The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer - Despotović, Sanja Z.; Ćosić, M. (Frontiers in Physics, 2022)
The morphological method, based on the topology and singularity theory, was extended to be applicable for the analysis of biological data. The usefulness of the topological viewpoint was demonstrated by quantification of collagen fiber straightness in the human colon mucosa (healthy mucosa, colorectal cancer, and uninvolved mucosa far from cancer). This was achieved by modeling the distribution of collagen segment angles by the polymorphic beta-distribution. Biologically relevant shapes were observed as shapes without preferable orientation, transitional forms and highly oriented forms. Thus, changes in the fiber organization were linked to the metamorphoses of the beta-distribution forms. The obtained classification was used to define a new, shape-based, measure of the collagen straightness. At 20 cm and 10 cm away from cancer, the transition forms redistribute into unoriented and highly oriented forms. Closer to cancer the number of unoriented forms decreases rapidly living only highly oriented forms present in the samples of the cancer tissue, whose distribution has minimal information entropy. The polarization of the distribution was followed by a significant increase in the number of quasi-symmetrical forms in samples 20 cm away from cancer which decreases closer to cancer. Evolution of the distribution of the beta-distribution forms follows the familiar laws of statistical mechanics. Additionally, the polarization of the beta-distribution forms together with the described change in the number of quasi-symmetrical forms, can be an useful indicator of the early stages in the development of colorectal cancer.