| Abstract | A connection is established between a discrete stochastic model describing the microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards a chemical gradient (process called chemotaxis) with their shapes randomly fluctuating. A nonlinear diffusion equation is derived from the microscopic dynamics in dimensions one and two using an excluded volume approach. The nonlinear diffusion coefficient depends on the cellular volume fraction and demonstrated to prevent collapse of cellular density. A very good agreement is shown between Monte Carlo simulations of the microscopic Cellular Potts Model and numerical solutions of the macroscopic equations for relatively large cellular volume fractions of about 0.3. A combination of microscopic and macroscopic models are used to simulate growth of structures similar to early vascular networks. |
|---|
