Tomography

Computed tomography (CT) scanner

Tomography-based imaging: a huge medical advance

The last few decades have seen revolutionary progress in medicine. We have new understandings of the causes of diseases, new surgical techniques, and new medications. But advances in tissue imaging alone have been revolutionary. Back in the day, we had only X-rays. Now we have a host of techniques, such as magnetic resonance imaging (MRI) that give us much more detail about what's going on in soft tissue. In this post, however, I'll discuss techniques that fall under the category of tomography, such as computed tomography (CT).

The principle of tomography

The basic idea of tomography can be explained with an analogy, shown below.

Looking at shadows of a cylinder Jean-Christophe BENOIST, CC BY-SA 3.0 <http://creativecommons.org/licenses/by-sa/3.0/>, via Wikimedia Commons

Suppose we have a cylinder but we don't know its actual three-dimensional shape. So we shoot a broad beam of light at it from different directions and capture photographs of the shadows that it casts. The picture shows two examples:we get a circular shadow when the cylinder is illuminated at the end and a rectangular shadow when it is illuminated from the side. These two pictures are not enough information to conclude that we're looking at a cylinder. For example, suppose some demon drilled a cylindrical notch into the side of the cylinder, so that it looks like this:

Cylinder with a notch cut out

Now we'd need to get a third shadow, maybe by illuminating the object from above, to discover this feature.

A physicist named Allan MacLeod Cormack (1924 – 1998) asked how many directions of illumination you would need to infer the 3D shape of an object as well as its internal structure with no ambiguity. He worked with electrical engineer Sir Godfrey Newbold Hounsfield (1919 – 2004) to develop the first CT scanner, which used X-rays. In 1979, they won the Nobel Prize in Physiology or Medicine for this contribution.

The CT scanner

The "object" being illuminated in a CT scanner is a slice through the brain, abdomen, or other part of the body, depicted in the animation below as a circle. The scanner rotates a set of X-ray beams as shown to obtain many angles of illumination. The tissue has density variations and an image of these variations is what the scanner produces. Denser tissue (represented as darker blue) is more opaque to X-rays, while less dense tissue (more white) is more transparent.

X-ray beams through a tissue slice are rotated to obtain many views

At each angle of illumination, a line of detectors records the strengths of the transmitted X-ray beams. Let's show two of these angles below. On the left, the slice is illuminated from the bottom. The bar chart at the top shows the detector readings, very strong in the center where the X-rays have traversed a more transparent region and weak on the left and right sides where the X-rays have traversed more opaque regions.  On the right side of the figure, the slice is illumated from the left side, and the bar chart on the right shows the detector readings, very strong at the top and bottom where where the X-rays have traversed more transparent regions and weak in the middle where the X-rays have traversed a more opaque region.

Tissue slice illuminated from the below (left) and from the left side (right). Bar charts show the detector readings.

The bar chart is like a one-dimensional shadow. Each detector reading is the result of an entire path through the slice. What Cormack figured out is how to combine the data from multiple angles of illumination to produce an image of the slice.

A life-saving technology

If you ever fall and bump your head, err on the safe side and have it checked out. A cranial CT scan takes less than five minutes. Here is an example of a CT image of the brain showing a microbleed.

CT scan of the brain showing a microbleed