On Complexity and Topology Measures for Evaluation of Intercellular Connectivity in Human Colon Adenocarcinomas

We report here on the results of co-application of complexity and topological measures in the evaluation of intercellular connectivity; a critical feature of cancer cells that determines their metastatic potential. We studied fractal geometry and topology of intestinal crypts in 10 different specimens of human normal colon and in 40 colon carcinomas. Our findings confirm the previous observations made in a model of prostate carcinomas. The natural evolution of the spatial structure in carcinomas is determined by increasing values of entropy and goes towards increased complexity. Intercellular connectivity in colon carcinomas is decreased in comparison with normal intestinal crypts. That conclusion is supported by changes in both global and local measures of complexity as well as topology. The values of both the global and local spatial fractal dimensions are increased and the values of the 1st-Betti numbers are decreased. At the local scale, one observes variability of the local clustering coefficient from zero to one. The combination of complexity and topology measures enables the objective selection of the reference set of carcinomas for the quantitative evaluation of biological tumor aggressiveness by convoluted neural network.