Elasticity-based targeted growth models of morphogenesis

Embryonic tissue mechanics play an important role in regulating morphogenesis during organ formation, both in a bottom-up sense, where changes in gene expression drive mechanical shape changes, and in a topdown sense, where perturbations in tissue mechanics feed back to drive changes in gene expression. In growing tissues that can generate internal forces and have complex geometries, like those in the embryo, it can often be difficult to empirically determine the mechanical state of the tissue, let alone the relationships between gene expression and mechanical behavior. Mathematical models can be used to fill this gap. Here, we discuss elasticity-based models for growing tissues with a specific focus on targeted growth in embryonic tissues.