## 5 Conclusions  
In this paper, we propose a multi-constraint cascade attention network (MCANet) based on unsupervised learning for deformable brain MRI registration. In the subnet design, we combine the expansion convolution combination and the attention mechanism strategy. These methods have played an active role in improving many factors that affect the registration effect. We tested MCANet using the Mindboggle101 and Neurite OASIS datasets, and calculated Dice scores and SDlogJ. The number of voxels folded and registration time were used to quantitatively evaluate the registration effect of 3D brain MRI. The experimental results show that, compared with several existing advanced registration methods (including traditional algorithms and learning based methods), MCANet achieves the highest level of registration accuracy and can smoothly deform moving images. This indicates that MCANet performs well in aligning two brain MR images, and this research has made substantial progress in this field. However, MCANet still has some limitations and needs further improvement in future research.  
1. Although the network structure and regularization constraint mechanism of MCANet can theoretically solve the voxel folding problem and ensure smooth deformation, they still need to be further optimized in practical applications. In the future, we plan to further improve the smoothness and biological rationality of deformation by introducing more complex regularization strategies (such as deformation models based on physical constraints).
2. MCANet is currently mainly aimed at the registration task of brain MRI, but its applicability has not been verified in the 3D image registration of other organs. In the future, we plan to expand MCANet to other medical imaging fields, such as abdomen, chest, and other organ registration tasks, to verify its versatility and cross domain applicability.
3. The training process of MCANet relies on unsupervised learning. Although it avoids the need to annotate data, its performance may be affected by the quality and distribution of training data. In the future, we plan to explore semi-supervised learning or self-supervised learning methods to further improve the performance and robustness of the model.  
In conclusion, MCANet has shown good performance in brain MRI registration tasks, but it still needs to be improved in data set size, network structure optimization, cross domain applicability, and experimental comparative analysis. We believe that through these improvements, MCANet will be able to play a greater role in the field of medical image registration and provide a valuable reference for related research.  
Writing--original draft, M.H.; Writing--review & editing, H.W.; Supervision, G.R. All authors have read and agreed to the published version of the manuscript.  
The work is partially supported by the Henan Provincial Department of Science and Technology Research Project (Grant No. 242102210107 and Grant No. 252102210127).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
We sincerely appreciate the assistance provided by the School of Software at Zhengzhou University of Light Industry in the use of experimental equipment, which played a crucial role in ensuring the smooth conduct of the experiments.  
The authors declare no conflicts of interest.