# Generation of Synthetic Rat Brain MRI Scans with a 3D Enhanced Alpha Generative Adversarial Network
## 4 Discussion  
The initial evaluation of the models was based on the quantitative results of Table 2 to discard the worse models more quickly, e.g., the MS-SSIM value should not be very close to one, as it is important that the model can generate a large variety of scans. Table 2 shows that the \(\alpha\)-WGANSigmaRat1 model has the second highest MS-SSIM value and the value closest to the real distribution that is higher than the real distribution, which means that the generated scans are more repetitive than the real ones. This is not necessarily a problem, as the value is far from one, but it does not correspond to the real distribution of the sigma dataset of rat brains. This value is even higher for the \(\alpha\)-WGANSigmaRat2 model, but the generated scans appear to be more realistic after a qualitative visual inspection by the experts. The remaining metrics were too close to each other, so it was necessary to use other tools to further compare these two models. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Tests** & **Test1** & **Test2** & **Test3** & **Test4** & **Test5** & **Test6** & **Test7** & **Test8** & **Test9** \\ \hline \multirow{2}{*}{\begin{tabular}{c} Data \\ sets \\ \end{tabular} } & \(\text{D}_{\text{r}}\)174 & \(\text{D}_{\text{r}}\)174 & \(\text{D}_{\text{r}}\)174 & \(\text{D}_{\text{r}}\)174 & \(\text{D}_{\text{r}}\)174 & \(\text{D}_{\text{s}}\)174 & \(\text{D}_{\text{s}}\)348 & \(\text{D}_{\text{r}}\)87 & \(\text{D}_{\text{r}}\)87 \\  & \(\text{D}_{\text{s}}\)87 & \(\text{D}_{\text{s}}\)174 & \(\text{D}_{\text{s}}\)261 & \(\text{D}_{\text{s}}\)348 & & \(\text{D}_{\text{s}}\)174 & \(\text{D}_{\text{s}}\)348 \\ \hline \multirow{2}{*}{\begin{tabular}{c} Global \\ GM \\ \end{tabular} } & 0.8969 & 0.9138 & 0.9083 & 0.9078 & **0.9141** & 0.8238 & 0.7646 & 0.8979 & 0.8259 \\ \hline \multirow{2}{*}{\begin{tabular}{c} GM \\ WM \\ \end{tabular} } & 0.9381 & **0.9419** & 0.9384 & 0.9376 & 0.9412 & 0.8863 & 0.8586 & 0.9316 & 0.8863 \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} WM \\ \end{tabular} } & 0.8969 & 0.9077 & 0.9037 & 0.9014 & **0.9098** & 0.8202 & 0.7262 & 0.8897 & 0.8301 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} CSF \\ \end{tabular} } & 0.7468 & **0.8232** & 0.8098 & 0.8170 & 0.8180 & 0.6095 & 0.4418 & 0.7442 & 0.6273 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Segmentation of Grey Matter (GM), White Matter (WM), and CerebroSpinal Fluid (CSF) dice score, where r refers to real and s refers to synthetic scans. If two datasets are included in the same test, this means that the test was performed with the union of both datasets. The best results are in bold. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Tests** & **Test1** & **Test2** & **Test5** & **Test10** & **Test11** & **Test12** \\ \hline \multirow{2}{*}{ \begin{tabular}{c} Data \\ sets \\ \end{tabular}  } & \(\text{D}_{\text{r}}\)174 & \(\text{D}_{\text{r}}\)174 & \(\text{D}_{\text{r}}\)174 & \(\text{D}_{\text{r}}\)174 & \(\text{D}_{\text{r}}\)174 & \(\text{D}_{\text{r}}\)174 \\  & \(\text{D}_{\text{s}}\)87 & \(\text{D}_{\text{s}}\)348 & \(\text{D}_{\text{s}}\)266 &In the loss function plots of the \(\alpha\)-WGANSigmaRat2 model (Figure 8), it can be seen that the training of the discriminator was very stable and after 60,000 iterations, the training of the generator also stabilised. It is not good practice to compare different generative models using loss function diagrams, as they do not correspond to human perception. These diagrams are only a good tool to check for the presence of mode collapse, which is characterised by the divergence between the discriminator and the generator loss function diagrams, one tending to \(-\infty\) and the other to \(+\infty\). Normally, the training runs until this divergence occurs, but since an \(\alpha\)-GAN architecture with VAE was used, this would never happen or it would require many more iterations, so it was decided to run 200,000 iterations.