## 3 Results
### Training of the CNN Model for GBM Detection
As shown in Figure 6, the first experiment with a single-layer configuration [8] exhibited a baseline validation accuracy of approximately 32%. With the increasing depth of the architecture, the accuracy improved gradually to about 45% in architectures comprising more sophisticated configurations, such as [8; 32] and [8; 16; 32; 64], which correspond to convolutional networks of three and four layers. The enhancement of accuracy was observed with the five-layer configuration [8; 16; 32; 64; 128], which reached and stabilised at around 61% \(\pm\) 0.3. Figure 5: Distribution of MRI slices per patient. Blue bars represent patients from the training set, while the red bar corresponds to the test set. Models comprising fewer than five layers were found to lack the capacity to extract relevant features from MRI images, resulting in lower performance. Although deeper architectures, such as six-layer models, exhibited slightly higher performance, they introduced a greater standard deviation (0.038), indicating diminishing returns and potential overfitting. Based on these observations, the five-layer configuration was selected for final optimisation and evaluation. As shown in Figure 7, this structure enabled the modelling of complex hierarchical patterns while maintaining stable training. Accordingly, two activation functions were applied based on their advantages. The Leaky ReLU function was used in the initial layers to mitigate the dead-neuron problem and improve the gradient flow for negative inputs, while ReLU was employed in deeper layers due to its computational efficiency and effectiveness in image processing. The specifications of the CNN model are detailed in Table 3.  
Figure 6: Performance of CNN models with different layer configurations. The graph illustrates the AUC-ROC metric across various CNN layer configurations, with error bars representing standard deviations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Layers** & **Filter Size** & **No. Filters** & **Activation** & **Output** & **TP** \\ \hline _InputLayer_ & N/A & N/A & N/A & (64, 512, 512, 8) & 0 \\ Conv2D & \(3\times 3\) & 8 & Leaky ReLU & (64, 510, 510, 8) & 224 \\ MP & \(2\times 2\) & N/A & N/A & (64, 255, 258, 8) & 0 \\ Conv2D & \(3\times 3\) & 16 & Leaky ReLU & (64, 253, 253, 16) & 1168 \\ MP & \(2\times 2\) & N/A & N/A & (64, 126, 126, 126) & 0 \\ Conv2D & \(3\times 3\) & 32 & ReLU & (64, 124, 124, 32) & 4640 \\ MP & \(2\times 2\) & N/A & N/A & (64, 62, 62, 32) & 0 \\ Conv2D & \(3\times 3\) & 64 & ReLU & (64, 60, 60, 64) & 18,496 \\ MP & \(2\times 2\) & N/A & N/A & (32, 30, 30, 64) & 0 \\ Conv2D & \(3\times 3\) & 128 & ReLU & (64, 28, 28, 128) & 73,856 \\ MP & \(2\times 2\) & N/A & N/A & (64, 14, 128) & 0 \\ Flatten & N/A & N/A & N/A & (64, 25,088) & 0 \\ Dense & N/A & 128 & ReLU & (64, 128) & N/A \\ Dense & N/A & 1 & Sigmoid & (64, 1) & N/A \\ \hline \hline \end{tabular} Note: MP stands for MaxPooling2D, and TP stands for trainable params.  
\end{table} 
Table 3: The CNN model architecture. The Adam optimiser was selected for its adaptive learning rate properties, enabling efficient training and noise management. In order to determine the optimal configuration, a hyperparameter tuning process was performed by assessing several combinations of learning rates and batch sizes. This exploration aimed to balance convergence behaviour and performance across evaluation metrics. As shown in Table 4, a learning rate of \(1\times 10^{-3}\) was selected after testing values between \(1\times 10^{-2}\) and \(1\times 10^{-4}\). Higher rates led to oscillations, while lower rates slowed convergence. Furthermore, a batch size of 64 was determined as optimal among the tested values (32, 64, and 128), providing the best balance between speed and convergence stability. The model architecture consisted of 98.38 \(\times\) 10\({}^{3}\) trainable parameters, requiring approximately 384.3 kilobytes of memory, with 32-bit precision (4 bytes per parameter).