Measurements and predictions of growth for Listeria monocytogenes and Salmonella during fluctuating temperature II. Rapidly changing temperatures

Growth of Listeria monocytogenes and Salmonella was examined during various rates of increase and decrease in temperature from and to the minimum for growth. Growth was little affected by even the most rapid changes and injury or lag was not observed. Subsequent investigations of growth during periods of rapid variation in temperature from and to temperatures below the growth minimum again had little effect and growth was satisfactorily predicted using the dynamic model of Baranyi and Roberts [Int. J. Food Microbiol. 23 (1994) 277] in conjunction with the data of Food Micromodel.     

Modeling and predicting the simultaneous growth of Listeria monocytogenes and natural flora in minced tuna

The growth kinetics of Listeria monocytogenes and natural flora (NF) in minced tuna from 2 to 30 °C were examined, and a simultaneous growth model was developed. The inhibiting effect of the NF on the growth of L. monocytogenes was examined by inoculating different levels of NF isolated from the minced tuna. The kinetic data were fitted to the Baranyi model and estimated the growth parameters such as specific growth rate (μ(max)), maximum population density (N(max)), and lag time. The temperature and inoculated NF dependency on the μ(max) of L. monocytogenes and NF were described by modified Ratkowsky's square-root model. As the initial NF level increased, the slopes of the square-root models were decreased for both L. monocytogenes and NF. The N(max) of L. monocytogenes was described as a function of temperature and inoculated NF level. Simultaneous growth prediction of L. monocytogenes and NF under constant temperature conditions was examined by using the differential equations based on the Baranyi model with the effect of interspecies competition substituted into the developed μ(max) and N(max) models. The root mean square errors between the model prediction and the observation for L. monocytogenes and NF were 0.42 and 0.34, respectively. Predictive simulation under fluctuating temperature conditions also demonstrated a high accuracy of simultaneous prediction for both L. monocytogenes and NF, representing the root mean square errors of 0.19 and 0.34, respectively. These results illustrate that the developed model permits accurate estimation of the behavior of L. monocytogenes in minced tuna under real temperature history until consumption.     

生鲜猪肉中单增李斯特菌动态生长预测与数值模拟

构建生鲜猪肉中单增李斯特菌的动态生长预测模型。猪肉样品接种由3 株单增李斯特菌制备的混合菌液,并置于3 组波动温度（1～45 ℃）条件下培养,采用一步法对获得的生长数据进行分析,构建并比较由初级模型（Baranyi或Two-compartment模型）与二级模型（Cardinal模型）集成的组合模型。结果表明,Baranyi-Cardinal和Two-compartment-Cardinal模型均适合用于描述猪肉中单增李斯特菌的生长,由两者估计的猪肉样品中单增李斯特菌最低、最适、最高生长温度分别为0.94、38.37、45.36 ℃和1.03、37.96、45.58 ℃,最适生长速率分别为0.891 h－1和0.858 h－1,最大生长浓度分别为9.07（lg（CFU/g））和9.09（lg（CFU/g））;通过另设的4 组动态生长实验和3 组等温（4、20、37 ℃）生长实验对模型进行验证,分析表明,模型可以准确预测动态及等温条件下的单增李斯特菌的生长,预测曲线的均方根误差介于0.13～0.48 （lg（CFU/g））,残差服从均值为－0.02 （lg（CFU/g））、标准差为0.29（lg（CFU/g））的正态分布。最后,基于构建的模型开展生鲜猪肉家庭冰箱冷藏过程中单增李斯特菌的生长数值模拟,以证明模型潜在的应用性。本研究结果可用于猪肉中单增李斯特菌的生长预测及风险评估。     

A MODEL FOR PREDICTING THE GROWTH OF LISTERIA MONOCYTOGENES IN PACKAGED WHOLE MILK

Experiments were conducted to determine growth characteristics of Listeria monocytogenes in sterilized whole milk at nine temperatures in the range of 277.15 to 308.15K (4 to 35C). Based on these data, the parameter values of the Baranyi dynamic growth model were statistically determined. Finite element software, ANSYS, was used to determine temperature distributions in milk cartons subject to a time‐varying ambient temperature profile. The space‐time‐temperature data were input to the Baranyi dynamic growth model, to predict the microbial population density distribution and the average population density in the milk carton. The Baranyi dynamic growth model and the finite element model were integrated and validated using experimental results from inoculated sterilized whole milk in half‐gallon laminated paper cartons. In all experiments, the milk cartons were subjected to the same temperature profile as the Baranyi dynamic growth model. Experimental microbial counts were within predicted upper and lower bounds obtained using the integrated Baranyi dynamic growth and finite element models. In addition, the growth curve at the mean value of initial physiological state parameter for L. monocytogenes underpredicted the microbial growth (standard error = 0.54 log (cfu/mL) and maximum relative difference = 15.49%).     

Development and validation of a dynamic growth model for Listeria monocytogenes in fluid whole milk

Listeria monocytogenes, a psychrotrophic microorganism, has been the cause of several food-borne illness outbreaks, including those traced back to pasteurized fluid milk and milk products. This microorganism is especially important because it can grow at storage temperatures recommended for milk (< or =7 degrees C). Growth of L. monocytogenes in fluid milk depends to a large extent on the varying temperatures it is exposed to in the postpasteurization phase, i.e., during in-plant storage, transportation, and storage at retail stores. Growth data for L. monocytogenes in sterilized whole milk were collected at 4, 6, 8, 10, 15, 20, 25, 30, and 35 degrees C. Specific growth rate and maximum population density were calculated at each temperature using these data. The data for growth rates versus temperature were fitted to the Zwietering square root model. This equation was used to develop a dynamic growth model (i.e., the Baranyi dynamic growth model or BDGM) for L. monocytogenes based on a system of equations which had an intrinsic parameter for simulating the lag phase. Results from validation of the BDGM for a rapidly fluctuating temperature profile showed that although the exponential growth phase of the culture under dynamic temperature conditions was modeled accurately, the lag phase duration was overestimated. For an alpha0 (initial physiological state parameter) value of 0.137, which corresponded to the mean temperature of 15 degrees C, the population densities were underpredicted, although the experimental data fell within the narrow band calculated for extreme values of alpha0. The maximum relative error between the experimental data and the curve based on an average alpha0 value was 10.42%, and the root mean square error was 0.28 log CFU/ml.     

Comparison of primary predictive models to study the growth of Listeria monocytogenes at low temperatures in liquid cultures and selection of fastest growing ribotypes in meat and turkey product slurries

This study compared the performance of four primary mathematical models to study the growth kinetics of Listeria monocytogenes ribotypes grown at low temperature so as to identify the best predictive model. The parameters of the best-fitting model were used to select the fastest growing strains with the shortest lag time and greatest growth rate. Nineteen food, human and animal L. monocytogenes isolates with distinct ribotype were grown at 4, 8, and 12 degrees C in tryptic soy broth and slurries prepared from cooked uncured sliced turkey breasts (with or without potassium lactate and sodium diacetate, PL/SD) and cooked cured frankfurters (with or without PL/SD). Separate regressions were performed on semi-logarithm growth curves to fit linear (based on Monod) and non-linear (Gompertz, Baranyi-Roberts, and Logistic) equations and performance of each model was evaluated using an F-test. No significant differences were found in the performance of linear and non-linear models, but the Baranyi model had the best fit for most growth curves. The maximum growth rate (MGR) of Listeria strains increased with the temperature. Similarly MGR was found significantly greater when no antimicrobials were present in the formulation of turkey or frankfurter products. The variability in lag times and MGRs in all media as determined by the Baranyi model was not consistent among strains. No single strain consistently had the fastest growth (shortest lag time, fastest MGR, or shortest time to increase 100-fold), but nine strains were identified as fastest growing strains under most growth conditions. The lack of association between serotype and fastest strain was also observed in the slurry media study. The fastest growing strains resulting from this study can be recommended for future use in L. monocytogenes challenge studies in delicatessen meat and poultry food matrices, so as to develop conservative pathogen growth predictions.     

Modeling the Growth Rate of Listeria Monocytogenes Using Absorbance Measurements and Calibration Curves

ABSTRACT:  The influence of environmental conditions (temperature and pH) on the relationship between growth data expressed by absorbance (ABS) and data transformed to cell count (CC) measurements was studied, using calibration curves for predicting Listeria monocytogenes growth rate. With this aim, 19 calibration curves at different stress conditions were performed. A shift in the calibration curves was observed for the most stringent conditions, which affected cell viability. Subsequently, a Baranyi model was fitted to ABS and CC data to obtain growth rate (GR_ABS and GR_CC) and a linear regression was performed. Absorbance was found to be a reliable technique for measuring microbial growth, as a strong relationship between GR_ABS and GR_CC (R²= 0.9717) was observed. Furthermore, 2 different response surface models were developed to link GR_ABS and GR_CC data with temperature, citric acid, and ascorbic acid. The goodness of fit of both ABS and CC models to the data was observed (RMSE = 0.0223 and 0.0221; SEP [%]= 29 and 25, respectively). Mathematical validation was carried out by calculating bias and accuracy factors, providing reasonably acceptable values for both absorbance and cell count models (B_f= 1.11 and 1.09, A_f= 1.44 and 1.41, respectively). Predictions for GR_CC were compared to data taken from Growth Predictor software at different temperatures and pH. Response surface model predictions showed that a suitable combination of preservative factors can inhibit L. monocytogenes growth. These results highlight accurate predictions of growth parameters of L. monocytogenes .     

Determination of the growth limits and kinetic behavior of Listeria monocytogenes in a sliced cooked cured meat product: validation of the predictive growth model under constant and dynamic temperature storage conditions

To describe the growth limits of Listeria monocytogenes NCTC10527 in a sliced vacuum-packaged cooked cured meat product, the binary logistic regression model was used to develop an equation to determine the probability of growth or no growth of L. monocytogenes as a function of temperature (from 0 to 10 degrees C) and water activity (from 0.88 to 0.98). Two inoculum concentrations were used (10 and 10(4) CFU g(-1)), and the growth limits for the two inocula were different. The kinetic behavior of L. monocytogenes as a function of temperature (4, 8, 12, and 16 degrees C) on the same meat product at the lower concentration (10 CFU g(-1)) was also studied. The Baranyi model appeared to fit the overall experimental data better than did the modified Gompertz and the modified logistic models. Maximum specific growth rate (micromax), lag phase duration (LPD), and maximum cell concentration (Nmax) derived from the primary model were modeled using the square root function (micromax and LPD) and a second order polynomial (Nmax) (secondary models). The selection of the best model (primary or secondary) was based on some statistical indices (the root mean square error of residuals of the model, the regression coefficient, the F test, the goodness of fit, and the bias and accuracy factor). The developed kinetic behavior model was validated under constant and dynamic temperature storage conditions. This prediction of L. monocytogenes growth provides useful information for improving meat safety and can be used for in-depth inspection of quality assurance systems in the meat industry.     

Development of a predictive model describing the growth of Yersinia enterocolitica in Camembert‐type cheese

Behaviour of Yersinia enterocolitica in mould‐ripened Camembert‐type cheese during storage at temperature range 3–15 °C was evaluated and mathematically described. The Baranyi and Gompertz models were adjusted to the results of the study to calculate the growth rate (GR) and lag time (LT) for Y. enterocolitica at each temperature. Goodness of fit was assessed by calculating the Akaike information criterion (AIC) and mean square error (MSE). Square root models were constructed which described the relations between GR, LT and applied storage temperature. The secondary models were mathematically validated based on the results generated by ComBase Predictor. Moreover, generated models were validated using external, independent data from ComBase database. Based on this, it was found that the square root models of Ratkowsky constructed on GR that were determined based on the Baranyi and Roberts model most accurately described the behaviour of Y. enterocolitica in Camembert‐type cheese during storage under refrigerated conditions.     

Prediction of pathogen growth on iceberg lettuce under real temperature history during distribution from farm to table

The growth of pathogenic bacteria Escherichia coli O157:H7, Salmonella spp., and Listeria monocytogenes on iceberg lettuce under constant and fluctuating temperatures was modelled in order to estimate the microbial safety of this vegetable during distribution from the farm to the table. Firstly, we examined pathogen growth on lettuce at constant temperatures, ranging from 5 to 25 degrees C, and then we obtained the growth kinetic parameters (lag time, maximum growth rate (micro(max)), and maximum population density (MPD)) using the Baranyi primary growth model. The parameters were similar to those predicted by the pathogen modelling program (PMP), with the exception of MPD. The MPD of each pathogen on lettuce was 2-4 log(10) CFU/g lower than that predicted by PMP. Furthermore, the MPD of pathogens decreased with decreasing temperature. The relationship between mu(max) and temperature was linear in accordance with Ratkowsky secondary model as was the relationship between the MPD and temperature. Predictions of pathogen growth under fluctuating temperature used the Baranyi primary microbial growth model along with the Ratkowsky secondary model and MPD equation. The fluctuating temperature profile used in this study was the real temperature history measured during distribution from the field at harvesting to the retail store. Overall predictions for each pathogen agreed well with observed viable counts in most cases. The bias and root mean square error (RMSE) of the prediction were small. The prediction in which mu(max) was based on PMP showed a trend of overestimation relative to prediction based on lettuce. However, the prediction concerning E. coli O157:H7 and Salmonella spp. on lettuce greatly overestimated growth in the case of a temperature history starting relatively high, such as 25 degrees C for 5 h. In contrast, the overall prediction of L. monocytogenes under the same circumstances agreed with the observed data.     

Biological implications from an autonomous version of Baranyi and Roberts growth model

An autonomous version of Baranyi and Roberts model (Int. J. Food Microbiology, 23, 1994, pp. 277-294) is developed and analyzed to reveal some subtle points, which are difficult to observe accurately from its equivalent non-autonomous form. In particular we are able to provide a meaningful interpretation to the "physiological state of the cells at inoculation", a parameter introduced by Baranyi and Roberts [Baranyi, J., Roberts, T. A., 1994. A dynamic approach to predicting bacterial growth in food. International Journal of Food Microbiology 23, 277-294] that has a profound impact on microbial growth but is not a direct measurable quantity. In addition, the analysis shows that the transient growth depends on the initial cell concentration and the initial growth rate, but is independent of "the history of the cells" and depends only indirectly (via the initial growth rate) on the previous (pre-inoculation) environment. The stationary solution is independent of the initial conditions. A new, more natural, and biologically meaningful formulation of LAG duration is being suggested in terms of initial conditions being in the neighborhood of one of the unstable stationary points revealed by this autonomous version of the model.     

Analysis of a novel class of predictive microbial growth models and application to coculture growth

In this paper, a novel class of microbial growth models is analysed. In contrast with the currently used logistic type models (e.g., the model of Baranyi and Roberts [Baranyi, J., Roberts, T.A., 1994. A dynamic approach to predicting bacterial growth in food. International Journal of Food Microbiology 23, 277–294]), the novel model class, presented in Van Impe et al. (Van Impe, J.F., Poschet, F., Geeraerd, A.H., Vereecken, K.M., 2004. Towards a novel class of predictive microbial growth models. International Journal of Food Microbiology, this issue), explicitly incorporates nutrient exhaustion and/or metabolic waste product effects inducing stationary phase behaviour. As such, these novel model types can be extended in a natural way towards microbial interactions in cocultures and microbial growth in structured foods. Two illustrative case studies of the novel model types are thoroughly analysed and compared to the widely used model of Baranyi and Roberts. In a first case study, the stationary phase is assumed to be solely resulting from toxic product inhibition and is described as a function of the pH-evolution. In the second case study, substrate exhaustion is the sole cause of the stationary phase. Finally, a more complex case study of a so-called P-model is presented, dealing with a coculture inhibition of Listeria innocua mediated by lactic acid production of Lactococcus lactis.     

Model on the microbial quality change of seasoned soybean sprouts for on-line shelf life prediction

The growth of aerobic bacteria on Korean seasoned soybean sprouts was modelled as a function of temperature to estimate microbial spoilage and shelf life on a real-time basis under dynamic storage conditions. Counts of aerobic bacteria on seasoned soybean sprouts stored at constant temperatures between 0 degrees C and 15 degrees C were recorded. The bootstrapping method was applied to generate many resampled data sets of mean microbial plate counts that were then used to estimate the parameters of the microbial growth model of Baranyi and Roberts. The distributions of the model parameters were quantified, and their temperature dependencies were expressed as mathematical functions. When the temperature functions of the parameters were incorporated into differential equations describing microbial growth, predictions of microbial growth under fluctuating temperature conditions were similar to observed microbial growth.     

Predicting Growth of Weissella Viridescens in Culture Medium under Dynamic Temperature Conditions

The lactic acid bacteria (LAB) are among the main spoilage microorganisms of foods, and the Weissella viridescens (formerly Lactobacillus viridescens) is well known to cause deterioration on the meat surface in vacuum packed meat products, even under refrigerated conditions. Therefore, this study evaluated the predictive ability of Baranyi and Roberts dynamic model to describe W. viridescens growth in culture medium (which simulates a food rich in nutrients), subjected to dynamic temperature conditions. Baranyi and Roberts primary model was fitted to the growth curves of W. viridescens in culture medium under six different isothermal temperatures (4, 8, 12, 16, 20 and 30°C) previously obtained in our laboratory. Four secondary models (linear, square root, exponential and Arrhenius type) were assessed to describe the influence of temperature on the growth parameters. The square root was the best model to describe temperature influence on μ_max parameter. For Y_max parameter, the secondary model was considered the mean values obtained experimentally in the studied temperature range. Experimental data were used to evaluate the model predictions under dynamic conditions for two different temperature profiles, NIP-1 (12-16-20-25°C) and NIP-2 (16-12-8-4°C). According to the statistical indexes, the model showed better predictive ability for NIP-1, with RMSE of 0.3341, R² of 0.9939, bias factor of 1.0046 and accuracy factor of 1.0197; the growth of W. viridescens under NIP-2 conditions was underestimated, indicating a fail dangerous prediction. The results showed that the predictive model can be used to predict the shelf life of meat products spoiled by W. viridescens.     

Structural model requirements to describe microbial inactivation during a mild heat treatment

The classical concept of D and z values, established for sterilisation processes, is unable to deal with the typical non-loglinear behaviour of survivor curves occurring during the mild heat treatment of sous vide or cook-chill food products. Structural model requirements are formulated, eliminating immediately some candidate model types. Promising modelling approaches are thoroughly analysed and, if applicable, adapted to the specific needs: two models developed by Casolari (1988), the inactivation model of Sapru et al. (1992), the model of Whiting (1993), the Baranyi and Roberts growth model (1994), the model of Chiruta et al. (1997), the model of Daughtry et al. (1997) and the model of Xiong et al. (1999). A range of experimental data of Bacillus cereus, Yersinia enterocolitica, Escherichia coli O157:H7, Listeria monocytogenes and Lactobacillus sake are used to illustrate the different models' performances. Moreover, a novel modelling approach is developed, fulfilling all formulated structural model requirements, and based on a careful analysis of literature knowledge of the shoulder and tailing phenomenon. Although a thorough insight in the occurrence of shoulders and tails is still lacking from a biochemical point of view, this newly developed model incorporates the possibility of a straightforward interpretation within this framework.     

Modeling the effect of temperature on growth of Salmonella in chicken

Growth data of Salmonella in chicken were collected at several isothermal conditions (10, 15, 20, 25, 28, 32, 35, 37, 42, and 45 degrees C) and were then fitted into primary models, namely the logistic model, modified Gompertz model and Baranyi model. Measures of goodness-of-fit such as mean square error, pseudo-R(2), -2 log likelihood, Akaike's information, and Sawa's Bayesian information criteria were used for comparison for these primary models. Based on these criteria, modified Gompertz model described growth data the best, followed by the Baranyi model, and then the logistic model. The maximum growth rates obtained from each primary model were then modeled as a function of temperature using the modified Ratkowsky model. Pseudo-R(2) values for this secondary model describing growth rate obtained from Baranyi, modified Gompertz, and logistic models were 0.999, 0.980, and 0.990, respectively. Mean square error values for corresponding models were 0.0002, 0.0008, and 0.0009, respectively. Both measures clearly show that the Baranyi model performed better than the modified Gompertz model or the logistic model.     

不同温度下椰汁中金黄色葡萄球菌的生长动力学模型比较

探讨不同温度下椰汁中金黄色葡萄球菌的生长预测模型。将菌悬液接种到椰汁中,测定不同温度(20、25、30、36℃)下的生长数据。使用Matlab软件拟合得到修正Gompertz(MGompertz)、修正Logistic(MLloistic)和Baranyi模型,比较残差和拟合度选择最优一级模型,并拟合出生长参数。用平方根和二次多项式方程建立二级模型,通过相关系数、偏差因子和准确因子对二级模型进行检验。在20~36℃下,Baranyi模型拟合出的各个拟合度最优,Baranyi模型适宜作为模拟金黄色葡萄球菌在椰汁中生长的一级预测模型。二次多项式相较于平方根模型可以更好地表达温度与最大比生长速率及延滞期的关系。因此选择Baranyi模型和二次多项式模型描述不同温度下椰汁中金黄色葡萄球菌的生长。     

Dynamic model for predicting growth of Salmonella spp. in ground sterile pork

A predictive model for Salmonella spp. growth in ground pork was developed and validated using kinetic growth data. Salmonella spp. kinetic growth data in ground pork were collected at several isothermal conditions (between 10 and 45 °C) and Baranyi model was fitted to describe the growth at each temperature, separately. The maximum growth rates (μ_max) estimated from the Baranyi model were modeled as a function of temperature using a modified Ratkowsky equation. To estimate bacterial growth under dynamic temperature conditions, the differential form of the Baranyi model, in combination with the modified Ratkowsky equation for rate constants, was solved numerically using fourth order Runge-Kutta method. The dynamic model was validated using five different dynamic temperature profiles (linear cooling, exponential cooling, linear heating, exponential heating, and sinusoidal). Performance measures, root mean squared error, accuracy factor, and bias factor were used to evaluate the model performance, and were observed to be satisfactory. The dynamic model can estimate the growth of Salmonella spp. in pork within a 0.5 log accuracy under both linear and exponential cooling profiles, although the model may overestimate or underestimate at some data points, which were generally < 1 log. Under sinusoidal temperature profiles, the estimates from the dynamic model were also within 0.5 log of the observed values. However, underestimation could occur if the bacteria were exposed to temperatures below the minimum growth temperature of Salmonella spp., since low temperature conditions could alter the cell physiology. To obtain an accurate estimate of Salmonella spp. growth using the models reported in this work, it is suggested that the models be used at temperatures above 7 °C, the minimum growth temperature for Salmonella spp. in pork.     

PREDICTIVE MODELING AND VALIDATION OF GROWTH AT DIFFERENT TEMPERATURES OF BROCHOTHRIX THERMOSPHACTA

The growth of Brochothrix thermosphacta affect by temperatures (0, 2, 5, 7 and 10C) were studied in laboratory medium. Growth curves were fitted using logistic, Gompertz and Baranyi models. Statistical characteristics like r ², mean square error, bias factor and accuracy factor were using for comparison of these models. Based on the criteria, the Gompertz described the data best, Baranyi performed the predicting best. The maximum growth rates obtained from primary model were then modeled as a function of temperature using the square root model. Statistically for the secondary model, the bias and accuracy factors are 0.9978, 0.9943 and 0.9712, and 1.0513, 1.0639 and 1.2225 for logistic, Gompertz and Baranyi, respectively, which may indicate that Baranyi model fitted and performed best of the others. The 95% confidence limits for a new prediction were estimated for each validation temperatures condition using a SPSS procedure.

PRACTICAL APPLICATIONS

Brochothrix thermosphacta was isolated from chilled pork used for growth modeling in broth (tryptone soya broth) at pH 7 and NaCl 0.5% (w/w), at various temperatures. Data obtained from experiments were then fitted by three types of primary models, to estimate the maximum growth rate. A secondary model was created, describing how the maximum growth rate responds to the temperatures. The goodness-of-fit and statistical characteristics of the equations were tested.