title: 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.
  
  
  OBJECTIVE
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Department of Radiation Oncology, Beaumont Health Systems, Royal Oak, MI, USA. ec@rice.edu.|Department of Computational and Applied Mathematics, Rice University, Houston, TX, USA. ec@rice.edu.
authors.forename: Edward
authors.identifier: http://orcid.org/0000-0003-0523-487X
authors.initials: E
authors.lastname: Castillo
authors.affiliation: Department of Radiation Oncology, University of Texas Medical Branch, Galveston, TX, USA.
authors.forename: Richard
authors.initials: R
authors.lastname: Castillo
authors.affiliation: Department of Radiation Oncology, University of Colorado, Denver, CO, USA.
authors.forename: Yevgeniy
authors.initials: Y
authors.lastname: Vinogradskiy
authors.affiliation: Department of Radiation Oncology, Beaumont Health Systems, Royal Oak, MI, USA.
authors.forename: Thomas
authors.initials: T
authors.lastname: Guerrero
mesh_terms: D000465:Algorithms; D056973:Four-Dimensional Computed Tomography / Q000379:methods*; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012119:Respiration; D015899:Tomography, Emission-Computed, Single-Photon
keywords: Computed tomography; Deformable image registration; Functional image analysis; Ventilation