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.     

Mathematical Modeling of Lactobacillus Viridescens Growth in Vacuum Packed Sliced Ham under non Isothermal Conditions

Lactic acid bacteria (LAB) are responsible for the spoilage of vacuum packed meat products, as ham. Temperature is the main factor affecting the microbial dynamics and its variation during the production, distribution and storage of foods is considerable. Thus, the use of mathematical models to describe the microbial behavior under variable temperatures can be very useful in predicting the food shelf life. This study evaluated the growth of Lactobacillus viridescens in sliced ham under non isothermal conditions, and assessed the predictive ability of the Baranyi and Roberts model using parameters obtained isothermally in culture medium (MRS). To obtain the BAL growth, the fresh ham piece was sterilized, sliced, inoculated with bacteria and stored in a temperature-controlled incubator. For the establishment of the secondary models, the primary model parameters were obtained isothermally in the culture medium at 4, 8, 12, 16, 20 and 30° C, in which there was no lag phase observed; the square root model was selected to describe the dependence of the μ_max parameter (maximum specific growth rate) with the temperature, and the y_max parameter (maximum population) was represented by an average because there was no significant influence of the temperature. The mathematical models were validated with L. viridescens growth data in ham under five variable temperature conditions (NI-1 (4-8-12-16°C), NI-2 (12-16-20-25°C), NI-3 (25-20-16-12-8-4°C), NI-4 (16-12-8-4°C) and NI-5 (12-8-4-8-12°C)), and its predictive ability were assessed through statistical indexes (bias factor, accuracy factor and RMSE), with good results (bias factor between 0.9450 and 1.0326; accuracy factor between 1.0382 and 1.0682, and RMSE between 0.7641 and 1.3317), especially in increasing temperature, where the prediction was safe. The validated model can be used to estimate the shelf life of a commercial ham under different temperature conditions.     

Influence of different storage conditions on production of trimethylamine and microbial spoilage characteristics of mackerel products

Gradual accumulation of the fishy-odor compound trimethylamine (TMA) from bacterial reduction of trimethylamine oxide (TMAO) is one of the characteristic chemical changes attributed to fish spoilage. Changes in TMA values were correlated with sensory testing results, storage temperature, storage time, and viable bacteria counts. TMA contents were determined under different storage conditions. Headspace solid-phase micro extraction analysis with gas chromatography using flame ionization detection was used with different storage times and temperatures. Mackerel samples were inoculated with Pseudomonas fragi to monitor changes in the TMA content and pH. The TMA content increased proportionally with time during storage, and pH values and the microbiological quality were evaluated to analyze correlations with the TMA content in fish products. The TMA content increased with an increasing number of P. fragi with good linearity (R ²=0.997). Basic data are provided for developing a freshness indicator for fish spoilage.     

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.     

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.     

Estimation of the Temperature Dependent Growth Parameters of Lactobacillus Viridescens in Culture Medium with Two-step Modelling and Optimal Experimental Design Approaches

In predictive microbiology, the model parameters has been estimated using the traditional two-step modeling approach (TS), in which primary models are fitted to the microbial growth data and secondary models represent the dependence of model parameters with environmental variables. The optimal experimental design approach (OED) has been used as an alternative to TS, mainly because the improvement of model identifiability and reduction of the experimental workload and costs. The fitting of mathematical model to experimental data in TS is sequential, whereas in OED is simultaneous. Lactobacillus viridescens is a lactic acid bacteria that is of great interest to the meat products preservation. The objective of this study was to estimate the growth parameters of L. viridescens in culture medium with TS and OED. For TS, the experimental data were obtained in six temperatures; for OED, the data were obtained in four optimal non-isothermal experiments, two experiments with increasing temperatures (ITOED) and two with decreasing temperatures (DTOED). The Baranyi and Roberts, and the Square Root models were used to describe the microbial growth, in which the b and T_min parameters (± 95% confidence intervals) were estimated from the experimental data. The parameters obtained for TS were b = 0.0290 (±0.0020) h^-0.5°C^-1 and T_min = -1.33 (±1.26) °C, with R² = 0.991; for ITOED were b = 0.0314 (±0.0019) h^-0.5°C^-1 and T_min = 0.12 (±0.71) °C, with R² = 0.995; for DTOED were b = 0.0295 (±0.0019) h^-0.5°C^-1 and T_min = -1.57 (±1.05) °C, with R² = 0.999. The parameters obtained in the OED approach presented smaller confidence intervals, higher R² and less experimental time than the parameters obtained in the traditional TS approach. In this way, it is possible to answer positively that OED approach is feasible and could be widely applied in predictive microbiology.     

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%).     

Predictive Modeling of the Growth of Lactobacillus Viridescens under Non-isothermal Conditions

Food spoilage by microorganisms is a major problem that can generate large economic losses to industries, making critical the application of technologies for predicting shelf life, aiming to obtain products with higher quality. The Lactic Acid Bacteria (LAB), including Lactobacillus viridescens, are among the main groups of microorganisms responsible for spoilage of refrigerated meat products, vacuum packed and under modified atmosphere. The growth of the LAB can be predicted by mathematical models, which describe the influence of various environmental factors (such as non-isothermal conditions) on microbial growth. The objective of this study was to obtain a mathematical model able to predict the growth of L. viridescens in non-isothermal conditions in culture medium (MRS broth). Six isothermal growth curves (at 4, 8, 12, 16, 20 and 30̊C) were described by Baranyi and Roberts model and the dependence of maximum specific growth rate (μ_max) parameter on the temperature was described by square root secondary model. The model was validated using L. viridescens experimental data in the temperature ranging from 6 to 10°C and 5 to 11°C, changing every 12 and 24h, respectively. The results showed that it was possible to predict safely (bias factor greater than 1) the growth of L. viridescens in MRS broth under non-isothermal conditions. The observed prediction deviations may have been caused by abrupt temperature changes, generating intermediate adaptation phases.     

Modelling the effect of environmental factors on the growth of Aspergillus parasiticus and mycotoxin production in paddy during storage

The simulated experiment of A. parasiticus isolated from the paddy was carried out during the paddy storage for 20 days. The growth and mycotoxin data were collected for constructing kinetic and probability models of moulds. The Baranyi and Gompertz model was employed as the primary model and estimated the lag phase and maximum specific growth rate. Secondary models, such as polynomial, Davey and Gibson model were used and completely evaluated under different conditions. The polynomial equation was highly rated compared with Gibson and Davey model and gave realistic temperatures and a_w for mould growth. Logistic model showed promising results on the prediction of growth boundary and AFB₁ production. Employed models showed promising predicted results, indicating that it is an effective tool for describing and predicting the growth of moulds under different temperatures and a_w. The results can be applied to develop the optimal strategy to prevent fungal spoilage and aflatoxin production during paddy storage.     

Towards a novel class of predictive microbial growth models

Food safety and quality are influenced by the presence (and possible proliferation) of pathogenic and spoilage microorganisms during the life cycle of the product (i.e., from the raw ingredients at the start of the production process until the moment of consumption). In order to simulate and predict microbial evolution in foods, mathematical models are developed in the field of predictive microbiology. In general, microbial growth is a self-limiting process, principally due to either (i) the exhaustion of one of the essential nutrients, and/or (ii) the accumulation of toxic products that inhibit growth. Nowadays, most mathematical models used in predictive microbiology do not explicitly incorporate this basic microbial knowledge. In this paper, a novel class of microbial growth models is proposed. 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 explicitly incorporates nutrient exhaustion and/or metabolic waste product effects. As such, this novel model prototype constitutes an elementary building block to be extended in a natural way towards, e.g., microbial interactions in co-cultures (mediated by metabolic products) and microbial growth in structured foods (influenced by, e.g., local substrate concentrations). While under certain conditions the mathematical equivalence with classical logistic type models is clear and results in equal fitting capacities and parameter estimation quality (see Poschet et al. [Poschet, F., Vereecken, K.M., Geeraerd, A.H., Nicolaï, B.M., Van Impe, J.F., 2004. Analysis of a novel class of predictive microbial growth models and application to co-culture growth. International Journal of Food Microbiology, this issue] for a more elaborated analysis in this respect), the biological interpretability and extendability represent the main added value.     

A kinetic model and endpoints method for volatiles formation in stored fresh fish

Based on experimental data reported by Koutsoumanis and Nychas (2000), the rise in the trimethylamine (TMA) and total volatile basic nitrogen (TVBN) concentrations during fish fillets isothermal storage is described by a power-law model. This model has a fixed exponent (m ~ 2), and a temperature-dependent coefficient that follows the two-parameters exponential model, a substitute for the Arrhenius equation. The model's two adjustable parameters were calculated by the endpoints method, i.e., from a pair of final concentrations determined at the end of storage at two temperatures, with an interactive program posted as freeware on the Internet. Their values were then used to reconstruct the entire formation curves at the two temperatures and predict the curves at two other temperatures that were not used in their calculation. A dynamic version of the model was also developed, based on the assumption that the momentary volatiles formation rate is the rate at the momentary temperature at the time which corresponds to their momentary concentration. It was tested for consistency and used to simulate volatiles formation patterns under rising and fluctuating temperatures.     

Modeling survival of high hydrostatic pressure treated stationary- and exponential-phase Listeria innocua cells

High Hydrostatic Pressure (HHP) inactivation (325–400 MPa; 0–20 min; maximum temperature 30 °C) of cells of Listeria innocua CECT 910 was studied in two different growth phases (exponential and stationary), and the corresponding survival curves were obtained for each case. The curves were fitted to two nonlinear models, the modified Gompertz equation and the Baranyi model. The kinetic constants calculated for both models, µ_max and k_max, indicated that cells in exponential growth phase were more sensitive to pressure than those in stationary phase. Both mathematical models were suitable for describing L. innocua HHP survival curves, rendering kinetic constants that increased with increasing pressure. When considering the experimental models validation, both Gompertz and Baranyi predicted in a similar way, however Baranyi had slightly lower A_f (Accuracy factor) and B_f (Bias factor) values, which indicated better prediction values. In summary, both mathematical models were perfectly valid for describing L. innocua inactivation kinetics under HHP treatment.Industrial relevanceThe mathematical models for inactivation and growth of microorganisms are the foundation of predictive microbiology and are used in risk assessments procedures as part of the food safety management system. Besides, these models together with those applied to inactivation of enzymes and destruction of quality factors are essential to optimize processes and thus to lay the foundations for industrial processing. It is therefore necessary to identify generally applicable kinetic models that will produce primary and secondary kinetic parameters and are statistically reliable as a key tool to predict the behaviour of microorganisms, enzymes and quality factors after processing.     

When is simple good enough: a comparison of the Gompertz,Baranyi, and three-phase linear models for fitting bacterial growth curves

The use of primary mathematical models with curve fitting software is dramatically changing quantitative food microbiology. The two most widely used primary growth models are the Baranyi and Gompertz models. A three-phase linear model was developed to determine how well growth curves could be described using a simpler model. The model divides bacterial growth curves into three phases: the lag and stationary phases where the specific growth rate is zero (gm=0), and the exponential phase where the logarithm of the bacterial population increases linearly with time (gm=constant). The model has four parameters: N_o(Log₈of initial population density), NMAX(Log₈of final population density), tLAG(time when lag phase ends), and tMAX(time when exponential phase ends). A comparison of the linear model was made against the Baranyi and Gompertz models, using established growth data forEscherichia coli0157:H7. The growth curves predicted by the three models showed good agreement. The linear model was more ‘robust' than the others, especially when experimental data were minimal. The physiological assumptions underlying the linear model are discussed, with particular emphasis on assuring that the model is consistent with bacterial behavior both as individual cells and as populations. It is proposed that the transitional behavior of bacteria at the end of the lag phase can be explained on the basis of biological variability.     

Predictive modelling of the microbial lag phase: a review

This paper summarises recent trends in predictive modelling of microbial lag phenomena. The lag phase is approached from both a qualitative and a quantitative point of view. First, a definition of lag and an analysis of the prevailing measuring techniques for the determination of lag time is presented. Furthermore, based on experimental results presented in literature, factors influencing the lag phase are discussed. Major modelling approaches concerning lag phase estimation are critically assessed. In predictive microbiology, a two-step modelling approach is used. Primary models describe the evolution of microbial numbers with time and can be subdivided into deterministic and stochastic models. Primary deterministic models, e.g., Baranyi and Roberts [Int. J. Food Microbiol. 23 (1994) 277], Hills and Wright [J. Theor. Biol. 168 (1994) 31] and McKellar [Int. J. Food Microbiol. 36 (1997) 179], describe the evolution of microorganisms, using one single (deterministic) set of model parameters. In stochastic models, e.g., Buchanan et al. [Food Microbiol. 14 (1997) 313], Baranyi [J. Theor. Biol. 192 (1998) 403] and McKellar [J. Appl. Microbiol. 90 (2001) 407], the model parameters are distributed or random variables. Secondary models describe the relation between primary model parameters and influencing factors (e.g., environmental conditions). This survey mainly focuses on the influence of temperature and culture history on the lag phase during growth of bacteria.     

Rapid freshness evaluation of cow milk at different storage temperatures using in situ electrical conductivity measurement

The present study investigated the efficacy of in situ electrical conductivity measurement was evaluated to estimate the freshness of cow milk. Accordingly, the same for the refrigerated milk (5 °C) gradually increased from 0.505 to 0.610 S/m during 42 days, whereas that for the milk stored at room temperature (20 °C) promptly increased from 0.708 to 1.195 S/m during 30 days. In the empirical model, the electrical conductivity freshness index (EF_i) presented a good correlation between pH and microbial growth with the freshness parameters. In the pH analysis, the EF_i could predict the pH decline in spoiled milk with a non-linear curve. Likewise, the growth of total aerobic bacteria (TAB) at 20 °C exhibited a good correlation with EF_i (ß₂ coefficient and R² values of 9.330 and of 0.977, respectively). This study thus demonstrated the practical application of in situ electrical conductivity measurement for rapid prediction of milk freshness during storage.Industrial relevance textIn the cold change system of milk, rapid assessment of freshness has its significance for food safety. Conventional evaluation of milk freshness required the analytical equipment, trained technician, labor, and time. Electrical conductivity measurement could represent the freshness of foods associated with pH changes and microbial growth. This study proposed the potential of electrical conductivity measurement for rapid assessment of milk freshness.     

Mathematical modelling for predicting the growth of Pseudomonas spp. in poultry under variable temperature conditions

A dynamic growth model under variable temperature conditions was implemented and calibrated using raw data for microbial growth of Pseudomonas spp. in poultry under aerobic conditions. The primary model was implemented using measurement data under a set of fixed temperatures. The two primary models used for predicting the growth under constant temperature conditions were: Baranyi and modified Gompertz. For the Baranyi model the maximum specific growth rate and the lag phase at constant environmental conditions are expressed in exact form and it has been shown that in limit case when maximal cells concentration is much higher than the initial concentration the maximum specific growth rate is approximately equal to the specific growth rate. The model parameters are determined in a temperature range of 2-20 degrees C. As a secondary model the square root model was used for maximum specific growth rate in both models. In both models the main assumption, that the initial physiological state of the inoculum is constant and independent of the environmental parameters, is used, and a free parameter was implemented which was determined by minimizing the mean square error (MSE) relative to the measurement data. Two temperature profiles were used for calibration of the models on the initial conditions of the cells.     

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.     

Establishment of kinetic models based on electrical conductivity and freshness indictors for the forecasting of crucian carp (Carassius carassius) freshness

To study quality changes in cold chain circulation, kinetic models were developed to predict the freshness of crucian carp at different temperatures during storage. Electrical conductivity (EC) and freshness indictors (Total volatile basic nitrogen, Total aerobic count and K-value) at 270, 273, 277, 282 and 288 K were accessed to investigate the relation between the crucian carp’s freshness and storage condition (storage temperature and storage time). The kinetic models were developed based on Arrhenius equation. Activation energies (E_A) of EC and Total aerobic count (TAC) are 97.75 and 105.93 kJ mol⁻¹, and corresponding rate constants (k₀) are 5.25 × 10¹⁶ and 5.70 × 10¹⁸, respectively. Relative errors between predicted and values of EC are all within ±5%. The kinetic model established through EC can accurately describe the changes of crucian carp’s quality during the storage within 270-288 K. The kinetic model established based on TAC can accurately forecast crucian carp’s early freshness.     

Quantitative assessment of the shelf life of ozonated apple juice

Sterile apple juice inoculated with S. cerevisiae ATCC 9763 (10³ CFU/mL) was processed in a bubble column with gaseous ozone of flow rate of 0.12 L/min and concentration of 33–40 μg/mL for 8 min. The growth kinetics of S. cerevisiae as an indicator of juice spoilage was monitored at 4, 8, 12 and 16 °C for up to 30 days. The kinetics was quantitatively described by the primary model of Baranyi and Roberts, and the maximum specific growth rate was further modeled as a function of temperature by the Ratkowsky type model. The developed model was successfully validated for the microbial growth of control and ozonated samples during dynamic storage temperature of periodic changes from 4 to 16 °C. Two more characteristic parameters were also evaluated, the time of spoilage of the product under static temperature conditions and the temperature quotient, Q ₁₀. At lower static storage temperature (4 °C), no spoilage occurred either for unprocessed or ozone-processed apple juice. In the case of ozone-processed apple juice, the shelf life was increased when compared with the controls, and the Q ₁₀ was found to be 7.17, which appear much higher than that of the controls, indicating the effectiveness of ozonation for the extension of shelf life of apple juice.