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Applied and Environmental Microbiology, July 1999, p. 3095-3099, Vol. 65, No. 7
0099-2240/99/$04.00+0
Visualization and Modelling of the Thermal
Inactivation of Bacteria in a Model Food
Sanjay R.
Bellara,1
Peter J.
Fryer,1,*
Caroline
M.
McFarlane,1
Colin R.
Thomas,1
Paul M.
Hocking,2 and
Bernard
M.
Mackey2
School of Chemical Engineering, University of
Birmingham, Edgbaston, Birmingham B15 2TT,1 and
Institute of Food Research, Reading Laboratory, Whiteknights,
Reading RG6 2EF,2 United Kingdom
Received 16 November 1998/Accepted 1 April 1999
 |
ABSTRACT |
A large number of incidents of food poisoning have been linked to
undercooked meat products. The use of mathematical modelling to
describe heat transfer within foods, combined with data describing bacterial thermal inactivation, may prove useful in developing safer
food products while minimizing thermal overprocessing. To examine this
approach, cylindrical agar blocks containing immobilized bacteria
(Salmonella typhimurium and Brochothrix
thermosphacta) were used as a model system in this study. The
agar cylinders were subjected to external conduction heating by
immersion in a water bath. They were then incubated, sliced open, and
examined by image analysis techniques for regions of no bacterial
growth. A finite-difference scheme was used to model thermal conduction and the consequent bacterial inactivation. Bacterial inactivation rates
were modelled with values for the time required to reduce bacterial
number by 90% (D) and the temperature increase required to reduce D by
90% taken from the literature. Model simulation results agreed well
with experimental results for both bacteria, demonstrating the utility
of the technique.
| |
INTRODUCTION |
Food-borne diseases continue to be a
problem of global concern. Active surveillance of infections caused by
bacterial food-borne pathogens in the United States revealed 130,000 culture-confirmed cases in the population in 1997 (3).
Confirmed cases represent only a fraction of the total, and it was
estimated that the true incidence was likely to have been approximately
8 million cases. In the United Kingdom, the incidence of food-borne
illness continues to increase, and in 1997 over 94,000 cases were
reported (8). Poultry, eggs, and red meat products are
frequently identified as vehicles of food poisoning, and the most
common factors contributing to outbreaks include inappropriate storage
of food, cross-contamination, and inadequate cooking or reheating
(21).
Consumer demand for fresher, more natural food has resulted in a trend
towards milder methods of food processing that inactivate microbes
without having a deleterious effect on food quality. In this context,
an ability to predict the safety margins of inactivation or
preservation processes becomes particularly important. Mathematical modelling has been used to assist food process engineers in optimizing sterilization or pasteurization processes. In particular, much effort
has focused on modelling the sterilization of canned foods (14,
26, 27). Teixeira et al. (26) presented a numeric technique for computationally determining spore survival distribution spatially within a can exposed to conduction heating. Banga et al.
(4) used finite-difference and finite-element methods to model the conduction heating of canned tuna and demonstrated good agreement between theoretical and experimental temperature profiles. As
a consequence of the presence of Escherichia coli O157:H7 in undercooked hamburger patties, Vijayan et al. (29) modelled the inactivation of this bacterium in frozen patties during frying using a finite-difference scheme. It was those researchers' opinion that such computational modelling may be useful in developing safe
cooking processes.
Mathematically, the inactivation of bacteria has traditionally been
expressed with the well-known concepts of D and z values (the time [in seconds] required to reduce bacterial number by 90%
and the increase in temperature [in kelvins] required to reduce D by
90%, respectively) (13). These values are available in the
literature for all commonly occurring food poisoning and food spoilage
bacteria in a range of foods. Much work has been done to examine the
heat resistance of pathogenic bacteria such as E. coli
O157:H7 (2, 15), Salmonella spp. (25),
and Listeria monocytogenes (11, 25). The majority
of such studies have been conducted with homogenized foods or liquid
media, without any consideration of the spatial (three-dimensional)
element of solid foods as they are heated.
In spite of all the research conducted on modelling heat conduction in
packaged foods and the corresponding experimental work performed with
pathogenic bacteria, relatively very little research combining the two
has been performed. Some work, however, has been performed with
bacterial spores or enzymes as time-temperature indicators. Brown et
al. (7) prepared alginate and pureed food cubes inoculated
with bacterial spores. Mathematical modelling was used to predict heat
transfer and the consequent sporal destruction as particles were
heated. Significant deviations were found between experimental and
theoretical results. Teixeira et al. (28) used a model to
simulate heat conduction through cans of pea puree inoculated with
Bacillus stearothermophilus spores. Experimental results
attained for spore destruction were used to determine the heat
resistance of these spores. Results compared well with those in the
literature from isothermal spore inactivation experiments with pea
puree (24). Bhamidipati and Singh (6) and
Ramaswamy et al. (23) used enzymes (horseradish peroxidase
and bovine pancreas trypsin, respectively) embedded in particles heat
treated in a liquid flow system to validate the process of numeric
modelling. Both studies reported good agreement between values for
predicted and measured retention of enzyme activity.
Conventional thermal-processing calculations assume that the heat
resistance of microbes under changing conditions can be predicted from
their behavior at static temperatures. This assumption has been shown
not to be true for a number of vegetative bacteria, including
Salmonella typhimurium (17) and L. monocytogenes (22), whose resistance can increase
during heating at slowly rising temperatures. It is our opinion that
the heating rates typically observed during the conduction heating of
foods are too fast to allow vegetative microorganisms sufficient time
to acquire any increased heat resistance. This study will, in part,
test this hypothesis for a food simulant exposed to external conduction heating.
The aim of this collaborative work between researchers in Reading and
Birmingham, United Kingdom, was to establish how predictive microbiology can be applied in engineering environments. The thermal inactivation of the food-borne pathogen S. typhimurium and
meat spoilage organism Brochothrix thermosphacta immobilized
in agar cylinders simulating sausages subjected to external conduction heating was studied (1). Cylinder slices were examined by
image analysis techniques for regions of bacterial inactivation, and results were compared to those from mathematical modelling. Numeric simulations were also performed to examine inactivation profiles of
E. coli O157:H7 in lean ground beef sausages.
| |
MATERIALS AND METHODS |
Organisms and growth conditions.
S. typhimurium LT2
(NCIMB 10248) and B. thermosphacta MR165 (NCIMB 702891) were
maintained on glass beads at 
70°C. Cultures of S. typhimurium for thermal inactivation experiments were produced as
follows: 10 ml of tryptone soya broth (Oxoid, Basingstoke, United
Kingdom) was inoculated with a single colony taken from a tryptone soya
agar (TSA) plate and incubated for 7 to 8 h at 37°C. The culture
was then diluted 1:500 into fresh broth and incubated on a shaking
platform for a further 22 to 24 h. B. thermosphacta cultures were obtained by inoculating 100 ml of brain heart infusion (BHI) broth (Difco Laboratories) with a colony taken from BHI agar and
incubating the inoculated broth at 25°C for 16 h.
Preparation and inoculation of agar cylinders.
Dialysis
tubing (27-mm diameter; Sigma Chemical Co.) was rinsed in running water
to remove glycerol and cut into 0.35-m lengths. The tubing was knotted
at one end and sterilized by autoclaving. Flasks containing 150 ml of
molten TSA (for S. typhimurium) at 50°C or BHI agar (for
B. thermosphacta) at 45°C were inoculated with 1.5 ml of
culture. After being mixed, the agar was quickly poured into the
sterile dialysis tubing through a funnel and the open end was sealed by
tying it with string. The tubing was hung vertically at room
temperature (approximately 25°C) to allow the agar to set. The agar
cylinders so produced were of uniform diameters.
Thermal inactivation experiments.
Thermal inactivation
experiments were performed with the agar cylinders encased within
dialysis tubing. Cylinders inoculated with S. typhimurium
were heated not long after the agar had set (i.e., within approximately
1 h). The agar cylinders were heated for different times by
submerging them in a circulating water bath set at 70°C. After heat
treatment, the cylinders were cut into lengths of 2 to 3 cm and the
sections were incubated overnight (for 18 to 22 h) at 37°C. The
protocol for B. thermosphacta was similar except that the
agar cylinder was held at 5°C for 1 h before being heated and
the heating temperature used was 60°C. All thermal inactivation
experiments were conducted in duplicate.
Image analysis of cylindrical agar slices.
After incubation,
the agar blocks were cut into smaller slices with thicknesses of 5 to 6 mm and analyzed for regions of bacterial growth or destruction by an
image analysis system (Photonics Science Ltd., E. Sussex, United
Kingdom). Cylinder slices were placed on a lighting stage in a dark
box. Pictures were taken of these slices with a charge-coupled-device
camera. A dark circular region of bacterial growth and a clearer zone
around it where the bacteria had been inactivated could be observed
towards the center of the slice (Fig. 1).
Image-Pro Plus Imaging software (Media Cybernetics, Silver Spring, Md.)
was used to analyze these pictures. The dark circular region was
manually traced out with the computer mouse, and the radius of the
growth zone (Rgrowth) (in meters) as a fraction of the slice radius (R) was evaluated by the imaging
software. The ratio evaluated by the use of this technique was found to be highly reproducible, as when the same slice was examined by this
technique, differences in readings were found to be less than 1%. Each
slice was analyzed three times, and means were taken.
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FIG. 1.
Pictures show slices taken from agar cylinders which had
been inoculated with S. typhimurium and then heated. Darker
regions indicate zones where bacteria have grown. (a) Slice from a
cylinder heated for 90 s; (b) slice from a cylinder heated for
360 s.
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Mathematical modelling.
Heat conduction within a cylinder
can be described by the cylindrical form of the heat conduction
equation (9):
|
(1)
|
where 
is the thermal diffusivity, T is the
temperature (in kelvins), t is time (in seconds), and
r is the radial coordinate (in meters). As the agar sausages
were approximately 95% water by weight, a value for that was the
same as that of water (1.45 × 10
7 m2 s1) was used. Numeric simulations were also performed for
heat conduction in a ground beef sausage, for which a value for of
1.26 × 107 m2 s1 was used
(10). It was also assumed that the dialysis tubing had
little influence on heat transfer into the agar, as the tubing was both
relatively thin (less than 100 µm) and water permeable. Equation 1
was solved by using a finite-difference scheme with the boundary
conditions described below. For cylinders undergoing conduction
heating, the following boundary conditions are commonly used:
|
(2)
|
and
|
(3)
|
where equation 2 describes the symmetry of the system and
equation 3 describes the interfacial heat transfer between surface and
surroundings. In these equations, L is the sausage length (in meters), q is the heat flux into the sausage (in watts
per square meter), h is the local heat transfer coefficient
(in watts per square meter per kelvin), and
Tliquid and Tsurface are
the temperatures (in kelvins) of the liquid and surface, respectively. In experiments with equation 3, heating is provided by water undergoing forced circulation. The heating rate is thus controlled by internal conduction and does not depend on the heat transfer coefficient (i.e.,
the value of h is high). Therefore, instead of the boundary condition written for equation 3, the following approximation was used:
|
(4)
|
In conjunction with the modelling of heat conduction, bacterial
destruction throughout the cylinder was modelled as the temperature dynamically varied, by the following equation (29):
|
(5)
|
where N is the bacterial concentration (in CFU per
milliliter) and Dref is D at the reference temperature
(Tref). Simulations were performed for E. coli O157:H7, S. typhimurium, and B. thermosphacta. The D and z values were obtained from
literature (in part from work previously done at Reading) as shown in
Table 1. The data for E. coli
O157:H7 were obtained from inactivation experiments with ground beef,
whereas the data for the other two organisms were obtained with liquid
broth. All simulations were performed with the assumption that a
cylinder with a diameter of 0.027 m and a length of 0.20 m was
used. Simulation results are for a radial cross section taken from the
middle of a cylinder. Sample simulations showed that owing to the high
aspect ratio of the cylinder, the results were not significantly
different along the length of most of the cylinder.
Validation of heat transfer model.
To demonstrate that heat
transfer within the agar sausage is accurately described by this model,
agar cylinders were made (as described above, but uninoculated with
bacteria) and halved so as to create two cylinders of half the original
length. Each half-cylinder possessed a flat end (where the cut had been
made) and a rounded end. A type K thermocouple (RS Components Ltd.), threaded through a Pasteur pipette such that it just protruded out of
the thin end of the pipette, was inserted axially into the agar through
the flat end of the cylinder. Only cylinders in which the radial
distance of the thermocouple from the centers of the cylinders was 10%
of the radius of the cylinders were used in heat transfer experiments.
These agar cylindrical blocks were then immersed (vertically) into a
water bath. The temperature change (accuracy, ±0.1°C) over time was
recorded and compared to the theoretical temperature change.
| |
RESULTS AND DISCUSSION |
Validation of heat transfer model.
Heat conduction into the
agar cylinder was modelled by using equations 1, 2, and 4. Experimental
validation of this model can be seen in Fig.
2, which illustrates a typical
temperature profile with r/R equal to 0.1 for an agar
cylinder heated at 67.3°C. It can be seen that excellent agreement
between theoretical and experimental results was obtained. The
closeness of fit confirms (i) that there is little to be gained by way
of increased accuracy in modelling by the use of an external heat
transfer coefficient and (ii) that the other physical properties used
in the model provide a good description of the heat transfer properties
of the agar cylinder. There is still a need to identify the validity of
the model and details of data in all circumstances.
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FIG. 2.
Profile of the temperatures inside an agar cylinder,
showing experimental results and the fit of the mathematical model to
data.
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|
Numeric simulations of the thermal inactivation of E. coli O157:H7.
Numeric simulations were performed to
determine the destruction of E. coli O157:H7 in a ground
beef sausage (at an initial temperature of 25°C) exposed to external
heating for a specified time followed by cooling (at 20°C) to a point
where bacterial inactivation is no longer significant. The model
parameters used in the simulations are listed in Table 1. Figure
3 shows profiles for predicted bacterial
inactivation as a function of r/R within such a sausage
exposed to a temperature of 70°C for different heating times. As heat
penetrates into the sausage, bacterial count begins to rapidly drop
off. Wherever log(N/N0) (where
N0 is the initial bacterial concentration) was
less than 2 (2D inactivation) within the sausage, the temperature at
some point in the process rose above 61.0°C, at which point E. coli O157:H7 has a D value of 38 s. At 60.0°C or less, the
D value is greater than a minute, thus indicating the sharp sensitivity
of bacterial inactivation rates to small changes in temperature. Figure
3 also shows that at early heating times, there was a steep gradient of
inactivation as a function of distance from the center but that at
later times, the effect of position on degree of inactivation was less
(when the profiles for 2 and 8 min are compared).
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FIG. 3.
Effect of exposure time on predicted E. coli
O157:H7 inactivation along the radius of a ground beef sausage exposed
to 70°C.
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|
Figure
4 shows the effect of different
heating temperatures (65, 70, and 75°C) on inactivation of
E. coli O157:H7 as a function
of exposure time in the center of a
sausage. Clearly, it is important
to pay attention to the effects of
both time and temperature in
thermal processing to identify the
critical regions which lead
to such a rapid drop in bacterial numbers.
Figure
4 shows that
the critical time interval over which viable
numbers decrease
rapidly is much narrower at 75°C than at 65°C.
Thus, at 65°C numbers
at the center began to decrease after 5 min,
but a 7D inactivation
was not achieved until 12 min, whereas at 75°C
viable numbers
began to decline at about the same time (5 min), but a
7D inactivation
was reached only 2 min later.
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FIG. 4.
Predicted E. coli O157:H7 inactivation in the
center of a ground beef sausage at different heating temperatures.
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It is also important to note the effect of the cooling period on
bacterial inactivation. As the sausage is already loaded
up with heat,
heat continues to diffuse into the center of the
sausage even as the
outside is being cooled. Consider results
after 9 min of heating at
70°C (Fig.
4). After the heating period,
the center of the cylinder
reaches a temperature of 61.7°C and
a 1.9D inactivation is produced.
After cooling, an inactivation
of 8.7D is attained. A peak temperature
of 63.2°C was reached
during thermal processing of the
sausage.
Measurement of bacterial inactivation in agar cylinders.
Figure 1 shows examples of slices taken from TSA sausages inoculated
with S. typhimurium which were externally heated in a water
bath at 70°C. A distinction can be seen between darker regions, where
surviving bacteria have regrown, and clearer regions on the outside,
where thermal inactivation took place. The centers of the cylinders in
Fig. 1 appear somewhat lighter than the surrounding regions. This was
believed to be a consequence of oxygen depletion by bacteria closer to
the perimeter of the slice. This effect creates an anaerobic
environment in the center of the cylinder which restricts the extent of
growth in this region. Fortunately, for the purposes of this study, it
is necessary only to visualize the outer perimeter of bacterial growth.
The initial bacterial concentration within the agar sausage was known.
However, in order to compare experimental data of the
type in Fig.
1
with model predictions, one needs to have a defined
bacterial
concentration below which one would not expect to see
a dark region on
an agar slice. To this end, BHIA cylinders were
made (as described in
Materials and Methods) with diluted
B. thermosphacta inoculum to produce bacterial concentrations of 10, 100, and 1,000
CFU/ml. In the instance of a concentration of 1,000 CFU/ml, dark
slices
were produced. With a concentration of 100 CFU/ml, sausage
slices
appeared cloudy, with a large number of colonies suspended
in the agar.
At 10 CFU/ml, slices were much clearer, with few
colonies visible. The
threshold for bacterial inactivation, as
viewed under the image
analysis system was thus assumed to be
within the range 1 to 10 CFU/ml.
Experimental data from the growth zone radii of slices taken at
differing thermal exposure times are shown in Fig.
5 and
6 for
S. typhimurium and
B. thermosphacta,
respectively. The results
of simulations of bacterial inactivation for
which bacterial concentrations
of 1 and 10 CFU/ml were used as
threshold values for inactivation
are also shown in these graphs. For
both bacteria, the simulations
document inactivation of bacteria within
the agar cylinder extremely
well.
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FIG. 5.
Experimental validation of the inactivation of S. typhimurium in an agar cylinder (exposure temperature, 70°C).
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FIG. 6.
Experimental validation of the inactivation of B. thermosphacta in an agar cylinder (exposure temperature,
60°C).
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The mean deviation of experimental data from that predicted by theory
is 2.9% if we assume a 10-CFU/ml criterion and 3.6%
if we assume a
1-CFU/ml criterion. Finite-difference simulations
use mesh spacings for
r/
R of 0.01. The experimental error involved
in evaluating
Rgrowth/
R by image analysis was also
believed to
be approximately ±1% after slices taken from the
same cylindrical
agar block were examined. Hence, differences between
theoretical
and experimental values for growth zone radii were not
thought
to be significant. Simulations also indicated little deviation
between the results for 1- and 10-CFU/ml criteria, which is to
be
expected, as simulations shown in Fig.
3 indicate a very rapid
drop in
bacterial count after the temperature reached a critical
point within
the
solid.
It is evident from the data that the integrated lethal effect of a
dynamically varying temperature within the agar cylinder
can be used to
predict bacterial kill based on isothermal data.
This lethal effect is
believed to be a consequence of the relatively
high rates of heating
involved in this study. Under conditions
of low heating rates
(2°C/min or less),
S. typhimurium has been
shown to
exhibit increased heat resistance as a consequence of
heat
shock-induced thermotolerance (
17). Heat shock-induced
thermotolerance may become significant when food is heated up
very
slowly, i.e., at rates an order of magnitude less than the
heating
rates used in this
study.
Agar forms a macroreticular network of several sideways linked helices
whose ends are joined together randomly to form pores.
At agar
concentrations of 0.7% (wt/vol) or greater, bacteria become
immobilized (
30). Given the closeness of agreement between
experimental
and theoretical results, our results suggest that
immobilization
within agar does not affect bacterial thermal
resistance. The
implication of this conclusion is that agar can be used
as a model
food to immobilize bacteria and experimentally
validate the modelling
of bacterial thermal destruction in process
systems. A pertinent
example of this would be heat transfer to a
flowing food-liquid
suspension (
18).
Conventional food processing operations entail heating food until the
center reaches the desired lethal temperature, at which
point heating
is continued for a period of time sufficient to
ensure adequate
microbial killing, followed by cooling. In some
processing operations,
for example, the tuna canning process (
4),
this procedure
has been found to overprocess food nearer the outside
of the container.
A suitable knowledge of the heat transfer properties
of food and the
necessary approaches to process modelling can
help ameliorate this
problem, as it has already been demonstrated,
with numeric simulations,
that the cooling period can contribute
considerably to the destruction
of bacteria at the center of food.
Furthermore, Fig.
5 and
6 exhibit a
sharp decrease in
Rgrowth with exposure time.
The ability to predict this point is useful,
as it will allow one to
optimize thermal inactivation while minimizing
the overprocessing of
foodstuffs.
The modelling of heat transfer and the consequent microbial kill in
real foods, however, is a major challenge because the
physiochemical
composition of food can affect both heat penetration
and the thermal
resistance of microbes. For example, Franz and
von Holy (
12)
found that the fat contained in vacuum-packed
sausages provided a
significant protective effect for lactic acid
bacteria when the
sausages were exposed to heat. It has also been
demonstrated that the
thermal properties of foodstuffs can vary
extensively when different
samples are compared, which in turn
has a pronounced effect on
temperature profiles within foods (
19).
Nonetheless, Nicolai
et al. (
20) demonstrated that it was possible,
using
finite-element modelling, to model heat conduction in lasagna
using
steam heating. More comprehensive data on the thermal properties
of food components and more systematic data on thermal resistance
under
differing environmental conditions (water activity, pH,
fat content,
etc.) will help provide a solid basis upon which
to predict the safety
of cooked or thermally processed
foods.
The study presented in this paper modelled and experimentally validated
thermal inactivation of the bacteria
S. typhimurium and
B. thermosphacta immobilized in an agar cylindrical block.
While previous studies have pointed out the importance of
finite-difference
modelling for predicting bacterial inactivation
spatially within
a solid object exposed to conduction heating
(
26), this is the
first study to visually demonstrate it
with bacteria. The good
agreement between model simulation and
experimental data demonstrates
well the appropriateness of the
application of mathematical modelling
in food
microbiology.
| |
ACKNOWLEDGMENTS |
This project was sponsored by the Biotechnology and Biological
Sciences Research Council (Swindon, United Kingdom), which provided
funds for the support of S.R.B. and P.M.H.
| |
FOOTNOTES |
*
Corresponding author. Mailing address: School of
Chemical Engineering, University of Birmingham, Edgbaston, Birmingham
B15 2TT, United Kingdom. Phone: 44 121 414 5451. Fax: 44 121 414 5324. E-mail: P.J.Fryer{at}bham.ac.uk.
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Applied and Environmental Microbiology, July 1999, p. 3095-3099, Vol. 65, No. 7
0099-2240/99/$04.00+0
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Abstract
Introduction
