Full text of DOI:10.1111/j.1365-2621.2002.tb09462.x

JFS: Food Engineering and Physical Properties
Salmonella Enteritidis Risk Assessment:
A Kinetic Analysis
S. ALMONACID, J. GUTIERREZ, A. JAQUES, AND R. SIMPSON
ABSTRACT: Egg and egg preparations are important vehicles for Salmonella enteritidis infections. The influence of
time-temperature becomes important when the presence of this microorganism is found in commercial shell eggs,
particularly in countries where refrigeration is not mandatory as in Chile. The objective of this research was to
develop a mathematical model to analyze the Salmonella enteritidis risk under variable ambient temperatures.
Breakdown of vitelline egg membrane was assumed to be required for initiation of bacterial growth. When the
critical factor concerning safety is the vitelline membrane breakdown, 15 °C was found to be the storage threshold
temperature for a 30-d shelf life. This computer based tool can be used as a contribution in current regulation
adjustments or modifications.
Keywords: egg safety, Salmonella enteritidis, risk assessment
Introduction
ALMONELLA ENTERITIDIS (SE) SPREADING, AND THE
growing number of infections due to this microorganism
tellectually in the modification of current regulations. A research
study is being conducted at Universidad Técnica Federico Santa
María, Valparaiso, Chile, specifically, in the 2 cities which have
the largest concentrated population in the region: Viña del Mar
and Valparaiso. This region receives large quantities of tourists
during the summer season, as this activity is one of the main
sources of income for the area. The local Provincial Government,
knowing the risk of salmonellosis, supports this research study.
The objective of this research was to analyze the SE risk of infec-
tion from a kinetic point of view, which will be affected by the
common practice of egg storage in minimarkets and supermar-
kets. A coupled mathematical model which considers a heat
transfer simulator that accounts for the actual egg shape and
composition, and a biological model to estimate the vitelline
membrane degradation and SE growth under different tempera-
ture profiles, was implemented.
S
have motivated research programs in several countries. Investi-
gations of outbreaks of SE infection have shown that its most fre-
quent source is shell eggs (Humphrey 1994). More than 46 billion
eggs are distributed and sold annually in the United States. An
estimate points out that 2.3 million eggs contain SE which results
in 637000 cases of human illness per year (FSIS 1998). A recent
report from The American Heart Association states that healthy
people - about 75% of the world population - could consume an
average of 1 egg per d without concerns of an increase in both
cholesterol level or cardiovascular diseases (Osorio 2001). This
statement could enhance egg consumption, and then, its associ-
ated infections. In Chile, the risk of infection is greatly enhanced
during the summer season because refrigeration is not a com-
mon practice in minimarkets and supermarkets; and also be-
cause full shelf life is arbitrarily assumed to be 30 d (Gutierrez
2000). At present, Chilean regulation is changing towards man-
datory refrigeration, but without a clear scientific background.
The number of SE infection cases per year in Chile has increased
from 7 in 1990 to 954 in 1998. In this latter year, 91% of them oc-
curred during the warmer months, November through May, and
9% in the low temperature months, June through October. Strict
and systematic monitoring of SE started in 1994, however, 1000
infection cases are concretely reported per year (ISP 1998). This
high figure partially reflects the increase in egg consumption, a
constant rate of 2% per year since 1991. It has been reported that
almost 96% of the Chilean population considers eggs to be a vital
food for health and life, the same as vegetables, milk, and fruits
(Osorio 2001). Many authors have reported SE growth in eggs, af-
fected by temperature. Therefore, it shows that the temperature
could be of extreme importance, especially when eggs are stored
at the retail outlets (Humphrey and others 1989; Kim and others
1989; Bradshaw and others 1990; Humphrey 1994; Schoeni and
others 1995). There has been much debate however on the ad-
visability of holding eggs under refrigeration in retail outlets
(Humphrey 1994). Recent outbreaks in Chile have opened this
debate, and more scientific support is needed to collaborate in-
Materials and Methods
Mathematical model background
A SE risk assessment tool is needed to estimate rationally both
the risk and the impact of refrigeration on the reduction of cases
per year. The U.S. Department of Agriculture, Food Safety and In-
spection Service USDA (1999) prepared a SE risk assessment com-
puter tool based on 5 modules ranging from an Egg production
Module to a Public Health Module. The risk was assessed by the
incidence’s probabilistic distribution for each module. This tool
also includes a Storage and Distribution module which uses an
empirical formulation for eggs cooling with uniform initial temper-
ature. Therefore, it cannot be used for variable ambient tempera-
ture. Mathematical models are used in the phenomenological and
kinetic simulation of food processes. In this particular case the
problem includes a heat transfer phenomena—cooling and heat-
ing from environment to egg package and egg contents—along
with a kinetic model of vitelline membrane breakdown and SE
growth as a function of temperature at different egg locations.
The biological problem indicated that microbial growth accel-
erates when the vitelline membrane breaks down and that this
breakdown is temperature dependent (Humphrey and others
© 2002 Institute of Food Technologists
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Salmonella enteridis risk assessment . . .
1989; Kim and others 1989; Bradshaw and others 1990; Hum- tion has been studied only recently (Gutierrez 2000; Almonacid
phrey 1994; Schoeni and others 1995; Whiting and others 2000).
and others 2000). In the aforementioned studies a computer aid
Egg contents could be contaminated with SE by migration mathematical tool was validated to estimate temperature at dif-
through the shell and associated membranes, the so-called hori- ferent egg locations under variable ambient temperatures.
zontal way, or as a result of infection of the reproductive tissue of
A mathematical model that accounts for both the shape and
laying hens, the so-called vertical way. Research studies strongly the complex nature of the egg system was fed with a finite differ-
suggest that eggs are vertically contaminated (Humphrey 1994; ence algorithm written in C++. Two extreme cases were simulat-
Dolman and Board 1992), based on the following facts:
Eggs are infected from the reproductive tissue of the hen.
ed: a) low temperature with forced air, and b) ambient tempera-
ture with stagnant air. Parameters of interest, such as local heat
SE becomes entrapped in the eggs albumen near vitelline transfer coefficient (h) and global heat transfer coefficient (U
membrane. considering package material), were estimated and adjusted by
SE in albumen does not grow, as long as the vitelline mem- an inverse procedure using experimental data.
brane is able to keep them separated from egg yolk nutrients.
Breakdown of vitelline membrane is temperature dependent
and at some point will allow: (a) egg yolk nutrients to diffuse
through egg white, (b) bacteria to penetrate egg yolk, or (c) both
mechanisms acting together.
The main assumptions for the model were:
Heat transfer within egg content is totally by conduction.
Egg content is made of egg yolk and egg white.
Thermal properties do not change within the simulated tem-
perature range (5 to 37 °C).
When the vitelline membrane is broken down, SE starts expo-
nential growth.
The heat transfer mechanism up to the egg’s surface is con-
vective.
The numbers of SE per egg can ranges from 1 to 400 microor-
ganisms (Aserkoff and others 1970; Humphrey 1994).
Good agreement was found between experimental and theo-
retical data, mean temperature errors were in the range of 0.19
A kinetic model for vitelline membrane breakdown and SE ex- through 0.32 °C. Global heat transfer coefficients were found to
ponential growth was developed by the USDA Food Safety and be 4.4 through 15 (W/m2 K) and 2.4 through 8.0 (W/m2K) when
Inspection Service (FSIS) in its farm-to-table assessment of the eggs were stored in a typical cardboard package.
risk of human illness from SE in eggs and reported by USDA
Simulation scenarios
(1999) and Whiting and others (2000). The model was validated
with experimental data provided by Dr. T. Humphrey to the FSIS
team (USDA 1999). In his study, intact eggs with shells free of fe-
cal contamination were obtained within 2 h of being lain and
were stored, at 8 to 37 °C. At time intervals of about 3 d, 10 eggs
were removed and broken, using aseptic techniques. The con-
tents of each egg were inoculated with approximately 500 cells of
SE into the albumen next to the vitelline membrane. This site
was chosen because studies with eggs from artificially (Gast and
Beard 1990) and naturally infected hens (Humphrey and others
1991b) have shown it to be an important site of contamination
with SE. The inoculated eggs were held at 20 °C for 5 d. If more
than 2 of 10 eggs sampled at a storage time had SE exceeding 104
cfu/egg, estimated with standard laboratory techniques, that
time-temperature period was designated as growth permitting.
The average time for vitelline membrane breakdown is esti-
mated by the following exponential expression:
As previously stated the kinetic problem of SE growth in egg
contents encompasses 2 phases, which take place sequentially.
First, the time calculation for vitelline membrane breakdown
YMT = 10(2.1-0.043T)
YMT: Yolk membrane time (d)
T: Temperature °C
(1)
Two studies reporting the growth rates of SE in blended whole
eggs provided the best estimate of SE growth after YMT is ex-
ceeded. These results are reported by Whiting and others (2000).
The average exponential growth rate as a function of temper-
ature is estimated by:
EGR = (0.026T-0.14)2
EGR: Exponential growth rate (1/h)
T: Temperature °C
(2)
The heat transfer problem in solids for irregular shape has
been investigated by many authors and applied for different
food systems. A rather complete list of cases can be found in liter-
ature (Holdsworth 1992). Although irregular and oval shapes are
considered; egg shaped solids with multicomponent conforma-
Figure 1—Three-dimensional view of the egg shape as
modeled by Finite difference
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Salmonella enteridis risk assessment . . .
which is temperature dependent, as shown by equation 1; and temperature of 15 °C
2nd, the exponential growth rate shown in equation 2. The bac-
teria concentration can be expressed as a dimensionless number
by the following expression:
5. Simulation 3: Refrigerated temperature at 5 °C
Situations 1 to 4 considered eggs packed in a typical card-
board package in stagnant air, therefore, the global heat transfer
coefficient U was assumed to be 4.5 (W/m2K) (Gutierrez 2000).
Situation 5 considered eggs in a typical cardboard package in
forced refrigerated air, therefore, the global heat transfer coeffi-
cient U was 9.4 (W/m2K) (Gutierrez 2000).
(3)
Yolk membrane time (YMT) calculations under
variable temperature
The total Yolk membrane time (YMTTotal) under fluctuating
conditions was calculated by noting that, if YMTi, Dqi are the YMT
and incubation period at temperature Ti, respectively, then:
where, N is the microbial concentration in (cfu/g) after a Dq hours
held at a constant temperature T ( °C), and N0 is the initial con-
centration.
This 2-phased-kinetic problem was analyzed under several
different time-temperature scenarios. Computer experiments
were divided into the following expected and temperature con-
trolled situations:
1. Expected situation 1: Winter average conditions.
24 h at a constant temperature (15 °C): Eggs after being lain,
selected and packed remain 24 h at constant room temperature
before transportation to the supermarket.


i 



=

i

in the fraction of time accumulated to attain yolk breakdown
30 d at a sinusoidal temperature regime (24 h period) with a
maximum of 20 °C at 3 PM and a minimum of 15 °C at 3 AM.
2. Expected situation 2: Summer average conditions 24 h at a
constant temperature (20 °C): Eggs after being lain, selected and
packed remain 24 h at constant room temperature before trans-
portation to the supermarket.
30 d at a sinusoidal temperature regimen (24 h period) with a
maximum of 30 °C at 3 PM and a minimum of 20 °C at 3 AM.
3. Simulation 1: Controlled temperature at 20 °C
during incubation period Dqi
Therefore:
1
2
3
+
+
+
+
==> Yolk breakdown
completed
1
2
3
YMTi is related to temperature (Ti) according to the following
expression:
This situation would simulate an average air conditioning
temperature of 20 °C.
YMTi = 10(2.1-0.043 Ti)
(4)
4. Simulation 2: Controlled temperature at 15 °C
This situation would simulate an average air conditioning
After time YMTTotal = åDqi, vitelline membrane breakdown is
completed, then microorganisms begin to grow exponentially.
The concentration of cells can be calculated using equation 3.
Heat transfer model
Temperature profiles within eggshells with variable environ-
mental temperature can be calculated numerically, based on an
energy balance (Gutierrez 2000). Assuming heat transfer sym-
metry along the major axis, and expressing mathematical model
in cylindrical coordinates, a space grid in terms of r and z was
generated with one half of the product (Figure 1 and Figure 2).
Temperatures at the generated nodes were predicted using
an energy balance for a control volume surrounding each node,
for example:
Figure 2—Schematic representation of the numeric method
for heat transfer calculations
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Salmonella enteridis risk assessment . . .
egg white were considered with individual thermophysical prop-
erties. Salmonella enteritidis growth calculations, would proceed
as follows, with the aid of a PC computer: For the 1st time incre-
ment, an average temperature T, over the time interval Dq1 at the
center of each element, is supplied. Consequently, the final con-
centration N1 at that time interval is calculated by equation 3.
T −
2 ∆θ1
where N0 is the known initial concentration in the respective vol-
ume element.
This value is then multiplied by the volume fraction repre-
sented by the element to obtain the weight of the dimensionless
relative concentration represented by the volume element Vj.
The mass average of the dimensionless relative concentration,
for the time interval, is finally obtained as follow:
n
j
Total
(5)
j=
j
With the aforementioned procedure, temperatures can be calcu-
lated for each node. Also global heat transfer coefficients includ-
ing package resistance can be estimated when required (Almo-
nacid and Torres 1993).
Where VTotal is the total volume considered in the analysis and
n the numbers of elements in the total volume. Repeating this
process up to the storage time under study, allows obtaining the
final mass average relative concentration for each element. The
accumulated time effect is evaluated by equation
Combined heat transfer and biological model
Heat transfer equations were solved using an explicit finite
difference scheme with time increments of 5 s. Microbial growth
was calculated using kinetics constants, which ones were as-
sessed using an average temperature along the time interval, as
follows: If at a given point (node), which also happens to be con-
sidered the center of a very small volume element (relative to the
whole egg), the temperature is known, it can be assumed that
this temperature is representative of the whole element. This
principle also applies to the dimensionless relative concentration
(N/N0). Using this concept, the egg was virtually divided into vol-
ume elements in the shape of concentric ring layers having rect-
angular cross sections. This idea is illustrated in Figure 2. This
one shows the right hand side of an egg, where the egg yolk and
f
(6)
where m is the number of time intervals
In which the final average SE concentration Nf can be calcu-
lated by multiplying by the known homogeneous initial concen-
tration N0 :
f
f
(7)
Model application for SE risk assessment
Regular egg’s average physical dimensions, were used:
Width: 4.5 x 10-2 (m) (at the widest point)
Height: 6.0 x 10-2 (m)
Total volume: 63 x 10-6 (m3)
Total mass: 57.9 x 10-3 (kg) (11% of shell weight was not con-
sidered)
Yolk mass: 13.8 x 10-3 (kg)
White mass: 44.1 x 10-3 (kg)
Initial egg contamination, N0 = 400 (cell/egg)
For simulation accomplishment of the 5 detailed experi-
ments, 3 different initial SE concentration were used, consider-
ing the time when vitelline membrane is permeable to material
exchange (YMT completed):
i. It is assumed that all cells penetrate into the yolk and nutri-
ents remain in it, so that, N0 is uniform in the volume of yolk and
its value is:
Figure 3—Temperature gradient in egg contents as affected
by a constant temperature of 15 °C
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Salmonella enteridis risk assessment . . .
Table 1—Time in d for vitelline membrane breakdown and
growth of Salmonella enteritidis. Effect of the 5 different
scenarios and microorganism’s initial concentration.
Results and Discussion
IMULATIONS WERE CONDUCTED TO EVALUATE BOTH THE EFFECT OF
S
different time-temperature records—on a 30 d period—on
the safety of eggs and the effect of initial concentration of SE.
Vitelline membrane
breakdown time
(day)
Exponential growth,
time to N=106 (CFU/g)(day)
(N0)Whole
(N0)Yolk
(N0)White
Temperature distribution within egg
Winter
Summer 10
20 °C
15 °C
5 °C
22
2.25
0.88
1.54
3.54
-
1.88
0.79
1.33
3.08
-
2.17
0.88
1.50
3.46
-
When eggs are held at constant temperature, in 6 to 8 h a uni-
form temperature distribution is reached. This short transient
effect is fully described in Figure 3, in which the temperatures of
the center of the egg yolk, at the surface of the vitelline mem-
brane and the surface of the egg are plotted against time. This
short thermal inertia could severely affect the safety of the egg,
especially when temperature abuse occurs. The same result is
obtained when eggs are kept at a sinusoidal temperature regime.
Situation 1 (winter) and situation 2 (summer) render sinusoidal
pattern for the internal temperatures of the eggs, with maximum
difference of approximately 1 °C with the external temperature
(Figure 4). This fact illustrates the importance of using conceptu-
al mathematical models for temperature estimations, especially
when fluctuating temperature effect are being studied.
17
28
>>30
=
=
Yolk
ii. It is assumed that nutrients migrate to egg white and all
cells remain in egg white, so that, N0 is uniform in the volume of
egg white and its value is:
Kinetic analysis
=
=
In all situations analyzed in this research -shown in Table 1 -
the required time to attain membrane breakdown was less than
30 d, except for the simulation trial carried out at refrigeration
conditions (5 °C). In the latter case, simulations showed that af-
White
iii. It is assumed that both, cells and nutrients are uniformly
distributed in the whole egg, so that, C0 is uniform in the volume
of the egg and its value is:
=
=
Whole
Simulations were stopped, as an end of process criterion,
when SE concentration was 106 (cfu/g), which is considered haz-
ardous for human consumption. In general, minimum numbers
for gastroenteritis caused by salmonella range between 105-106/g
for S. bareilly and S. newport to 109 to 1010/g for S. pullorum (Jay
2000; Gutierrez 2000).
Figure 5—Microbial growth simulation under constant 15 °C
temperature. Effect of initial concentration of Salmonella
enteritidis
Figure 4—Temperature gradient in egg contents as affected Figure 6—Microbial growth simulation under sinusoidal
by a sinusoidal temperature variation with a maximum of temperature fluctuation for the winter season. Effect of
20 °C and minimum of 15 °C. Winter situation
initial concentration of Salmonella enteritidis
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Salmonella enteridis risk assessment . . .
ter 40 d at 5 °C, only 55% of the YMT fraction was consumed. since its depletion time, for most cases, is more than 90% of the
Therefore, storage at 5 °C could be considered as an over dimen- total safety time. In the same way, the growth phase could be
sioned alternative, in terms of controlled temperature for safety considered as safety factor. In other words, the safety period for
reasons. In all 3 scenarios given by situations 1, 2, and 3, the total shell egg consumption is over, when vitelline membrane deple-
time (addition of membrane breakage time and growth time to tion finishes.
achieve 106 (CFU/g)) was always less than 30 d, therefore indi-
15 °C is the advisable control temperature to ensure consum-
cating high-risk situation occurrences. On the other hand, for sit- er health when eggs are kept less that 30 d in a retail supermar-
uation 4 (15 °C constant temperature) the total time was always ket.
longer then 30 d, regardless of the SE initial concentration used
20 °C is the advisable control temperature to ensure consum-
for simulations, being an indicative result of advisable storage er health when eggs are kept less that 15 d in a retail supermar-
condition. Figure 5 and 6 show the required time to achieve 106 ket. This recommendation might be applied in those market-
(CFU/ g) as affected by initial concentration and ambient tem- places in which rotation times of eggs are less than 15 d or
perature profile for winter and constant temperature (15 °C) sim- generally 10 d.
ulating experiments, respectively.
The developed combined-model can be used to analyze other
When eggs are stored under fluctuating temperature condi- scenarios and offer sound scientific support for future regulation
tions (between 18 °C to 20 °C) - simulating those that might be adjustments or modifications.
found in a kitchen - rapid SE growth is possible after 6 to 10 d in
References
the majority of examined eggs as stated in a research conducted
by Humphrey and Whitehead (1993). Humphrey‘s results are in
agreement with those obtained in this research for situation
number 2 (summer) in which 10 d, the upper limit of the above
mentioned research, was necessary to attain YMT depletion. It is
presumed that insulated packaging, considered in our research,
might have some effect on the results as the experiments carried
out by Humphrey and Whitehead where done without taking
that factor into account.
There has been much debate on the advisability of holding
eggs under refrigeration in retail outlets. The data on storage-re-
lated effects on the growth rate of SE in egg contents (Humphrey
and Whitehead 1993; Humphrey and others 1991b) coupled with
data on naturally contaminated eggs stored at 20 °C, suggests
that refrigerated storage might not be necessary provided that
temperatures do not exceed 20 °C (Humphrey 1994). This recom-
mendation may also be a result from this research study, but
with a new constraint on holding time, which is no more than 17
d, the time for YMT breakdown under situation number 3 (20 °C).
Whiting generated a biological model for YMT depletion and
SE growth estimation, which was used in this research (Whiting
and others 2000). However, the former research used an empiri-
cal heat transfer model to estimate the temperature inside eggs
which is only valid for a cooling procedure at constant ambient
temperature and constant initial temperature. The error of this
empirical model arose from using it for transportation or storage
conditions, that consider fluctuating ambient temperatures.
Their results are not comparable with the ones obtained in this
research, because theirs considered eggs arranged in pallets,
and ours considered packaged eggs which is the way supermar-
kets usually display this product.
Almonacid SF, Simpson R, Nuñez P, Saavedra, O. 2000. Salmonella enteritidis risk
assessment: heat transfer model. 2000. Proceedings of ICEF8, International
Conference of Engineering and Food. 1727-1731.
Almonacid SF, Torres, JA. 1993. Mathematical models to evaluate temperature
abuse effects during distribution of refrigerated solid foods. J of Food Eng 20:223-
245
Aserkoff B, Schroeder SA, Brachman PS. 1970. Salmonellosis in The United States-
a five-year review. Am J Epidemiol 92:13-24
Bradshaw JG, Dhirendra Shah B, Forney E, Madden JM. 1990. Growth of Salmo-
nella enteritidis in yolk of shell eggs from normal and seropositive hens. J
Food Protect 53:12 1033-1036.
Dolman J, Board, RG. 1992. The influence of temperature on the behavior of
mixed bacterial contamination of shell membrane of hen’s eggs. Epidemiol
Infect 108: 115-121
Gast RK, Beard CW. 1990. Production of Salmonella enteritidis-contaminated
eggs by experimentally infected hens. Avian Dis 34, 438-446.
Gutierrez JA. 2000. Evaluación de riesgo de Salmonella enteritidis en huevos
frescos: Modelo matemático. Chemical Engineering Thesis. Universidad Téc-
nica Federico Santa María
Holdsworth SD. 1997. Thermal Processing of Packaged Foods. 1st ed. New York:
Chapman & Hall. p 25-29
Humphrey TJ, Greenwood M, Gilbert RJ, Rowe B, Chapman PA. 1989. The surviv-
al of Salmonella in shell eggs cooked under simulated domestic conditions.
Epidem Inf 103:35-45.
Humphrey TJ, Whitehead A, Gawler AHL, Henley A, Rowe B. 1991b. Number of
Salmonella enteritidis in the contents of naturally contaminated hen eggs.
Epidemiol Infect 106:489-496.
Humphrey TJ, Whitehead A. 1993. Egg age and the growth of Salmonella enterit-
idis in egg contents. Epidemiol Infect 111:209-219.
Humphrey TJ. 1994. Contamination of eggshell and contents with Salmonella
enteritidis: a review. Int J Food Microbiol 21:31-40.
Jay JM. 2000. Modern Food Microbiology, Sixth ed. Gaitherburg, Md.: Aspen Pub-
lications, Inc. p. 519.
Instituto de Salud Pública de Chile, Informes Mensuales 1998
Kim CJ, Emery DA, Rinke H, Nagaraja KV, Halvorson DA. 1989. Effect of time and
temperature on growth of Salmonella enteritidis in experimentally inoculat-
ed eggs. AVIAN Diseases 33:735-742.
Schoeni JL, Glass KA, McDermont JL, Wong ACL. 1995. Growth and penetration
of Salmonella enteritidis, Salmonella heidelberg and Salmonella typhimitium
in eggs. Int J Food Microbiol 24:385-396.
U.S. Department of Agriculture 1999. Food Safety and Inspection Service, Wash-
ington DC 20250. www.fsis.usda.gov/ophs/risk/index.htm
Osorio H. 2001. Consumo de huevos en Chile. Industria de Alimentos 4:40-42.
Whiting RC, Hogue A, Schlosser WD, Ebel ED, Morales RA, Baker A, McDowell
RM. 2000. A quantitative process model for Salmonella enteritidis in shell eggs.
J Food Sci 65:864-869.
Conclusions and Recommendations
ONCEPTUAL MATHEMATICAL MODELS COULD BE USE-
MS 20010240 Submitted 5/14/01, Revised 8/20/01, Revised 11/8/01, Accepted
11/10/01, Received 11/10/01
C
ful tools to estimate important variables or parameters in
This research was partially supported by the Provincial Government of Valparaiso-Chile and
from a research Grant 992725 from the Santa María University.
real practical situations. Rapid progress of both software and
hardware allows it to simulate real situations with fewer assump-
tions.
The authors are with Departamento de Procesos Químicos, Biotecnológicos,
y Ambientales Universidad Técnica Federico Santa María; P.O. Box 110-V;
Valparaíso, Chile. Direct inquiries to author Almonacid (E-mail:
salmonac@pqui.utfsm.cl).
The breakdown of vitelline membrane could be used as safe-
ty criterion for shelf life estimations under different situations
1120 JOURNAL OF FOOD SCIENCE—Vol. 67, Nr. 3, 2002