GraphMorph: Equilibrium adjustment regularized dual-stream GCN for 4D-CT lung imaging with sliding motion

Four-dimensional computed tomography (4D-CT) is crucial for radiation therapy, enabling motion tracking of thoracic and abdominal tumors. However, respiratory-induced sliding motion at organ interfaces poses a significant challenge for existing registration algorithms, leading to difficulties in accurately modeling discontinuous deformations. We propose an Equilibrium Adjustment Regularized Dual-Stream Graph Convolutional Network (GCN), dubbed GraphMorph, for addressing the challenges of sliding motion in 4D-CT lung registration. This network ensures physically consistent deformations while balancing smoothness and discontinuity at sliding interfaces. To address the challenge of global large deformations, we propose a Topology Enhanced Graph Attention (TEGA) module, which harnesses the topological information of the graph structure and the global dependencies modeled by the Transformer, facilitating the learning of regional relationships in sliding organs. We also construct a Cross-Scale Contextual Aggregation (CSCA) module that aggregates contextual information by leveraging content correlations between images from different respiratory phases, thus addressing subtle local deformations. To balance continuous and discontinuous deformations, we designed a biomechanics-inspired Equilibrium Adjustment Regularization (EAR) method, which eliminates discretization dependencies and effectively mitigates the impact of local intensity inhomogeneities on registration accuracy. Experiments on public and in-house 4D datasets demonstrate that GraphMorph achieves an average target registration error (TRE) of 0.96 mm, outperforming existing methods even on out-of-distribution (OOD) data. GraphMorph enhances 4D-CT lung imaging by accurately modeling sliding motion, enabling precise deformable registration for lesion localization in image-guided interventions. The source code is available at https://github.com/computerAItest/GraphMorph.