Monte Carlo algorithms have a growing impact on nuclear medicine reconstruction processes. One of the main limitations of myocardial perfusion imaging (MPI) is the effective mitigation of the scattering component, which is particularly challenging in Single Photon Emission Computed Tomography (SPECT). In SPECT, no timing information can be retrieved to locate the primary source photons. Monte Carlo methods allow an event-by-event simulation of the scattering kinematics, which can be incorporated into a model of the imaging system response. This approach was adopted since the late Nineties by several authors, and recently took advantage of the increased computational power made available by high-performance CPUs and GPUs. These recent developments enable a fast image reconstruction with an improved image quality, compared to deterministic approaches. Deterministic approaches are based on energy-windowing of the detector response, and on the cumulative estimate and subtraction of the scattering component. In this paper, we review the main strategies and algorithms to correct for the scattering effect in SPECT and focus on Monte Carlo developments, which nowadays allow the three-dimensional reconstruction of SPECT cardiac images in a few seconds.
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