The numerical stability of transformation-based CT ventilation

Edward Castillo,Richard Castillo,Thomas Guerrero,Yevgeniy Vinogradskiy

doi:10.1007/s11548-016-1509-x

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.PurposeThe purpose of this study is to examine how small changes in the DIR displacement field can affect the calculation of transformation-based CT ventilation.MethodsFirst, 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.ResultsUsing 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.ConclusionThe 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.

Highlights

Deformable image registration (DIR) methods compute a spatial transformation that describes the apparent motion depicted by a pair of images [1]
The analysis and experiments indicate that while transformation-based Computed tomography (CT) ventilation is a promising modality, small changes in the DIR displacement field can result in large relative changes in the ventilation image
We mathematically prove that the maximum change in ventilation metric that can be induced by a perturbation to a single displacement vector is on the order of perturbation magnitude

Summary

Introduction

Deformable image registration (DIR) methods compute a spatial transformation that describes the apparent motion depicted by a pair of images [1]. Medical imaging applications, such as radiation dose accumulation [2,3] and intensity variation analysis [4], rely on DIR algorithms to link corresponding voxel locations. Other applications, such as brain morphometric analysis [5,6] and cardiac strain rate imaging [7,8], utilize DIR-measured structural changes to quantify the effects of disease and injury.

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