Generating microbial survival curves during thermal processing in real time

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.

Inactivation kinetics of a surrogate yield conservative predictions of foodborne pathogen reductions from low water activity foods of varying size and composition during low-temperature steam processing

There is a growing interest in using models to predict foodborne pathogen inactivation as a way to validate or verify preventive controls. Unlike liquid foods, solid, low water activity foods (LWAF) are heterogenous in composition and structure and do not transfer heat uniformly. Using models constructed from one food to predict pathogen inactivation on another LWAF is complex and may not always be possible, even if the foods have similar composition. Using models constructed from inactivation kinetics of three foodborne pathogens and a surrogate from vacuum-steam-pasteurized (72 and 82 °C) whole macadamia nuts and dried apricot halves, 3-log reductions were predicted for the same pathogens and foods of reduced size. Model fits (First-order, Weibull, and Gompertz) were significantly impacted by the food type regardless of particle size. Despite the foods being identical in composition with particle size as the only altered characteristic, best-fit models accurately predicted the 3-log reductions only 50% of the time, but the surrogate inactivation models provided conservative predictions for pathogen reductions, highlighting that a surrogate's model may be a suitable tool for predicting pathogen reduction on LWAFs.

The probability of bacterial spores surviving a thermal process: The 12D myth and other issues with its quantitative assessment

The concepts of "D-value," "thermal death time" and "commercial sterility," innovative and useful at their inception, are based on untenable assumptions, notably that the log-linear isothermal inactivation model has universal applicability, that extrapolation over several orders of magnitude below the detection level is permissible, and that total microbial inactivation is theoretically impossible. Almost all commonly observed inactivation patterns, the log-linear is just a special case, can be described by both deterministic and fully stochastic models, examples of which are given. Unlike the deterministic, the stochastic models predict either complete elimination of the targeted cells or spores in realistic finite time, or residual survival. In most cases, the published survival data do not contain enough information to establish which actually happens. The microbial safety of thermally processed foods can be compromised not only by under-processing but also by a variety of mishaps whose occurrence probabilities are unrelated to the inactivation kinetics. Moreover, the available sampling plans to detect microbial contamination in sterilized containers through incubation alone are insensitive to levels of potential safety concerns. In principle, many of these issues could be resolved by developing new dramatically improved detection methods and/or verifiable methods to predict very low levels of microbial survival.

Growth Response and Recovery of Corynebacterium glutamicum Colonies on Single-Cell Level Upon Defined pH Stress Pulses

Bacteria respond to pH changes in their environment and use pH homeostasis to keep the intracellular pH as constant as possible and within a small range. A change in intracellular pH influences enzyme activity, protein stability, trace element solubilities and proton motive force. Here, the species Corynebacterium glutamicum was chosen as a neutralophilic and moderately alkali-tolerant bacterium capable of maintaining an internal pH of 7.5 ± 0.5 in environments with external pH values ranging between 5.5 and 9. In recent years, the phenotypic response of C. glutamicum to pH changes has been systematically investigated at the bulk population level. A detailed understanding of the C. glutamicum cell response to defined short-term pH perturbations/pulses is missing. In this study, dynamic microfluidic single-cell cultivation (dMSCC) was applied to analyze the physiological growth response of C. glutamicum to precise pH stress pulses at the single-cell level. Analysis by dMSCC of the growth behavior of colonies exposed to single pH stress pulses (pH = 4, 5, 10, 11) revealed a decrease in viability with increasing stress duration w. Colony regrowth was possible for all tested pH values after increasing lag phases for which stress durations w were increased from 5 min to 9 h. Furthermore, single-cell analyses revealed heterogeneous regrowth of cells after pH stress, which can be categorized into three physiological states. Cells in the first physiological state continued to grow without interruption after pH stress pulse. Cells in the second physiological state rested for several hours after pH stress pulse before they started to grow again after this lag phase, and cells in the third physiological state did not divide after the pH stress pulse. This study provides the first insights into single-cell responses to acidic and alkaline pH stress by C. glutamicum.

Engineering modeling frameworks for microbial food safety at various scales

The landscape of mathematical model-based understanding of microbial food safety is wide and deep, covering interdisciplinary fields of food science, microbiology, physics, and engineering. With rapidly growing interest in such model-based approaches that increasingly include more fundamental mechanisms of microbial processes, there is a need to build a general framework that steers this evolutionary process by synthesizing literature spread over many disciplines. The framework proposed here shows four interconnected, complementary levels of microbial food processes covering sub-cellular scale, microbial population scale, food scale, and human population scale (risk). A continuum of completely mechanistic to completely empirical models, widely-used and emerging, are integrated into the framework; well-known predictive microbiology modeling being a part of this spectrum. The framework emphasizes fundamentals-based approaches that should get enriched over time, such as the basic building blocks of microbial population scale processes (attachment, migration, growth, death/inactivation and communication) and of food processes (e.g., heat and moisture transfer). A spectrum of models are included, for example, microbial population modeling covers traditional predictive microbiology models to individual-based models and cellular automata. The models are shown in sufficient quantitative detail to make obvious their coupling, or their integration over various levels. Guidelines to combine sub-processes over various spatial and time scales into a complete interdisciplinary and multiphysics model (i.e., a system) are provided, covering microbial growth/inactivation/transport and physical processes such as fluid flow and heat transfer. As food safety becomes increasingly predictive at various scales, this synthesis should provide its roadmap. This big picture and framework should be futuristic in driving novel research and educational approaches.

On optimum dynamic temperature profiles for thermal inactivation kinetics determination

Determination of inactivation kinetics, associated with thermal processing of foods and obtained from dynamic temperature experiments, requires carefully designed experiments, the primary element being the selection of the appropriate temperature profile along with a carefully planned sampling schedule. In the present work, a number of different dynamic temperature profiles were investigated in terms of their ability to generate accurate kinetic parameters with low confidence intervals (CIs). Although alternative models have been also tested, our work was concentrated on thermal inactivation kinetics that could be described by the classical D-z values. A pair of D and z values was assumed, and for each temperature profile tested, concentration data at different processing times were generated through the appropriate models. Next, an error (up to ±2.5% or ±5%) was introduced on these theoretical values to generate pseudo-experimental data, and the back-calculation of the assumed kinetic parameters by non-linear regression was performed. The accuracy and the 95% CIs of the estimated kinetic parameters were evaluated; joint confidence regions were also constructed to investigate parameters correlation. The effect of temperature profile pattern, level of error, number of experimental points, and reference temperature was assessed. A stepwise increasing and a single triangle-pattern temperature profile were the best profiles among those tested. As a general observation, based on different kinetic models investigated, temperature profiles and sampling intervals that result in concentration versus time diagrams having shapes as suggested by the primary model used when isothermally applied are not considered appropriate for parameter estimation.

Thermal inactivation of Salmonella, Shiga toxin-producing Escherichia coli, Listeria monocytogenes, and a surrogate (Pediococcus acidilactici) on raisins, apricot halves, and macadamia nuts using vacuum-steam pasteurization

Salmonella, Shiga toxin-producing Escherichia coli (STEC), and Listeria monocytogenes have been isolated from low water activity foods (LWAF), where they may survive for extended periods. The ready-to-eat nature of many LWAF, such as dried fruits and nuts, warrants effective post-harvest thermal treatment for the reduction of pathogens such as low-temperature, saturated steam, also known as vacuum-assisted steam pasteurization. The objective of this study was to determine reductions of Salmonella, STEC, L. monocytogenes, and a possible surrogate (Pediococcus acidilactici) on dried apricot halves, whole macadamia nuts, and raisins after treatment with vacuum-assisted steam at three temperatures (62 °C, 72 °C, or 82 °C) and multiple time intervals. Bacterial inactivation was variable between commodities, with higher temperatures and longer times necessary to achieve comparable reductions of pathogens on apricot halves and macadamia nuts compared to raisins. Reductions of the tested pathogens were comparable; therefore, one species was not more resistant than the others. Pathogens were reduced by 5-log CFU/g on apricot halves after 20 min at 72 °C and after 5 min at 82 °C. Longer treatment times were necessary to achieve reductions of each pathogen on macadamia nuts. Pathogens were reduced by nearly 5 log CFU/g on macadamia nuts after 38 min at 72 °C (4.6-6.5 log CFU/g) and after 12 min at 82 °C (4.9-5.7 log CFU/g). Reductions of pathogens on raisins were achieved at lower temperatures than necessary for the other foods. A 5-log reduction for each of the pathogens (CFU/g) on raisins occurred after 20 min at 62 °C and after 5 min at 72 °C. Overall, the reductions of the pathogens exceeded those of P. acidilactici on both the dried fruits and macadamia nuts. Statistically significant differences, indicating greater confidence as a conservative surrogate, were observed at lower treatment temperatures. Inactivation kinetics were modeled for each pathogen on each food type and temperature. Bacterial survival was best described by the Weibull model for raisins and macadamia nuts, while the Gompertz model best described reductions on apricot halves according to Akaike information criterion (AIC) and root-mean-square error (RMSE) evaluations. Water activity and moisture content were increased due to the treatments, which could be addressed through implementation of drying steps. Thermal inactivation kinetic models and 5-log reduction parameters can help food processors design and evaluate similar vacuum-assisted steam interventions to comply with FSMA regulations and preventive control plans. However, results or model predictions should not be extrapolated to assume the safety of other types of foods.

Describing the Individual Spore Variability and the Parameter Uncertainty in Bacterial Survival Kinetics Model by Using Second-Order Monte Carlo Simulation

The objective of this study was to separately describe the fitting uncertainty and the variability of individual cell in bacterial survival kinetics during isothermal and non-isothermal thermal processing. The model describing bacterial survival behavior and its uncertainties and variabilities during non-isothermal inactivation was developed from survival kinetic data for Bacillus simplex spores under fifteen isothermal conditions. The fitting uncertainties in the parameters used in the primary Weibull model was described by using the bootstrap method. The variability of individual cells in thermotolerance and the true randomness in the number of dead cells were described by using the Markov chain Monte Carlo (MCMC) method. A second-order Monte Carlo (2DMC) model was developed by combining both the uncertainties and variabilities. The 2DMC model was compared with reduction behavior under three non-isothermal profiles for model validation. The bacterial death estimations were validated using experimentally observed surviving bacterial count data. The fitting uncertainties in the primary Weibull model parameters, the individual thermotolerance heterogeneity, and the true randomness of inactivated spore counts were successfully described under all the iso-thermal conditions. Furthermore, the 2DMC model successfully described the variances in the surviving bacterial counts during thermal inactivation for all three non-isothermal profiles. As a template for risk-based process designs, the proposed 2DMC simulation approach, which considers both uncertainty and variability, can facilitate the selection of appropriate thermal processing conditions ensuring both food safety and quality.

Modeling the pressure inactivation of Escherichia coli and Salmonella typhimurium in sapote mamey ( Pouteria sapota (Jacq.) H.E. Moore & Stearn) pulp

High hydrostatic pressure inactivation kinetics of Escherichia coli ATCC 25922 and Salmonella enterica subsp. enterica serovar Typhimurium ATCC 14028 ( S. typhimurium) in a low acid mamey pulp at four pressure levels (300, 350, 400, and 450 MPa), different exposure times (0-8 min), and temperature of 25 ± 2℃ were obtained. Survival curves showed deviations from linearity in the form of a tail (upward concavity). The primary models tested were the Weibull model, the modified Gompertz equation, and the biphasic model. The Weibull model gave the best goodness of fit ( R²_adj > 0.956, root mean square error < 0.290) in the modeling and the lowest Akaike information criterion value. Exponential-logistic and exponential decay models, and Bigelow-type and an empirical models for b'( P) and n( P) parameters, respectively, were tested as alternative secondary models. The process validation considered the two- and one-step nonlinear regressions for making predictions of the survival fraction; both regression types provided an adequate goodness of fit and the one-step nonlinear regression clearly reduced fitting errors. The best candidate model according to the Akaike theory information, with better accuracy and more reliable predictions was the Weibull model integrated by the exponential-logistic and exponential decay secondary models as a function of time and pressure (two-step procedure) or incorporated as one equation (one-step procedure). Both mathematical expressions were used to determine the t_d parameter, where the desired reductions ( 5D) (considering d = 5 ( t₅) as the criterion of 5 Log₁₀ reduction (5 D)) in both microorganisms are attainable at 400 MPa for 5.487 ± 0.488 or 5.950 ± 0.329 min, respectively, for the one- or two-step nonlinear procedure.

Evaluation of Different Dose-Response Models for High Hydrostatic Pressure Inactivation of Microorganisms

Modeling of microbial inactivation by high hydrostatic pressure (HHP) requires a plot of the log microbial count or survival ratio versus time data under a constant pressure and temperature. However, at low pressure and temperature values, very long holding times are needed to obtain measurable inactivation. Since the time has a significant effect on the cost of HHP processing it may be reasonable to fix the time at an appropriate value and quantify the inactivation with respect to pressure. Such a plot is called dose-response curve and it may be more beneficial than the traditional inactivation modeling since short holding times with different pressure values can be selected and used for the modeling of HHP inactivation. For this purpose, 49 dose-response curves (with at least 4 log10 reduction and ≥5 data points including the atmospheric pressure value (P = 0.1 MPa), and with holding time ≤10 min) for HHP inactivation of microorganisms obtained from published studies were fitted with four different models, namely the Discrete model, Shoulder model, Fermi equation, and Weibull model, and the pressure value needed for 5 log10 (P₅) inactivation was calculated for all the models above. The Shoulder model and Fermi equation produced exactly the same parameter and P₅ values, while the Discrete model produced similar or sometimes the exact same parameter values as the Fermi equation. The Weibull model produced the worst fit (had the lowest adjusted determination coefficient (R²adj) and highest mean square error (MSE) values), while the Fermi equation had the best fit (the highest R²adj and lowest MSE values). Parameters of the models and also P₅ values of each model can be useful for the further experimental design of HHP processing and also for the comparison of the pressure resistance of different microorganisms. Further experiments can be done to verify the P₅ values at given conditions. The procedure given in this study can also be extended for enzyme inactivation by HHP.

Microclimates Might Limit Indirect Spillover of the Bat Borne Zoonotic Hendra Virus

Infectious diseases are transmitted when susceptible hosts are exposed to pathogen particles that can replicate within them. Among factors that limit transmission, the environment is particularly important for indirectly transmitted parasites. To try and assess a pathogens' ability to be transmitted through the environment and mitigate risk, we need to quantify its decay where transmission occurs in space such as the microclimate harbouring the pathogen. Hendra virus, a Henipavirus from Australian Pteropid bats, spills-over to horses and humans, causing high mortality. While a vaccine is available, its limited uptake has reduced opportunities for adequate risk management to humans, hence the need to develop synergistic preventive measures, like disrupting its transmission pathways. Transmission likely occurs shortly after virus excretion in paddocks; however, no survival estimates to date have used real environmental conditions. Here, we recorded microclimate conditions and fitted models that predict temperatures and potential evaporation, which we used to simulate virus survival with a temperature-survival model and modification based on evaporation. Predicted survival was lower than previously estimated and likely to be even lower according to potential evaporation. Our results indicate that transmission should occur shortly after the virus is excreted, in a relatively direct way. When potential evaporation is low, and survival is more similar to temperature dependent estimates, transmission might be indirect because the virus can wait several hours until contact is made. We recommend restricting horses' access to trees during night time and reducing grass under trees to reduce virus survival.

Predicting Salmonella Typhimurium reductions in poultry ground carcasses

To improve understanding of Salmonella Typhimurium LT2 inactivation in ground poultry carcasses, a series of experiments were carried out at multiple temperatures. Subsequently, a non-linear model was developed to predict Salmonella inactivation at composting and low rendering temperatures. The Salmonella inactivation study was conducted using bench-top experiments at 38, 48, 55, 62.5, 70, and 78°C in mixed and non-mixed reactors using ground poultry carcasses as a feedstock. Subsequently, these observations were used for developing a non-linear model. The model predictions were compared with the observations of a different set of experiments. The comparisons among predictions and observations showed that the model predictions are reasonable and can be useful to determine the time required for Salmonella inactivation in poultry carcasses at multiple temperatures. Results showed that at composting conditions, when temperature varies between 48 and 62.5°C, Salmonella survival can prolong between 10,000 and 25,000 min (7 to 17 d). If ambient temperature is maintained at low temperature rendering range (70 to 78°C), then Salmonella survival can last for 90 to 120 minutes. We anticipate that this study will help in improving the existing understanding of Salmonella survival in poultry carcasses.

Diversity of spore-forming bacteria in cattle manure, slaughterhouse waste and samples from biogas plants

AIMS

As biowaste intended for biogas production can contain pathogenic micro-organisms, the recommended treatment is pasteurization at 70°C for 60min. This reduces pathogens such as Salmonella spp., whereas spore-forming bacteria (Bacillus spp. and Clostridium spp.) survive. Most spore-forming bacteria are harmless, but some can cause diseases such as blackleg, botulism and anthrax. In this study, the effect of the biogas process on Bacillus spp. and Clostridium spp. was investigated.

METHODS AND RESULTS

We analysed 97 faecal samples, 20 slaughterhouse waste samples and 60 samples collected at different stages in the biogas process. Bacillus spp. and Clostridium spp. were quantified and subcultured. The isolates were identified by biochemical methods and by 16S rRNA gene sequencing. Phylogenetic trees were constructed from the sequences obtained from isolates from the samples. Clostridium botulinum/Clostridium spp. and Clostridium sordellii were found both before and after pasteurization, but not after digestion (AD). Some of the isolated strains probably represented new members of the genera Clostridium and Bacillus.

CONCLUSION

After digestion, the numbers of clostridia decreased, but none of the pathogenic bacteria did, whereas Bacillus spp. remained constant during the process.

SIGNIFICANCE AND IMPACT OF THE STUDY

Biogas is gaining in importance as an energy source and because the residues are used as fertilizers, we needed to study the prevalence of pathogenic bacteria in such material.

Modeling Penicillium expansum resistance to thermal and chlorine treatments

Apples and apple products are excellent substrates for Penicillium expansum to produce patulin. In an attempt to avoid excessive levels of patulin, limiting or reducing P. expansum contamination levels on apples designated for storage in packinghouses and/or during apple juice processing is critical. The aim of this work was (i) to determine the thermal resistance of P. expansum spores in apple juice, comparing the abilities of the Bigelow and Weibull models to describe the survival curves and (ii) to determine the inactivation of P. expansum spores in aqueous chlorine solutions at varying concentrations of chlorine solutions, comparing the abilities of the biphasic and Weibull models to fit the survival curves. The results showed that the Bigelow and Weibull models were similar for describing the heat inactivation data, because the survival curves were almost linear. In this case, the concept of D- and z-values could be used, and the D-values obtained were 10.68, 6.64, 3.32, 1.14, and 0.61 min at 50, 52, 54, 56, and 60 degrees C, respectively, while the z-value was determined to be 7.57 degrees C. For the chlorine treatments, although the biphasic model gave a slightly superior performance, the Weibull model was selected, considering the parsimony principle, because it has fewer parameters than the biphasic model has. In conclusion, the typical pasteurization regimen used for refrigerated apple juice (71 degrees C for 6 s) is capable of achieving a 6-log reduction of P. expansum spores.

Development of a log-quadratic model to describe microbial inactivation, illustrated by thermal inactivation of Clostridium botulinum

In the commercial food industry, demonstration of microbiological safety and thermal process equivalence often involves a mathematical framework that assumes log-linear inactivation kinetics and invokes concepts of decimal reduction time (D(T)), z values, and accumulated lethality. However, many microbes, particularly spores, exhibit inactivation kinetics that are not log linear. This has led to alternative modeling approaches, such as the biphasic and Weibull models, that relax strong log-linear assumptions. Using a statistical framework, we developed a novel log-quadratic model, which approximates the biphasic and Weibull models and provides additional physiological interpretability. As a statistical linear model, the log-quadratic model is relatively simple to fit and straightforwardly provides confidence intervals for its fitted values. It allows a D(T)-like value to be derived, even from data that exhibit obvious "tailing." We also showed how existing models of non-log-linear microbial inactivation, such as the Weibull model, can fit into a statistical linear model framework that dramatically simplifies their solution. We applied the log-quadratic model to thermal inactivation data for the spore-forming bacterium Clostridium botulinum and evaluated its merits compared with those of popular previously described approaches. The log-quadratic model was used as the basis of a secondary model that can capture the dependence of microbial inactivation kinetics on temperature. This model, in turn, was linked to models of spore inactivation of Sapru et al. and Rodriguez et al. that posit different physiological states for spores within a population. We believe that the log-quadratic model provides a useful framework in which to test vitalistic and mechanistic hypotheses of inactivation by thermal and other processes.

Thermal effects on bacterial bioaerosols in continuous air flow

Exposure to bacterial bioaerosols can have adverse effects on health, such as infectious diseases, acute toxic effects, and allergies. The search for ways of preventing and curing the harmful effects of bacterial bioaerosols has created a strong demand for the study and development of an efficient method of controlling bioaerosols. We investigated the thermal effects on bacterial bioaerosols of Escherichia coli and Bacillus subtilis by using a thermal electric heating system in continuous air flow. The bacterial bioaerosols were exposed to a surrounding temperature that ranged from 20 degrees C to 700 degrees C for about 0.3 s. Both E. coli and B. subtilis vegetative cells were rendered more than 99.9% inactive at 160 degrees C and 350 degrees C of wall temperature of the quartz tube, respectively. Although the data on bacterial injury showed that the bacteria tended to sustain greater damage as the surrounding temperature increased, Gram-negative E. coli was highly sensitive to structural injury but Gram-positive B. subtilis was slightly more sensitive to metabolic injury. In addition, the inactivation of E. coli endotoxins was found to range from 9.2% (at 200 degrees C) to 82.0% (at 700 degrees C). However, the particle size distribution and morphology of both bacterial bioaerosols were maintained, despite exposure to a surrounding temperature of 700 degrees C. Our results show that thermal heating in a continuous air flow can be used with short exposure time to control bacterial bioaerosols by rendering the bacteria and endotoxins to a large extent inactive. This result could also be useful for developing more effective thermal treatment strategies for use in air purification or sterilization systems to control bioaerosols.

An integral model of microbial inactivation taking into account memory effects: power-law memory kernel

In this article, we propose an alternative framework for the description of non-log-linear thermal inactivation of microorganisms. The proposed framework generalizes classical views by explicitly taking into account memory effects, such as those often associated with cumulative cell damage or progressive cell adaptation. Within this general framework, specialized memory models can be easily accommodated to describe different modes of microbial response to previous thermal stresses. In this introductory study, the advantages and limitations of the simplest nontrivial memory model, the power-law memory model, were explored. Our results indicate that for isothermal treatments the assumption of power-law memory leads to a simple solution that is known to describe a large number of non-log-linear survival curves. For nonisothermal treatments, the power-law memory model leads to predictions that agree well with experimental data. This research may lead to new insights into predictive microbiology with a new appreciation for the importance of memory effects.

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.

Modeling the effect of prior sublethal thermal history on the thermal inactivation rate of Salmonella in ground turkey

Traditional models for predicting the thermal inactivation rate of bacteria are state dependent, considering only the current state of the product. In this study, the potential for previous sublethal thermal history to increase the thermotolerance of Salmonella in ground turkey was determined, a path-dependent model for thermal inactivation was developed, and the path-dependent predictions were tested against independent data. Weibull-Arrhenius parameters for Salmonella inactivation in ground turkey thigh were determined via isothermal tests at 55, 58, 61, and 63 degrees C. Two sets of nonisothermal heating tests also were conducted. The first included five linear heating rates (0.4, 0.9, 1.7, 3.5, and 7.0 K/min) and three holding temperatures (55, 58, and 61 degrees C); the second also included sublethal holding periods at 40, 45, and 50 degrees C. When the standard Weibull-Arrhenius model was applied to the nonisothermal validation data sets, the root mean squared error of prediction was 2.5 log CFU/g, with fail-dangerous residuals as large as 4.7 log CFU/g when applied to the complete nonisothermal data set. However, by using a modified path-dependent model for inactivation, the prediction errors for independent data were reduced by 56%. Under actual thermal processing conditions, use of the path-dependant model would reduce error in thermal lethality predictions for slowly cooked products.