |
|---|---|---|
| Air | 0.0002 | about 35 m |
| Fat | 0.175 | 4.0 cm |
| Water | 0.19 | 3.6 cm |
| Muscle, blood, organs | 0.20 | 3.5 cm |
| Dense bone | 0.48 | 1.4 cm |
| Steel | about 7 | 1 mm |
Values are for photons of about 70 keV, a typical average energy in a CT beam. Real values change with energy.
Two things make μ large:
- Density. A denser material has more atoms in each centimetre, so a photon meets more atoms.
- Atomic number. Large atoms, with many electrons, absorb X-rays much more strongly. Soft tissue is mostly hydrogen, carbon and oxygen (atomic numbers 1, 6 and 8). Bone contains calcium (atomic number 20). Chapter 08 uses this idea again for the dye.
From numbers to a rule
Numbers. A body is about 30 cm wide. That is 30 ÷ 3.6 ≈ 8.3 half-value thicknesses. One half multiplied by itself 8.3 times is about 0.0033. So only about 1 photon in 300 gets through the width of your body.
Words. The fraction that gets through depends on the product of μ and the thickness. Physicists write this with the number e (about 2.718), because it makes the maths simple.
I = I0 × e−μ×xI0 photons go in. I photons come out. x is the thickness. Check: 0.19 × 30 = 5.7, and e−5.7 ≈ 0.0033, the same 1 in 300.
This rule is called the Beer–Lambert law.
Many materials on one line: the ray sum
A real line through you crosses skin, fat, muscle, bone and organs. Each part lets through its own fraction. The fractions multiply. And when you multiply powers of e, the exponents add:
e−μ1x1 × e−μ2x2 = e−(μ1x1 + μ2x2)Multiplying the fractions is the same as adding the products μ × x, then taking one power of e.
The scanner knows how many photons went in and counts how many came out. From these two numbers it calculates the total in the brackets. We call that total the ray sum: the sum of μ × length for every piece of material along one line. (Mathematicians call it a line integral.)
Worked example: three lines, one answer
| Line | What it crosses | Ray sum | Fraction through |
|---|---|---|---|
| A | 10 cm tissue, then 2 cm bone | 0.19×10 + 0.48×2 = 2.86 | e−2.86 ≈ 5.7% |
| B | 2 cm bone, then 10 cm tissue | 0.48×2 + 0.19×10 = 2.86 | 5.7% |
| C | 15.05 cm tissue, no bone | 0.19×15.05 = 2.86 | 5.7% |
The detector gives the same number for all three lines. It cannot tell where the bone is. It cannot even tell whether there is bone at all.
KEY POINT
One detector reading gives only one number: the ray sum along its line. It does not tell where along the line each material is.
KEY PART
This is the basic limit of a single X-ray, and it is the same limit as the flat shadow in chapter 01. Chapter 05 shows how many lines from many directions remove it.
Model · one line through you
Photons that arrive, of 1,000,000
22,371
Ray sum (μ × length, added)3.80Fraction through2.24%About 1 photon in45
Try this: set 15 cm of tissue and no bone. Then set 10 cm of tissue and 2 cm of bone. The ray sums are almost the same, so the detector cannot tell the two lines apart.
ANALOGY
Think of sheets of tinted glass. Each sheet lets through half of the light. Two sheets let through a quarter, three sheets an eighth. The order of the sheets does not matter.
Where this stops working: a real X-ray beam has photons of many energies. Materials remove low-energy photons faster. So the beam changes as it goes, and the “half per layer” rule is only close to true. Chapter 09 shows when this matters.
COMMON MISTAKE
“Bone blocks X-rays and soft tissue lets them all through.” Both remove a share. Per centimetre, bone removes about 2.5 times more than tissue. But 30 cm of tissue removes 99.7% of the X-rays. The picture comes from small differences between already small numbers.
CheckA line crosses 20 cm of tissue (μ = 0.19). What fraction gets through? What if you add 1 cm of bone (μ = 0.48)?
Ray sum 0.19 × 20 = 3.8, and e−3.8 ≈ 0.022, so about 2.2%. With bone, the ray sum is 3.8 + 0.48 = 4.28, and e−4.28 ≈ 0.014, so about 1.4%. The bone does not add a fixed number of lost photons. It multiplies what is left by e−0.48 ≈ 0.62.
FP-04
The machine around you
Ray sums from all around each thin slice, in a fraction of a second.
Why we need this. A single shadow loses depth. The idea of CT is to measure ray sums along many lines, from every direction around you, inside one thin slice of your body.
- You lie on the table at the centre of a ring. We call the ring the gantry. You see only its plastic cover.
- Inside the cover, the X-ray tube sits on a heavy frame that can turn around you.
- Metal plates shape the X-rays into a thin, flat fan. We call it the fan beam. It is wide enough to cross your whole body, and only a few centimetres thick along your body.
- Opposite the tube is a curved row of small sensors. Each one measures the X-rays that reach it along one line from the tube. We call each sensor a detector.
- The tube and the detectors turn together around you, once every 0.25 to 0.5 seconds. In each turn they take roughly 1,000 sets of readings, each from a slightly different angle.
- At the same time, the table moves you through the ring. So the beam covers your body one section after another.
In short: the ring is the gantry. The thin, flat beam is the fan beam. Each small sensor opposite the tube is a detector.
The parts in more detail
- Detectors. Each detector has a crystal that glows when X-rays hit it, and a light sensor under it. The light sensor turns the glow into an electric signal. A modern scanner has 64 to 320 rows of detectors, with about 900 detectors in each row. So one turn measures many slices at once.
- Speed. The turning frame is heavy. At 0.25 seconds per turn, a part 0.65 m from the centre feels a force of about 40 times its own weight. (Calculation: 4 × π² × 0.65 m ÷ 0.25² s² ≈ 410 m/s², and gravity is 9.8 m/s².)
- Power and data. Cables would twist on a frame that never stops turning. So sliding contacts on a ring carry power in and data out. We call this the slip ring. A fast scanner sends more than a gigabyte of readings each second.
The spiral path
The frame turns while the table moves. Seen from your body, the tube follows a spiral, like the thread of a screw. We call this a helical scan (or spiral scan).
Diagram · the tube’s path around you
Worked example. The fan beam is 4 cm thick. The table moves 4 cm in each turn. One turn takes 0.5 s, so the table moves 8 cm each second. A chest is about 35 cm long. The scan takes 35 ÷ 8 ≈ 4.4 seconds.
Why you lie at the centre
Your body is thinner at its edges than at its middle. A shaped metal filter makes the beam weaker at its edges and stronger at its centre, to match. When you are at the centre, the filter matches your body. When you are off-centre, some parts get more dose than they need, and others get too few photons, so the picture is grainier. The red laser lines on your body help the radiographer put you in the correct place.
The first, quick pass
Before the main scan, the table moves you through the ring once while the tube stays still. This gives a flat picture, like a normal X-ray. We call it the scout image (some scanners call it a topogram or surview). The radiographer uses it to mark where the scan starts and stops. The scanner also uses it to measure how thick you are at each level. Chapter 10 shows why.
KEY POINT
A CT scanner collects ray sums along hundreds of thousands of lines around each thin slice of your body. It does this in a fraction of a second, while the table moves you through the ring.
CheckA scanner turns once every 0.35 s. The table moves 8 cm per turn. How long does a 35 cm chest scan take?
35 ÷ 8 ≈ 4.4 turns. 4.4 × 0.35 s ≈ 1.5 seconds. Fast scanners can scan a whole chest in one or two seconds.
FP-05
From line totals to a slice
How a computer finds what is at each point, when it knows only totals along lines.
Why we need this. Each reading is a ray sum: a total along one line (chapter 03). The scanner must find the value of μ at each point in the slice. This is a puzzle: find the numbers in a grid when you know only totals along lines.
A small puzzle first
- Four unknown numbers, a, b, c and d. You cannot look inside the grid. You can only send lines through it and learn the total along each line.
- Two horizontal lines give the row totals: a + b = 5 and c + d = 9.
- Two vertical lines give the column totals: a + c = 6 and b + d = 8.
- Four totals, four unknowns. But two different grids fit all four totals. Lines from only two directions are not enough.
- Add one line from a third direction, along the diagonal: a + d = 5. The second grid gives 7, so it is wrong.
- Only one grid fits every total: a = 1, b = 4, c = 5, d = 4. More directions removed the doubt.
KEY POINT
Totals along lines from one or two directions allow many answers. Totals from many directions allow only one. CT takes lines from hundreds of directions.
The real size. A CT slice is usually a grid of 512 × 512 = 262,144 squares. In one turn, the scanner takes roughly 1,000 sets of readings from about 900 detectors in each row. That is about 900,000 ray sums for each row of detectors. There are more equations than unknowns, so the grid has one best answer.
What the scanner records
The set of all ray sums from one angle is a projection. It is like one flat shadow, as a row of numbers. Put the projections from all angles one under another, and you get a picture called a sinogram. Each point in your body draws a wave in it, because the point moves from side to side in the shadow as the tube turns. The sinogram is the raw data. The slice image must be calculated from it.
Rebuild, version 1: smear back
Take one projection. Spread each ray sum evenly back along its own line, across the whole grid. Do this for every angle and add the results. Where lines that crossed a dense object meet, the values pile up. We call this back projection.
It finds the right places, but the image is blurred. Each point becomes a star of lines. With many angles, the star becomes a soft glow around the point.
Rebuild, version 2: sharpen first
The fix: before you smear a projection back, sharpen it. Each value is made a little larger, and a small part of its neighbours is taken away. This puts small negative values beside each edge. When the projections are added, these negative parts cancel the glow. We call this method filtered back projection. It was the standard method in scanners for decades.
Model · rebuild a chest slice
Angles
Sharpen filter
This is a real calculation in your browser, on a simple model chest. Start with 1 angle: each ray sum is smeared along its line. Then try 4, 30 and 180 angles. At 180 angles, turn the sharpen filter on and off. In the sinogram, look for the wave drawn by each bright point.
Rebuild, version 3: guess and correct
Most modern scanners improve on filtered back projection. They make a first image. They calculate the ray sums this image would give. They compare these with the measured ray sums, and correct the image where they differ. They repeat this many times. We call this iterative reconstruction. It handles noise better, so the scanner can use a lower dose for the same quality. Many new scanners also use trained neural networks in this step.
ANALOGY
A Kakuro puzzle gives you the totals of rows and columns, and you find the digits in the squares. CT is the same kind of puzzle, with lines at hundreds of angles.
Where this stops working: Kakuro has strict rules (digits 1 to 9, no repeats), so rows and columns are enough. A body has no such rules. So CT needs many more directions, and the measured totals contain noise, so the answer is the best fit, not an exact solution.
COMMON MISTAKE
“A CT image is a photograph of a slice.” No detector ever sees the slice. The computer calculates each square from all the lines that pass through it, from all angles. So one bad line can damage many squares. Chapters 07 and 09 show two ways this happens.
CheckOne ray sum has a large error. Why does the error appear as a streak across the image, and not as one bad dot?
Back projection spreads each ray sum evenly along its whole line. So the error is spread along that line too. The sharpening filter also adds bright and dark edges beside it. The result is a straight streak through the slice.
Deep dive · why the sinogram shows waves, and why the filter works
Take a point at distance r from the centre, at angle φ. When the tube is at angle θ, the point lands in the shadow at position s = r × cos(θ − φ). As θ changes, s moves as a sine wave. That is where the name “sinogram” comes from.
Plain back projection blurs each point by a factor that falls off as 1 ÷ distance. In terms of fine and coarse detail, it gives too much weight to coarse detail. The sharpen filter (called a ramp filter) gives each level of detail a weight in proportion to how fine it is. This exactly cancels the blur. The maths behind this is the Fourier slice theorem.
FP-06
Numbers into greys
A fixed scale for every scanner, and a way to see small differences.
Why we need this. The rebuild gives a value of μ for each square of the slice. Doctors need one scale that means the same on every scanner, and a way to see very small differences.
Each square of the slice is really a small box, because the slice has a thickness, often 0.5 to 1 mm. We call this box a voxel (a “volume pixel”).
The Hounsfield scale
The scanner turns each μ into a number on a fixed scale. Water is 0. Air is −1000. We call the unit the Hounsfield unit (HU), after Godfrey Hounsfield. He built the first medical CT scanner in England, which scanned its first patient in 1971.
HU = 1000 × (μ − μwater) ÷ μwaterHow much more (or less) a material stops X-rays than water does, in thousandths. Example: muscle, 1000 × (0.20 − 0.19) ÷ 0.19 ≈ +50.
Diagram · the Hounsfield scale
Choosing which greys to show
A screen shows 256 shades of grey, and your eye separates far fewer. The scale covers more than 3,000 HU. If the screen spreads the whole scale from black to white, a liver and a spleen look the same.
So the viewer chooses a range to show. Values below the range are black. Values above it are white. The full grey range is used only for the values inside. We call this range the window. It has a centre (the level) and a width. Doctors look at the same data in several windows: one for lungs, one for soft tissue, one for bone.
Model · window the same slicePoint at the image to read HU
Shown as grey: from −160 to +240 HU. Below is black, above is white.
Try the Lung window: the lungs show detail and a small spot in the left lung of the picture. Then try Soft tissue: the lungs go black, but the heart, muscle and fat separate. The data does not change. Only the grey mapping changes.
KEY POINT
Every voxel holds a number in Hounsfield units. The image you see is one choice of window on that much larger range of numbers.
CheckIn a soft-tissue window (level 40, width 400), what grey is lung (−850 HU)? And fat (−100 HU)?
The window shows −160 to +240 HU. Lung is below −160, so it is black. Fat is (−100 − (−160)) ÷ 400 = 0.15 of the way up, so it is dark grey.
FP-07
“Breathe in. Hold. Breathe normally.”
What happens in those seconds, and why your stillness matters so much.
Why we need this. The rebuild in chapter 05 assumes one thing: during all the angles, every part of you stays in the same place. If a part moves, the ray sums from different angles describe different bodies. No single image fits all of them.
The sequence
Timeline · a typical chest scan
- Often, a recorded voice gives the instructions. The scanner plays it at the correct moment in its program.
- You breathe in and hold. The scanner waits a moment, so that your chest and belly stop moving.
- The tube turns on and the table moves you through the ring. For a chest or abdomen, this takes a few seconds. Hospitals usually say a hold of about 5 to 10 seconds.
- The tube turns off. The voice says “Breathe normally”. Your part of the work is done. The calculation continues on the computer.
Sometimes the scanner repeats this, for example before and after the dye (chapter 08). Each pass needs its own breath-hold.
Why the breath-hold matters
Your diaphragm is the dome of muscle under your lungs. It moves about 1 to 2 cm in a quiet breath, and several centimetres in a deep breath. It pushes your liver, spleen and kidneys down and lets them back up. The front of your chest rises and falls too.
Movement causes two problems:
- Inside one slice: part of the turn sees the body in one place, and part sees it in another. Filtered back projection then makes doubled edges, blur and streaks. We call any false feature like this an artefact, and one caused by movement a motion artefact.
- Between slices: the table moves on while you breathe. A small spot in your lung can move out of the slice that is being measured, into a slice that was already measured. Then it is missed, or it appears twice.
Model · moving during one turn
In the second setting, the whole chest moves up by 1 cm for the second half of the angles. Look at the doubled edges and the streaks from the spine and ribs. The scanner cannot tell which position is the true one.
Why a deep breath
Diagram · lungs and diaphragm
- More contrast in the lungs. Full lungs hold more air. The air spreads small vessels and airways apart, and the lung background becomes darker (about −850 HU). A small spot of tissue (+40 HU) stands out well against it.
- No false shadows. When you lie on your back with half-empty lungs, the lowest parts of the lungs partly collapse. They look denser, and can hide disease or look like disease.
- More of you is visible. The diaphragm moves down, so the bottom of the lungs is not hidden behind it.
- Repeatable. A full breath is easy to repeat the same way. The scout image and the main scan match, and next year’s scan can be compared with this one.
KEY POINT
Holding your breath keeps your body in the same place for every angle of every slice. The deep breath also fills the lungs with air, so small details stand out against a dark background.
COMMON MISTAKE
“The breath-hold protects my lungs from the radiation.” It does not change the dose. It protects the picture. But a picture spoiled by movement may need a second scan, and that second scan would add dose.
CheckYour heart beats during the breath-hold. Why does a normal chest scan still work?
Each slice uses data from about half to one turn, which is about 0.13 to 0.5 seconds. The heart moves during that time, so its edges can blur a little. But the lungs, which are usually the target, stay still. For pictures of the heart itself, scanners time the data to the heartbeat, using an ECG.
FP-08
The dye
What the injection is, why it shows up, and why some scans do not need it.
Why we need this. Look again at the Hounsfield scale in chapter 06. Blood, liver, kidney, muscle and many tumours are all near +40 HU. In a normal scan, a blood clot or an inflamed area can look almost the same as healthy tissue.
The idea: add a large atom to your blood
The injection is a clear liquid that contains iodine. Patients often call it dye or ink, but it has no colour. Staff call it a contrast agent (or contrast medium).
Iodine has atomic number 53. Soft tissue is mostly atoms with atomic numbers 1 to 8. In chapter 03 you saw that large atoms absorb X-rays much more strongly. For the energies in a CT beam, the absorption grows roughly with the cube of the atomic number:
| Atom | Where you find it | Atomic number | Absorption per atom, compared with oxygen (rough) |
|---|---|---|---|
| Hydrogen | water, all tissue | 1 | 0.002 × |
| Carbon | fat, all tissue | 6 | 0.4 × |
| Oxygen | water, all tissue | 8 | 1 × |
| Calcium | bone | 20 | 16 × |
| Iron | steel | 26 | 34 × |
| Iodine | the dye | 53 | about 290 × |
There is a second reason. Iodine absorbs X-rays much more strongly above 33 keV than below it. That jump sits inside the energy range of a CT beam, so many photons are at energies where iodine absorbs well.
Wherever the dye goes, that place becomes bright. Blood rises from about +40 HU to a few hundred HU. Organs with a rich blood supply become brighter. Tissue with a poor or unusual blood supply stands out from its neighbours.
The journey of the dye
A pump pushes the dye through the small tube in your arm, a few millilitres each second. The total is usually less than a small cup. The scanner must take the picture when the dye is in the right place.
- The pump pushes the dye into a vein in your arm. This is often when you feel the warmth start.
- The vein carries the dye to the right side of your heart.
- The heart pumps it through the lungs. Scans that look for clots in the lung arteries are timed for this part.
- The dye returns to the left side of the heart, which pumps it out to the whole body.
- The dye fills the aorta and the arteries. Scans of arteries are timed for this moment. This moment is the arterial phase.
- About a minute after the start, the dye has passed into the organs and the veins. Many scans of the abdomen are timed for this venous phase.
- Your kidneys filter the dye out of your blood into the urine. Most of it leaves within a day.
Each moment that a scan is timed for is a phase. The two most common are the arterial phase and the venous phase.
Hearts and blood vessels differ from person to person. So the scanner often watches the dye arrive. It takes very quick, low-dose images at one level, and measures the brightness of the aorta. When the brightness passes a set value, it starts the scan. We call this bolus tracking.
Model · with and without dye
Without dye, the heart is one grey shape and the aorta is hard to separate from what is around it. With dye, the blood inside the heart and the aorta becomes bright, and the heart wall shows as a darker rim.
What you feel
Many people feel a warm flush that spreads through the body, a metal taste in the mouth, and a feeling that they have passed urine. They have not. The liquid is more concentrated than blood, and for a short time it widens small blood vessels. These feelings pass within a minute or two.
Why one scan had dye and the others did not
The choice depends on the question the doctor asks. Dye helps when the answer depends on blood supply. It is not needed when the parts already differ strongly.
Dye usually helps
Blood vessels: clots, bleeding, narrowing or swelling of arteries. Many tumours and infections in organs. Checking how organs such as the liver and kidneys take up blood.
Dye usually not needed
Lungs, where air (−850 HU) and tissue (+40 HU) already differ strongly. Bones. Kidney stones, where dye in the urine could hide the stone. Many follow-up scans of a spot already known.
Before the dye, staff check that your kidneys work well (often with a blood test). They ask about past reactions to dye, asthma and allergies. Chapter 11 explains why.
KEY POINT
The dye contains iodine, a large atom that stops X-rays strongly. For a short time it makes your blood, and organs with a rich blood supply, bright on the scan. The scan is timed to catch the dye in the right place.
COMMON MISTAKE
“I am allergic to shellfish, so I am allergic to the iodine in the dye.” Reactions to the dye are not caused by the iodine atom. A shellfish allergy does not mean a special risk from the dye. People with several allergies or asthma do have a somewhat higher chance of a reaction, so staff still ask.
CheckWhy is a CT for kidney stones usually done without dye?
Stones are already much denser than the tissue around them, so they show well without help. Dye collects in the urine inside the kidneys, and it is about as bright as a stone. It could hide the stone you want to find.
FP-09
Why metal comes off
The danger is to the picture, not to you.
Why we need this. Staff ask you to remove jewellery, hair clips, a bra with wires, clothes with zips, and sometimes dentures or hearing aids. Is metal dangerous in the scanner?
In CT, it is not. A CT scanner has no strong magnet. Metal does not get pulled, move or get hot. (An MRI scanner is different: it uses a very strong magnet, and metal there can be dangerous.) In CT, metal is a problem for the picture.
Problem 1: almost nothing gets through
Steel has μ of about 7 per cm, which is about 35 times that of water. One centimetre of steel lets through e−7 ≈ 1 photon in 1,100. Add 30 cm of body (1 in 300), and only about 1 photon in 330,000 reaches the detector. Then the detector counts only a few photons, or none. A count that small is mostly chance, so the ray sum for that line is badly wrong. We call this photon starvation.
Diagram · two lines, one through metal
Problem 2: the beam changes
The X-ray beam has photons of many energies. Metal removes the low-energy photons much faster than the high-energy ones. The photons that remain go through more easily. So the scanner measures less loss than the simple rule predicts, and it calculates a ray sum that is too small. We call this beam hardening. Bone causes a smaller amount of it too.
Result: streaks
Now recall chapter 05. Back projection spreads every ray sum along its whole line. So the wrong ray sums from lines through metal become bright and dark streaks across the whole slice. They look like a star around the metal, and they can hide the organs nearby.
Model · a metal pendant on the chest
Turn the pendant on. In the sinogram, the metal draws one very bright wave: the lines through it, with huge ray sums. In the slice, those bad lines become streaks that cross the heart and lungs, far from the metal.
What about metal inside you?
Metal that is part of you, such as a hip joint, dental fillings or a pacemaker, stays in place. Modern scanners use metal artefact reduction software. It finds the lines through metal, replaces their values with estimates from the lines nearby, and then rebuilds the slice. Higher tube voltages also help, because high-energy photons get through metal better.
Metal outside the scanned section does not matter, because no line through you passes through it. That is why staff sometimes ask you to remove metal only from the area of the scan.
| CT scanner | MRI scanner | |
|---|---|---|
| Uses | X-rays | A very strong magnet and radio waves |
| Loose metal | Spoils the picture with streaks | Can be pulled into the machine; a real danger |
| Metal implants | Safe; may cause streaks | Must be checked before the scan |
| Ionising radiation | Yes | No |
KEY POINT
Metal stops almost all X-rays on the lines through it. The wrong ray sums on those lines become streaks across the whole slice. Removing metal protects the picture, not your body.
COMMON MISTAKE
“Metal is dangerous in a CT scanner, like in an MRI scanner.” CT has no strong magnet. Metal is not pulled and does not heat. The rule exists only because of artefacts.
CheckYou keep a metal hair clip in, but the scan covers only your abdomen. Does the clip spoil the picture?
No. No line through your abdomen passes through your head, so no ray sum is wrong. Staff may still ask you to remove it, because the scout image or the plan can cover more of you.
FP-10
Radiation dose and risk
How much energy stays in you, what it can do, and how experts estimate the chance of harm.
Why we need this. The picture uses only the X-rays that get through you. The X-rays that stop inside you leave their energy there. In chapter 01, you saw that X-rays ionise atoms. What does that do, and how much of it does a CT scan cause?
Step 1: how much energy stays in you
The first measure is energy per kilogram of tissue. We call it the absorbed dose. Its unit is the gray (Gy): 1 joule of energy in each kilogram. A CT scan usually gives the organs in the scanned section about 10 to 40 thousandths of a gray (10 to 40 mGy).
Worked example. 20 mGy is 0.02 joules in each kilogram. Heating 1 kg of water by 1 °C takes about 4,200 joules. So 20 mGy warms your tissue by about 0.000005 °C. Heat is not the problem. The problem is how the energy arrives: as many separate ionisations, packed along the paths of fast electrons.
Step 2: what ionisation does to a cell
- Ionisations can break chemical bonds, including bonds in DNA, the molecule that carries the instructions of a cell.
- Cells find and repair almost all of this damage, usually within hours. Normal life causes DNA damage all the time, and cells repair that too.
- Very rarely, a repair goes wrong and leaves a permanent change in the DNA.
- Very rarely again, such a change is one step on the path to a cancer, many years later.
This is a matter of chance. A larger dose gives a larger chance of harm, not a worse harm. We call this kind of effect a stochastic effect (“stochastic” means “by chance”).
There is a second kind of effect. A very large dose kills many cells at once, and causes skin burns or hair loss. We call these tissue reactions. They happen only above a threshold. Skin reddening needs about 2,000 mGy. A normal CT scan is tens of times below that.
Step 3: one number for the whole body
Some organs are more sensitive than others. Bone marrow, lung, breast, stomach and bowel are more sensitive. Skin and bone surfaces are less sensitive. A head scan and a chest scan put dose into different organs.
To compare them, experts multiply each organ’s dose by a weight for its sensitivity, and add the results. We call the total the effective dose. Its unit is the sievert (Sv). For scans, we use thousandths: millisieverts (mSv). Effective dose is a tool for comparing averages. It is not an exact measure for one person.
Step 4: compare with daily life
You get radiation all the time, from natural sources: radon gas from the ground, rocks, food, and cosmic rays from space. In the UK, this is about 2.3 mSv each year on average.
Chart · effective dose, typical adult values
Step 5: from dose to a chance of harm
Experts learned about radiation risk mainly from survivors of the atomic bombs in Japan, and from workers and patients followed for many years. Above about 100 mSv, studies can measure how the extra cancer risk rises with dose. Below about 100 mSv, the extra risk is too small to measure directly, even in very large groups.
For safety, radiation protection assumes that the risk stays in proportion to the dose, all the way down to zero. We call this the linear no-threshold model. It is a cautious assumption. The true risk at low doses may be lower, but it is not known.
The UK Health Security Agency (UKHSA) uses this kind of model. For adults aged 16 to 69, it gives these estimates of the extra lifetime chance of cancer:
| Scan | Effective dose | Same as natural background for | Extra lifetime risk |
|---|---|---|---|
| CT head | 1.4 mSv | about 8 months | about 1 in 14,000 |
| CT abdomen | 5.6 mSv | about 2.5 years | about 1 in 3,600 |
| CT chest | 6.6 mSv | about 3 years | about 1 in 3,000 |
| CT abdomen and pelvis | 6.7 mSv | about 3 years | about 1 in 3,000 |
| CT chest, abdomen and pelvis | 10 mSv | about 4.5 years | about 1 in 2,000 |
The pattern is close to 1 in 20,000 for each mSv. For comparison, about 1 person in 2 in the UK gets cancer at some time in their life, from all causes.
Worked example. 1 in 3,000 is about 0.03%. Under this model, a chest CT changes a lifetime cancer chance of about 50% to about 50.03%.
Model · add up scans
Add a scan (typical adult values)
Total effective dose
0 mSv
Same as UK natural background for—Estimated extra lifetime risk—Lifetime cancer chance, all causesabout 50%
No scans added.
This uses the linear no-threshold model and UKHSA’s typical values, about 1 in 20,000 per mSv. Real doses differ between hospitals, scanners and body sizes. Your age and sex change the risk too.
Who is more sensitive
- Children and young adults have a higher risk per mSv. Their cells divide more, and they have more years for a cancer to develop. Scanners use lower settings for children.
- Older adults have a lower risk per mSv, for the opposite reasons.
- An unborn baby is more sensitive. That is why staff ask if you could be pregnant.
How hospitals keep the dose low
- Each scan must have a reason. In the UK, a law called IR(ME)R (the Ionising Radiation (Medical Exposure) Regulations) controls this. A trained person must agree that the benefit of each exposure is larger than its risk. We call this justification.
- The tube adapts to you. The scanner uses the scout image (chapter 04) to measure your thickness at each level. As it turns, it lowers the X-ray output where you are thin and raises it where you are thick. We call this dose modulation.
- Better rebuilds. Iterative reconstruction (chapter 05) gives a clean image from fewer photons, so the dose can be lower.
- Only the needed section. The radiographer sets the scan to start and stop where the doctor needs it.
KEY POINT
A CT scan gives an effective dose of a few mSv. That is about the same as one to several years of natural radiation. Under cautious assumptions, it adds a small chance of cancer later in life: about 1 in 20,000 for each mSv, for adults.
KEY PART
Keep three ideas apart. Absorbed dose (mGy) is energy in an organ. Effective dose (mSv) is a weighted sum for comparing scans. Risk is a chance, estimated from effective dose with a model. Each step adds an assumption.
COMMON MISTAKE
“Radiation from scans builds up in the body like a poison.” Nothing stays in you, and cells repair most DNA damage within hours. What adds up is the small chance that a repair went wrong. Under the linear no-threshold model, the chances from several scans add.
NOTE
Not having a scan also has a risk: a serious illness can be missed. Doctors weigh both. If you have questions about the dose of your own scans, ask the radiographer or your doctor. The hospital keeps a record of it.
CheckSomeone has two CT chest scans and one CT head scan in a month. Use the values above. What is the total effective dose, and the estimated extra risk?
6.6 + 6.6 + 1.4 = 14.6 mSv. That is about 6 years of UK natural background (14.6 ÷ 2.3 ≈ 6.3). At about 1 in 20,000 per mSv, the estimated extra lifetime risk is about 1 in 1,400 (20,000 ÷ 14.6 ≈ 1,370). This uses the linear no-threshold model.
FP-11
Other risks and safety checks
The dye, and the things you do not need to worry about.
Why we need this. Radiation is not the only risk. When a scan uses dye, the dye has its own risks. Staff ask their questions for these reasons.
| Risk | How often (about) | What staff do |
|---|---|---|
| Mild reaction to the dye: itching, rash, feeling sick | Less than 1 in 100 injections | Watch you; sometimes give a tablet or injection |
| Severe reaction to the dye: trouble breathing, low blood pressure | About 1 to 4 in 10,000 injections | Keep you nearby for 15–30 minutes with the small tube in your arm; treat at once |
| Harm to the kidneys | Rare; mostly in people whose kidneys already work poorly | Check kidney function first; ask you to drink fluids |
| Dye leaks under the skin instead of into the vein | Uncommon | Stop the pump; usually only swelling and discomfort for a short time |
We call a leak of the dye under the skin an extravasation.
Most severe reactions start within minutes of the injection. So the short wait after the scan is the time when staff can help fastest.
Things that are not risks
- Radioactivity. None stays in you (chapter 02).
- Magnetism. CT has no strong magnet (chapter 09).
- The sound. The hum and whirr come from the turning frame and the cooling fans.
- The red lines. They are weak laser beams that help with your position. Staff may ask you to close your eyes while they are on.
KEY POINT
The dye can cause reactions and, rarely, kidney harm. The questions before the scan and the wait after it exist to find and manage these risks.
CheckWhy do staff leave the small tube in your arm while you wait after a scan with dye?
If a reaction starts, staff can give medicine straight into the vein at once. Most serious reactions begin within minutes, inside that waiting time.
FP-12
Putting it together
Your scan in one pass, with the correct terms.
- You remove metal from the area of the scan, so no line has its ray sum spoiled by photon starvation or beam hardening.
- If the scan needs dye, a nurse or radiographer puts a small tube into a vein in your arm.
- You lie at the centre of the gantry, so the shaped filter matches your body. The laser lines help with this.
- The scanner takes a scout image. The radiographer marks the start and end. The scanner plans its dose modulation from your thickness.
- If there is dye, the pump starts. Bolus tracking or a set delay times the scan for the correct phase.
- The voice says “Breathe in and hold.” The X-ray tube turns on. The tube and detectors turn around you 2 to 4 times a second, while the table moves: a helical scan.
- Each detector counts the photons that arrive. From the counts, the scanner calculates a ray sum for each line: about a million each turn for each row of detectors. Together they form the sinogram.
- The voice says “Breathe normally.” The tube turns off.
- The computer rebuilds hundreds of slices with filtered back projection or iterative reconstruction. Each voxel gets a value in Hounsfield units.
- A radiologist looks at the slices in several windows, from several directions, and writes a report.
Model · the whole scannerPoint at the image to read HU
Patient
Window
Combine the settings. For example: dye on, metal on, then switch between the lung and soft-tissue windows. Each change in the patient changes the sinogram first. The slice is only ever calculated from it.
KEY POINT
A CT scanner measures one kind of number, the ray sum, along a million lines a second. Everything else follows from how those numbers are made and how the computer combines them: the slices, the greys, and the effects of dye, breath and metal.
FP-13
Where the simple picture stops
Limits of this model, and what to learn next.
NOTE
The models in this document use parallel lines, one X-ray energy, no scattered photons and a simple model chest. Real scanners differ in the ways below.
- Fan and cone shapes. Real lines spread out from one point in the tube, and many detector rows make the beam a cone. The rebuild maths is adjusted for these shapes.
- Many energies. μ depends on photon energy, and the beam has many energies. Scanners correct for this for water and soft tissue. Dual-energy scanners measure at two energies, and can separate materials, for example to make a map of iodine alone.
- Scatter. Some photons bounce off atoms and reach the wrong detector. Thin plates between the detectors block most of them.
- Noise and dose. Photon counts are random. To halve the noise, the scanner needs four times as many photons, so four times the dose. This trade-off drives most dose-saving work.
- Counting each photon. Most detectors measure the total glow from many photons. A newer photon-counting detector counts each photon and measures its energy. These scanners entered clinical use in 2021. They give sharper images with less noise, and can lower the dose.
What to learn next
- The Radon transform and the Fourier slice theorem: the exact maths of why filtered back projection works.
- MRI: a completely different way to make slices, with magnets and radio waves instead of X-rays.
- PET-CT: a CT scan combined with a scan that follows a weakly radioactive tracer.
FP-GL
Glossary
Every term, in the order it first appears. Type to filter.
- Photon
- One small packet of light energy. FP-01
- Electronvolt (eV)
- A small unit for the energy of one photon. 1 keV = 1,000 eV. FP-01
- X-ray
- Light whose photons carry tens of thousands of times more energy than visible light. FP-01
- Ionisation
- Knocking an electron out of an atom or molecule. The source of radiation risk. FP-01
- X-ray tube
- The device that makes X-rays by firing electrons at a metal target. FP-02
- Tube voltage (kV)
- The voltage that speeds up the electrons. It sets the highest photon energy. FP-02
- Attenuation
- The loss of X-rays from the beam as it passes through material. FP-03
- Half-value thickness
- The thickness of a material that removes half of the X-rays. About 3.6 cm for water. FP-03
- Attenuation coefficient (μ)
- How fast a material removes X-rays, per cm. FP-03
- Beer–Lambert law
- The rule I = I₀ × e^(−μx) for the fraction of X-rays that gets through. FP-03
- Ray sum
- The total of μ × length along one line. The one number each reading gives. FP-03
- Gantry
- The ring of the scanner that holds the turning tube and detectors. FP-04
- Fan beam
- The thin, flat, fan-shaped beam of X-rays. FP-04
- Detector
- One small sensor that measures the X-rays arriving along one line. FP-04
- Slip ring
- Sliding contacts that carry power and data to and from the turning frame. FP-04
- Helical scan
- A scan in which the tube turns while the table moves, so the tube follows a spiral. FP-04
- Scout image
- A quick flat picture taken first, to plan the scan and its dose. FP-04
- Projection
- The set of all ray sums from one angle. FP-05
- Sinogram
- All projections stacked by angle: the raw data of a slice. FP-05
- Back projection
- Spreading each ray sum back along its line and adding all angles. Gives a blurred image. FP-05
- Filtered back projection
- Back projection after sharpening each projection. Gives a sharp image. FP-05
- Iterative reconstruction
- Rebuilding by guessing an image, comparing its ray sums with the measured ones, and correcting, many times. FP-05
- Voxel
- One small box of the slice, with one value. FP-06
- Hounsfield unit (HU)
- The CT scale: water 0, air −1000. FP-06
- Window
- The range of HU shown as greys, set by a level and a width. FP-06
- Artefact
- A false feature in the image, for example from movement or metal. FP-07
- Contrast agent
- The iodine liquid (“dye”) injected to make blood bright. FP-08
- Phase
- The moment, after the injection, that the scan is timed for (for example arterial or venous). FP-08
- Bolus tracking
- Watching the dye arrive at one level, and starting the scan when it is bright enough. FP-08
- Photon starvation
- Too few photons reach a detector, so its ray sum is mostly noise. FP-09
- Beam hardening
- The beam loses low-energy photons first, so it gets through more easily than the simple rule predicts. FP-09
- Metal artefact reduction
- Software that replaces the bad ray sums through metal before rebuilding. FP-09
- Absorbed dose (gray, Gy)
- Energy left in tissue, in joules per kilogram. FP-10
- Stochastic effect
- A harm that happens by chance; more dose gives more chance. Cancer is the main one. FP-10
- Tissue reaction
- Direct harm from a very large dose, such as a skin burn. Has a threshold far above CT doses. FP-10
- Effective dose (sievert, Sv)
- Organ doses weighted by sensitivity and added. Used to compare scans. FP-10
- Linear no-threshold model
- The cautious assumption that risk is in proportion to dose, down to zero. FP-10
- Justification
- The legal check that the benefit of a scan is larger than its risk. FP-10
- Dose modulation
- The scanner changes its X-ray output to match your thickness at each level and angle. FP-10
- Extravasation
- A leak of the dye under the skin instead of into the vein. FP-11
- Photon-counting detector
- A detector that counts each photon and measures its energy. FP-13