Study of architectural forms of invasive carcinoma based on the measurement of pattern complexity

Dmitry Bratsun¹ ; Ivan Krasnyakov¹

¹ Department of Applied Physics, Perm National Research Polytechnic University, 614990 Perm, Russia

Mathematical modelling of natural phenomena, Tome 17 (2022), article no. 15.

Résumé

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.

Détail

DOI : 10.1051/mmnp/2022013

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