Fast hybrid SPECT simulation including efficient septal penetration modelling (SP-PSF)

Single photon emission computed tomography (SPECT) images are degraded by the detection of scattered photons and photons that penetrate the collimator septa. In this paper, a previously proposed Monte Carlo software that employs fast object scatter simulation using convolution-based forced detection (CFD) is extended towards a wide range of medium and high energy isotopes measured using various collimators. To this end, a fast method was developed for incorporating effects of septal penetrating (SP) photons. The SP contributions are obtained by calculating the object attenuation along the path from primary emission to detection followed by sampling a pre-simulated and scalable septal penetration point spread function (SP-PSF). We found that with only a very slight reduction in accuracy, we could accelerate the SP simulation by four orders of magnitude. To achieve this, we combined: (i) coarse sampling of the activity and attenuation distribution; (ii) simulation of the penetration only for a coarse grid of detector pixels followed by interpolation and (iii) neglection of SP-PSF elements below a certain threshold. By inclusion of this SP-PSF-based simulation it became possible to model both primary and septal penetrated photons while only 10% extra computation time was added to the CFD-based Monte Carlo simulator. As a result, a SPECT simulation of a patient-like distribution including SP now takes less than 5 s per projection angle on a dual processor PC. Therefore, the simulator is well-suited as an efficient projector for fully 3D model-based reconstruction or as a fast data-set generator for applications such as image processing optimization or observer studies.