Half-life

Radioactive decay is first-order: the rate of decay is proportional to the number of undecayed atoms present. Mathematically dN/dt = −λN, which integrates to N(t) = N₀·e^(−λt) and equivalently A(t) = A₀·e^(−λt) where A is activity. The decay constant λ and half-life t½ are linked by λ = ln(2) / t½ = 0.693 / t½. Every isotope has its own immutable t½ — that constant is what makes calibration time meaningful.

• F-18 — 109.77 min — PET tracers (FDG, PSMA-1007, fluciclovine). The classic conditional-release tracer.
• Tc-99m — 6.0058 h — workhorse SPECT isotope eluted from a Mo-99 / Tc-99m generator on the dispense floor.
• Ga-68 — 67.71 min — PET tracers eluted from a Ge-68 / Ga-68 generator (DOTATATE, PSMA-11).
• Lu-177 — 6.6443 d — beta-emitting therapy nuclide (Pluvicto, Lutathera).
• I-131 — 8.0252 d — thyroid therapy + diagnostic.
• Y-90 — 64.053 h — pure beta therapy (radioembolisation microspheres).
• Sm-153 — 46.284 h — bone-pain palliation.
• Cu-64 — 12.701 h — emerging PET / theranostic pair with Cu-67.
• Zr-89 — 78.41 h — immuno-PET (long enough to track antibody pharmacokinetics).
• Ra-223 — 11.4 d — alpha-emitting prostate-cancer therapy.
• Ac-225 — 9.92 d — emerging targeted-alpha therapy.
• C-11 — 20.36 min — research PET, on-site cyclotron only.
• N-13, O-15, Rb-82 — minutes-to-seconds, all on-site only.

Half-life sets the entire production geography: minute-scale isotopes (C-11, N-13, O-15, Rb-82) demand an on-site cyclotron and a metres-long path from synthesis to patient. Hours-scale isotopes (F-18, Ga-68) ship by van from regional radiopharmacies. Days-scale isotopes (Lu-177, I-131, Y-90, Ra-223) ship by air across continents.

Every unit dose carries a calibration time (calibration_at) and an activity at that time (activity_bq, MBq, or mCi). The administering technologist reads the label, notes the planned injection time, and recomputes the activity at injection:

• A(t) = A₀ · e^(−λ · Δt) where Δt = (administration time − calibration time).
• For Δt positive (administration after calibration) activity has decayed — A < A₀.
• For Δt negative (administration before calibration, common with F-18 first-thing-in-the-morning batches) activity is higher than the labelled value — A > A₀ — and the technologist draws a smaller volume.

Recording calibration time on the batch record is a Part 11 / 21 CFR 212 requirement — without it the dose cannot be reconstructed, and the as-administered activity cannot be reconciled against the prescribed dose.

Radiopharmaceutical expiry is a hybrid of two clocks:

• Physical decay clock — at some Δt the activity drops below the minimum useful diagnostic / therapeutic dose. For F-18 that is typically 8–10 hours from end-of-synthesis (≈ 4–6 half-lives).
• Chemical / radiochemical purity clock — radiolysis (the tracer molecule destroyed by its own radiation) and microbiological growth set independent limits. Stability data backs both.

The shorter of the two clocks wins. The Beyond Use Date (BUD) for compounded radiopharmaceuticals is governed by USP <797> + <825>.

Short-lived radwaste is held in shielded decay-in-storage for >10 half-lives (residual activity < 0.1 %) and then surveyed against RG 1.86 surface contamination limits (≤ 2× background fixed; ≤ 1000 dpm / 100 cm² removable for beta-gamma). After a passing survey + two-person e-signature, the waste enters the ordinary non-radioactive waste stream. Long-lived nuclides (Lu-177 at 6.6 days, I-131 at 8 days) sit in decay storage for 66+ and 80+ days respectively before they can be released — that storage time is a real facility-design constraint.

Short-half-life production runs are scheduled backward from the patient injection slot. For an FDG batch destined for a 9:30 AM PET scan:

• End-of-synthesis (EOS) typically 60–90 min before the first injection.
• QC release tests (radiochemical purity, pH, K-222 residual solvent, half-life ID, pre-release sterility filter integrity) run in parallel.
• Calibration time set to a clinically convenient anchor (often the first injection slot of the day).
• Dispense unit-dose draws into tungsten-shielded syringes for the patient list.
• Release authorisation (qualified person sign-off) before delivery, with the conditional-release path documented if sterility result is pending.

• Calibration time omitted or recorded only on the label, not the batch record.
• λ computed using log base 10 instead of natural log — silent factor-of-2.3 error.
• Δt computed in minutes when activity_bq label is per hour, or vice versa — unit mismatch.
• Activity-at-administration reported but activity-at-calibration not retained for the audit trail.
• Decay-in-storage waste released after only one half-life — the > 10 half-life rule is mandatory.
• Long-lived therapy nuclides (Lu-177, I-131) co-mingled with short-lived diagnostic waste in the same storage room, blocking the diagnostic waste from release.
• Expiry treated as a pure decay calculation, ignoring radiolysis / microbiological clocks.
• Manual half-life arithmetic without a peer check on the high-activity batch — error rates in mental decay-correction maths are well documented.