The modeling of multiple order Compton scatter in SPECT

In the authors' previous work, an efficient slice-by-slice blurring model was developed based on the Klein-Nishina formula to model first order Compton scatter in both parallel beam and converging beam SPECT. The first order Compton scatter projection was generated by first forming an effective scatter source imaging (ESSI) corresponding to first order Compton scatter and then forward-projecting the ESSI to the detector surface, using a projector that modeled both the non-uniform attenuation effect and the depth-dependent detector response effect. In this work, the technique was extended to model multiple order Compton scatter. At each scattering voxel, first order Compton scattered photons confined in a scattering cone which was determined by the energy window used for emission projection acquisition were used as the source for second order Compton scatter. The effective scatter source image (ESSI) corresponding to the second order Compton scatter was then obtained using the slice-by-slice blurring model. Forward-projecting this ESSI to the detector gave the second order Compton scatter projection. For a point source in a non-uniform scattering object for fan beam geometry, the second order Compton scatter point responses generated using the proposed method matched well with those using Monte Carlo simulations at the peak region, but not as well at the tails. This work proposed an efficient method to model multiple order Compton scatter in both parallel beam and converging beam SPECT.