3. X-Ray Imaging

How it Works

• X-ray particles are called photons
• X-ray photons are delivered in packets called quanta.
• If the particle energy is greater than the binding energy of the electron, then the photons \n are capable of ionizing atoms.
• Diagnostic radiation is typically in the range of 100 nm to about 0.01 nm, or from 12 eV to 125 \n keV.

Components

• The number of X-ray photons produced depends on the number of electrons striking the target material (so tube current)

• The anode is made of either tungsten or molybdenum. The cathode is composed of two parts: the filament made of tungsten, and a focusing cup.

• A change in filament current changes the intensity of the X-ray photons.

• The X-ray beam coming off the cathode material is polychromatic.

  • Filtering out the undesired portion of the X-ray spectrum can substantially reduce the radiation dose delivered to the patient.

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Math

• c = λ * f
  • c = 3E8 m/s
• 1 angstrom = 10E-10 m
• High frequency range is from 3E16 to 3E19 Hz
• E = h * f
  • h = Plank’s constant = 6.63E-34 J*s = 4.13E-18 keV*s
  • f is frequency, or ν (Greek letter nu)
• eV is an electron volt, a unit of energy representing the amount of energy one electron can obtain from accelerating between the potential difference of 1 volt
  • 1 V = 1.602E-19 columbs = 1.602E-19 J
• A pjoton with 3E18 Hz frequency has what energy?
  • 4.13E-18 keV*s x 3E-18 Hz = 12.39 keV

Ionization in X-Rays

• Simplest atom to ionize is an H atom (only 1 e-, super easy to ionize because we have a lot of H in our bodies)
• If it can ionize, it has enough energy to eject an electron
  • 13.6 eV is enough to kick out an electron, and is the threshold of ionizing

X-Ray Generation

• X-rays are generated from an x-ray tube
• High potential difference between cathode and anode
• Acelerated electrons from a heated filament
• Electrons strike the target (sometimes tungsten
• Heat and x-rays are generated
  • 99% of generated energy goes to heat
• Electrons interact with the target material mainly in 2 ways to generate radiation…. Braking and Characteristic

Braking “Bremsstrahlung” Radiation

• Electrons are slowed down (lose E)
• Change on energy is emitted as photon energy
• Generally, more photons in lower energy
• Max energy is related to max kV across tube
  • E tube = kV * e

Characteristic Radiation

• Electron strikes another inner shell electron
• Inner electron is ejected with lower energy
• Electrons reconfigure to fill the void
• Photon is produced with specific photon energy
  • Photon energy depends on the shell (closer to nucleus = more E)

X-Ray Spectrum

• Spectrum can also be characterized by its “effective energy” defined as the energy of a mono-energetic beam with the same penetrating ability
• Effective energy is a weighted sum of the spectrum
• Filtration whether intended or not, increases the effective energy of spectrum
• Number of photons is the “quantity” of the x-ray beam
• Energy level of the beam is the “quality”

How Might X-Rays Interact with Matter?

Coherent (Rayleigh) scattering

• Photon bounces off in a new direction with little energy change
• The electric field of the incident photon’s EM wave expends energy by making all of the electrons in the atom to oscillate in phase
  • Atom’s electron cloud then radiates the energy as a scattered photon
• Coherent scattering is used mostly with low energy diagnostic x-rays (mammography, thyroid scans)
• Electrons are not ejected so ionization does not occur

Compton scattering

• If it’s above 30keV with soft tissue, it’s probably compton scattering
• Steps
  • Photon interacts with an electron (usually valence) and only some energy from the photon goes to the electron
  • Photon moves on with reduced energy and new direction
  • Electron is ejected
• Energy of the initial photon must be equal to the energy of the scattered photon + energy of ejected electron
• More dense the tissue = more likely Compton scattering occurs
• Compton scattering makes up most of the background noise & tissue damage
• If the initial energy is low, then the scattered energy doesn’t matter on the scattering angle
• If the initial energy is high, the scattered energy is higher for a smaller scattering angle
• Scattered photons with higher energies will continue in pretty much the same direction
• Compton scattering in which a photon is not absorbed but rather scattered. The photon energy is reduced, and an electron is ejected. This is the major source of noise in X-ray (and CT) images.

Photoelectric effect

• In the photoelectric effect, all of the initial energy is transferred to an electron

• Photoelectric effect in which a photon is absorbed, characteristic radiation is emitted along with photoelectrons, and possibly Auger electrons.

• Steps

  • All photon energy transfers to electron
  • Electron ejects
  • Electron becomes a photoelectron
  • Energy of the photoelectron is the energy of the initial photon minus the energy it took to bind to the orbital electron
  • Called an Auger electron
  • A lower orbital electron will jump up to take its place
  • Energy needs to decrease now, so energy is given off as fluorescent energy

• Probability of characteristic x-ray emission (dangerous) decreases as the atomic number of the absorber atom decreases (less protons = less possibility of radiation)

• Soft tissue has lower atomic number so it’s not super frequent

• Probability of characteristic x-ray emission also decreases with increasing photon energy

  

Pair Production

• Pair production can occur when the energy of the incident photon exceeds 1.02 MeV
• Steps
  • High energy photons are absorbed by a nucleus
  • A positron (positive electron, a form of anti-matter) is emitted with an electron
  • Energy above 1.02 MeV goes to the electron as kinetic energy
  • The positron and electron interact and shoots oppositely directed 511 keV annihilation photons
• Unusual because it takes so much energy
• Describes the same anti-matter formation used in PET scans
• Pair production in which a photon is absorbed by the nucleus, a positron is emitted, and an electron is ejected.

Photo-disintegration

• Interaction of an incident photon with a nucleus, which produces one (or more) ejected nuclear particle

• One element becomes a different element

• Super unusual so it takes so much energy

  

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