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MED-107 Medical Physics II: Medical Imaging and Radiotherapy > 5.1 CT: image formation and reconstruction > Flashcards

5.1 CT: image formation and reconstruction Flashcards

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1
Q

CT is abbreviation of? what kind of images does it produce?

A
  • computed tomography
  • tomography = obtaining images in 3D
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2
Q

what advantage do 3D images have over 2D images?

A
  • in 2D images, structures overlap (ex: ribs overlap with heart & lungs in a chest x-ray)
  • in 3D images, we can avoid this overlap
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3
Q

what is CT?

A

a volumetric imaging modality based on X-ray absorption

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4
Q

why does it mean for CT to be “volumetric”?

A

takes volume into consideration during measurement (3D)

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5
Q

in practice, what do CT images measure?

A

the absorption of X-rays into structures

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6
Q

how does CT compare to X-ray imaging?

A
  • CT vastly exceeds X-ray imaging in soft tissue contrast
  • however, CT spatial resolution is significantly lower than that of plain X-ray imaging
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7
Q

why does CT have better soft tissue contrast?

A

CT has great sensitivity to contrast, providing excellent visualization of soft tissue

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8
Q

CT exceeds X-ray imaging in _____, while X-ray imaging exceeds CT in _____

A
  • soft tissue contrast
  • having higher spatial resolution
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9
Q

what was special about CT when first invented?

A

it was the first imaging modality where the computer was essential in image reconstruction

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10
Q

describe the progress that was made with CT

A
  • in early days, data acquisition was fairly slow, taking ≈ 4min for each rotation, while nowadays it takes ≈ 0.4sec
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11
Q

what is an advantage and disadvantage to modern clinical CT scanners?

A
  • very fast and can now produce 2D cross-sectional images in less than a second
  • expensive, high cost per CT scan
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12
Q

do CTs or normal X-rays cause higher patient radiation dose? explain

A
  • CT results in higher patient radiation dose compared to normal X-rays
  • this is because energies used in acquisition of images in CTs are in the high range of diagnostic X-rays
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13
Q

what is an issue that we face in standard X-ray projection image, but not in a CT scan?

A
  • in a projection image, the exact location of an area of interest cannot be determined (we cannot tell if this area is in front of behind another, so the 2 overlap in the image)
  • this means we cannot obtain any info regarding the depth of the organ/structure, and cannot localize the structure in a 2D image
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14
Q

how is this issue with X-ray projection images resolved?

A

radiologists often take 2 perpendicular projections :
(1) lateral
(2) AP (anterior–posterior)

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15
Q

why do CT scans not share this same issue?

A

because we obtain 3D images in CTs (an image that gives us info in 3 directions)

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16
Q

what is data acquisition?

A

the collection of X-ray transmission measurements through the patient

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17
Q

what does data acquisition require?

A

an X-ray source which is collimated into the shape of a fan or cone

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18
Q

what is one possible geometry for CT scanner source and detectors?

A
  • both the source and arc-shaped detector array rotate in tandem
  • recording projections through a single plane within the body for many different angles
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19
Q

explain the 3D image acquisition process in this geometry

A
  • the position of the X-ray tube and detector is fixed, and rotates together
  • the detector faces the X-ray
  • we have only 1 X-ray tube, but we have multiple detectors
  • the rotation creates images from different angles
  • we combine these 2D images & reconstruct them into one 3D image
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20
Q

describe how a CT works

A
  • CT is a procedure that creates cross-sectional images with the help of computer processing
  • special digital x-ray detectors are located directly opposite the x-ray source
  • as the x-ray passes through the patient, they are immediately picked up by the detectors and transmitted to a computer
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21
Q

compare conventional X-rays to CT scans

A
  • conventional x-ray uses a fixed tube that sends x-rays in only one direction
  • CT scanner uses a motorized x-ray source that shoots narrow beams of x-rays as it rotates around the patient
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22
Q

what is an advantage that CT images have over conventional x-ray images?

A

CT images are more detailed and can reveal bones, soft tissue, organs

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23
Q

what are the ways image slices can be displayed?

A
  • displayed individually in 2D form
  • stacked together to generate a 3D image that can reveal abnormal structures or help the physician plan & monitor treatments
24
Q

what happens to photons when an X-ray beam passes through an object, what does this result in?

A
  • some of the photons are absorbed or scattered
  • this results in the reduction of X-ray transmission (attenuation)
25
Q

what is X-ray attenuation?

A
  • attenuation is the reduction of the intensity of an x-ray beam as it traverses matter
  • the reduction may be caused by absorption or by deflection (scatter) of photons from the beam
26
Q

what does attenuation (the reduction of x-ray transmission) depend on?

A
  • the atomic number of the crossed tissues
  • density of the crossed tissues
  • the energy of the photons
27
Q

give an example of how attenuation of x-rays depends on the atomic number or composition of tissues

A

the bone has a high atomic number, so x-rays are highly absorbed due to that

28
Q

explain how x-ray attenuation depends on the energy of the photons

A
  • low energy photons are absorbed into the structures
  • higher energy photons can exit the patient body & reach the detector for the formation of an image
  • therefore, low-energy photons are more easily attenuated than those with higher energy during X-ray scans
  • increasing photon energy generally decreases the probability of interactions (attenuation) and, therefore, increases penetration
29
Q

where are partially attenuated x-rays collected after passing through an objected?

A

by x-ray detectors on the opposite side

30
Q

what then happens to x-rays that are detected from the receptor?

A
  • they are then converted from x-ray photons to electrical signals
  • these signals are then converted into digital data
  • after which the attenuation value is calculated
31
Q

what is the filtered back projection method?

A

a mathematical technique to convert x-ray projections into cross-sectional images

32
Q

why do we use the filtered back projection method?

A

to obtain attenuation value for each pixel of the digital image

33
Q

what do the detectors measure in the filtered back projection method?

A

the forward projection (the shaded areas)

34
Q

in the forward projection, what do the shaded regions and the white regions represent each?

A
  • the shaded region represents the x-ray absorber (absorption of x-rays)
  • the white regions represent no absorption of x-rays
35
Q

describe the filtered back projection method

A

(1) first we measure the number of absorbing regions in both directions (vertical & horizontal)
(2) we then add the contribution for each region
(3) we translate these numbers into different shades of grey

36
Q

in the reconstructed image, how do the regions with high absorption and regions with low absorption appear each?

A
  • regions with high absorption appear white
  • regions with low absorption appear black
  • (inverse of the forward projection)
37
Q

what do we obtain for each projection?

A
  • for each projection we obtain a 2D image
  • we then reconstruct these slices into a 3D image
38
Q

what is the aim of CT?

A
  • to obtain a spatially resolved map of absorption coefficients in one slice of the patient’s body
  • if such map is sampled at a finite resolution, it provides an image
39
Q

describe the mathematical foundations behind image reconstruction

A
  • μ1, μ2, μ3, μ4 are linear coefficients, each represents structures of different materials
    S1 = μ1 + μ2 ,
    S2 = μ3 + μ4 ,
    S3 = μ2 + μ4 ,
    S4 = μ1 + μ3
  • we can obtain 4 different projections and determine the overall attenuation (attenuated beams I1, I2, I3, I4)
  • since each projection follows Lambert Beer’s law, we obtain a linear equation system that we can solve for μ1, μ2, μ3, μ4
  • Beer’s law: we can find the intensity (I) of the x-ray beam based on the thickness & linear coefficient of each material
  • Law formula: I1 = I0exp^(-μ1d-μ2d) ,
    I2 = I0exp^(-μ4d-μ5d) , etc
  • this simple equation system can only one solved when one of the absorption coefficients is known
40
Q

why do we use computers during CT when it comes to image formation?

A
  • an arbitrary object, composed of n-by-n different materials requires n^2 independent equations
  • however in CT, we obtain data from MANY angles (many projections)
  • to solve this more projections are taken at different angles
  • this requires a lot of time to do the calculations, so using a computer helps solve these equations very quickly
41
Q

what steps does the reconstruction of images to 3D form from the x-ray measurements involve?

A
  1. measurements
  2. pre-processing
  3. raw data
  4. filtering
  5. filtered data
  6. interpolation
  7. back-projection
  8. axial source images
42
Q

what is another image reconstruction method that does not involve filtering the projection data before the back projection known as?

A

convolution
(or convolution-back projection procedure)

43
Q

what is convolution?

A
  • a mathematical operation that combines two functions to produce a third
  • you drag the projections back through the image and sum them to obtain an approximation of the original image
44
Q

what advantage does using convolution back-projection method have over not using using convolution?

A

using convolution back-projection method, we produce images of higher quality (compared to images obtained without convolution)

45
Q

the selected ‘field of view’ is divided into small image elements, known as?

A

pixels

46
Q

what is a voxel?

A
  • voxel = volume pixel
  • the pixels that make up each cross-sectional image represent a small volume of tissue, called a voxel
  • in other words, the 3D representation of a pixel
47
Q

what is the function of a voxel?

A
  • a voxel is used for volume element, as it takes into consideration volume
  • represents a quantity of 3-D data just as a pixel represents a point or a cluster of points in 2-D data
  • used in scientific and medical applications that process 3-D images
48
Q

what is the relationship between pixel size and image resolution?

A

the smaller the pixel, the higher the resolution (as more information is given about the structure)

49
Q

what does the density value of each pixel depend on?

SOS

A

the composition of the tissue it represents

50
Q

how is the density value of each pixel expressed?

SOS

A

in Hounsfield units (HU)

51
Q

CT scanners represent x-ray absorption using a quantity called the _____, which we measure in _____

A
  • the CT number
  • Hounsfield units (HU)
52
Q

how are the Hounsfield units calculated? what is the reference for HU?

SOS!!!

A

the Hounsfield units are calculated from the attenuation measurements relative to the ATTENUATION OF WATER

53
Q

what do Hounsfield units range from?

A

-1024 to +3071

54
Q

since water is the reference, structures before water on the HU scale have _____ densities, and structures past water have _____ densities

A

lower, higher

55
Q

what is the HU of each of the following:
(1) air
(2) lung
(3) fat
(4) water
(5) CSF (any simple fluid)
(6) blood / soft tissue
(7) muscle
(8) adrenal tumor
(9) white matter
(10) grey matter
(11) liver
(12) bone

SOS!!!

A

(1) -1000
(2) -500 (mainly have air)
(3) -100 to -50
(4) 0
(5) +15 (range: -10 to 20)
(6) +30 to +45
(7) +10 to +40
(8) less than +10
(9) +20 to +30
(10) +37 to +45
(11) +40 to +60
(12) +700 to +3000 (>1000)

56
Q

why is the Hounsfield scale very important for physicians?

A

it is very important for physicians as they can decide from the HU if a structure is a cyst, soft tissue, or a cancer

MED-107 Medical Physics II: Medical Imaging and Radiotherapy (16 decks)

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