Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-30T20:09:56.915Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical simulation of chemotactic bacteria aggregation via mixedfinite elements

Published online by Cambridge University Press:  15 November 2003

Americo Marrocco
Americo Marrocco*
Affiliation:
Inria, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay, France. [email protected].
Get access

Abstract

We start from a mathematical model which describes the collective motion of bacteria taking into account the underlying biochemistry. This model was first introduced by Keller-Segel [13]. A new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi-Fermi level in the framework of semiconductor modelling). This new system of P.D.E. is approximated via a mixed finite element technique. The solution algorithm is then described and finally we give some preliminary numerical results. Especially our method is well adapted to compute the concentration of bacteria.

Keywords

Biophysicschemotaxisnumerical simulationmixed finite element.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 4: Special issue on Biological and Biomedical Applications , July 2003 , pp. 617 - 630
Copyright
© EDP Sciences, SMAI, 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Betterton, M.D. and Brenner, M.P., Collapsing bacterial cylinders. Phys. Rev. E 64 (2001) 061904. CrossRef
Brenner, M.P., Levitov, L.S. and Budrene, E.O., Physical mechanisms for chemotactic pattern formation bybacteria. Biophys. J. 74 (1998) 1677-1693. CrossRef
Brenner, M.P., Constantin, P., Kadanof, L.P., Schenkel, A. and Venhataramani, S.C., Diffusion, attraction and collapse. Nonlinearity 12 (1999) 1071-1098. CrossRef
L. Corrias, B. Perthame and H. Zaag, A model motivated by angiogenesis. C. Rendus Acad. Sc. Paris, to appear.
A El Boukili and A. Marrocco, Arclength continuation methods and applications to 2d drift-diffusion semiconductor equations. Rapport de recherche 2546, INRIA (mai 1995).
A. El Boukili, Analyse mathématique et simulation numérique bidimensionnelle des dispositifs semi-conducteurs à hétérojonctions par l'approche éléments finis mixtes. Ph.D. thesis, Univ. Pierre et Marie Curie, Paris (décembre 1995).
R. Glowinski and P. Le Tallec, Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics, Studies in Applied Mathematics. SIAM, Philadelphia (1989).
Herrero, M.A. and Velázquez, J.J.L., Chemotactic collapse for the keller-segel model. J. Math. Biol. 35 (1996) 177-194. CrossRef
Herrero, M.A., Medina, E. and Velázquez, J.J.L., Finite time aggregation into a single point in a reaction-diffusion system. Nonlinearity 10 (1997) 1739-1754. CrossRef
F. Hecht and A. Marrocco, Numerical simulation of heterojunction structures using mixed finite elements and operator splitting, in 10th International Conference on Computing Methods in Applied Sciences and Engineering, R. Glowinski Ed., Nova Science Publishers, Le Vésinet (February 1992) 271-286.
Hecht, F. and Marrocco, A., Mixed finite element simulation of heterojunction structures including a boundary layer model for the quasi-fermi levels. COMPEL 13 (1994) 757-770. CrossRef
Jäger, W. and Luckhaus, S., On explosion of solution to a system of partial differential equations modelling chemotaxis. Trans. Amer. Math. Soc. 239 (1992) 819-824. CrossRef
Keller, E.F. and Segel, L.A., Model for chemotaxis. J. Theor. Biol. 30 (1971) 225-234. CrossRef
A. Marrocco and Ph. Montarnal, Simulation des modèles energy-transport à l'aide des éléments finis mixtes. C.R. Acad. Sci. Paris I 323 (1996) 535-541.
Ph. Montarnal, Modèles de transport d'énergie des semi-conducteurs, études asymptotiques et résolution par des éléments finis mixtes. Ph.D. thesis, Université Paris VI (octobre 1997).
A. Marrocco, 2d simulation of chemotactic bacteria aggregation. Rapport de recherche 4667, INRIA (décembre 2002).