The numerical stability of transformation-based CT ventilation

ABSTRACT: Computed tomography (CT)-derived ventilation imaging utilizes deformable image registration (DIR) to recover respiratory-induced tissue volume changes from inhale/exhale 4DCT phases. While current strategies for validating CT ventilation rely on analyzing its correlation with existing functional imaging modalities, the numerical stability of the CT ventilation calculation has not been characterized. PURPOSE: The purpose of this study is to examine how small changes in the DIR displacement field can affect the calculation of transformation-based CT ventilation. METHODS: First, we derive a mathematical theorem, which states that the change in ventilation metric induced by a perturbation to single displacement vector is bounded by the perturbation magnitude. Second, we introduce a novel Jacobian constrained optimization method for computing user-defined CT ventilation images. RESULTS: Using the Jacobian constrained method, we demonstrate that for the same inhale/exhale CT pair, it is possible to compute two DIR transformations that have similar spatial accuracies, but generate ventilation images with significantly different physical characteristics. In particular, we compute a CT ventilation image that perfectly correlates with a single-photon emission CT perfusion scan. CONCLUSION: The analysis and experiments indicate that while transformation-based CT ventilation is a promising modality, small changes in the DIR displacement field can result in large relative changes in the ventilation image. As such, approaches for improving the reproducibility of CT ventilation are still needed.