Skip to content

Research at St Andrews

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

Research output: Contribution to journalArticle


N. Sfakianakis, A. Brunk

School/Research organisations


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.



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

    Research areas

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

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model

    Giesselmann, J., Kolbe, N., Lukácová-Medvidov á, M. & Sfakianakis, N., Dec 2018, In : Discrete and Continuous Dynamical Systems - Series B. 23, 10, p. 4397-4431 35 p.

    Research output: Contribution to journalArticle

  2. Modelling cell-cell collision and adhesion with the Filament Based Lamellipodium Model

    Sfakianakis, N., Peurichard, D., Brunk, A. & Schmeiser, C., 28 Nov 2018, In : BIOMATH. 7, 2, 14 p., 1811097.

    Research output: Contribution to journalArticle

  3. Energy intake functions and energy budgets of ectotherms and endotherms derived from their ontogenetic growth in body mass and timing of sexual maturation

    Werner, J., Sfakianakis, N., Rendall, A. D. & Griebeler, E. M., 7 May 2018, In : Journal of Theoretical Biology. 444, p. 83-92 10 p.

    Research output: Contribution to journalArticle

  4. Chemotaxis and haptotaxis on cellular level

    Brunk, A., Kolbe, N. & Sfakianakis, N., 2018, Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016. Westdickenberg, M. & Klingenberg, C. (eds.). Springer, Vol. 236. p. 249-261 13 p. (Springer Proceedings in Mathematics & Statistics; vol. 236).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

Related by journal

  1. A mathematical framework for modelling the metastatic spread of cancer

    Franssen, L. C., Lorenzi, T., Burgess, A. & Chaplain, M. A. J., 22 Mar 2019, In : Bulletin of Mathematical Biology. First Online, 46 p.

    Research output: Contribution to journalArticle

  2. Computational approaches and analysis for a spatio-structural-temporal invasive carcinoma model

    Hodgkinson, A., Chaplain, M. A. J., Domschke, P. & Trucu, D., Apr 2018, In : Bulletin of Mathematical Biology. 80, 4, p. 701-737

    Research output: Contribution to journalArticle

  3. Computational modelling of cancer development and growth: modelling at multiple scales and multiscale modelling

    Szymanska, Z., Cytowski, M., Mitchell, E., Macnamara, C. K. & Chaplain, M. A. J., May 2018, In : Bulletin of Mathematical Biology. 80, 5, p. 1366-1403 38 p.

    Research output: Contribution to journalArticle

ID: 259100167