Homogenised model linking microscopic and macroscopic dynamics of a biofilm: Application to growth in a plug flow reactor

Ecological Modelling

Volumn 250, Issue , 2013, Pages 15-24

  Deygout, C ^a,b   Lesne, A ^c,d   Campillo, F ^a,b   Rapaport, A ^a,b  

^a CEMAGREF   (France)

^b UMR 729 MISTEA   (France)

^c INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

^d UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

Advection diffusion; Attachment detachment; Biofilm; Individual based model; Partial differential equations; Plug flow reactor

Indexed keywords

ADVECTION-DIFFUSION; ATTACHMENT-DETACHMENT; BIOFILM DEVELOPMENT; BIOFILM GROWTH; BIOLOGICAL MECHANISMS; CHANGE OF SCALE; COARSE GRAINED MODELS; COARSE-GRAINED; INDIVIDUAL-BASED; INDIVIDUAL-BASED MODELS; MACROSCOPIC DYNAMICS; MACROSCOPIC MODEL; MESOSCOPICS; PLUG FLOW; PLUG FLOW REACTOR; SMALL POPULATION; STOCHASTICITY; SUBSTRATE CONCENTRATIONS;

BIOFILMS; PARTIAL DIFFERENTIAL EQUATIONS;

COMPUTER SIMULATION;

ADVECTION-DIFFUSION EQUATION; BACTERIUM; BIOFILM; BIOREACTOR; GROWTH; HOMOGENEITY; MICROSCOPY; NUMERICAL MODEL; POPULATION STRUCTURE;

BACTERIA (MICROORGANISMS);

EID: 84870688890     PISSN: 03043800     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ecolmodel.2012.10.020     Document Type: Article

References (23)

1. Acharya A., Sawant A. On a computational approach for the approximate dynamics of averaged variables in nonlinear ode systems: toward the derivation of constitutive laws of the rate type. Journal of the Mechanics and Physics of Solids 2006, 54(10):2183-2213.
2. Ballyk M., Smith H.L. A model of microbial growth in a plug flow reactor with wall attachment. Mathematical Biosciences 1999, 158(2):95-126.
3. Ballyk M., Jones D., Smith H.L. The biofilm model of Freter: a review. Structured Population Models in Biology and Epidemiology 2008, 265-302. Springer Edition, Berlin. P. Magal, S. Ruan (Eds.).
4. Cariboni J., Gatelli D., Liska R., Saltelli A. The role of sensitivity analysis in ecological modelling. Ecological Modelling 2007, 203(1-2):167-182.
5. Dochain D., Vanrolleghem P. Dynamical modelling and estimation in wastewater treatment processes 2001, IWA Publishing, Padstow, UK.
6. Duddu R., Chopp D.L., Moran B. A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment. Biotechnology and Bioengineering 2009, 103(1):92-104.
7. Eberl H.J., Parker D.F., van Loosdrecht M.C.M. A new deterministic spatio-temporal continuum model for biofilm development. Journal of Theoretical Medicine 2001, 3(3):161-175.
8. Freter R., Brickner H., Fekete J., Vickerman M.M., Carey K.E. Survival and implantation of Escherichia coli in the intestinal tract. Infection and Immunity 1983, 39(2):686-703.
9. Givon D., Kupferman R., Stuart A. Extracting macroscopic dynamics: model problems and algorithms. Nonlinearity 2004, 17:55-127.
10. Hellweger F.L., Bucci V. A bunch of tiny individuals - individual-based modeling for microbes. Ecological Modelling 2009, 220(1):8-22.
11. Klapper I., Dockery J. Mathematical description of microbial biofilms. SIAM Review 2010, 52(2):221-265.
12. Kreft J.-U., Picioreanu C., Wimpenny J.W.T., van Loosdrecht M.C.M. Individual-based modelling of biofilms. Microbiology 2001, 147:2897-2912.
13. Laspidou C.S., Kungolos A., Samaras P. Cellular-automata and individual-based approaches for the modeling of biofilm structures: pros and cons. Desalination 2010, 250(1):390-394.
14. Lesne A. Multiscale approaches. Encyclopedia of Mathematical Physics 2006, 465-482. Elsevier, Amsterdam. G.N.J.P. Françoise, T.S. Tsun (Eds.).
15. A. Lesne, 2013. Multiscale analysis of biological systems, Acta Biotheoretica 61, in press.
16. Mabrouk N., Deffuant G., Tolker-Nielsen T., Lobry C. Bacteria can form interconnected microcolonies when a self-excreted product reduces their surface motility: evidence from individual-based model simulations. Theory in Biosciences 2010, 129(1):1-13.
17. Mabrouk, N., 2010. Analyzing individual-based models of microbial systems. Ph.D. Thesis. Université Blaise Pascal de Clermont-Ferrand.
18. Picioreanu C., van Loosdrecht M.C.M., Heijnen J.J. A new combined differential-discrete cellular automaton approach for biofilm modeling: application for growth in gel beads. Biotechnology and Bioengineering 1998, 57(6):718-731.
19. Torquato S. Random Heterogeneous Materials: Microstructure and Macroscopic Properties 2002, Springer, New-York.
20. Wang Q., Zhang T. Review of mathematical models for biofilms. Solid State Communications 2010, 150(21-22):1009-1022.
21. Wanner O., Eberl H.J., Morgenroth E., Noguera D., Picioreanu C., Rittmann B., van Loosdrecht M.C.M. Mathematical Modeling of Biofilms 2006, IWA Publishing Edition, London.
22. Weinan E., Engquist B. The heterogeneous multiscale methods. Communications in Mathematical Sciences 2003, 1:87-133.
23. Weinan E., Ren W., Vanden-Eijnden E. A general strategy for designing seamless multiscale methods. Journal of Computational Physics 2009, 228(15):5437-5453.