# Dual-Tracer PET Image Separation by Deep Learning: A Simulation Study
## 1 Introduction
However, the solution of the fitting problem was not unique in this method. Although additional non-CM-based methods have also been suggested, including reference-tissue model-based dual-tracer separation [21], principal component analysis (PCA) [19], generalised factor analysis of dynamic sequences [33] and basis pursuit [34], their accuracy is still insufficient, and a long time-delayed injection protocol is required. A machine-learning-based dual-tracer separation method was conducted in [35], where a recurrent extreme gradient boosting (rXGBoost) algorithm [36] was presented to separate the dual-tracer TACs for a region of interest (ROI). It permits a shorter delay (5 min) between the injection of two tracers than that described in the literature [19; 20; 22; 25; 34], while high separation accuracy is still maintained. This method, however, only employs the temporal information of the measured signals for separation and still requires the knowledge of the AIFs of each tracer. Over the years, deep learning has provided powerful new tools for the separation of dual-tracer PET signals. The DL-based method has two advantages over the aforementioned ones: (i) the ability to separate dual-tracer signals without explicitly knowing the input functions, (ii) use of spatiotemporal information for dual-tracer separation, and (iii) fast separation and processing using a trained network. Two main (supervised) deep learning strategies have been proposed for dual-tracer PET image separation in the literature. The indirect strategy employs a neural network to separate the dynamic dual-tracer images reconstructed using traditional reconstruction algorithms into dynamic single-tracer images [37; 38; 39; 40; 41; 42; 43]. Alternatively, the direct strategy incorporates the reconstruction task with the separation task to perform an end-to-end learning from dual-tracer dynamic sinograms to separated single-tracer dynamic images using a neural network [44; 45; 46]. In [47], an unsupervised joint method based on a GAN (pix2 pix [48]) is presented to separate simultaneous dual-tracer PET signals and perform ROI segmentation. However, only a simultaneous injection protocol was considered in all the aforementioned deep-learning-based dual tracer separation methods, neglecting the investigation of the impact of the time interval \(\Delta t\) between the injections of the two tracers. In this work, we investigate the impact of the number of training pairs and \(\Delta t\) for indirect deep learning dual-tracer separation and conduct a comparative analysis between the proposed method and the CM-based method, which has not thus far been reported anywhere in the literature. In particular, we construct a customised 2D CED to separate dynamic [18]FDG and [11C]MET dual-tracer images into two static single-tracer images, one for each tracer, in a single dynamic scan when two tracers are injected sequentially with a specified short time interval \(\Delta t\). The proposed DL-based method and the CM-based method are summarised in Figure 1. The reminder of the paper is organised as follows. In Section 2, we outline our proposed methodology. Section 3 describes the design of the simulated experiments. In Section 4, we demonstrate the separation performance of our framework in the simulation study. Sections 5 and 6 provide outlook and conclusions.