03 Nuclear
Positron range (empirical)
FWHM range in water ≈ 0.35 × E_mean(MeV) mm — a blur on top of the 2-mm annihilation physics.
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Simulation
Positron range (empirical) — 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
Typical values
Variables
Results
R_FWHM
Range FWHM
0.875mm
R_rms
Range RMS (approx.)
0.375mm
Explanation
What it means
The positron is not born at rest: it travels a random-walk millimetres before annihilating. That range is a fundamental blur, independent of the scanner. F-18 (E_mean 250 keV) ~0.2 mm RMS — negligible next to a 4 mm PET voxel. Rb-82 (E_mean 1.5 MeV) ~2–3 mm FWHM, which you can see as extra blur on a cardiac Rb scan. Ga-68 sits in between (~1 mm). 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
Enter mean (or max/2.8 as a stand-in) β⁺ energy in MeV. Presets: F-18, C-11, Ga-68, Rb-82, I-124. Compare to your reconstructed FWHM to see whether range is worth modelling. Change one input and watch the curve and the simulation follow.
Symbols
- E_meanMean β⁺ energy0.25 MeV
Worked example
A typical case from the default values: E_mean = 0.25 MeV (Mean β⁺ energy). Substituting into the relation gives R_FWHM = 0.875 mm; R_rms = 0.375 mm. These are teaching numbers — align them with your machine.
Typical values give
- R_FWHM = 0.875mm
- R_rms = 0.375mm
Where it comes from
The displayed formula is the working relation. FWHM range in water ≈ 0.35 × E_mean(MeV) mm — a blur on top of the 2-mm annihilation physics. Usual reference: Levin & Hoffman / Cherry. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Levin & Hoffman / Cherry
Assumptions & limits
Empirical linear fit, not a full distribution (which is cusp-shaped, not Gaussian). Tissue density scales 1/ρ. Does not include acollinearity (~0.002 rad, ~1.8 mm FWHM on an 80 cm diameter ring) which often dominates F-18 blur.
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. Empirical linear fit, not a full distribution (which is cusp-shaped, not Gaussian). Tissue density scales 1/ρ. Does not include acollinearity (~0.002 rad, ~1.8 mm FWHM on an 80 cm diameter ring) which often dominates F-18 blur.
Keep this
Write the assay time next to every activity. Decay does the rest. Empirical linear fit, not a full distribution (which is cusp-shaped, not Gaussian). Tissue density scales 1/ρ. Does not include acollinearity (~0.002 rad, ~1.8 mm FWHM on an 80 cm diameter ring) which often dominates F-18 blur.
In this specialty