Simulating tissue morphogenesis and signaling.

During embryonic development tissue morphogenesis and signaling are tightly coupled. It is therefore important to simulate both tissue morphogenesis and signaling simultaneously in in silico models of developmental processes. The resolution of the processes depends on the questions of interest. As part of this chapter we introduce different descriptions of tissue morphogenesi s. In the simplest approximation tissue is a continuous domain and tissue expansion is described according to a predefined function of time (and possibly space). In a slightly more advanced version the expansion speed and direction of the tissue may depend on a signaling variable that evolves on the domain. Both versions will be referred to as "prescribed growth." Alternatively tissue can be regarded as incompressible fluid and can be described with Navier-Stokes equations. Local cell expansion, proliferation, and death are then incorporated by a source term. In other applications the cell boundaries may be important and cell-based models must be introduced. Finally, cells may move within the tissue, a process best described by agent-based models.