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Physics and Biomedical Engineering > XR imaging > Flashcards

XR imaging Flashcards

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1
Q

Formula for scattered photon energy? (Compton Scatter).

A

h = Planck’s constant
v’ = Frequency of the photon
mo = Rest mass of electron
c = Speed of light
phi = Scattering angle of photon
a = Initial XR energy expressed in units of electron rest mass (mo)

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2
Q

What is Beer’s Law?

A

Expresses the number of photons (N) transmitted through a material with thickness t and attenuation coefficient (u) hit by N0 photons. (How many photons are NOT attenuated).

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3
Q

Define attenuation

A

The removal of photons from the primary beam (includes scattering AND absorption. BOTH remove photons from the beam.)

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4
Q

Define attenuation coefficient

A

This is a property specific to a material. A high attenuation coefficient means a high probability of interaction, a low attenuation coefficient means a low probability of interaction.

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5
Q

What are the three things that can happen when a photon passes through matter?

A
  • Transmission
  • Absorption
  • Scatter
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6
Q

What is Compton scatter?

Is it elastic or inelastic?

Is it coherent or incoherent?

A

XR is scattered by a loosely bound (free) electrons. This is inelastic (energy is lost to the recoil electron) and incoherent (all the free electrons are independent of one another, so all scatter events occur independently from one another).

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7
Q

When is there maximum energy transfer to the recoil electron in Compton scatter?

A

When the photon is scattered at 180 degrees (straight backwards from the way it came in.

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8
Q

How does the wavelength of the incoming photon relate to the wavelength of the scattered photon following Compton scatter?

A

The change in wavelength is independent of the initial photon energy. It only depends on the scattering angle.

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9
Q

What is coherent scattering?Describe the process

A
  • XR is scattered by an interaction with the entire atom (nucleus + all electrons around it).
  • The incoming photon (now think of this photon as an EM wave), is absorbed by the atom, which starts to oscillate in phase with the incoming EM wave. This then emits EM radiation in the form of a scattered photon.
  • The scattered photon is the same frequency/energy as the incident photon, but just travels in a slightly (VERY slight) different direction.
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10
Q

Is coherent scattering elastic or inelastic?

A

Elastic

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11
Q

Is coherent scatter coherent or incoherent?

A

Coherent

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12
Q

What is an elastic interaction?

A

Energy of the incident wave and the scattered wave is the same.

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13
Q

What is a coherent interaction?

A

Interaction is with the whole atom and all associated electrons rather than just an individual free electron.

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14
Q

When is coherent scatter included in the total attenuation coefficient?

A

If the XR machine has well defined geometry - because even a tiny deviation in direction will mean the photons are no longer detected.

If the geometry is poor, coherent scatter will still be detected and therefore will not contribute to the attenuation coefficient in any calculations.

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15
Q

When does Compoton scatter vs coherent scatter primarily occur?

A

Compton is at higher energy levels (like XRs). Coherent is more likely to occur for lower energy photons.

The exact point that compton becomes dominant depends on the material.

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16
Q

What is photoelectric absorption?

A

The XR is completely absorbed by an atom. This results in an electron being ejected (photoelectron) and the atom will obtain recoil momentum to conserve energy.

Most photoelectic effect occurs in electrons in the inner shell close to the nucleus of the atom.

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17
Q

What are the two possible outcomes if photoelectric absorption occurs in an atom?

A

1) XR emission when an electron drops from a higher energy level to fill the gap.

2) Auger electron release. Another electron is emitted from an outer shell.

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18
Q

What determines the probability of XR emission vs Auger electron emission?

A
  • Lower atomic number (<30) Auger dominates.
  • Higher atomic number (>30) XR dominates.
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19
Q

How does photon energy affect probability of photoelectric interaction with a given atom?

What is the exception to this?

A
  • Increased photon energy decreases the likelihood of photoelectric interaction.
  • Except for at K or L edges. These are thresholds for photon energy that correspond to the energy needed to remove electrons from another of the atom’s shells. As a result, when these thresholds are passed there is a sudden spike in photoelectron interaction likelihood.
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20
Q

What are the four possible interactions a photon can have with an atom?

A
  • Compton scatter.
  • Coherent scatter.
  • Photoelectric absorption.
  • Pair production.
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21
Q

What is pair production (photon interaction)?

A
  • If the photon has an energy greater than 2x electron mass (2x 511KeV), a positron/electron pair might be produced.
  • Positron annihilates as soon as it meets another electron. This is instantaneous, and releases 2 0.511MeV gamma rays.
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22
Q

How do frequency and wavelength relate to the energy of a photon?

A
  • Frequency is proportional to photon energy.
  • Wavelength is inversely proportional to photon energy.
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23
Q

How are XRs produced for medical use?

How efficient is medical XR production? Why is this?

A

1) Electron production (heat up a filament and then apply a magnetic field to accelerate the electrons towards the target).

2) Electrons interact with the target. Approx. 1% of these interactions will be radiative, and produce XRs. The rest will be collisional, where the electron will just change direction until it loses all energy and the electron comes to rest.

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24
Q

What are the two types of radiative interaction an electron can have with the target?

A

1) Characteristic radiation: Electron enters the metal and kicks an electron from one of the atoms in the target. An electron then will drop from a higher energy level to fill the vacancy, in the process releasing an XR.

2) Bremsstrahlung radiation: Incoming electron passes extremely close to the nucleus of an atom, so experiences an extreme slowing effect. This change in momentum releases an XR. Higher energy XR released if the decelleration is more abrupt.

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25
Q

What is the difference between energy and intensity of a photon beam?

A

Energy - Refers to the energy of the individual photons.

Intensity - Refers to the number of photons in a given area.

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26
Q

What is thin target theory? What type of radiation does it model?

What are the two key assumptions made in thin target theory?

What spectrum is generated using a thin target model? Why is the spectrum this shape?

A

Used to model Bremsstrahlung radiation.

Assumptions:
- Slices are extremely thin and only one interaction happens in each slice.
- The probability of an XR of any energy being produced is equal.

Thin target model generates a triangular spectrum. This is becase low energy XR’s can come from ANY layer (photons in all levels have enough kinetic energy to produce these low energy XRs) wheras higher energy XR’s can only come from the outer layers (electrons must have their maximum kinetic energy).

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27
Q

What is the self-absorption effect? (electron interaction with target)

Which energy photons is self-absorption most likely to happen? How does this effect the energy spectrum of the XR beam produced?

A
  • XRs that are produced and never leave the target material.
  • Lower energy photons are more likely to be self-absorbed.
  • The spectrum therefore tails off at the lower energies, as more of the photons are being self absorbed.
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28
Q

What is characteristic radiation?

A

Occurs when an electron moves between energy levels following ejection of an electron in an atom of the target material.

  • Electrons can move between a variety of different energy levels (shell 1 to shell 3, shell 1 to shell 2, shell 2 to shell 3, etc) so there is a range of XR energies that can be produced by characteristic radiation.
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29
Q

What are the two primary mechanisms for XR production when a target is bombarded with electrons?

A
  • Bremsstrahlung radiation (electrons being decelerated when they pass close to the nuclei of atoms in the target. This change in momentum results in the release of an XR).
  • Characteristic radiation (incident electrons knock electrons from the orbit of atoms in the target. Electron then drops from a higher energy to fill vacancy, resulting in XR emission).

Both mechanisms are occurring at the same time in reality.

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30
Q

Why is the XR beam further filtered after leaving the target in XR imaging?

A

Further filtering is done to remove low energy photons that do not contribute to the image (they do not make it through the patient to the detector).

These photons would otherwise serve no purpose except dose deposition in the patient.

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31
Q

What is the optimal spread of photons that stop in the patient vs photons that reach the detector?

A

50/50 split

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32
Q

How does filtration work?

A

Lower energy photons have a higher probability of being stopped by the filter than higher energy ones. As a result, the beam is hardened.

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33
Q

Even after filtration, a K-edge spike will be present in the beam. How is this spike removed.

A

Add an additional extremely thin layer of another material with a different K-edge. This will remove the K-edge spike.

34
Q

What happens if the same material is used for both the target and the filter?

A

An extremely narrow beam is made, with both the high and low energy photons removed.

35
Q

Hard vs Soft beam?

A

Hard - high energies
Soft - low energies

36
Q

What are the key features of an XR tube (in terms of the engineering)?

A
  • Target is rotating so heat deposition is spread out.
  • Vacuum between the filament (electron source) and the target, so all electrons will reach the target rather than stopping in the air.
  • Exit window in the XR tube. Only route XRs can leave, all others are absorbed by the housing.
  • Low energy XRs are produced more spread out than high energy XRs, which are relatively uniform in terms of direction. Diagnostic radiography uses low energy XRs, making the exit window of the tube even more important.
  • The anode (target) is inclined to balance heat deposition and sharpeness.
37
Q

What is the heel effect?

A

Due to the incline, some XRs produced by the target must travel further than others through the target. This means there is a greater likelihood of those XRs being absorbed, epecially for low energy XRs. As a result, the average photon energy will be higher on one side of the FOV than the other.

38
Q

What is the formula for magnification (in terms of detector, object and source)?

A
39
Q

What is the focal spot of an XR machine?

How does focal spot of an XR machine affect the image?

A

Focal spot - the source of the XRs.

Smaller focal spot = sharper image. Therefore, an XR machine with a smaller focal spot is better.

40
Q

How is the focal spot of an XR machine measured? (diagram)

A
41
Q

What is the formula to measure the focal spot of an XR machine?

A
42
Q

How is the blur caused by a focal spot commonly modelled?

A

Take the convolution of the original signal and a gaussian function.

The gaussian function is characterized by the FWHM which will be set to correspond to the amount of blur being modelled.

43
Q

How can blurring be caused by the detector? 2 examples

A

Pixels in a digital detector mean there is no way to discriminate between points within a pixel.

If a detector requires photons to be converted to visible light to be detected, the material that is doing this conversion will attenuate some of the XRs causing blur.

44
Q

Resolution vs pixel size

A

Resolution - Includes all effects that contribute to blurring of an image.

Pixel size - One of the contributing factors to image blurring (detector dependant).

45
Q

What is total unsharpness?

A

The total blur of an image as a cumulative effect of both detector and source blurring factors.

46
Q

How does the contribution of both the source and the detector to blur vary with relative distances between source/detector and the object?

A

Closer to source - more contribution from source, less from detector.

Closer to detector - more contribution from detector, less from source.

47
Q

What is the formula for total unsharpness?

A

U = Total unsharpness
M = magnification
F = Focal spot size
D = Detector resolution

NOTE: F and D must have the same units for the equation to work.

48
Q

What is the key physical principle that underpins contrast in XR imaging?

What are the three factors that affect this principle?

A

Attenuation generates contrast.

Depends on:
- Atomic number.
- Density of the material
- Thickness of the material

49
Q

How does contrast change as the energy of XRs increases?

What is the exception to this?

A
  • Contrast is reduced (due to reduced attenuation).

EXCEPTION: At K/L edges.

50
Q

How does contrast vary with intensity of the incident XR?

A

Intensity of the incident XR does NOT affect contrast, as all the whole object is receiving the incident XR so it just scales uniformly across all features.

51
Q

What is the formula for contrast?

A
52
Q

What is the formula for subject contrast

A
53
Q

What is the formula for background intensity?

A
54
Q

How can contrast be improved?

A

1) Remove scatter.

2) Increase inherent contrast (e.g. use a contrast agent).

3) Reduce kV (lower energy increases the chance of attenuation in the beam - however increases dose).

4) Remove effects of overlying tissues (e.g. reposition patient).

5) Use post-processing software.

55
Q

How can scatter be reduced (in the interest of improving contrast)?

A

1) Reduce field size - limits scatter coming from areas outside region of interest.

2) Use an air gap between the object and detector. Results in more of the scattered XRs missing the detector, reducing noise and improving contrast.

3) Use an antiscatter grid.

4) Scanning slit (strong collimation of the beam).

5) Reduce tissue thickness. Limits opportunity for scatter to occur.

56
Q

What is the trade-off with an antiscatter grid?

A
  • Reduces the number of scattered XRs that reach the detector.
  • Also decreases the number of good photons that reach the detector due to the presence of physical grid bars.
57
Q

What is the formula for grid ratio?

A
58
Q

What is the formula for grid selectivity?

A

Selectivity = % primary photons transmitted/ % secondary photons transmitted

(primary = straight photons, secondary = scattered photons).

59
Q

What is the formula for new contrast when using a grid?

A
60
Q

What is the Bucky factor? What is the formula??

A

Measures how the ratio of additional dose required to detect the same number of good photons when using a grid.

61
Q

What is SNR?

A

Signal-to-noise ratio

62
Q

What is the formula for SNR (generalized)?

A
63
Q

How does SNR change with increased size of feature? Why is this?

A
  • Increasing the size of the feature increases the SNR. This is because it occupies more pixels of the detector, so can be visualised more clearly in the image.
64
Q

What is figure of merit?

A

Figure of merit (FOM) determines the optimal XR energy to visualise a specific detail.

65
Q

What is the formula for figure of merit?

A
66
Q

In brief, what is dual energy radiography?

A

Take two different XRs with two different beam energies. Use software to compare the images in terms of relative contribution from Compton scatter and photoelectric effect to highlight specific tissues/features.

67
Q

What is the formula for efficiency of an XR detector?

A

NOTE: Both t and u are in relation to the material the detector is made of.

68
Q

Why can the detector not be made infinitely thick so 100% efficiency is achieved?

A

Increases other unwanted effects such as scatter and blurring.

69
Q

What is the exception to calculating detector efficiency? How do these detectors work and why are they so effective?

A

Edge-on silicon strip detectors.

Comprised of many individual silicon strips, so photons cannot pass between strips.

Really effective because they allow each strip to be made of extremely thick silicon (efficiency approx. 100%) but the presence of individual strips limits the unwanted side effects (scatter and blur).

70
Q

What is the formula for efficiency of an edge-on silicon strip detector?

A

NOTE: This can be used because the detector itself can be approximated to be 100% efficient. Only lost photons are in the dead region.

71
Q

How can the efficiency equation be applied to a polychromatic beam?

A

Take a weighted average across all beam energies (weighted in relation to the number of photons of each energy).

For each efficiency calculation, the appropriate absorption coefficient should be used that relates to the photon energy in question.

72
Q

What is the most common way to represent spatial variation?

A

Line pairs per mm (lp/mm).

More line pairs per mm, the better the resolution of the system.

73
Q

What is the definition of modulation?
What is the best modulation? What is the worst modulation?

A

How clear the difference between black and white is in the image.

Best modulation is 1, meaning there is a perfect contrast between black and white.

Worst modulation is 0, meaning there is no contrast between black and white and both appear as grey.

74
Q

What three things determine the modulation of an image?

A
  • The object.
  • The system.
  • The position (phase) of the object within the system.
75
Q

What is modulation transfer function?

A

MTF - Shows the modulation of a given XR system plotted against spatial frequency.

76
Q

How is MTF normally measured?

What is the normal relationship between modulation and spatial frequency for an MTF?

A

Place a phantom in the system that contains many bar patters with different lp/mm (spatial frequencies).

Normally, as spatial frequency increases (more lp/mm), the modulation will decrease.

77
Q

What is the importance of the high spatial frequencies of an image?

A

High spatial frequencies are responsible for providing crisp edges and sharpness.

78
Q

What are the two key FT to be aware of in XR imaging?

A

FT of a gaussian is another gaussian (blur is modelled by a gaussian).

FT of a top hat is a sinc function.

79
Q

How do signals appear relative to each other in real space vs fourier space?

A

Something wide in real space is narrow in fourier space and vice versa.

80
Q
A

Physics and Biomedical Engineering (3 decks)

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