# Dual-Tracer PET Image Separation by Deep Learning: A Simulation Study
## 4 Results
### CM-Based Dual-Tracer Separation Results  
A test example of the separated images using the CM-based method is shown in the last column of Figure 8 (\([^{18}\text{F}]\)FDG) and Figure 9 (\([^{11}\text{C}]\)MET) for different \(\Delta t\). Compared to the results obtained from the DL-based method, the separated images using the CM-based method are much noisier because the model fitting (4) may fall into local minima even when the noise level is low. Although several strategies, such as using differing initial values or an exhaustive search algorithm [22], have been suggested to reduce local minima, their use in clinical practice is challenging because of their high computational cost. Figure 7: Brain phantom (whole brain region): NRMSE (over 10 test datasets) of separated static [\({}^{18}\)F]FDG images (**a**–**e**) and [\({}^{11}\)C]MET images (**f**–**j**) using the DL-based method for the whole brain region \(\Omega_{\text{Brain}}\). Figure 8: Brain phantom (whole brain region): the static [\({}^{18}\)F]FDG images recovered using the DL-based method (Columns 1 to 5) and the CM-based method (Column 6). Figure 10: Average NRMSE (over 10 test datasets) for the whole brain region: \(\Omega_{\text{brain}}\) (**a**,**c**) DL-based method, (**b**,**d**) CM-based method and frame integrated (FI) method. Figure 9: Brain phantom (whole brain region): the static [\({}^{11}\)C]MET images recovered using the DL-based method (Columns 1 to 5) and the CM-based method (Column 6). We now investigate the impact of \(\Delta t\) on the CM-based separation for dynamic dual-tracer noisy MLEM images. Figure 10b,d (solid lines) show longer \(\Delta t\) results in more accurate separation using the CM-based method. High average NRMSE values were obtained (\(\sim\)45% for \({}^{[18}\)F]FDG and \(\sim\)55% for \({}^{[11}\)C]MET) when a simultaneous injection protocol is used. The average NRMSE values improve rapidly (by \(\sim\)7% for \({}^{[18}\)F]FDG and and \(\sim\)20% \({}^{[11}\)C]MET) from simultaneous to 5 min delay and then gradually decrease for longer \(\Delta t\) (10 and 15 min). This is because only the \({}^{[18}\)F]FDG signal was measured in the first 5 min, providing temporal prior information of a single tracer to aid in the disentangling of dual-tracer signals, whereas no prior information is given for simultaneous injection, which makes the dual-tracer separation problem more challenging. Longer \(\Delta t\) means more temporal prior information of \({}^{[18}\)F]FDG is available before the \({}^{[11}\)C]MET injection, and thus the average NRMSE values steadily improve for the cases of \(\Delta t\) = 10 and 15 min. For \(\Delta t\) = 2 days, much lower average NRMSE values were obtained (\(\sim\)10% for \({}^{[18}\)F]FDG and \(\sim\)12% for \({}^{[11}\)C]MET) as dual-tracer signals have been entirely separated by a large \(\Delta t\) (see Section 3.1 for details). We also integrated the last 4 frames of the reconstructed dynamic single-tracer noisy MLEM images (we refer to herein as the frame integrated (FI) method) for \(\Delta t\) = 2 days to estimate the target images (20 min static images of each tracer), and obtained a level of average NRMSE comparable to that of the CM-based method (see the pentagram markers in Figure 10b,d). This result indicates that the CM-based method is equivalent to the FI method for recovering the static single-tracer images from the dynamic single-tracer images when dual-tracer signals were separated by a sufficiently long time delay. We then applied the CM-based method to the reconstructed dynamic dual-tracer noise-free MLEM images to examine the impact of the noise. Again, longer \(\Delta t\) results in more accurate separation as illustrated in Figure 10b,d (dashed lines). The average NMRSE values of noise-free dual-tracer separations are substantially lower than those of noisy dual-tracer separations for all \(\Delta t\), indicating that noise has a massive effect on the separation performance when using the CM-based method.