Radiation Interactions with Matter

Fundamental Types of X-ray Interactions with Tissue

• No Interaction: The X-ray photon passes completely through the tissue without interacting with any atoms and strikes the image recording device.

• Complete Absorption: The X-ray energy is entirely absorbed by the tissue, resulting in no imaging information for that specific photon.

• Partial Absorption with Scatter: This involves a partial transfer of energy to the tissue. The resulting scattered X-ray has less energy and a different trajectory than the incident photon.

  • Implications of Scatter: Scattered radiation degrades image quality by creating fog. It is also the primary source of radiation exposure for the operator and staff.

Classical / Coherent / Thompson / Rayleigh Scattering

• Mechanism: An incident photon interacts with matter and excites an atom, causing it to vibrate. The target atom then releases excess energy as a scattered X-ray.

• Energy and Wavelength: The scattered X-ray has a wavelength equal to the incident photon ($\lambda = \lambda'$). This means the energy remains equal ($E_{in} = E_{out}$); the only change is in the direction of the photon (no loss in energy).

• Atomic Interaction: The incident photon electric field expends energy, causing all target electrons to oscillate in phase. This is an excitation of the total complement of atomic electrons.

• Ionization Status: No ionization occurs during this process; only excitation.

• Occurrence in Radiology:

  • Primarily occurs in low-energy X-rays (< 10\,keV).

  • At $30\,keV$, there is a $12\%$ occurrence rate.

  • At $70\,keV$, there is a $5\%$ occurrence rate.

• Radiographic Effect: Scattered X-rays contribute to film fog and have no useful effect on the final radiograph.

• Directionality: Most scattered X-rays are deviated in the forward direction. The scattering angle increases as the incident X-ray energy decreases.

Compton Interaction (Compton Scattering / Incoherent / Inelastic)

• General Definition: This is the predominant interaction in the diagnostic range (above $26\,keV$) when interacting with soft tissue.

• Mechanism: An incident photon of relatively high energy ejects an outer-shell (valence) electron. This electron is deflected and travels in a new direction as secondary radiation.

• Energy Equation: The energy of the incident photon ($E_i$) is equal to the sum of the energy of the scattered photon ($E_s$) and the kinetic energy of the ejected electron ($E_{ke}$):

  • $E_i = E_s + E_{ke}$

• Characteristics:

  • The scattered X-ray retains most of the energy. At $100\,keV$, $90\%$ of the energy is retained by the scattered X-ray.

  • It causes ionization and changes the direction of the incident X-ray.

  • Angles: The ejected electron's scattering angle cannot exceed $90$ degrees, but the scattered photons can include a $180$-degree backscatter.

• Hazards: This is the most hazardous interaction for radiation workers due to the production of scatter radiation, particularly during fluoroscopic procedures.

• Probabilities:

  • The probability is nearly independent of the atomic number ($Z$) of the absorber.

  • The probability is approximately proportional to the density of the material.

  • Hydrogenous materials have a higher probability of occurrence than non-hydrogenous materials of equal mass.

  • Probability is highly dependent on $kVp$ or X-ray energy; as photon energy increases, the probability of Compton effect increases relative to other interactions.

• Radiographic Impact: Provides no useful diagnostic information. It produces a uniform optical density (fog) that reduces image contrast.

Photoelectric Effect

• Historical Background: First observed by Heinrich Hertz in 1887 and later explained in detail by Albert Einstein.

• Mechanism: Occurs when an incident X-ray is totally absorbed during the ionization of an inner-shell (K-shell) electron. The incident photon disappears, and the ejected electron is called a photoelectron.

• Photoelectron Energy: The kinetic energy of the photoelectron is equal to the difference between the incident photon energy and the electron binding energy ($E_k = E_i - E_b$).

  • Low Z Atoms: Binding energy is low; the photoelectron is released with kinetic energy nearly equal to the incident X-ray energy.

  • High Z Atoms: Binding energy is high; the photoelectron has lower kinetic energy.

• Atomic Transitions: The vacancy in the K-shell is filled by an electron from a higher shell. This transition is accompanied by the emission of a characteristic X-ray.

• Auger Electron: Sometimes, instead of a photon being emitted, the energy is transferred to another electron which is then ejected from the atom. This is called an Auger electron.

• Probabilities and Contrast:

  • The probability is inversely proportional to the third power of X-ray energy ($1/E^3$).

  • If photon energy is doubled, the probability decreases eight-fold.

  • The effect is more likely in absorbers with high atomic numbers ($Z^3$), such as bone or positive contrast media.

  • This effect is responsible for short-scale contrast (high contrast) and significant patient dose, as it involves total energy absorption.

Pair Production and Photodisintegration

• Pair Production:

  • Requires X-ray energies greater than $1.022\,MeV$.

  • The photon interacts with the electric field of the nucleus, causing the photon to disappear.

  • The energy is transformed into an electron-positron pair. Each particle (negatron and positron) possesses $0.511\,MeV$.

  • This is important in Positron Emission Tomography (PET) but does not occur in diagnostic radiology.

• Photodisintegration:

  • Requires X-ray energies greater than or equal to $7-10\,MeV$.

  • The high-energy photon is absorbed directly by the nucleus.

  • The nucleus is raised to an excited state and instantaneously emits a nucleon or other nuclear fragment.

  • This is important in megavoltage therapy and high-energy accelerator physics.

Attenuation and Differential Absorption

• Attenuation: Defined as the total reduction in the number of photons remaining in an X-ray beam after penetration through tissue.

  • $\text{Attenuation} = \text{Absorption} + \text{Scattering}$

  • Absorption: X-ray disappears (Photoelectric, Pair Production, Photodisintegration).

  • Scattering: X-ray emerges with a different direction and potentially less energy (Compton, Coherent).

• Differential Absorption: The difference between X-rays absorbed and those transmitted to the Image Receptor (IR).

  • Fundamental for image formation.

  • Approximately $1\%$ of photons in the primary beam reach the IR. Of that $1\%$, only about $0.5\%$ interact to form the image.

  • Image Components:

    1. Compton scatter: No useful information.

    2. Photoelectric absorption: Produces light (white) areas.

    3. Transmitted X-rays: Produce grey/dark areas.

  • Differential absorption increases as $kVp$ is reduced.

Energy Transfer and Radiation Quality

• Pathlength: The actual total distance a particle travels.

• Range: The actual depth of penetration of a particle in matter.

• Linear Energy Transfer (LET): The amount of energy deposited per unit path length ($eV/cm$).

  • LET is proportional to the square of the charge ($Q^2$) and inversely proportional to the particle's kinetic energy ($KE$).

  • $\text{LET} = \text{specific ionization (IP/cm)} \times \text{average energy deposited per ion pair (eV/IP)}$

  • Used to determine the radiation weighting factor ($W_R$).

Bremsstrahlung and Characteristic Radiation

• Bremsstrahlung (Braking Radiation):

  • Electrons undergo inelastic interactions with atomic nuclei, causing them to decelerate and lose kinetic energy.

  • Conversion of Kinetic Energy into Electromagnetic Energy.

  • Probability is directly proportional to $Z^2$ of the absorber and inversely proportional to the square of the mass of the incident particle.

  • Produces a continuous spectrum of X-ray energies up to the maximum $kVp$.

  • High Energy Bremsstrahlung: Occurs close to the nucleus; high projectile KE loss, greater deflection.

  • Low Energy Bremsstrahlung: Occurs far from the nucleus; less influence by nuclear field, less projectile energy loss.

• Characteristic Radiation:

  • Projectile electron removes an inner-shell electron.

  • Radiation is produced when an outer-shell electron fills the vacancy.

  • Energies are discrete and characteristic of the specific atom (e.g., Tungsten).

  • K-characteristic X-rays for Tungsten require a tube potential of at least $70\,kVp$.

Measuring Beam Performance and Attenuation

• Linear Attenuation Coefficient (\mu): The fraction of photons removed from a mono-energetic beam per unit thickness of material ($cm^{-1}$). It is proportional to material density.

• Mass Attenuation Coefficient (MAC): The linear attenuation coefficient normalized to unit density ($\mu / \rho$).

• Half Value Layer (HVL): The thickness of material required to reduce beam intensity to one-half of its initial value. This characterizes beam "hardness."

• Tenth Value Layer (TVL): The thickness required to reduce intensity to one-tenth of its original value. Used in shielding design. $1\,TVL = 3.3\,HVL$.

• Beam Hardening: The shift of the X-ray spectrum to higher effective energies as the beam traverses matter. Low-energy "soft" X-rays are removed by filtration (e.g., aluminum plates), resulting in a higher HVL.

Radiological Quantities and Units

• Kerma (K): Kinetic Energy Released in Matter. Energy transferred to charged particles by indirectly ionizing radiation. Unit: gray ($Gy$) or $J/kg$.

• Absorbed Dose (D): Energy deposited by ionizing radiation per unit mass.

  • SI Unit: gray ($Gy$). $1\,Gy = 1\,J/kg$.

  • Traditional Unit: rad. $1\,rad = 0.01\,J/kg$. $100\,rads = 1\,Gy$.

• Exposure: Electrical charge produced in air.

  • SI: Air Kerma ($Gy_a$).

  • Special unit: $C/kg$.

  • Old unit: Roentgen (R). $1\,R = 2.58 \times 10^{-4}\,C/kg$.

• Equivalent Dose ($H_T$): Product of absorbed dose and radiation weighting factor ($W_R$).

  • $H_T = \sum W_R D_{T,R}$

  • SI Unit: sievert ($Sv$).

  • Traditional Unit: rem. $1\,Sv = 100\,rem$. $1\,rem = 10\,mSv$.

• Effective Dose (E): Sum of the products of equivalent dose and tissue weighting factor ($W_T$).

  • $E = \sum W_T H_T$

Tissue Weighting Factors and Remainder Organs

• Remainder Organs include:

  • Adrenals

  • Upper large Intestine

  • Small Intestine

  • Kidney

  • Pancreas

  • Brain

  • Spleen

  • Thymus

  • Uterus

  • Muscle