Numerical Treatment of the Filament-Based Lamellipodium Model (FBLM)

  • Angelika Manhart
  • Dietmar Oelz
  • Christian Schmeiser
  • Nikolaos SfakianakisEmail author
Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 11)


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 the more complex terms. We also present novel numerical simulations and compare to in-vitro experiments of moving cells.


Piecewise Linear Function Piecewise Constant Function Finite Element Space Piecewise Constant Approximation Adhesive Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work has been supported by the Austrian Science Fund through grant no. J-3463 and through the PhD program Dissipation and Dispersion in Nonlinear PDEs, grant no. W1245. The authors also acknowledge support by the Vienna Science and Technology Fund, grant no. LS13-029. N. Sfakianakis wishes to thank the Alexander von Humboldt Foundation and the Center of Computational Sciences (CSM) of Mainz for their support, and M. Lukacova for the fruitful discussions during the preparation of this manuscript.


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Angelika Manhart
    • 1
  • Dietmar Oelz
    • 2
  • Christian Schmeiser
    • 1
  • Nikolaos Sfakianakis
    • 3
    Email author
  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  3. 3.Johannes-Gutenberg UniversityMainzGermany

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