Biofilms in Wastewater Treatment

by Stefan Wuertz, Paul L. Bishop, Peter A. Wilderer

Overview

The central theme of the book is the flow of information from experimental approaches in biofilm research to simulation and modeling of complex wastewater systems. Probably the greatest challenge in wastewater research lies in using the methods and the results obtained in one scientific discipline to design intelligent experiments in other disciplines, and eventually to improve the knowledge base the practitioner needs to run wastewater treatment plants. The purpose of Biofilms in Wastewater Treatment is to provide engineers with the knowledge needed to apply the new insights gained by researchers. The authors provide an authoritative insight into the function of biofilms on a technical and on a lab-scale, cover some of the exciting new basic microbiological and wastewater engineering research involving molecular biology techniques and microscopy, and discuss recent attempts to predict the development of biofilms. This book is divided into 3 sections: Modeling and Simulation; Architecture, Population Structure and Function; and From Fundamentals to Practical Application, which all start with a scientific question. Individual chapters attempt to answer the question and present different angles of looking at problems. In addition there is an extensive glossary to familiarize the non-expert with unfamiliar terminology used by microbiologists and computational scientists.   The colour plate section of this book can be downloaded by clicking here. (PDF Format 1 MB)

Product Details

ISBN-13:	9781843390077
Publisher:	IWA Publishing
Publication date:	04/30/2003
Edition description:	New Edition
Pages:	417
Product dimensions:	6.12(w) x 9.25(h) x 0.75(d)

Read an Excerpt

CHAPTER 1

What do biofilm models, mechanical ducks, and artificial life have in common?

Mathematical modeling in biofilm research

Hermann J. Eberl

While I have sought to show the naturalist how a few mathematical concepts and dynamical principles may help and guide him, I have tried to show the mathematician a field for his labour.

D'Arcy Wentworth Thompson (1917)

She said welcome to the real world kid.

Butch Hancock (1995)

1.1 MATHEMATICS AND BIOLOGY: HOW DO THEY GO TOGETHER?

Biofilm research is interdisciplinary research: biofilms occur in many different branches of science and technology, from wastewater engineering to medicine. Therefore, not surprisingly, biofilm researchers come from a broad variety of different scientific backgrounds and have a broad variety of scientific interests. Biologists may be interested in fundamental questions of bacterial behavior, environmental engineers in substrate conversion, and medical engineers in avoiding biofilm formation on artificial implants. But biofilms do not appear in mathematical systems, bacteria do not colonize abstract Banach spaces, and nobody is afraid of biofouling and biocorrosion of partial differential equations. Thus, why should mathematicians think about biofilms?

Mathematics is the language in which scientific theories are formulated. Or, rephrasing it in the words of medieval English scientist Roger Bacon: it is the door and key to science. The close relationship of mathematics on the one side and science and technology on the other one is mutual: not only are well- established mathematical methods used as tools in the study of technical or natural processes; mathematics, indeed, grows with its applications, and the applications have an important impact on mathematics' development by guiding its directions. The most famous example comes from physics. Newton had to develop differential calculus to be able to formulate his theory of gravity. But the same holds for biology, as the following examples will show.

Many mathematical results in the theory of semi-linear parabolic partial differential equations have been motivated by biological questions: for example, the spread of a favorable gene in a population. This question leads to the so- called Fisher equation, which is the canonical equation of its type and the starting point for many mathematical studies on nonlinear diffusion-reaction interactions. But not only complicated mathematical concepts like partial differential equations arise in the study of biological phenomena. Even the study of simple objects, such as iterative maps, benefited a lot from biology: In the 1970s it was found that rather simple interactions of populations or even the population dynamics of only one species (e.g. the discrete logistic growth model) can lead to virtually unpredictable behavior. The term chaos was coined for these effects, and studying them attracted many mathematicians. Eventually a new mathematical discipline was born.

Neural nets and genetic algorithms are two modern mathematical concepts for modeling and optimization. Their origin lies in mimicking learning processes in neurobiology and natural selection, respectively. The mathematical results obtained by studying these mathematical concepts that were originally stimulated by biology, flow back to the life sciences and often can be applied to problems in biology or bioengineering that are very different from the starting point. For example, neural nets and evolutionary algorithms are used to identify model parameters or to suggest control strategies in wastewater engineering. A more detailed survey of biological impacts in mathematics and mathematical impacts in biology can be found in Mathematics and Biology, The Interface on the World Wide Web at http://www.bio.vu.nl/nvtb/Interface.html. In the meantime, mathematical biology is considered to be a mathematical discipline in its own right, and research centers and research programs dedicated to the application of mathematics in the life sciences are currently being founded all over the world.

1.2. WHAT ACTUALLY ARE MATHEMATICAL MODELS AND WHAT IS MATHEMATICAL MODELING?

In this essay we shall try to explain how mathematics can contribute to biofilm research; in particular, how mathematics can help to explain and understand the highly heterogeneous biofilm architectures that are observed under the microscope. When we talk about the contribution of mathematics to biofilm research, we will be talking about mathematical modeling. (There are many other methods of applied mathematics that are very valuable for scientists and engineers of all disciplines, including biofilm research. For example, statistics and approximation theory are used to evaluate and process experimental data, optimization theory is deployed to identify model parameters or to determine best management strategies, as well as for optimal reactor design.) Mathematical models are abstract images of biological, physical, or other scientific systems. There are many different types of mathematical model, based on different mathematical concepts. In mathematical biology, the most important ones are differential and difference equations, stochastic models, and cellular automaton models. All these model concepts have different properties, and which one to choose depends on the object to be modeled and on the a priori information one has about the system, such as parameters. Chapter 3 of this volume contains a more detailed description and comparison of modeling concepts.

The behavior of the original system in the real world must be reflected in the behavior of its mathematical image. On the other hand, the image should not show a behavior and dependencies that cannot be found in its real world paragon. Of course, in realiter total equivalence of mathematical model and reality will never be observed because reality is too complex by far. Thus, mathematical models are always idealizations of reality, formulated to display some particular properties, which are of special interest for the researcher. Being idealizations of a complex process, mathematical models are always incomplete and they include empty, and for the particular purpose irrelevant, dependencies and relations. Several mathematical models might exist for one process, having different numbers of those empty relations. The modeler will always try to formulate and select a model, which has as few irrelevant relations as possible and is as complete as necessary for the scientific question he or she is interested in (Hertz 1894). A model serving very well for one purpose may be useless for another one because of being overcomplicated or incomplete. Recently, some spatial models have been suggested for biofilm growth (e.g. Wimpenny and Colasanti 1997; Picioreanu et al. 1998, 1999, 2001; Hermanowicz 1999, 2001; Noguerra et al. 1999; Eberl et al. 2001; Mehl 2001; Dockery and Klapper 2002). These models can be very valuable to understand local biofilm development. Owing to the complexity of multidimensional mathematics and computation, however, only small parts of a biofilm system can be described this way, but not an entire reactor. Therefore, these models are not suitable for quantitative engineering tasks, like design or control of a wastewater treatment plant, and they cannot be applied for these purposes. In return, classical zero-dimensional (lumped) approaches or one-dimensional models (e.g. Rittmann and McCarty 1980; Wanner and Gujer 1986; Saez and Rittmann 1992) can deal with many more different species and substrates and they give good results on global mass conversion rates for a full reactor. However, they do not give any knowledge on the local spatial architecture of the biofilm. Thus, the extent to which simplifications and idealizations must or can be introduced depends on the particular purpose of the mathematical model. (Another very well known example can be found in the history of Physics: From the viewpoint of Einstein's relativity theory, Newton's gravity theory is wrong and only valid (though in very good approximation) in special cases of our world, now called non-relativistic. And from the viewpoint of Newton's theory, Kepler's law was wrong. It is well accepted in Physics that Einstein's theory is a better (due to being more general) model than Newton's theory, which was already a better (due to being more accurate) model than Kepler's law. But if we are only interested in a rough estimation of the moon's motion around the earth, the latter one might be sufficient in accuracy for our purpose. We will prefer it because it is much easier to evaluate than its successors, though being proven wrong from an overall point of view. However, we would never expect to learn from Kepler's Law anything about the future development of the universe. On the other hand, we prefer Newton's theory of gravity for non-relativistic calculations, because it has fewer, and for this purpose irrelevant, relations than Einstein's theory. Indeed, the non-relativistic view holds for most observations of our intuitive world, including biofilms.) But there are further important constraints for the formulation of a mathematical model. It is useful only if we are able to derive the desired information from it, i.e. if we can solve it quantitatively or discuss the qualitative behavior of model solutions. That is, if our computational and mathematical capabilities are sufficient to work with the model. Typically, a mathematical model will consist of a set of equations with some model parameters, input data, and probably initial and boundary conditions, which are connecting the spatial domain of the model with the exterior world. If the purpose of modeling is a quantitative solution, quantitatively knowing this information a priori is essential. Thus, one must be aware that the model formulation should not contain parameters being too difficult or even impossible to be determined. If the purpose of modeling is a qualitative analysis, the actual values of the model parameters and boundary conditions might not be so important, but the model must have a mathematical structure that allows rigorous analytical treatment. Another restriction can come from economics and technology, if the modeling work must be done with given finite resources in a given finite time.

Other restrictions are conceptual. Because mathematical models always formulate a sort of hypothesis, they must be subject to tests for falsification. One method of model falsification is direct comparison with measurement data. Those, however, often are not available with the required accuracy. Thus, often falsification tests can only be done qualitatively, by comparing model behavior with the behavior of the real world's paragon, expected by experience. An evolutionary approach can be comparison with other theories and models. Thus, competition between models takes place. Falsification never stops until a model is definitely proven wrong. This means the model must undergo new falsifications whenever new scientific knowledge of relevance for the range of model validity is gained or whenever new, stronger methods for falsification become available. Accepting a hypothesis or a model finally and forever and stopping falsification tests is leaving the scientific game (Popper 1982). Testing models for falsification is very closely linked to model extrapolation. Because if a model, which has been formulated and falsified for one approach, is applied to another one not yet covered by previous tests, it must be tested for falsification again.

The idea of using idealized mathematical models to study scientific systems and processes dates back at least to Galileo's insight that the book of nature is written in the language of mathematics and his idea to formulate abstract laws for ideal objects (von Glaserfeld 1996). Whereas physics and mathematics have been closely linked since Galileo's days, the systematic application of mathematical modeling methods in biology is much newer and started only during the 1920s. Although there were contributions to a mathematical biology before that time, they can only be considered to be isolated researches in biology with mathematical techniques (Israel 1994). This may be so because biological systems appear more complex and irregular than many physical systems and, therefore, they seem to be more difficult to idealize. Another reason may be the strong influence of theology and the idea of Creation. A third possible factor is the biologists' feeling that every species is unique. Therefore, they often prefer to emphasize the diversity of species rather than to achieve generalizations, which is one of the base concepts of mathematics. Although theoretical, mathematical, or computational physics have been considered scientific disciplines in their own right for a very long time, a comparable theoretical, mathematical, or computational biology only evolved in recent decades. Surveying this historical development, it seems quite natural that in particular the physical processes of biological systems are under consideration for classical mathematical modeling. In biofilm research, examples are nutrient consumption and mass conversion which can be described as diffusion-reaction equations on different length scales (e.g. Wanner and Gujer 1986; Wood and Whitaker 1998), hydrodynamics and mass transfer in the bulk liquid (Picioreanu et al. 2000; Eberl et al. 2000b), and detachment due to shear forces (Picioreanu et al. 2001). These are known as classic problems in applied and computational mathematics: fluid dynamics, (reactive) mass transfer, and fluid-structure interactions.

A famous and early historical example for models of a biological system from the times before systematic theoretical biology evolved is Vaucanson's mechanical duck from 1735, an automaton that moved like a duck, looked like a duck, and seemed to digest like a duck (e.g. Hillier 1976; see figure 1.1). Of course, this mechanical duck is not what we understand as a mathematical model. But the principle is the same: underlying is the thought (or hypothesis) that the motion of a duck can be described by mechanical laws and the mathematical theory of mechanics already started with Newton some decades earlier; speaking in mathematical terms, kinematics is a part of differential geometry and therefore a mathematical discipline. Therefore, the mechanical model can be seen as an analog realization of this idea like computer simulations are modern day digital realizations. Nobody will claim that Vaucanson's duck really describes the nature of a duck; e.g. already the question Why does a duck move like this? is excluded and also 'How can ducks reproduce themselves?'. It is quite similar with biofilm models: the diffusion- reaction model for substrate concentrations is meant to describe mass transfer and conversion processes in biofilms. If mass transfer is not the only one thing about biofilms, this model should not be expected to tell the whole truth about biofilms. The underlying idea is: idealizing and reducing the complex system into smaller and easier to handle modules, which are of particular interest (motion of a duck, mass transfer in biofilms) and then studying them.

With the advent and general availability of powerful computers, mathematical modeling received a new boost, and it got the status of a key technique in science and engineering under the shiny label of simulation. This means, laboratory experiments are replaced with the aid of a computer by quantitatively solving established and accepted model equations. The advantages of computer experiments are well known. They are cheaper than laboratory experiments and often can be done and repeated much faster; the conditions under which the processes are studied can be well defined and are not subject to disturbing external influences; interesting processes easily can be isolated; the system behavior can be investigated in extreme situations, which are often very difficult to generate in a laboratory reactor. Having already an adequate model description in the beginning is a necessary prerequisite for computer simulation, not its goal. To simulate fluid motion in a biofilm reactor, for example, the well-established incompressible Navier-Stokes equations (the basic equations of hydrodynamics) must be solved. This is achieved by an application of methods of computational fluid dynamics (CFD). No new mathematical model must be formulated at all, and therefore we cannot talk about modeling in this context, but of simulation. Because closed analytical and exact solutions do not exist for many problems of relevance, typically numerical methods must be applied to obtain an approximation of the desired model solution. The more complicated the mathematics of a model is and the bigger the amount of data to be mastered, the more important are computational aspects. Accurate and fast algorithms must be selected to obtain an approximate model solution with available computing resources, and an efficient implementation of these algorithms is necessary. Even if a lower dimensional model shows every important qualitative property, often three-dimensional models are needed for a realistic quantitative description. The numerical effort increases tremendously when going to a higher dimensional spatial resolution. Hence, the more dimensions we consider in a computer realization, the more important are these issues. Spatial biofilm models made up from several multidimensional partial differential equations require an enormous amount of computational work and, therefore, are naturally an application for high performance computing on powerful parallel computers (Eberl et al. 2000a). The computer will yield all numerical results in long columns of data that are too voluminous to be surveyed by eye. They must be processed for further interpretation, validation, and usage. In most cases, graphical representations are very helpful and necessary, at least for qualitative purposes. In three-dimensional modeling, this is a complicated problem of its own, again involving extensive mathematics and requiring huge computational resources. These three tasks together – algorithms, implementation, and visualization – are the kernel of scientific computing, a discipline at the interface between mathematics and computer science, whereas mathematical modeling is a discipline at the interface between mathematics and science. The computational issues are not considered in this essay. Chapter 4 deals with them in more detail in the framework of scientific computing.

(Continues…)

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Table of Contents

Preface, viii,
About the editors, x,
List of contributors, xi,
PART ONE: MODELING AND SIMULATION, 1,
Modeling and simulation: Introduction Stefan Wuertz, 3,
1 What do biofilm models, mechanical ducks, and artificial life have in common? Mathematical modeling in biofilm research Hermann J. Eberl, 8,
2 Biofilm architecture: interplay of models and experiments Slawomir W. Hermanowicz, 32,
3 Towards new mathematical models for biofilms Volker Hösel and Volkmar Liebscher, 49,
4 Beyond models: requirements and chances of computational biofilms Hans-Joachim Bungartz and Miriam Mehl, 60,
5 On the influence of fluid flow in a packed-bed biofilm reactor Stefan Esterl, Christoph Hartmann and Antonio Delgado, 88,
PART TWO: ARCHITECTURE, POPULATION STRUCTURE AND FUNCTION, 121,
Architecture, population structure and function: Introduction Stefan Wuertz, 123,
6 The effect of biofilm heterogeneity on metabolic processes Paul L. Bishop, 125,
7 Mass transport in heterogeneous biofilms Zbigniew Lewandowski and Haluk Beyenal, 147,
8 The crucial role of extracellular polymeric substances in biofilms Hans-Curt Flemming and Jost Wingender, 178,
9 The importance of physicochemical properties in biofilm formation and activity Rosario Oliveira, Joana Azeredo and Pilar Teixeira, 211,
10 Influence of population structure on the performance of biofilm reactors Axel Wobus, Frank Kloep, Kerstin Roske and Isolde Roske, 232,
11 Detachment: an often-overlooked phenomenon in biofilm research and modeling Eberhard Morgenroth, 264,
Architecture, population structure and function: Conclusions Stefan Wuertz, 291,
PART THREE: FROM FUNDAMENTALS TO PRACTICAL APPLICATIONS, 295,
From fundamentals to practical applications: Introduction Peter A. Wilderer, 297,
12 Deduction and induction in design and operation of biofilm reactors Poul Harremoes, 299,
13 Effect of clay particles on biofilm composition and reactor efficiency Luis F. Melo and Maria J. Vieira, 299,
14 Bioprocess engineering and microbiologists: a profit-sharing alliance Peter A. Wilderer and Martina Hausner, 343,
From fundamentals to practical applications: Conclusions Peter A. Wilderer, 374,
Glossary, 377,
Index, 391,