Corrections of PET Data for Photon Attenuation, Scatter and Positron Range

The evaluation of PET data acquired during C therapeutic irradiations initiated a modification of the treatment planning data base improving the precision of the particle range in-vivo [1]. Thus, to an increasing extent delicate therapeutic situations characterized by high dose in close vicinity of organs at risk are treated. The validation of the correctness of such irradiations by means of PET requires precise and reliable methods of data processing. Since the PET control of therapy is based on the comparison of the β-activity distributions predicted from the treatment plan with those reconstructed from the data acquired during the patient treatment, both data sets have to be processed the same way. Therefore, the first step of the prediction is a Monte Carlo calculation [2] that describes the stopping of the therapeutic ion beam in tissue, the nuclear fragmentation, the decay of the β-emitters, the propagation of positrons and the annihilation photons and finally the γ-ray detection. This code produces a list mode data set like a measurement and thus it can be reconstructed in the same way as measured data. For the calculation of the positron propagation a new model was developed. Up to now the probability distribution of the positron emitter range was supposed to be a bilinear exponential function [3] with three parameters depending on the maximum positron energy. These parameters have been estimated for β-endpoint energies up to 3.5 MeV, which is sufficient for PET applications in nuclear medicine. However, in the nuclear fragmentation reactions between the therapeutic carbon ion beam and the atomic nuclei of the tissue β-emitters of much higher endpoint energy (up to 16.7 MeV) are produced for which the parameterization of [3] is not proved. Therefore, the positron range distributions have been calculated by means of GEANT [4] simulations for all positron emitting isotopes that may be produced by the fragmentation of C ions in tissue. In Fig. 1 the projection of the 3D spatial distribution on an arbitrary oriented axis (denoted with x) obtained by GEANT is compared with those of Hasch [2] and Derenzo [3]. A look-up table was generated on the basis of the GEANT results. This database is used for the sampling of positron ranges by means of choosing equally distributed random numbers within the interval [0,1]. In the original Monte Carlo code photon scattering was processed in a simplified way by assuming a homogeneous scatter volume (ρ = 1.18 g/cm) centred in the field of view (FOV) of the positron camera. Thus, the simulated data had to be reconstructed without attenuation correction. Obviously this approach is quantitatively incorrect and neglects the large tissue inhomogeneities of the head and neck region, as the typical target for carbon ion therapy at GSI. Therefore, a more comprehensive scatter description has been developed. It requires an attenuation map containing the information on the tissue composition and densities within and nearby the camera FOV. These information are derived from the X-ray computed tomograms (CT) of the patient and the head rest CT [5]. The two data sets (Fig. 2) are automatically merged. The created data set is also the basis for the calculation of the attenuation correction factors which are used in the reconstruction. The Fig. 2 shows that there is a significant influence of absorption by the head rest on the detector response leading, if not corrected, to image artefacts in the reconstruction. The dashed lines denote the acceptance cone of the tomograph. Several approaches are applied to the modified code that do not influence the accuracy but reduce the computing time by a factor of 4 in comparison with the original method. The CT based photon scatter estimation allows the reconstruction algorithm to be applied to the measured and simulated PET list mode data in the same way. This is, furthermore, the condition for including a scatter correction algorithm in the reconstruction in order to evaluate both simulated and measured data quantitatively.