  We investigate morphologies of proliferating cellular tissues using a newly
developed numerical simulation model for mechanical cell division and migration
in 2D. 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
dendrite-like network structure. When soft cells are placed inside a tissue
consisting of stiff cells (to model cancer growth), the soft cells develop to a
fast growing tumor-like 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 U.S.A., 100, 9274--9279 (2003) and
2) that the orientation and force generation continue a few cell rows behind
the soft-stiff interface. With increasing inter-cell 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 new light on established
experimental data.
