Image reconstruction in Single Photon Emission Computed Tomography (SPECT) is affected by physical effects such as photon attenuation, Compton scatter and detector response. These effects can be compensated for by modeling the corresponding spread of photons in 3D within the system matrix used for tomographic reconstruction. The fully 3D Monte Carlo (F3DMC) reconstruction technique consists in calculating this system matrix using Monte Carlo simulations. The inverse problem of tomographic reconstruction is then solved using conventional iterative algorithms such as maximum likelihood expectation maximization (MLEM). Although F3DMC has already shown promising results, its use is currently limited by two major issues: huge size of the fully 3D system matrix and long computation time required for calculating a robust and accurate system matrix. To address these two issues, we propose to calculate the F3DMC system matrix using a spatial sampling matching the functional regions to be reconstructed. In this approach, different regions of interest can be reconstructed with different spatial sampling. For instance, a single value is reconstructed for a functional region assumed to contain uniform activity. To assess the value of this approach, Monte Carlo simulations have been performed using GATE. Results suggest that F3DMC reconstruction using functional regions improves quantitative accuracy compared to the F3DMC reconstruction method proposed so far. In addition, it considerably reduces disk space requirement and duration of the simulations needed to estimate the system matrix. The concept of functional regions might therefore make F3DMC reconstruction practically feasible.
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