Influence of the System Matrix on the Quality of the Reconstruction of In-Beam PET Data

At the experimental heavy ion therapy facility at the GSI Darmstadt an in-beam PET scanner is operated for quality assurance monitoring simultaneously to the therapeutic irradiation. A fully 3D maximum likelihood expectation maximization (MLEM) reconstruction algorithm has been developed and adapted to the special conditions of in-beam PET [1]. The system response function (system matrix) for that algorithm is implemented by separately calculating its components (geometry, scatter, attenuation and detector sensitivity). The system matrix itself includes the geometry component only. The geometry component of the system matrix is calculated "on-thefly" during the reconstruction. In order to determine this component, the volume of each tube of response (TOR) is sampled by a number of lines whose endpoints are randomly distributed over the crystal surfaces. The number of lines used in the method is called a level. The higher the level, the more accurate and slower is the calculation. We investigated the accuracy for this approach as well as for another method for calculating of the geometry component of the system matrix based on the approximation with splines [2]. An influence of the system matrix on the quality of reconstructed images was evaluated for MLEM and ordered subsets expectation maximization (OSEM) algorithms using real treatment data collected during the therapeutic irradiations at the GSI. The accuracy of both methods for the system matrix calculation ("on-the-fly" and with splines approximation) was checked by means of analyzing the normalized mean square error (NMSE) (Fig.1 left). The method with splines approximation achieves high accuracy (NMSE = 0.00047) and performs with the same speed as "on-the-fly" method with level equal to 50. For visual comparison of accuracy the system matrix was calculated for one TOR with the two different methods (Fig. 1 right). The influence of system matrix on the reconstruction quality was evaluated by means of an ensemble mean square error (EMSE) [3]. The true + β activity distributions were generated by means of the PosGen Monte Carlo code based on real treatment data of 9 patients. EMSE was calculated for reconstructions with the MLEM algorithm (50 iterations) and with the OSEM algorithm (8 subsets, 10 iterations). EMSE does not depend significantly on the quality of the system matrix when reconstructions are performed by MLEM algorithm, but significant deviations are observed when using the OSEM algorithm (Fig. 2). As a conclusion, it is profitable to use the splines approximation method for reconstructions with OSEM algorithm where higher quality of the system matrix leads to lower mean square error and slightly better images. However, in the specific conditions of in-beam PET (dualhead geometry and low counting statistics) the best result for reconstructions performed by the MLEM algorithm by means of EMSE is achieved with the system matrix of poor quality (with "on-the-fly" method with level = 3) and visual comparison gives no significant difference.