كتب في علم الميكروبيولوجي

CRC Series in
CONTEMPORARY FOOD SCIENCE

MODELING MICROBIAL
RESPONSES in FOOD

© 2004 by Robin C. McKellar and Xuewen Lu

CRC Series in

CONTEMPORARY FOOD SCIENCE

Fergus M. Clydesdale, Series Editor
University of Massachusetts, Amherst

Published Titles:

America's Foods Health Messages and Claims:
Scientific, Regulatory, and Legal Issues
James E. Tillotson

New Food Product Development: From Concept to Marketplace
Gordon W. Fuller

Food Properties Handbook
Shafiur Rahman

Aseptic Processing and Packaging of Foods:

Food Industry Perspectives

Jarius David, V. R. Carlson, and Ralph Graves

The Food Chemistry Laboratory: A Manual for Fxperimental Foods,
Dietetics, and Food Scientists, Second Fdition
Connie M. Weaver and James R. Daniel

Handbook of Food Spoilage Yeasts
Tibor Deak and Larry R. Beauchat

Food Fmulsions: Principles, Practice, and Techniques
David Julian McClements

Getting the Most Out of Your Consultant: A Guide
to Selection Through Implementation
Gordon W. Fuller

Antioxidant Status, Diet, Nutrition, and Health
Andreas M. Papas

Food Shelf Life Stability

N.A. Michael Eskin and David S. Robinson

Bread Staling

Pavinee Chinachoti and Yael Vodovotz

Interdisciplinary Food Safety Research
Neal M. Hooker and Elsa A. Murano

Automation for Food Engineering: Food Quality Quantization

and Process Control

Yanbo Huang, A. Dale Whittaker, and Ronald E. Lacey

Modeling Microbial Responses in Food
Robin C. McKellar and Xuewen Lu

2004 by Robin C. McKellar and Xuewen Lu

CRC Series in
CONTEMPORARY FOOD SCIENCE

MODELING MICROBIAL
RESPONSES in FOOD

Edited by

Robin C. McKellar
Xuewen Lu

CRC PRESS

Boca Raton London New York Washington, D.C.

2004 by Robin C. McKellar and Xuewen Lu

1237_C00.fm Page 4 Wednesday, November 12, 2003 12:29 PM

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Library of Congress Cataloging-in-Publication Data

Modeling microbial responses in foods / edited by Robin C. McKellar and Xuewen Lu.
p. cm. — (CRC series in contemporary food science)
Includes bibliographical references and index.
ISBN 0-8493- 1237-X (alk. paper)
1. Food — Microbiology. I. McKellar, Robin C, 1949-11. Lu, Xuewen. III. Series.

QR115.M575 2003
664'.001'579— dc22

2003055715

This book contains information obtained from authentic and highly regarded sources. Reprinted material
is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable
efforts have been made to publish reliable data and information, but the author and the publisher cannot
assume responsibility for the validity of all materials or for the consequences of their use.

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© 2004 by Robin C. McKellar and Xuewen Lu for the Department of Agriculture and Agri-Food,

Government of Canada
Minister of Public Works and Government Services of Canada

No claim to original U.S. Government works

International Standard Book Number 0-8493- 1237-X

Library of Congress Card Number 2003055715

Printed in the United States of America 1 234567890

Printed on acid-free paper

2004 by Robin C. McKellar and Xuewen Lu

1237_C00.fm Page 5 Wednesday, November 12, 2003 12:29 PM

Preface

The field of food microbiology is a broad one, encompassing the study of microor-
ganisms that have both beneficial and deleterious effects on the quality and safety
of raw and processed foods. The microbiologist's primary objective is to identify
and quantify food-borne microorganisms; however, the inherent inaccuracies in the
enumeration process and the natural variation found in all bacterial populations
complicate the microbiologist's job. Accumulating sufficient data on the behavior
of microorganisms in foods requires an extensive amount of work and is costly. In
addition, while data can describe a microorganism's response in food, they provide
little insight into the relationship between physiological processes and growth or
survival. One way this link can be made is through the use of mathematical models.

In its simplest form, a mathematical model is a simple mathematical description
of a process. Models have been used extensively in all scientific disciplines. They
were first used in food microbiology in the early 20th century to describe the
inactivation kinetics of food-borne pathogens during thermal processing of foods.
Since then, with the advent of personal computers and more powerful statistical
software packages, the use of modeling in food microbiology has grown to the point
of being recognized as a distinct discipline of food microbiology, termed predictive
microbiology. This concept was introduced and extensively discussed (with partic-
ular reference to growth of food-borne pathogens) by McMeekin and his colleagues
at the University of Tasmania. 1

Predictive microbiology has application in both microbial safety and quality of
foods; indeed, early development of the concept was based on seafood spoilage.
Extensive research in recent years has shown, however, that the most important
application of predictive microbiology is in support of food safety initiatives. Micro-
bial growth and survival models are now sufficiently detailed and accurate to make
important contributions — scientists and regulators can make reasonable predictions
of the relative risk posed by a particular food or food process. It has been argued,
however, that predictive microbiology is a misnomer, for predictive microbiology
does not actually make predictions at all. To examine this further, we need to first
look at some definitions of modeling.

In a general sense, a model simplifies a system by using a combination of
descriptions, mathematical functions or equations, and specific starting conditions.
There are two general classes of models: descriptive and explanatory, the latter being
composed of analytical and numerical models. Descriptive (i.e., observational,
empirical, "black box," or inductive) models are data-driven — approaches such as
polynomial functions, artificial neural nets, and principal component analysis are
used to classify the data. True predictions with this class of models are difficult to
make because models cannot be extrapolated beyond the data used to build the

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model. In spite of this, descriptive models have been used extensively with consid-
erable success in predictive microbiology.

Explanatory (i.e., mechanistic, "white box," or deductive) models aim to relate
the given data to fundamental scientific principles, or at least to measurable physi-
ological processes. Many predictive microbiology models have parameters that are
related to observed phenomena and are therefore considered mechanistic. Analytical
models — explicit equations that can be fit to data — are the most common form
of mechanistic models. To be truly mechanistic, however, a model should raise new
questions and hypotheses that can be tested. This is not always easy with explicit
functions, however, because it is difficult to extend such functions to dynamic
situations or add additional steps to the model. Numerical approaches are designed
specifically to allow further development of the model. These models are hierarchi-
cal, containing submodels at least one level deeper than the response being described.
They have been extensively developed for complex ecological systems, but have not
been applied to any great extent in predictive microbiology. Because their use
requires extensive programming skills, numerical models have been difficult for
nonmathematicians to apply. New software platforms and concepts, such as object-
oriented programming, have provided new tools, allowing microbiologists to expand
on traditional modeling approaches.

The models discussed so far (and the majority of existing predictive microbiol-
ogy models) have all been deterministic. In a deterministic model, knowledge of the
starting conditions, combined with a mathematical function describing the behavior
of the system over time, is sufficient to predict the state of the system at any point
in time. Bacteria, however, are not so cooperative. While it may be possible to define
a function, the starting conditions are less clear — particularly when dealing with
individual bacterial cells. Models that recognize and account for uncertainty or
variability in an experimental system are called stochastic or probabilistic models.
Probability models have been used extensively in the past to predict the probability
of germination of pathogenic spore-forming bacteria. Recently, the behavior of
individual bacteria has been likened to that of atoms, in a concept referred to as
quantal microbiology, analogous in some ways to quantum mechanics. 2 In addition,
the effect of environmental stress on microorganisms leads to interpopulation diver-
sity, where individual cells may be phenotypically but not genetically different from
each other. 3 Recent advances in the use of software that allows the development of
probability models have helped to make these approaches more accessible and
provided more support for the development of risk assessment procedures.

McMeekin's monograph set the stage for an explosive increase in predictive
microbiology research in the last decade of the 20th century. As we begin the new
millennium, there is a need for a definitive work on the subject, above and beyond
the many comprehensive and stimulating reviews that have appeared. This book is
intended to serve many purposes. First, we believe it will be a primer for many who
are not familiar with the field. Chapter 1, "Experimental Design and Data Collection";
Chapter 2, "Primary Models"; and Chapter 3, "Secondary Models" are designed in
part to give the uninitiated sufficient information to start developing their own models.
Other chapters address more complex issues such as the difficulties in fitting models
(Chapter 4, "Model Fitting and Uncertainty") and the relevance of models to the real

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world (Chapter 5, "Challenge of Food and the Environment"). Extensive applications
of predictive microbiology are covered in Chapter 6, "Software Programs to Increase
the Utility of Predictive Microbiology Information," and in Chapter 7, "Modeling
Microbial Dynamics under Time-Varying Conditions." The important contribution
made by predictive microbiology to quantitative risk assessment is described in
Chapter 8, "Predictive Microbiology in Quantitative Risk Assessment"; and the
further complication of individual cell behavior and intercell variability is addressed
in Chapter 9, "Modeling the History Effect on Microbial Growth and Survival:
Deterministic and Stochastic Approaches." The future of predictive microbiology is
the subject of Chapter 10, "Models — What Comes after the Next Generation?"
Application of predictive microbiology concepts to the study of fungi is dealt with
in Chapter 11, "Predictive Mycology"; and in Chapter 12, "An Essay on the Unre-
alized Potential of Predictive Microbiology," Tom McMeekin discusses the contri-
bution made by predictive modeling to the field of food microbiology.

We have attempted to cover the basics of predictive microbiology, as well as
the more up-to-date and challenging aspects of the field. There are extensive refer-
ences to earlier work, as well as to recent publications. It is anticipated that this
book will reflect the extensive research that has been instrumental in placing pre-
dictive microbiology at the forefront of food microbiology, and that it will stimulate
future discussion and research in this exciting field.

REFERENCES

1. McMeekin, T.A., Olley, J.N., Ross, T, and Ratkowsky, D.A., Predictive Microbiol-
ogy: Theory and Application, John Wiley & Sons, New York, 1993.

2. Bridson, E.Y. and Gould, G.W., Quantal microbiology, Lett. Appl. Microbiol., 30, 95,
2000.

3. Booth, I.R., Stress and the single cell: intrapopulation diversity is a mechanism to
ensure survival upon exposure to stress, Int. J. Food Microbiol., 78, 19, 2002.

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About the Editors

Robin C. McKellar is a senior research scientist
who obtained a B.Sc. in biology and chemistry,
an M.Sc. in microbiology from the University of
Waterloo, and a Ph.D. in microbiology from the
University of Ottawa. Dr. McKellar joined the
Food Research Institute in Ottawa in 1979 to
study the problem of psychrotrophic bacteria in
milk. After the formation of the Centre for Food
and Animal Research, he served as team leader
of the Food Safety Team and initiated a research
program on the control of food-borne pathogens.
He relocated to Guelph in 1996, and now serves
as program science advisor for Theme 410 (Food Safety), and research leader of
the Food Preservation Technologies section at the Food Research Program. He has
been actively involved in research in such areas as quality of dairy products; enzy-
matic and microbiological methods development; characterization of the virulence
factors of food-borne pathogens; control of pathogens using antimicrobial agents;
use of the electronic nose to monitor quality of foods and beverages; and mathe-
matical modeling of pathogen survival and growth in foods. He is currently an
adjunct professor with the Department of Food Science, University of Guelph, and
has cosupervised several graduate students.

Xuewen Lu is an assistant professor of statistics
in the Department of Mathematics and Statistics at
the University of Calgary, Canada. Before he
joined the university, he was a research scientist in
the Atlantic Food and Horticulture Research Cen-
tre, Agriculture and Agri-Food Canada from 1997
to 1998, a biostatistician at the Food Research Pro-
gram, Agriculture and Agri-Food Canada, and a
Special Graduate Faculty member at the University
of Guelph from 1998 to 2002. He is a member of
the Statistical Society of Canada and the Canadian Research Institute for Food Safety,
University of Guelph. His main research areas are functional data analysis, survival
analysis, and predictive microbiology. He has cosupervised several graduate students.
He received his B.Sc. degree (1987) in mathematics from Hunan Normal University,
China, M.Sc. degree (1990) in statistics from Peking University, China, and Ph.D.
degree (1997) in statistics from the University of Guelph.

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Contributors

Jozsef Baranyi

Institute of Food Research

Norwich Research Park

Colney, Norwich, United Kingdom

Kristel Bernaerts

BioTeC-Bioprocess Technology and

Control
Department of Chemical

Engineering
Katholieke Universiteit Leuven
Leuven, Belgium

Tim Brocklehurst

Institute of Food Research

Norwich Research Park

Colney, Norwich, United Kingdom

Paw Dalgaard

Department of Seafood Research
Danish Institute for Fisheries

Research
Ministry of Food, Agriculture, and

Fisheries
Lyngby, Denmark

Philippe Dantigny

Laboratoire de Microbiologic
Universite de Bourgogne
Dijon, France

Johan Debevere

Laboratory for Food Microbiology and

Food Preservation
Department of Food Technology and

Nutrition
Ghent University, Belgium

Els Dens

BioTeC-Bioprocess Technology and

Control
Department of Chemical Engineering
Katholieke Universiteit Leuven
Leuven, Belgium

Frank Devlieghere

Laboratory for Food Microbiology and

Food Preservation
Department of Food Technology and

Nutrition
Ghent University
Ghent, Belgium

Annemie Geeraerd

BioTeC-Bioprocess Technology and

Control
Department of Chemical Engineering
Katholieke Universiteit Leuven
Leuven, Belgium

Anna M. Lammerding

Health Canada

Laboratory for Foodborne Zoonoses

Guelph, Ontario, Canada

Xuewen Lu

Department of Mathematics and

Statistics
University of Calgary
Calgary, Alberta, Canada

Robin C. McKellar

Food Research Program
Agriculture and Agri-Food Canada
Guelph, Ontario, Canada

2004 by Robin C. McKellar and Xuewen Lu

1237_C00.fm Page 12 Wednesday, November 12, 2003 12:29 PM

Tom McMeekin

Centre for Food Safety and Quality
School of Agricultural Science
University of Tasmania
Hobart, Tasmania, Australia

Greg Paoli

Decisionalysis Risk Consultants
Ottawa, Canada

Carmen Pin

Institute of Food Research

Norwich Research Park

Colney, Norwich, United Kingdom

Maria Rasch

Department of Seafood Research
Danish Institute for Fisheries Research
Ministry of Food, Agriculture, and

Fisheries
Lyngby, Denmark

David A. Ratkowsky

Centre for Food Safety and Quality
School of Agricultural Science
University of Tasmania
Hobart, Tasmania, Australia

Donald W. Schaffner

Cook College

Rutgers University

New Brunswick, New Jersey

Mark Tamplin

Microbial Food Safety Research

Unit
United States Department of

Agriculture
Agricultural Research Service
Eastern Regional Research Center
Wyndmoor, Pennsylvania

Jan F. Van Impe

BioTeC-Bioprocess Technology and

Control
Department of Chemical Engineering
Katholieke Universiteit Leuven
Leuven, Belgium

Karen Vereecken

BioTeC-Bioprocess Technology and

Control
Department of Chemical Engineering
Katholieke Universiteit Leuven
Leuven, Belgium

Thomas Ross

Centre for Food Safety and Quality
School of Agricultural Science
University of Tasmania
Hobart, Tasmania, Australia

2004 by Robin C. McKellar and Xuewen Lu

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Contents

Chapter 1 Experimental Design and Data Collection
Maria Rasch

Chapter 2 Primary Models

Robin C. McKellar and Xuewen Lu

Chapter 3 Secondary Models

Thomas Ross and Paw Dalgaard

Chapter 4 Model Fitting and Uncertainty
David A. Ratkowsky

Chapter 5 Challenge of Food and the Environment
Tim Brocklehurst

Chapter 6 Software Programs to Increase the Utility of Predictive
Microbiology Information

Mark Tamplin, Jozsef Baranyi, and Greg Paoli

Chapter 7 Modeling Microbial Dynamics under Time-Varying
Conditions

Kristel Bernaerts, Els Dens, Karen Vereecken, Annemie Geeraerd,
Frank Devlieghere, Johan Debevere, and Jan F. Van Impe

Chapter 8 Predictive Microbiology in Quantitative Risk Assessment
Anna M. Lammerding and Robin C. McKellar

Chapter 9 Modeling the History Effect on Microbial Growth and Survival:
Deterministic and Stochastic Approaches

Jozsef Baranyi and Carmen Pin

Chapter 10 Models — What Comes after the Next Generation?
Donald W. Schaffner

2004 by Robin C. McKellar and Xuewen Lu

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Chapter 11 Predictive Mycology
Philippe Dantigny

Chapter 12 An Essay on the Unrealized Potential of Predictive
Microbiology

Tom McMeekin

2004 by Robin C. McKellar and Xuewen Lu