Mapping Tumor Heterogeneity via Local Entropy Assessment: Making Biomarkers Visible
Guido Costa, Lara Cavinato, Francesco Fiz, Martina Sollini, Arturo Chiti, Guido Torzilli, Francesca Ieva, Luca Viganò
Abstract
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.