03 Nuclear
Non-paralyzable dead time
True rate n = m / (1 − mτ) from observed rate and dead time.
Listen
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Simulation
Non-paralyzable dead time — Change the numbers; the scene follows.
Where it works
Gamma camera
Detector head
In the gamma-camera crystal and PMTs — counts, dead time, energy window, resolution.
Open this machineFormula
Variables
Results
n
True rate
55.5556kcps
loss
Fractional loss
0.1
loss
Fractional loss
10%
m_par
Paralyzable observed from n
49.7133kcps
Explanation
What it means
Detectors need a finite time τ to process a count. In the non-paralyzable model the true rate is n = m/(1−mτ). Losses of a few percent already appear at tens of kcps in older cameras; PET and well counters have their own τ. This is a working relation in Nuclear medicine.
Where it is used
Clinically it sits on the Gamma camera — Detector head. In the gamma-camera crystal and PMTs — counts, dead time, energy window, resolution. 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.
Gamma camera · Open this machineHow to use it
Enter observed kcps and τ in µs. Typical NaI camera τ ~ 1–2 µs. If mτ ≥ 1 the model saturates. The paralyzable (PET, some GM) observed rate is n e^{−nτ} — shown as a comparison from the recovered n. Change one input and watch the curve and the simulation follow.
Symbols
- mObserved count rate50 kcps
- τDead time2 µs
Worked example
A typical case from the default values: m = 50 kcps (Observed count rate); τ = 2 µs (Dead time). Substituting into the relation gives n = 55.5556 kcps; loss = 0.1; loss = 10 %; m_par = 49.7133 kcps. These are teaching numbers — align them with your machine.
Typical values give
- n = 55.5556kcps
- loss = 0.1
- loss = 10%
- m_par = 49.7133kcps
Where it comes from
The displayed formula is the working relation. True rate n = m / (1 − mτ) from observed rate and dead time. Usual reference: Cherry, detectors. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Cherry, detectors
Assumptions & limits
Single τ, no extending dead time, no pile-up energy loss. Calibrate τ with a decaying-source (two-source) method on your device.
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. Single τ, no extending dead time, no pile-up energy loss. Calibrate τ with a decaying-source (two-source) method on your device.
Keep this
Write the assay time next to every activity. Decay does the rest. Single τ, no extending dead time, no pile-up energy loss. Calibrate τ with a decaying-source (two-source) method on your device.
In this specialty