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It has already been proved that Fully Three Dimensional Monte Carlo (F3DMC) is a robust image reconstruction algorithm that can be applied in Single Photon Emission Computed Tomgraphy (SPECT) and small animal Positron Emission Tomography (PET). F3DMC has still not yet been validated on real data in small animal SPECT application. The advantage of such image reconstruction technique is that all the physical processes occuring within the detector and its geometrical parameters can be precisely modelled within the system matrix thanks to powerful Monte Carlo Simulation toolkit. Once the system matrix is computed, it can be integrated within an iterative reconstruction algorithm such as Maximum Likelihood Estimation Maximization (MLEM) in order to resolve the inverse image reconstruction problem. However, such reconstruction technique is penalized by the huge time consumption required for the computation of the system matrix since the accuracy of this latter requires the simulation of large number of photons tracks from the imaged subject to the detector. In this study, we proposed two main solutions to tackle the problem of time consumption. The first has already been proposed in anterior works and consists in parallelizing the Monte Carlo simulations performed with the Geant4 toolkit on a Computing Grid (CG) and the second suggests to apply a Forced Detection (FD) technique in order to accelerate the convergence of the system matrix elements. Results show that an accelerated version of a F3DMC technique is feasible in a reasonable delay and leads to reconstructed images with good spatial resolution and a good capability of restoring relative quantification. Hence, it has been proven that F3DMC is an applicable reconstruction technique in small animal SPECT.