Baranyi Model Research Articles

Development and evaluation of a model predicting the survival of Escherichia coli O157:H7 NCTC 12900 in homemade eggplant salad at various temperatures, pHs, and oregano essential oil concentrations.

Homemade eggplant salad, a traditional Greek appetizer, was inoculated with Escherichia coli O157:H7 NCTC 12900 supplemented with different concentrations of oregano essential oil (0.0, 0.7, 1. 4, and 2.1% [vol/wt]) and stored at different temperatures (0, 5, 10, and 15 degrees C). The product's pH was adjusted to 4.0, 4.5, or 5. 0 with lemon juice. For each combination of the environmental factors, the bacterial counts were modeled, using the Baranyi model, as a function of time to estimate the kinetic parameters of the pathogen. A reduction of more than 1 log unit in E. coli O157:H7 counts was observed in all cases, and the death rate depended on the pH, the storage temperature, and the essential oil concentration. Separate quadratic models were developed with natural logarithms of the shoulder period and death rate as estimated by the growth model, as a function of temperature, pH, and oregano essential oil concentrations. These were further used to predict the population of E. coli O157:H7 NCTC 12900 from other inoculated eggplant salads at random conditions of temperature, pH, and oregano oil concentration. The predicted values were compared with viable-count measurements for validation.

Estimating the parameters of the Baranyi model for bacterial growth

The identifiability properties of the Baranyi model for bacterial growth were investigated, both structurally and applied to real-life data. Using the Taylor-series approach, it was formally proven that the model is structurally identifiable, i.e. it is now ascertained that it is certainly possible to give unique values to all parameters of the model, provided the bacterial growth data are of sufficiently good quality. The model also has acceptable practical identifiability properties in the presence of realistic data, which means that the confidence intervals on the parameter values are reasonable. However, there was a relatively high correlation between the maximum specific growth rate μmaxand the suitability indicator h0. An optimal experimental design to improve parameter estimation uncertainty was worked out, using the sampling times of the microbial growth curve as experimental degree of freedom. Using a D-optimal design criterion, it could be shown that the optimal sampling times were concentrated in four time periods (initial, start and end of exponential growth, end of experiment), each providing maximum information on a particular parameter. Because the optimal experimental design requires a priori estimates of the parameters, the propagation of the parameter uncertainty into the experimental design was assessed with a Monte Carlo simulation. In this way, 95% confidence intervals could be established around the optimal sampling times to be used in the optimal experiment. Based on these intervals, a design was proposed and experimentally validated. The error on the parameter estimates was more than halved, their correlation diminished and the nonlinearity of the result improved.

Comparison of the Baranyi model with the modified Gompertz equation for modelling thermal inactivation of Listeria monocytogenes Scott A

The Baranyi model was used to fit the four commonly observed survival curves: linear curves, those with a lag phase, those with a tailing phase and sigmoidal curves. It was validated by using published experimental data for thermal inactivation of Listeria monocytogenes Scott A heated in infant formula and compared with the modified Gompertz equation. For the prediction performance, the Baranyi model was better and more robust than the modified Gompertz equation.

Predictive model of the effect of CO 2, pH, temperature and NaCl on the growth of Listeria monocytogenes

The growth responses of L. monocytogenes as affected by CO 2 concentration (0–100% v v , balance nitrogen), NaCl concentration (0.5–8.0% w v ), pH (4.5–7.0) and temperature (4–20 °C) were studied in laboratory medium. Growth curves were fitted using the model of Baranyi and Roberts, and specific growth rates derived from the curve fit were modelled. Predictions for specific growth rate, doubling time and time to a 1000-fold increase could be made for any combination of conditions within the matrix. Predictions of growth from the model were compared with published data and this showed the model to be suitable for predicting growth of L. monocytogenes in a range of foods packaged under a modified atmosphere.

Predictive models of the effect of temperature, pH and acetic and lactic acids on the growth of Listeria monocytogenes

The combined effect of temperature (1–20 °C), pH (4.5–7.2) and acetic acid (0–10 000 mg/l; model 1) or lactic acid (0–20000 mg/l; model 2) on growth of Listeria monocytogenes in laboratory media was studied. Growth curves at various combinations of temperature, pH and acid concentration were fitted by the model of Baranyi and Roberts (1994), and specific growth rates derived from the curve fit were modelled. Predictions of growth from the models were compared with data in the literature, and this showed the models to be suitable for use in predicting growth of L. monocytogenes in a range of foods including meat, poultry, fish, egg and milk and dairy products. The two models are compatible i.e. they give similar predictions for cases when no acid is present.

Predictive modeling of the growth of Listeria monocytogenes in CO 2 environments

The effects of pH (5.5, 6.5), temperature (4, 7 and 10 °C) and carbon dioxide (10, 30, 50, 70 and 90%) on the growth and/or survival of a five strain mixture of Listeria monocytogenes were examined in brain heart infusion broth. All three variables had a major influence on the growth characteristics of the organism. As expected, both the lag time and generation time increased as the CO 2 level increased, and as pH and temperature decreased. Growth over a 30-day period was observed at all parameter combinations tested, except at pH 5.5, 4 °C in the presence of either 50, 70 or 90% carbon dioxide. Two primary models, the Gompertz and Baranyi equations, were compared for their ability to describe the growth of L. monocytogenes. In general, the Gompertz model predicted both longer lag and shorter generation times, compared to the Baranyi model. The Baranyi model appeared to fit the overall data better than the Gompertz model. However, these differences were often small. Response surface models were developed for predicting the effects and interactions of the three independent variables on the growth and/or survival of L. monocytogenes in the different modified atmospheres. Results demonstrate the importance of strict temperature control for maintaining the advantages of food shelf life extension in enriched carbon dioxide environments. The information obtained in this study could be used as a guide to manufacturers of modified-atmosphere packaged foods, especially when designing products in which this organism may be a concern.

Predictive model of the effect of temperature, pH and sodium chloride on growth from spores of non-proteolytic Clostridium botulinum

Non-proteolytic strains of Clostridium botulinum are capable of growth at chill temperatures and thus pose a potential hazard in minimally-processed chilled foods. The combined effect of pH (5.0–7.3), NaCl concentration (0.1–5.0%) and temperature (4–30 °C) on growth of non-proteolytic C. botulinum in laboratory media was studied. Growth curves at various combinations of pH, NaCl concentration and temperature were fitted by the Gompertz and Baranyi models, and parameters derived from the curve-fit were modelled. Predictions of growth from the models were compared with data in the literature and this showed them to be suitable for use with fish, meat and poultry products. This model should contribute to ensuring the safety of minimally-processed foods with respect to non-proteolytic C. botulinum.

Modelling of microbial activity and prediction of shelf life for packed fresh fish

Prediction of shelf life based on growth of specific spoilage organisms (SSO) in model substrates was studied. The effect of CO 2 on the growth kinetics for Photobacterium phosphoreum and Shewanella putrefaciens was quantified and modelled. Results showed that microbial spoilage of packed cod stored with various concentrations of CO 2 was accurately predicted from the effect of CO 2 on P. phosphoreum grown in model substrates. The short shelf life extensions previously reported for packed cod therefore can be explained by the high CO 2 resistance of this Gram negative organism. S. putrefaciens was very sensitive to CO 2 and growth rates could not be related to the shelf life of packed cod. Growth curves without lag phases were found for all concentrations of CO 2 and for both the microorganisms studied. For the fitting of these growth curves the log-transformed Logistic models were selected after comparision with the ‘modified Gompertz’ models and with the model of Baranyi et al. (1993). The effect of CO 2 on μ max was well described by a 2 parameter square root model. Validation of kinetic models by comparison of shelf life predictions with shelf life determined by sensory evaluations in product experiments was preferred for comparision of microbial growth rates determined in product and model system experiments. Kinetic modelling was found to be valuable for both evaluation and prediction of microbial fish spoilage and an iterative approach for development of kinetic shelf life models was suggested.

The effect of temperature on the growth of non-proteolytic type B Clostridium botulinum

The effect of temperature between 4 and 35°C on the growth rate of a non-proteolytic type B strain of Clostridium botulinum was examined. Growth was in culture media at pH 6.7 and was measured by viable counts using the Most Probable Number (MPN) method. Doubling times were derived from the curve fitting model of Baranyi et al. (1992) and ranged from 42.3 h at 3.9°C to 22 min at 35°C.