MRI Brain Tumour Segmentation Using Multiscale Attention U-Net

2.1Brain Tumour Segmentation

In the realm of medical image segmentation tasks, the continual advancement of deep learning has given rise to numerous methods for brain tumour segmentation. These segmentation approaches, rooted in deep learning, autonomously acquire image features, yielding commendable segmentation outcomes. Notably, U-Net variant methods, founded upon the U-Net architecture, have gained considerable attention and prominence. Zhou et al. (2019) introduced Unet++, a U-Net variant incorporating multi-scale feature fusion and more efficient skip connections. This modification aims to augment the model’s capacity for extracting and fusing features at varied scales, thereby diminishing redundant features in the skip connections and enhancing the model’s efficiency and performance. Milletari et al. (2016) proposed V-Net, which fine-tunes the U-Net structure on 3D MRI data. The model employs the Dice coefficient as a loss function, calculating the similarity between predicted images and the Ground Truth. Subsequently, the Dice loss has become a prevalent choice for loss functions in medical image segmentation tasks. Akbar et al. (2022) presented a shallow 3D U-Net model featuring a distinctive downsampling strategy. This streamlined architecture utilizes a multipath convolutional block, incorporating residual modules and atrous convolution to mitigate gradient instability. Attention gates are integrated into the skip connections, amplifying the segmentation target features. González et al. (2021) employed an asymmetric U-Net, enhancing feature extraction and reconstruction capabilities for improved brain tumour segmentation results. Moreover, Guo et al. (2020) cascaded multiple segmentation networks using U-Nets within a single network. This approach segments different regions of brain tumours sequentially, with each U-Net incorporating a global context block to capture long-range dependencies, inter-channel dependencies, and depth supervision. This enables the network to finely segment brain tumours in a stage-wise manner. Cirillo et al. (2021) proposed a GAN-based brain tumour segmentation method employing a U-Net generative model and the same discriminative model as the encoder in the U-Net. This configuration enables the network to generate realistic segmentation results from MRIs through a zero-sum game.

2.2Attention Mechanism

In vision tasks, attention mechanisms play a pivotal role in the selection of key information and the deliberate exclusion of extraneous details. SENet (Hu et al., 2018) places emphasis on channels with noteworthy contributions to optimize the selection of feature maps. Concurrently, CBAM (Woo et al., 2018) attains superior results by incorporating considerations for both channels and spatial dimensions. The Non-Local (Wang et al., 2018) method introduces a global receptive field into the network by computing interactions between any two positions in the feature map. This facilitates the direct capture of long-range dependencies, effectively substantiating the visual task importance of such dependencies.

In the brain tumour segmentation task, the attention mechanism is similarly able to assign different weights to the input information, effectively suppressing uninteresting features and focusing the network on more discriminative features. For example, Jun et al. (2021) introduced attention gates into the skip connections of U-Net to suppress features irrelevant to the task, enhancing the performance of brain tumour segmentation. Liu et al. (2021a) introduced a context-guided attention network proficient in capturing high-dimensional and high-temporal resolution features by leveraging contextual information within the convolutional space and the feature interaction graph. This approach adeptly discriminates brain tumour features. Moreover, they introduced a context-guided conditional random field for selective feature aggregation, refining the segmentation of brain tumours. Wang et al. (2020) proposed a global aggregation block serving as an encoder and decoder based on self-attention, enabling the network to aggregate global information without necessitating a deep encoder. Additionally, Wang et al. (2021) introduced the self-attention-based Transformer into the bottleneck layer in U-Net, presenting TransBTS. This model exhibits exceptional brain tumour segmentation performance attributed to the potent remote modelling capabilities of the Transformer.

3.1Overall Structure

MAU-Net adopts the 3D brain tumour segmentation U-Net as the base network, primarily incorporating a down-sampled coding layer module, an up-sampled decoding layer module, a skip connection module interconnecting coding and decoding layers, and a decoder feature map integration module within its structure. Notably, both the number of encoders and decoders is established at four, as depicted in Fig. 1. To facilitate the understanding of MAU-Net, the network structure table is given Table 1. Figure 1 illustrates the specific structure of the MAU-Net. Each encoder incorporating one Mixed Depth-wise Convolution (MDConv) Block and one max pooling. Within this context, MDConv Block comprises one regular convolutional unit and one MDConv unit connected sequentially. The regular convolutional unit serves the initial extraction of network features, while the mixed convolutional unit is employed for capturing feature maps with differing receptive field sizes. The max pooling is utilized for size reduction in the feature maps, thereby lowering computational resource consumption and mitigating network overfitting. After four layers of encoding, the feature map dimensions of the brain tumour image are ultimately reduced from 128×128×128 to 8×8×8, and the number of channels increases from 4 to 256. Each decoder employs a structure identical to that of the encoder, with the exception that MPL is substituted with Trilinear Interpolation to restore the feature map dimensions. After four decoders, a feature map matching the size of the input image is achieved.

The skip connections merge the shallow features, imbued with valuable location information in the encoder, with the corresponding deep features in the decoder, within the channel dimension. Nevertheless, it is relevant to note that the shallow features also incorporate redundant original information. To address this concern, a Context Pyramid Module (CPM) has been introduced to mitigate feature responses in irrelevant regions and enhance overall performance. Considering the computational resources needed for network training, the CPM is exclusively integrated within the fourth skip connection, while the remaining layers 1–3 utilize basic skip connections. Finally, a self-ensemble operation is included to facilitate the gradual fusion of feature maps from the upper three levels of the decoder, which enhances the robustness of the model for brain tumour segmentation.

Fig. 1

Structure of the proposed MAU-Net.

3.2Mixed Depth-Wise Convolution (MDConv)

In recent convolutional neural networks, Depth-wise Convolution (DConv) is often used instead of conventional convolution to reduce the amount of computation and the number of parameters, e.g. MobileNets (Sandler et al., 2018), ShuffleNets (Zhang et al., 2018), and MnasNet (Tan et al., 2019), but this type of DConv also extracts features using a fixed-size convolution kernel similarly to the conventional convolution, which results in a fixed convolutional sensory field and makes it difficult to capture spatial information of different sizes. To this end, Tan and Le (2019) combined different sized convolution kernels to construct a new Mixed Depth-wise Convolution (MDConv), which can use a large convolution kernel to capture high-resolution information, and a small convolution kernel to capture low-resolution information, which effectively improves the performance of convolution to extract spatial features.

In the context of specific implementation, MDConv differs somewhat from conventional convolution and DConv. The number of channels within each convolution kernel in the standard convolution aligns with the number of channels in the input feature map, while the count of channels in the output feature map corresponds to the quantity of convolution kernels used. In DConv, each convolution kernel possesses a channel count of 1 with each kernel responsible for computing a single channel in the feature map. Consequently, the number of convolution kernels aligns with the number of channels in both the input and output feature maps. Based on DConv, MDConv organizes convolution kernels of diverse sizes into groups for each channel. Different groups employ convolution kernels with a channel count of 1 and it should be noted that MDConv is equivalent to DConv when the grouping is set to 1. Since the number of output channels in both DConv and MDConv matches the number of input channels, a modification of channel count is implemented using a 1×1×1 convolution to facilitate insertion at various positions within the network. The specific structure of MDConv and its distinction from conventional convolution and DConv is depicted in Fig. 2. Given that brain tumour MRI involves three-dimensional imaging, we initially extended MDConv from a 2D context to its 3D counterpart. Subsequently, we integrated this extended MDConv into the 3D U-Net framework. To mitigate the substantial increase in computation arising from the fusion of 3D convolution with large-sized convolution kernels, the feature map channels entering MDConv were equally partitioned into two groups. One group employed convolution kernels of dimensions 3×3×3 while the other utilized convolution kernels sized 5×5×5. These kernels were introduced in place of the second convolution in the coding and decoding layers. The incorporation of MDConv into brain tumour segmentation facilitates the capture of spatial features of varying scales, leading to an enhancement in the performance of brain tumour segmentation.

Fig. 2

Differences among (a) Convolution, (b) Depth-wise Convolution and (c) Mixed Depth-wise Convolution.

3.3Context Pyramid Module (CPM)

Global information plays a pivotal role in image analysis and comprehension. The incorporation of non-local attention mechanisms to capture long-range dependencies and acquire global information represents a typical approach. To overcome the limitations of calculating non-local attention solely at a single scale, Zhang et al. (2021) introduced an Attention-Guided Context Block (AGCB). This AGCB amalgamates both local and non-local attention and integrates it with the original feature maps in a multi-scale configuration, constituting a Context Pyramid Module (CPM). This approach has demonstrated robust performance in the detection of small infrared targets. Given the distinct morphological variations in brain tumour images and the presence of numerous small tumour regions that pose challenges for accurate segmentation, this paper endeavours to extend the CPM module from 2D to its 3D counterpart. The aim is to improve network segmentation performance by introducing this extension module within the framework of a 3D brain tumour segmentation.

Fig. 3

Structure of Attention-Guided Context Block.

The AGCB module primarily comprises two branches. In the upper branch, global context module attention is employed to compute global correlations, enabling the network to differentiate small targets through the utilization of global information. In the lower branch, the input feature map is partitioned into non-overlapping segments, facilitating the computation of voxel correlations within each segment. This process enhances local feature extraction capabilities, as depicted in Fig. 3. The top branch applies adaptive average pooling to the input feature map X∈RC×D×H×W to derive the sparse feature map G∈RC×s×s×s Subsequently, the feature map G is subjected to three parallel 1×1×1 convolutions to produce three distinct feature maps, denoted as q (query), k (key), and v (value). Autocorrelations between voxels are computed through the multiplication of the q and k values and are further processed using Softmax to derive attention weight coefficients. These coefficients are then multiplied with the v values, resulting in the non-local correlation. Subsequently, a 1×1×1 convolution is applied to enhance and combine these correlations with the input feature maps, yielding the non-local attention. Finally, the global features are passed through the Sigmoid function to generate the weight coefficients G′∈RC×s×s×s. The lower branch divides the input feature map X∈RC×D×H×W into i smaller feature map parcels, denoted as P∈RC×d×h×w, where i∈s×s×s, d=D/s, w=W/s, and h=H/s. Within each parcel of feature maps, voxel correlations are computed using non-local attention. Subsequently, each non-local attention parcel is integrated into a newly formed locally correlated feature map, represented as Pi∈RC×D×H×W. This process restricts the perceptual field of the network to a localized region and exploits the correlation between voxels in the local range to aggregate like voxels. To merge the feature maps from the upper and lower branches, the weights in the global correlation feature map are multiplied by the corresponding parcels in the local correlation feature map to identify the salient parcels. Finally, all the small parcels are concatenated to form a complete block. Simultaneously, the original input feature map is summed to restore inter-block edge information, and the ReLU activation function is applied to introduce nonlinearity. This results in the output of an AGCB module, as depicted in equation (1), where δ signifies the ReLU activation function and β represents the adaptive learning parameters.

The CPM module comprises multiple AGCB modules of varying scales, thereby amalgamating multi-scale features to augment network performance. The CPM structure is visually depicted in Fig. 4. The feature map X∈RC×D×H×W is subjected to downsizing through a 1×1×1 convolution, following which it is concurrently input into multiple AGCB modules of distinct scales. The result is denoted as A={As1,As2,As3,…}, where s signifies the scale vector. Subsequently, multiple feature maps A={Ai} are fused with the original feature maps. Then, the number of channels is reduced using 1×1×1 convolution to dimension c, culminating in the output of the CPM module, and thereby establishing a context pyramid encompassing various AGCB scales.

The computational load of the CPM module escalates as it is required to compute non-local attention on the 3D feature maps multiple times, causing a size difference of 2×2×2 for each layer of feature maps. Furthermore, considering hardware constraints, this paper exclusively incorporates the CPM module within the fourth layer of the transversal connection. The AGCB module employed in this context utilizes only two scales, specifically s=1 and s=2. Despite the augmented computational demand on the model, it yields a substantial enhancement in brain tumour segmentation.

Fig. 4

Structure of context pyramid module.

3.4Self-Ensemble

Although U-Net uses skip connection to enhance the decoder ability to recover high-resolution spatial information, it falls short for fine segmentation of brain tumours with blurred edges. For this reason, Zhao et al. (2020) fused features from different layers in a serial structure to form a Self-ensemble (S.E) module, which reduces the loss of spatial information during up-sampling and enables the network to segment finer tumour edges. In the specific implementation, the decoders of the first to the third layers in the 3D U-Net are reduced to the number of channels to the number of categories using 1×1×1 convolution, respectively, and the three dimensionality-reduced feature maps are cascaded to the final brain tumour segmentation result, which is structured as in Fig. 1.

4.1Experimental Environment

In our study, the experiments were conducted using a single Nvidia RTX 3090 GPU with 24 GB of memory, and the PyTorch deep learning framework was employed. The model was trained using the Adam optimizer, with a momentum value of 0.95 and a weight decay factor of 1×10−5. The learning rate decayed exponentially, starting with an initial rate of 0.001, and the batch size was set to 4. A total of 500 training epochs were completed.

4.2Datasets and Data Processing

4.2.1Datasets

Three publicly available datasets were used for the experiments, namely BraTS 2019, BraTS 2020 and BraTS 2021 (Bakas et al., 2017; Menze et al., 2014; Baid et al., 2021). The BraTS 2019 dataset consists of 335 glioma patient cases for training and 125 samples of unknown tumour types for validation. The BraTS 2020 dataset training set consists of 369 glioma patient cases and the validation set consists of 125 cases of unknown tumour types. Due to the closure of the official validation process for BraTS 2021, we conducted a five-fold cross-validation using the BraTS 2021 training set, which includes 1251 glioma patient cases. Each sample in the dataset consists of four modalities: T1-weight (T1), post-contrast T1-weighted (T1ce), T2-weighted (T2), and T2 Fluid Attenuated Inversion Recovery (FLARE), as depicted in Fig. 5. The image size for each modality is 240×240×155. Furthermore, the training set includes manually annotated ground truth labels by an expert, encompassing background (label 0), Non-Enhancing tumour (label 1), Peritumoural Edema (label 2), and Enhancing Tumour (label 4). To maintain the fairness of the experimental results, the validation set does not disclose the ground truth, and its segmentation results must be evaluated through an online server available at https://ipp.cbica.upenn.edu/. The MRI brain tumour segmentation objectives comprise three distinct regions: Enhancing Tumour (ET), Tumour Core (TC), and Whole Tumour (WT). Each tumour region corresponds to different labels: ET contains label 4, TC contains labels 1 and 4, and WT contains labels 1, 2, and 4.

Fig. 5

MRI in different modes and ground truth.

4.3Evaluation Metrics

In our study, we employed two key metrics, namely the Dice Similarity Coefficient (DSC) and the Hausdorff Distance (HD), for the evaluation of brain tumour segmentation across the regions of WT, TC, and ET. The DSC quantifies the degree of similarity between two samples, with values ranging from 0 to 1. A value closer to 1 indicates a higher degree of similarity. Meanwhile, the HD measures the maximum distance between any two sets within an array in the spatial domain. To mitigate the impact of potential outliers within the dataset, the final result is adjusted by a factor of 95%. Smaller Hausdorff95 values correspond to reduced spatial distances between subsets, indicative of improved segmentation outcomes.

4.4Loss Function

To address the substantial class imbalance issue inherent in brain tumour segmentation, we employ a hybrid loss function represented as L. This function combines the Cross Entropy (CE) loss, represented as LCE, and the Dice similarity coefficient loss, represented as LDice. These components can be formulated as equations (4), (5), and (6), respectively:

5.1Ablation Experiment

To comprehensively assess the effectiveness of the incorporated modules, we conducted ablation experiments on the BraTS 2019 dataset and BraTS 2020 dataset. These experiments involved using the 3D U-Net as the baseline method and separately adding MDConv and CPM to the 3D U-Net. We initially examined the performance of incorporating both the MDConv and CPM modules. Subsequently, we verified the validity of the final method, MAU-Net, by introducing the self-ensemble module. To facilitate comparisons, we use “Mix”, “CPM” to denote the experimental results when incorporating MDConv and CPM, respectively.

First, we implemented a five-fold cross-validation strategy on the BraTS 2019 and BraTS 2020 training sets. The datasets were randomly divided into five subsets, with each iteration reserving one subset as the validation set and using the remaining subsets for training. This approach ensured comprehensive and stable evaluation. The results of the ablation experiments, averaged over the five iterations, are presented in Table 2. The experiments demonstrated that the MAU-Net model, which integrates MixConv, CPM, and S.E modules within a 3D U-Net architecture, achieved optimal performance across both datasets. Compared to the baseline U-Net model, MAU-Net showed significant improvements in DSC and reductions in Hausdorff95 distance. Specifically, in BraTS 2019, DSC improvements were observed for ET, WT, and TC, with increases of 2.2%, 0.8%, and 2%, respectively, while Hausdorff95 was reduced by 3.03 mm, 1.55 mm, and 3.11 mm. In BraTS 2020, DSC improvements were 1.3% for ET, 0.8% for WT, and 2.5% for TC, with corresponding reductions in Hausdorff95 by 0.29 mm, 0.79 mm, and 2.57 mm.

To further validate the effectiveness of the individual modules, we conducted additional ablation experiments on the validation sets of BraTS 2019 and BraTS 2020. The segmentation models trained on the training sets were used to predict the validation sets, with the results submitted to an online evaluation platform to enhance the reliability and impartiality of the findings. The results are shown in Table 3. In the BraTS 2019 validation set, incremental introduction of the MixConv and CPM modules into the 3D U-Net resulted in notable increases in DSC values for ET, WT, and TC, particularly for TC, where the inclusion of MixConv and CPM led to a 1.5% improvement. This highlights their effectiveness in segmenting small-volume targets. When both modules were integrated into U-Net, further improvements of 0.7% for ET and 1.8% for TC were observed. To further optimize brain tumour segmentation performance, MAU-Net incorporated a self-assembly module, achieving DSC values of 77.9%, 90.6%, and 82.7% for ET, WT, and TC, respectively. Compared to U-Net, MAU-Net demonstrated substantial performance advantages, with DSC improvements of 1.4% for ET and 2.4% for TC, validating the positive impact of the embedded modules in brain tumour segmentation tasks. Additionally, MAU-Net significantly reduced Hausdorff95 distance, with reductions of 0.89 mm for ET, 0.61 mm for WT, and 1.42 mm for TC, further confirming the effectiveness of MixConv, CPM, and the self-assembly mechanism in enhancing segmentation accuracy. In the BraTS 2020 validation set, MAU-Net achieved outstanding DSC values of 78.5% for ET, 90.2% for WT, and 82.8% for TC, surpassing the 3D U-Net by 1.6%, 0.9%, and 2.9%, respectively, thus affirming the efficacy of the MAU-Net model. Similarly, in terms of Hausdorff95 distance, MAU-Net exhibited significant advantages, with values of 26.96 mm for ET, 7.61 mm for WT, and 8.61 mm for TC, representing reductions of 5.6 mm, 0.09 mm, and 3.5 mm compared to U-Net. The superior performance of MAU-Net, particularly for ET and TC, further underscores its excellence in brain tumour segmentation tasks.

Fig. 6

Training loss for the BraTS2020 training set.

To validate the reasonableness of the training hyper-parameter settings, we systematically conducted ablation experiments on learning rate (LR) and batch size. The results of these experiments are summarized in Table 4, and visually represented by the training loss curves (Fig. 6). First, under the condition of a consistent learning rate, we explored the effect of different batch sizes on brain tumour segmentation accuracy. Through detailed comparative analysis, we found that moderately increasing the batch size can slightly improve segmentation accuracy. This finding suggests that, when resources permit, increasing the batch size helps the model better capture statistical characteristics of the data, thereby optimizing segmentation outcomes. Next, with the batch size fixed, we thoroughly examined the effect of learning rate on segmentation accuracy. Specifically, we tested several learning rates, including 0.005, 0.001, 0.0005, and 0.0001, to comprehensively evaluate their impact on the training process and final performance. The results indicated that a learning rate of 0.001 yielded the best segmentation performance, a conclusion visually supported by Fig. 6, which shows a smooth decline in training loss and successful convergence before 500 epochs at this learning rate. In contrast, when the learning rate was set to 0.0001, the training process was slower and failed to fully converge. This observation is clearly reflected in the loss curve in Fig. 6, and the quantitative data in Table 4 further confirm that the model’s segmentation performance was suboptimal with a lower learning rate.

As shown in Table 5, we conducted a series of experiments on the BraTS 2020 training set to determine the optimal value of the hyper-parameter α in the loss function. Notably, α=0 corresponds to using only cross-entropy loss, and α=1 corresponds to using only Dice loss. The results indicated that the combination of cross-entropy and Dice loss with α=0.25 yields the best segmentation performance. This may be attributable to the complementary nature of these two losses, with the Dice loss effectively solving the category imbalance problem, while the cross-entropy improves the segmentation results in terms of target similarity.

To evaluate the impact of different padding methods on segmentation performance, we compared Zero Padding, Reflection Padding, and Replication Padding. Our results, as summarized in the Table 6, reveal that zero padding tends to introduce edge artifacts, which negatively affect performance, especially in the Hausdorff95 metric. In contrast, reflection padding offers a more natural treatment of image edges, leading to a significant improvement in Hausdorff95. While replication padding also prevents edge artifacts, it was slightly outperformed by reflection padding, likely due to the latter’s better ability to preserve edge information. Therefore, we decided to use MAU-Net with added reflection padding in subsequent comparison experiments with other methods. Additionally, we validated the robustness of the model by introducing different types of noise, as shown in Table 6. We added three common types of noise to the data, Gaussian noise, Pretzel noise, and Rayleigh noise. The experimental results indicate that while MAU-Net exhibited a significant increase in the Hausdorff95 metric for ET under Rayleigh noise, no significant differences were observed in any other evaluation metrics. This further demonstrates the stability and reliability of the MAU-Net model across different noisy.

5.2Visualization

Fig. 7

Visualization of segmentation results on the BraTS 2020 training set. WT contains red (labels 1), green (labels 2) and yellow (labels 4); TC contains red (labels 1) and yellow (labels 4); ET contains yellow (labels 4).

To better demonstrate the results of the method, Fig. 7 provides visual representations of select samples within the BraTS 2020 training set. Distinct colours correspond to varying label, with red signifying areas of necrotic and non-enhanced regions (label 1), green signifying areas of edema (label 2), and yellow signifying areas of enhancing tumour (label 4). The images describe the segmentation results of Flair, Ground Truth, 3D U-Net, and MAU-Net, respectively. In contrast to the 3D U-Net model, the figure underscores that MAU-Net excels in the segmentation of whole tumour (WT), tumour core (TC) and enhancing tumuor (ET) region.

5.3Comparison with Representative Methods

To validate the effectiveness and competitiveness of the proposed method, we conducted comparisons with representative brain tumour segmentation approaches using the BraTS 2019 and BraTS 2020 validation sets, with results uploaded to the online platform. Additionally, we performed five-fold cross-validation on the BraTS 2021 training set to further confirm its performance.

The comparative experiments on the BraTS2019 and BraTS2020 validation sets are presented in Table 7 and Table 8. To demonstrate the superiority of MAU-Net among similar methods, we first compared it with various 3D U-Net variants, including V-Net (Milletari et al., 2016), Attention U-Net (Jun et al., 2021; Zhao et al., 2020), CANet (Liu et al., 2021a; Akbar et al., 2022; González et al., 2021), and (Vu et al., 2021). The experimental results clearly show that MAU-Net outperforms these methods, particularly in segmenting small tumours like the ET, with significant improvements. Additionally, we compared MAU-Net with the more recent dual-path attention fusion network proposed by Chang et al. (2023), which also employs attention mechanisms. MAU-Net demonstrated a marked advantage over this method across multiple brain tumour regions, further underscoring its effectiveness and competitiveness.

Additionally, we compared MAU-Net with brain tumour segmentation networks based on different architectures to further establish its competitiveness. Guo et al. (2020) introduced a cascaded global semantic convolutional network, which uses multiple U-Nets to sequentially segment WT, TC, and ET. Compared to this method, MAU-Net significantly reduced the Hausdorff95 distance for ET, WT, and TC by 1.39 mm, 3.03 mm, and 2.28 mm, respectively, demonstrating superior performance. MAU-Net also shows strong competitiveness compared to the 3D CNN proposed by González et al. (2021), the multi-encoder network with multiple denoising inputs proposed by Vu et al. (2021), and the GAN-based method proposed by Cirillo et al. (2021). We further evaluated MAU-Net against U-Net models incorporating Transformers, such as TransBTS (Wang et al., 2021) and SwinBTS (Jiang et al., 2022). While TransBTS and SwinBTS expand the receptive field at a single scale by replacing the bottleneck layer with transformers, MAU-Net effectively enhances segmentation accuracy by extracting features with different receptive fields across multiple scales, highlighting its advanced capabilities. Finally, Li et al. (2024b) proposed a multi-level fusion brain tumour segmentation method within a hybrid architecture, where MAU-Net demonstrated a clear advantage in DSC, further validating the competitiveness of our approach.

In the BraTS 2021 training set, we employed five-fold cross-validation, with the results presented in Table 9. The rationale for selecting comparative methods is consistent with that used in BraTS 2019 and BraTS 2020. Compared to the dual-branch network proposed by Jia et al. (2023)., which integrates attention mechanisms with super-resolution reconstruction techniques, MAU-Net achieved significant improvements in the DSC evaluation metric, particularly with a 3.8% lead in the ET region, a 1.6% lead in the WT region, and a 3.1% lead in the TC region. Furthermore, when compared to the residual spatial pyramid pooling-enhanced 3D U-Net employed by Vijay et al. (2023), MAU-Net demonstrated clear advantages across all metrics, validating the superiority of the MAU-Net architecture. Additionally, in comparison to Transformer-based architectures like UNETR (Hatamizadeh et al., 2022) and VTU-Net (Peiris et al., 2022), MAU-Net also exhibited superior performance, further proving its advanced capabilities. Finally, compared to the multi-scale residual U-Net proposed by Li et al. (2024a), MAU-Net maintained a lead in segmentation accuracy for both the WT and TC regions, further confirming its effectiveness and competitiveness.