Unit 10 : Additional Problems

Unit 10 : Additional Problems#

For those looking for additional problems outside of past exam questions and the worked problems in the lectures please consider the following in the reading list.

Unworked Problem : Cardiac Collimation#

Calculate the efficiency and resolution for the “Cardiac High Resolution” collimator (\( d = 2.03 \, \text{mm} \), \( t = 0.15 \, \text{mm} \), \( l = 48 \, \text{mm} \)).

Unworked Problem : Collimator Shielding#

For \( ^{99m}Tc \) gamma rays in soft tissue (\( a = 0.15 \, \text{cm}^{-1} \)), what fraction of \( \gamma \)-rays will be observed for a tumor at \( x = 4 \, \text{cm} \) and a collimator half-angle of \( 0.18 \, \text{radians} \)? Assume efficiency \( \eta = 2.1 \times 10^{-4} \).

Unworked Problem : Collimated Gamma Count Rates#

Cardiac perfusion imaging typically uses \( 550-1100 \, \text{MBq} \) of \( ^{99m}Tc \). What is the count rate observed with the “Cardiac High Resolution” collimator? State any assumptions.

Unworked Example: Brachytherapy for Lung Cancer#

A clinical trial found that \( ^{125}I \) brachytherapy was more effective than conventional radiotherapy for treating inoperable lung cancer. \( ^{125}I \) decays by electron capture with a half-life of 59.4 days, emitting a 35.5 keV X-ray.

Given that:

  • Mean tumor volume = 312.7 cm³

  • Mean radiation dose = 141.6 Gy

  • Mean density of the human body = 985 g/cm³

Determine:

  1. The average mass of \( ^{125}I \) implanted.

  2. The activity of \( ^{125}I \) at the time of implantation.

State any assumptions made in the calculations.

Problems#

  1. Calculate the Q-value for the reaction \( ^{14}N(p, \alpha)^{11}C \) used to produce the PET isotope \( ^{11}C \). Consulting the JANIS database, we see that the threshold for this reaction is approximately 4 MeV proton kinetic energy. Is this what you would expect? Briefly justify your answer.

  2. Calculate the Q-value for the reaction \( ^{88}Sr(n, \gamma)^{89}Sr \) used to produce the therapeutic isotope \( ^{89}Sr \). Is it possible to produce this isotope using thermal neutron capture? If so, what is the expected photon energy?

  3. The recommended dose of \( ^{131}I \) for treatment of hyperthyroidism is 550 MBq. If this is administered in the form of Na\( ^{131}I \), what mass of Na\( ^{131}I \) should the patient be given?

    • The half-life of \( ^{131}I \) is 8.0 days. The mean atomic mass of sodium is 23.0 u.

Additional questions to consider#

  • Why do neutrons have a higher weighting factors than gammas in dosimetry?

  • What does a collimator do in PET detector?

  • What is the energy of the gammas used in PET and why?

  • Why is there Tl in a sodium iodide scintillator?

  • Why is the decay time of the scintillator important in PET scanners?

  • Explain why Hadron Therapy can be safer patients than gamma therapy?