An innovative type of biofilm model is derived by combining an individual description of microbial particles with a continuum representation of the biofilm matrix. This hybrid model retains the advantages of each approach, while providing a more realistic description of the temporal development of biofilm structure in two or three spatial dimensions. The general model derivation takes into account any possible number of soluble components. These are substrates and metabolic products, which diffuse and react in the biofilm within individual microbial cells. The cells grow, divide, and produce extracellular polymeric substances (EPS) in a multispecies model setting. The EPS matrix is described by a continuum representation as incompressible viscous fluid, which can expand and retract due to generation and consumption processes. The cells move due to a pushing mechanism between cells in colonies and by an advective mechanism supported by the EPS dynamics. Detachment of both cells and EPS follows a continuum approach, whereas cells attach in discrete events. Two case studies are presented for model illustration. Biofilm consolidation is explained by shrinking due to EPS and cell degradation processes. This mechanism describes formation of a denser layer of cells in the biofilm depth and occurrence of an irregularly shaped biofilm surface under nutrient limiting conditions. Micro-colony formation is investigated by growth of autotrophic microbial colonies in an EPS matrix produced by heterotrophic cells. Size and shape of colonies of ammonia and nitrite-oxidizing bacteria (NOB) are comparatively studied in a standard biofilm and in biofilms aerated from a membrane side.

Bacterial biofilms, while made up of microbial-scale objects, also function as meso- and macroscale materials. In particular, macro-scale material properties determine how biofilms respond to large-scale mechanical stresses, e.g. fluid shear. Viscoelastic and other constitutive properties influence biomass structure (through growth and fluid shear stresses) by erosion and sloughing detachment. In this paper, using the immersed boundary method, biofilm is modelled by a system of viscoelastic, breakable springs embedded in a fluid flow, evolving according to the basic physical laws of conservation of mass and momentum. We demonstrate in the context of computer simulation biofilm deformation and detachment under fluid shear stress.

In the html abstract portion of the online publication of "A Multidimensional Multispecies Continuum Model for Heterogeneous Biofilm Development" (DOI: 10.1007/s11538-006-9168-7) the last name of the first author was erroneously misspelled. The authors' names should have appeared as above. Springer regrets the error.* The online version of the original article can be found at http://dx

We propose a multidimensional continuum model for heterogeneous growth of biofilm systems with multiple species and multiple substrates. The new model provides a deterministic framework for the study of the interactions between several spe1cies and their effects on biofilm heterogeneity. It consists of a system of partial differential equations derived on the basis of conservation laws and reaction kinetics. The derivation and key assumptions are presented. The assumptions used are a combination of those used in the established one dimensional model, due to Wanner and Gujer, and for the viscous fluid model, of Dockery and Klapper. The work of Wanner and Gujer in particular has been extensively used through the years, and thus this new model is an extension to several spatial dimensions of an already proven working model. The model equations are solved using numerical techniques, for purposes of simulation and verification. The new model is applied to two different biofilm systems in several spatial dimensions, one of which is equivalent to a system originally studied by Wanner and Gujer. Dimensionless formulations for these two systems are given, and numerical simulation results with varying initial conditions are presented.

Until now, only few attempts have been made to assess biofilm models simulating microenvironments in a biofilm. As a first step, we compare the microenvironment observed in a membrane aerated biofilm (MAB) to that derived from a two-dimensional computational model with individual ammonia oxidizing bacteria (AOB) and nitrite oxidizing bacteria (NOB) embedded in a continuum EPS matrix. Gradients of oxygen were determined by means of microelectrodes. The change in nitrifying bacterial populations with the biofilm depth was quantified using fluorescence in situ hybridization (FISH) in combination with a confocal laser scanning microscopy (CLSM). Microelectrode measurements revealed that oxic and anoxic or anaerobic regions exist within the MAB. The oxygen profile predicted by the model showed good agreement with that obtained by microelectrode measurements. The oxic part of the biofilm was dominated by NSO190 probe-hybridized AOB, which formed relatively large clusters of cells directly on the membrane surface, and by the NOB belonging to genus Nitrobacter sp. On the other hand, NOB belonging to genus Nitrospira sp. were abundant at the oxic-anoxic interface. The model prediction regarding AOB and Nitrobacter sp. distribution was consistent with the experimental counterpart. Measurements of AOB cluster size distribution showed that colonies are slightly larger adjacent to the membrane than at the inner part of the biofilm. The sizes predicted by the current model are larger than those obtained in the experiment, leading to the arguments that some factors not contained in the model would affect the cluster size.