System dynamics: A Complementary Tool for Predictive
microbiology
Gabriela Guadalupe Gastélum-Reynoso
Departamento de Ingenieria Quimica y Alimentos, Universidad de las Américas Puebla.
Cholula, Puebla, 72820. MEXICO
+52 (222) 229-2126
gabriela.gastelumro@udlap.mx
Enrique Palou
Centro para la Educacién de las Ciencias, Ingenierias y Tecnologias, Universidad de las
Américas Puebla. Cholula, Puebla, 72820. MEXICO
+52 (222) 229-2658
enrique.palou@udlap.mx
Aurelio Lépez-Malo
Departamento de Ingenieria Quimica y Alimentos, Universidad de las Américas Puebla.
Cholula, Puebla, 72820. MEXICO
+52 (222) 229-2409
aurelio.lopezm@udlap.mx
Abstract
One of the most important concerns for food industry is safety. Predictive microbiology
is the application of mathematical models to describe microbial behavior in order to
prevent food spoilage as well as food-borne illness. Because of complexity of microbial
behavior and food systems, predictive microbiology presents some limitations. System
dynamics could be a useful alternative and complementary tool to model and predict
microbiological behavior in foods while providing a graphical interface and structures
linked with a series of equations, to clarify and improve quantitative predictive
microbiology descriptions.
Key words: Predictive microbiology, Food Microbiology, Food Safety
Introduction
One of the most important concerns for the food industry is safety. The modern concept
of food safety has been influenced first by consumer’s demand for fresher and healthier
foods and second by the industry, producing safer products lowering the risk of the
presence of food-borne pathogens and spoilage microorganisms in food products
(Martinez et al., 2005).
Microbial ability to survive or die depends on product composition and combinations of
a variety of food factors (pH, water activity and temperature among others). These food
factors act as barriers (or hurdles) to the microorganism. The goal in terms of food
safety therefore is to prevent the growth and/or toxin production of the pathogenic and
spoilage microorganisms by determining the optimum conditions of food preservation
processes (Lopez-Malo, Guerrero and Alzamora, 2000).
There are several tools to assure food safety. Storage stability tests, microbial challenge
tests and predictive microbiology. Predictive microbiology is the application of
mathematical models to describe microbial behavior during food processing (Alzamora,
Tapia and Lépez-Malo, 2000; Betts and Everis, 2005).
Because of the complexity of microbial behavior and food systems, predictive
microbiology presents some limitations. The most relevant limitation for the purposes
of this paper is that existing microbial modeling tools are not integrated. Furthermore,
mathematical models are simplifications of complex microbial and biochemical
processes; in some cases not every important variable or factor that is affecting the
system is included (Buchanan and Whiting, 1997); and finally, some aspects like
fluctuating conditions (microbial behavior food environment and food processing steps)
are not usually considered (Lebert and Lebert, 2006). System dynamics could be an
alternative approach for describing simulating and predicting microbial food models
since it is a methodology that studies complex feedback systems, within an integrated
point of view, using simple algebraic equations and structures that function as building
blocks for more complex models.
The aim of this paper is to suggest system dynamics as an alternative and
complementary approach to model and predict food microbial behavior. In this way, the
rest of the paper is organized in three sections: First, a brief review of predictive
microbiology and its limitations are presented, while introducing system dynamics as an
alternative and complementary approach to model microbiological processes in foods.
Next, there is an example of a work in progress to model bacterial inhibition by heat
treatment, using system dynamics. The paper ends with suggestions for further work.
Review of the Approaches
PREDICTIVE MICROBIOLOGY
In respond to consumer’s demand for fresher, testier and healthier foods, food industry
has developed new alternatives such as hurdle technology. This methodology combines
several factors or hurdles (temperature, antimicrobials, ay reduction, etc.) in order to
ensure food quality and safety. The hurdles applied are milder than in traditional
techniques (pasteurization, canned foods). Therefore, there is an increased risk of
growth of pathogenic or spoilage microorganisms (Gould, 1995). In this way storage
stability tests (SST), microbial challenge tests (MCT) along with predictive
microbiology are common tools to predict and assure food safety. SST and MCT are
laboratory experiments performed with products and microorganisms under controlled
conditions. These experiments along with predictive microbiology provide information
about the effects of different factors influencing safety of food products.
Predictive microbiology is the application of mathematical models to describe and
predict microbial growth, survival, and/or inactivation as well as biochemical processes
under specific time and conditions. Usually, microorganisms are grown under certain
controlled factors (conditions) such as variations on pH, water activity (ay),
temperature, and antimicrobial concentration, among others. The results of their
responses (biological parameters) are fitted into mathematical equations. Such models
can be used to predict microbial responses under new conditions, within tested ranges of
studied factors or its combinations (Betts and Everis, 2005; Alzamora, Tapia and
Lopez-Malo, 2000; Whiting and Buchanan, 1994; Lebert and Lebert, 2006).
McMeekin and his colleagues (1992) proposed some guidelines for developing effective
models. Some of these guidelines consist of fitting precision, capacity to predict
combinations of factors that have not been proven, incorporation of every outstanding
factor, minimum number of variables, specification of the error term, parameters having
biological meaning and real values, and reparameterization to improve statistical
properties (McMeekin, Roos and Olley, 1992; Martinez et al., 2005).
Predictive microbiology models are classified in three levels. Primary level models
describe the changes in microbial population over time (colony forming units (CFU)/
ml, toxin production, etc.) and provide information about microbial behavior such as lag
phase duration. Secondary level models describe the changes in parameters of primary
level (e.g. CFU/ml) when environmental factors change (pH, ay, temperature, among
others). Tertiary level models are interfaces, which convert the primary and secondary
level models in friendly software where users can input environmental factors for
different microorganisms and obtain a prediction of microbial population parameters.
Pathogen Modeling Program, Food MicroModel and Seafood Spoilage Predictor are
examples of available tertiary level models.
Models help understand and predict the behavior of microorganisms for specific
conditions. Nevertheless, in some cases there is not an accurate fit for extrapolation to
real life conditions. Then validation of a model becomes necessary before it is used to
make food safety decisions. The validation process is done considering biological
knowledge of the system and statistical tools. Once models are validated and users are
aware of the limitations of the models, they are useful tools to obtain information and
make decisions for the following situations (Alzamora, Tapia and Lopez-Malo, 2000;
Buchanan and Whiting, 1997):
1. Prediction of safety: Estimate the risk of growth or survival of pathogens during
food processing.
2. Quality control: Improve systems like HACCP (Hazard Analysis of Critical Control
Points) to ensure food safety.
3. Product development: Redesign processes and recipes, set priorities in product
design and evaluation.
4. Data analysis and laboratory planning: The model could save resources, time and
money.
5. Risk assessment models: Evaluate the probability that a food could cause food-
borne illness.
Limitations of predictive microbiology
Even thought predictive microbiology models are widely used when correctly validated,
they have several limitations because of the complexity of microbial behavior and food
systems:
- Mathematical models are simplifications of complex biochemical processes and in
some cases not every important variable or factor that is affecting the system is included
in the model (Alzamora et al., 2005; Buchanan and Whiting, 1997).
- Usually, models are not designed for the same conditions in which microorganisms
exist in food systems (biofilms, starved and unknown nutrients among many others),
since the majority of the data to generate the predictive model are derived form broth-
based experiments. It is known that bacterial pathogens are more resistant in real food
products than in broth cultures (Alzamora et al., 2005) .
- Most of the models describe changes of microbial behavior for homogeneous
populations; nevertheless, competition among microorganisms affect the food
environment (Lebert and Lebert, 2006).
- Some models make a good description of linear relationships; but when more than one
factor is involved, reparameterization of the model becomes necessary. Response
surface models can describe microbial growth when more factors are involved, however
it is necessary to assume that biological parameters are independent and only works
well within variable ranges for which the experiment was designed, that means
extrapolation is not possible (Alzamora et al., 2005; Lebert and Lebert, 2006).
- On the other hand, accuracy of the model depends on the quality of the data, the
standardization of the experimental and statistical methodology and the statistical
measures of uncertainty. Literature or industry data usually lacks these types of
information (Alzamora et al., 2005; Buchanan and Whiting, 1997; Marks, 2008).
- Finally, several inaccurate predictions are because of the models predict microbial
growth or inactivation as an isolated event. It is necessary to integrate dynamic bacterial
behavior (predictive microbial models), fluctuating conditions within the system
(thermodynamics of the food product) and processing models (mass and heat transfer),
in order to have the whole picture regarding the microbiological safety of foods. New
approaches like integrated modeling (Lebert and Lebert, 2006) and Van Impe model
(2005) describe microbial growth evolution as a self-limiting process, and consider
both, physico-chemical food properties as well as mass and heat transfer during food
processing as can be seen in Fig.1 (Marks, 2008). Although the effort to predict food
microbial behavior as a complex event exists, the solutions are few, since models have
been designed for specific conditions and objectives; then it is necessary to separately
validate and to verify assumptions about the system before the integration model can be
utilized (Lebert and Lebert, 2006).
For the reasons above mentioned, it is very important to explore and research other
possibilities to integrate and validate food-processing variables. Since system dynamics
is a methodology that studies complex feedback systems, could be an alternative and
complementary approach to understand, model, and predict microbial behavior in foods.
Liquid or solid media Microorganisms
Physicochemicaleal
properties Growth
parameters
= f(T, pH, au)
(TPH, ay)
F}
3
g
‘Thermodynamic Bactortal
balance aon
1
T
|
|
|
is nett
|
|
|
Eomposition
of the medium
(solututes, water,
concentration)
Bacterial
Production,
population
| consumption of
| ae
|
|
|
|
|
|
ah
gro |
|
|
|
|
|
Fig. 1. An integrated modeling approach to predict bacterial behavior (Lebert and
Lebert, 2006).
System dynamics as a complementary tool for Predictive microbiology
Food microbiology deals with complex feedback systems such as growing, surviving
and dying populations of microorganisms, which can be found in culture media,
laboratory-model systems or food products. Some microbiologists describe food as
complex ecosystems that are conformed by the environment represented by food
components and the microorganisms that can grow in the food product (Montville,
1997). Microbial ability to grow, survive or die (level variable) depends on the rate
variables of growth and deaths (microorganism behavior), which in turn depend on
both, inhibition factors related to food physico-chemical properties (pH, ay, etc.) and
extrinsic factors that are part of process engineering (temperature, ultrasound, natural
antimicrobials, among others). On the other hand, bacteria tend to come back to its
normal status (homeostasis). These homeostasis mechanisms involve a considerable
energy cost for the microorganism that is to say, bacteria will use the energy for cell
regeneration instead of cell reproduction and eventually the microorganism will die
(Fig. 2). In consequence if bacterial homeostasis is perturbed by preservation hurdles,
the microorganism will not multiply or even die before its homeostasis is repaired
(Gould, 1995). Combinations of factors could promote dominance of either positive or
negative feedback loops (Fig. 3).
Energy for
reproduction
Energy for
Cell regeneration
Cell availab]
Ener
oy Energy for
osmoregulation
Energy for
exchanging protons
Fig. 2. Energy available for bacterial metabolism and homeostasis.
Averaye Cell
Energy for
reproduction
New Cells
viability
Death Cells
viability
Eroding cell
Regenerating viabilty
Ultrasound
Energy for
cel generat a
Natural
antimicribial
Fig. 3. Hurdle technology and system dynamics building blocks.
Example: Bacterial Thermal Inactivation
Fig. 4 represents an example of a work in progress for bacterial inactivation by heat
treatment, which is applied in order to prevent microbial growth and reproduction
enhancing food safety (Valdramidis et al., 2006). The number of bacterial cells (stock 1)
depends on cell viability (stock 2); when cell viability decreases, bacterial accumulation
decreases as well. Cell viability is affected by the rate variables: Energy (for bacterial
homeostasis) and temperature goal (heat treatment). The flows that affect bacterial
accumulations are growing and dying. The flows affecting cell viability are reinforcing
cell viability, deteriorating viability by natural death, deteriorating viability by heat
treatment, and regenerating cell viability. The clouds represent the boundaries of the
system.
average cell TeProduction'pnergy ‘raimum — maximun death rate
Mibilty feproduction rate
effective
avalilability effect on Sascheviesin rate
reproduction
reproduction energy “Produ baeaia
reproducto
energy avaliable
energy growing ‘ying
available for
homeostasis
average cell lettect ofcetl iadity
viability in death rate
ability goa
cell abil
fraction of
imjersion spaidy minimum vabilty
reinforcing
deteriorating by
death
regenération roy w cell viability.
available
regeneratin deteriorating
by femperature setting
nedtieatment ae
& ptimal =
effectiness in thé treatment
ty uration
te temperatyeettect / temp
on viability déterioratidn
temperature
joal
enviromental & inpnelly
temperature
Fig. 4. Biological system dynamics model: an example of a bacterial thermal
inactivation process.
Temperature is one of the most important food preservation factors, since it affects
microbial growth and reproduction rates. The optimal growth temperature for a
microorganism is the one that allows the maximum growth rate. Below the minimum
temperature and above the maximum temperature, microbial growth does not exist due
to changes in bacterial metabolism. The optimal growth temperature for mesophilic
bacteria is between 25°C and 40°C.
In this example, the model predicted the number of bacteria, deaths, births and cell
viability (Figs. 5 and 7) as well as the average cell viability and the effective death and
reproduction rates (Figs. 6 and 8). The experiment was carried out for two different
conditions. The temperature of the first tested condition was 25°C, which corresponds
to low optimal growth temperature for mesophilic bacteria. The temperature of the
second tested condition was 70°C, temperature used for pasteurization. The time of the
experiment duration was 10 min and maximum death rate and minimal viability
remained constant for both tested conditions.
At 25°C, experiment results were as expected. The number of bacteria and viability
were high and they correspond with the birth values, which were slightly higher than the
deaths at the end of the treatment (10 min). After the treatment, the births are still
growing (Fig. 5) because the reproduction rate and average cell viability are both above
the death rate (Fig. 6).
1: bacterias 2: deaths 3: births 4: cell viability
1, 5.47¢+009%
24 7e+012.E4U
4° 340000000
1, 2.735e+009
. 3564012
4° 220000000
1 0
%
4] 0
4° 100000000:
0.00 10.00 20.00 30.00 40.00
Time (min)
XQ thermal inactivation at 25°C
Fig. 5. Effect of heat treatment on system variables at 25°C: 1. Bacterial number, 2.
Deaths, 3. Births, and 4. Cell viability.
1: effective death rate 2: average cell viability 3: effective reproduction rate
19
=
1
2
3: 0
0.00 10.00 20.00 30.00 40.00
Time (min)
XQ ‘Thermal inactivation at 25°C
Fig. 6. Effect of heat treatment over the system variables at 25°C: 1. Effective death
rate, 2. Cell viability, and 3. Effective reproduction rate.
When heat treatment was applied (70°C), bacterial inhibition was observed. In the first
minute, births begin to decrease; the same happened with cell viability and the number
of bacteria for three minutes. On the other hand, the deaths reached their peak at the
fifth minute (Fig. 8). Average cell viability decreased in a way that gave no chance for
the bacteria to increase its effective reproduction rate, yielding to total bacterial death
before the heat treatment ended (Fig. 9).
1: bacterias 2: deaths 3: births 4: cell viability
4, 5.47@+009
2] 200000000
340000000
2.735e+009
100000000:
4° 220000000
20.00 40.00
Time (min)
Fig. 7. Effect of heat treatment on system variables at 70°C: 1. Bacterial number, 2.
Deaths, 3. Births, and 4. Cell viability
1: effective death rate 2: average cell viability 3: effective reproduction rate
19
|
| -—--------
‘ rae —————
0.00 10.00 20.00 30.00 40.00
Time (min)
°
NX
Fig. 8. Effect of heat treatment on system variables at 70°C: 1. Effective death rate, 2.
Cell viability, and 3. Effective reproduction rate.
Final Remarks
Foods are complex feedback systems. Predictive microbiology has developed several
mathematical models to describe and predict food microbial behavior within these
systems in order to achieve food safety while enhancing food quality. System dynamics
seems to be a complementary approach to model and predict microbial behavior in food
systems within an integrated point of view, since complex behaviors can be described
with simple structures such as the casual-loop and stock-and-flow diagrams.
Furthermore, the structural diagram can be quantitatively described with simple
algebraic equations using friendly software. Therefore, further work is underway to
model biological parameters of a specific food system by means of predictive
microbiology models and compare the results with those obtained by means of system
dynamics models.
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