PET Scanner Simulator

What the simulation actually computes

• Decay and positron range. Activity follows A(t) = A₀ · 2^(-t/T½) times the positron branching ratio. Each positron travels a distance drawn from an exponential with the tracer's mean range in water before annihilating, so a high endpoint energy isotope such as ⁸²Rb blurs the image before the detectors ever see a photon.
• Non-collinearity. The two 511 keV photons are emitted back to back plus a Gaussian angular deviation of 0.5° FWHM, because the positron and electron are not quite at rest. At a ring diameter D this contributes roughly 0.0022 · D of blur, about 1.8 mm here.
• Attenuation and scatter. Photons are transported through a water equivalent body (μ = 0.096 cm⁻¹ at 511 keV, with a bone shell on the brain phantom). Interaction depth is sampled from the optical depth, the Compton scattering angle is sampled from the Klein-Nishina cross section, and the scattered photon keeps energy E' = 511 / (2 - cosθ) keV. The crystal measures that energy with a 12% FWHM resolution at 511 keV, and photons outside the window are discarded. Lowering the threshold to 250 keV lets in most of the scatter, while raising it to 500 keV cuts the scatter fraction to a few percent and throws away a large share of the true coincidences along with it.
• Coincidence sorting. Detected photons are paired within the timing window τ. A pair from one annihilation with no scatter is a true, a pair where a photon scattered is a scatter whose LOR misses the emission point, and a pair of unrelated singles is a random. The randoms rate follows R = 2τS², so it grows as the square of the activity while trues grow linearly.
• Dead time and NECR. Singles are thinned by a paralyzable dead time model, and the noise equivalent count rate NECR = T² / (T + S + 2R) peaks and then falls. That peak, not the raw prompt rate, is why injecting more tracer eventually makes images worse.
• Reconstruction. Each accepted coincidence is binned by radial offset s and projection angle φ, and by time-of-flight offset when TOF is on. Filtered backprojection convolves every row with a Hann windowed ramp filter and backprojects it; the plain ramp cannot exploit timing, so summing the TOF bins gives it exactly the ordinary sinogram. The iterative option runs maximum likelihood expectation maximization, warm started so the estimate keeps improving as counts arrive, and its system model does include the TOF kernel.
• What time of flight buys. Timing resolution Δt localizes the annihilation along the LOR to Δx = c·Δt / 2, about 30 mm at 200 ps. An event then updates only the part of the line it plausibly came from, so MLEM converges in far fewer iterations: with 200 ps timing the hot spheres reach full contrast in about two iterations, where the same data without timing needs eight and arrives with roughly twice the background noise. TOF also pushes mispositioned randoms toward the edge of the field of view.
• Corrections. Attenuation correction multiplies each LOR by exp(∫μ dl) along its chord through the body, the measured correction a CT scan supplies in a PET/CT. Turn it off and watch the center of the phantom go cold. Randoms subtraction estimates the randoms with an independent delayed window and subtracts it, removing the bias but adding its own noise.

Tracer properties used here

Things worth trying

• Run the Derenzo phantom with ¹⁸F, then switch to ⁸²Rb without touching anything else. The smallest rod groups disappear into the positron range.
• Push the activity to 2000 MBq and watch the randoms fraction, the NECR curve, and the haze that randoms lay across the reconstruction. More tracer is not more signal.
• Drop the lower energy threshold to 250 keV. The scatter fraction roughly doubles and the cold sphere fills in. Then push it to 500 keV and watch the true rate collapse as the energy resolution eats into the photopeak.
• Turn attenuation correction off on the brain phantom. The cortex looks hot and the white matter looks cold, the classic uncorrected PET artifact.
• Set the crystals to 160 and compare the sinogram: coarse detectors quantize the radial samples and the rods smear tangentially.
• Switch the reconstruction to MLEM, then turn on 200 ps TOF. Watch the iteration counter: the spheres separate from the background far earlier, and at matched contrast the background is about half as noisy.
• Compare filtered backprojection with MLEM on the same data. The ramp filter has to amplify high frequencies to undo the backprojection blur, and it amplifies the noise with them.