Volumetric analysis of pulmonary nodules: reducing the discrepancy between the diameter-based volume calculation and voxel-counting method

Background: When assessing the volume of pulmonary nodules on computed tomography (CT) images, there is an inevitable discrepancy between values based on the diameter-based volume calculation and the voxel-counting method, which is derived from the Euclidean distance measurement method on pixel/voxelbased digital image. We aimed to evaluate the ability of a modified diameter measurement method to reduce the discrepancy, and we determined a conversion equation to equate volumes derived from different methods. Methods: Two different anthropomorphic phantoms with subsolid and solid nodules were repeatedly scanned under various settings. Nodules in CT images were detected and segmented using a fully automated algorithm and the volume was calculated using three methods: the voxel-counting method (V-vc), diameter based volume calculation (V-d), and a modified diameter-based volume calculation (Vd+1), in which one pixel spacing was added to the diameters in the three axes (x-, y-, and z-axis). For each nodule, V-d and Vd+1 were compared to Vvc by computing the absolute percentage error (APE) as follows: APE =100 x (V - V-vc)/V-vc. Comparisons between APEd and APEd+1 according to CT parameter setting were performed using the Wilcoxon signed-rank test. The Jonckheere-Terpstra test was used to evaluate trends across the four different nodule sizes. Results: The deep learning-based computer-aided diagnosis (DL-CAD) successfully detected and segmented all nodules in a fully automatic manner. The APE was significantly less with Vd+1 than with V-d (Wilcoxon signed-rank test, P<0.05) regardless of CT parameters and nodule size. The APE median increased as the size of the nodule decreased. This trend was statistically significant (Jonckheere-Terpstra test, P<0.001) regardless of volume measurement method (diameter-based and modified diameter-based volume calculations). Conclusions: Our modified diameter-based volume calculation significantly reduces the discrepancy between the diameter-based volume calculation and voxel-counting method.