03 Nuclear
Counting statistics
Poisson: σ = √N, %SD = 100/√N. Time to reach a %SD at rate R.
Listen
Listen · English
Simulation
Counting statistics — 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
σ
Standard deviation
100counts
%SD
Percent SD
1%
N
Counts needed
10,000
t
Time needed
20s
Curve
Explanation
What it means
Nuclear counting is Poisson: variance equals the mean, so σ = √N and the percent standard deviation is 100/√N. 10 000 counts give 1% SD. Time needed is N/R. 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
Set the %SD you can tolerate (often 1–5% for uptake probes) and the expected rate to get counting time. Background adds in quadrature: σ_net = √(N_tot + N_bkg). Change one input and watch the curve and the simulation follow.
Symbols
- NCounts10,000
- RCount rate500 cps
- pDesired %SD1 %
Worked example
A typical case from the default values: N = 10,000 (Counts); R = 500 cps (Count rate); p = 1 % (Desired %SD). Substituting into the relation gives σ = 100 counts; %SD = 1 %; N = 10,000; t = 20 s. These are teaching numbers — align them with your machine.
Typical values give
- σ = 100counts
- %SD = 1%
- N = 10,000
- t = 20s
Where it comes from
The displayed formula is the working relation. Poisson: σ = √N, %SD = 100/√N. Time to reach a %SD at rate R. Usual reference: Cherry. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Cherry
Assumptions & limits
Poisson, no dead-time distortion, no background. Low rates with large background need a different optimum split of counting time.
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. Poisson, no dead-time distortion, no background. Low rates with large background need a different optimum split of counting time.
Keep this
Write the assay time next to every activity. Decay does the rest. Poisson, no dead-time distortion, no background. Low rates with large background need a different optimum split of counting time.
In this specialty