Scheduling a Technetium Dose and Deciding When Waste Is Waste
A nuclear medicine department elutes its Mo-99/Tc-99m generator at 07:00, obtaining 12 GBq of technetium-99m in 15 mL of saline. Tc-99m has a half-life of 6.0 h and emits a 140 keV gamma ray; it is a pure gamma emitter. The first patient is scheduled for 09:30 and is prescribed 800 MBq, injected intravenously. A second elution is not possible until the following morning, so any unused activity must be stored until it falls below the statutory disposal limit of 10 MBq. A colleague suggests using iodine-131 instead, since it is also taken up by tissue and is cheaper per MBq; I-131 has a half-life of 8.0 days and emits both beta particles and gamma rays.
1. Calculate the activity concentration at 09:30 and the volume that must be drawn for the 800 MBq dose. Comment on whether the 15 mL vial is a practical size.
Read the worked answer
Time elapsed from elution: 2.5 h. Number of half-lives: 2.5/6.0 = 0.417.
A = A₀(½)^(t/T½) = 12 × (0.5)^0.417 = 12 × 0.749 = 9.0 GBq at 09:30.
Concentration: 9.0 GBq / 15 mL = 0.60 GBq mL⁻¹ = 600 MBq mL⁻¹.
Volume for 800 MBq: 800/600 = 1.33 mL.
So the vial is very practical - it holds roughly 11 doses' worth at 09:30. The judgement point is that this is a time-critical calculation: at 07:00 the same 800 MBq would need only 1.00 mL, and every hour of delay increases the volume drawn. Because the drawn volume (1.3 mL) is small compared with the vial, the syringe must be measured carefully - a 0.1 mL error is 60 MBq, 7.5% of the prescribed dose. It also means the department must either use the remaining activity within the day or plan to store it.
2. How long after elution must the residual activity be stored before it can be discarded as waste? Show your reasoning and sanity-check the answer.
Read the worked answer
We need A to fall from 12 GBq = 12 000 MBq to 10 MBq, a factor of 1200.
A/A₀ = (½)^n → 1200 = 2^n → n = log₂1200 = ln1200/ln2 = 7.090/0.693 = 10.2 half-lives.
t = 10.2 × 6.0 h = 61 h, i.e. about 2.6 days - discard from about 20:00 on the third day after elution.
Sanity check by the standard rule of thumb: 10 half-lives leaves 1/1024 ≈ 0.1% of the original activity, which takes 12 000 MBq down to about 12 MBq - close to the 10 MBq limit, so a slightly longer wait is needed. That confirms the order of magnitude.
The judgement point: because the half-life is short, storage is a matter of days, not centuries. This is precisely why Tc-99m is convenient in a hospital and why the same rule applied to a long-lived isotope (say Cs-137, 30 y) would require storage for centuries - those isotopes must be returned to the supplier instead.
3. Evaluate the colleague's suggestion to use I-131 instead, using half-life, radiation type and biological behaviour as your criteria.
Read the worked answer
Half-life: 8.0 days means the activity in the patient falls by only 1/16 in a month. For imaging, that delivers a much larger radiation dose to the patient than Tc-99m, whose 6.0 h half-life means most of it has decayed before it can do harm - but the same short half-life means Tc-99m cannot be stockpiled and must be used within hours of elution. That is a logistics cost, not a patient cost.
Radiation type: Tc-99m emits a 140 keV gamma only. This energy is high enough to escape the body and be imaged by a gamma camera but is not densely ionising in tissue. I-131 emits beta particles as well; betas deposit their energy in a very short range, causing localised tissue damage. That is useful therapeutically (thyroid ablation) and undesirable for a diagnostic scan.
Biological behaviour: iodine is actively concentrated by the thyroid, so an I-131 scan irradiates that organ heavily regardless of where the tracer was meant to go. Tc-99m labelled to a pharmaceutical follows the chosen chemistry instead.
Conclusion: for a diagnostic 800 MBq image, Tc-99m is the correct choice on all three criteria; I-131 belongs in therapy, where its beta dose is the point.