A 3D point-kernel multiple scatter model for parallel-beam SPECT based on a gamma-ray buildup factor

A three-dimensional (3D) point-kernel multiple scatter model for point spread function (PSF) determination in parallel-beam single-photon emission computed tomography (SPECT), based on a dose gamma-ray buildup factor, is proposed. This model embraces nonuniform attenuation in a voxelized object of imaging (patient body) and multiple scattering that is treated as in the point-kernel integration gamma-ray shielding problems. First-order Compton scattering is done by means of the Klein-Nishina formula, but the multiple scattering is accounted for by making use of a dose buildup factor. An asset of the present model is the possibility of generating a complete two-dimensional (2D) PSF that can be used for 3D SPECT reconstruction by means of iterative algorithms. The proposed model is convenient in those situations where more exact techniques are not economical. For the proposed model's testing purpose calculations (for the point source in a nonuniform scattering object for parallel beam collimator geometry), the multiple-order scatter PSF generated by means of the proposed model matched well with those using Monte Carlo (MC) simulations. Discrepancies are observed only at the exponential tails mostly due to the high statistic uncertainty of MC simulations in this area, but not because of the inappropriateness of the model.