Use of a Monte Carlo-based probability matrix for 3-D iterative reconstruction of MADPET-II data

The small animal PET scanner MADPET-II, currently under development, is characterized by a small diameter (71 mm), two radial layers of detectors and by small lutetium-oxyorthosilicate crystal elements read out individually by avalanche photodiodes. To exploit this configuration, aimed at achieving high resolution and high sensitivity, we intend to reconstruct a field-of-view (FOV) almost as large as the physical opening of the device. The effects of crystal penetration may, however, hinder this task. To overcome this problem, we implemented fully (three-dimensional) 3-D reconstruction techniques (MLEM and OSEM) based on an accurate description of the system response. The main feature of our method is the off-line calculation of the system probability matrix by means of Monte Carlo simulations. This approach requires the sorting of the simulated data into the matrix, a computationally expensive procedure hindered by the large size of the matrix and the large amount of simulated data. In order to handle this problem, we have employed a database management system (DB2), which has proven to be a practical solution. In this paper, we also studied the effect of applying the underlying symmetries within the matrix to reduce statistical noise affecting the matrix elements and to save disk space. The results showed that this procedure both increases the detectability and contrast, and reduces the ratio of mispositioned events and the coefficient of variation. The transaxial resolution calculated from a phantom consisting of 7 point sources degraded slowly toward the edges of the FOV: for a source at r=0 the FWHM was 0.9 mm, while for a source at r=30 mm, the FWHM was 1.7 mm. The use of the symmetries allowed us to reduce the resolution degradation (FWHM=0.6 mm for r=0 mm and FWHM=1.3 mm for r=30 mm). Despite the gaps between modules and between detectors, rotation of the scanner was not needed. For the 3-D case, an important issue is to improve the accuracy and the statistical quality of the matrix. This is the objective of our future work.