Three-dimensional shape and topology analysis of tissue-cleared tumor samples

Purpose: We developed a semi-automated framework to obtain numerical descriptors of surface morphology and topology from volumetric microscopy of human cleared cancer tissues to enable quantitative studies of 3D tumor microarchitecture. Methods: Individual slices of immunolabeled confocal or light-sheet microscopic images of cleared cancer tissue samples are first segmented using the Chan-Vese morphological snake method. Then, the Marching Cubes algorithm is used to generate 3D models of the tumors. Surface area-volume ratio (SAV) of the 3D models is computed using the discrete divergence theorem. Geometries of model centerlines (obtained as shortest paths of maximal inscribed spheres) are quantified in terms of their curvature, torsion, and bifurcations angles. Topological analysis is performed on 3D point clouds generated by uniformly sampling the 3D models. Vietoris-Rips (VR) simplicial complexes of the point clouds are constructed, and their persistent diagrams are used to compute the lifetime of homological features such as connected components, loops, and voids. The framework is applied to cleared samples of extrahepatic cholangiocarcinoma labeled with CK19. Specifically, we investigate whether the proposed quantitative descriptors of tumor microarchitecture can differentiate cancers showing low-grade (LG) tumor budding (TB) from those presenting high-grade (HG) TB. Results: The proposed framework yielded 3D surface models of the tumors that retained the major morphological features (e.g., glands and protrusions) observable in the microscopic image stacks. Initial evidence from quantitative analysis of the 3D models (3 samples each of HG and LG tumors) indicates quantitative differences in the microarchitecture of HG and LG cancer tissues. The average SAV ratio of HG tumors was 0.153±0.0036 μm-1 compared to 0.235±0.0089 μm-1 for LG samples. Analysis of centerline geometries found less curvature in HG samples compared to LG (average curvature of 15.87±0.122 mm-1 vs. 20.87±0.122 mm-1), less torsion (51.54±1.077 mm-1 vs. 62.73±1.120 mm-1), and narrower bifurcation angles (0.543±0.0303 rads vs. 0.671±0.0281 rads). Persistent homology, via VR filtration, indicated that the connected components (homological dimension H0) have longer lifetime in LG tumors (mean lifetime 0.0349 ±0.00297) than in HG ones (mean lifetime 0.0284 ±0.00307). Conclusion: The proposed quantitative analysis framework yields potential geometrical and topological descriptors for statistical analysis of the rich 3D imaging data made available by the application of tissue clearing to human tumor samples.