A method for accurate modelling of the crystal response function at a crystal sub-level applied to PET reconstruction

Positron emission tomography (PET) images suffer from low spatial resolution and signal-to-noise ratio. Accurate modelling of the effects affecting resolution within iterative reconstruction algorithms can improve the trade-off between spatial resolution and signal-to-noise ratio in PET images. In this work, we present an original approach for modelling the resolution loss introduced by physical interactions between and within the crystals of the tomograph and we investigate the impact of such modelling on the quality of the reconstructed images. The proposed model includes two components: modelling of the inter-crystal scattering and penetration (interC) and modelling of the intra-crystal count distribution (intraC). The parameters of the model were obtained using a Monte Carlo simulation of the Philips GEMINI GXL response. Modelling was applied to the raw line-of-response geometric histograms along the four dimensions and introduced in an iterative reconstruction algorithm. The impact of modelling interC, intraC or combined interC and intraC on spatial resolution, contrast recovery and noise was studied using simulated phantoms. The feasibility of modelling interC and intraC in two clinical (18)F-NaF scans was also studied. Measurements on Monte Carlo simulated data showed that, without any crystal interaction modelling, the radial spatial resolution in air varied from 5.3 mm FWHM at the centre of the field-of-view (FOV) to 10 mm at 266 mm from the centre. Resolution was improved with interC modelling (from 4.4 mm in the centre to 9.6 mm at the edge), or with intraC modelling only (from 4.8 mm in the centre to 4.3 mm at the edge), and it became stationary across the FOV (4.2 mm FWHM) when combining interC and intraC modelling. This improvement in resolution yielded significant contrast enhancement, e.g. from 65 to 76% and 55.5 to 68% for a 6.35 mm radius sphere with a 3.5 sphere-to-background activity ratio at 55 and 215 mm from the centre of the FOV, respectively, without introducing additional noise. Patient images confirmed the usefulness of interC and intraC modelling for improving spatial resolution and contrast. Based on Monte Carlo simulated data, we conclude that four-dimensional modelling of the inter- and intra-crystal interactions during the reconstruction process yields a significantly improved contrast to noise ratio and the stationarity of the spatial resolution in the reconstructed images.