Dataset Information

Robust CT ventilation from the integral formulation of the Jacobian.

ABSTRACT: Computed 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.

SUBMITTER: Castillo E

PROVIDER: S-EPMC6510605 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:PurposeThe computed tomography (CT)-derived ventilation imaging methodology employs deformable image registration (DIR) to recover respiratory motion-induced volume changes from an inhale/exhale CT image pair, as a surrogate for ventilation. The Integrated Jacobian Formulation (IJF) and Mass Conserving Volume Change (MCVC) numerical methods for volume change estimation represent two classes of ventilation methods, namely transformation based and intensity (Hounsfield Unit) based, respectively. Both the IJF and MCVC methods utilize subregional volume change measurements that satisfy a specified uncertainty tolerance. In previous publications, the ventilation images resulting from this numerical strategy demonstrated robustness to DIR variations. However, the reduced measurement uncertainty comes at the expense of measurement resolution. The purpose of this study was to examine the spatial correlation between robust CT-ventilation images and single photon emission CT-ventilation (SPECT-V).MethodsPreviously described implementations of IJF and MCVC require the solution of a large scale, constrained linear least squares problem defined by a series of robust subregional volume change measurements. We introduce a simpler parameterized implementation that reduces the number of unknowns while increasing the number of data points in the resulting least squares problem. A parameter sweep of the measurement uncertainty tolerance, τ , was conducted using the 4DCT and SPECT-V images acquired for 15 non-small cell lung cancer patients prior to radiotherapy. For each test case, MCVC and IJF CT-ventilation images were created for 30 different uncertainty parameter values, uniformly sampled from the range 0.01,0.25 . Voxel-wise Spearman correlation between the SPECT-V and the resulting CT-ventilation images was computed.ResultsThe median correlations between MCVC and SPECT-V ranged from 0.20 to 0.48 across the parameter sweep, while the median correlations for IJF and SPECT-V ranged between 0.79 and 0.82. For the optimal IJF tolerance τ=0.07 , the IJF and SPECT-V correlations across all 15 test cases ranged between 0.12 and 0.90. For the optimal MCVC tolerance τ=0.03 , the MCVC and SPECT-V correlations across all 15 test cases ranged between -0.06 and 0.84.ConclusionThe reported correlations indicate that robust methods generate ventilation images that are spatially consistent with SPECT-V, with the transformation-based IJF method yielding higher correlations than those previously reported in the literature. For both methods, overall correlations were found to marginally vary for τ∈[0.03,0.15] , indicating that the clinical utility of both methods is robust to both uncertainty tolerance and DIR solution.

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