Biomechanical models of living tissue

The evolution of living things has led to the emergence of multicellular organisms in which cells differentiate, specializing in performing various functions. Cells interact and unite into large groups, forming tissues and transferring the control function to an organ or organism. In fact, the latter is a complex biomechanical system controlled by chemical and mechanical signals. The development of computer technologies and high-speed computing systems gradually leads to the possibility of realistic modeling of the biomechanics of cellular tissue, which reproduces both the averaged dynamics of the tissue and the behavior of cells. Mathematical modeling allows us to study the historical aspects of the evolution of living things, describe the morphogenesis of specific organisms, understand the healing processes in organs when they are damaged, consider the appearance of tumors, and develop the technology for artificial tissue growth. This paper presents an overview of works devoted to mathematical models of multicellular tissue of living organisms. Specifically, we focus on those models where the cell is a structural unit of a complex system. We classify biomechanical models according to the approach describing the tissue, the method of constructing cells, and the dimension of the tissue formed by the cells. We discuss the interaction forces between cells and topological rearrangements in tissue during intense cell movement. Finally, we discuss the results of some selected applied research.