A conditional point cloud diffusion model for deformable liver motion tracking via a single arbitrarily-angled x-ray projection

<i>Objective.</i>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 (PCD) model-based framework for accurate and robust liver motion tracking from arbitrarily angled single x-ray projections.<i>Approach.</i>We propose a conditional PCD model for liver motion tracking (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. It is a patient-specific model of two main components: a rigid alignment model to estimate the liver's overall shifts, and a conditional PCD model that further corrects for the liver surface's deformation. Conditioned on the motion-encoded features extracted from a single x-ray projection by a geometry-informed feature pooling layer, the diffusion model iteratively solves detailed liver surface DVFs in a projection angle-agnostic fashion. The liver surface motion solved by PCD-Liver is subsequently fed as the boundary condition into a U-Net-based biomechanical model to infer the liver's internal motion to localize liver tumors. A dataset of 10 liver cancer patients was used for evaluation. We used the root mean square error (RMSE) and 95-percentile Hausdorff distance (HD95) metrics to examine the liver point cloud motion estimation accuracy, and the center-of-mass error (COME) to quantify the liver tumor localization error.<i>Main Results.</i>The mean (±s.d.) RMSE, HD95, and COME of the prior liver or tumor before motion estimation were 8.82 mm (±3.58 mm), 10.84 mm (±4.55 mm), and 9.72 mm (±4.34 mm), respectively. After PCD-Liver's motion estimation, the corresponding values were 3.63 mm (±1.88 mm), 4.29 mm (±1.75 mm), and 3.46 mm (±2.15 mm). Under highly noisy conditions, PCD-Liver maintained stable performance.<i>Significance.</i>This study presents an accurate and robust framework for liver deformable motion estimation and tumor localization for image-guided radiotherapy.