Mathematical modeling of invasive carcinoma under conditions of anisotropy of chemical fields: budding and migration of cancer cells

The recent decade is known for changes in approaches to malignant tumor treatment. It has become known that a tumor is a heterogeneous agglomeration of cancer cells and can develop different spatial structures for collective invasion and migration over the course of its evolution Cancer cell budding at the invasive front of a tumor is one of the processes which determine its malignant nature. A new approach to tumor and its manifested effects in its evolution should be examined both with the medical methods and the methods of mathematical modeling. The methods of mathematical modeling applied in studies of malignant entities help observe the processes in their dynamics running during tumor growth. We develop a mathematical model of heterogeneous invasive carcinoma growth. The model derives from the model of a cell with its individual dynamics that enables us to describe the object under analysis in detail to some extent. Modeling reproduces the effect of budding during the growth of a cribriform carcinoma. This has been qualitatively compared with the results of clinical studies of histological sections. We also measured quantitative characteristics, the index of epithelial-mesenchymal transition which is compared with a cell phenotype in epithelial tissue. The paper shows dynamics in the development of cells-buds, their migration near the tumor front, and amoeboid migration in epithelial tissue. The paper also describes the development of a second tumor source triggered by the mesenchymal-epithelial transition. The results of the study demonstrate the dynamics in the development of malignant entities and their inherent effects.