## 2 Methods
### Deep Learning Models  
#### 2.3.1 nnU-Net for Deep Learning Framework  
Convolutional neural networks (CNNs), particularly U-Net [14] and its automated version nnU-Net [15], have become highly effective in medical image segmentation, with nnU-Net offering an easy-to-use, state-of-the-art solution by automating key hyperparameter selection and preprocessing steps, maintaining high performance even in a recent study [16]. In this study, three different models were trained within the nnU-Net framework: (1) 2D U-Net; (2) 3D full-resolution U-Net; (3) 3D U-Net cascade, where the first 3D U-Net operated on low-resolution images, followed by a second, high-resolution 3D U-Net that refined the predictions of the first network.  
Importantly, all preprocessing steps were fully handled by the nnU-Net pipeline without manual intervention. Default nnU-Net preprocessing steps included resampling to a standardized voxel spacing, intensity normalization, and spatial cropping. No additional manual preprocessing of the dataset was performed prior to training. The default nnU-Net architecture settings were used without any manual modifications to the number of layers, input patch size, or convolutional kernels. Data augmentation during training, including random rotations, scaling, elastic deformations, and intensity variations, was automatically applied through the nnU-Net's default augmentation pipeline.  
All three nnU-Net configurations were trained on the CT and T1 CE MRI of the training set, with slight adjustments to the default nnU-Net settings. The T1 CE MRI and CT of each case were used as input into a single trained model for each configuration. The standard hybrid loss function combining the DSC loss and Cross-Entropy loss was used. This combination leads to more robust segmentation performances by balancing their complementary strengths in handling class imbalance [17]. A stochastic gradient descent (SGD) optimizer with a learning rate of 0.01 and momentum of 0.99 was used. We reduced the number of training epochs from the default 1000 to 250, as preliminary experiments indicated that the model converged on our dataset within this reduced number of epochs. Given the limited size of the dataset, five-fold cross-validation was used during training for all three models to prevent overfitting and enhance the model's robustness. The data splitting for the five-fold cross-validation was carried out using the nnU-Net framework. Specifically, a deterministic (seeded) randomization process was used to split the dataset into five folds, ensuring the splits were reproducible. After training, predictions were generated using an ensemble of the models from the five cross-validation folds. During inference, the nnU-Net utilized both the CT and T1 CE MRI scans as input, reflecting its training process and the real-world clinical scenario where both modalities are available for radiotherapy planning. The training was conducted on a single NVIDIA GeForce RTX 2080 Ti graphics card. The total training times for three different nnU-Net models were as follows: 52 h and 30 min for the 2D model, 29 h and 10 min for the 3D full-resolution model, and 50 h and 15 min for the 3D cascade model.