Shape Features

A dimensionless shape feature measuring how closely the three-dimensional shape of a tumor approximates a perfect sphere. It is calculated as the ratio of the surface area of a sphere with the same volume as the tumor to the actual surface area of the tumor.

• Value Range: 0 to 1, where 1 is a perfect sphere.
• Clinical Relevance: High sphericity is often associated with benignity or a less aggressive phenotype, while low sphericity indicates an irregular, invasive margin.
• Calculation: Sensitive to segmentation smoothness; mesh-based computation is preferred over voxel-based methods to avoid discretization errors.

A measure of how efficiently the tumor volume is packed relative to its surface area, independent of scale. It is mathematically defined as Volume / (√π * Surface Area^(3/2)), comparing the shape to a sphere.

• Alternative Formulations: Compactness 1 and Compactness 2 are defined by the IBSI, using different normalization factors based on sphere or cube references.
• Interpretation: A highly compact mass has a low surface-area-to-volume ratio, suggesting a solid, cohesive growth pattern rather than a spiculated or infiltrative one.

The largest pairwise Euclidean distance between any two voxels on the surface mesh of the segmented region of interest. This is a fundamental measure of tumor burden.

• Utility: Used in oncology standards like RECIST (Response Evaluation Criteria in Solid Tumors) for assessing treatment response, though RECIST traditionally uses 1D axial measurements.
• Robustness: Highly robust to minor segmentation variations but sensitive to the presence of non-tissue outliers in the mask.

A fundamental descriptor of morphological complexity, calculated by dividing the total surface area of the segmented object by its volume. It provides insight into the irregularity of the tumor boundary.

• Biological Correlate: A high SA:V ratio indicates a highly irregular, spiculated, or infiltrative margin, which is a hallmark of aggressive malignancies.
• Scale Dependence: Unlike sphericity, this metric is not dimensionless and is inherently dependent on the overall size of the lesion, requiring careful normalization in multi-center studies.

The volume enclosed by the triangulated surface mesh of the region of interest, computed using the divergence theorem. This is distinct from simple voxel counting, which can be biased by partial volume effects.

• Method: The volume is calculated by summing the signed volumes of tetrahedra formed by connecting each mesh triangle to the origin.
• Precision: Mesh-based volume is the gold standard in radiomics as it provides a sub-voxel approximation of the true boundary, reducing the stair-step artifacts inherent in voxel-based volume.

A shape feature that quantifies the relationship between the longest and shortest principal axes of the region of interest, derived from an eigenvalue decomposition of the physical coordinates.

• Calculation: Defined as sqrt(λ_minor / λ_major), where λ represents the eigenvalues of the principal component analysis.
• Interpretation: A value close to 0 indicates a flat, elongated, or sheet-like structure, while a value close to 1 suggests a more equiaxed or spherical shape. This is critical for distinguishing between nodular and diffuse growth patterns.