A scatter model for parallel and converging beam SPECT based on the Klein-Nishina formula

A scatter model is proposed for parallel-, fan-, and cone-beam SPECT imaging. In this model, a photon is allowed to be scattered only once, and the probability of scatter for given angle and energy is computed by using the Klein-Nishina formula. The detector is assumed to have perfect energy resolution. The scatter counts are computed for every projection bin. From the scatter counts, the scatter line source response function and scatter-to-primary ratio (SPR) are obtained. They agree well with those from Monte Carlo (MC) simulation including only single scattering, but deviate from those from full MC simulation including both single and multiple scattering. The deviation depends on the source depth within the medium. For a source depth of 6 cm, the difference of the scatter-to-primary ratio between the model and full MC simulation is less than 7%, while for a 21.6 cm source depth, the difference goes up to 27% for parallel-beam geometry and 32% for cone-beam geometry. Since scatter accounts for 20-40% of the total counts in most clinical studies, the scatter model yields a SPR accuracy that ranges from 3% to 12%. The scatter model provides an effective means to estimate the scatter response with reasonable accuracy, and can be used in developing scatter compensation techniques in parallel- and converging-beam SPECT