Geodesic
A Fluid-Structure Interaction Model of the Cell Membrane Deformation: Formation of a Filopodium
N. El Khatib1
1 Department of Computer Science and Mathematics Lebanese American University - Byblos campus, P.O. Box: 36, Byblos, Lebanon
Mathematical modelling of natural phenomena, Tome 9 (2014) no. 1, pp. 27-38

Voir la notice de l'article provenant de la source EDP Sciences

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.
DOI : 10.1051/mmnp/20149103

N. El Khatib 1

1 Department of Computer Science and Mathematics Lebanese American University - Byblos campus, P.O. Box: 36, Byblos, Lebanon 
@article{10_1051_mmnp_20149103,
     author = {N. El Khatib},
     title = {A {Fluid-Structure} {Interaction} {Model} of the {Cell} {Membrane} {Deformation:} {Formation} of a {Filopodium}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {27--38},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2014},
     doi = {10.1051/mmnp/20149103},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149103/}
}
TY  - JOUR
AU  - N. El Khatib
TI  - A Fluid-Structure Interaction Model of the Cell Membrane Deformation: Formation of a Filopodium
JO  - Mathematical modelling of natural phenomena
PY  - 2014
SP  - 27
EP  - 38
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149103/
DO  - 10.1051/mmnp/20149103
LA  - en
ID  - 10_1051_mmnp_20149103
ER  - 
%0 Journal Article
%A N. El Khatib
%T A Fluid-Structure Interaction Model of the Cell Membrane Deformation: Formation of a Filopodium
%J Mathematical modelling of natural phenomena
%D 2014
%P 27-38
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149103/
%R 10.1051/mmnp/20149103
%G en
%F 10_1051_mmnp_20149103
N. El Khatib. A Fluid-Structure Interaction Model of the Cell Membrane Deformation: Formation of a Filopodium. Mathematical modelling of natural phenomena, Tome 9 (2014) no. 1, pp. 27-38. doi: 10.1051/mmnp/20149103

[1] B. Alberts, A. Johnson, J. Lewis J. Molecular Biology of the Cell (4th ed.). Garland Science. New York, 2002.

[2] F. Xue, D. M. Janzen, D. A. Knecht. Contribution of Filopodia to Cell Migration: A Mechanical Link between Protrusion and Contraction. International Journal of Cell Biology, vol. 2010, Article ID 507821, 13 pages, 2010.

[3] I. Budin, N.K. Devaraj Journal of the American Chemical Society 2011 751 753

[4] Jb Alberts, Gm Odell PLoS Biol 2004 2054 2066

[5] D. Boal. Mechanics of the cell. Cambridge University Press, 2002.

[6] Nicolas Huc. Modèle pour l’étude du rôle de la membrane dans la df´ormation cellulaire : application à la spinogénèse. Université de Grenoble, 2004.

[7] N. El-Khatib, N. Huc, Y. Goldberg, J-L Martiel. Analysis of Cell deformation with FEMLAB. Proceedings of the COMSOL Multiphysics User’s Conference, Paris 2005.

[8] E. Evans, R. Skalak. Mechanics and thermodynamics of biomembranes. CRC Press (1980).

[9] F. Gerbal, P. Chatin, Y. Rabin, J. Prost Biophysical J. 2000 2259 2275

[10] S. Hénon, G. Lenormand, A. Richert, F. Gallet Biophysical J. 1999 1145 1151

[11] W.C. Hwang, R.E. Waugh Biophysical J. 1997 2669 2678

[12] G. Lenormand, S. Hénon, A. Richert, J. Siméon, F. Gallet Biophysical J. 2001 43 56

[13] A. Mogilner, G. Oster Biophysical J. 1996 3030 3045

[14] A. Mogilner, L. Edelstein-Keshet Biophysical J. 2002 1237 1258

[15] D. Needham, R.M. Hochmuth Biophysical J. 1992 1664 1670

[16] T. Pollard, G. Borisy Cell 2003 453 465

[17] T.M. Svitkina, E.A. Bulanova, O.Y. Chaga, D.M. Vignjevic, S. Kojima, J.M. Vasiliev, G. Borisy J. Cell. Biol. 2003 409 421

[18] R. E. Waugh, R. G. Bauserman Ann. Biomed. Eng. 1995 308 321

[19] F. Nobile. Numerical Approximation of Fluid- Structure Interaction Problems with Aplication to Haemodynamics. PhD thesis, 2001.

[20] J. Janela, A. Moura, A. Sequeira Journal of Computational and Applied Mathematics 2010 2783 2791

[21] L. Formaggia, A. Moura, F. Nobile ESAIM: Mathematical Modelling and Numerical Analysis 2007 743 769

[22] A. Chambolle, B. Desjardins, M. Esteban, C. Grandmont J. Math. Fluid Mech. 2005 368 404

[23] H. Beirão Da Veiga J. Math. Fluid Mech. 2004 21 52

[24] D. Coutand, S. Shkoller Arch. Ration. Mech. Anal. 2006 303 352

[25] T.J.R. Hughes, W.K. Liu, T.K. Zimmermann Computer Methods in Applied Mechanics and Engineering 1981 329 349

[26] M. À. Fernández, M. Moubachir A Newton method using exact jacobians for solving fluid-structure coupling. Computers and Structures, v.83, 2005, 127-142.

Cité par Sources :