In this talk, we propose to measure the impact of the adhesion properties in the two dimensional cell migration using mathematical model based on phase-field methods previously studied by Igor Aranson and Falko Ziebert in 2013 and 2014 (see references). We then present the specific finite volume approach that we will use for this problem: the Discrete Duality Finite Volume methods.
We finally present a DDFV approximation of this model which couples a non-local Allen Cahn type equation with advection reaction-diffusion equations and present some numerical results for this model.
Ziebert F, Aranson IS (2013). Effects of Adhesion Dynamics and Substrate Compliance on the Shape and Motility of Crawling Cells. PLoS ONE 8(5):e64511. doi:10.1371/journal.pone.0064511
Löber J, Ziebert F, Aranson IS (2014). Modeling crawling cell movement on soft engineered substrates. Soft matter 10(9):1365-1373.