Invasion occurs preferentially at the ends of cylindrical ducts.

(A) 0.5% probability of apoptosis, mitosis every 48 MCS, and random cell division: morphology begins as micropapillary and develops into cribriform with necrotic cells in the center and some invasion. Eventually the tissue becomes comedo. (B) 1% probability of apoptosis, mitosis every 32 MCS, and random cell division: morphology begins as micropapillary and develops into cribriform. As the tissue expands there are some necrotic cells in the duct and some cells break through the myoepithelial layer. (C) 0.5% probability of apoptosis, mitosis every 48 MCS, random cell division, and preferential proliferation: morphology begins as micropapillary and develops into cribriform morphology in the duct region with comedo morphology and invasion at the ends. Eventually the entire tissue becomes comedo. (D) 1% probability of apoptosis, mitosis every 32 MCS, random cell division, and preferential proliferation: morphology begins as micropapillary and develops into cribriform. As the tissue expands there are some necrotic cells in the duct and some cells break through the MEP layer. Quantification of tissues with invasion at the end and the duct region of each tissue at (E) 2000 MCS, (F) 2500 MCS and (G) 3000 MCS. Simulations were run 20 times each for the parameters described in A–D. Invasion occurs preferentially at the ends of the tissues.