Deformable image registration with local rigidity constraints for cone-beam CT-guided spine surgery

Image-guided spine surgery (IGSS) is associated with reduced co-morbidity and improved surgical outcome. However, precise localization of target anatomy and adjacent nerves and vessels relative to planning information (e.g., device trajectories) can be challenged by anatomical deformation. Rigid registration alone fails to account for deformation associated with changes in spine curvature, and conventional deformable registration fails to account for rigidity of the vertebrae, causing unrealistic distortions in the registered image that can confound high-precision surgery. We developed and evaluated a deformable registration method capable of preserving rigidity of bones while resolving the deformation of surrounding soft tissue. The method aligns preoperative CT to intraoperative cone-beam CT (CBCT) using free-form deformation (FFD) with constraints on rigid body motion imposed according to a simple intensity threshold of bone intensities. The constraints enforced three properties of a rigid transformation-namely, constraints on affinity (AC), orthogonality (OC), and properness (PC). The method also incorporated an injectivity constraint (IC) to preserve topology. Physical experiments involving phantoms, an ovine spine, and a human cadaver as well as digital simulations were performed to evaluate the sensitivity to registration parameters, preservation of rigid body morphology, and overall registration accuracy of constrained FFD in comparison to conventional unconstrained FFD (uFFD) and Demons registration. FFD with orthogonality and injectivity constraints (denoted FFD+OC+IC) demonstrated improved performance compared to uFFD and Demons. Affinity and properness constraints offered little or no additional improvement. The FFD+OC+IC method preserved rigid body morphology at near-ideal values of zero dilatation (D = 0.05, compared to 0.39 and 0.56 for uFFD and Demons, respectively) and shear (S = 0.08, compared to 0.36 and 0.44 for uFFD and Demons, respectively). Target registration error (TRE) was similarly improved for FFD+OC+IC (0.7 mm), compared to 1.4 and 1.8 mm for uFFD and Demons. Results were validated in human cadaver studies using CT and CBCT images, with FFD+OC+IC providing excellent preservation of rigid morphology and equivalent or improved TRE. The approach therefore overcomes distortions intrinsic to uFFD and could better facilitate high-precision IGSS.