Model construction of photon propagation based on the geometrical symmetries and GPU technology for the quad-head PET system

Compact quad-head PET systems have been developed by many researchers. This compact configuration leads to depth of interaction (DOI) blurring, which greatly reduces the quality of the reconstructed image. How to accurately model the photon propagation is the key to relieving DOI blurring. In this study, photon propagation is modelled by using the multi-ray method. As we all know, the precision of the multi-ray model is proportional to its computational complexity. Focusing on this problem, we have developed the symmetries of the quad-head PET system according to the different structural features of the opposite and adjacent detector heads. Given all the symmetrical properties, the construction of the photon propagation model becomes a trade-off between the calculation precision and computational complexity of the multi-ray method. In addition, when photon propagation is stored in the system response matrix (SRM), the storage cost is also reduced largely. In the proposed quad-head PET system, the SRM is compressed about 559 times, and the matrix scale is approximately 1.7 GB. The calculation of the SRM can be finished in 60 s when the graphics processing unit (GPU) acceleration technology is adopted. In order to verify the imaging performances, several simulated experiments are carried out. The metrics FWHM, location accuracy, Contrast Recovery (CR), and Coefficient of Variation (COV) are adopted to quantify the imaging results. We find that the mean location difference can reach 1.29% based on a simulated multi-spheres experiment. Through this experiment, the FWHMs can reach to about 1.0 mm in the center or close to the edge of the field of view (FOV). In the image quality experiment, the CR can up to 0.95 in the hot region, and the COV reaches 5.82% in the background region.