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

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

Abstract

Wedescribeinthis 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.

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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
  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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