International audience; Nowadays, the use of gold standard Monte Carlo Simulation (MCS) based modeling of the acquisition process in a way to compute the System Matrix (SM) is one of the well-established methods that has been used in small animal SPECT image reconstruction. However, MCS requires extensive computation time to obtain a low noise SM. Such reconstruction methods are therefore largely penalized by the huge time consumption required for the SM generation since a large number of photons has to be generated: an improvement in simulation speed is thus mandatory. Simplified analytical approach has the potential to lead to efficient SM computation, in a reduced time while requiring neither particular computing skills nor heavy informatics resources (cluster). In this work, we proposed to evaluate several modeling types (analytical and MCS) of the acquisition process of a pinhole SPECT system available at our institute. Secondly, various complexity degrees of an efficient and simplified analytical modeling of the physical effects occurring into the detector during SPECT examinations will be investigated. The two-developed analytical modeling of detector response represent some fast and efficient alternatives strategies to the implemented MCS based one. Although, even if they are less accurate, they allow coherent estimation while overcoming the disadvantages of the MCS like excessive computation time, high technical complexity and heavy computation infrastructures. However, the performance obtained, both qualitatively and quantitatively, do not allow their use in a quantitative reconstruction process. Nevertheless, recovery coefficient divergences with respect to the MCS reference modeling are on average of the order of ~ 6%.