Lesson 4 of 5

Medical imaging.

About 25 minutes · 6 practice questions

Read the full article: Medical imaging

A CT scanner measures how much X-ray light gets through the body from many directions, and rebuilds a slice from it. Why one reading is not enough, how many directions it takes, and why the lungs show black.

Step 1 of 6 · One reading

X-rays are light of very high frequency, far beyond violet in the electromagnetic spectrum. They pass through soft tissue, and bone absorbs more of them. The Scene shows a CT scanner: an X-ray tube and a detector turning round a patient, with the slice rebuilt from their readings beside the Scene.

Step 1 of 6

One reading

Each centimetre of tissue weakens the beam by its absorption coefficient, $\mu$ ⁠: a little in air, more in soft tissue, and a lot in bone. Under Build the slice choose Projections, and watch the rays leaving the tube.

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Step 2 of 6

Half a turn

To find out where the absorption is, the scanner measures the same plane from many directions: Projection angles. It spreads them evenly.

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Step 3 of 6

More views

Slice shows the rebuild. The Projection angles are now fixed at just 6. Predict what will happen with many more.

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Step 4 of 6

Reading the slice

The Slice position sets where the plane crosses the body. In the slice each point is shaded by its $\mu$ ⁠. Try Head and Abdomen too.

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Step 5 of 6

How little gets through

Every tissue absorbs some of the X-rays passing through it. How much it absorbs in each centimetre is its $\mu$ ⁠, and the sum along the whole ray is $\int \mu \, dl$ ⁠.

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Step 6 of 6

From reading to sum

The scanner works the other way round: it measures how much got through, and works out the sum along the ray from it.

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Interactive scene

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Each step sets up the Scene for you, and a control marked “fixed” stays put for that step.

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Practice · Choose

One detector measures how much of an X-ray beam got through the body. What does that reading tell you?

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Practice · Calculate

The scanner takes 24 Projection angles, evenly spaced over half a turn. What is the angle between two neighbouring views?

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Practice · Predict, then look

The slice is built from just 6 Projection angles, and streaks cross it. What will happen when it is built from 180?

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Practice · Choose

In the chest slice the lungs are almost black. Why?

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Practice · Calculate

Slice position is locked at Chest. Along the ray straight from front to back through the middle of the slice, $\int \mu \, dl \approx 5.29$ ⁠. What percentage of the X-rays gets through the body? Use $I = I_0 e^{-\int \mu \, dl}$ ⁠.

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Practice · Calculate

Slice position is locked at Head. The detector at the back measures that only 1.40% of the X-rays that went in at the front, through the middle of the slice, got through. What is $\int \mu \, dl$ ⁠ along the ray?