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Stability, convergence, and sensitivity analysis of the FBLM and the corresponding FEM

Research output: Contribution to journalArticle

Author(s)

N. Sfakianakis, A. Brunk

School/Research organisations

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.

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Details

Original languageEnglish
Pages (from-to)2789-2827
Number of pages39
JournalBulletin of Mathematical Biology
Volume80
Issue number11
Early online date29 Aug 2018
DOIs
Publication statusPublished - Nov 2018

    Research areas

  • Actin filaments, Cell motility, Convergence, Lamellipodium, Sensitivity analysis, Stability

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