03 Nuclear

Noise-equivalent counts NEC

NEC = T² / (T + S + 2R) (or k=1 for a delayed window). The figure of merit for PET count-rate.

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Simulation

Noise-equivalent counts NEC — Change the numbers; the scene follows.

Where it works

PET/CT

PET detectors

In the PET detector ring — coincidence timing, noise-equivalent counts, randoms.

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Formula

\mathrm{NEC}=\frac{T^2}{T+S+k R}

Variables

T · TruescpsS · ScattercpsR · Randomscpsk · Randoms weight

Results

NEC
Noise-equivalent counts
35,555.6cps
SF
Scatter fraction
0.3333

Explanation

\mathrm{NEC}=\frac{T^2}{T+S+k R}

What it means

Raw coincidence rate is a poor figure of merit because scatter and randoms add variance without adding signal. NEC is the true-coincidence rate that, in a scatter- and random-free scanner, would give the same SNR. Peak NEC (typically 20–40 kcps on a clinical torso phantom) is how vendors compare count-rate performance; it occurs well below the dead-time peak. This is a working relation in Nuclear medicine.

Where it is used

Clinically it sits on the PET/CT — PET detectors. In the PET detector ring — coincidence timing, noise-equivalent counts, randoms. 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.

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How to use it

Enter trues T, scatter S and randoms R in cps, and k (2 for a delayed-window randoms subtraction that adds variance, 1 if randoms are estimated noiselessly). Read NEC and the scatter fraction SF = S/(T+S). Change one input and watch the curve and the simulation follow.

Symbols

TTrues80,000 cps
SScatter40,000 cps
RRandoms30,000 cps
kRandoms weight2

Worked example

A typical case from the default values: T = 80,000 cps (Trues); S = 40,000 cps (Scatter); R = 30,000 cps (Randoms); k = 2 (Randoms weight). Substituting into the relation gives NEC = 35,555.6 cps; SF = 0.3333. These are teaching numbers — align them with your machine.

Typical values give

NEC = 35,555.6cps
SF = 0.3333

Where it comes from

The displayed formula is the working relation. NEC = T² / (T + S + 2R) (or k=1 for a delayed window). The figure of merit for PET count-rate. Usual reference: NEMA NU 2 / Strother. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: NEMA NU 2 / Strother

Assumptions & limits

Single-bed, no decay, no dead-time model. Activity-varying NEC curves need T,S,R vs activity (NEMA NU 2 protocol). 2R is the NEMA default for noisy randoms subtraction.

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-bed, no decay, no dead-time model. Activity-varying NEC curves need T,S,R vs activity (NEMA NU 2 protocol). 2R is the NEMA default for noisy randoms subtraction.

Keep this

Write the assay time next to every activity. Decay does the rest. Single-bed, no decay, no dead-time model. Activity-varying NEC curves need T,S,R vs activity (NEMA NU 2 protocol). 2R is the NEMA default for noisy randoms subtraction.

In this specialty

Nuclear medicine