Microscopic simulation of the chemomechanics of squamous cell tissue

The development of computer technologies makes it possible to implement a mathematical model of tissue dynamics, which includes the behavior of individual cells. The paper describes a mathematical model of a quasi-two-dimensional tissue, which consists of cells represented by dynamically changing polygons. The model includes two important processes that mimic the properties of real cells, namely mitotic division and intercalation. An equation of motion based on the elastic potential energy is written for each vertex of the polygonal cell. In the course of evolution, the tissue tends to take a position corresponding to the minimum of potential energy. The model allows a simple extension to the case of the feedback between the biomechanical and chemical properties of the medium and the introduction of several competing tissue types. The results of numerical simulation of heterogeneous carcinoma of the solid type are given as an example. The prospects for the development of this approach to simulation are discussed.