We investigate morphologies of proliferating cellular tissues using a numerical simulation model for mechanical cell division and migration in two dimensions. The model is applied to a bimodal mixture consisting of stiff cells with a low growth potential and soft cells with a high growth potential; cancer cells are typically considered to be softer than healthy cells. In an even mixture, the soft cells develop into a tissue matrix and the stiff cells into a dendritelike network structure. When soft cells are placed inside a tissue consisting of stiff cells (to model cancer growth), the soft cells develop into a fast-growing tumorlike structure that gradually evacuates the stiff cell matrix. The model also demonstrates (1) how soft cells orient themselves in the direction of the largest effective stiffness as predicted by the theory of Bischofs and Schwarz [Proc. Natl. Acad. Sci. USA 100, 9274 (2003)PNASA60027-842410.1073/pnas.1233544100] and (2) that the orientation and force generation continue a few cell rows behind the soft-stiff interface. With increasing intercell friction, tumor growth slows down, and cell death occurs. The contact force distribution between cells is demonstrated to be highly sensitive to cell type mixtures and cell-cell interactions, which indicates that local mechanical forces can be useful as a regulator of tissue formation. The results shed light on established experimental data.
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