A Conditional Point Cloud Diffusion Model for Deformable Liver Motion Tracking Via a Single Arbitrarily-Angled X-ray Projection

Deformable liver motion tracking using a single X-ray projection enables real-time motion monitoring and treatment intervention. We introduce a conditional point cloud diffusion model-based framework for accurate and robust liver motion tracking from arbitrarily angled single X-ray projections (PCD-Liver), which estimates volumetric liver motion by solving deformable vector fields (DVFs) of a prior liver surface point cloud based on a single X-ray image. The model is patient-specific and consists of two main components: a rigid alignment model to estimate the liver's overall shifts and a conditional point cloud diffusion model that further corrects for liver surface deformations. Conditioned on motion-encoded features extracted from a single X-ray projection via a geometry-informed feature pooling layer, the diffusion model iteratively solves detailed liver surface DVFs in a projection angle-agnostic manner. The liver surface motion estimated by PCD-Liver serves as a boundary condition for a U-Net-based biomechanical model to infer internal liver motion and localize liver tumors. A dataset of ten liver cancer patients was used for evaluation. The accuracy of liver point cloud motion estimation was assessed using root mean square error (RMSE) and 95th-percentile Hausdorff distance (HD95), while liver tumor localization error was quantified using center-of-mass error (COME). The mean (standard deviation) RMSE, HD95, and COME of the prior liver or tumor before motion estimation were 8.82(3.58) mm, 10.84(4.55) mm, and 9.72(4.34) mm, respectively. After PCD-Liver motion estimation, the corresponding values improved to 3.63(1.88) mm, 4.29(1.75) mm, and 3.46(2.15) mm. Under highly noisy conditions, PCD-Liver maintained stable performance. This study presents an accurate and robust framework for deformable liver motion estimation and tumor localization in image-guided radiotherapy.