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Diagnostic Imaging Exam > CT > Flashcards

CT Flashcards

1
Q

What is a tomogram?

A

A tomogram is an image of a plane or slice within the body

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2
Q

Explain the basic mechanism of CT.

A

One way to think about the basic mechanism of Computed Tomography (CT) is to image taking a series of conventional chest x-rays, where the patient is rotated slightly around the axis running from head to foot between each exposure.

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3
Q

The projection data from CT is used for?

A

The projection data is used to reconstruct crosssectional images.

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4
Q

Compared to Radiographic Imaging, CT eliminates which artifacts?

A

Compared to Radiographic Imaging, CT eliminates the artifacts from overlaying tissues.

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5
Q

When was the first CT scanner developed?

A

The first clinical CT scanner developed by Houndsfield in 1971

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6
Q

How many generations of CT-scanners are presented in the lectures?

A

7 generations of CT-scanners.

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7
Q

Explain X-ray Source and Collimation for CT.

A

X-ray Source and Collimation

  • Similar to those using for Projection Radiography
  • CT system (Fan beam 30 – 60 degree) requires collimation and filtration that is different to radiography system (Cone Beam)
  • Collimation (beam restriction) is accomplished by using two pieces of lead that form a slit between them
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8
Q

Give examples of CT Detectors?

A

CT Detectors

  • Solid-state Detector
  • Xenon Gas detector
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9
Q

Describe Solid-state Detector.

A

Solid-state Detector

  • X-ray interacts with crystal by photoelectric effect (similar to phosphor in an intensifying screen)
  • Electrons are excited and emitted visible light when they spontaneously de-excite.
  • Such scintillation process results in a burst of light
  • The light is converted to electric current using photo-diode
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10
Q

Explain Xenon Gas detector.

A

Xenon Gas detector

  • Small and highly directional detectors required for 3G system
  • Use Xenon gas in long, thin tubes.
  • When Xenon gas ionized, it generates current between an anode and cathode.
  • Less efficient, but highly directional.
  • For same performance, solid state detectors must be accomplished by external collimations
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11
Q

What is Parallel Beam projection?

A

Parallel Beam Projection

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12
Q

Explain the Line integral.

A

Line integral

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13
Q

For Parallel Beam Projection, if the l=1 and \theta=0, what does the integral become?

A

Parallel Beam Projection,

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14
Q

What is g(l,\theta) when \theta is fixed and l varies?

A

Parallel Beam Projection

g(l,\theta) is then a projection.

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15
Q

What is an image of g(l,\theta) called?

A

Parallel Beam Projection

  • An image of g(l,\theta) with l and \theta as rectilinear coordinates is called a sinogram.
  • g(l,\theta) is also known as the radon transform of f(x,y) .
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16
Q

Explain Back Projection.

A

Back Projection

  • Intuition tells us that if g(l,\theta) takes on a large value at \theta=\theta0, then f(x,y) must be large over the line L(l,\theta).
  • One way to reconstruct an image with this property is to simply assign every point on the value L(l,\theta).
  • The resultant function is called the back projection image and is given by:
  • b\theta(x,y)=g(xcos(\theta)+ysin(\theta),\theta)
  • To incorporate information about the projections at other angles, we can simply add up (integrate) their back projection images, which results:
  • fb(x,y)=int(0->\pi)b\theta(x,y)d\theta
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17
Q

Explain Projection-Slice Theorem.

A

Projection-Slice Theorem (Fourier Slice Theorem)

  • G(w,\theta)=F(w*cos(\theta),w*sin(\theta))
    • w= the spatial frequency
  • The 1-D Fourier Transform of a projection equals a line passing through the origin of the 2-D Fourier Transform at an angle corresponding to the projection.
  • It forms the basis of three image reconstruction methods.
    • Fourier Method
    • Filtered Back Projection
    • Convolution Back Projection
  • Consider the 1-D Fourier Transform of a projection with respect to l:
  • G(w,\theta)=F1D[g(l,\theta)=int(-inf->inf)g(l,\theta)e-j2\pi*w*ldl
18
Q

Explain the Fourier Method.

A

Fourier Method

  • A conceptually simple reconstruction method based on Projection-Slice Theorem.
    • f(x,y)=F2D-1[G(w,\theta)}
  • Problems:
    • Interpolating polar data onto Cartesian Grid
    • Time consuming to compute the 2D Inverse Fourier Transform
  • Not widely used in CT
19
Q

What are the differences in the results between back-projection, filtered back-projection or filtered back-projection using a Hamming Window?

A

Back Projection

20
Q

Explain Filtered Back Projection

A

Filtered Back Projection

21
Q

What is the flow of reconstructing images using filtered back projection with a HP-rampfilter?

A

Reconstructing images using filtered back projection with a HP-rampfilter

22
Q

Explain Convolution Back Projection

A

Convolution Back Projection

  • The filtered backward projection can be rewritten as:
  • f(x,y)=int(0->\pi)[F1D1(|w|)*g(l\theta)] l=xcos(\theta)+ysin(\theta)d\theta
23
Q

Explain Fan Beam Reconstruction.

A

Fan-Beam Reconstruction

  • Fan-Beam Reconstruction
  • (i) equal angles between the measured raypaths
  • (ii) equal detector spacing
  • (iii) both equal angles and equal detector spacing
  • Advantage: Faster
  • Disadvantage: More complicated Algorithm
24
Q

Name some examples of artifacts related to CT

A

Artifacts associated with CT:

  • Polychromaticity Artifacts in X-Ray CT
  • Artifacts due to insuffucient views
  • Artifacts due to strong scatterers
  • Metal artifacts
  • Aliasing artifact and noise
  • Electronic or system drift
    • Mis-calibration or Gain Drift
    • Detector Faulty
  • X-ray Scatter
    • Strong Scatter that blurs the image
  • Motion
    • Typical scan takes 1 to 10 second
    • Heart Beats, breathing
    • Gate data acquisition so that data will be taken only at a certain stage in the cardiac cycle and/or breathing cycle.
25
Q

How does Polychromatic artifacts look like?

A

Polychromatic artifacts

  • Polychromatic; having or exhibiting a variety of colors.
26
Q

How does Artifact due to defect detector looks like?

A

Artifact due to defect detector

27
Q

How does Artifacts due to insuffucient views appear like?

A

Artifacts due to insuffucient views

28
Q

Appearance of Artifacts due to strong scatterers?

A

Artifacts due to strong scatterers

29
Q

How does Metal artifacts present themselves?

A

Metal artifacts

30
Q

What causes Aliasing artifact and noise?

A

Aliasing artifact and noise

  • Insufficiency of data
    • Under sampling projection data
    • Not enough projections
    • Under sampled grid for display
  • Presence of random noise in the measurements
31
Q

When does Aliasing errors in projection data occur?

A

Aliasing errors in projection data occur

  • N (sample of projections) is small and K (number of projections) is large
  • Choose sample interval \tau
  • The corresponding band width is W=1/2\tau
  • Further assume W < B
  • Linearity holds so the images can be analyzed as a sum of:
    • The image made from the bandlimited projections
    • The image made from the aliased portion of the spectrum
  • Subtracting the two reconstructions => The streaks are gone
32
Q

What happens during Insufficient number of projections?

A

Insufficient number of projections

  • N (samples of projections) is large and K (number of projections) is small
  • A small number of filtered projections of a small object that are backprojected will result is a star shaped pattern
  • The number of projections should be roughly equal to the number of rays in each projection
33
Q

Explain Projections vs. Samples/projection

A

Projections vs. Samples/projection

  • The number of projections should be roughly equal to the number of rays in each projection.
  • Assume Mproj projections distributed over 180˚. The angular separation is: \delta=\pi/Mproj
  • With sampling interval τ, the highest spatial frequency is; W=1/2τ
  • Number of samples per projection: N
  • Number of projections: N
  • Reconstruction grid: N x N
34
Q

What are the limitations when using Algebraic Reconstruction Algorithms.

A

Algebraic Reconstruction Algorithms

  • The relationship between the image sample and the projection can be given by Σ{1->N}wijfj=pi, i=1,2,…M
  • where M:projections and N:cells..
  • When M and N are small, the matrix equation can be solved by direct matrix inversion.
  • For a 256 x 256 image, N =65536.
  • Number of projections is also in the same scale.
  • Direct Matrix Inversion is not feasible especially not in the 1970s or 1980s.
  • Noise in measurement can also deteriorate the quality of the reconstructed image.
35
Q

Explain the method of Algebraic Reconstruction Algorithms

A

Algebraic Reconstruction Algorithms

  • Initial Guess, project on the first line.
  • The resultant point is re-projected on the second line.
  • And then project back to the first line.
  • The above process is repeated iteratively.
  • In an unique solution exist, the iterations will always converge to the solution point.

Example: Kaczmarz Method

  • Consider the case of 2 equations with 2 unknowns:
    • w11f1+w12f2=p1
    • w21f1+w22f2=p2
  • In vector form: v** \dot **f**=**p
  • By applying the algorithm:
  • f(i)=f(i-1)-(f(i-1) \dot wi-pi)/(wi \dot wi) * wi
36
Q

Give examples of Algebraic Reconstruction Algorithms

A

Algebraic Reconstruction Algorithms

  • Numerical implementation of the algorithm by various approximations.
    • ART (Algebraic Reconstruction Techniques)
    • SIRT (Simultaneous Iterative Reconstruction Technique)
    • SART (Simultaneous Algebraic Reconstruction Techniques)
37
Q

What are the advantages and disadvantages with Algebraic Reconstruction Algorithms?

A

Advantages and Disadvantages with Algebraic Reconstruction Algorithms

  • Advantages:
    • Conceptually Simple
  • Disadvantages
    • Computationally extensive
    • Does not work well with high inhomogeneity (10%)
    • Refraction and Diffraction effects are substantials, result in meaningless results (due to ray tracing)
    • Recent advancements make it become popular for PET reconstruction.
38
Q

Explain Iterative Methods.

A

Iterative Methods

  1. Starts with an initial estimate of the twodimensional matrix of attenuation coefficients
  2. By comparing
    • (i) the projections predicted from the initial estimate
    • (ii) those that actually acquired
  3. Changes are then made in the estimations
  4. Repeats until the residue error becomes small
39
Q

Name one Iterative method

A

Iterative method

  • Ray-by-Ray
40
Q

Clinical application Iterative Method?

A

Iterative Methods

  • The entire process is repeated for all projections.
  • Not usually applied for CT due to high SNR.
  • More widely used in nuclear medicine where the SNR is low.
  • Similar approach is used in microwave tomography.
41
Q
A

Diagnostic Imaging Exam (8 decks)

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