SPaR-liver: sparse point–aware registration for intraoperative liver-deformation compensation using Geometric Deformation Graph Neural Network

Background: Image-guided liver surgery (IGLS) improves precision and safety during oncologic liver resections; however, accurate alignment of preoperative images to the intraoperative position of the liver is invalidated by respiration, repositioning, pneumoperitoneum, and retraction. Accurate intraoperative registration is critical to preserve safe margins, avoid vascular injury, and ensure complete tumor resection in liver surgery. Methods: We propose the SPaR-Liver pipeline, a Sparse Point–aware Registration approach that uses the Sparse Geometric Deformation Graph Neural Network (SGD-GNN), for intraoperative liver-deformation compensation. SGD-GNN extends equivariant, graph-based message passing by incorporating local frames and orientation-aware edge descriptors, yielding pose-stable features even under arbitrary non-rigid motions. By using the DIR-Liver dataset, we first extracted liver surface point clouds from manually halved, segmented computed tomography images. Finally, we evaluated our method in open liver surgery using the navigation system. Results: On the DIR-Liver dataset, with 5 landmarks per hemiliver, SPaR-Liver achieved the best root mean square error of 1.17 mm, Hausdorff distance of 1.56 mm, and fiducial registration error of 1.88 mm. During the intraoperative validation, SPaR-Liver achieved a single-digit millimetric Target registration error (7.99 ± 1.56 mm) at the anatomical target without intraoperative imaging. Conclusions: SPaR-Liver delivers OR-ready deformation compensation from sparse, partial liver surfaces by fusing equivariant graph reasoning with analytic geometry. It restores navigation accuracy with 5–10 landmarks, addressing key translational barriers of speed, reliability, and workflow burden in IGLS.