Fig. 9.

Formation of a duct by the mathematical model. A) cells are represented in green and the ductal lumen in orange, in three dimensions and over time. B) depiction of a plane of the model over time. The lines represent collagen orientation; shorter lines mean that the orientation of collagen is mostly along the vertical axis. Circles represent cells, and crosses represent lumen. Cells organize collagen over time by exerting forces, and collagen constrains cell proliferation and motility. These interactions lead to the emergence of a main direction of growth. See also corresponding Videos 5 and 6.