RESUMEN
I am Ivan Krasnyakov, a senior lecturer at the Department of Applied Physics at Perm National Research Polytechnic University. I hold a degree of Candidate of Physical and Mathematical Sciences. My main area of research revolves around the biophysics of multicellular tissues. One of my initial research projects focused on creating a mathematical model to understand the growth of carcinoma. What intrigued me was the fresh perspective from clinical medicine researchers regarding the spatial structure of tumors. It was discovered that tumors display cellular heterogeneity and undergo self-organization, forming diverse architectural patterns during their development. At the moment, I continue to develop our model.
RESUMEN
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.