Numerical treatment of the Filament Based Lamellipodium Model (FBLM)

Abstract

We describe in this work the numerical treatment of the Filament Based Lamellipodium Model (FBLM). The model itself 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 these problem. It is comprised of composite Lagrange-Hermite two dimensional elements defined over two dimensional space. We present some elements of the FEM and emphasise in the numerical treatment of the more complex terms. We also present novel numerical simulations and compare to in-vitro experiments of moving cells