Robust HU-based CT ventilation from an integrated mass conservation formulation

Computed tomography (CT) ventilation algorithms estimate volume changes induced by respiratory motion. Existing Hounsfield Unit (HU) methods approximate volume change from the measured HU variations between spatially corresponding voxel locations within a temporally resolved CT image pair, assuming that volume changes are caused solely by changes in air content. Numerical implementations require a deformable image registration to determine the inhale/exhale spatial correspondence, a preprocessing lung volume segmentation, a preprocessing high-intensity vessel segmentation, and a post-processing smoothing applied to the raw volume change estimates obtained for each lung tissue voxel.

We introduce the novel mass-conserving volume change (MCVC) method for estimating voxel volume changes from the HU values within an inhale/exhale CT image pair. MCVC is based on subregional volume change estimates that possess quantitatively characterized and controllable levels of uncertainty. MCVC is therefore robust to small variations in DIR solutions and the resulting ventilation images are overall more reproducible. In contrast to existing HU methods, MCVC does not require a preprocessing lung vessel segmentation or pre/post-processing Gaussian smoothing.

Subregional volume change estimates are defined in terms of mean density ratios. As such, the corresponding uncertainty is characterized using Gaussian statistics and standard error analysis of the sample density means. A numerical solution is obtained from the MCVC formulation by solving a constrained linear least squares problem defined by a series of subregional volume change estimates. Reproducibility of the MCVC method with respect to DIR solution was assessed using expert-determined landmark point pairs and inhale/exhale phases from 10 four-dimensional CTs (4DCTs) available on www.dir-lab.com. MCVC was also compared to the robust Integrated Jacobian Formulation (IJF), a transformation-based ventilation method.

The ten Dir-Lab 4DCT cases were registered twice with the same DIR algorithm, but using different degrees of freedom (DIR 1 and DIR 2). Standard HU ventilation (HUV) and MCVC ventilation images were computed for both solutions. The average spatial errors (300 landmarks per case) for DIR 1 ranged between 0.74 and 1.50 mm, whereas for DIR 2 they ranged between 0.68 and 1.18 mm. Despite the differences in spatial errors between the two DIR solutions, the average Pearson correlation between the corresponding HUV images was 0.94 (0.03), while for the MCVC images it was 1.00 (0.00). The average correlation between MCVC and IJF ventilation over the ten test cases was 0.81 (0.14), whereas for HUV and IJF it was 0.56 (1.11).

While HUV is robust to DIR solution, its implementation depends on heuristic Gaussian smoothing and vessel segmentation. MCVC is based on subregional volume change measurements with quantifiable and controllable levels of uncertainty. The subregional approach eliminates the need for Gaussian smoothing and lung vasculature segmentation. Numerical experiments are consistent with the underlying mathematical theory and indicate that MCVC ventilation is more reproducible with respect to DIR algorithm than standard HU methods. MCVC results are also more consistent with the robust IJF method, which suggests that incorporating robustness leads to more consistent results across both DIRs and ventilation algorithms.