3 Computed tomography

The aim of computed tomography (CT) is to produce an image of a slice of the body. (The Greek word ‘tomos’ means slice.) This is achieved by rotating a thin, fan-shaped beam of X-rays around the patient and measuring the intensity on the opposite side of the patient with a very large number of detectors.

Figure 6: Schematic diagram showing the direction of the X-ray beams. The beams in any one direction are called a projection.

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Figure 6

Figure 6: Schematic diagram showing the direction of the X-ray beams. The beams in any one direction are called a projection.

The following video clip shows Alan having a CT scan of his head to see if he has a base of skull fracture. Listen and watch the video clip carefully, with the following questions in mind:

Activity 5

1. What are the main differences between the skull X-rays and CT images produced of Alan?

2. What colour do the skull bone and brain tissue appear on the CT images and why?

3. How does the video say a two dimensional ‘slice’ is produced through the body?

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Transcript: Computed Tomography (CT)

An initial X-ray of this patient revealed a fracture; however the doctor responsible is also worried that there might be damage to the top of the spine - so a CT scan is being performed.

Alan is now being placed in the CT scanner and the radiographer uses a laser beam to place his head in precisely the right location.

CT scanning is essentially an X-ray procedure, but the X-ray source is rotated around the patient and the intensity recorded on the opposite side of the patient. Using data from a large number of angles a computer reconstruction can produce a two-dimensional map of the tissues in a slice of the body.

Planning is done by taking a pilot scan. The patient is moved through the gantry, but the source remains stationary on one side. This produces an image similar to a planar X-ray.

This pilot scan is taken in what is called the saggital plane. The final images will be in the axial plane.

The concern over the potential for injury to the top of the spine has been dismissed, but there is a concern that there may be some damage to the brain, so it’s decided to do an MRI scan.

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Answer

1. The skull X-rays showed ‘projections’ of Alan's skull (a 3D object represented in 2D) and the brain tissue could not be seen. The CT slices show the skull and internal brain tissue as a series of ‘slices’, and therefore, in much more detail.

2. The skull bone appears white and the brain tissue grey. This is because the skull attenuates X-rays to a greater extent than the brain tissue, and just like a planar X-ray the more a tissue attenuates X-rays, the whiter it will appear in the final image.

3. The X-ray source is rotated around the patient and the intensity recorded on the opposite side of the patient. Using data from a large number of angles a computer reconstruction can produce a two-dimensional map of the tissues in a slice of the body.

Let's look at the answer to the final question in more detail. First we will consider exactly how the X-ray source rotates around the patient.

In modern scanners the source and the detectors rotate around the patient at more than one revolution per second. In the older scanners the couch was moved after one rotation and the subsequent rotation had to be in the opposite direction to avoid twisting the cables (called ‘stop and go’ by Dr Klaus Klingenbeck in the following video clip). However, with the introduction of slip-rings it became possible to keep the source and detectors rotating continuously and to move the couch at the same time. This means that the X-ray source describes a helix around the patient and a set of data covering the complete volume of the patient can be collected. This is known as spiral (or helical) scanning and has the advantage that the data for the entire thorax or other section of the body can be collected in one breath hold. More recently, multislice scanners, in which there is more than one arc of detectors, allow even faster data collection.

Click to view part 1 of the clip about X-rays and CT [2 minutes 1 second]

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Transcript: X-rays and CT - part 1

Elizabeth Parvin:

This collimator can be adjusted electronically to define a slice as thin as 1 mm or as thick as 10 mm, depending on clinical requirements.

Now, what about rotation of the gantry?

Klaus:

For a standard CT scan we need to acquire projection data over a full rotation of 360 degrees, and at the time when the high voltage was still supplied at the tube via cables we had to reverse the direction of rotation from scan to scan in order not to twist the cables. And of course continuous data acquisition wasn’t possible at this time, only stop and go from scan to scan.

But things are different today – look at this.

Elizabeth Parvin:

Continuous rotation of the gantry was impossible before the development of electrical slip-rings for getting power into the X-ray tube and data out of the detectors.

Klaus:

The weight of the rotating parts adds up to almost a ton, and we can accelerate the machine to an angular speed of one rotation in three quarters of a second. The radial acceleration at this speed is 4 to 5 times the gravitational acceleration.

Elizabeth Parvin:

In the original version of the third generation scanner, the problem of the twisting cables meant that the scanner had to reverse direction after each slice.

This limited the speed of the scan as well as causing wear and tear on the components through repeated accelerations and decelerations. Continuous rotation overcomes all the disadvantages of “stop and go” and, when combined with continuous patient feed into the scanner, creates the so-called spiral scan.

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X-rays and CT - part 1

Now let's consider how a ‘slice’ through the patient can be reconstructed by the transmission data obtained at a large number of different angles, using a technique called ‘filtered back projection’. The following video clip will look at the transmission data from simple objects and how back projection, and finally filtered back projection, are used to reconstruct the original object from the transmission data. This clip introduces some complex topics – you only need a general overview of how CT image reconstructions work.

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Transcript: X-rays and CT - part 2

Elizabeth Parvin:

Let’s consider how these images of body slices are generated from the data recorded by the scanner. The basic mathematics behind this problem was actually solved in general terms as long ago as 1917. In many ways, it’s rather like trying to calculate the positions of all the trees in a forest from photographs taken through the forest in various different directions.

Here’s Dr. James Cubillo of Coventry University.

James Cubillo:

The tomographic imaging process begins of course with data acquisition. This is referred to as the forward projection. The data are in the form of attenuation profiles, obtained at equal intervals as the instrument rotates about the body. I’ll demonstrate that with this simple object.

Here we have a square object with uniform high attenuation. This is the imaging plane. If we irradiate the object with a parallel beam of X-rays from the left here you can see that we obtain an attenuation profile here.

Outside of the object area we have zero attenuation. Where we have the object we have uniform high attenuation level. As we rotate the instrument through some angle you can see that we still have zero attenuation outside of the object here, uniform attenuation here between these two points where we have equal path lengths.

Between these two points the path length is gradually increasing and we see that we have an attenuation profile which also increases uniformly.

At 45 degrees you can see that we have maximum attenuation here corresponding to the diagonal of the square which of course is maximum for this object, between these two points we have uniformly increasing attenuation as the path length increases.

And the process continues as we rotate the instrument relative to the object.

Elizabeth Parvin:

In these forward projections, James has actually rotated the object and fixed the direction of the beam, to make it easier to compare one attenuation profile with the next.

However, in an actual scan and in the reconstructions to come, it’s the instrument that rotates and not the object.

James:

Now let’s look at a slightly more complicated scene in which we have two squares, each of high uniform attenuation.

We irradiate the scene as before and you can see that we have rectangular attenuation profiles here for each of the squares.

Rotating the beam through 45 degrees, we have two triangular profiles corresponding to each of these two squares. Then at 90 degrees we’re back to the rectangular profiles. However at 135 degrees the two squares are in line and therefore we have maximum attenuation corresponding to the maximum path length of these two squares in line.

Elizabeth Parvin:

These attenuation profiles and knowledge of the direction of each forward projection are all that’s required to reconstruct the original object.

This process is known as simple back projection.

James:

Here we have the original object. This scale here is known as the hot body scale, with white and yellow representing high attenuation and red and black representing low attenuation.

Applying a back projection at zero degrees we have an equal likelihood of the objects occurring anywhere along these paths. Now if we apply a back projection at 90 degrees we can see that surprisingly enough we have four candidate positions for these squares leaving us with an ambiguous situation.

It is only when we add the 45 degree projection that we confirm the positions of the two squares.

Going on further to the 135 degree projection, again the position is reinforced once more.

Elizabeth Parvin:

This ambiguity would not have existed with the single square. And this illustrates a general point. The more complex the images are, the more projections are required to avoid ambiguity in the reconstructed image.

James:

Now, if we go on further to reconstructing the whole image, starting with zero degree projection and building up at 15 degree intervals, we can see the two squares forming with each projection. And now with the completed image, with 24 back projections we can see clearly the two squares that we started with.

However they do appear slightly blurred.

Elizabeth Parvin:

Convolution of the object with the point-spread function leads to a blurring effect, as you can see more clearly in this three-dimensional mesh plot of the same data. This problem is inherent to the back projection process and cannot be avoided, even by taking extra projections. But as you can see, a simple object, consisting of two squares, can still be reconstructed reasonably well.

However, when simple back projection is applied to real CT data, the blurring effect seems to be much more serious. There are two reasons for this. Firstly, the objects imaged in a real CT scan have a whole range of density values whereas the squares in James’ model have just one, and secondly, a much higher spatial resolution is required.

Nevertheless, the technique can be improved by filtering the data before carrying out the reconstruction. And this is known as filtered back projection.

James:

Here is an infinite ramp filter that can be applied to the reconstruction.

Along the horizontal axis you can see the spatial frequency, and on the vertical axis you can see the relative amplitude of the signal passed by the filter.

You can see that the filter itself discriminates against low frequencies in favour of the high frequencies.

However, with such a filter we will run into aliasing problems, and so we need to apply the Nyquist criteria to cut off the filter at half the maximum spatial sampling frequency as we have here.

Now let’s see what we get when we apply this filter to the back projections we saw earlier.

Here we have the two original objects, and here is the filtered back projection. As you can see we get a much clearer, sharper image. Although it is still not perfect, much of the blurring has been removed.

And here is the mesh plot. There is obviously a vast improvement over the simple back projection.

And here we have a comparison of the simple back projection compared with the filtered back projection with their respective mesh plots. And the improvement is clear to see.

Elizabeth Parvin:

OK. So, filtering the data greatly improves the reconstruction of this simple model. But how well does it perform on the pelvic slice we saw earlier? Well, as you can see, we now have a clear, sharp image in which we can identify the top of the femur, the bladder, and the spinal cord – a vast improvement over the blurred image we obtained with simple back projection.

Filtered back projection is the method of reconstruction used in modern CT imaging.

The only difference from the process you’ve just seen is that the filters are rather more sophisticated than the cut-off ramp filter James used.

End transcript: X-rays and CT - part 2

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X-rays and CT - part 2