A Fluid-Structure Interaction Model of the Cell Membrane Deformation: Formation of a Filopodium

Department of Computer Science and Mathematics Lebanese American University - Byblos campus, P.O. Box: 36, Byblos, Lebanon

^⋆ Corresponding author. E-mail: nader.elkhatib@lau.edu.lb

Abstract

In this paper we present a fluid-structure interaction model of neuron’s membrane deformation. The membrane-actin is considered as an elastic solid layer, while the cytoplasm is considered as a viscous fluid one. The membrane-actin layer is governed by elasticity equations while the cytoplasm is described by the Navier-Stokes equations. At the interface between the cytoplasm and the membrane we consider a match between the solid velocity displacement and the fluid velocity as well as the mechanical equilibrium. The membrane, which faces the extracellular medium, is free to move. This will change the geometry in time. To take into account the deformation of the initial configuration, we use the Arbitrary Lagrangian Eulerian method in order to take into account the mesh displacement. The numerical simulations, show the emergence of a filopodium, a typical structure in cells undergoing deformation.