Advanced Methods and Mathematical Modeling of Biofilms: Applications in Health Care, Medicine, Food, Aquaculture, Environment, and Industry

By Mojtaba Aghajani Delavar and Junye Wang

Advanced Mathematical Modelling of Biofilms and its Applications covers the concepts and fundamentals of biofilms, including sections on numerical discrete and numerical continuum models and different biofilms methods, e.g., the lattice Boltzmann method (LBM) and cellular automata (CA) and integrated LBM and individual-based model (iBM). Other sections focus on design, problem-solving and state-of-the-art modelling methods. Addressing the needs to upgrade and update information and knowledge for students, researchers and engineers on biofilms in health care, medicine, food, aquaculture and industry, this book also covers areas of uncertainty and future needs for advancing the use of biofilm models.

Over the past 25-30 years, there have been rapid advances in various areas of computer technologies, applications and methods (e.g. complex programming and algorithms, lattice Boltzmann method, high resolution visualization and high-performance computation). These new and emerging technologies are providing unprecedented opportunities to develop modeling frameworks of biofilms and their applications.

• Introduces state-of-the-art methods of biofilm modeling, such as integrated lattice Boltzmann method (LBM) and cellular automata (CA) and integrated LBM and individual-based model (iBM)
• Provides recent progress in more powerful tools for a deeper understanding of biofilm complexity by implementing state-of-the art biofilm modeling programs
• Compares advantages and disadvantages of different biofilm models and analyzes some specific problems for model selection
• Evaluates novel process designs without the cost, time and risk of building a physical prototype of the process to identify the most promising designs for experimental testing

• Language: English
• Publisher: Academic Press
• Release date: May 14, 2022
• ISBN: 9780323903745

Mojtaba Aghajani Delavar

Dr. Mojtaba Aghajani Delavar is a postdoctoral fellow at Athabasca University. He received his B.Sc. in mechanical engineering from Amirkabir University of Technology in 2001, M.Sc. and Ph.D. in mechanical Engineering from Mazandaran University in 2003 and 2010, respectively. He worked at Babol Noshirvani University of Technology in Iran as assistant and associate professor from 2010 until 2019. Then he joined professor Wang’s research group at Athabasca university. Dr. Delavar has about 20 year’s experience in modelling of various industrial and biological systems using different modelling schemes including mathematical and numerical analysis and simulation. He has authored/co-authored over 80 papers including more than 45 peer reviewed journal papers.

Book preview

Advanced Methods and Mathematical Modeling of Biofilm

Applications in health care, medicine, food, aquaculture, environment, and industry

Mojtaba Aghajani Delavar

Research Fellow, Athabasca University, Athabasca, Alberta, Canada

Junye Wang

Professor, Athabasca University, Athabasca, Alberta, Canada

Research Chair, Campus Alberta Innovation Program (CAIP), Athabasca University, Athabasca, Alberta, Canada

Table of Contents

Cover image

Title page

Copyright

Author bios

Preface

Chapter 1. Introduction

1.1. Background

1.2. History of biofilms studies

1.3. Problems and objectives of biofilm research

Chapter 2. Concept and fundamentals of biofilms

2.1. Overview

2.2. Spatiotemporal heterogeneity

2.3. Nutrient availability and environmental conditions

2.4. Competition and cooperation

2.5. Modeling approaches and selection

2.6. Numerical solutions

2.7. Classification and selection of mathematical models

Chapter 3. Kinetic models

3.1. Monod model

3.2. Extended Monod's models

3.3. Substrate consideration

3.4. Other unstructured models

3.5. Summary

Chapter 4. Continuum models

4.1. Continuum models overview

4.2. One-dimensional continuum models

4.3. Multidimensional continuum models

4.4. Quorum sensing, antimicrobial persistence, and EPS modeling

4.5. Summary

Chapter 5. Discrete models

5.1. Discrete models overview

5.2. Biological cellular automata

5.3. Individual-based models

5.4. Hybrid model of computational fluid dynamics and cellular automata

5.5. Summary

Chapter 6. Hybrid lattice Boltzmann continuum–discrete models

6.1. Biofilm growth and development in reactive transport systems

6.2. Hybrid lattice Boltzmann and cellular automaton models

6.3. Hybrid lattice Boltzmann and individual-based models

6.4. Summary

Chapter 7. Bioreactor concepts, types, and modeling

7.1. Bioreactor definition and functions

7.2. Bioreactor types

7.3. Bioreactor components and control system

7.4. Bioreactor modeling

7.5. Challenges and trends for bioreactor modeling

7.6. Summary

Index

Copyright

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Author bios

Dr. Mojtaba Aghajani Delavar is a Research Fellow at Athabasca University. He received his B.Sc. in Mechanical Engineering from Amirkabir University of Technology in 2001, M.Sc., and Ph.D. in Mechanical Engineering from Mazandaran University in 2003 and 2010, respectively. He worked at the Babol Noshirvani University of Technology in Iran as an associate professor from 2010 until 2019. Then he joined professor Wang's research group at Athabasca University. Dr. Delavar has over 20 years of experience in modeling various industrial and biological systems using different modeling schemes including mathematical and numerical analysis and simulation. He has authored/coauthored over 100 papers including more than 60 peer-reviewed journal papers.

Dr. Junye Wang is a Professor and the Campus Alberta Innovation Program (CAIP) Research Chair at Athabasca University, Canada. He received his M.Sc. in Thermo-physics from Harbin Shipbuilding Engineering Institute and Ph.D. in Chemical and Mechanical Engineering from East China University of Science and Technology in 1989 and 1996, respectively. Then he joined Shanghai Jiaotong University as an associate professor in 1996. From 1999 till 2013, he worked at the Universities of Sheffield, Greenwich, and Loughborough, and Scottish Crop Research Institute, and Rothamsted Research, UK, as a research associate, research scientist, and principal research scientist, respectively. Dr. Wang has over 30 years' experience in multiscale and multidisciplinary modeling and is an internationally recognized leader in microbiology, bioenergy, and environment. He has authored/coauthored over 160 papers, including over 120 refereed journal papers, and serves as associate editor and editorial board member on several international journals. He is also a reviewer of papers for over 130 international journals.

Preface

Biofilms are a complex and heterogeneous aggregation of microorganisms held together by their excreting extracellular polymer substances. Even though microorganisms can cause many serious issues, such as chronic infections, food contamination, and equipment corrosion, they can also be used constructively for things such as wastewater treatment, heavy metal removal from hazardous waste sites, biofuel production, and power generation through microbial fuel cells. Because of the great variety of biofilm applications, a lot of work has gone into figuring out how biofilms form and interact with their surroundings. However, biofilm growth and evolution are very complex interactions among physicochemical and biological processes. Considerable challenges exist in understanding microbial processes where macroscopic dynamics of nutrient transport must be coupled with microscopic bacteria growth and their elementary biochemical reactions at reactive or enzymatic interfaces, in addition to the microbiological and/or ecological aspects of the micro organisms involved in biofilms. Furthermore, biofilm processes' intrinsic interdisciplinary character provides a platform for interdisciplinary research from a variety of fields, including biofouling, soil microbial ecology, bioremediation, wastewater engineering, tissue engineering, biosynthesis, and chronic infections. If we are to be able to link biofilm function to biotechnologies, this will allow scientists and engineers to redesign their devices or processes to inhibit harmful biofilms or to promote beneficial ones in clinical, environmental, or industrial applications. Hence, it is essential for understanding and controlling how bacteria interact with their environment and space and affect the production or degradation of a variety of compounds in an interdependent environment, such as nutrients, temperature, pH, and moisture. Mathematical models are critical to modern biotechnology—both in research and in engineering practice. Thus, many models of biofilms have been developed to include various biofilm reactor modules. Modeling plays a similar function in 21st-century microbiology as the microscope did in previous centuries; it is undoubtedly the most essential study tool for examining complicated phenomena and processes in all sectors of biofilms, from individual cells to microbial community ecosystems. We believe that the mathematical model has a lot of potential in terms of furthering our understanding of how biofilms interact with their environments, as well as how they are transferred into biotechnologies and microbiome-based diagnostics and therapies.

However, the bulk of the engineering community either does not use the readily available biofilm reactor models or utilizes them as effective design tools. This is because the book of mathematical biofilm models is still scarce, leading to insufficient documented knowledge and formulations that have been historically applied to biofilm reactor design. Over the past 25–30 years, there have been rapid advances in various areas of computer technologies and applications (e.g., complex programming and algorithms, lattice Boltzmann method, high-resolution visualization, and high-performance computation). These new and emerging technologies are providing unprecedented opportunities to develop modeling frameworks for biofilms and their applications. However, this progress is scattered in the different disciplines, such as biofuel production, biological wastewater treatment, infection, and contaminated soil bioremediation. It is a challenge to have an overview of biofilm modeling for the students, researchers, and engineers because no such a book introduces this progress.

The objectives of the book are to provide an introduction to biofilm modeling, including the state-of-the-art modeling methods. Therefore, this can address the need to upgrade and update information and knowledge for the audience. The book presents an overview of current models, areas of uncertainty in accounting for the importance of bulk liquid hydrodynamics and biofilm formation, and future requirements for increasing the use of biofilm models in engineering design. We will use examples from a variety of microbiological and bioengineering disciplines to demonstrate the applicability of integrated biofilm models for modeling biofilm formation and growth, and we will illuminate the benefits of applying different mathematical approaches to specific biofilm subfields, as well as the distinct challenges that mathematical models require to conquer.

This book provides an up-to-date broad review of the many algorithms and mathematical approaches that are generally found spread throughout different disciplines to cover that gap for anyone who is interested in the most relevant topics and wishes to teach themselves. As a result, it provides ambitious students with a toolbox of tactics that will serve them well in modeling issues taken from a variety of areas of microbiology. This will assist students in exploring the fundamental principles of modeling, including how to formulate mathematical models of biofilm systems that are tractable to computational analysis and what the student needs to use them effectively, as well as references for further reading on more advanced applications of each approach covered.

Chapter 1: Introduction

Abstract

Biofilm communities are now thought to be the dominant type of microbial life in most aquatic environments, human health and illness, and biotechnology, owing to a growing understanding of their importance. As a result, ecological theory is required to enhance our understanding of biofilms. In this chapter, we revisit the history of biofilm research and biofilm modeling, which may serve as a general approach to the study of biofilms' many features. We also talk about the issues and goals of biofilm research, as well as the relevance of advanced modeling tools that allow for the construction and prediction of microbial community structures.

Keywords

Bioaggregate; Biofilm; Extracellular polymeric molecules; Microorganism; Modeling

1.1. Background

Microorganisms are one of the most extensively spread and successful forms of life on earth, living in natural habitats, industrial equipment, and clinical devices (Stoodley et al., 2002). In natural habitats, most microorganisms thrive in communities rather than planktonic cells. Microorganisms tend to grow not only as a single species community of pathogens and nonpathogens but also as multispecies communities (Donlan, 2002; Kragh et al., 2016; Melaugh et al., 2016). Biofilms can adhere to various solid–liquid, air–liquid, or liquid–liquid interfaces, such as implanted medical devices, living tissues, industrial or potable water pipes, and devices, or natural aquatic surfaces. It is widely accepted that biofilms are the primary lifestyle of bacteria, with a unique phenotype in terms of gene transcription and growth rate. It was discovered that 99.9% of all bacteria adhered to an aqueous surface and proliferated together as their crucial survival strategy (Geesey et al., 1977; Donlan and Costerton, 2002). In some situations, biofilms can form as swimming clusters in activated slimes in an aquatic environment where they are not adherent to a solid substratum. The ratio of epilithic to planktonic microorganisms is greater than 1000–10,000:1 (https://www.cs.montana.edu/webworks/projects/stevesbook/contents/chapters/chapter001/section003/green/page002.html).

The characteristics of biofilms in natural habitats can differ substantially, as evidenced by scanning electron micrographs of biofilms from an industrial water device and a river stream (Fig. 1.1) (Donlan, 2002; Suarez et al., 2019). As multicellular communities of microbial cells, biofilms are immersed in a self-produced matrix of extracellular polymeric molecules (EPS). Fluorescence in situ hybridization (FISH) analyses of biofilm cryosections showed that the Z400 biofilm was likely stratified, where Nitrospira was more abundant in the middle of the biofilm and the anaerobic anammox bacteria presented in the deeper layers while Nitrosomonas biovolume was the same along the depth gradient (Fig. 1.1A and B) (Suarez et al., 2019). In the thin Z50 biofilms, no stratification was observed as the ammonia oxidizing bacteria (AOB) and the oxygenated water and nitrite oxidizing bacteria (NOB) populations were located side by side. Many microbial communities have cell densities ranging from 10⁸ to 10¹¹ cells per gram of wet mass, comprising 1 million to 100 billion cells (Byrne and Drasdo, 2009; Gebreyohannes et al., 2019). In honeycomb configurations, stream biofilms can cohabit with algae, EPS, and diatom cells (Battin et al., 2003). Although the chemistry and physiology of biofilms might differ due to different bacteria and their surrounding environment, the biomass of biofilms contains around 90% EPS, which adds to the resemblance of the mushroom-like structure (Jamal et al., 2018; Stewart and Franklin, 2008).

Figure 1.1  Physical structure and building blocks of biofilms: (A) Fluorescence in situ hybridization (FISH) images of a Z400 biofilm cryosection with the water–biofilm interface on the top (Green: Nitrosomonas, Red: Nitrospira. Yellow: Nitrotoga. Blue: Brocadia. Gray: SYTO), (B) FISH images of a Z50 biofilm cryosection with the water–biofilm interface on the top (Green: Nitrosomonas, Red: Nitrospira. Yellow: Nitrotoga. Blue: Brocadia. Gray: SYTO) (Suarez et al., 2019), and (C) SEM (scanning electron micrograph) image of a native biofilm formed on low carbon steel intersurface in an industrial water system over an 8-week period, scale bar, 20μm (Donlan, 2002).

Biofilms in populations are typically made up of numerous colonies of various bacterial species (Vidakovic et al., 2018). Wastewater treatment systems consist of thousands of operating taxonomic groups at the species level (Law et al., 2016; Saunders et al., 2016). In the natural environment, biofilms contain over 750 distinct species (Ley et al., 2006), and oral biofilms contain a variety of thousands of microorganisms as an embrace of bacteria and eukaryotes.

Microorganisms thriving in a communal lifestyle have some benefits over planktonic cells: (1) increased rigidity to erosion by streamflow stress; (2) enhanced resistance to antimicrobials; (3) higher biomass density for the treatment of various inorganic and inorganic substrates in bioengineering; (4) improved cell-to-cell interaction, gene delivery, and metabolic workload sharing; and (5) provided heterogeneous structures for diffusion and consumption of nutrients benefits (Wang and Zhang, 2010).

Fig. 1.1A and B depicts the heterogeneity of the EPS matrix development (Suarez et al., 2019). Deterministic assembly in biofilms depends on specific mechanisms. For example, structured microenvironments may limit the diffusion of electron donors and acceptors in biofilms, resulting in form steep gradients. The thickness of the liquid boundary layer that limits diffusion of soluble substrates, including dissolved oxygen (DO), from the bulk liquid to the biofilm was determined by comparing the ammonium oxidation rates calculated by the model to those measured during the nitrogen transformation activity tests (Suarez et al., 2019). Microorganisms that live in soil aggregates or habitats can adapt their activity and composition in response to the changes in nutrient and environmental circumstances (Young and Crawford, 2004). The persistent gradients were created to enable distinct local habitats on a fine scale. Microorganisms in an aerobic copiotrophic biofilm stratify in terms of oxygen availability. Because oxygen is extracted by aerobic organisms in the higher layers of the biofilm, a layer of anaerobes develops in the lower layers of the biofilm due to oxygen depletion. This can be attributed to the fact that the rate of oxygen consumption exceeds the rate of diffusion.

Flemming et al. (2016) showed that bacteria in the upper layers of aerobic oligotrophic biofilms are likely to consume the majority of the nutrients, causing starving microorganisms in the bottom layers (Fig. 1.2). These microbes adapt to sluggish growth states, such as inactive cells, or even cell death. Other gradients in biofilms produced by heterotrophic metabolism include pH gradients and gradients of signaling chemicals that vary with distance from generating cells.

Most elements in water, soil, sediment, and subsurface environments are cycled biogeochemically by microorganisms (Battin et al., 2008; Ehrlich and Newman, 2008; Bhanja et al., 2019; Bhanja and Wang, 2020, 2021; Meckenstock et al., 2015). The metabolism of terrestrial organic carbon in freshwater environments contributes significantly to the emission of carbon dioxide into the atmosphere (Battin et al., 2008). Biofilms through well-defined interactions for specially designed purposes have been used in a range of bioindustries, such as improved safety of foods (Stiles, 1996), biosynthesis and bioremediation (Tsoi et al., 2019), and inhibition of pathogenic growth in nonfermented, refrigerated foods (Gombas, 1989).

Biofilms are found numerously in a wide range of infectious diseases in both clinical and public health settings (Donlan, 2002). They can persistently grow on both biotic and abiotic surfaces, such as a human tooth or lung, a cow's intestine, or rock immersed in a fast-moving stream. Biofilms can colonize on various medical devices, including intrauterine contraceptive devices, prosthetic medical devices, catheters, heart valves, implant devices, dental materials, and contact lenses, resulting in a variety of device-associated illnesses. Clinical investigations have emphasized the significance of biofilms in producing human illnesses, accounting for up to 60% of all infections (Chen and Wen, 2011). Biofilms have a substantial influence on the industrial environment, including biofouling, biocorrosion, oil field souring, and effluent (Klapper and Dockery 2002).

Figure 1.2  Biofilm heterogeneity characteristics, and social competition and cooperation (Flemming et al., 2016).

1.2. History of biofilms studies

1.2.1. Biofilm and bioaggregates

Most of the history of microbiology has classified microbes as planktonic, freely swinging cells in a nutritionally abundant aquatic environment depending on their growth environment. However, the majority of microbes in aquatic environments are not free-suspended microorganisms but instead dwell on immerged surfaces, where they form organized colonies known as biofilms. Until the 17th century, biofilms were first characterized by Van Leeuwenhoek from Delft (1632–1723), who observed microbial colonies on shavings of plaque from his teeth with his crude microscope (Dobell, 1932). The genes transcribed by biofilm bacteria differ from those done by planktonic counterparts (Henrici 1933). As early as 1933, the word biofilm was termed in technical and environmental microbiology (Henrici, 1933; Zobell and Allen, 1935).

Earlier studies of biofilms were mainly in wastewater filtering, industrial equipment biofouling, and dental plaque. Louis Pasteur (1822–95) discovered and sketched bacterial aggregation as the origin of acetic wine (Hoiby, 2014, 2017). For biofilm description, much of the biofilm studies depend on the development of instruments, such as scanning electron microscopy (SEM) or traditional microbial culture techniques. Two key advances in biofilm research occurred in the past few decades: the first one was the use of the confocal laser scanning microscope to analyze biofilm ultrastructure, and the second was the study of the genes related to cell adhesion and biofilm development (Battin et al., 2007).

Robert Koch (1843–1910) was a pioneering microbiologist who attempted to isolate and characterize microbes from their natural habitats. The pure culture technique allows the high level of replication and handling to better understand how microorganisms culture respond to different situations. In microbiology, this led to the Golden Age since it provided an opportunity to study organisms in the lab in considerable detail under tightly controlled settings (such as growth conditions) or with genetic modifications. Because most bacteria exist as multispecies communities, pure culture cannot describe multispecies community phenomena. Because of this, biofilm research increasingly employs methods previously reserved for studying populations, such as meta-omics-based methodologies and high-resolution scanning (Battin et al., 2007).

The biofilm research was revived in the 1970 and 1980s. Microorganisms that grew on a surface were considered as flat and uniform films of cells encased in slime. The nature of biofilms in the human host can be significantly different from that at the surfaces exposed to the environment. In the mid-20th century, scientists discovered that biofilms are primarily composed of diverse populations of bacteria (Kragh et al., 2016; Melaugh et al., 2016).

Environmental changes or the metabolism and migration of other communities cause dynamic changes in nutritional gradients for each population. Therefore a certain biofilm community's success rate is highly dependent on the other members' performance as well as regulation and control of quorum sensing (QS). In medical microbiology, Nickel et al. (1985) introduced the concept of biofilm growth in their pioneer research into the physiological and biochemical features of bacteria. They found that biofilm-growing bacteria exhibited greater resistance than planktonically developing bacteria.

The term film is insufficient to describe bacterial life; hence the name biofilm is somehow misleading. Biofilm cells do not just pile up on top of each other; instead, they create complex, self-organized structures from the bottom up. There are a wide range of biofilms that differ from one microorganism population to another, depending on the type of bacterial community and environmental conditions, such as streamers, columns, mushrooms, bioclusters, microbial mats, microcolonies, and bioaggregates (Atkinson et al., 1967). Apparently, because these terms are already widely used in their respective fields, whether the term of biofilms needs to be replaced or is controversial (Baveye, 2020; Flemming et al., 2021). As a result, the word biofilm here refers to the extensive bacterial attachment on surfaces to differentiate aggregated bacteria from free suspended planktonic bacteria. Biofilms represent multicellular microbial aggregates that are not limited to microbial films on surfaces.

1.2.2. Biofilm modeling

Modeling of biofilms dates back to the 1970s. Biofilms were described as homogeneous biomass of a single microbial species (Atkinson and Davies, 1974; Williamson and McCarty 1976; Harremoes, 1976; Rittmann and McCarty, 1980). The first-generation approaches were quick and easy to implement, sometimes using a simple spreadsheet. However, they describe only uniform growth and cannot capture all noneven growth. Following that, stratified dynamic models were developed as second-generation models (Wanner and Gujer, 1986). These layered models were developed to represent interactions between multiple substrates and species inside the biofilm. They were, however, unable to account for the typical structural diversity. Therefore, the third-generation models are developed to represent the characteristic structural heterogeneity inside a biofilm.

In the third-generation models, the coupled model of biomass growth submodels (e.g., detachment, decay, biomass division, and spreading), and transport submodels (e.g., flow, substrate transport, and reactions) are solved using the finite difference method (FDM) or the finite volume method (FVM) (Picioreanu et al., 2004). The Navier–Stokes equations, and reactive transport equations have been developed to simulate biofilm growths (Picioreanu et al., 1998a,b, 2001, 2004; Eberl et al., 2001; Pizarro et al., 2001; Laspidou and Rittmann, 2004; Xavier et al., 2005). Both continuum models and discrete models for biofilm growth started to be developed to describe the formation of multidimensional biofilm morphology in the 1990s and carry to today as the third-generation mathematical models. In the continuum models, biofilm growth is described using a transport equation (Eberl et al., 2001) and couples with hydrodynamics and substrate transport processes. The term discrete denotes that the system's space, time, and characteristics can only have a finite number of states. In the early stage, a domain space is discretized into regular grid elements, establishing a lattice. The large-scale dynamics of mass transport and hydrodynamics are solved using the FDM or the FVM while the biofilm structures are done