Interaction with matter


Attenution of x-rays

A beam of x-rays may be:

  1. Transmitted: pass through unaffected or with a lower energy
  2. Absorbed: transfer all energy to matter and not pass through the patient to the film
  3. Scattered: diverted with or without energy loss

Attenuation

Attenuated x-rays are those that are absorbed, transmitted with a lower energy or scattered. It is an exponential process and, therefore, the beam intensity never reaches zero. There are two main methods through which attenuation occurs:

  • Compton scatter
  • Photoelectric effect

Attenuation of the beam can be represented numerically by:

  • Half value layer
  • Linear attenuation coefficient
  • Mass attenuation coefficient

Interactions with matter

Three processes may occur and contribute to attenuation:

  • Compton effect (aka Compton scatter, inherent scatter)
  • Photoelectric absorption
  • Elastic scatter;

Compton effect

  1. X-ray photon hits free/ loosely bound outer shell electron
  2. Electron absorbs some of the photon's energy and is deflected
  3. The photon, having lost some energy, is deflected and scattered. Because of the production of a scattered photon the Compton effect is considered a scattering process.

 

Compton scatter

 

The Compton effect is also called incoherent scatter as the photon energy change is not always orderly and consistent. The change in energy of the x-ray photon depends on the resulting angle of scatter and not on the scattering medium. The larger the energy discharged by the photon to the electron the:

  • Lower the residual deflected photon energy
  • Higher the subsequent electron energy
  • Larger the angle of the deflected photon

Compton scatter occurs more often with:

  • Outer shell electrons
  • Loosely bound electrons

Compton attenuating coefficient

This is the probability that an x-ray photon is attenuated via Compton scatter. It is dependent on the number of available electrons - the electron density of the material - and on the physical density but not on the atomic number of the material. This is because, with the exception of hydrogen, all materials have approximately the same number of available electrons per gram of material. Materials with a significant proportion of hydrogen have more electrons per gram and the probability of Compton attenuation is increased.

Compton attenuating coefficient = density / energy

Summary

The amount of Compton scatter increases with:

  • Increasing mass density
  • Increasing electron density of the material
  • Lower x-ray beam energy (minimal range over the diagnostic radiation range)

No effect with:

  • Atomic number of material (except for materials with significant proportion of hydrogen)

 

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Photoelectric effect

  1. An x-ray photon interacts with a bound electron from the inner shell.
  2. All of the energy of the photon is transferred to the electron.
  3. The electron then has enough energy to be freed as a photoelectron and leaves a 'hole' in the shell.
  4. The hole is filled by electrons from outer shells. As these electrons move from a lower energy outer shell to a higher energy inner shell, the electrons release the energy at a characteristic energy (i.e. characteristic radiation).
  5. The released electron only travels a short distance and deposits its energy into the surrounding matter. In low Z materials (e.g. tissue and bone) the high energy photon collides with a bound electron. The released photon has very little energy and is absorbed immediately with the ejection of a further, low-energy or "Auger" electron and all the energy is said to have been absorbed by the material.

 

Photoelectric radiation step 1

 

Photoelectric radiation step 2

 

 

Photoelectric radiation step 3

Photoelectric LAC

The probability of photoelectric interactions depends on a few factors as demonstrated in the equation:

  • Energy of the x-ray photon
  • Atomic number
  • Mass density
τ = ρZ3 / E3
Key:
τ = photoelectric LAC
ρ = mass density
Z = atomic number
E = photon energy

 

Energy of the x-ray photon

The probability of photoelectric interactions is highest when the x-ray photon energy is slightly above the electron binding energy. If the photon energy is too low it cannot free the electron. If the energy is too high the probability of an interaction significantly decreases due to the inverse relationship with the cube of the energy.

 

l-edge and k-edge attenuation graph

 

As the photon energy increases, there are values where there is a sudden jump in attenuation (k-edge and l-edge. For example, at energies just below the k-edge the photons don't have enough energy to free the k-shell electrons. As the energy increases to just over the required energy, a much larger number of electrons become available for interaction and the probability of the photon being attenuated by a photoelectric reaction significantly increases. This is particularly useful in iodine in which the k-edge is 33 keV which is in the diagnostic radiation range and is utilised to massively increase the photoelectric effect and therefore give greater tissue contrast.

Atomic number

An increase in the photoelectric interactions occurs with increasing atomic number as the binding energies of electrons moves closer to the photon energy.

Summary

The photoelectric effect occurs more often with:

  • Inner-shell electrons.
  • Tightly bound electrons.
  • Incident x-ray energies just higher than the electron-binding energy i.e. closely match the electron-binding energy.

The photoelectric effect increases with:

  • Higher atomic number of the material.
  • Increasing mass density of the material.

 

Elastic scatter

Aka coherent, classical, unmodified or Rayleigh scattering.

  • Photon bounces off an electron that is firmly bound to its parent atom
  • Occurs if photon energy less than binding energy of electron
  • No secondary electron is set moving and no ionisation or other effect is produced in the material
  • Little significance in radiology

Competitive interactions

Both photoelectric and Compton scatter contribute to the total attenuation of a beam as it passes through material. The relative contribution of photoelectric and Compton interactions depends on a few factors.

 

Graph of photoelectric and compton effects over range of energies

 

As the x-ray photon energy increases:

  • There are fewer Compton interactions.
  • But there is a much more significant decrease in photoelectric interactions (i.e. Compton scatter becomes the predominant cause of attenuation at higher energies).
  • There is a reduction in the total attenuation (i.e. more photons are transmitted through the material).

As the atomic number increases:

  • There is no change in Compton interactions.
  • Many more photoelectric interactions.
  • Greater attenuation of the x-ray photons.

As the tissue mass density increases:

  • There is an increase in both Compton and photoelectric interactions.
  • Greater attenuation of the x-ray photons.

Measuring attenuation

Half value layer (HVL)

This is the measure of the penetrating power of the x-ray beam and is the amount of matter required to attenuate the beam to half its energy value. The smaller the HVL the more attenuating the material is or the weaker the x-ray beam is. It differs for different materials and strengths of beams. To calculate the factor of reduction use: 2HVL

e.g. if the HVL of a beam is 2 mm, by what factor is the beam attenuated if it passes through 8 mm of material?

8 mm = 4 HVLs
24 = 16
The beam is attenuated by a factor of 16

 

Linear attenuation coefficient (LAC)

This is the probability of the material to attenuate the beam. It can also be expressed as the amount of energy transferred to the material per unit of track length of the particle. The LAC (μ) is calculated by:

μ = 0.693 / HVL
Key:
μ = LAC, units: cm-1

 

Mass attenuation coefficient

The MAC is a measure of the rate of energy loss by a photon beam as it travels through an area of material. By dividing LAC by the density of the material the effect of density is removed. The MAC is, therefore, independent of density and depends only on the atomic number of the material and the photon energy.

MAC = μ / ρ
Key:
μ = LAC, units: cm-1
MAC units: cm2g-1
ρ = density

 

Effect of beam quality on attenuation

The above only really apply to a monoenergetic (one energy value) beam of x-rays from a point source (infinitely small area) travelling in a vacuum. In reality, the x-ray beam focus is not a fine point and contains photons of different energies that, once they leave the x-ray tube, do not travel in a vacuum.

Wider beam

Increased width of beam = increased scatter produced and measured = larger measured HVL

Heterogeneous beam

  • The beams produced by x-ray tubes are photons of a wide range of energies.
  • The lower-energy photons are attenuated proportionally more than the higher-energy photons and are removed, leaving behind higher energy photons aka "beam hardening".
  • The resulting beam is of a higher average energy.
  • It can, therefore, penetrate tissue easier and the HVL is increased.

Σ  Summary
  • Attenuation is an exponential process - beam intensity never reaches zero
  • Penetrating power of a beam is measured by its half value layer (HVL) - the depth of material that results in a 50% reduction in the beam intensity - factor of reduction = 2HVL
  • Mass attenuation coefficient independent of density of material - depends only on atomic number of material and photon energy
  • Wide beam - increases measured HVL due to increased scatter
  • Heterogeneous beam - HVL increases with distance traveled due to beam hardening
Compton effect Photoelectric effect
Interactions with free / outer shell electrons Interactions with inner shell electrons
Part of electron energy transferred Whole of photon energy transferred

Depends on:

  • Electron density of target
  • Physical density of target
  • Photon energy (minimally)
  • NOT atomic number

Depends on:

  • Atomic number of target
  • Photon energy
  • Physical density of target
More important in low density structures (e.g. air, water, soft tissues) and with high energy photons More important in high Z structures (e.g. iodine, lead) and with low photon energy

Both processes occur equally at:

  • 30 keV for air, water and tissue
  • 50 keV for aluminium and bone
  • 300 keV for iodine and barium
  • 500 keV for lead

Next page: Digital radiography


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