The math behind organ growth.

Organogenesis is a tightly regulated process that has been studied experimentally for decades. Computational models can help to integrate available knowledge and to better understand the underlying regulatory logic. We are currently studying mechanistic models for the development of limbs, lungs, kidneys, and bone. We have tested a number of alternative methods to solve our spatio- temporal differential equation models of reaction-diffusion type on growing domains of realistic shape, among them finite elements in COMSOL Multiphysics. Given the large number of variables (up to fifteen), the sharp domain boundaries, the travelling wave character of some solutions, and the stiffness of the reactions we are facing numerous numerical challenges. To test new ideas efficiently we have developed a strategy to optimize simulation times in COMSOL.

http://arxiv.org/abs/1202.0428