The complexity of tumor shape, spiculatedness, correlates with tumor radiomic shape features

Radiomics extracts high-throughput quantitative data from medical images to contribute to precision medicine. Radiomic shape features have been shown to correlate with patient outcomes. However, how radiomic shape features vary in function of tumor complexity and tumor volume, as well as with method used for meshing and voxel resampling, remains unknown. The aims of this study are to create tumor models with varying degrees of complexity, or spiculatedness, and evaluate their relationship with quantitatively extracted shape features. Twenty-eight tumor models were mathematically created using spherical harmonics with the spiculatedness degree d being increased by increments of 3 (d = 11 to d = 92). Models were 3D printed with identical bases of 5 cm, imaged with a CT scanner with two different slice thicknesses, and semi-automatically delineated. Resampling of the resulting masks on a 1 × 1 × 1 mm³ grid was performed, and the voxel size of each model was then calculated to eliminate volume differences. Four MATLAB-based algorithms (isosurface (M1), isosurface filter (M2), isosurface remeshing (M3), and boundary (M4)) were used to extract nine 3D features (Volume, Surface area, Surface-to-volume, Compactness1, Compactness2, Compactness3, Spherical Disproportion, Sphericity and Fractional Concavity). To quantify the impact of 3D printing, acquisition, segmentation and meshing, features were computed directly from the stereolithography (STL) file format that was used for 3D printing, and compared to those computed. Changes in feature values between 0.6 and 2 mm slice acquisitions were also compared. Spearman's rank-order correlation coefficients were computed to determine the relationship of each shape feature with spiculatedness for each of the four meshing algorithms. Percent changes were calculated between shape features extracted from the original and resampled contoured images to evaluate the influence of spatial resampling. Finally, the percent change in shape features when the volume was changed from 25% to 150% of their original volume was quantified for three distinct tumor models and compared to the percent change observed when modifying the spiculatedness of the model from d = 11 to d = 92. Values extracted using isosurface remeshing method are the closest to the STL reference ones, with mean differences less than 10.8% (Compactness2) for all features. Seven of the eight features had strong significant correlations with tumor model complexity irrespective of the meshing algorithm (r > 0.98, p < 10^-4), with fractional concavity having the lowest correlation coefficient (r = 0.83, p < 10^-4, M2). Comparisons of features extracted from the 0.6 and 2 mm slice thicknesses showed that mean differences were from 2.1% (Compactness3) to 12.7% (Compactness2) for the isosurface remeshing method. Resampling on a 1 × 1 × 1 mm³ grid resulted in between 1.3% (Compactness3) to 9.5% (Fractional Concavity) mean changes in feature values. Compactness2, Compactness3, Spherical Disproportion, Sphericity and Fractional Concavity were the features least affected by volume changes. Compactness1 had a 90.4% change with volume, which was greater than the change between the least and most spiculated models. This is the first methodological study that directly demonstrates the relationship of tumor spiculatedness with radiomic shape features, that also produced 3D tumor models, which may serve as reference phantoms for future radiomic studies. Surface Area, Surface-to-volume, and Spherical Disproportion had direct relationships with spiculatedness while the three formulas for Compactness, Sphericity and Fractional Concavity had inverse relationships. The features Compactness2, Compactness3, Spherical Disproportion, and Sphericity should be prioritized as these have minimal variations with volume changes, slice thickness and resampling.