Advanced quantitative microbiology for foods and biosystems : models for predicting growth and inactivation

Models for Predicting

Growth and Inactivation

Advanced Quantitative

Microbiology for Foods

and Biosystems

© 2006 by Taylor & Francis Group, LLC

CRC Series in

CONTEMPORARY FOOD SCIENCE

Fergus M. Clydesdale, Series Editor

University of Massachusetts, Amherst

Published Titles:

Advanced Quantitative Microbiology for Foods and Biosystems:

Models for Predicting Growth and Inactivation

Micha Peleg

Antioxidant Status, Diet, Nutrition, and Health

Andreas M. Papas

Aseptic Processing and Packaging of Foods: Food Industry Perspectives

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

Automation for Food Engineering: Food Quality Quantization and Process Control

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

Bread Staling

Pavinee Chinachoti and Yael Vodovotz

The Food Chemistry Laboratory: A Manual for Experimental Foods,

Dietetics, and Food Scientists, Second Edition

Connie Weaver and James Reuben Daniel

Food Consumers and the Food Industry

Gordon W. Fuller

Food Emulsions: Principles, Practice, and Techniques

David Julian McClements

Food Microboilogy Laboratory

Lynn McLandsborough

Food Properties Handbook

Shafiur Rahman

Food Shelf Life Stability

N.A. Michael Eskin and David S. Robinson

Getting the Most Out of Your Consultant: A Guide to Selection

Through Implementation

Gordon W. Fuller

Handbook of Food Spoilage Yeasts

Tibor Deak and Larry R. Beauchat

Interdisciplinary Food Safety Research

Neal M. Hooker and Elsa A. Murano

Introduction to Food Biotechnology

Perry Johnson-Green

Modeling Microbial Responses in Food

Robin C. McKellar and Xuewen Lu

© 2006 by Taylor & Francis Group, LLC

CRC is an imprint of the Taylor & Francis Group,

an informa business

Micha Peleg

Boca Raton London New York

Models for Predicting

Growth and Inactivation

Advanced Quantitative

Microbiology for Foods

and Biosystems

© 2006 by Taylor & Francis Group, LLC

Published in 2006 by

CRC Press

Taylor & Francis Group

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Boca Raton, FL 33487-2742

© 2006 by Taylor & Francis Group, LLC

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10 9 8 7654321

International Standard Book Number-10: 0-8493-3645-7 (Hardcover)

International Standard Book Number-13: 978-0-8493-3645-4 (Hardcover)

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Library of Congress Cataloging-in-Publication Data

Peleg, Micha.

Advanced quantitative microbiology for foods and biosystems : models for predicting growth and

inactivation / by Micha Peleg.

p. cm. -- (CRC series in contemporary food science)

Includes bibliographical references and index.

ISBN 0-8493-3645-7 (alk. paper)

1. Food--Microbiology--Mathematical models. 2. Biological systems--Mathematical models. 3.

Microbial growth--Mathematical models. I. Title. II. Series.

QR115.P45 2006

664.001’579--dc22 2005046679

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© 2006 by Taylor & Francis Group, LLC

Dedication

In memory of my late parents and brother, and to my family, friends,

teachers, and students, from all of whom I have received so much.

© 2006 by Taylor & Francis Group, LLC

Preface

A theory is believed by no one except the person who created it.

Experimental results are believed by everyone except the person who

got them.

Harlow Shapely

Predictive, or perhaps more accurately, quantitative microbiology has

been an active field of research in recent years. Numerous papers have

been written on the subject, as well as many review articles and book

chapters. A large amount of tabulated quantitative data and simulated

growth and survival curves can now be downloaded from Websites, nota￾bly those posted by the USDA–ERRC (Eastern Regional Research Center)

in the United States and IFR (Institute of Food Research) in the United

Kingdom. Also posted on the Web are long lists of references that have

dozens and sometimes hundreds of entries. Most recently, Robin C.

McKellar and Xuewen Lu have edited Modeling Microbial Responses in

Foods (CRC Press, 2003) — an update to the classic Predictive Microbiology

by Tom. A. McMeekin, June N. Olley, Thomas Ross, and David A. Rat￾kowsky (John Wiley & Sons, 1983, 1993). Together with numerous other

publications, they provide existing comprehensive coverage of the math￾ematical properties of the various existing quantitative models of micro￾bial growth and inactivation, their origins and development during the

years, and their application to specific organisms of interest in food and

water safety or in disease control or eradication.

A large number of the publications in the food literature addresses the

statistical aspects of a model derivation from experimental data, comple￾menting the statistics textbooks that deal with sampling, data analysis,

regression, distributions, quality control charts, and the like. Therefore,

the purpose this book, by an author who is neither a practicing food or

water microbiologist nor a statistician, is certainly not to add another

compilation of inactivation and growth models and data or to provide an

updated references list. The book is also not intended to discuss the strictly

statistical aspects of mathematical models derivation and curve fitting.

Discussion of these, as already stated, are readily available to the reader

in many convenient forms.

The reason for writing this book is the feeling that research in the field of

quantitative microbiology, especially of foods but also of other biosystems,

needs new directions. In most scientific disciplines reaching maturity in

© 2006 by Taylor & Francis Group, LLC

h

which a massive body of literature exists, certain thought patterns become

so ingrained that the foundations of the prevalent concepts, theories, and

models are rarely questioned. A main objective of this book is to do just this

— that is, to re-examine and challenge some of the dogmatic concepts that

have dominated the field of quantitative microbiology for many years.

Another objective is to offer an alternative approach to modeling certain

aspects of microbial growth and inactivation. The discussion will prima￾rily focus on the mathematical forms of the proposed alternative models

and on the rationale of their introduction as substitutes to those currently

in use. Only when it is absolutely necessary will reference to biological

aspects of the modeled phenomena be made. The mechanisms of micro￾bial cell division and death and of spore formation, germination, and

inactivation have been studied in great detail by professional microbiol￾ogists and other scientists. They should not concern us here, except when

they have a quantitative manifestation and/or affect the shape of a growth

or survival curve.

It is well known that different experimental procedures to grow, isolate,

and count microorganisms can yield somewhat different results. Still, the

published microbial count records to be analyzed and interpreted in this

volume will be always considered as correctly determined and faithful

representatives of the systems in question. The roles of sampling and

uncertainties, for example, even when pertinent to the data interpretation,

will only be assessed in terms of their possible effect on the mathematical

model’s structure and the magnitude of its parameters. The reliability of the

reported experimental data is an issue that has been intentionally left out.

This book is primarily a summary of microbial modeling work done at

the Department of Food Science of the University of Massachusetts

Amherst in the last 10 years. Many individuals participated in the concept

and model development and we have been helped in various ways by

experts from outside the department. Several food companies and other

institutions helped us considerably by allowing us to share records and,

in one case, to create new data. Their contributions, without which this

book could have never been written, are gratefully acknowledged.

We have been fortunate to be provided not only with challenging data

but also with crucial mathematical ideas and technical assistance in pro￾gramming. In writing this volume, no attempt has been made to offer an

updated comprehensive list of pertinent works published by others and

an assessment of their merits. Long lists of related publications can now

be found easily in books and reviews, as well as in various sites on the

Internet. Unfortunately, very few of these sources of information contain

critical assessment of the cited publications even though, at least in some

cases, they have obvious shortcomings. Whenever we deal with the

publications of others, the emphasis will be primarily on the mathematical

properties of the models that they present or propose. Only rarely will

© 2006 by Taylor & Francis Group, LLC

their data quality be addressed. Also, and as already stated, we have not

tried to document the historical roots of published models and thus credit

to the original authors might not have been given. For these omissions, I

take full responsibility and apologize in advance to everyone whose work

might not have received the proper acknowledgment that it deserves.

Many if not all of the concepts presented and discussed in this book’s

chapters will probably be controversial and even objectionable to some.

This is quite understandable. In fact, although most of the ideas presented

have been welcomed in mathematically oriented biological, food, and

engineering publications, some were initially turned down by leading

food and general microbiology journals for reasons that are still hard to

understand. That the rejection came from expert referees demonstrates

that a critical re-evaluation of the field’s foundations is necessary and

timely.

Comments made in several reviews have raised doubts about the open￾ness of the field to any criticism of its long-held beliefs. The same can be

said about the current attitude of certain governmental programs that

fund food safety research. The verdicts of their review panels and admin￾istrators explicitly stated that revision of the currently held concepts of

microbial inactivation, although acknowledged to be deficient, is not a

welcome proposition, let alone a research priority. This attitude may be

changing now and it is possible that this change is partly due to issues

raised in the publications on which the first part of this book is based.

A growing circle of microbiologists and scientists in industry, academia,

and government share our concerns about the quantitative models and

calculation methods now in use in the food industry. Some have actively

encouraged us to search for new models and to develop our nontradi￾tional approach. This book will present growth, inactivation, and fluctu￾ation models based on a departure from many of the established concepts

in the field. Because the models that we propose are now available to

professionals and students together in a single volume rather than scat￾tered in many journals, they might invite criticism as well as trigger a

debate on whether some of the theories that currently dominate the field

of quantitative microbiology should be replaced.

It is to be hoped that the debate will result in the abandonment of some

old ideas and open the way to novel and more effective solutions to the

outstanding problems of predicting microbial growth and inactivation.

Even if initiating such a debate is all that this book will ever achieve, the

effort invested in writing it would be worthwhile. Still, I hope that some

readers will discover the utility of the proposed approach and find that

at least some of the models described here can be useful to their work. I

also hope that the models originally developed for food and water will

find applications in other fields, notably in environmental, pharmaceuti￾cal, and perhaps even clinical medical microbiology.

© 2006 by Taylor & Francis Group, LLC

Acknowledgments

This book would have never seen the light and the studies on which it is

based never come to fruition without the contributions and assistance of

many individuals and several institutions. The help came in many forms:

suggested key ideas, solutions to mathematical problems, programming,

sharing or producing essential experimental data, computer simulations

book’s chapters and of the original journal articles summarized in them.

During the years in which the research was done, we received much

encouragement from friends and colleagues in other institutions.

Although they did not participate directly in any of the projects, their

moral support was invaluable to us, especially at times when some of our

ideas have received an irrationally hostile response in certain quarters. At

the same time, we have always appreciated the sympathetic and construc￾tive comments of several anonymous referees and lament, of course, that

we cannot thank them in person.

the results of research that, by and large, has never been funded, except

for modest internal support from the Massachusetts Agricultural Exper￾iment Station at Amherst. We have benefited greatly from a project funded

by Nabisco (now Kraft); although it did not support us directly, it allowed

us to participate in some of the experiments and gave us access to crucial

data that we could not obtain from other sources. We have also been

allowed to take a modest part in projects sponsored by Unilever, which

also gave us access to helpful data and boosted our morale at the time.

reports the results of work funded by the USDA–NRICGP (National

Research Initiative Competitive Grants Program). (The project was

approved when the program had been under a previous management,

before a concept development could be labeled “passive research.”) We

gratefully acknowledge this old program’s support.

The list of individuals and institutions to whom I am indebted is long

and I wonder if it will ever be complete. It includes principal collaborators

Joseph Horowitz, Claude Penchina, programmer Mark Normand, and

Maria Corradini, who produced many of the figures that appear in this

book. It also includes Martin Cole, Amos Nussinovitch, Osvaldo

Campanella, Ora Hadas, and former graduate students Robert Engel and

Karen Mattick, who have made significant direct contributions to our

© 2006 by Taylor & Francis Group, LLC

The first part of the book (Chapter 1 through Chapter 8) summarizes

and graphing, and patient typing and retyping of the many drafts of the

Much of the second part of the book (Chapter 9 through Chapter 12)

research. Among those who have showed their support by inviting us to

present our ideas and by other means are Peter ter Steeg, David Legan,

Cindy Stewart, Betsy Reilley–Mathews, Helmar Schubert, Walter Spiess,

Gustavo Barbosa–Canovas, Jorge Welti, Miguel Aguillera, Ricardo Simpson,

Isreal Saguy, Michael Davidson, Tiny van Boekel, Peter McClure, Donald

Schaffner, Christopher Doona, Pilar Cano, Janet Luna, Giovanna Ferrari,

Gustavo Gutiérez, and Joy Gaze, the students of UDLA (Univerisad de

Las Américas), the organizers of the IFT (Institute of Food Technologists)

summit on microbial modeling of a USDA sponsored workshop on non￾thermal food preservation, and those of the IFTPS (Institute for Thermal

Processing Specialists) meeting on thermal processing.

I also express my gratitude to those in industry who provided us with

very important data but have preferred that their sources would not

become public. I thank Beverly Kokoski and Frances Kostek for patiently

typing and editing the manuscript and for accepting the endless revisions

and corrections with a smile. I also want to thank Judith Simon and Jill

Jurgensen of Taylor & Francis for their help in editing the book and

bringing it to press. Last but not least, I want to thank my department

head, Fergus Clydesdale, for his continued moral and material support,

especially at the most difficult times of the research.

I have been fortunate and privileged to have the cooperation of so many.

© 2006 by Taylor & Francis Group, LLC

About the Author

Micha Peleg has been a professor of food engineering at the University

of Massachusetts at Amherst since 1975. He holds a B.Sc. in chemical

engineering and M.Sc. and D.Sc. in food engineering and biotechnology

from the Technion-Israel Institute of Technology. He teaches unit opera￾tions and food processing. Dr. Peleg’s current research interests are in the

rheology of semiliquid and foamy foods, the mechanical properties of

particulated brittle food materials, powder technology, and mathematical

modeling of microbial growth and inactivation. He is an editorial board

member of several food journals and has been a reviewer for many sci￾entific journals in a variety of fields. Dr. Peleg has more than 300 technical

publications, and is listed by ISI (Information Sciences Institute) as a

highly cited researcher. He has been elected a member of the International

Academy of Food Science and Technology and a Fellow of the World

Innovation Foundation.

© 2006 by Taylor & Francis Group, LLC

A theory is a good theory if it satisfies two requirements: it must

accurately describe a large class of observations on the basis of a model

that contains only a few arbitrary elements, and it must make definite

predictions about the results of future observations.

Stephen Hawking

© 2006 by Taylor & Francis Group, LLC

Contents

1 Isothermal Microbial Heat Inactivation...................................1

Primary Models — the Traditional Approach .................................... 1

The First-Order Kinetics and the D Value ...................................... 1

The “Thermal Death Time” ............................................................... 4

Biphasic and Multiexponential Decay Models and

Their Limitations ................................................................................. 5

The Logistic Models............................................................................ 9

Concluding Remarks to This Section............................................. 10

The Survival Curve as a Cumulative Form of the Heat

Distribution Resistances........................................................................ 11

The Weibull Distribution.................................................................. 17

Interpretation of the Concavity Direction ................................ 22

The Fermi (Logistic) Distribution Function .................................. 23

The Activation Shoulder .................................................................. 27

Estimation of the Number of Recoverable Spores.................. 30

Sigmoid and Other Kinds of Semilogarithmic Survival

Curves ................................................................................................. 33

Sigmoid Curves............................................................................. 33

Residual Survival (Strong “Tailing”)......................................... 37

Can an Absolute Thermal Death Time Exist? .............................. 38

Secondary Models.................................................................................. 40

The “z” Value and the Arrhenius Equation.................................. 41

The Log Logistic Model ................................................................... 44

A Discrete b(T) vs. T..................................................................... 46

Other Empirical Models................................................................... 47

2 Nonisothermal Heat Inactivation............................................49

The Traditional Approach..................................................................... 49

The F0 Value and Its Limitations .................................................... 50

The Proposed Alternative ..................................................................... 53

Nonisothermal Weibuillian Survival .................................................. 57

The Rate Model.................................................................................. 57

Heating and Cooling ........................................................................ 59

Simulation of Heating Curves by Empirical Models ............. 59

Simulated Survival Curves for Processes with Different

Target Temperature and Holding Durations ........................... 62

© 2006 by Taylor & Francis Group, LLC

Temperate Oscillations................................................................. 64

Discontinuous Temperature Profiles ......................................... 65

The Special Case of Log Linear Isothermal Survival ............. 66

Non-Weibullian Survival Models........................................................ 68

Logistic (Fermian) Survival ............................................................. 69

Extreme Tailing .................................................................................. 70

Sigmoid Survival Curves ................................................................. 73

Isothermal Survival Model’s Equation with No Analytic

Inverse ................................................................................................. 75

Independence of the Calculated Nonisothermal Survival

Curve of the Chosen Survival Model ............................................ 77

Experimental Verification of the Model ............................................. 78

The Isothermal and Nonisothermal Inactivation Patterns

of L. monocytogenes ............................................................................ 80

The Isothermal and Nonisothermal Inactivation

of Salmonella........................................................................................ 81

Isothermal and Nonisothermal Survival Curves

of B. sporothermodurans Spores in Soups........................................ 84

The Isothermal and Nonisothermal Inactivation of E. coli ........ 84

Heat-Induced Chemical and Physical Changes................................ 90

3 Generating Nonisothermal Heat Inactivation Curves

with Difference Equations in Real Time

(Incremental Method)...............................................................95

The Difference Equation of the Weibullian–Log Logistic

Nonisothermal Survival Model ........................................................... 96

Non-Weibullian Survival Curves ...................................................... 102

Comparison between the Continuous and

Incremental Models ............................................................................. 106

4 Estimation of Microbial Survival Parameters

from Nonisothermal Inactivation Data ................................ 111

The Linear Case.................................................................................... 113

Linear Survival at Constant Rate Heating .................................. 113

Linear Survival at Varying Heating Rate.................................... 116

The Nonlinear Case ............................................................................. 120

Weibullian–Power Law Inactivation at Arbitrary

Heating Rate History...................................................................... 120

Testing the Concept with Simulated Data .................................. 120

Testing the Method with Salmonella Survival Data ................... 124

Salmonella in a Growth Medium .............................................. 124

Salmonella in Minced Chicken Meat ........................................ 129

Concluding Remarks ........................................................................... 130

© 2006 by Taylor & Francis Group, LLC