  During organogenesis tissue grows and deforms. The growth processes are
controlled by diffusible proteins, so-called morphogens. Many different
patterning mechanisms have been proposed. The stereotypic branching program
during lung development can be recapitulated by a receptor-ligand based Turing
model. Our group has previously used the Arbitrary Lagrangian-Eulerian (ALE)
framework for solving the receptor-ligand Turing model on growing lung domains.
However, complex mesh deformations which occur during lung growth severely
limit the number of branch generations that can be simulated. A new Phase-Field
implementation avoids mesh deformations by considering the surface of the
modelling domains as interfaces between phases, and by coupling the
reaction-diffusion framework to these surfaces. In this paper, we present a
rigorous comparison between the Phase-Field approach and the ALE-based
simulation.
