Continuous DoI determination by gaussian modelling of linear and non-linear scintillation light distributions

The Depth of Interaction (DoI) detection is crucial in many medical imaging applications such as small ring PET and high resolution SPECT. In this work we investigate the possibility to discriminate the DoI using continuous crystals. A LaBr₃(Ce) crystal has been used in the detection system for its intrinsic high light yield, that especially at low energies (e.g. 140 keV) reduces considerably the statistical uncertainties increasing the DoI discrimination power. The innovative suggestion of this work is the use of spectrometric observables to discriminate events on top and bottom of the crystal, under the hypothesis that scintillation light distributions can be parameterized by a gaussian model. The spread of the light cone (σ) is proportional to the DoI simply by geometrical considerations, but under the gaussian hypothesis relations between the spectrometric variables (maximum high I and integral of the distribution N) and the DoI become a straightforward consequence. Two methods are proposed and discussed: a linear treatment of the light distribution and a non linear (quadratic) manipulation of it. The expected correlations between the spectrometric variables (N and I), according to the gaussian model, are checked using a specific Monte Carlo simulation of the experimental apparatus. Those are then compared with experimental data obtained irradiating the LaBr3:Ce crystal with a Tc^99m collimated source. A close agreement between experimental data and MC is verified. Finally, a preliminary test on experimental data has been performed irradiating the crystal with a Co⁵⁷ source, in order to investigate the strong dependence of the non linear manipulation of the light distribution to the DoI.