Math. Model. Nat. Phenom.
Volume 17, 2022
|Number of page(s)||21|
|Published online||16 June 2022|
Study of architectural forms of invasive carcinoma based on the measurement of pattern complexity
Department of Applied Physics, Perm National Research Polytechnic University,
* Corresponding author: firstname.lastname@example.org
Accepted: 6 April 2022
Several years ago, a new paradigm of cancer perception emerged, considering a tumor not as a senseless heap of cells but as a self-organizing heterogeneous tissue of cancer cells that collectively fight for survival. It implies that the various architectural forms that a tumor takes during its growth are not occasional but are a synergistic response of a group of cancer cells in competition for the organism’s resources. In this work, we generate various patterns of a two-dimensional tumor using our previously developed individual-based model mimicking carcinoma features. Every cell is represented by a polygon dynamically changing its form and size. The dynamics of tissue are governed by the elastic potential energy. We numerically obtain various patterns of carcinoma and estimate empirical spatial entropy and complexity measures applying the approach based on the fast finite shearlet transform. We show how the complexity of growing carcinoma changes over time and depending on the values of the cell intercalation parameters. In each case, we give a rational explanation of why this form is beneficial to the tumor. Our results show that one can use complexity measurements for quantitative classification of tumors obtained in silico, which potentially could find its application in medical practice.
Mathematics Subject Classification: 92C17
Key words: Tumor structures / collective cell migration / cancer modeling / complexity measurement
© The authors. Published by EDP Sciences, 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.