Limit behaviour of spatially growing cell cultures

Growing cell cultures often exhibit branch patterns. The cultures are usually modelled as free boundary problems. Here, we review some of these models and investigate the appearance of branch patterns using methods from asymptotic analysis. Two extreme cases—large kinetics and small kinetics—are considered. For large kinetics the models reduce to the well-studied Stefan problem, which is known to exhibit a diffusive-instability and hence shows branch patterns. Considering small kinetics, small perturbations are smoothed out resulting in regular shapes of the cultures. The branching phenomenon in general can be understood as somewhere between these two extremes. Not relying on special assumptions, the presented analysis is very general.