Estimation of random coincidences: Revisiting the singles rate method for high resolution PET

Abstract

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Objectives: We have revised the well-established singles rate (SR) estimation method for random coincidences. Some studies reported in the literature show a disagreement between the true number of random coincidences and the estimate yielded by the SR method. Our goal was to investigate the source of this disagreement, to revise the model on which the SR method is based, and to find and to test a more accurate formula for correction purposes.

Methods: The conventional SR method (SR0) relies on computing the random rate for LOR ij as r_ij = 2 Tau Si Sj, being Si the singles rate in detector i and Tau the coincidence window width. If the existence of true coincidences is taken into account, the random rate can be better estimated. We have used a correction (SR1) that considers the contribution of these true coincidences. To test it we have performed MonteCarlo simulations which have been done using GATE. We have simulated a small animal PET together with a cylinder of approximately the size of a mouse. The activity, 0.2 mCi, was distributed homogeneously.

Results: The agreement between our method SR1 and the simulated true rate is better than for the traditional one, SR0. Defining D_Method= |R_GATE-R_Method|/R_GATE, we find approximately D_SR0 = 0.03 D_SR1 = 0.002.

Conclusions: When true coincidences are taken into account the well-established SR estimation can be improved. In addition, we have found that this correction, SR1, does not systematically overestimate the randoms rate, as SR0 does. On the other hand, it poses the problem that the true coincidences need to be estimated. In our case these were taken directly from the simulation. Investigations of other possible corrections to the simple SR formula, aside from the one already studied here, are envisaged.

Research Support: Spanish Ministry of Education and Science grants: FPA2003-03878-C02-01 & TEC2007-61047.