MKI67 and ductal breast carcinoma in situ: As in prior work [14], the simulations predict cell-scale details observed in DCIS pathology, such as the appearance of pairs of Ki67+ daughter cells, the spatially isolated apoptotic cells (which arises from the model assumption that apoptosis is a stochastic, low-frequency event that is independent of oxygenation), and the higher occurrence of Ki67+ cells near the duct wall (where we modeled the probability of cell cycle entry as proportional to oxygenation).