Mathematical-physical characterization of the response function of a clinical positron emission tomography

A major goal in clinical positron emission tomography is to measure the radioisotope concentrations with the best spatial resolution possible. In spite of different factors affecting the spatial resolution, in this work we focused on the geometrical system response, and in particular on the problem arising from the interactions of the gamma rays in the detector array. Starting from the single detector response (intrinsic aperture function, IAF), we modeled the absorption of gamma rays on a probabilistic base. Then, in order to obtain the PET response function, we correlated the IAF with the opposite detector response, so obtaining the coincidence aperture function (CAF). It was possible to obtain an analytical expression of the CAF and of its normalization factor for a generic source position inside the field of view. The CAF experimental validations we are performing are giving a good experimental-theoretical matching, so the future step will be the CAF implementation in reconstruction algorithms.