Estimation of the non-isothermal inactivation patterns of Bacillus sporothermodurans IC4 spores in soups from their isothermal survival data

3-D stochastic modeling approach in thermal inactivation: estimation of thermal survival kinetics of Escherichia coli O157:H7 in a hamburger after exposure to desiccation stress

Desiccation tolerance of pathogenic bacteria is one strategy for survival in harsh environments, which has been studied extensively. However, the subsequent survival behavior of desiccation-stressed bacterial pathogens has not been clarified in detail. Herein, we demonstrated that the effect of desiccation stress on the thermotolerance of Escherichia coli O157:H7 in ground beef was limited, and its thermotolerance did not increase. E. coli O157:H7 was inoculated into a ground beef hamburger after exposure to desiccation stress. We combined a bacterial inactivation model with a heat transfer model to predict the survival kinetics of desiccation-stressed E. coli O157:H7 in a hamburger. The survival models were developed using the Weibull model for two-dimensional pouched thin beef patties (ca. 1 mm), ignoring the temperature gradient in the sample, and a three-dimensional thick beef patty (ca. 10 mm), considering the temperature gradient in the sample. The two-dimensional (2-D) and three-dimensional (3-D) models were subjected to stochastic variations of the estimated Weibull parameters obtained from 1,000 replicated bootstrapping based on isothermal experimental observations as uncertainties. Furthermore, the 3-D model incorporated temperature gradients in the sample calculated using the finite element method. The accuracies of both models were validated via experimental observations under non-isothermal conditions using 100 predictive simulations. The root mean squared errors in the log survival ratio of the 2-D and 3-D models for 100 simulations were 0.25-0.53 and 0.32-2.08, respectively, regardless of the desiccation stress duration (24 or 72 h). The developed approach will be useful for setting appropriate process control measures and quantitatively assessing food safety levels.IMPORTANCEAcquisition of desiccation stress tolerance in bacterial pathogens might increase thermotolerance as well and increase the risk of foodborne illnesses. If a desiccation-stressed pathogen enters a kneaded food product via cross-contamination from a food-contact surface and/or utensils, proper estimation of the internal temperature changes in the kneaded food during thermal processing is indispensable for predicting the survival kinetics of desiccation-stressed bacterial cells. Various survival kinetics prediction models that consider the uncertainty or variability of pathogenic bacteria during thermal processing have been developed. Furthermore, heat transfer processes in solid food can be estimated using finite element method software. The present study demonstrated that combining a heat transfer model with a bacterial inactivation model can predict the survival kinetics of desiccation-stressed bacteria in a ground meat sample, corresponding to the temperature gradient in a solid sample during thermal processing. Combining both modeling procedures would enable the estimation of appropriate bacterial survival kinetics in solid food.

Effect of water activity on inactivation of Listeria monocytogenes using gaseous chlorine dioxide - A kinetic analysis

The aim of this study was to investigate the effect of water activity (a_w) on inactivation of Listeria monocytogenes using gaseous chlorine dioxide (ClO_{2 (g)}) under room temperature. Surface-inoculated tryptic soy agar (TSA) plates adjusted to 9 different water activity levels ranging from 0.994 to 0.429 were used as samples exposed to ClO_{2 (g)} at 150, 250, and 350 ppm for different durations of treatment time. Results showed that the antimicrobial effect of ClO_{2 (g)} significantly decreases as the a_w level and ClO_{2 (g)} concentration decrease. Nonlinear models, such as the modified Chick model and the Weibull model, were used to describe the inactivation kinetics of L. monocytogenes. The results showed that the modified Chick model, which is based on chemical reaction kinetics, was more suitable to describe the inactivation of L. monocytogenes (RMSE < 0.5 log CFU/g) than the Weibull model (RMSE < 1.0 log CFU/g). A multiple regression model was developed for the describing the effect of a_w and ClO_{2 (g)} concentration on bacterial inactivation. The results of this study may be used to design ClO_{2 (g)} treatment processes to inactivate L. monocytogenes in low-moisture foods.

Microbiological and process variability using biological indicators of inactivation (BIIs) based on Bacillus cereus spores of food and fish-based animal by-products to evaluate microwave heating in a pilot plant

Microwave processing can be a valid alternative to conventional heating for different types of products. It enables a more efficient heat transfer in the food matrix, resulting in higher quality products. However, for many food products a uniform temperature distribution is not possible because of heterogeneities in their physical properties and non-uniformtiy in the electric field pattern. Hence, the effectiveness of microwave inactivation treatments is influenced by both intrinsic (differences between cells) and extrinsic variability (non-uniform temperature). Interpreting the results of the process and considering its impact on microbial inactivation is essential to ensure effective and efficient processing. In this work, we quantified the variability in microbial inactivation attained in a microwave pasteurization treatment with a tunnel configuration at pilot-plant scale. The configuration of the equipment makes it impossible to measure the product temperature during treatment. For that reason, variability in microbial counts was measured using Biological Inactivation Indicators (BIIs) based on spherical particles of alginate inoculated with spores of Bacillus spp. The stability of the BIIs and the uncertainty associated to them was assessed using preliminary experiments in a thermoresistometer. Then, they were introduced in the food product to analyse the microbial inactivation in different points of the products during the microwave treatment. Experiments were made in a vegetable soup and a fish-based animal by-product (F-BP). The results show that the variation in the microbial counts was higher than expected based on the biological variability estimated in the thermoresistometer and the uncertainty of the BIIs. This is due to heterogeneities in the temperature field (measured using a thermographic camera), which were higher in the F-BP than in the vegetable soup. Therefore, for the process studied, extrinsic variability was more relevant than intrinsic variability. The methodology presented in this work can be a valid method to evaluate pasteurization treatments of foods processed by heating, providing valuable information of the microbial inactivation achieved. It can contribute to design microwave processes for different types of products and for product optimization.

Holistic Approach to the Uncertainty in Shelf Life Prediction of Frozen Foods at Dynamic Cold Chain Conditions

Systematic kinetic modeling is required to predict frozen systems behavior in cold dynamic conditions. A one-step procedure, where all data are used simultaneously in a non-linear algorithm, is implemented to estimate the kinetic parameters of both primary and secondary models. Compared to the traditional two-step methodology, more precise estimates are obtained, and the calculated parameter uncertainty can be introduced in realistic shelf life predictions, as a tool for cold chain optimization. Additionally, significant variability of the real distribution/storage conditions is recorded, and must be also incorporated in a kinetic prediction scheme. The applicability of the approach is theoretically demonstrated in an analysis of data on frozen green peas Vitamin C content, for the calculation of joint confidence intervals of kinetic parameters. A stochastic algorithm is implemented, through a double Monte Carlo scheme incorporating the temperature variability during distribution, drawn from cold chain databases. Assuming a distribution scenario of 130 days in the cold chain, 93 ± 110 days remaining shelf life was predicted compared to 180 days assumed based on the use by date. Overall, through the theoretical case study investigated, the uncertainty of models’ parameters and cold chain dynamics were incorporated into shelf life assessment, leading to more realistic predictions.

On the use of in-silico simulations to support experimental design: A case study in microbial inactivation of foods

The mathematical models used in predictive microbiology contain parameters that must be estimated based on experimental data. Due to experimental uncertainty and variability, they cannot be known exactly and must be reported with a measure of uncertainty (usually a standard deviation). In order to increase precision (i.e. reduce the standard deviation), it is usual to add extra sampling points. However, recent studies have shown that precision can also be increased without adding extra sampling points by using Optimal Experiment Design, which applies optimization and information theory to identify the most informative experiment under a set of constraints. Nevertheless, to date, there has been scarce contributions to know a priori whether an experimental design is likely to provide the desired precision in the parameter estimates. In this article, two complementary methodologies to predict the parameter precision for a given experimental design are proposed. Both approaches are based on in silico simulations, so they can be performed before any experimental work. The first one applies Monte Carlo simulations to estimate the standard deviation of the model parameters, whereas the second one applies the properties of the Fisher Information Matrix to estimate the volume of the confidence ellipsoids. The application of these methods to a case study of dynamic microbial inactivation, showing how they can be used to compare experimental designs and assess their precision, is illustrated. The results show that, as expected, the optimal experimental design is more accurate than the uniform design with the same number of data points. Furthermore, it is demonstrated that, for some heating profiles, the uniform design does not ensure that a higher number of sampling points increases precision. Therefore, optimal experimental designs are highly recommended in predictive microbiology.

Mathematical modelling of the stress resistance induced in Listeria monocytogenes during dynamic, mild heat treatments

Modelling of stress acclimation induced by thermal inactivation of Listeria monocytogenes under dynamic conditions is analyzed in this work. A mathematical model that separates the effect of the instantaneous temperature from the one of stress acclimation, was used. The model was trained using isothermal inactivation experiments, and one biphasic dynamic treatment with a heating rate of 1 °C/min and a holding phase of 60 °C. These experiments were performed in laboratory media (Tryptic Soy Broth; TSB). The model parameters estimated through these experiments (D₅₅=12.87±0.82min, z=4.58±0.04°C, a=0.11±0.01min^-1, E=0.50±0.01°C and c=1.23±0.03) were successfully used to predict the microbial inactivation for another seven inactivation profiles, with and without a holding phase. Moreover, similar experiments were performed using milk as heating media, obtaining a good agreement between the model predictions and the empirical observations. The results of this study are compatible with the hypothesis that L. monocytogenes is able to develop a physiological response during dynamic treatments that increases its thermal resistance. Also, that the model used can be used to predict microbial inactivation of this microorganism taking into consideration stress acclimation.

Predicting heat process efficiency in thermal processes when bacterial inactivation is not log-linear

The food industry widely uses the F-value which considers microbial log-linear inactivation, while microbial heat inactivation may result in a non-log-linear inactivation pattern due to genetic or phenotypical heterogeneity. This may yield discrepancies in predicting microbial heat inactivation under dynamic conditions of heat treatment. In this paper, we suggest the calculation of the equivalent time of heat treatment at a given temperature to overcome these constraints. To validate our proposal, the heat inactivation of Bacillus pumilus, showing non-log-linear behavior, was predicted for 4 different heat inactivation profiles and bacterial enumeration was performed to determine whether prediction errors were acceptable. When the proportion of residuals in an acceptable zone from 1 log (fail safe) to 0.5 log (fail dangerous) was greater or equal to 70%, the model was considered as acceptable for predictions of the tested data. The new approach gave four different temperature profiles, with 96, 85, 85 and 100% of the residuals in the acceptable zone, indicating satisfactory prediction. Thus the proposed practical alternative to simulate microbial heat inactivation kinetics is able to extend the F-value to non-log-linear inactivation patterns.

Development of antimicrobial active packaging materials based on gluten proteins

BACKGROUND

The incorporation of natural biocide agents into protein-based bioplastics, a source of biodegradable polymeric materials, manufactured by a thermo-mechanical method is a way to contribute to a sustainable food packaging industry. This study assesses the antimicrobial activity of 10 different biocides incorporated into wheat gluten-based bioplastics. The effect that formulation, processing, and further thermal treatments exert on the thermo-mechanical properties, water absorption characteristics and rheological behaviour of these materials is also studied.

RESULTS

Bioplastics containing six of the 10 examined bioactive agents have demonstrated suitable antimicrobial activity at 37 °C after their incorporation into the bioplastic. Moreover, the essential oils are able to create an antimicrobial atmosphere within a Petri dish.

CONCLUSION

Depending on the selected biocide, its addition may alter the bioplastics protein network in a different extent, which leads to materials exhibiting less water uptake and different rheological and thermo-mechanical behaviours. © 2015 Society of Chemical Industry.

Ultra high pressure homogenization (UHPH) inactivation of Bacillus amyloliquefaciens spores in phosphate buffered saline (PBS) and milk

Ultra high pressure homogenization (UHPH) opens up new areas for dynamic high pressure assisted thermal sterilization of liquids. Bacillus amyloliquefaciens spores are resistant to high isostatic pressure and temperature and were suggested as potential surrogate for high pressure thermal sterilization validation. B. amyloliquefaciens spores suspended in PBS buffer (0.01 M, pH 7.0), low fat milk (1.5%, pH 6.7), and whole milk (3.5%, pH 6.7) at initial concentration of ~10⁶ CFU/mL were subjected to UHPH treatments at 200, 300, and 350 MPa with an inlet temperature at ~80°C. Thermal inactivation kinetics of B. amyloliquefaciens spores in PBS and milk were assessed with thin wall glass capillaries and modeled using first-order and Weibull models. The residence time during UHPH treatments was estimated to determine the contribution of temperature to spore inactivation by UHPH. No sublethal injury was detected after UHPH treatments using sodium chloride as selective component in the nutrient agar medium. The inactivation profiles of spores in PBS buffer and milk were compared and fat provided no clear protective effect for spores against treatments. Treatment at 200 MPa with valve temperatures lower than 125°C caused no reduction of spores. A reduction of 3.5 log₁₀CFU/mL of B. amyloliquefaciens spores was achieved by treatment at 350 MPa with a valve temperature higher than 150°C. The modeled thermal inactivation and observed inactivation during UHPH treatments suggest that temperature could be the main lethal effect driving inactivation.

Effect of heating rate on highly heat-resistant spore-forming microorganisms

Highly heat-resistant spore-forming Bacillus cause nonsterility problems in canned food and reduce the shelf life of many processed foods. The aim of this research was to evaluate the thermal inactivation of Bacillus sporothermodurans IIC65, Bacillus subtilis IC9, and Geobacillus stearothermophilus T26 under isothermal and nonisothermal conditions. The data obtained showed that B. sporothermodurans and B. subtilis were more heat resistant than G. stearothermophilus. The survival curves of B. sporothermodurans and B. subtilis showed shoulders, while the survival curves of G. stearothermophilus showed tails. Under nonisothermal treatment, at heating rates of 1 and 20 ℃/min, time needed to completely inactivate G. stearothermophilus was shorter than that required for B. sporothermodurans and B. subtilis. In complex heat treatments (heating-holding-cooling), the survival curves of B. sporothermodurans and B. subtilis showed the same activation shoulders than those obtained under isothermal treatments and the activation shoulders were again absent in the case of G. stearothermophilus. Predictions fitted quite well the data obtained for B. sporothermodurans. In contrast, the data for B. subtilis showed half a log cycle more survival than expected and in the case of G. stearothermophilus, the survival curve obtained showed much higher inactivation than expected.

Dynamic model of heat inactivation kinetics for bacterial adaptation

The Weibullian-log logistic (WeLL) inactivation model was modified to account for heat adaptation by introducing a logistic adaptation factor, which rendered its "rate parameter" a function of both temperature and heating rate. The resulting model is consistent with the observation that adaptation is primarily noticeable in slow heat processes in which the cells are exposed to sublethal temperatures for a sufficiently long time. Dynamic survival patterns generated with the proposed model were in general agreement with those of Escherichia coli and Listeria monocytogenes as reported in the literature. Although the modified model's rate equation has a cumbersome appearance, especially for thermal processes having a variable heating rate, it can be solved numerically with commercial mathematical software. The dynamic model has five survival/adaptation parameters whose determination will require a large experimental database. However, with assumed or estimated parameter values, the model can simulate survival patterns of adapting pathogens in cooked foods that can be used in risk assessment and the establishment of safe preparation conditions.

Estimating the heat resistance parameters of bacterial spores from their survival ratios at the end of UHT and other heat treatments

Accurate determination of bacterial cells or the isothermal survival curves of spores at Ultra High Temperatures (UHT) is hindered by the difficulty in withdrawing samples during the short process and the significant role that the come up and cooling times might play. The problem would be avoided if the survival parameters could be derived directly from the final survival ratios of the non-isothermal treatments but with known temperature profiles. Non-linear inactivation can be described by models that have at least three survival parameters. In the simplified version of the Weibullian -log logistic model they are n, representing the curvature of the isothermal semilogarithmic survival curves, T(c), a marker of the temperature where the inactivation accelerates and k, the slope of the rate parameter at temperatures well above T(c). In principle, these three unknown parameters can be calculated by solving, simultaneously, three rate equations constructed for three different temperature profiles that have produced three corresponding final survival ratios, which are determined experimentally. Since the three equations are constructed from the numerical solutions of three differential equations, this might not always be a practical option. However, the solution would be greatly facilitated if the problem could be reduced to the solution of only two simultaneous equations. This can be done by progressively changing the value of n by small increments or decrements and solving for k and T(c). The iterations continue until the model constructed with the calculated k and T(c) values correctly predicts the survival ratio obtained in a third heat treatment with a known temperature profile. Once n, k, and T(c) are established in this way, the resulting model can be used to predict the complete survival curves of the organism or spore under almost any contemplated or actual UHT treatment in the same medium. The potential of the method is demonstrated with simulated inactivation patterns and its predictive ability with experimental survival data of Bacillus sporothermodurans. Theoretically at least, the shown calculation procedure can be applied to other thermal preservation methods and to the prediction of collateral biochemical reactions, like vitamin degradation or the synthesis of compounds that cause discoloration. The concept itself can also be extended to non-Weibullian inactivation or synthesis patterns, provided that they are controlled by only three or fewer kinetic parameters.

Inactivation kinetics of inoculated Escherichia coli O157:H7, Listeria monocytogenes and Salmonella Poona on whole cantaloupe by chlorine dioxide gas

The objectives of this study were to examine inactivation kinetics of inoculated Escherichia coli O157:H7, Listeria monocytogenes and Salmonella Poona inoculated onto whole cantaloupe and treated with ClO(2) gas at different concentrations (0.5, 1.0, 1.5, 3.0 and 5.0 mg l(-1)) for different times (0, 2.0, 4.0, 6.0, 8.0 and 10.0 min). The effect of ClO(2) gas on the quality and shelf life of whole cantaloupe was also evaluated during storage at 22 degrees C for 12 days. A 100 microl inoculation of each targeted organism was spotted onto the surface (5 cm(2)) of cantaloupe rind (approximately 8-9 log CFU 5 cm(-2)) separately, air dried (60 min), and then treated with ClO(2) gas at 22 degrees C and 90-95% relative humidity for 10 min. Surviving bacterial populations on cantaloupe surfaces were determined using a membrane transferring method with a non-selective medium followed by a selective medium. The inactivation kinetics of E. coli O157:H7, L. monocytogenes and S. Poona were determined using nonlinear kinetics (Weibull model). A 3 log CFU reduction of E. coli O157:H7, L. monocytogenes and S. Poona were achieved with 5.0 mg l(-1) ClO(2) gas for 5.5, 4.2 and 1.5 min, respectively. A 5l og CFU reduction of S. Poona was achieved with 5.0 and 3.0 mg l(-1) ClO(2) gas for 6 and 8 min, respectively. A 4.6 and 4.3 log reduction was achieved after treatment with 5.0 mg l(-1) ClO(2) gas at 10 min for E. coli O157:H7 and L. monocytogenes, respectively. Treatment with 5.0 mg l(-1) ClO(2) gas significantly (p<0.05) reduced the initial microflora (mesophilic bacteria, psychrotrophic bacteria, and yeasts and molds) on cantaloupe by more than 2 log CFU cm(-2) and kept them significantly (p<0.05) lower than the untreated control during storage at 22 degrees C for 12 days. Treatment with ClO(2) gas did not significantly (p>0.05) affect the color of whole cantaloupe and extended the shelf life to 9 days compared to 3 days for the untreated control, when stored at ambient temperature (22 degrees C).

The characterisation of Bacillus spores occurring in the manufacturing of (low acid) canned products

Spore-forming bacteria can be a problem in the food industry, especially in the canning industry. Spores present in ingredients or present in the processing environment severely challenge the preservation process since their thermal resistance may be very high. We therefore asked the question which bacterial spore formers are found in a typical soup manufacturing plant, where they originate from and what the thermal resistance of their spores is. To answer these questions molecular techniques for bacterial species and strain identification were used as well as a protocol for the assessment of spore heat stress resistance based on the Kooiman method. The data indicate the existence and physiological cause of the high thermal resistance of spores of many of the occurring species. In particular it shows that ingredients used in soup manufacturing are a rich source of high thermal resistant spores and that sporulation in the presence of ingredients rich in divalent metal ions exerts a strong influence on spore heat resistance. It was also indicated that Bacillus spores may well be able to germinate and resporulate during manufacturing i.e. through growth and sporulation in line. Both these spores and those originating from the ingredients were able to survive certain thermal processing settings. Species identity was confirmed using fatty acid analysis, 16SrRNA gene sequencing and DNA-DNA hybridisation. Finally, molecular typing experiments using Ribotyping and AFLP analysis show that strains within the various Bacillus species can be clustered according to the thermal resistance properties of their spores. AFLP performed slightly better than Ribotyping. The data proofed to be useful for the generation of strain specific probes. Protocols to validate these probes in routine identification and innovation aimed at tailor made heat processing in soup manufacturing have been formulated.

Bacillus sporothermodurans and other highly heat-resistant spore formers in milk

A recent example of a micro-organism causing undesired growth in consumer milk is Bacillus sporothermodurans producing highly heat-resistant spores (HRS) which may survive ultra-high temperature (UHT) treatment or industrial sterilization. Molecular typing showed a heterogeneous group of farm isolates (non-HRS strains), but a clonal group of UHT isolates from diverse European countries and other continents (HRS-clone) suggesting a common source. During a survey of Belgian dairy farms for the presence of potentially highly heat-resistant spore formers, high numbers of these spores were detected in filter cloth, green crop and fodder samples. The strain collection showed a high taxonomic diversity with 18 potentially new species and with Bacillus licheniformis and Geobacillus pallidus as predominating species overall. Seventeen B. sporothermodurans isolates were identified, mainly originating from feed concentrate. Heat resistance studies showed the UHT resistance of B. sporothermodurans spores present in industrially contaminated UHT milk, but a lower heat resistance of laboratory-grown strains (HRS and non-HRS). Hydrogen peroxide, used as sanitizer in the dairy industry, was found to induce higher heat resistance of laboratory-grown B. sporothermodurans strains to a certain level. This indicates that sublethal stress conditions may affect the heat resistance. By transmission electron microscopy, structural differences at the spore level were found between HRS and non-HRS strains. The data indicate that the attainment of extreme heat resistance is rather multifactorial.

Use of the Weibull model for lactococcal bacteriophage inactivation by high hydrostatic pressure

Four lactococcal bacteriophages (phiLl6-2, phiLl35-6, phiLd66-36 and phiLd67-42) in M17 broth were pressurized at 300 and 350 MPa at room temperature and their survival curves were determined at various time intervals. Tailing (monotonic upward concavity) was observed in all survival curves. The resulting non-linear semi-logarithmic survival curves were described by the Weibull model and goodness of fit of this model was investigated. Regression coefficients (R2), root mean square error (RMSE), residual and correlation plots strongly suggested that Weibull model produced a better fit to the data than the traditional linear model. Hazard plots suggested that the Weibull model was fully appropriate for the data being analyzed. These results have confirmed that the Weibull model, which is mostly utilized to describe the inactivation of bacterial cells or spores by heat and pressure, could be successfully used in describing the lactococcal bacteriophage inactivation by high hydrostatic pressure.

Assessment of heat resistance of bacterial spores from food product isolates by fluorescence monitoring of dipicolinic acid release

This study is aimed at the development and application of a convenient and rapid optical assay to monitor the wet-heat resistance of bacterial endospores occurring in food samples. We tested the feasibility of measuring the release of the abundant spore component dipicolinic acid (DPA) as a probe for heat inactivation. Spores were isolated from the laboratory type strain Bacillus subtilis 168 and from two food product isolates, Bacillus subtilis A163 and Bacillus sporothermodurans IC4. Spores from the lab strain appeared much less heat resistant than those from the two food product isolates. The decimal reduction times (D values) for spores from strains 168, A163, and IC4 recovered on Trypticase soy agar were 1.4, 0.7, and 0.3 min at 105 degrees C, 120 degrees C, and 131 degrees C, respectively. The estimated Z values were 6.3 degrees C, 6.1 degrees C, and 9.7 degrees C, respectively. The extent of DPA release from the three spore crops was monitored as a function of incubation time and temperature. DPA concentrations were determined by measuring the emission at 545 nm of the fluorescent terbium-DPA complex in a microtiter plate fluorometer. We defined spore heat resistance as the critical DPA release temperature (Tc), the temperature at which half the DPA content has been released within a fixed incubation time. We found Tc values for spores from Bacillus strains 168, A163, and IC4 of 108 degrees C, 121 degrees C, and 131 degrees C, respectively. On the basis of these observations, we developed a quantitative model that describes the time and temperature dependence of the experimentally determined extent of DPA release and spore inactivation. The model predicts a DPA release rate profile for each inactivated spore. In addition, it uncovers remarkable differences in the values for the temperature dependence parameters for the rate of spore inactivation, DPA release duration, and DPA release delay.

Estimating non-isothermal bacterial growth in foods from isothermal experimental data

AIM

To develop a mathematical method to estimate non-isothermal microbial growth curves in foods from experiments performed under isothermal conditions and demonstrate the method's applicability with published growth data.

METHODS AND RESULTS

Published isothermal growth curves of Pseudomonas spp. in refrigerated fish at 0-8 degrees C and Escherichia coli 1952 in a nutritional broth at 27.6-36 degrees C were fitted with two different three-parameter 'primary models' and the temperature dependence of their parameters was fitted by ad hoc empirical 'secondary models'. These were used to generate non-isothermal growth curves by solving, numerically, a differential equation derived on the premise that the momentary non-isothermal growth rate is the isothermal rate at the momentary temperature, at a time that corresponds to the momentary growth level of the population. The predicted non-isothermal growth curves were in agreement with the reported experimental ones and, as expected, the quality of the predictions did not depend on the 'primary model' chosen for the calculation.

CONCLUSIONS

A common type of sigmoid growth curve can be adequately described by three-parameter 'primary models'. At least in the two systems examined, these could be used to predict growth patterns under a variety of continuous and discontinuous non-isothermal temperature profiles.

SIGNIFICANCE AND IMPACT OF THE STUDY

The described mathematical method whenever validated experimentally will enable the simulation of the microbial quality of stored and transported foods under a large variety of existing or contemplated commercial temperature histories.

Generating microbial survival curves during thermal processing in real time

AIMS

To develop a method to calculate and record theoretical microbial survival curves during thermal processing of foods and pharmaceutical products simultaneously with the changing temperature. Moreover, to demonstrate that the method can be used to calculate nonisothermal survival curves, with widely available software such as Microsoft Excel.

METHODS AND RESULTS

It has been assumed that the targeted organism's isothermal survival curves are not log linear and hence, the inactivation rate in nonisothermal processes is a function of the momentary temperature and the corresponding survival ratio. This could be expressed by a difference equation, which is an approximation to the continuous rate model. The concept was tested with the isothermal survival parameters of Clostridium botulinum and Bacillus sporothermodurans spores, and Salmonella enteritidis cells, using different kinds of survival models and under temperature profiles resembling those of commercial processes. As expected, there was an excellent agreement between the curves produced by solving the differential equation of the continuous model and by the incremental method, which has been posted on the web as freeware.

CONCLUSIONS

It is possible to calculate nonisothermal survival curves, in real time, with an algorithm that can be written in the language of general purpose software, to follow the inactivation of one or more targeted organisms simultaneously and to simulate microbial survival patterns under existing or planned industrial thermal processes.

SIGNIFICANCE AND IMPACT OF THE STUDY

Replacement of the traditional 'F0-value', which requires the log linearity of the organism's isothermal survival curves, by the more realistic theoretical survival ratio estimate as a measure of the thermal process efficacy.

Demonstration of the applicability of the Weibull-log-logistic survival model to the isothermal and nonisothermal inactivation of Escherichia coli K-12 MG1655

Published isothermal semilogarithmic survival curves of Escherichia coli K-12 MG1655, in the range of 49.8 to 60.6 degrees C, all had noticeable downward concavity. They could be described by the model log S(t) = -b(T)t n, where S(t) = N(t)/N0, N(t) and N0 being the momentary and initial number of organisms, respectively; b(T) is a temperature-dependent rate parameter; and n is a constant found to be about 1.5. The temperature dependence of b(T) could be described by the log-logistic model, b(T) = ln[1 + exp[k(T - Tc)]], which had an almost perfect fit, with k = 0.88 degrees C(-1) and Tc = 60.5 degrees C. The constants, n, k, and Tc were considered the organism's survival parameters in the particular medium. They were incorporated into a rate equation on the assumption that in nonisothermal heating, the momentary inactivation rate is the isothermal rate at the momentary temperature at a time that corresponds to the momentary survival ratio. This model's estimates matched the actual survival curves obtained in the same work under two different nonisothermal heating profiles, lending support to the notion that the Weibull-log-logistic model combination can be used not only to describe isothermal inactivation mathematically, but also to predict survival patterns under nonisothermal conditions.