Numerical treatment of the Filament Based Lamellipodium Model (FBLM)

We describe in this work the numerical treatment of the Filament-Based LamellipodiumModel (FBLM). This model is a two-phase two-dimensional continuum model, describing the dynamics of two interacting families of locally parallel F-actin filaments. It includes, among others, the bending stiffness of the filaments, adhesion to the substrate, and the cross-links connecting the two families. The numerical method proposed is a Finite Element Method (FEM) developed specifically for the needs of this problem. It is comprised of composite Lagrange–Hermite twodimensional elements defined over a two-dimensional space. We present some elements of the FEM and emphasize in the numerical treatment of the more complex terms. We also present novel numerical simulations and compare to in-vitro experiments of moving cells.