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10

Models —

What Comes after the

Next Generation?

Donald W. Schaffner

CONTENTS

10.1 Introduction

10.2 Cross-Contamination

10.2.1 Issues of Concern

10.2.1.1 Statistical Treatment

10.2.1.2 Additive Nature of Cross-Contamination

10.2.1.3 Factors Influencing Transfer Rate

10.2.1.4 Types of Transfers

10.2.1.5 Multiple Transfers and Complexity

10.2.2 Cross-Contamination Summary

10.3 Inoculum Size Modeling

10.3.1 Clostridium botulinum

10.3.2 Nonspore-Forming Bacteria

10.3.3 Inoculum Size Summary

10.4 Cross-Contamination and Inoculum Size

10.5 Summary
References

10.1 INTRODUCTION

This chapter will highlight two separate and generally unrelated areas of predictive
food microbiology: models for cross-contamination and inoculum size (or models
that consider the initial number of organisms present). These two classes of models
are being included together here, because they represent some of the newer areas
of predictive modeling that are less well developed compared to the more well-
known and established research areas such as growth and inactivation modeling.
This chapter will summarize the current state of research in these two rapidly
evolving areas and will conclude with a short example describing preliminary inves-
tigations into the integration of these two fields of study.

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10.2 CROSS-CONTAMINATION

Predictive models for microbial behavior have traditionally focused on describing
increasing concentrations (as a result of multiplication) and decreasing concentra-
tions (as a result of cell death). A number of lines of inquiry have pointed out the
need for a third class of models that may be required in some cases: cross-contam-
ination models. The three lines of inquiry all come from the interaction of risk
assessment and epidemiology, and are related to three very different microorganisms:
Listeria monocytogenes, Campylobacter jejuni, and food-borne viruses.

L. monocytogenes is a psychrotrophic pathogen that can cause mild illness in
healthy adults and spontaneous abortion in pregnant women. The organism is easily
destroyed by heating but readily recontaminates the cooked product prior to pack-
aging. 25 While this recontamination is known to take place, (and can contribute to
significant disease outbreaks) very few mathematical models are available for micro-
bial risk assessors to use.

The situation with Campylobacter is slightly different. In this case, the organism
is known to cause cross-contamination in a significant number of cases 1 but the
means by which this occurs is not clear. 11 Risk assessment models for Campylobac-
teriosis have incorporated cross-contamination events during final preparation in a
kitchen environment, but as with Listeria risk assessment models, few suitable
models are available.

Finally, it is known that a number of foodborne disease agents (primarily viruses)
can contaminate foods, and in many cases the source of the agent has been an ill
food worker. 12 While quantitative microbial risk assessments have yet to address ill
workers, hand-to-food and other cross-contamination rates using a nonpathogenic
surrogate have been calculated with sufficient detail to be suitable for risk assessment. 7

10.2.1 Issues of Concern

There are a number of issues of particular concern that are important in modeling
cross-contamination — issues that are unique to these sorts of models as compared
to the traditional growth and decline models: appropriate statistical treatment of data,
transfer from one location to another, factors influencing transfer, and the possibility
of multiple transfers.

1 0.2.1 .1 Statistical Treatment

Data on cross-contamination are typically presented as percent transfer, as shown
below:

CFU on target , _ _
— * 100 = percent transfer

CFU on source

The problem arises when multiple observations of the same conditions are to
be combined and reported as an average. It has been shown that when large numbers
of observations are made, the distribution of "percent transfer rates" is distinctly

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"i 1 1 r

25 50 75 100
Percent Transfer

-2-1 1 2
Log Percent Transfer

FIGURE 10.1 Distribution of percent transfer data with linear (left panel) and logarithmic
transformation (right panel).

nonnormal. 7 This point is made clearer when the data are presented visually. Figure
10.1 shows the same data set plotted as number of observations vs. percent transfer
(left panel) and number of observations vs. log 10 percent transfer (right panel). This
same pattern is borne out for many different types of surface-to-surface transfers. 710
Since percent transfer is nonnormally distributed, but log 10 percent transfer is approx-
imately normally distributed, this means data should be log transformed before
averages are calculated. This apparently subtle distinction has important conse-
quences as illustrated below.

Let us assume we have two observed transfer rates of 5 and 50%. If the mean
is calculated arithmetically:

(50 + 5)/2 = 27.5% transfer

Alternatively, using the statistically appropriate log 10 transformed rates leads to
a more complex series of calculations:

(log 0.05 + log 0.50)/2 = (-1.30103 + -0.30105)/2 = -0.80103
Then this number should be converted back to the untransformed percent scale:

1O-0.80103 = 15>8% trans fer

So this simple difference leads to a calculated transfer rate that is over half that
obtained when the statistically incorrect method is used.

10.2.1.2 Additive Nature of Cross-Contamination

Another key feature of any cross-contamination model is that some consideration
should be made of both the source of the contaminant and the destination. If the
source is a contaminated surface, then the number of organisms on that surface must

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be known, since (at least in theory) a more contaminated source will yield a more
contaminated destination. Care must be taken to ensure that the number of organisms
to be added to an already contaminated item is added in a numerically correct manner.
For example, most calculations in a microbial risk assessment will be log 10 CFU
increases or decreases. This would not be correct in cross-contamination. If a food
contained 10 organisms and 100 were added, this would not be a two log 10 increase,
1 + 2 = 3 or 1000 organisms, but 10 + 100 =110 organisms.

10.2.1.3 Factors Influencing Transfer Rate

The next issue that should be addressed would be a consideration of the factors
influencing transfer rate. There are a whole host of factors that may influence transfer,
like source (air, liquid, or solid), the pressure applied (for solid-to-solid transfers),
menstrum effects, contact time, number of organisms present, and surface charac-
teristics. Some of these factors have been investigated for transfer from hands in a
healthcare setting, but little data applicable to food systems have been published.
What has been published in the food and healthcare literature has not been systematic
or comprehensive. 21

1 0.2.1 .4 Types of Transfers

A recent review 10 describes some of the currently available models for recontami-
nation via air, via processing equipment (i.e., biofilms), or via hand contact. These
authors point out that not many available models are directly applicable to the food
industry as most models are developed for aquatic or environmental systems. In
some cases currently available models are contradictory or incompatible. For exam-
ple, competing air recontamination models assume that when the concentration in
the air increases linearly, the concentration in the product increases either linearly 28
or quadratically. 23 The implications of such assumptions obviously have a critical
impact on model predictions.

Models for recontamination that consider the effect of biofilms are quite well
developed, not because of their importance in food processing, but because of their
application in wastewater treatment. Biofilm models can be one-dimensional, or
multidimensional, 16 but the key feature of any biofilm model used for food recon-
tamination is not its dimensionality, but its ability to consider attachment, growth,
and detachment averaged over the food contact surface. 10 Some biofilm models
appropriate for use in food systems have been developed. 31

den Antrekker et al. 10 conclude their review by proposing a schematic for a
general contamination model that is suitable for modeling recontamination via air,
via surfaces, or via hands. This model uses a source, an intermediate phase, and a
product, with transfer rates between source and intermediate phases and intermediate
and product phases that govern the overall transfer to the product.

10.2.1.5 Multiple Transfers and Complexity

The last issue of concern is the modeling of multiple transfers. The food preparation
or handling environment may be such that multiple transfers between many different

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environments may occur. In a processing plant it may be from air to surface, surface
to product, product to clean surface, and finally surface to clean product. In a food
service environment it may be from a contaminated surface to workers' hands, and
then from hands to food. In a home environment it may be from a contaminated
food product to a surface, and then from that surface to another food.

Each of these simple examples would require a series of calculations, using
models that generally do not yet exist. At the same time, it should be realized that
the real world is considerably more complex than these simple examples show, and
that there may be literally dozens of cross-contamination possibilities in even a
simple food process or meal preparation.

10.2.2 Cross-Contamination Summary

The development of mathematical models suitable for describing cross-contamina-
tion events in food production, processing, and preparation is still in its infancy, and
might be likened to the general state of predictive food microbiology in the 1980s.
The past two decades have seen many improvements in the general state of the art
of predictive food microbiology, and there is no reason to believe the next two
decades would not experience similar improvements in cross-contamination model-
ing. This field has attracted the interest of a number of research groups around the
world, and the beginnings of a comprehensive body of work are beginning to emerge.

10.3 INOCULUM SIZE MODELING

Predictive models have traditionally been developed using starting bacterial concen-
tration that may be quite high relative to the levels found in some foods. Modelers
developing models in this way were quite justified in their choice of this approach.
In some cases, inoculum size does not have a significant effect on the response to
be modeled (i.e., growth rate). 5 High initial inoculum size also represents a conser-
vative worst-case approach to modeling, and these high starting concentrations
helped to assure repeatability and simplified some of the considerations about micro-
bial variability, often called "biovariability."

Despite the logic seen in this worst-case approach, modelers have always sought
to improve their models by making them more realistic and representative of real-
world conditions. Also, as predictive food microbiologists' modeling tools and
abilities have improved, their ability to handle more complex models and modeling
techniques have improved concomitantly. As part of this evolutionary improvement
in modeling ability, some modelers have sought to address this shortcoming by
developing models that take initial microbial concentrations into consideration.

10.3.1 Clostridium Botulinum

One of the earliest examples of a predictive model that explicitly acknowledged the
influence of inoculum size were models developed for C. botulinum. nM The authors'
specific objective in this case was to develop models capable of predicting the
probability of toxin formation from a single C. botulinum spore. Later research in

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this same lab also showed an inoculum size effect in fish 3 and poultry 19 systems
inoculated with C. botulinum.

The importance of inoculum size for models for C. botulinum has since been
well documented in the literature. 17 ' 26 ' 2729 ' 30 These C. botulinum models were devel-
oped as an aid to the food industry, but also served to point the way towards a more
mechanistic understanding of populations of C. botulinum spores. The model for
nonproteolytic C. botulinum developed by Whiting and Oriente, 26 for example,
showed that not only did lower population of spores exhibit longer time-to-turbidity,
the variability around that time increased markedly with decreasing inoculum size
as well. This same effect was also seen with proteolytic C. botulinum spores. 27 These
results supported the observations made by others conducting microscopy studies
that there was a marked variability seen in the germination, outgrowth, and lag time
in individual C. botulinum spores observed directly. 4 These apparent interactions
between spores of C. botulinum have also been demonstrated using computer sim-
ulation of different inoculum sizes 30 and seem to be caused by the release of a
signaling molecule into the culture media by germinating spores.

This inoculum phenomenon does not appear to be unique to C. botulinum, as
it has also been observed in Bacillus cereus 9 and Bacillus megaterium 6 using direct
microscopic observation and in Bacillus stearothermophilus 15 indirectly by time to
turbidity.

10.3.2 Nonspore-Forming Bacteria

The effect has also been seen in models for nonspore-forming bacteria, like Bro-
chothrix thermosphacta, ls as well as in nonmodeling research with Salmonella 8 and
L. monocytogenes. 2,2224 These publications show that the effect is most pronounced
when cells are stressed 224 or cultured in inhospitable environments. 8 The response
in vegetative cells has been interpreted by some as being due to death of a proportion
of cells in the inoculum rather than communication, as appears to be the case with
C. botulinum, 22 although others have shown that addition of spent medium from a
stationary -phase culture reduces the variability and length of lag times. 24

10.3.3 Inoculum Size Summary

Clearly modelers have moved beyond predictive models developed using high initial
bacterial concentrations to models using a range of contamination levels. Most of
the effort in this area has focused on models for spore-forming organisms, specifi-
cally C. botulinum. A limited amount of work has also been done with other spore-
forming organisms and vegetative cells. It appears that inoculum size has the most
dramatic effect on the lag time (for vegetative cells) or germination, outgrowth, and
lag time (for spores).

10.4 CROSS-CONTAMINATION AND INOCULUM SIZE

While the two subjects of this chapter do not appear to have much in common,
except for both being aspects of modeling on the "cutting edge," there appears to

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FIGURE 10.2 Percent transfer as a function of inoculum size.

be some evidence that inoculum size is not only important in traditional growth
modeling, but that it may also be an important consideration in modeling cross-
contamination. Figure 10.2 presents a reanalysis of a portion of the data originally
published by Chen et al. 7 for cross-contamination rate from bare hands contaminated
with Enterobacter aerogenes to lettuce. While the r 2 value (0.49) and a visual
inspection of the plot show that the correlation is not ideal, the effect is highly
significant (p > 10~ 10 ). The regression model for the plot indicates that changing the
starting concentration by 1.5 log 10 CFU will change the log 10 percent transfer rate
by about 1 (i.e., from 10 to 1%). It is also interesting to note that the relationship
between starting concentration and log 10 percent transfer rate is an inverse one, so
that as the starting concentration decreases, the transfer rate increases. This could
have very profound food safety consequences since low levels of pathogens would
have a correspondingly greater ability to transfer. This simple example has been
used to illustrate the exciting and complex nature of predictive food microbiology
at the expanding edges of the discipline.

10.5 SUMMARY

Models for cross-contamination and inoculum size represent areas at the expanding
edge of predictive food microbiology. Both areas characterize modelers' attempts
to make models more useful and representative of microbial behaviors seen in the
real world. Both areas continue to present mathematical, statistical, and method-
ological challenges to those working in the field.

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