Physics and Dosimetry of Brachytherapy

, Foster D. Lasley², Indra J. Das², Marc S. Mendonca² and Joseph R. Dynlacht²

(1)

Department of Radiation Oncology, CHRISTUS St. Patrick Regional Cancer Center, Lake Charles, LA, USA

(2)

Department of Radiation Oncology, Indiana University School of Medicine, Indianapolis, IN, USA

Definitions

AAPM TG–43: Task Group Report 00 of the American Association for Physics in Medicine.
Activity (A): Amount of radioactive material.
- Units: 1 Curie (Ci) = 3.7 × 10¹⁰ Becquerel (Bq)
Radius (r): aka distance, depth.
Dose Rate ( $\dot{\mathrm{D}}$ ): not to be confused with total dose (D)
Initial Dose Rate ( $\dot{\mathrm{D}}$ ⁰)
Exposure Rate Constant (Γ), aka Gamma Constant: Exposure rate per millicurie of isotope at 1 cm distance.
Exposure Rate ( $\dot{\mathrm{X}}$ ) = ΓA
Milligrams Radium Equivalent (mgRaEq):
- 1 mgRaEq = 8.25 R–cm ²–h ⁻¹–mg ⁻¹exposure rate
Air kerma strength (S _K): Kerma (kinetic energy released in matter) measured in air @ 1 m.
- 1 U = 1 cGy–cm ⁻²–h ⁻¹ = 1 μGy–m ⁻²–h ⁻¹
- Proportional to Activity.
Dose rate constant (Λ): Dose rate to water for 1U air kerma strength at 1 cm (cGy-cm⁻²-h⁻¹/U).
Low Dose Rate (LDR): 0.4–2 Gy/h
Medium Dose Rate (MDR): 2–12 Gy/h
High Dose Rate (HDR): >12 Gy/h
Pulse Dose Rate (PDR): HDR fractionated over time to approximate LDR dose rates.
Details of the units and activities along with dosimetry can be found in AAPM TG–43.

²²⁶Ra brachytherapy was used for many decades prior to ⁶⁰Co, ¹³⁷Cs, ¹⁹²Ir, or megavoltage X-rays.
Radium sources consist of radium chloride powder placed within a double-sealed platinum tube.
²²⁶Ra comes to a secular equilibrium with ²²²Rn and its decay products by emitting alpha rays.
- This results in accumulation of multiple radioactive daughter nuclides emitting alphas, betas and gammas.
- The encapsulation is designed to absorb everything except for the gammas.
  
  Average photon energy 0.83 MeV (range 0.18–2.29 MeV).
²²⁶Ra is no longer used because of the risk of radon gas leakage and other safety concerns.
Many LDR brachytherapy systems are based on “milligrams radium equivalent” (mgRaEq).
- For a source of activity A and gamma constant Γ:
$\mathrm{Radium}\ \mathrm{Equivalent}\ \left(\mathrm{mCi}\right)=\frac{\Gamma \mathrm{A}\times mg\times Ra\times Eq}{8.25\; R/ c{m}^2/ hr}$

(11.1)

Common sealed source nuclides include ²²⁶Ra, ¹⁹²Ir, ¹³⁷Cs, ¹²⁵I, ¹⁰³Pd, and ⁶⁰Co.
Common unsealed source include ¹³¹I, ⁹⁰Y, and ³²P.
Nuclides are chosen for their desired characteristics such as type of radiation, half-life, energy, etc.
- ¹²⁵I and ¹⁰³Pd emit very low energy characteristic X-rays (22–28 keV); this gives them a very steep dose fall-off.
- The other sealed source nuclides are high energy gamma emitters.
- Most unsealed source nuclides emit short range beta radiation with a short half-life, thus limiting the risk of systemic and environmental contamination.
Refer to Appendix B for a list of nuclides used in imaging and therapy.

Naturally Occurring: Byproducts of uranium decay, these nuclides can be mined from the Earth.
- ²²⁶Ra, ²²³Ra, ²²²Rn among others.
Fission Byproduct: Obtained from nuclear reactors.
- ¹³⁷Cs, ¹³¹I, ⁹⁰Sr among others.
Neutron Bombardment: Creates beta-minus emitters. Cyclotrons can produce high intensity proton and neutron flux. Nuclear reactors can produce very high intensity neutron flux.
- ¹⁹⁸Au, ¹⁹²Ir, ¹⁵³Sm, ¹²⁵I, ¹⁰³Pd, ⁸⁹Sr, ⁶⁰Co, ³²P among others.
Proton Bombardment: Creates beta-plus emitters, often used for PET imaging. Protons are accelerated by a cyclotron.
- ¹²³I, ¹⁸F, ¹⁵O, ¹¹C, ³H among others.
Daughter Elution: A longer-lived mother nuclide (“cow”) decays into a shorter-lived daughter nuclide (“milk”) that can be repeatedly eluted for clinical use. This is an example of transient equilibrium.
- ⁹⁰Y, ^99mTc among others.

Classically, source strength is measured as activity (Ci or Bq) or milligrams radium equivalent (mgRaEq).
- Two sources with the same Activity (Ci) may emit very different amounts, energies and types of radiation due to encapsulation and filtration. Hence, their dose rate may be different.
Source strength is specified as air kerma rate at a distance of 1 m as mentioned above. (1 U = 1 μGy/h/m ²).

Unsealed sources do not have to worry about encapsulation so they simply are specified as nuclide, activity, and chemical formulation. (ie elemental vs. colloidal vs. antibody-bound).
An unsealed source will have separate physical and biological half-lives.
- Effective half–life equation:
${\mathbf{t}}_{\mathrm{eff}}=\frac{\left({t}_{biol}\times {t}_{phys}\right)}{\left({t}_{biol}+{t}_{phys}\right)}$

(11.2)
See Chapt. 2 for more half-life equations.