Parallel Beam Approximation for Calculation of Detection Efficiency of Crystals in PET Detector Arrays

In this work we propose a parallel beam approximation for the computation of the detection efficiency of crystals in a PET detector array. In this approximation the detection efficiency of a crystal is estimated using the distance between source and the crystal and the pre-calculated detection cross section of the crystal in a crystal array which is calculated for a uniform parallel beam of gammas. The pre-calculated detection cross sections for a few representative incident angles and gamma energies can be used to create a look-up table to be used in simulation studies or practical implementation of scatter or random correction algorithms. Utilizing the symmetries of the square crystal array, the pre-calculated look-up tables can be relatively small. The detection cross sections can be measured experimentally, calculated analytically or simulated using a Monte Carlo (MC) approach. In this work we used a MC simulation that takes into account the energy windowing, Compton scattering and factors in the "block effect". The parallel beam approximation was validated by a separate MC simulation using point sources located at different positions around a crystal array. Experimentally measured detection efficiencies were compared with Monte Carlo simulated detection efficiencies. Results suggest that the parallel beam approximation provides an efficient and accurate way to compute the crystal detection efficiency, which can be used for estimation of random and scatter coincidences for PET data corrections.