Interactions with Matter Comprehensive Notes

Interactions with Matter

Last Lecture: Photon Interactions

• Attenuation mechanisms of photons in materials:
  • Coherent Scatter:
    • Small contribution at lower energies (approximately 5%).
    • Probability is proportional to $Z$ and $E^2$. ($P \propto Z E^2$)
    • Example: The reason why the sky is blue.
  • Photoelectric Effect:
    • Pure absorption.
    • Primary source of X-ray contrast.
    • Probability is proportional to $Z^3$ and $E^3$. ($P \propto Z^3 / E^3$)
  • Compton Effect:
    • Dominant attenuation mechanism at mid-high energies.
    • Main cause of scatter, leading to lower Signal-to-Noise Ratio (SNR) in images.
    • Probability is proportional to $\rho$ and $E$. ($P \propto \rho / E$)

Compton Effect Details

• Inversely proportional to energy.
• Fall-off is slower compared to the photoelectric effect.
• Dominant at higher energies.
• Diagnostic radiography energies typically range from 20-150 kVp.
  • Maximum photon energy equals kVp.
  • Most probable energy equals 1/3 kVp.
• Radiation therapy energies range from 4-20 MeV.

Today's Lecture: Attenuation Mechanisms of Photons

• Attenuation mechanisms:
  • Pair production.
  • Annihilation.
  • Photodisintegration.
• Clinical significance of the five photon attenuation processes.

Photon Energy Spectrum

• Visible light: Wavelength ~ 1 μm, Energy ~ 1 eV
• Ultraviolet light: Wavelength ~ 100 nm, Energy ~ 10 eV
• Soft X-rays: Wavelength ~ 10 nm, Energy ~ 100 eV
• Hard X-rays: Wavelength ~ 100 pm, Energy ~ 100 keV
• Gamma rays: Wavelength ~ 1 pm, Energy ~ 1 MeV
• Applications:
  • X-ray crystallography.
  • Mammography.
  • Medical CT.
  • Airport security.

Pair Production

• Can only occur with photons of energies exceeding 1.022 MeV.
• The photon interacts with the electric field of the nucleus.
• Photon energy is converted into matter, producing:
  • An electron (negative charge).
  • A positron (positive charge).

Energy Conversion in Pair Production

• Based on Einstein's equation: $E = mc^2$
• An X-ray photon has energy but no mass.
• The photon energy is converted into mass.
  • Rest mass of an electron: 0.511 MeV.
  • Rest mass of a positron: 0.511 MeV.
• Therefore, pair production requires at least $(2 \times 0.511 \text{ MeV}) = 1.022 \text{ MeV}$ of energy.
• Remaining energy beyond 1.022 MeV is carried as kinetic energy of the electron and positron.
• Occurs in the electric field of an atomic nucleus (or electron cloud) to conserve momentum.
• Requires higher photon energies due to less concentrated charges.

Why 0.511 MeV?

• Mass of an electron (or positron): $m = 9.110 \times 10^{-31} \text{ kg}$
• Speed of light: $c = 3 \times 10^8 \text{ m/s}$
• Energy contained in the mass of an electron/positron:
  • $E = mc^2 = 9.110 \times 10^{-31} \times (3 \times 10^8)^2 = 8.198 \times 10^{-14} \text{ J}$
  • Converting Joules to electron volts: $E = \frac{8.198 \times 10^{-14}}{1.602 \times 10^{-19}} \approx 511,000 \text{ eV} = 511 \text{ keV} = 0.511 \text{ MeV}$

Annihilation

• When an electron and positron combine, they produce two photons traveling at 180° from each other.
• This is known as annihilation radiation.
• Forms the basis of Positron Emission Tomography (PET) imaging.

Factors Affecting Pair Production

• Photon Energy: Probability increases with photon energy (in MeV).
• Atomic Number: Probability increases with atomic number (Z) due to a greater electric field.
• Probability of Pair Production is proportional to: $E - 1.02 \times Z$

Photodisintegration

• Requires a minimum energy of approximately 7 MeV (nucleon binding energy).
• The photon is absorbed by the nucleus.
• The atom becomes unstable and radioactive.
• To stabilize, the nucleus ejects particles such as protons, neutrons, or alpha particles.
• This effect primarily occurs in radiation therapy due to the high energies involved.

Photodisintegration Details

• Observed during Radiation Therapy (RT) external exposure: 0.9 mSv/a.
• 54% decay of activation products.
• 7% leakage neutrons during treatment.
• Mitigated by closing collimator jaws and waiting a few minutes after treatment (Donadille et al., 2008).
• Probability increases with photon energy and atomic number.
• Metallic objects should not be near the treatment area unless necessary.
• Requires operator caution upon entering the room after treatment.
  • Wait before entering once the linear accelerator is switched off.
  • Neutrons released from photodisintegration of the anode target can make materials inside and outside the LINAC radioactive, e.g., 28Al ($t<em>{1/2} = 2.25$ minutes) and 15O ($t</em>{1/2} = 2.04$ minutes).

Dominant Regions of Interaction

• Photoelectric effect (PE), Compton effect (CE), and pair production (PP) depend on energy.
• PE and PP depend on atomic number (Z).
• The dominant beam attenuation process is determined by both Z and energy.
• At the boundaries, the contribution of each effect is equal.
• Pair production is not possible at most diagnostic radiography (DR) and nuclear medicine (NM) energies (sub-MeV range).
• Attenuation is primarily determined by the photoelectric effect and Compton scattering below 1.022 MeV.

Attenuation

• These interactions stop the photon from transmitting through a material, thereby contributing to the overall attenuation coefficient of a material.

Mass Attenuation Coefficient

• Graphs showing attenuation vs. energy for air and lead, illustrating the contributions of photoelectric effect, Compton scattering, and pair production.

Clinical Aim in Diagnostic Radiography (DR)

• Diagnostic Radiography is a transmission process.
• Goal: Obtain a diagnostic image while minimizing detriment to the patient.
  • Maximize the primary radiation incident on the detector.
  • Minimize scatter radiation hitting the detector.
  • Minimize radiation absorbed in the patient.
• ALARA: As Low As Reasonably Achievable.

Importance of Knowledge of Interaction Processes

• Allows for the optimization of imaging technique and protection.
  • Choose an appropriate kVp to:
    • Maximize contrast between tissues of interest.
    • Ensure adequate penetration of X-rays.
    • Minimize dose.
  • Choose correct filters to reduce dose and improve image quality.
  • Decide where and when to use anti-scatter grids.
  • Choose the best material for radiation protection purposes.

Important Interactions in Diagnostic Radiology

• Photoelectric Effect.
• Compton Scattering.
• Coherent scattering has a too small probability to be significant.
• Pair production and Photodisintegration occur at too low energies to be relevant.

Percentage of X-ray Interactions in Water (Soft Tissue)

• For bone, Compton Scattering dominates over 40 keV.
• Specific values are not required, but knowing the energy where each interaction dominates is important.

Different Materials in the Body

• Different materials have different atomic numbers (Z) and densities.
  • Higher Z materials are more important in the photoelectric effect.
  • Higher density materials are more important in Compton scattering.
• Differences in materials lead to differences in attenuation, which leads to contrast in the image (differential absorption).
  • Soft tissues: Z ≈ 7, ρ = 1060 kg/m3
  • Lung: Z < 7, ρ = 400 kg/m3
  • Bone: Z ≈ 14, ρ = 1912 kg/m3

Comparing Attenuation in Different Materials

• Comparing tissue vs. lead for the same energy.
• Large differences in attenuation between Lead and Tissue are mainly due to the effect of atomic number and the photoelectric effect.

Effect of Different Energies on Image Formation

• Some absorption must take place in the body to get an image.
  • If everything passes through, the image will be black.
  • If everything is absorbed, the image will be white, and patient doses will be high.
• Carefully choose energy depending on the body part being imaged.

Effect of Low Energies

• More absorption (photoelectric effect).
• Smaller thicknesses of tissues.
• Better contrast between tissues.
• Necessary when looking at similar tissues (e.g., breast tissue).
• Photoelectric absorption accounts for 15-30% in general radiography.

Effect of High Energies

• Less absorption (photoelectric effect).
• Thicker thicknesses of tissues.
• Less contrast between tissues (Compton).
• Lower resolution (Compton).
• Used when large differences in Z's, but high resolution is not critical.

Comparison of 50 kVp vs. 125 kVp

• 50 kVp: More photoelectric absorption (better contrast).
• 125 kVp: More Compton scatter (less dynamic range).

Clinical Aim in Diagnostic Nuclear Medicine (NM)

• Nuclear medicine is an emission process.
• Goal: Produce an image of diagnostic quality.
  • Minimize attenuation of radiation in the body.
    • Keep radiation dose ALARA.
    • Choose an appropriate keV to minimize attenuation, i.e., a higher energy.
    • Zero attenuation would be ideal but is impossible.
  • Maximize attenuation in the gamma/PET camera crystal.
    • Choose an appropriate detector material (high Z) to maximize attenuation due to the use of higher energies.

Specifics for Nuclear Medicine

• Energies are too low for pair production but annihilation of positrons is the basis for PET.
• Radionuclide positron (β+) source (e.g., FDG containing 18F).
• Minimal (or no) absorption should take place in the body, which dictates the use of higher energies to reduce photoelectric absorption.
• Need absorption in the detector, which decreases with high energies.
• Energy ranges approximately 140 keV - 300 keV depending on radiopharmaceutical (not kVp).

Material Choice in Nuclear Medicine

• Since using middle energy ranges, the main interaction in the body is Compton scatter.
• A collimator will reduce scatter:
  • Physical collimator in gamma/SPECT camera.
  • Electronic collimator in PET camera.
• For the crystal, choose a high Z material to increase photoelectric absorption (e.g., NaI).

Radiation Therapy (RT)

• Deals with the treatment of a disease rather than imaging.
• Goal:
  • Maximize radiation at the target site.
  • Minimize radiation at other sites.
• Need to be careful on radiation application using multiple fields.
• Different energies and particles are used depending on the depth of the target (e.g., photon/proton/electron/ion).
  • High energies for depth.
  • Low energies for surface.

Radiation Therapy Details

• Not primarily interested in producing an image, but it's necessary for:
  • Treatment planning (including absorption profile).
  • Dose verification.
• Can use:
  • Digital imaging.
  • Fluoroscopy.
  • Computed Tomography (currently main technique).
  • MRI (moving towards this as better contrast).
• Maximize the biological effects that occur.
• Electrons produce the damage.
• Photons (and heavy particles) interact with matter and produce electrons (ionization).
• Need to localize the electrons at specific areas.
• Electrons must travel a few mm in tissue to ensure whole target is “HIT”. Thus, electrons must have large energies.

Energy Considerations in Radiation Therapy

• Maximum production of electrons to increase biological effects.
• Photoelectric Absorption:
  • Prominent only at low energies.
  • Produces low energy electrons.
• Compton Scattering:
  • Produces high energy electrons (good).
  • Produces high energy scattered photons, which may result in high doses away from the target (bad).
• Pair Production:
  • Initially produces electrons (negatrons & positrons) - Good for treatment.
  • Then produces high energy photons (>511 keV) which may leave the body or interact via Compton or photoelectric.
  • Can generate the high energy electrons deeper in tissue once photons have penetrated.
• Compton is still the predominant interaction for RT.

Safety Measures in Radiation Therapy

• The “maze” design and high-Z materials provide safety.
  • Initially PP, PD.
  • Eventually CS, PE.
  • Enough matter to eventually absorb all photon energy.
  • Helps with neutrons from Photodisintegration.

Clinical Significance of Interaction Processes

• Coherent scattering represents about 5% of all interactions in diagnostic radiology and nuclear medicine and does not occur in radiation therapy because lacks the appropriate energies. Not typically significant.
• Photoelectric Effect:
  • Results in absorption of the photon.
  • Less radiation leaves the patient, leading to increased patient dose and more biological effects (DR).
  • Provides differential absorption and contrast in Diagnostic Radiography.
  • Occurs in detectors in Nuclear Medicine, which is the opposite because NM is an emission process, so reduced photoelectric absorption is wanted.
• Compton Effect:
  • Causes dose to surrounding tissues due to wide distribution of photon angles.
  • Causes dose to Imaging staff as scattered radiation has enough energy to leave the patient.
  • Decreases Image Quality due to scattered radiation.
  • Main interaction in Nuclear Medicine and Radiation Therapy.
• Pair Production:
  • Does not occur in Diagnostic Radiography because of low energies.
  • Does not directly occur in Nuclear Medicine (< 1.022 MeV) - instead, positron emitting nuclides are used for annihilation and gamma rays in PET imaging.
  • Increases the number of electrons, which increases biological damage in Radiation Therapy.
• Photodisintegration:
  • Does not occur in Diagnostic Radiography & Nuclear Medicine because of the low energies.
  • Occurs primarily inside the LINAC head in Radiation Therapy.
  • Resulting neutron + particle radiation can activate surrounding matter.
  • An important source of technician dose and secondary dose for the patient.
  • Mitigated by time + closing LINAC collimator jaw.

Review Questions

1. Why does pair production not occur at lower energies?
2. Pair production turns gamma rays into positrons (and electrons) but isn’t used in PET. Where do the positrons for this procedure come from?
3. What are anti-scatter grids used for in DR and NM?
4. What is the half-life of 99mTc?
5. Why are such high energy beams (in the MeV range) used in radiation therapy?