  Organogenesis has been studied for decades, but fundamental questions
regarding the control of growth and shape remain unsolved. We have recently
shown that of all proposed mathematical models only ligand-receptor based
Turing models successfully reproduce the experimentally determined growth
fields of the embryonic lung and thus provide a mechanism for growth control
during embryonic lung development. Turing models are based on at least two
coupled non-linear reaction-diffusion equations. In case of the lung model, at
least two distinct layers (mesenchyme and epithelium) need to be considered
that express different components (ligand and receptor, respectively). The
Arbitrary Lagrangian-Eulerian (ALE) method has previously been used to solve
this Turing system on growing and deforming (branching) domains, where
outgrowth occurs proportional to the strength of ligand-receptor signalling.
However, the ALE method requires mesh deformations that eventually limit its
use. Therefore, we incorporate the phase field method to simulate 3D embryonic
lung branching with COMSOL.
