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Bulletin of Mathematical Biology

, Volume 80, Issue 11, pp 2789–2827 | Cite as

Stability, Convergence, and Sensitivity Analysis of the FBLM and the Corresponding FEM

  • N. SfakianakisEmail author
  • A. Brunk
Original Article

Abstract

We study in this paper the filament-based lamellipodium model (FBLM) and the corresponding finite element method (FEM) used to solve it. We investigate fundamental numerical properties of the FEM and justify its further use with the FBLM. We show that the FEM satisfies a time step stability condition that is consistent with the nature of the problem and propose a particular strategy to automatically adapt the time step of the method. We show that the FEM converges with respect to the (two-dimensional) space discretization in a series of characteristic and representative chemotaxis and haptotaxis experiments. We embed and couple the FBLM with a complex and adaptive extracellular environment comprised of chemical and adhesion components that are described by their macroscopic density and study their combined time evolution. With this combination, we study the sensitivity of the FBLM on several of its controlling parameters and discuss their influence in the dynamics of the model and its future evolution. We finally perform a number of numerical experiments that reproduce biological cases and compare the results with the ones reported in the literature.

Keywords

Lamellipodium Actin filaments Cell motility Convergence Stability Sensitivity analysis 

Notes

Acknowledgements

The authors would like to thank Christian Schmeiser, Anna Marciniak-Czochra, and Mark Chaplain for the fruitful discussions and suggestions during the preparation of this manuscript. NS acknowledges also the support of the SFB 873: “Maintenance and Differentiation of Stem Cells in Development and Disease”.

Supplementary material

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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Institute of Applied MathematicsHeidelberg UniversityHeidelbergGermany
  2. 2.Institute of MathematicsJohannes Gutenberg-UniversityMainzGermany

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