A Shortened Model for Logan Reference Plot Implemented via the Self-Supervised Neural Network for Parametric PET Imaging

Dynamic PET imaging provides superior physiological information than conventional static PET imaging. However, the dynamic information is gained at the cost of a long scanning protocol; this limits the clinical application of dynamic PET imaging. We developed a modified Logan reference plot model to shorten the acquisition procedure in dynamic PET imaging by omitting the early-time information necessary for the conventional reference Logan model. The proposed model is accurate theoretically, but the straightforward approach raises the sampling problem in implementation and results in noisy parametric images. We then designed a self-supervised convolutional neural network to increase the noise performance of parametric imaging, with dynamic images of only a single subject for training. The proposed method was validated via simulated and real dynamic $^{{18}}\text{F}$ -fallypride PET data. Results showed that it accurately estimated the distribution volume ratio (DVR) in dynamic PET with a shortened scanning protocol, e.g., 20 minutes, where the estimations were comparable with those obtained from a standard dynamic PET study of 120 minutes of acquisition. Further comparisons illustrated that our method outperformed the shortened Logan model implemented with Gaussian filtering, regularization, BM4D and the 4D deep image prior methods in terms of the trade-off between bias and variance. Since the proposed method uses data acquired in a short period of time upon the equilibrium, it has the potential to add clinical values by providing both DVR and Standard Uptake Value (SUV) simultaneously. It thus promotes clinical applications of dynamic PET studies when neuronal receptor functions are studied.