Three-dimensional Liver Respiratory Motion Tracking in Ultrasound Images via Vascular Structural Projection Optimization and Multi-path Constrained Estimation

Two-dimensional ultrasound (US) imaging is widely used in abdominal interventional procedures. However, liver respiratory motion and the lack of spatial structure information in 2-D US images significantly impact the accuracy of interventions. This work aimed to construct a 3-D respiratory motion model of the liver based on optimized structural vector projection of US images to improve liver motion tracking accuracy. This work first extracts vascular topological information from 3-D US images and tracks 2-D vessel motion in 2-D US images. The 2-D vessel motions are spatially mapped to 3-D space via topological information, enabling 3-D liver motion estimation through structure vector projection optimization. To enhance estimation accuracy in sequential US images, a multi-path constrained optimization strategy is used to evaluate and select optimal 3-D motion vectors as the final estimation result. This framework ultimately establishes a 3-D respiratory motion model of the liver based on structural vector projection analysis. The proposed motion model is validated using both simulated and clinical US data. Experimental results demonstrate that the method achieves an average motion estimation error of less than 2mm and outperforms existing methods in the evaluated experiments, indicating its capability for accurate 3-D respiratory motion tracking tasks.