Morphogenesis of growing tubes

Formation, remodeling and shaping of growing tubes is a ubiquitous phenomenon observed during embryo development. Common examples include gastrulation, vascularization, and development of guts and lungs. The shaping of tubes typically occurs in response to patterned biochemical processes, which can produce mechanical forces either directly via molecular motors (e.g. the apical constriction in gastrulation) or indirectly via differential growth of connected tissues. The growth mismatch produces internal stresses, which can be released via shape transformations and mechanical instabilities, such as the formation of vili inside guts. Motivated by recent experiments, our goal is to construct a minimal mathematical model that will capture the processes involved in the branching morphogenesis of lungs. Our starting model are simple tubes constructed from an individual epithelium surrounded by the mesenchyme tissue. We investigate how patterned differential growth between the inner epithelium and the outer mesenchyme tissue can lead to formation of new branches and their subsequent development. I will also comment how stiff smooth muscles can be incorporated into our model, which will help us investigate what is the functional role of smooth muscles during the branching morphogenesis.