The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer
The morphological method—based on the topology and singularity theory and originally developed for the analysis of the scattering experiments—was extended to be applicable for the analysis of biological data. The usefulness of the topological viewpoint was demonstrated by quantification of the chang...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-07-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2022.915644/full |
| _version_ | 1818532769623441408 |
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| author | Sanja Z. Despotović M. Ćosić |
| author_facet | Sanja Z. Despotović M. Ćosić |
| author_sort | Sanja Z. Despotović |
| collection | DOAJ |
| description | The morphological method—based on the topology and singularity theory and originally developed for the analysis of the scattering experiments—was extended to be applicable for the analysis of biological data. The usefulness of the topological viewpoint was demonstrated by quantification of the changes in collagen fiber straightness in the human colon mucosa (healthy mucosa, colorectal cancer, and uninvolved mucosa far from cancer). This has been done by modeling the distribution of collagen segment angles by the polymorphic beta-distribution. Its shapes were classified according to the number and type of critical points. We found that biologically relevant shapes could be classified as shapes without any preferable orientation (i.e. shapes without local extrema), transitional forms (i.e. forms with one broad local maximum), and highly oriented forms (i.e. forms with two minima at both ends and one very narrow maximum between them). 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-aware/based, measure of the collagen straightness, which revealed a slight and moderate increase of the straightness in mucosa samples taken 20 and 10 cm away from the tumor. The largest increase of collagen straightness was found in samples of cancer tissue. Samples of healthy individuals have a uniform distribution of beta-distribution forms. We found that this distribution has the maximal information entropy. 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 leaving 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. This work shows that the evolution of the distribution of the beta-distribution forms—an abstract construction of the mind—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, clearly visible in the parametric space of the beta-distribution and very difficult to notice in the observable space, can be a useful indicator of the early stages in the development of colorectal cancer. |
| first_indexed | 2024-12-11T17:49:51Z |
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| id | doaj.art-21696fa462954578adfe26cd21cc9b67 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-11T17:49:51Z |
| publishDate | 2022-07-01 |
| publisher | Frontiers Media S.A. |
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| series | Frontiers in Physics |
| spelling | doaj.art-21696fa462954578adfe26cd21cc9b672022-12-22T00:56:15ZengFrontiers Media S.A.Frontiers in Physics2296-424X2022-07-011010.3389/fphy.2022.915644915644The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the CancerSanja Z. Despotović0M. Ćosić1Faculty of Medicine, Institute of Histology and Embryology, The University of Belgrade, Belgrade, SerbiaLaboratory of Physics, Vinča Institute of Nuclear Sciences—National Institute of Thе Republic of Serbia, The University of Belgrade, Belgrade, SerbiaThe morphological method—based on the topology and singularity theory and originally developed for the analysis of the scattering experiments—was extended to be applicable for the analysis of biological data. The usefulness of the topological viewpoint was demonstrated by quantification of the changes in collagen fiber straightness in the human colon mucosa (healthy mucosa, colorectal cancer, and uninvolved mucosa far from cancer). This has been done by modeling the distribution of collagen segment angles by the polymorphic beta-distribution. Its shapes were classified according to the number and type of critical points. We found that biologically relevant shapes could be classified as shapes without any preferable orientation (i.e. shapes without local extrema), transitional forms (i.e. forms with one broad local maximum), and highly oriented forms (i.e. forms with two minima at both ends and one very narrow maximum between them). 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-aware/based, measure of the collagen straightness, which revealed a slight and moderate increase of the straightness in mucosa samples taken 20 and 10 cm away from the tumor. The largest increase of collagen straightness was found in samples of cancer tissue. Samples of healthy individuals have a uniform distribution of beta-distribution forms. We found that this distribution has the maximal information entropy. 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 leaving 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. This work shows that the evolution of the distribution of the beta-distribution forms—an abstract construction of the mind—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, clearly visible in the parametric space of the beta-distribution and very difficult to notice in the observable space, can be a useful indicator of the early stages in the development of colorectal cancer.https://www.frontiersin.org/articles/10.3389/fphy.2022.915644/fullmorphological analysispattern formationtype I collagencollagen straightnesscolorectal cancer |
| spellingShingle | Sanja Z. Despotović M. Ćosić The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer Frontiers in Physics morphological analysis pattern formation type I collagen collagen straightness colorectal cancer |
| title | The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer |
| title_full | The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer |
| title_fullStr | The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer |
| title_full_unstemmed | The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer |
| title_short | The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer |
| title_sort | morphological analysis of the collagen fiber straightness in the healthy uninvolved human colon mucosa away from the cancer |
| topic | morphological analysis pattern formation type I collagen collagen straightness colorectal cancer |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2022.915644/full |
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