03 Nuclear
Marinelli thyroid dose
D(Gy) ≈ 0.034 × C(μCi/g) × T_eff(d) × Ē(MeV) for a uniformly distributed β/γ emitter.
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Simulation
Marinelli thyroid dose — Change the numbers; the scene follows.
Where it works
Hot lab
Dose calibrator
In the dose calibrator well — assayed activity, decay between two times, Marinelli.
Open this machineFormula
Variables
Results
D
Absorbed dose
33.6893Gy
D
Absorbed dose
3,368.928rad
Explanation
What it means
The Marinelli formula is the ancestor of MIRD: equilibrium dose in a large organ from a uniformly distributed emitter is activity concentration × effective half-life × mean energy per decay, with a unit-conversion constant. For I-131 thyroid (Ē_β ≈ 0.19 MeV, T_eff ≈ 6 d, uptake U, mass m) it becomes the classic 90–110 Gy from 3–4 MBq/g retained. Modern thyroid dosimetry uses OLINDA / voxel S-values, but Marinelli is how every textbook still introduces the idea. This is a working relation in Nuclear medicine.
Where it is used
Clinically it sits on the Hot lab — Dose calibrator. In the dose calibrator well — assayed activity, decay between two times, Marinelli. Nuclear-medicine relations sit in the hot lab, on the camera, and in the voxel: decay, SUV, TOF, and counting statistics. They decide whether an uptake is real or a clock error.
Hot lab · Open this machineHow to use it
Enter concentration in μCi/g, T_eff in days, and mean energy in MeV. I-131 thyroid: Ē_β ≈ 0.19 MeV (γ mostly escapes a 20 g gland). 40 μCi/g × 6 d × 0.19 MeV → D ≈ 3.4 Gy per this concentration; ablation typically aims at tens of Gy by raising retained activity. Change one input and watch the curve and the simulation follow.
Symbols
- CConcentration40 µCi/g
- T_effEffective half-life6 d
- ĒMean energy per decay0.19 MeV
Worked example
A typical case from the default values: C = 40 µCi/g (Concentration); T_eff = 6 d (Effective half-life); Ē = 0.19 MeV (Mean energy per decay). Substituting into the relation gives D = 33.6893 Gy; D = 3,368.928 rad. These are teaching numbers — align them with your machine.
Typical values give
- D = 33.6893Gy
- D = 3,368.928rad
Where it comes from
The displayed formula is the working relation. D(Gy) ≈ 0.034 × C(μCi/g) × T_eff(d) × Ē(MeV) for a uniformly distributed β/γ emitter. Usual reference: Marinelli, Quimby & Hine 1948 / MIRD. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Marinelli, Quimby & Hine 1948 / MIRD
Assumptions & limits
Uniform uptake, complete β local absorption, γ absorbed fraction = 0 (small organ) or 1 (large). I-131 thyroid γ contribution is ~10% and is omitted unless you raise Ē. Not a substitute for OLINDA/EXM or voxel dosimetry.
Pitfalls
Activity is not counts. SUV needs the true injected activity, the residual, and the correct decay time — a clock off by 10 min on ¹⁸F is a several-percent error. Do not compare SUVs across reconstructions. Uniform uptake, complete β local absorption, γ absorbed fraction = 0 (small organ) or 1 (large). I-131 thyroid γ contribution is ~10% and is omitted unless you raise Ē. Not a substitute for OLINDA/EXM or voxel dosimetry.
Keep this
Write the assay time next to every activity. Decay does the rest. Uniform uptake, complete β local absorption, γ absorbed fraction = 0 (small organ) or 1 (large). I-131 thyroid γ contribution is ~10% and is omitted unless you raise Ē. Not a substitute for OLINDA/EXM or voxel dosimetry.
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