Biological Growth In A Grid Independent Discrete Model

Costas Strouthos, Complex Biosystems Modeling Laboratory, Harvard University

To simulate tumor cell packing phenomena a biologically-inspired lattice-free model is introduced. The cells are represented by spheres in three dimensions and disks in two dimensions. The growing cell cluster is enlarged radially by random proliferation of parental cells. A cell enters a quiescence state if after N efforts it cannot find free space at an adjacent position to spawn a new daughter cell. For N larger than a critical value, N_cr, the interior density of the cell cluster is constant whereas the boundary exhibits non-trivial surface roughness. Further, a morphology transition takes place at N_cr between indefinitely growing non-fractal clusters and growth-arrested fractal ones. Certain properties of this non-equilibrium transition are discussed.