# Dual-Tracer PET Image Separation by Deep Learning: A Simulation Study
## 5 Discussion  
Multiplexed PET imaging can reveal different aspects of physiology in a single dynamic scan, providing complementary information for diagnosis. The present study explored the feasibility of using an indirect deep learning method for dual-tracer [\({}^{18}\)F]FDG and [\({}^{11}\)C]MET imaging with 2D simulated brain data. A tailored 2D CED was designed to learn to separate the dynamic dual-tracer images into two static single-tracer images without explicitly knowing the input functions. The results showed that the proposed DL-based separation method implicitly denoised the separated images when noisy MLEM images were used for the training labels. We also investigated the impact of the number of training pairs and time delay interval \(\Delta t\) on our proposed method and conducted a comparative analysis with the well-known compartment-modelling-based method. The performance of the proposed DL-based method was improved with more training pairs and achieved comparable results for different \(\Delta t\) (0, 5, 10 and 15 min and 2 days) at the pixel level for the whole brain region. With a small number of training pairs, the proposed DL-based method  
Figure 13: Brain phantom (tumour ROI): average \(\text{bias}_{\text{ROI}}\) and average \(\text{SD}_{\text{ROI}}\) at the ROI level of separated static [\({}^{18}\)F]FDG images (**a**) and [\({}^{11}\)C]MET images (**b**) using DL-based and CM-based methods for the tumour ROI \(\Omega_{\text{TM}}\). still outperformed the CM-based method for a short time delay \(\Delta t\) (0, 5, 10 and 15 min) in terms of NRMSE. However, for \(\Delta t\) = 2 days, i.e., when the dual-tracer TACs were entirely separated by a sufficiently long \(\Delta t\), the CM-based method achieved lower NRMSE (similar observations were obtained in the pixel-level bias and standard analysis), indicating more training data would be required for the DL-based method with inclusion of data for \(\Delta t\) = 2 days. We also performed a bias and standard deviation analysis for a tumour ROI. At the pixel level, much lower SD was obtained by the DL-based method compared to the CM-based method, and the SD stayed at a similar level for all \(\Delta t\) due to the aleatoric uncertainty. Using more training data helped to reduce the bias for the DL-based method. For \(\Delta t\) \(\leq\) 15 min, the DL-based method using 80 training pairs achieved lower bias than the CM-based method. However, lower bias was found using the CM-based method when \(\Delta t\) = 2 days. This is consistent with the aforementioned argument that the DL-based method needs more training pairs in order to surpass the CM-based method (as well as inclusion of \(\Delta t\) = 2 days in its training data). For the DL-based method, the situation is accentuated at the ROI level for the tumour ROI. For simultaneous injection (\(\Delta t\) = 0 min), the DL-based method overall delivers lower average bias and SD at the ROI level than the CM-based method (with and without post-denoising). However, the CM-based method can surpass the DL-based method by introducing a 2-4 mm FWHM kernel as post-denoising for \(\Delta t\) \(\geq\) 5 min for the tumour ROI at the ROI level. This study still has several limitations: (1) In the simulation study, we introduced 2D images with only 3 different homogeneous regions (white matter, gray matter and tumour region) and minor variations on the kinetic parameters. Further work is necessary to examine the proposed method for 3D PET images with multiple tissue classes and different levels of variation. (2) The total scan time was limited to 50 min, and the framing scheme was assumed to be the same for each dynamic scan with a given \(\Delta t\). The impact of the total scanning time and different framing schemes need to be investigated in order to optimise the separation performance. (3) The number of tracers was restricted to two. In the literature, a three-tracer separation task was feasible [25] using the CM-based method.