03 Nuclear
Residence time
τ = Ã / A₀. The MIRD source-organ residence time.
Listen
Listen · English
Simulation
Residence time — Change the numbers; the scene follows.
Where it works
PET/CT
Patient / uptake
In the patient on the PET couch — activity concentration, SUV, and internal dose.
Open this machineFormula
Variables
Results
τ
Residence time
2h
τ/T
Fraction of mean life if mono-exponential
1.3863
Explanation
What it means
Residence time τ = Ã / A₀ is the MIRD source-organ time, in hours, that 1 Bq of administered activity spends decaying in that organ. Multiply by S (mGy/MBq·s) after converting hours to seconds, or use consistent tables. This is a working relation in Nuclear medicine.
Where it is used
Clinically it sits on the PET/CT — Patient / uptake. In the patient on the PET couch — activity concentration, SUV, and internal dose. 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.
PET/CT · Open this machineHow to use it
Get à from a time-activity fit (or from A₀ T_e / ln2 for one exponential). ICRP/MIRD tables list τ per organ for standard radiopharmaceuticals. Change one input and watch the curve and the simulation follow.
Symbols
- ÃCumulated activity400 MBq·h
- A₀Administered activity200 MBq
Worked example
A typical case from the default values: Ã = 400 MBq·h (Cumulated activity); A₀ = 200 MBq (Administered activity). Substituting into the relation gives τ = 2 h; τ/T = 1.3863. These are teaching numbers — align them with your machine.
Typical values give
- τ = 2h
- τ/T = 1.3863
Where it comes from
The displayed formula is the working relation. τ = Ã / A₀. The MIRD source-organ residence time. Usual reference: MIRD primer. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: MIRD primer
Assumptions & limits
Definition only — no S-value. Remainder of body and excretory pathways need their own τ.
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. Definition only — no S-value. Remainder of body and excretory pathways need their own τ.
Keep this
Write the assay time next to every activity. Decay does the rest. Definition only — no S-value. Remainder of body and excretory pathways need their own τ.
In this specialty