Robust CT ventilation from the integral formulation of the Jacobian

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dc.citation.firstpage2115en_US
dc.citation.issueNumber5en_US
dc.citation.journalTitleMedical Physicsen_US
dc.citation.lastpage2125en_US
dc.citation.volumeNumber46en_US
dc.contributor.authorCastillo, Edwarden_US
dc.contributor.authorCastillo, Richarden_US
dc.contributor.authorVinogradskiy, Yevgeniyen_US
dc.contributor.authorDougherty, Micheleen_US
dc.contributor.authorSolis, Daviden_US
dc.contributor.authorMyziuk, Nicholasen_US
dc.contributor.authorThompson, Andrewen_US
dc.contributor.authorGuerra, Rudyen_US
dc.contributor.authorNair, Girishen_US
dc.contributor.authorGuerrero, Thomasen_US
dc.date.accessioned2019-12-06T15:32:19Zen_US
dc.date.available2019-12-06T15:32:19Zen_US
dc.date.issued2019en_US
dc.description.abstractComputed tomography (CT) derived ventilation algorithms estimate the apparent voxel volume changes within an inhale/exhale CT image pair. Transformation-based methods compute these estimates solely from the spatial transformation acquired by applying a deformable image registration (DIR) algorithm to the image pair. However, approaches based on finite difference approximations of the transformation's Jacobian have been shown to be numerically unstable. As a result, transformation-based CT ventilation is poorly reproducible with respect to both DIR algorithm and CT acquisition method. PURPOSE: We introduce a novel Integrated Jacobian Formulation (IJF) method for estimating voxel volume changes under a DIR-recovered spatial transformation. The method is based on computing volume estimates of DIR mapped subregions using the hit-or-miss sampling algorithm for integral approximation. The novel approach allows for regional volume change estimates that (a) respect the resolution of the digital grid and (b) are based on approximations with quantitatively characterized and controllable levels of uncertainty. As such, the IJF method is designed to be robust to variations in DIR solutions and thus overall more reproducible. METHODS: Numerically, Jacobian estimates are recovered by solving a simple constrained linear least squares problem that guarantees the recovered global volume change is equal to the global volume change obtained from the inhale and exhale lung segmentation masks. Reproducibility of the IJF method with respect to DIR solution was assessed using the expert-determined landmark point pairs and inhale/exhale phases from 10 four-dimensional computed tomographies (4DCTs) available on www.dir-lab.com. Reproducibility with respect to CT acquisition was assessed on the 4DCT and 4D cone beam CT (4DCBCT) images acquired for five lung cancer patients prior to radiotherapy. RESULTS: The ten Dir-Lab 4DCT cases were registered twice with the same DIR algorithm, but with different smoothing parameter. Finite difference Jacobian (FDJ) and IFJ images were computed for both solutions. The average spatial errors (300 landmarks per case) for the two DIR solution methods were 0.98 (1.10) and 1.02 (1.11). The average Pearson correlation between the FDJ images computed from the two DIR solutions was 0.83 (0.03), while for the IJF images it was 1.00 (0.00). For intermodality assessment, the IJF and FDJ images were computed from the 4DCT and 4DCBCT of five patients. The average Pearson correlation of the spatially aligned FDJ images was 0.27 (0.11), while it was 0.77 (0.13) for the IFJ method. CONCLUSION: The mathematical theory underpinning the IJF method allows for the generation of ventilation images that are (a) computed with respect to DIR spatial accuracy on the digital voxel grid and (b) based on DIR-measured subregional volume change estimates acquired with quantifiable and controllable levels of uncertainty. Analyses of the experiments are consistent with the mathematical theory and indicate that IJF ventilation imaging has a higher reproducibility with respect to both DIR algorithm and CT acquisition method, in comparison to the standard finite difference approach.en_US
dc.identifier.citationCastillo, Edward, Castillo, Richard, Vinogradskiy, Yevgeniy, et al.. "Robust CT ventilation from the integral formulation of the Jacobian." <i>Medical Physics,</i> 46, no. 5 (2019) Wiley: 2115-2125. https://doi.org/10.1002/mp.13453.en_US
dc.identifier.digitalCastillo_et_al-2019en_US
dc.identifier.doihttps://doi.org/10.1002/mp.13453en_US
dc.identifier.urihttps://hdl.handle.net/1911/107784en_US
dc.language.isoengen_US
dc.publisherWileyen_US
dc.rightsThis is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made.en_US
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.subject.keyword4DCTen_US
dc.subject.keywordcomputed tomographyen_US
dc.subject.keywordcone beam CTen_US
dc.subject.keyworddeformable image registrationen_US
dc.subject.keywordventilationen_US
dc.titleRobust CT ventilation from the integral formulation of the Jacobianen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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