# Dual-Tracer PET Image Separation by Deep Learning: A Simulation Study
## 3 2D Simulation Study
### Implementation of Deep-Learning-Based Dual-Tracer Separation Method  
The simulated brain phantoms were reconstructed using the classic maximum-likelihood expectation maximization (MLEM) algorithm [58]. A total of 128 iterations were used for EM reconstruction to maintain the balance between bias and noise as suggested in [28,59]. Given that the PET scanner measures average activity concentration over time, the reconstructed dynamic dual-tracer images were further normalised by frame widths, e.g., \(T_{m}=t_{m,s}-t_{m,e}\) for the \(m\)th frame, to obtain the (non-decay corrected) dual-tracer TACs of each voxel. The reconstructed single-tracer images were also normalised by 20 min static acquisition time to obtain the activity distributions. The reconstructed dynamic dual-tracer images and the reconstructed static single-tracer images were used as network inputs and training labels, respectively. Examples of reconstructed static single-tracer noisy MLEM images are shown in Figure 6c,f, together with the corresponding noise-free MLEM reconstructions (NF) (b,e) and the ground truths (a,d). When \(\Delta t=2\) days, the dual-tracer signals were entirely separated (reasons for which are discussed in Section 3.1), and thus two reconstructed dynamic single-tracer images were obtained, one for each tracer. In this case, the reconstructed dynamic single-tracer images (either \([^{18}\)F]FDG or \([^{11}\)C]MET) were employed as the network input. In this special case, the MSE loss is only applied to either \([^{18}\)F]FDG or \([^{11}\)C]MET, depending on the choice of the tracer considered in the network input. Notice that the decay correction cannot be performed in dual-tracer PET prior to separation because the proportion of each tracer (and hence its decay correction factor) is unknown prior to separation. While we do model decay, we do not seek to include decay correction in this present work.  
In our experiments, an individual 2D CED was trained for each \(\Delta t\) to investigate the impact of the time delay interval between the injections of the two tracers. We used 80 simulated 2D brain phantoms to generate the training pairs (dynamic dual-tracer reconstructed images and static single-tracer reconstructed images), 10 for validation and 10 for testing. We also retrained each CED using a different sample size (1, 4, 8 and 40 training pairs) to assess the impact of the number of training pairs. All network training was performed in the same manner. We chose [PERSON] [60] as the optimizer with [PERSON] initialization [61] and a learning rate of 0.005. Different batch sizes were chosen based on the number of training pairs; see Table 2 for additional information. To prevent overfitting, all networks were trained for 1000 epochs, with early stopping when the validation metrics no longer improved along with the training metrics. The training and evaluation of each network  
Figure 5: A simulated example of the total number of counts of the static single-tracer PET scans (20 min) and dynamic dual-tracer scans (50 min) for different \(\Delta t\).  
were implemented with PyTorch 1.11.0. All computations were conducted on a Quadro P6000 GPU with 24 GB memory.