Nuclear medical 3γ imaging is an innovative technique which is studied at the SUBATECH laboratory. It isbased on the three-dimensional localization of a (β+, γ) radioisotope emitter, the 44Sc, by using a liquid xenon Compton telescope. The position of the disintegration of this radioisotope is obtained by the intersection of the line of response, built by the detection of two 511 keVphotons from the annihilation of a positron, and the cone determined by the third photon. A small prototype XEMIS1 (XEnon Medical Imaging System) was developed to demonstrate experimentally the feasibility of 3γ imaging. The results of this prototype are quite encouraging in terms of energy resolution, purity of liquid xenon and electronic noise. The Monte Carlo simulation is an indispensable tool to support the R&D and to evaluate the new proposed technique of imaging ; this thesis work is to develop the simulation of 3γ imaging system by using GATE (Geant4 Application for Tomographic Emission). New functionalities have been added to GATE to simulate a TPC (Time Projection Chamber) detector. We performed a simulation of XEMIS1 prototype and obtained results in good agreement with our experimental data. The next step of the project is to build a full liquid xenon cylindrical camera for the small animal imaging. The results presented in this thesis of the simulations of this camera demonstrate the ability to locate every decayalong the line of response with very good accuracy and good detection sensitivity. The first direct images of simple phantoms, realized event by event, and after tomographic reconstruction are also presented.
