Physics of Nuclear Medicine

Atomic Structure & Radioactivity - Decay Dance

• Atom: Nucleus (protons Z, neutrons N), electrons. Mass no. A = Z+N.
  • Nuclide types: 📌 (P=Protons, N=Neutrons, R=Mass numbeR)
    • Isotopes: Same Z.
    • Isotones: Same N.
    • Isobars: Same A.
    • Isomers: Same Z, N, A; diff energy state (e.g., $^{99m}Tc$).
• Radioactivity: Unstable nuclei decay.
  • Activity = $\lambda N$. Units: Bq (1 dps); Ci ($3.7 \times 10^{10}$ dps).
  • Half-life ($T_{1/2}$) = $0.693/\lambda$.
• Decay Modes (Parent $\rightarrow$ Daughter):
  • $\alpha$: Emits $^{4}_{2}He$. $A \downarrow 4, Z \downarrow 2$.
  • $\beta^-$: $n \rightarrow p + e^-$. $A$ same, $Z \uparrow 1$.
  • $\beta^+$: $p \rightarrow n + e^+$. $A$ same, $Z \downarrow 1$. (Needs >1.022 MeV).
  • EC (Electron Capture): $p + e^- \rightarrow n$. $A$ same, $Z \downarrow 1$.
  • $\gamma$/IT (Isomeric Transition): Photon from excited nucleus (e.g., $^{99m}Tc \rightarrow ^{99}Tc + \gamma$). $A, Z$ same.

⭐ $^{99m}Tc$ (metastable Technetium-99) is an isomer that decays via Isomeric Transition, emitting a 140 keV gamma ray, making it ideal for SPECT imaging.

Radionuclides & Radiopharmaceuticals - Isotope Arsenal

• Radionuclide: Unstable nuclide; emits radiation.
  • Ideal for imaging: Short T½, pure $\gamma$-emitter (e.g., $^{\text{99m}}\text{Tc}$).
  • Ideal for therapy: Particle emitter (e.g., $\beta^-$ in $^{\text{131}}\text{I}$).
• Key Isotopes:
  • $^{\text{99m}}\text{Tc}$: T½ 6 hrs, 140 keV $\gamma$. Most common. From $^{\text{99}}\text{Mo}$/$^{\text{99m}}\text{Tc}$ generator.
  • $^{\text{131}}\text{I}$: T½ 8 days. $\beta^-$ & $\gamma$. Thyroid therapy/imaging.
  • $^{\text{123}}\text{I}$: T½ 13.2 hrs. Thyroid imaging.
  • $^{\text{18}}\text{F}$-FDG: T½ 110 mins. PET imaging.
  • $^{\text{67}}\text{Ga}$: T½ 78 hrs. Tumor/inflammation.
  • $^{\text{201}}\text{Tl}$: T½ 73 hrs. Myocardial perfusion.
• Radiopharmaceutical: Radionuclide + pharmaceutical (carrier). Localizes to target organ.
  • E.g., $^{\text{99m}}\text{Tc}$-MDP (bone scan), $^{\text{131}}\text{I}$-NaI (thyroid).

⭐ Technetium-99m is the workhorse isotope, used in over 80% of nuclear medicine procedures.

Radiation-Matter Interaction - Energy Exchange

• Energy Transfer:
  • Excitation: e⁻ to higher shell.
  • Ionization: e⁻ ejected → ion pair.
    • Directly ionizing: Charged particles (α, β).
    • Indirectly ionizing: Uncharged (γ, X-rays).
• Linear Energy Transfer (LET): Energy/path ($keV/\mu m$).
  • High LET (α): Dense ionization, short range.
  • Low LET (γ, β): Sparse ionization.
• Charged Particle Interactions:
  • α: Ionization/excitation.
  • β: Ionization, excitation, Bremsstrahlung (X-ray production, $\propto Z^2 \times E$).
• Photon Interactions (γ, X-rays):
  • Photoelectric Effect (PEA): Photon absorbed, e⁻ out. Dominant low E. $P \propto Z^3/E^3$.

  ⭐ PEA is crucial for contrast in diagnostic X-rays (e.g., bone vs. tissue) due to its strong Z dependence.

  • Compton Scattering: Photon scatters off e⁻, loses E. Dominant at diagnostic/NM E; causes scatter.
  • Pair Production: Photon > 1.022 MeV → e⁻ + e⁺. Basis of PET (→ 2 x 0.511 MeV photons).

Radiation Detection & Imaging - Photon Sniffers

• Core Principle: Detectors convert $\gamma$-ray energy into a measurable electrical signal.

• Detector Types:

  • Gas-Filled:
    • Geiger-Müller (GM) Counter: Detects radiation, area monitoring. Not for imaging.
  • Scintillation Detectors:
    • NaI(Tl) Crystal + PMT: Workhorse for imaging. $\gamma$-ray $\rightarrow$ light $\rightarrow$ $e^-$ $\rightarrow$ signal.
  • Semiconductor Detectors:
    • CZT (Cadmium Zinc Telluride): Direct conversion $\gamma$-ray $\rightarrow$ signal. $\uparrow$Energy resolution.

• Gamma Camera (Anger Camera):

• Key Parameters:

  • Energy Resolution: Distinguishes energies (e.g., $ ^{99m}Tc $ photopeak at 140 keV). Better for scatter rejection.
  • Spatial Resolution: Image detail. Collimator & crystal thickness dependent.
  • Sensitivity: Detection efficiency. Thicker crystal $\uparrow$ sensitivity.

⭐ The Pulse Height Analyzer (PHA) is crucial for rejecting scattered photons, improving image contrast by selecting only photopeak events.

High‑Yield Points - ⚡ Biggest Takeaways

• Technetium-99m (Tc-99m): workhorse isotope, 140 keV gamma energy, 6-hour half-life.
• PET imaging: uses positron emitters (e.g., F-18), produces 511 keV annihilation photons.
• Gamma cameras: use NaI(Tl) scintillation crystals and photomultiplier tubes (PMTs).
• Collimators: crucial for SPECT image quality by selecting photon direction.
• Effective half-life: combines physical decay and biological clearance rates.
• ALARA principle: key for radiation safety (minimize time, maximize distance, use shielding).