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Category: Environmental Microbiology; Microbial Genetics and Molecular Biology
Modeling Biofilms, Page 1 of 2
< Previous page | Next page > /docserver/preview/fulltext/10.1128/9781555817718/9781555818944_Chap13-1.gif /docserver/preview/fulltext/10.1128/9781555817718/9781555818944_Chap13-2.gifAbstract:
Because all levels of biofilm models are useful depending on the application, this chapter describes and discusses biofilm modeling starting from the simple, homogeneous case to the more complex, structurally and functionally heterogeneous cases. Obviously, the complexity of the model is reduced when a single-species biofilm is modeled (i.e., a functionally homogeneous but structurally heterogeneous biofilm); thus, the discussions in the chapter focus on this simplified problem. In the cellular automata (CA) biofilm model, there are two superimposed lattices, one of them containing information on the location of food particles (substrate lattice) and the other one describing the location of microbial particles (microbial lattice). The simulation of biofilm activity is done by evaluating these stochastic processes over a series of time steps. A section describes the fundamental rules for these stochastic processes and their relation to the physical and biological parameters that represent the biofilm system. Biofilm erosion at the surface, another possible process controlling biofilm growth, can be implemented by selecting a maximum biofilm height, beyond which any microbial outgrowth will be removed from the biofilm. The evolution of biofilm modeling from the 1970s until now shows different approaches to the mathematical abstraction of the biofilm problem, but it is evident that the conceptual basis for all the models is similar and relies on mathematically coupling substrate diffusion with substrate utilization, microbial growth, and microbial decay or detachment.
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Schematic representation of a homogeneous biofilm system.
Schematic representation of a homogeneous biofilm system.
Discretization of a 1D biofilm problem and corresponding explicit finite difference approximation of equations 2 to 4.
Discretization of a 1D biofilm problem and corresponding explicit finite difference approximation of equations 2 to 4.
The evaluation of growth and decay in a biofilm model produces an uneven distribution of the size of biofilm elements. A reevaluation of the boundaries between elements restores the equally sized element configuration.
The evaluation of growth and decay in a biofilm model produces an uneven distribution of the size of biofilm elements. A reevaluation of the boundaries between elements restores the equally sized element configuration.
Periodic boundaries in a 2D domain are illustrated by bending the planar domain to form a cylinder in which the left-most elements overlap with the right-most elements (i.e., elements in column 1 = elements in column n).
Periodic boundaries in a 2D domain are illustrated by bending the planar domain to form a cylinder in which the left-most elements overlap with the right-most elements (i.e., elements in column 1 = elements in column n).
Schematic representation of the mixing and transport steps in the CA diffusion rule. During mixing, all food particles change layers (shown in this figure is a 180° directional change). During the transport step, the particles are moved according to the layer in which they are located (e.g., north, east, south, or west, for the layers shown).
Schematic representation of the mixing and transport steps in the CA diffusion rule. During mixing, all food particles change layers (shown in this figure is a 180° directional change). During the transport step, the particles are moved according to the layer in which they are located (e.g., north, east, south, or west, for the layers shown).
Schematic representation of evaluation of connectivity and sloughing. Light squares represent microbial particles without an identified connection to the substratum. Dark squares represent connected microbial particles. Connectivity “flows” through microbial cells (steps 1 to 8) and unconnected cells are sloughed off (step 9).
Schematic representation of evaluation of connectivity and sloughing. Light squares represent microbial particles without an identified connection to the substratum. Dark squares represent connected microbial particles. Connectivity “flows” through microbial cells (steps 1 to 8) and unconnected cells are sloughed off (step 9).
Flowchart of algorithm used to simulate biofilm dynamics with the quantitative CA biofilm model.
Flowchart of algorithm used to simulate biofilm dynamics with the quantitative CA biofilm model.
Simulation of a functionally homogeneous and structurally heterogeneous biofilm using the CA model. The typical cycle includes growth, decay, and sloughing processes.
Simulation of a functionally homogeneous and structurally heterogeneous biofilm using the CA model. The typical cycle includes growth, decay, and sloughing processes.
Substrate flux (A) and biofilm thickness (B) during the simulation of a functionally homogeneous and structurally heterogeneous biofilm using the quantitative CA biofilm model.
Substrate flux (A) and biofilm thickness (B) during the simulation of a functionally homogeneous and structurally heterogeneous biofilm using the quantitative CA biofilm model.
Simulation of growth of a heterogeneous biofilm using the quantitative CA biofilm model. The biofilm has two microbial species, heterotrophs (dark areas) and nitrifiers (white areas).
Simulation of growth of a heterogeneous biofilm using the quantitative CA biofilm model. The biofilm has two microbial species, heterotrophs (dark areas) and nitrifiers (white areas).
Average concentration of microbial species (A) and chemical species (B) throughout the biofilm matrix at day 18 of the simulation.
Average concentration of microbial species (A) and chemical species (B) throughout the biofilm matrix at day 18 of the simulation.
Notation used in this chapter
Notation used in this chapter
Step-by-step instructions for using the pseudoanalytical model of Saéz and Rittmann a
Step-by-step instructions for using the pseudoanalytical model of Saéz and Rittmann a
Parameters used for the simulation of a functionally homogeneous, structurally heterogeneous biofilm presented in example 1
Parameters used for the simulation of a functionally homogeneous, structurally heterogeneous biofilm presented in example 1
Calculation of parameters for the quantitative CA biofilm model (example 1)
Calculation of parameters for the quantitative CA biofilm model (example 1)
Summary of parameters for microbial species in example 2, the functionally heterogeneous CA biofilm model
Summary of parameters for microbial species in example 2, the functionally heterogeneous CA biofilm model
Summary of parameters for microbial species in example 2, the functionally heterogeneous CA biofilm model
Summary of parameters for microbial species in example 2, the functionally heterogeneous CA biofilm model