• modellizzazione rivelatore
• ricostruzione immagini
• Tomografia ad Emissione di Positroni
• Monte Carlo
• detector modelling
• image reconstruction
• Positron Emission Tomography
• PET
• factorized system model

Positron emission tomography (PET) is an imaging technique which allows to measure the activity distribution of a positron-emitting radionuclide.
During a PET scan, the emission of 511 keV back-to-back photons, from the positron annihilation, is detected using pairs of opposing coincidence detectors. The result of this coincidence acquisition corresponds to line integral information of the activity distribution, also called projection data. The aim of tomographic image reconstruction is then to reproduce a three-dimensional map of the radiotracer concentration starting from this projection data.
The reconstruction techniques can roughly be subdivided in analytical and iterative ones. In PET imaging, iterative techniques are often preferred over analytical ones as they yield a better image quality, which is mainly due to the possibility of employing realistic system models during the reconstruction. However, the cost of the better quality is a greater computational demand.
The system model needed for iterative reconstruction is advantageously represented by a matrix which correlates positron emission with photon detection, i.e., the matrix elements model the acquisition process in that they represent the probabilities that the photons are detected at a certain position. Ideally the matrix includes all phenomena which describe the imaging process, such as the acquisition geometry, detector properties, photons interactions and positron range effects.
In this thesis a factorized system model for the YAP-(S)PET II small animal scanner is proposed comprising two components: an analytically computed geometric component and a Monte Carlo based detector response component.
The deterministic geometric component has been calculated using a multi-ray method which discretizes the solid angle using Gauss-Legendre integration and the image space using the Siddon algorithm.
The detector response component, instead, has been computed using a GEANT4 based Monte Carlo simulation which includes all photon interaction effects within the detector and the finite energy resolution. In this context, a probability threshold has been introduced to control the contributions to the detector response component and the dependence of the reconstructed image quality with respect to the threshold has been evaluated.
Finally, the images reconstructed with the Monte Carlo based system model have been analyzed according to the NEMA (National Electrical Manufacturers Association) quality standard; the analysis results have been compared with the ones obtained from images reconstructed with a pure geometric model and a multi-ray based model which additionally approximates the photon penetration effect. The comparison reveals a lower noise level with a higher or at least equal spatial resolution in the images reconstructed with the Monte Carlo based system model.