A numerical study of a biofilm disinfection model Linda El Alaoui LAGA Universit´e Paris 13 email: [email protected]

A biofilm is a community of microorganisms (bacteria, fungi, algae and protozoa), adhering each other on a surface. Biofilms are, generally, observed in aqueous media or in a media exposed to moisture. They can grow on any type of natural or artificial surface. This surface may be mineral (rock interfaces, air-liquid ...) or organic (skin, plants), industrial (pipes, oil, wastewater) or medical (prothesis, catheters ),... This presence of biofilms in a wide range of situations has led the researchers to study their properties both for their beneficial and detrimental impact. It turns out that mathematical modeling can be an efficient tool for the study of biofilms. We refer to [2] for a review on mathematical modeling of biofilms. Here, we are interested in a bacterial biofilm in presence of a single nutrient (e.g. oxygen), a single antimicrobial agent and a neutralizing agent which reacts with the antimicrobial. Thus we consider the model introduced in [1] describing the evolution of the fluid dynamics in and around the biofilm, the transport of chemical species and the mechanism of physiological resistance. We assume the biolfim attached to the bottom of the computational domain Ω = [0, m] × [0, mL], with m, L > 0, see figure 1. fluid Γ

Biofilm

Figure 1: A schematic description of the biofilm in Ω. The fluid flow is described by the incompressible Stokes equation µ∆u = ∇p − f, ∇·u = 0,

in Ω,

(1)

in Ω,

(2)

where the unknow u is the fluid velocity and p is the pressure. The coefficient µ is the viscosity, and f is the force at the interface Γ between the biofilm and the fluid. Homogeneous Dirichlet boundary condition on the velocity is enforced on the top, the bottom of Ω and on Γ. The concentration of nutrient S and antimicrobial agent A are modeled by the following advectiondiffusion-reaction equations ∂S S + u·∇S − ∇·(DS ∇S) − µS B = 0, ∂t KS + S ∂A + u·∇A − ∇·(DA ∇A) + HA (A, N ) = 0, ∂t

in (0, T ) × Ω,

(3)

in (0, T ) × Ω,

(4)

where B is the population of bacteria, HA describes the reaction between the antimicrobial agent and the biofilm, DS and DA denote the diffusion coefficients of the nutient and the antimicrobial, µS and KS are the specific growth rate and the Monod coefficient respectively. We underline that B depends on space and

1

time variable and DS and DA depend on the space variable. Homogeneous Neumann boundary conditions are enforced on S and A on the top and the bottom of Ω, and an initial conditions on S and A are given. The concentrations of the neutralizing agent, N , which is depleted by reaction with the antimicrobial, and B satisfy the following ordinary differential equations ∂N = pN (A)N, ∂t ∂B = pB (A, S)B, ∂t

(5) (6)

where pN (A) and pB (A, S) denote the rate of the neutralizing agent consumption and the desinfection rate respectively. The system (5)-(6) is closed by an uniform initial distribution of the population B and by an initial concentration on N . The aims of the Master internship are the following : • Derive a finite element/Euler scheme approximating the system (1)–(6). • Perform numerical simulations on using the softwares FreeFem++ [3] and/or Scilab [4]. • Derive a model from (1)–(6) that takes into account the fact that some bacteria cells which are not susceptible to the antimicrobial revert back to susceptible cells. • Propose a strategy for optimizing the antimicrobial dosing.

References [1] N.G. Cogan, R. Cortez, L. Fauci. Modeling physiological resistance in bacterial biofilms. Bulletin of Mathematical Biology, 67(831–853), 2005. [2] O. Wanner et al. Mathematical modeling of biofilms. IWA Publishing, 2006. [3] FreeFem++. Free finite element software. http://www.freefem.org/ff++ [4] Scilab. Free Open Source Software for Numerical Computation. http://www.scilab.org/

2

A numerical study of a biofilm disinfection model

Derive a model from (1)–(6) that takes into account the fact that some bacteria ... Free Open Source Software for Numerical Computation. http://www.scilab.org/.

41KB Sizes 0 Downloads 233 Views

Recommend Documents

a numerical study on a simplified tail model for turning ...
TONG Bing-gang. The Laboratory for Biomechanics of Animal Locomotion, Graduate University of Chinese Academy of Sciences,. Beijing 100049, China. (Received Apr. 19, 2005). ABSTRACT: Most freshwater fish are good at turning manoeuvres. A simulated fis

A Numerical Study of the Sensitivity of Cloudy-Scene ... - Sites
Jun 28, 1996 - Our civilization has been the single most important force in recent ... The solar energy absorbed and reflected by the earth occurs .... The design strategy of the experiment incorporated both old and new technology concepts.

An Experimental and Numerical Study of a Laminar ...
Department of Mechanical Power Engineering, University of Cairo, Egypt. A lifted laminar axisymmetric diffusion ... Published by Elsevier Science Inc. ..... computer program for the two-dimensional di- ...... stitute, Pittsburgh, pp. 1099–1106. 15.

An Experimental and Numerical Study of a Laminar ...
for broadband emissions by subtracting an im- ..... Figure 13 shows the comparison for the fuel ..... Lin˜án A., in Combustion in High Speed Flows (J. Buck-.

A multiscale approach for biofilm modelling
Jun 28, 2011 - situations, where neither a completely microscopic IBM or a PDE system are possible ...... Communications, 150(21-22):1009–1022, 2010. doi: ...

STERILIZATION, DISINFECTION & ANTISEPSIS.pdf
Page 2 of 41. 9/20/2011 2 Kher. Learning Objectives. Compare and contrast the processes of. sterilization disinfection and antisepsis. State principle of ...

A numerical model for the point contact of dissimilar ...
systems. The exact partial slip solution of cylindrical contacts of similar materials subjected ... doi:10.1016/j.mechmat.2008.06.002. * Corresponding author. Tel.: +1 847 467 6961; fax: +1 847 491 3915. ..... The element in contact has a positive.

A Pilot Study to Evaluate the Effectiveness of a Peer Support Model ...
A Pilot Study to Evaluate the Effectiveness of a Peer Support Model - Final Report.pdf. A Pilot Study to Evaluate the Effectiveness of a Peer Support Model - Final ...

Numerical model of the hydrothermal system beneath ...
Jun 5, 2008 - explain the Unzen fumarolic field and that two heat sources beneath ... Unzen area had been conducted by the New Energy Development.

Predictions of a Recurrent Model of Orientation
Jan 3, 1997 - linear and an analytic solution to the network can be found. The biases for certain numbers of peaks in the responses become evident once the ...

Conceptual and Numerical Flow Model of the Sines ...
the regional discharge area of the deep aquifer in the offshore. ... for the best possible reproduction of the aquifer equipotential surface, accommodating.

A rational fraction polynomials model to study vertical ...
E-mail address: [email protected] (E.G. Vadillo). ... very simple time domain model represented by a system of equations in the space ...... [22] F. H. Raven, Automatic control Engineering, 4th ed. ed., McGraw-Hill, New York, 1987.

Numerical study of a flat-tube high power density solid ...
Journal of Power Sources 153 (2006) 68–75. Numerical study of a ... SOFCs are clean, quiet, and highly efficient power genera- tion devices, and .... Overall : H2 + 1. 2. O2 ⇒ H2O. (3). The free energy change of the overall chemical reaction is.

Predictions of a Recurrent Model of Orientation
Jan 3, 1997 - run on a network of 5 12 units whose output represents the activity of .... on the initial state of the network. .... (O'Toole & Wenderoth, 1977).

Numerical study of a flat-tube high power density solid ...
In this paper, a three-dimensional numerical model to simulate the steady state ... The heat/mass transfer and fluid flow modeling and results will be used to simulate the overall performance of a ... +1 412 624 9793; fax: +1 412 624 4846.

Numerical study of a flat-tube high power density solid ...
Journal of Power Sources 140 (2005) 331–339. Numerical study ... C), a SOFC is a clean, quiet, and highly ... of fuel cells have to rely on a clean supply of hydrogen .... 2. O2 ⇒ H2O. (3). The free energy change of the overall chemical reaction.

A rational fraction polynomials model to study vertical ...
the publishing process, such as editing, corrections, structural formatting, and ... JOURNAL OF SOUND AND VIBRATION is available online and the final ... describe the real track dynamic behaviour to a great degree of precision, including rail.

a numerical study for the estimation of water pollution
to examine mathematical models and ensuing numerical methods for the estimation of the pollutants at different times ... In section 2, presents a short discussion on the derivation of a water pollution model treated as ADE. We describe ..... ground l

numerical evaluation of the vibroacoustic behavior of a ...
Oct 24, 2011 - The analytical solution of rectangular cavity (Blevins, 1979; Kinsler et al., .... The speaker box was placed in contact with the side of the cavity ...

Numerical model of the hydrothermal system beneath ...
b Graduate School of Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan ... Available online 5 June 2008. Keywords: numerical ...