Using Cramer-Rao theory combined with Monte Carlo simulations for the optimization of monolithic scintillator PET detectors

We are investigating the possibility of using monolithic scintillator blocks as detectors for small animal positron emission tomography (PET). These detectors consist of several cm³ of scintillating material, read out by one or more avalanche photo-diode (APD) arrays. The entry point of an incoming gamma photon is estimated from the distribution of the scintillation light over the APD pixels. To optimize the detector design, the influence of different design parameters is investigated using Geant4 simulations. To make it possible to study the influence of individual design parameters on the intrinsic spatial resolution of the detector, the use of a performance measure is proposed that is independent of the algorithm used to estimate the entry point, namely the Cramer-Rao lower bound on the estimation of the coordinates of a point source of light inside the crystal. To illustrate the use of this method, the influence of optical transport inside the detector is investigated for different detector designs, surface finishes and APD pixel sizes. A comparison with resolutions obtained from simulations involving beams of 511 keV annihilation photons indicates that this approach gives valid results.