An ODE-based multi-resolution parallel network for respiratory motion estimation.

During puncture procedures, respiratory motion can cause significant displacement of lesions. Fast and accurate estimation of pulmonary respiratory motion can provide valuable guidance during surgery. However, the large deformation of fine lung textures and the complex motion of internal structures such as airways and blood vessels pose significant challenges for motion estimation. In this study, we propose a multi-resolution parallel network architecture based on neural ordinary differential equations (neural ODE). By incorporating neural ODE, our method explicitly models the temporal continuity of 4DCT data, addressing the issue of unrealistic deformations in lung motion estimation and producing transformations that better align with the physiological patterns of respiratory motion. Furthermore, we introduce a multi-resolution parallel structure to recursively refine lung features. This enhances the network's feature representation and prediction capabilities, thereby improving registration accuracy. We conducted both qualitative and quantitative experiments on the TCIA and DirLab datasets, demonstrating that the proposed method outperforms other deep learning approaches and achieves consistently high performance across all respiratory phases.