Continuous sPatial-Temporal Deformable Image Registration (CPT-DIR) for motion modelling in radiotherapy: beyond classic voxel-based methods

Deformable image registration (DIR) is a crucial tool in radiotherapy for analyzing anatomical changes and motion patterns. Current DIR implementations rely on discrete volumetric motion representation, which often leads to compromised accuracy and uncertainty when handling significant anatomical changes and sliding boundaries. This limitation affects the reliability of subsequent contour propagation and dose accumulation procedures, particularly in regions with complex anatomical interfaces such as the lung-chest wall boundary. Given that organ motion is inherently a continuous process in both space and time, we aimed to develop a model that preserves these fundamental properties. Drawing inspiration from fluid mechanics, we propose a novel approach using implicit neural representation (INR) for continuous modeling of patient anatomical motion. This approach ensures spatial and temporal continuity while effectively unifying Eulerian and Lagrangian specifications to enable natural continuous motion modeling and frame interpolation. The integration of these specifications provides a more comprehensive understanding of anatomical deformation patterns. By leveraging the continuous representations, the CPT-DIR method significantly enhances registration and interpolation accuracy, automation, and speed. The method demonstrates superior performance in landmark and contour precision, particularly in challenging anatomical regions, representing a substantial advancement over conventional approaches in deformable image registration. The improved efficiency and accuracy of CPT-DIR make it particularly suitable for real-time adaptive radiotherapy applications.