Mapping Tumor Heterogeneity via Local Entropy Assessment: Making Biomarkers Visible

Advanced imaging and analysis improve prediction of pathology data and outcomes in several tumors, with entropy-based measures being among the most promising biomarkers. However, entropy is often perceived as statistical data lacking clinical significance. We aimed to generate a voxel-by-voxel visual map of local tumor entropy, thus allowing to (1) make entropy explainable and accessible to clinicians; (2) disclose and quantitively characterize any intra-tumoral entropy heterogeneity; (3) evaluate associations between entropy and pathology data. We analyzed the portal phase of preoperative CT of 20 patients undergoing liver surgery for colorectal metastases. A three-dimensional core kernel (5 × 5 × 5 voxels) was created and used to compute the local entropy value for each voxel of the tumor. The map was encoded with a color palette. We performed two analyses: (a) qualitative assessment of tumors' detectability and pattern of entropy distribution; (b) quantitative analysis of the entropy values distribution. The latter data were compared with standard Hounsfield data as predictors of post-chemotherapy tumor regression grade (TRG). Entropy maps were successfully built for all tumors. Metastases were qualitatively hyper-entropic compared to surrounding parenchyma. In four cases hyper-entropic areas exceeded the tumor margin visible at CT. We identified four "entropic" patterns: homogeneous, inhomogeneous, peripheral rim, and mixed. At quantitative analysis, entropy-derived data (percentiles/mean/median/root mean square) predicted TRG (p < 0.05) better than Hounsfield-derived ones (p = n.s.). We present a standardized imaging technique to visualize tumor heterogeneity built on a voxel-by-voxel entropy assessment. The association of local entropy with pathology data supports its role as a biomarker.