The Effect of Accidental Coincidences in Time-of-Flight Positron Emission Tomography

An accidental coincidence is defined as the erroneous registration of two photons, originating from separate positron annihilations, as having originated from the same positron annihilation. Previous analyses which did not consider accidental coincidences indicated that for a certain radioactivity distribution a gain in image signal-to-noise ratio of about 5 dB is achieved by the time-of-flight method over the conventional method. Subsequent experiments have validated this prediction in low counting rate situations. For higher, typical counting rates these experiments showed a significantly larger gain of about 9 dB, which was attributed to the way in which the time-of-flight method suppresses the degrading effects of accidental coincidences. We present an analytical model, extended from a previous model, which considers accidental coincidences. Calculations of signal-to-noise ratio, using this model, compare well with the experiments and show that the additional gain is indeed due to the treatment of accidental coincidences. An understanding of the model leads to an intuitive explanation of the gain mechanism and a determination of an effective coincidence-timing window that is achieved by the time-of-flight method.