Biomechanical modeling of invasive breast carcinoma under a dynamic change in cell phenotype: collective migration of large groups of cells

  • Dmitry A. BratsunEmail author
  • Ivan V. Krasnyakov
  • Len M. Pismen
Original Paper


According to recent studies, cancer is an evolving complex ecosystem. It means that tumor cells are well differentiated and involved in heterotypic interactions with their microenvironment competing for available resources to proliferate and survive. In this paper, we propose a chemo-mechanical model for the growth of specific subtypes of an invasive breast carcinoma. The model suggests that a carcinoma is a heterogeneous entity comprising cells of different phenotypes, which perform different functions in a tumor. Every cell is represented by an elastic polygon changing its form and size under pressure from the tissue. The mechanical model is based on the elastic potential energy of the tissue including the effects of contractile forces within the cell perimeter and the elastic resistance to stretching or compressing the cell with respect to the reference area. A tissue can evolve via mechanisms of cell division and intercalation. The phenotype of each cell is determined by its environment and can dynamically change via an epithelial–mesenchymal transition and vice versa. The phenotype defines the cell adhesion to the adjacent tissue and the ability to divide. In this part, we focus on the forms of collective migration of large groups of cells. Numerical simulations show the different architectural subtypes of invasive carcinoma. For each communication, we examine the dynamics of the cell population and evaluate the complexity of the pattern in terms of the synergistic paradigm. The patterns are compared with the morphological structures previously identified in clinical studies.


Cancer modeling Special subtypes of invasive breast carcinoma Collective cell migration Tumor structures Epithelial–mesenchymal transition 



We are grateful to Dr. Brazhe for sharing his open-source Python-based software for calculating the complexity of textures. We also thank the efforts of two anonymous referees whose many constructive comments lead to a number of improvements to the manuscript.


This study was funded by the Ministry of Science and High Education of Russian Federation (Grant No. 3.6990.2017/8.9).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied PhysicsPerm National Research Polytechnic UniversityPermRussia
  2. 2.Israel Institute of Technology – TechnionHaifaIsrael

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