Local rigidity constraints for deformable image registration in CBCT-guided radiotherapy

Deformable image registration (DIR) is a critical component for planning and quality assurance in CBCT-guided adaptive radiotherapy treatment. Conventional DIR methods apply a uniform regularization over the image domain, failing to account for the local biomechanical properties of different tissues. Recent advancements emphasize the need for spatially varying models to improve anatomical plausibility.

This study aims to introduce a novel, lightweight framework that incorporates local rigidity constraints in DIR to improve anatomical consistency and motion estimation accuracy. The approach is designed to be general, computationally efficient, and compatible with existing DIR pipelines.

The proposed framework jointly optimizes the rigid-body transformation and the surrounding tissue deformations. The proposed framework was evaluated on $57$ pelvic CT-CBCT image pairs with annotated landmarks. Local rigidity constraints were imposed on automatically segmented sacrum, hip, and femur bones. Four registration algorithms were tested, combining different regularization types, with and without rigidity constraints. Accuracy was measured using the target registration error (TRE) and biomechanical plausibility was assessed via the Jacobian of the estimated motion. Secondary verification was performed on a $4D$ thoracic CT database. With automatic segmentation and rigidity constraints placed upon the ribs and thoracic vertebrae, accuracy and plausibility were analyzed in these structures and inside the lungs.

Across $57$ cases, the constrained methods improved landmark alignment compared to baseline models, increasing the proportion of cases with mean TRE below 3 mm. Local rigidity constraints significantly reduced unphysical deformations in rigid bones as indicated by the Jacobian determinant mappings and analysis on the residual energy of the Jacobian orthogonality. Analysis of thoracic CT images showed improved alignment of the ribs and vertebrae with marginal increase in TRE of the landmarks in the lungs. The added constraints increased the runtime to a maximum of $40$  s.

The proposed framework enforces local rigidity constraints during DIR, increasing accuracy without significantly compromising speed. It removes anatomically implausible deformations in rigid structures. Its efficiency and anatomical reliability make it well-suited for CBCT-guided adaptive radiotherapy.