Hybrid model of photon propagation based on the analytical and Monte Carlo methods for a dual-head PET system

The construction of photon propagation has a close relationship with the quality of reconstructed images. The classical Monte Carlo (MC) based method can model the photon propagation precisely, but it is time-consuming. The analytical method can often quickly construct a model, but its precision is a problem. How to fully exploit the advantages of the MC simulation and analytical model is an open problem. Inspired by the characteristics of the depth of interaction (DOI) detectors, which can help confirm the deposited position of a photon with DOI-encoding technology, we virtually discretize each crystal into several subcrystals to obtain the statistical distribution by MC-based simulation. Then, the statistical distribution is combined with a spatially variant solid-angle model. This combination strategy provides a hybrid model to describe photon propagation with relatively high accuracy and low computational cost. Three discretization schemes are compared to optimize the constructed photon propagation model. Several experiments are carried out to evaluate the performance of the proposed hybrid method. The metrics of full width at half maximum (FWHM), contrast recovery (CR), and coefficient of variation (COV) are adopted to quantitate the imaging results. The classical MC-based method is compared as a gold-standard reference. When a crystal is divided into two discretized positions, the convergent tendencies of CRs and COVs are consistent with that based on MC simulation method, respectively. In terms of FWHMs, the resolutions of using the MC-based model and the proposed hybrid model are 0.71 mm and 0.68 mm in the direction parallel to the detector head, respectively. This indicates the potential of the proposed method in positron emission tomography imaging.