## 4 Experimental Results
### Ablation Study  
We designed a large number of ablation experiments to demonstrate the validity of our proposed dual-path encoder model principle. And based on five-fold cross-validation evaluations on the BraTS 2021 training set to verify our design principle, our design mainly includes the following aspects: (a) the impact of the Swin Transformer encoder on segmentation accuracy in the DualTrans model and (b) a focus on the influence of our innovative sensitive position coding on model accuracy when extracting feature information from the Swin Transformer encoder. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Dice Score (\%)**} & \multicolumn{3}{c}{**Hausdorff 95 (mm)**} \\ \cline{2-7}  & **ET** & **TC** & **WT** & **ET** & **TC** & **WT** \\ \hline Swin UNETR [27] & 85.8 & 88.5 & 92.6 & 6.02 & 3.77 & 5.83 \\ Reciprocal Adversarial [29] & 81.38 & 85.63 & 90.77 & 21.83 & 8.56 & 5.37 \\ [PERSON] et al. [30] & 81.87 & 84.34 & 90.97 & 17.85 & 16.69 & 4.51 \\ [PERSON] et al. [31] & 84.79 & 86.55 & 92.65 & 12.75 & 11.19 & 3.67 \\ Orthogonal-Nets [32] & 83.2 & 84.99 & 91.38 & 20.97 & 9.81 & 5.43 \\ Attention and Ensemble [33] & 83.79 & 86.47 & 91.99 & 6.39 & 7.81 & 3.86 \\ Swin–Unet [34] & 85.37 & 87.26 & 92.08 & 14.32 & 9.80 & 11.28 \\ Extending-nnUNet [21] & 84.51 & 87.81 & 92.75 & 20.73 & 7.62 & 3.47 \\ DualTrans (ours) & 86.23 & 88.12 & 92.83 & 6.37 & 3.64 & 4.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison between the DualTrans model and other SOTA models based on BraTS 2021 validation set. As to the **Swin Transformer encoder path**, our model adopts dual-path encoders, the first one being the Swin Transformer encoder, and the second one being a convolutional neural network encoder. As shown in Figure 2, when the Swin Transformer encoder path is removed, the network structure is similar to the UNet network architecture. In terms of specific operations, the input image is gradually transformed into a feature map with a low resolution but a high feature representation by using a 3 \(\times\) 3 \(\times\) 3 convolution block for downsampling (stride = 2 convolution), and rich local information is extracted via convolution. In order to prevent the loss of feature information in the downsampling process, the concat feature is carried out by jumping connections. The feature block of \(\frac{\text{H}}{\text{32}}\times\frac{\text{W}}{\text{32}}\times\frac{\text{D}}{ \text{32}}\times 768\) is obtained in the last layer of the encoder, and then, the upsampling operation is carried out through transposed convolution. The whole process is consistent with the 3D-UNet architecture, and the segmentation accuracy is shown in Table 4.  
As can be seen from Table 4, the segmentation accuracy of our proposed model is greatly improved after adding the Swin Transformer encoder, and the dice coefficients increase by 16.63%, 16.64%, and 5.45% in the ET, TC, and WT brain-tumor regions, respectively. It is strongly proven that combining the Swin Transformer encoder path is of great significance for extracting global semantic feature information. A convolution operation is used to extract local dependencies and rich local features, and the improved Swin Transformer is used to learn global dependencies for global modeling. Then, feature fusion is carried out. The model can, therefore, obtain rich semantic information. For the **DualTrans position**, the position information is included in the calculation of the multi-head attention mechanism, and the relative position information is further optimized by using trainable parameters. First, the relative position distance between each position abc \(\epsilon\)\(\text{H}_{\text{m}\times\text{m}\times\text{m}}\) and the center point is defined as jik in the window, and the relative distance is decomposed across dimensions.