Numerical Treatment of the Filament-Based Lamellipodium Model (FBLM)
We describe in this work the numerical treatment of the Filament-Based Lamellipodium Model (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 two-dimensional elements defined over a two-dimensional space. We present some elements of the FEM and emphasize in the numerical treatment of t…
An Extended Filament Based Lamellipodium Model Produces Various Moving Cell Shapes in the Presence of Chemotactic Signals
The Filament Based Lamellipodium Model (FBLM) is a two-phase two-dimensional continuum model, describing the dynamcis of two interacting families of locally parallel actin filaments (C.Schmeiser and D.Oelz, How do cells move? Mathematical modeling of cytoskeleton dynamics and cell migration. Cell mechanics: from single scale-based models to multiscale modeling. Chapman and Hall, 2010). It contains accounts of the filaments' bending stiffness, of adhesion to the substrate, and of cross-links connecting the two families. An extension of the model is presented with contributions from nucleation of filaments by branching, from capping, from contraction by actin-myosin interaction, and from a pr…