The bone rigidity error as a simple, quantitative, and interpretable metric for patient-specific validation of deformable image registration

Background and Purpose: Despite its potential, deformable image registration (DIR) is underutilized clinically, especially in time-sensitive cases, due to a lack of comprehensive metrics for assessing solution quality. Here, we propose a metric of physical plausibility, the bone rigidity error (BRE), that penalizes non-rigid transformations within individual bones, based on the assumption that bones do not deform. Materials and Methods: The BRE is calculated by segmenting bones individually and isolating the vectors of a deformable vector field within each bone. A rigid registration is least-square fitted to these vectors, and the BRE is calculated as the average deviation of these vectors from the fitted rigid registration. A lower BRE indicates better rigidity preservation. We evaluated the BRE for 6 DIR algorithms on 32 patients with 137 computed tomography (CT)-to-CT registrations across relevant anatomical sites. Results: The BRE varied widely between DIR algorithms, up to a factor of 3 on average for inhale-to-exhale thoracic CT registration. Despite large BRE differences between anatomical sites within each algorithm, some algorithms consistently outperformed others. Notably, a low BRE was not correlated with poorer image similarity, and the BRE was only weakly correlated to target registration error. Furthermore, we proposed bone-specific inspection thresholds for patient-specific validation. BRE calculation required less than 5.5 s. Conclusions: The BRE is an automatic, interpretable, fast, and easy-to-implement metric to assist validation of DIR algorithms, which show widely varying performance. It provides a useful complementary metric for patient-specific validation, especially in time-sensitive applications.