The model describes the elongation over time of an axon from a small neurite to its steady-state length. The elongation depends on the availability of tubulin dimers in the growth cone. The dimers are produced in the soma and then transported along the axon to the growth cone.
Mathematically the model consists of a partial differential equation coupled with two nonlinear ordinary differential equations.
The code implements a spatial scaling to deal with the growing (and shrinking) domain and a temporal scaling to deal with evolutions on different time scales. Further, the numerical scheme is chosen to fully utilize the structure of the problems. To summarize, this results in fast and reliable axon growth simulations.
Diehl S, Henningsson E, Heyden A (2016) Efficient simulations of tubulin-driven axonal growth. J Comput Neurosci [PubMed]