• Journal of Food Hygiene and Safety
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• v.26 no.1
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• pp.25-30
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• 2011

In this study, predictive mathematical models were developed to predict the kinetics of Listeria monocytogenes growth in the mixed fresh-cut vegetables, which is the most popular ready-to-eat food in the world, as a function of temperature (4, 10, 20 and $30^{\circ}C$). At the specified storage temperatures, the primary growth curve fit well ($r^2$=0.916~0.981) with a Gompertz and Baranyi equation to determine the specific growth rate (SGR). The Polynomial model for natural logarithm transformation of the SGR as a function of temperature was obtained by nonlinear regression (Prism, version 4.0, GraphPad Software). As the storage temperature decreased from $30^{\circ}C$ to $4^{\circ}C$, the SGR decreased, respectively. Polynomial model was identified as appropriate secondary model for SGR on the basis of most statistical indices such as mean square error (MSE=0.002718 by Gompertz, 0.055186 by Baranyi), bias factor (Bf=1.050084 by Gompertz, 1.931472 by Baranyi) and accuracy factor (Af=1.160767 by Gompertz, 2.137181 by Baranyi). Results indicate L. monocytogenes growth was affected by temperature mainly, and equation was developed by Gompertz model (-0.1606+$0.0574^*Temp$+$0.0009^*Temp^*Temp$) was more effective than equation was developed by Baranyi model (0.3502-$0.0496^*Temp$+$0.0022^*Temp^*Temp$) for specific growth rate prediction of L.monocytogenes in the mixed fresh-cut vegetables.

• Journal of Preventive Veterinary Medicine
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• v.42 no.4
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• pp.143-147
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• 2018

The present study aimed to develop growth prediction models of Listeria monocytogenes in processed meat products, such as mixed pressed hams, to perform accurate microbial risk assessments. Considering cold storage temperatures and the amount of time in the stages of consumption after opening, the growth of L. monocytogenes was determined as a function of temperature at 0, 5, 10, and $15^{\circ}C$, and time at 0, 1, 3, 6, 8, 10, 15, 20, 25, and 30 days. Based on the results of these measurements, a Baranyi model using the primary model was developed. The input parameters of the Baranyi equation in the variable temperature for polynomial regression as a secondary model were developed: $SGR=0.1715+0.0199T+0.0012T^2$, $LT=5.5730-0.3215T+0.0051T^2$ with $R^2$ values 0.9972 and 0.9772, respectively. The RMSE (Root mean squared error), $B_f$ (bias factor), and $A_f$ (accuracy factor) on the growth prediction model were determined to be 0.30, 0.72, and 1.50 in SGR (specific growth rate), and 0.10, 0.84, and 1.35 in LT (lag time), respectively. Therefore, the model developed in this study can be used to determine microorganism growth in the stages of consumption of mixed pressed hams and has potential in microbial risk assessments (MRAs).

• Food Science and Biotechnology
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• v.17 no.6
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• pp.1352-1356
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• 2008

Bootstrap method, a computer-intensive statistical technique to estimate the distribution of a statistic was applied to deal with uncertainty and variability of the experimental data in stochastic prediction modeling of microbial growth on a chill-stored food. Three different bootstrapping methods for the curve-fitting to the microbial count data were compared in determining the parameters of Baranyi and Roberts growth model: nonlinear regression to static version function with resampling residuals onto all the experimental microbial count data; static version regression onto mean counts at sampling times; dynamic version fitting of differential equations onto the bootstrapped mean counts. All the methods outputted almost same mean values of the parameters with difference in their distribution. Parameter search according to the dynamic form of differential equations resulted in the largest distribution of the model parameters but produced the confidence interval of the predicted microbial count close to those of nonlinear regression of static equation.

• Food Science of Animal Resources
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• v.30 no.1
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• pp.49-54
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• 2010

The aim of this research was to estimate the effect of temperature and develop predictive models for the growth of total viable cells (TVC) and Escherichia coli (EC) on chicken breast under aerobic and various temperature conditions. The primary models were determined by Baranyi model. The secondary models for the specific growth rate (SGR) and lag time (LT), as a function of storage temperature, were developed by the polynomial model. The initial contamination level of chicken breasts was around 4.3 Log CFU/g of TVC and 1.0 Log CFU/g of E. coli. During 216 h of storage, SGR of TVC showed 0.05, 0.15, and 0.54 Log CFU/g/h at 5, 15, and $25^{\circ}C$. Also, the growth tendency of EC was similar to those of TVC. As storage temperature increased, the values of SGR of microorganisms increased dramatically and the values of LT decreased inversely. The predicted growth models with experimental data were evaluated by $B_f$, $A_f$, RMSE, and $R^2$. These values indicated that these developed models were reliable to express the growth of TVC and EC on chicken breasts. The temperature changes of distribution and showcase in markets might affect the growth of microorganisms and spoilage of chicken breast mainly.

• Food Science of Animal Resources
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• v.35 no.1
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• pp.108-113
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• 2015

The purpose of this study was to develop predictive models for the growth of Listeria monocytogenes in pork Bulgogi at various storage temperatures. A two-strain mixture of L. monocytogenes (ATCC 15313 and isolated from pork Bulgogi) was inoculated on pork Bulgogi at 3 Log CFU/g. L. monocytogenes strains were enumerated using general plating method on Listeria selective medium. The inoculated samples were stored at 5, 15, and $25^{\circ}C$ for primary models. Primary models were developed using the Baranyi model equations, and the maximum specific growth rate was shown to be dependent on storage temperature. A secondary model of growth rate as a function of storage temperature was also developed. As the storage temperature increased, the lag time (LT) values decreased dramatically and the specific growth rate of L. monocytogenes increased. The mathematically predicted growth parameters were evaluated based on the modified bias factor ($B_f$), accuracy factor ($A_f$), root mean square error (RMSE), coefficient of determination ($R^2$), and relative errors (RE). These values indicated that the developed models were reliably able to predict the growth of L. monocytogenes in pork Bulgogi. Hence, the predictive models may be used to assess microbiological hygiene in the meat supply chain as a function of storage temperature.

• Food Science of Animal Resources
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• v.29 no.1
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• pp.47-54
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• 2009

Predictive modeling was applied to study the growth of microorganisms related to spoilage in frankfurter sausage containing various levels of dietary fiber (0, 1, 2, and 3%) from rice bran and to estimate its shelf-life. Using the Baranyi model, total viable cells, anaerobic and psychrotrophic bacteria were measured during 35 days of cold storage ($<4{\pm}1^{\circ}C$). The lag times (LT) demonstrated by control and treatment groups were 6.28, 623, 6.24, and 6.25 days, respectively. The growth rate of total viable cells in each group were 0.95, 0.91, 0.92, and 0.91 (Log CFU/g/day), respectively. The anaerobic and psychrotrophic bacteria had lower initial ($y_0$) and maximal bacterial counts ($y_{max}$) than total viable cells. Also, the anaerobic and psychrotrophic bacteria possessed lower growth rate and longer lag time than total viable cells. The estimated shelf-life of frankfurter containing rice bran fiber by the growth rate of total viable cells was 7.8, 7.9, 7.9, and 7.7 days, respectively. There were no significant differences in shelf-life as a function of fiber content. In other words, the addition of dietary fiber in sausage did not show the critically hazardous results in growth of microorganism. The 12 predictive models were then characterized by high $R^2$, and small RMSE. Furthermore, $B_f$ and $A_f$ values showed a very close relationship between the predictive and observed data.

• Food Science of Animal Resources
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• v.28 no.2
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• pp.232-239
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• 2008

The objective of this study is to estimate the shelf-life of Tteokgalbi containing dietary fiber extracted from rice bran by using the predictive microbiology. This Tteokgalbi was made with 0%, 1%, 2%, and 3% dietary fiber. The number of total viable cells, anaerobic, psychrotrophic, and heat-stable bacteria and coliforms was calculated during 15 days of storage under $4{\pm}1^{\circ}C$ and the obtained data was applied to Baranyi function. The evaluation of fitness between predicted and observed data showed that these were matched in a satisfactory way. Heat-stable bacteria was detected lower than <1 log CFU/g and coliforms were not detected during the storage. The changes of total viable cells and psychrotrophic bacteria in Tteokgalbi were increased gradually, but dramatically increased after 3 days of storage. The models of total viable cells and anaerobic bacteria showed very similar growth trends and values of growth parameters each other. The estimated shelf-life of each Tteokgalbi was calculated from the predictive model of total viable cells and the estimated shelf-life was 1.7, 2.3, 2.3, and 2.4 days, respectively. The results suggested that the prediction of bacteria growth could be used to evaluate the microbiological safety and determine the shelf-life of Tteokgalbi as ready-to-eat food in the local market.

• Preventive Nutrition and Food Science
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• v.13 no.4
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• pp.348-353
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• 2008

Aerobic bacterial growth on Korean pan.fried meat patties as a primary quality deterioration factor was modeled as a function of temperature to estimate microbial spoilage on a real.time basis under dynamic storage conditions. Bacteria counts in the stretch.wrapped foods held at constant temperatures of 0, 5, 10 and $15^{\circ}C$ were measured throughout storage. The bootstrapping method was applied to generate many resampled data sets of mean microbial counts, which were then used to estimate the parameters of the microbial growth model of Baranyi & Roberts in the form of differential equations. The temperature functions of the primary model parameters were set up with confidence limits. Incorporating the temperature dependent parameters into the differential equations of bacterial growth could produce predictions closely representing the experimental data under constant and fluctuating temperature conditions.

• Preventive Nutrition and Food Science
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• v.13 no.2
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• pp.104-111
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• 2008

As a way to account for the variability of the primary model parameters in the secondary modeling of microbial growth, three different regression approaches were compared in determining the confidence interval of the temperature-dependent primary model parameters and the estimated microbial growth during storage: bootstrapped regression with all the individual primary model parameter values; bootstrapped regression with average values at each temperature; and simple regression with regression lines of 2.5% and 97.5% percentile values. Temperature dependences of converted parameters (log $q_o$, ${\mu}_{max}^{1/2}$, log $N_{max}$) of hypothetical initial physiological state, maximum specific growth rate, and maximum cell density in Baranyi's model were subjected to the regression by quadratic, linear, and linear function, respectively. With an advantage of extracting the primary model parameters instantaneously at any temperature by using mathematical functions, regression lines of 2.5% and 97.5% percentile values were capable of accounting for variation in experimental data of microbial growth under constant and fluctuating temperature conditions.

• Asian-Australasian Journal of Animal Sciences
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• v.27 no.7
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• pp.1013-1018
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• 2014

In this study, we developed kinetic models to predict the growth of pathogenic Escherichia coli on cheeses during storage at constant and changing temperatures. A five-strain mixture of pathogenic E. coli was inoculated onto natural cheeses (Brie and Camembert) and processed cheeses (sliced Mozzarella and sliced Cheddar) at 3 to 4 log CFU/g. The inoculated cheeses were stored at 4, 10, 15, 25, and $30^{\circ}C$ for 1 to 320 h, with a different storage time being used for each temperature. Total bacteria and E. coli cells were enumerated on tryptic soy agar and MacConkey sorbitol agar, respectively. E. coli growth data were fitted to the Baranyi model to calculate the maximum specific growth rate (${\mu}_{max}$; log CFU/g/h), lag phase duration (LPD; h), lower asymptote (log CFU/g), and upper asymptote (log CFU/g). The kinetic parameters were then analyzed as a function of storage temperature, using the square root model, polynomial equation, and linear equation. A dynamic model was also developed for varying temperature. The model performance was evaluated against observed data, and the root mean square error (RMSE) was calculated. At $4^{\circ}C$, E. coli cell growth was not observed on any cheese. However, E. coli growth was observed at $10{\circ}C$ to $30^{\circ}C$C with a ${\mu}_{max}$ of 0.01 to 1.03 log CFU/g/h, depending on the cheese. The ${\mu}_{max}$ values increased as temperature increased, while LPD values decreased, and ${\mu}_{max}$ and LPD values were different among the four types of cheese. The developed models showed adequate performance (RMSE = 0.176-0.337), indicating that these models should be useful for describing the growth kinetics of E. coli on various cheeses.