Higher order scattering estimation for PET

The solution of the particle transport problem, which is the core part of tomography reconstruction, is mathematically equivalent to the evaluation of a Neumann series of increasing dimensional integrals, where the first term represents the direct contribution, the second the single scatter contribution, the third the double scattering etc. High dimensional integrals are computationally very expensive, thus this infinite series is truncated after a few (typically after the first or second) terms, which underestimates particle transport results, thus overestimating the radiotracer density in the reconstruction. This paper presents a simple approximate method to improve the accuracy of scatter computation in positron emission tomography without increasing the computation time. We exploit the facts that higher order scattering is a low frequency phenomenon and the Compton effect is strongly forward scattering in 100-511 keY range. Analyzing the integrals of the particle transfer, we come to the conclusion that the directly not evaluated terms of the Neumann series can approximately be incorporated by the modification of the scattering cross section while the highest considered term is calculated. The proposed model is built into the Teratomo™ system.