Monte Carlo investigation of positron annihilation in medical positron emission tomography

A number of Monte Carlo codes are available for simulating positron emission tomography (PET), however, physics approximations differ. A number of radiation processes are deemed negligible, some without rigorous investigation. Some PET literature quantify approximations to be valid, without citing the data source. The radiation source is the first step in Monte Carlo simulations, for some codes this is 511 keV photons 180° apart, not polyenergetic positrons with radiation histories of their own. Without prior assumptions, we investigated electron–positron annihilation under clinical PET conditions. Just before annihilation, we tallied the positron energy and position. Right after annihilation, we tallied the energy and separation angle of photon pairs. When comparing PET textbooks with theory, PENELOPE and EGSnrc, only the latter three agreed. From 106 radiation histories, a positron source of 15O in a chest phantom annihilated at as high as 1.58 MeV, producing photons with energies 0.30–2.20 MeV, 79–180° apart. From 106 radiation histories, an 18F positron source in a head phantom annihilated at energies as high as 0.56 MeV, producing 0.33–1.18 MeV photons 109–180° apart. 2.5% and 0.8% annihilation events occurred inflight in the chest and the head phantoms, respectively. PET textbooks typically either do not mention any deviation from 180°, or state a deviation of 0.25° or 0.5°. Our findings are founded on the well-established Heitler cross-sections and relativistic kinematics, both adopted unanimously by PENELOPE, EGSnrc and GEANT4. Our results highlight the effects of annihilation in-flight, a process sometimes forgotten within the PET community.