Mathematical modelling of the formation of small cell groups of invasive carcinoma

According to the latest research, cancer is a complex biosystem that develops in time and space. This means that cancer cells differ from each other in their function in the tumor. They are involved in various interactions with their microenvironment and compete for available nutrients for reproduction and survival. Identifying a specific structural type in the growth of a malignant tumor is one of the main problems today in oncology. The other no less important problem of mathematical modelling in oncology is the heterogeneity of a malignant neoplasm. In this work, we propose a chemomechanical model of the structure formation of small groups of cancer cells of invasive carcinoma of a non-special type. The model suggests that carcinoma is a heterogeneous mass of cells of different phenotypes that perform different functions in the tumor. Each cell is represented by an elastic polygon that changes its shape and size as the tissue develops. Numerical modelling implements various subtypes of invasive carcinoma of a non-special type structure. The patterns are compared with morphological structures previously identified in clinical studies.