CT utilizes x-rays to produce cross-sectional slices of the body. Multiple x-ray projections are taken at different angles and are reconstructed using algorithms like filtered backprojection to generate detailed images of internal structures. CT is advantageous over regular x-rays as it can distinguish between overlapping tissues. However, it also exposes patients to ionizing radiation. The number of projections taken is a tradeoff between image quality and radiation dose.

1. Computed Tomography (CT) Imaging
N A D A F I T R I E Y A T U L H I K M A H

2. Overview
• Different names, same device:
❑ Computed tomography (CT)
❑ CT scan
❑ Computed Axial Tomography (CAT) scan
• CT utilizes computer-processed x-rays to produce ‘slices’ of specific areas
of the body.

3. Tomogram
• A tomogram is an image of a plane or slice within the body.

4. Pixels vs Voxels
• CT slice thickness is
typically 1 - 10 mm.
• CT images are comprised
of pixels.
• A voxel is the 3D volume
element represented by
one pixel in a CT image.

5. Projection vs Tomography
• CT is advantageous over projection X-ray imaging because it shows overlaying
structures.

6. CT Equipment
• A bore ➔ contains a gantry
that x-ray tubes as well as x-ray
detectors and spin around this
bore.
• A table ➔ the patient lays on.
A table slides into and out of
the bore in order to make CT
image od any slice within the
body.
• A computer ➔ used to process
the images.

7. Imaging Method
• X-ray source and detector rotates around
the patient.
• Acquired data is processed with
tomographic reconstruction methods.
• A series of cross-sectional image slices are
produced.

8. Multiple Projections (1)
• When gantry is rotating around the patient, we pass x-
rays through this representation of the body, and we get
a view of the amount of absorption.
• The view tells us that there was very little absorption and
high absorption where the circle is located, meaning
that the x-rays were absorbed and blocked from the
detector.

9. Multiple Projections (2)
• We rotate our view and do the same for
x-rays passing through this projection
angle.
• We get a similar profile of the
absorption.
• There is a little shifted to the left
compared to the view 1, and then lower
absorption.

10. Multiple Projections (3)
• Then, we can again rotate and get a
third view that similarly represents
the amount of absorption.
• Therefore, CT measures the linear
attenuation between a source and a
detector.
• Attenuation is basically measure of
how rapidly x-rays are absorbed and
views one to three represents a
radon transform.
Views 1-3 represent a
Radon Transform

11. What is radon transform?
• We can represent this as an
image by stacking up
multiple different views
• The lower values in the
profile can be represented
as black, similar to an X-ray
image, meaning that most
of the X-rays were passed
through in this view.
• The brightest regions can
be represented as white ➔
x-rays were absorbed.
• Everything in between ➔
shades of grey.
• We do this for not just 3
views, but views of degrees
varying from 0 – 1800.

12. Sinogram (1)
• Sinogram ➔ graphical representation of the 2D Radon transform.
• We get a line profile through
one of the earlier degrees.
• Line 1: We get a peak in line
profile toward the bottom of
the detector.
• Line 2: another slice after
rotating a little bit more ➔ a
peak shifts more toward the
center of the detector.
• Line 3: rotate 900 from the
original profile ➔ a peak
shifts upward even more.
• Image views from 0 – 1800 ➔
sinogram.

13. Sinogram (2)
• Sinogram ➔ graphical representation of the 2D Radon transform.
• This is the same principle as
projections from 0 – 3600.
• Depending on where the
detector is rotated around
the source, sometimes the
projection peak is closer to
an earlier element of the
source or farther away.

14. Predict The Sinogram (1)
• We’re rotating the gantry around the object and getting projections with each rotation.
• For this example, notice that no matter where we project, the peak should always be at
the center.
• In this object (circle at the center), the sinogram would expect it to be a straight line ➔
so no matter what angle we’re looking at this object from, we see the same projection
on as a function of a detector number.

15. Predict The Sinogram (2)
• What if instead we have a square and not a circle?
• When we’re looking through the two corners of the square, we get the maximum intensity.
• When we’re off on the side, the values should be lower than the values at the center of the detector that passes
through the most, widest part of the square, or it passes through the part of the square that has a maximum value of
whiteness.
• We get two sinusoidal looking patterns that correspond to the square tips, the x-rays passing through the tips of this
white square.
• So, every time x-ray passes through the tips, that’s where we get a maximum projection on the detector.

16. Predict The Sinogram (3)
• When x-rays pass the direction horizontally, the detector would see the maximum
projection value at the center ➔ absorbed all of the x-rays.
• However, when we’re looking at any other angle (ex: vertically), the detector would
pink up values that pass through the black and white regions ➔ it’s going to be less
white ➔ it’s going to have a shade of gray.
• The regions correspond to “x” sign
side of the detector in passing X-rays.
➔ absorb x-rays.
• Gray ➔ indicating that x-rays have
passed through both black and white
regions.
x x

17. Predict The Sinogram (4)
• X-rays pass through the corners of the square (diagonally) ➔ it will give a
slightly higher profile value ➔ in sinogram, we will see sinusoidal pattern
because this object is off to the lower right quadrant.
• In sinogram, we see sign sort of oscillations due to the corners of the square.

18. Sinogram of
Head
Phantom
• Shepp-Logan head phantom: white ribbon ➔ the outside of the skull, black ➔
ventricles within the brain, gray ➔ slightly absorbs the tissue.
• Different shapes contribute differently to the overall sinogram.
• This model should look like in the sense that is the various levels of gray, black, and
white in a sort of a sinusoidal pattern that can be traced to one specific geometry
within the body.

19. Radon Transform
• All of the sinogram are graphical
representations of the radon transform.
• Rotation of (x,y) coordinate system to
(R,θ) where x cosθ + y sinθ = R for any
point on a line projection.
• That would give us where the point is
located in this (R,θ) coordinate system and
notice that it holds true for any point along
this x-ray.

20. Change of Coordinate Systems
• Now, we have multiple x-rays, in this case three, notice that all of
these points have same theta, but different are x and y values.
• All of these points can be described as the coordinate system g,
with subscript are representing each one of these x-rays and theta.
• Then, we change coordinate system from f(x,y) to coordinate
system g(R, θ).
• Coordinate system 1:
f(x,y) = fx,y
• Coordinate system 2:
g(R, θ) = gR,θ
• In CT imaging, we vary θ, take measurements for the same values of
R, and reconstruct back to (x,y) coordinate system.
• So, there’s a lot of math involved in CT imaging and it’s highly
computational work! ➔ that’s why called COMPUTED tomography.

21. Acquiring CT Data (1)
• Imagine that we are in the f coordinate system
f(x,y).
• If x-rays are passing through this way, CT images
measure the linear attenuation between the
source and detector ➔ it’s basically measure of
how rapidly x-rays are absorbed.
• We can sum the attenuation coefficients in this
manner to get a measure of the line profile that
pass through these three different pixels in the CT
image.
• There are different voxels that will eventually turn
into a pixel.

22. Acquiring CT Data (2)
• The line that passes through here can be
converted from the f coordinates system
to the g coordinate system.
• System of equations:
f11 + f12 = g11
f21 + f22 = g21
source detector

23. Acquiring CT Data (3)
• Now, if we’re rotating the coordinate
system, and we want to measure the
attenuation coefficient.
• The attenuation is sum of the attenuation
in each region of the body and each
voxel.
• System of equations:
f11 + f12 = g11
f21 + f22 = g21
f12 + f22 = g12
f11 + f21 = g22
source
detector

24. Acquiring CT Data (4)
• System of equations:
f11 + f12 = g11
f21 + f22 = g21
f12 + f22 = g12
f11 + f21 = g22
f11 + f12 + f22 = g13
f11 + f21 + f22 = g23
• 6 equations, 4 unknowns.
source
detector
Solve this system of equations

25. You’ve Acquired CT Data…
• The following values were measured
for each line projection:
• Given this data and solve your
solution to the system of equations,
what are the values of f11, f12, f21, f22
(i.e. the pixels in your CT image)?

26. Solution
• These are the values of the pixels
in your CT image :
• Do the values agree with the
projection line integrals?
g11 = 10, g12 = 13, g13 = 19,
g21 = 12, g22 = 9, g23 = 18
Remember, we don’t only have these 3 detection angle projections, but we have multiple projection angles!

27. Matrix Size
• A typical CT image uses more than 3 projections and 2 detectors.
• Matrix Reconstruction, also known as the Algebraic Reconstruction Techniques
(ART), is not commonly used in practice, because it is time consuming and
computationally intensive.
• So, that method is not used in the clinics today.
• Instead, a method known as backprojection could be used.

28. Backprojection
• Implemented by taking the line
profile and smearing it back
across a region.
• Then, we do that for each
projection at each different angle.
• This is what the sum of the
different smears look like when
they’re superimposed on one
another.
• We do this not just 3 views, but
many views!
• The results of image like the
original image, but we see some
blurring around the point in the
lower right quadrant.

29. Filtered Backprojection
• The measured data is first
filtered before it’s smeared
back across the region.
• Then, the linear
superposition of these three
different smears looks like
similar to the original point
image.

30. Image Formation Recapitulation
We take multiple projection at different angles ➔ form a sinogram ➔ the sinogram
can be reconstructed into an image using filtered backprojection ➔ we get CT image.

31. How Many Projections?
• An infinite number of
projection make our
original image ➔ But, we
can’t use an infinite
number of projections
because limited to the
space.
• How many detectors we
can actually fit?

32. Ideal Number of Projections
• Based on the application ➔ if we want to image a different region of the body, we
don’t necessarily need a lot of projections ➔ it depends on the type of resolution we
need.
• Trade-off between dose and image quality ➔ if we want to an infinite number of
projections, it means an infinite number of doses ➔ it’s harmful to the patient. If we want
to lower the doses to reduce the risk to the patient, it will make lowers the image quality.
• Measurements of image quality include:
❑ Noise
❑ Contrast: the brightness ratio between one region and another (e.g. bone and soft
tissue)
❑ Signal-to-noise ratio (SNR)
❑ Contrast-to-noise ratio (CNR)
❑ Resolution

33. Video
• How Does a CT Scan Work? – YouTube

34. Liver Cancer
• This is a picture of a liver.
• The patient has liver cancer
• The cancer look very smooth in the
picture.

35. Liver Metastases
• When a patient has metastatic liver
cancer, we see not just one lession on
the image ➔ multiple lesions or spots
within the liver.
• This is what happens when one liver
cancer spreads throughout the liver and
metastases.

36. Head CT – Basal Ganglia
• This is the head of an 86
years old man who has a
complication in the region
(arrow pointed).
• The complication looks
different before death
(antemortem) and after
death (post-mortem).
• There’s more attenuation in
the region of the head
(postmortem)

37. Aneurysm Coils
• Aneurysm ➔ little bubble in a blood vessel ➔
bubbles can rupture ➔ dangerous!
• Stop the aneurysm from rupturing without cutting
off blood circulation ➔ Aneurysm Coils ➔
Catheter inserted in leg to access the arteries in the
brain ➔ Coils are inserted in the aneurysm.
• A blood clot forms around the coils to prevent
rupturing ➔ Coils permanently remain in
aneurysm throughout the rest of patient’s life.

38. Streak Artifact Due to Aneurysm Coils
• The coils are made from metal ➔ metal
causes streak artifacts in CT images ➔
image is very distorted.
• Radiating white streaks due to metallic coil
used to prevent an aneurysm from
rupturing.
• In CT images, streak artifacts are common
around metal, bone, and other materials
that block x-rays.

39. Motion Artifact
• Patient moves when taking
CT image ➔ Shift between
one rotation and another
➔ the image will not be
reconstructed very
faithfully ➔ sometimes will
form line in CT image ➔
motion artifact.

40. Motion Artifact Correction
• Sometimes we would have
made another CT image if
patient moves ➔ increase
the radiation doses.
• So, patient must remain as
still as possible when
taking CT image!
• We can correct motion
artifact using Image
Registration (image
processing).

41. CT: Pros and Cons
Advantages
• Multi-planar images.
• High contrast resolution
(especially between bone and
soft tissue).
• Detailed anatomy, because it
shows image depth.
• Capable of whole-body
imaging.
Disadvantages
• Adverse effects of ionizing
radiation. The images are
created by making multiple
projections through the body
➔ each production requires
radiation doses.
• Noise artifacts, some of which
can not be corrected.

42. CHEST CT-SCAN IN
COVID-19

43. Pixels vs Voxels

44. Pixels vs Voxels

54. ………
Let’s play Kahoot!!

55. Other Modalities
1. Fluoroscopy
2. Diffusion Weighted Imaging (DWI)
3. Functional Magnetic Resonance Imaging (fMRI)
4. Single Photon Emission Computed Tomography (SPECT)
5. Coronary Computed Tomographic Angiography (CCTA)
6. Scintigraphy or Gamma scan
7. Elastography
8. Photoacoustic imaging
9. Functional near-infrared spectroscopy (fNIRS)
10. Magnetic particle imaging (MPI)
11. Infrared Thermography
Assignment 1:
- Bentuk kelompok 3 orang.
- Cari referensi dan pelajari terkait modalitas yang ditunjuk
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- Konten : Konsep modalitas, cara kerja, proses rekonstruksi citra, contoh aplikasi, pros dan kons, video youtube.