# Dual-Tracer PET Image Separation by Deep Learning: A Simulation Study
## 3 2D Simulation Study  
### 2D Dataset Simulation  
The proposed DL-based dual-tracer separation method was validated through 2D numerical simulations. A total of 5 non-contiguous slices were selected from each of the 20 3D BrainWeb phantoms (the BrainWeb dataset is available from [[https://brainweb.bic](https://brainweb.bic)]([https://brainweb.bic](https://brainweb.bic)). mni.mcgill.ca/, accessed on 1 July 2021) to generate the simulated dataset of 2D brain phantoms [53]. The simulated dataset consists of 100 brain images. Each image is of resolution \(128\times 128\), assuming a uniform voxel size 0.78 mm, and contains gray matter (GM) and white matter (WM). Randomised structures were introduced, and a tumour region with random radii of 2.5-4 mm and random locations was added to each phantom (the BrainWeb-based image processing toolbox is available from [[https://github.com/casperdcl/brainweb](https://github.com/casperdcl/brainweb)]([https://github.com/casperdcl/brainweb](https://github.com/casperdcl/brainweb)), accessed on 1 July 2021). The combination of two tracers of different isotopes, \([^{18}\)F]FDG and \([^{11}\)C]MET, with radioactive decay rates of \(\lambda_{[^{18}\mathrm{F}]}=\log(2)/109.7\) min\({}^{-1}\) and \(\lambda_{[^{11}\mathrm{C}]}=\log(2)/20.4\) min\({}^{-1}\), respectively, was considered in our simulation study. Following the simulation process in [46; 54; 55], each kinetic parameter was modelled as a Gaussian variable with the coefficient of variation equal to 0.1 to simulate the population variation in the dataset [54; 55]. The mean values of the kinetic parameters were taken from [28] and are presented in Table 1. [PERSON]'s input function model [56] was used to generate the \([^{18}\mathrm{F}]\)FDG and \([^{11}\mathrm{C}]\)MET AIFFs. The parameters for [PERSON]'s model were selected to match the shapes of the AIFFs presented in [28]; see Table A1 for the details. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **ROIs** & \(K_{1}\) & \(k_{2}\) & \(k_{3}\) & \(k_{4}\) & \(V_{B}\) \\ \hline \multirow{3}{*}{\([^{18}\mathrm{F}]\)FDG} & GM & 0.10 & 0.14 & 0.17 & 0.013 & 0.103 \\  & WM & 0.05 & 0.11 & 0.05 & 0.006 & 0.026 \\  & Tumour & 0.11 & 0.10 & 0.15 & 0.015 & 0.173 \\ \hline \multirow{3}{*}{\([^{11}\mathrm{C}]\)MET} & GM & 0.08 & 0.08 & 0.10 & 0.017 & 0.103 \\  & WM & 0.04 & 0.06 & 0.04 & 0.028 & 0.026 \\ \cline{1-1}  & Tumour & 0.13 & 0.03 & 0.06 & 0.012 & 0.173 \\ \hline \hline \end{tabular}  
* Units: \(K_{1}\): cc/min/g; \(k_{2}\)-\(k_{4}\): min\({}^{-1}\); \(V_{B}\): unitless.  
\end{table} 
Table 1: Mean values of the ground-truth kinetic parameters of \([^{18}\mathrm{F}]\)FDG and \([^{11}\mathrm{C}]\)MET for different tissue ROIs. Figure 2: The proposed 2D CED structure. The input is the dynamic dual-tracer images with \(L\) consecutive frames. The numbers shown in the plot are based on the simulation study described in Section 3.1. Figure 3 depicts the dynamic dual-tracer PET scanning protocols for different \(\Delta t\), as well as the static PET scanning protocols for each tracer in our simulation. We consider a 50 min dual-tracer PET scan: the [\({}^{11}\)C]MET injection was followed by the injection of [\({}^{18}\)F]FDG with a time delay \(\Delta t\). To explore the impact of the time-delayed interval, different \(\Delta t\) were taken into account in our experiments, e.g., 0 min, 5 min, 10 min, 15 min and 2 days. The reversible two-tissue compartment model was used to simulate the 50 min dual-tracer TACs. The AIFs and a simulation of a dual-tracer TAC for \(\Delta t=15\) min without decay correction are shown in Figure 4. We note that the dual-tracer signals were entirely separated in time by \(\Delta t=2\) days since [\({}^{18}\)F]FDG was metabolised and cleared from brain tissues prior to the injection of [\({}^{11}\)C]MET. In this instance, two separate dynamic PET scans were performed, one for each tracer.