Detector Response Modeling with Asymmetric 2D Gaussian Functions for GPU-based Image Reconstruction of the Whole-body Dual-ring OpenPET

We are developing the OpenPET which can provide an open space to make the patient observable and accessible during PET measurements. One of the key technologies for realizing the OpenPET geometry is the depth of interaction (DOI) detectors because the geometry has many oblique lines of response (LORs). Even if the DOI detectors reduce the blurring effect of the thick crystals, it is important to model the detector response function (DRF) in the reconstruction algorithm to achieve high spatial resolution images. In this study, therefore, we developed a new DRF model based on asymmetric 2D Gaussian functions perpendicular to the LOR for on-the-fly DRF calculation by GPUs during image reconstruction. In the proposed model, we virtually separated the detector crystal into two parts: head and tail. The head part has the shape of a cube. We set the center position of the asymmetric 2D Gaussian function at the center of the head part. The parameters of the asymmetric 2D Gaussian functions were calculated according to the size of the head part and tail part components perpendicular to the LOR. The proposed model was implemented on GPUs using the CUDA framework. We compared the proposed model with a simple Gaussian model and a crystal subsampling model which is an analytical model. We found DRFs in the proposed method provided a similar shape to that in the analytical model. In addition, the proposed model could include the blurring effect. The analytical model could represent only the effect of crystal shape, while the simple Gaussian model could represent only the blurring effect. Finally, the proposed method was applied for a prototype whole-body dual-ring OpenPET. As a result, the proposed method could improve the spatial resolution especially in the gap region of the OpenPET.