IV.3 Modelling the Development of Complex Tissues using Individual Viscoelastic Cells

This chapter describes a biomechanical model of individual deformable viscoelastic cells that can be arranged into tissues of various topologies. The model is based on an immersed boundary method with distributed sources and couples a continuous description of a viscous incompressible cytoplasm with the dynamics of separate elastic cells. Several key cellular processes, such as cell growth, division, apoptosis and polarisation, are also defined within this framework. This approach enables one to focus on the biomechanical properties of individual cells and on communication between cells and their microenvironment, and to investigate how individual cells cooperate and contribute to the overall structure and function of a particular tissue. Three applications of this model are presented: the folding of a trophoblast bilayer, clonal tumoural growth and self-arrangement into a hollow acinus, the hollow multicellular sphere. Further extensions of this model are also discussed.