Absorption of X-Rays

Different types of X-ray absorptions

There are four main mechanisms of X-ray attenuation, and they depend on the energy of the incident photon. The four types consist of two scattering and two absorbing X-ray absorptions.

Simple (Rayleigh) scattering

Simple scattering affects low-energy photons in the range of one to 20 kiloelectronvolts (keV). These photons do not have sufficient energy to displace an electron when colliding with atoms. The oscillating electric field of an X-ray photon interacts with an atom in the tissue, which induces a force between them. This force alters the trajectory of the photon and causes scattering.

Because the mass of the photon is much smaller than the atom, it is deflected from its path and scattered with no change in momentum. Typically, the photon continues to travel in a scattered forward direction; however, there is a low chance of it being deflected backwards after a head-on collision with an atom nucleus. This type of scattering only makes a minor contribution to the attenuation coefficient because X-rays used in imaging typically have energy higher than 20keV.

Compton scattering

Compton scattering occurs when an X-ray photon with energy between 30keV and five MeV (megaelectronvolts) collides with an electron of a tissue atom. These photons have sufficient energy to eject the electron from its atomic orbit by exceeding its binding energy. The photons also transfer some of their energy to the electron in the process. The new lower-energy photon is also scattered by the interaction, resulting in this type of scattering, which produces both a free electron and a scattered, lower-energy X-ray photon.

Photoelectric effect absorption

The photoelectric effect affects photons with energies less than 100keV. In this range, X-ray photons can have an energy equal to the shell binding energy of atoms in the tissue. This allows the photon and its energy to be absorbed by the atom, and energy is transferred to an electron that is ejected from the atom. This creates an ionised atom in a higher energy state, which returns to its ground state by emitting X-ray(s) with a wavelength characteristic of the atom type. These emitted X-rays are at a different energy level than the incident photon and will not travel coherently with X-ray photons from the source.

Pair production absorption

This mechanism affects very high-energy photons over 1.022MeV. At these energy levels, a photon can interact with an atom’s nucleus, transferring all its energy to produce an electron and a positron. These antiparticles may travel for a short distance before interacting with each other (or other nearby electrons/positrons), where they are annihilated and transformed into a pair of 511keV photons. The pair of newly produced photons travel from the point of annihilation in diametrically opposite directions, ensuring momentum is conserved. The effect of pair production absorption grows as the photon energy increases, meaning it is the dominant mechanism at high energies.

Overview of the different types of X-ray absorptions

Low-energy photons are more easily attenuated than those with higher energy during X-ray scans. This is because the probability of photoelectric absorption (the primary attenuation mechanism at X-ray scan energy levels) is proportional to (Z/E)³, where Z is the atomic number of the atoms in the tissue and E is the X-ray photon energy.

This also means that the lower-energy photons in the X-ray beam are, on average, absorbed sooner as they pass through the patient, resulting in increasing average photon energy from the front to the back of the patient. Since low-energy photons are more likely to be absorbed, the energy deposition dose is highest at the patient’s skin and decreases as the beam passes through.

Implications of attenuation on the X-ray procedure

Because most energy deposition occurs near the skin, one of the risks of X-rays is skin injuries. This risk is greater for larger patients, as they will require higher doses for the beam to penetrate body parts and produce a helpful image.

Attenuation coefficients can estimate what types of tissue different regions represent based on the amount of attenuation of the initial beam intensity.

Absorption of X-rays formula: attenuation coefficient

The four main attenuation mechanisms outlined above show that for photons with a given energy, the material (influences Z) and tissue thickness control the amount of attenuation the X-ray beam undergoes. The intensity of X-Rays transmitted through a substance relative to the initial beam intensity is given by the equation below.

\[I = I_0 \cdot e^{-\mu x}\]

I₀ is the initial intensity of the photons, x is the tissue thickness (distance travelled), and μ is the linear attenuation coefficient for the photon energy. Larger values of μ indicate greater X-ray attenuation, meaning substances like bone have a larger coefficient than soft tissues. The SI unit of attenuation coefficients is m^-1.

Effect of attenuation on dose

If we want to produce an X-ray image with a good level of detail, the digital detector plate needs to measure a large enough number of photons to stand out against the background noise. The noise comes from photons that have been scattered as they travel through the body, or it can randomly arrive from an alternative source. The ratio of unattenuated photons in the X-ray beam (signal) to background noise is the signal-to-noise ratio (SNR). In X-rays, the SNR is related to the number of photons N in the X-ray dose.

\[SNR \propto \sqrt N\]

The SNR improves as the number of photons increases, producing an image with more useful detail.

We can increase the number of photons in two ways: prolonging the exposure time (mA) or increasing the accelerating voltage in the X-ray tube (as N \(\propto\) KV³).

Increasing the photon energy level also results in a lower proportion being attenuated by the patient’s tissue, which offsets the higher photon energy and results in a lower overall dose being absorbed. However, since the X-ray energy level increases and the attenuation rate decreases, the level of contrast in the image produced is poorer due to attenuation creating the contrast between tissue types. Therefore, balancing the image contrast, noise, and patient dose requires a trade-off between the photon energy/accelerating voltage and exposure time.

Contrast mediums

Some soft tissues have attenuation coefficients too low to create enough contrast in a radiograph image, so we can use contrast mediums to improve the visibility of these structures. Bromine or iodine compounds are the two most commonly used contrast mediums as they are harmless to humans and have large atomic numbers (Z), representing large atoms with many electrons.

The primary attenuation mechanism for X-ray imaging is the photoelectric effect. As this relies on the incoming photon colliding with an electron, larger atoms with a greater number of electrons are more likely to cause photoelectric scattering than smaller ones. Because of this, the photoelectric attenuation coefficient is proportional to the cube of the atomic number (μ \(\propto\) Z³), making iodine or bromine far more absorbent than soft tissues, which primarily contain smaller atoms. This allows these compounds to be injected into blood vessels or the digestive tract to capture X-ray images of soft tissue structures.