# Brain Teaser #14

### A) Question:

What is the difference between a voxel and a pixel?

A pixel is in two dimensions and the voxel is in three dimensions.

You can think of a pixel as an area of a square, and a voxel as the volume of a cube.

### B) Question:

If a CT scanner has a matrix size of 1024 X 1024 and a field of view of 50 cm, what is the size in mm of one pixel?

With a matrix size of 1024 and a field of view of 50 cm, each pixel size would .5 mm

This can be solved by the following equation:

field of view
-------------------------------------------------------------------------= pixel size
matrix size

In this case our field of view is 50 cm. Since we want to know the pixel size in mm we can convert 50 cm to 500 mm. The matrix size is 1024.

500 mm
-------------------------------------------------------------------------= .5 mm
1024

### C) Question:

If the field of view increases, but your matrix size stays the same, will your spatial resolution increase, decrease, or remain the same?

### D) Question:

Please give the following nominal CT numbers in order of air, water, then bone.

Air = -1000

Water = 0

Bone = 1000

### E) Question:

What two factors is pitch dependent on?

Pitch is dependent on couch movement and slice thickness. Couch movement is usually expressed in how much the couch moved (length) for one tube rotation (360 degrees).

### F) Question:

If a couch moved 5 mm for half a rotation, and the section collimation is 5 mm, what is the pitch?

If a couch moved 5 mm for half a rotation and the section collimation is 5 mm, the pitch would be 2:1

The equation for pitch is couch movement for one rotation divided by the slice thickness or section collimation. In this example, we have 5 mm of couch movement for half a rotation, so 5 mm multiplied by 2 (to give a full rotation) is 10 mm. Take 10 mm and dived that by 5 mm and you get a ratio of 2:1

10 mm
------------------------------------------------------- = 2:1
5 mm

### G) Question:

What is noise for a CT scanner?

Noise for a CT scanner is any voxel above or below the average CT number value when scanned with a reference phantom.

"Noise represents the portion of the CT image that contains no useful information. It is defined a the random variation of CT numbers about the mean value when an image of a uniform object (an acrylic or water phantom) is obtained. The contrast resolution of a CT system is primarily determined by the amount of noise in the image. The source of noise in CT image includes: quantum noise (statistical), electronic noise, object size, reconstruction algorithm, and artifacts. Of these the predominant source of noise is quantum noise, which is defined as the statistical variation in the number of photons detected."

Quality Management in the Imaging Sciences, 2nd edition, Jeffery Papps, p. 200

### H) Question:

In the perfect world, what value would all CT numbers have to be to have no noise?

For a scanner to have no noise at all, the CT numbers for each voxel would all have to 0 when a water phantom was scanned.

### I) Question:

Under the same circumstances, what will have a larger attenuation coefficient, air or bone?