Continuum-based modeling of collective cell migration

In this paper, we present a computationally efficient cellular mathematical model that accounts for the boundary collective behavior of a cell group by hepatocyte growth factor. The large cell group is modeled using continuum-based finite elements with incompressible hyperelastic materials for the nonlinear elastic behaviors. The total Lagrangian formulation is used enabling for large deformations, and the explicit time integration scheme without the Newton-Raphson iterative solution required for a time step is adopted to model the dynamics of the collective cell migration. With the explicit time integration and low order finite elements under the total Lagrangian framework, the proposed model is much computationally efficient for modeling the dynamic mechanical behavior of a cell colony. Detailed comparison to the experimental data shows that the proposed mathematical model provides a quantitatively accurate description of the collective cell motion in three different concentrations of hepatocyte growth factor.