Microbial dynamics versus mathematical model dynamics: The case of microbial heat resistance induction

Radio Frequency Treatment of Food: A Review on Pasteurization and Disinfestation

Radio frequency (RF) is a novel technology with several food processing and preservation applications. It is based on the volumetric heating generated from the product's dielectric properties. The dielectric properties of each material are unique and a function of several factors (i.e., temperature, moisture content). This review presents a list of dielectric properties of several foods and describes the use of RF as an innovative technology for the food industry. This paper includes several examples of pasteurization, fungi inactivation, and disinfestation in selected food products. The aim of this review is to present the potential applications of RF in pasteurization and disinfestation and research needs that should be addressed. RF has been successfully applied in the inactivation of pathogens such as Salmonella spp., Listeria monocytogenes, and Escherichia coli in low- and high-moisture food. The disinfestation of crops is possible using RF because of selective heating. This process inactivates the insects first because of the different dielectric properties between the pests and the food. The products' final quality can be considerably better than conventional thermal processes. The processing time is reduced compared to traditional heating, and thermal damage to the food is minimized. The main drawback of the technology is the lack of uniform heating, mainly when the product is surrounded by a packaging material with different dielectric properties from the food.

Impact of Heating Rates on Alicyclobacillus acidoterrestris Heat Resistance under Non-Isothermal Treatments and Use of Mathematical Modelling to Optimize Orange Juice Processing

Alicyclobacillus acidoterrestris is a spoilage microorganism responsible for relevant product and economic losses in the beverage and juice industry. Spores of this microorganism can survive industrial heat treatments and cause spoilage during posterior storage. Therefore, an effective design of processing treatments requires an accurate understanding of the heat resistance of this microorganism. Considering that industrial treatments are dynamic; this understanding must include how the heat resistance of the microorganism is affected by the heating rate during the heating and cooling phases. The main objective of this study was to establish the effect of heating rates and complex thermal treatments on the inactivation kinetics of A. acidoterrestris. Isothermal experiments between 90 and 105 °C were carried out in a Mastia thermoresistometer, as well as four different dynamic treatments. Although most of the inactivation takes place during the holding phase, our results indicate the relevance of the heating phase for the effectiveness of the treatment. The thermal resistance of A. acidoterrestris is affected by the heating rate during the heating phase. Specifically, higher heating rates resulted in an increased microbial inactivation with respect to the one predicted based on isothermal experiments. These results provide novel information regarding the heat response of this microorganism, which can be valuable for the design of effective heat treatments to improve product safety and stability. Moreover, it highlights the need to incorporate experimental data based on dynamic treatments in process design, as heating rates can have a very significant effect on the thermal resistance of microorganisms.

Variability in the heat resistance of Listeria monocytogenes under dynamic conditions can be more relevant than that evidenced by isothermal treatments

Heterogeneity in the response of microbial cells to environmental conditions is inherent to every biological system and can be very relevant for food safety, potentially being as important as intrinsic and extrinsic factors. However, previous studies analyzing variability in the microbial response to thermal treatments were limited to data obtained under isothermal conditions, whereas in the reality, environmental conditions are dynamic. In this article we analyse both empirically and through mathematical modelling the variability in the microbial response to thermal treatments under isothermal and dynamic conditions. Heat resistance was studied for four strains of Listeria monocytogenes (Scott A, CECT 4031, CECT 4032 and 12MOB052), in three different matrices (buffered peptone water, pH 7 Mcllvaine buffer and semi-skimmed milk). Under isothermal conditions, between-strain and between-media variability had no impact in the heat resistance, whereas it was very relevant for dynamic conditions. Therefore, the differences observed under dynamic conditions can be attributed to the variability in the ability for developing stress acclimation. The highest acclimation was observed in strain CECT 4031 (10-fold increase of the D-value), while the lowest acclimation was observed in strain CECT 4032 (50% increase of the D-value). Concerning the different media, acclimation was higher in buffered peptone water and semi-skimmed milk than in Mcllvaine buffer of pH 7.0. To the knowledge of the authors, this is the first research work that specifically analyses the variability of microbial adaptation processes that take place under dynamic conditions. It highlights that microbial heat resistance under dynamic conditions are sometimes determined by mechanisms that cannot be observed when cells are treated in isothermal conditions (e.g. acclimation) and can also be affected by variability. Consequently, empirical evidence on variability gathered under isothermal conditions should be extrapolated with care for dynamic conditions.

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.

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.

Tail or artefact? Illustration of the impact that uncertainty of the serial dilution and cell enumeration methods has on microbial inactivation

The estimation of the concentration of microorganisms in a sample is crucial for food microbiology. For instance, it is essential for prevalence studies, challenge tests (growth and/or inactivation studies) or microbial risk assessment. The application of serial dilutions followed by viable counts in Petri dishes is probably the most extended experimental methodology for this purpose. However, this enumeration technique is also a source of uncertainty. In this article, the uncertainty of the serial dilution and viable count methodology related to the sampling error is analyzed, as well as the approximation of the microbial concentration by the number of colonies in a Petri dish. We analyze from a theoretical point of view (statistical analysis) the application of the binomial and Poisson models, demonstrating that the Poisson distribution increases the variance when used to model individual serial dilutions. On the other hand, the binomial model produces unbiased results. Therefore, the Poisson distribution is only applicable when it is a good approximation of the binomial distribution, so the use of the latter is recommended. The relevance of this uncertainty is demonstrated by Monte Carlo simulations of a generic microbial inactivation experiment, where the only source of uncertainty/variability considered is the one generated by serial plating and viable cell enumeration. Due to both the uncertainty of the methodology and the omission of zero-count plates because of the log-transformation, the simulated survival curve can have a tail. Therefore, this phenomenon, which is usually attributed to biological variability, can be to some extent an artefact of the experimental design and/or methodology.

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.

Relevance of the Induced Stress Resistance When Identifying the Critical Microorganism for Microbial Risk Assessment

Decisions regarding microbial risk assessment usually have to be carried out with incomplete information. This is due to the large number of possible scenarios and the lack of specific data for the problem considered. Consequently, risk assessment studies are based on the information obtained with a small number of bacterial cells which are considered the most heat resistant and/or more capable of multiplying during storage. The identification of the most resistant strains is usually based on D and z-values, normally estimated from isothermal experiments. This procedure omits the potential effect that the shape of the dynamic thermal profile applied in industry has on the microbial inactivation. One example of such effects is stress acclimation, which is related to a physiological response of the cells during sub-lethal treatments that increases their resistance. In this article, we use a recently published mathematical model to compare the development of thermal resistance for Escherichia coli K12 MG1655 and E. coli CECT 515 using inactivation data already published for these strains. Based only on the isothermal experiments, E. coli K12 MG1655 would be identified as more resistant to the thermal treatment than the CECT 515 strain in the 50-65°C temperature range. However, we conclude that stress acclimation is strain (and/or media)-dependent; the CECT 515 strain has a higher capacity for developing a stress acclimation than K12 MG1655 (300% increase of the D-value for CECT 515, 50% for K12 MG1655). It, thus, has the potential to be more resistant to the thermal treatment than the K12 MG1655 strain for some conditions allowing acclimation. A methodology is proposed to identify for which conditions this may be the case. After calibrating the model parameters representing acclimation using real experimental data, the applicability of the proposed approach is demonstrated using numerical simulations, showing how the CECT 515 strain can be more resistant for some heating profiles. Consequently, the most resistant bacterial strain to a dynamic heating profile should not be identified based only on isothermal experiments (D- and z-value). The relevance of stress acclimation for the treatment studied should also be evaluated.

Bioinactivation FE: A free web application for modelling isothermal and dynamic microbial inactivation

Mathematical models developed in predictive microbiology are nowadays an essential tool for food scientists and researchers. However, advanced knowledge of scientific programming and mathematical modelling are often required in order to use them, especially in cases of modelling of dynamic and/or non-linear processes. This may be an obstacle for food scientists without such skills. Scientific software can help making these tools more accessible for scientists lacking a deep mathematical or computing background. Recently, the R package bioinactivation was published, including functions (model fitting and predictions) for modelling microbial inactivation under isothermal or dynamic conditions. It was uploaded to the Comprehensive R Archive Network (CRAN), but users need basic R programming knowledge in order to use it. Therefore, it was accompanied by Bioinactivation SE, a user-friendly web application including selected functions in the software for users without a programming background. In this work, a new web application, Bioinactivation FE, is presented. It is an extension of Bioinactivation SE which includes an interface to every function in the bioinactivation package: model fitting of isothermal and non-isothermal experiments, and generation of survivor curves and prediction intervals. Moreover, it includes several improvements in the user interface based on the users' feedback. The capabilities of the software are demonstrated through two case studies using data published in the scientific literature. In the first case study, the response of Escherichia coli to isothermal and non-isothermal treatments is compared, illustrating the presence of an induced thermal resistance. In the second, the effect of nanoemulsified d-limonene on the thermal resistance of Salmonella Senftenberg is quantified.

Mathematical quantification of the induced stress resistance of microbial populations during non-isothermal stresses

This contribution presents a mathematical model to describe non-isothermal microbial inactivation processes taking into account the acclimation of the microbial cell to thermal stress. The model extends the log-linear inactivation model including a variable and model parameters quantifying the induced thermal resistance. The model has been tested on cells of Escherichia coli against two families of non-isothermal profiles with different constant heating rates. One of the families was composed of monophasic profiles, consisting of a non-isothermal heating stage from 35 to 70°C; the other family was composed of biphasic profiles, consisting of a non-isothermal heating stage followed by a holding period at constant temperature of 57.5°C. Lower heating rates resulted in a higher thermal resistance of the bacterial population. This was reflected in a higher D-value. The parameter estimation was performed in two steps. Firstly, the D and z-values were estimated from the isothermal experiments. Next, the parameters describing the acclimation were estimated using one of the biphasic profiles. This set of parameters was able to describe the remaining experimental data. Finally, a methodology for the construction of diagrams illustrating the magnitude of the induced thermal resistance is presented. The methodology has been illustrated by building it for a biphasic temperature profile with a linear heating phase and a holding phase. This diagram provides a visualization of how the shape of the temperature profile (heating rate and holding temperature) affects the acclimation of the cell to the thermal stress. This diagram can be used for the design of inactivation treatments by industry taking into account the acclimation of the cell to the thermal stress.

One-step global parameter estimation of kinetic inactivation parameters for Bacillus sporothermodurans spores under static and dynamic thermal processes

Bacillus sporothermodurans produces highly heat-resistant endospores, that can survive under ultra-high temperature. High heat-resistant sporeforming bacteria are one of the main causes for spoilage and safety of low-acid foods. They can be used as indicators or surrogates to establish the minimum requirements for heat processes, but it is necessary to understand their thermal inactivation kinetics. The aim of the present work was to study the inactivation kinetics under both static and dynamic conditions in a vegetable soup. Ordinary least squares one-step regression and sequential procedures were applied for estimating these parameters. Results showed that multiple dynamic heating profiles, when analyzed simultaneously, can be used to accurately estimate the kinetic parameters while significantly reducing estimation errors and data collection.

High Heating Rates Affect Greatly the Inactivation Rate of Escherichia coli

Heat resistance of microorganisms can be affected by different influencing factors. Although, the effect of heating rates has been scarcely explored by the scientific community, recent researches have unraveled its important effect on the thermal resistance of different species of vegetative bacteria. Typically heating rates described in the literature ranged from 1 to 20°C/min but the impact of much higher heating rates is unclear. The aim of this research was to explore the effect of different heating rates, such as those currently achieved in the heat exchangers used in the food industry, on the heat resistance of Escherichia coli. A pilot plant tubular heat exchanger and a thermoresistometer Mastia were used for this purpose. Results showed that fast heating rates had a deep impact on the thermal resistance of E. coli. Heating rates between 20 and 50°C/min were achieved in the heat exchanger, which were much slower than those around 20°C/s achieved in the thermoresistometer. In all cases, these high heating rates led to higher inactivation than expected: in the heat exchanger, for all the experiments performed, when the observed inactivation had reached about seven log cycles, the predictions estimated about 1 log cycle of inactivation; in the thermoresistometer these differences between observed and predicted values were even more than 10 times higher, from 4.07 log cycles observed to 0.34 predicted at a flow rate of 70 mL/min and a maximum heating rate of 14.7°C/s. A quantification of the impact of the heating rates on the level of inactivation achieved was established. These results point out the important effect that the heating rate has on the thermal resistance of E. coli, with high heating rates resulting in an additional sensitization to heat and therefore an effective food safety strategy in terms of food processing.

Explicit numerical solutions of a microbial survival model under nonisothermal conditions

Differential equations used to describe the original and modified Geeraerd models were, respectively, simplified into an explicit equation in which the integration of the specific inactivation rate with respect to time was numerically approximated using the Simpson's rule. The explicit numerical solutions were then used to simulate microbial survival curves and fit nonisothermal survival data for identifying model parameters in Microsoft Excel. The results showed that the explicit numerical solutions provided an easy way to accurately simulate microbial survival and estimate model parameters from nonisothermal survival data using the Geeraerd models.

Growth and inactivation of Salmonella enterica and Listeria monocytogenes in broth and validation in ground pork meat during simulated home storage abusive temperature and home pan-frying

Ground pork meat with natural microbiota and inoculated with low initial densities (1-10 or 10-100 CFU/g) of Salmonella enterica or Listeria monocytogenes was stored under abusive temperature at 10°C and thermally treated by a simulated home pan-frying procedure. The growth and inactivation characteristics were also evaluated in broth. In ground pork meat, the population of S. enterica increased by less than one log after 12-days of storage at 10°C, whereas L. monocytogenes increased by 2.3 to 2.8 log units. No unusual intrinsic heat resistance of the pathogens was noted when tested in broth at 60°C although shoulders were observed on the inactivation curves of L. monocytogenes. After growth of S. enterica and L. monocytogenes at 10°C for 5 days to levels of 1.95 log CFU/g and 3.10 log CFU/g, respectively, in ground pork meat, their inactivation in the burger subjected to a simulated home pan-frying was studied. After thermal treatment S. enterica was undetectable but L. monocytogenes was recovered in three out of six of the 25 g burger samples. Overall, the present study shows that data on growth and inactivation of broths are indicative but may underestimate as well as overestimate behavior of pathogens and thus need confirmation in food matrix conditions to assess food safety in reasonably foreseen abusive conditions of storage and usual home pan-frying of meat burgers in Belgium.

Effect of the medium characteristics and the heating and cooling rates on the nonisothermal heat resistance of Bacillus sporothermodurans IC4 spores

In recent years, highly thermo-resistant mesophilic spore-forming bacteria belonging to the species Bacillus sporothermodurans have caused non-sterility problems in industrial sterilization processes. The aim of this research was to evaluate the effect of the heating medium characteristics (pH and buffer/food) on the thermal inactivation of B. sporothermodurans spores when exposed to isothermal and non-isothermal heating and cooling treatments and the suitability of non-linear Weibull and Geeraaerd models to predict the survivors of these thermal treatments. Thermal treatments were carried out in pH 3, 5 and 7 McIlvaine buffer and in a courgette soup. Isothermal survival curves showed shoulders that were accurately characterized by means of both models. A clear effect of the pH of the heating medium was observed, decreasing the D120 value from pH 7 to pH 3 buffer down to one third. Differences in heat resistance were similar, regardless of the model used and were kept at all temperatures tested. The heat resistance in courgette soup was similar to that shown in pH 7 buffer. When the heat resistance values obtained under isothermal conditions were used to predict the survival in the non-isothermical experiments, the predictions estimated the experimental data quite accurately, both with Weibull and Geeraerd models.

Do alternate bacterial indicators and pathogens increase after centrifuge dewatering of anaerobically digested biosolids?

The objectives of this research were to evaluate the potential for sudden increase and/or regrowth of alternative bacteria as either indicators or pathogens after dewatering of thermophilic and mesophilically digested biosolids. The results showed that, in general, for thermophilic processes, even when a statistically significant (p < 0.05) sudden increase and regrowth occurred for fecal coliforms, Escherichia coli, and Enterococci, it did not occur for Salmonella or Aeromonas. For the mesophilic process evaluated, sudden increase did not occur, but regrowth occurred for fecal coliforms, E. coli, Enterococci, and Salmonella. The results have implications for Class A and B biosolids regulations, as both fecal coliform and Salmonella are part of the regulatory limits. The results also suggest that the public health risks are minimal, as a result of the potential sudden increase and regrowth that may occur.

Escherichia coli population heterogeneity: subpopulation dynamics at super-optimal temperatures

In the past years, we explored the dynamics of Escherichia coli K12 at super-optimal temperatures under static and dynamic temperature conditions (Van Derlinden et al. (2008b, 2009, 2010). Disturbed sigmoid growth curves, i.e., a sequence of growth, inactivation and re-growth, were observed, especially close to the maximum growth temperature. Based on the limited set of experiments (i.e., 2 static temperatures and 2 dynamic temperature profiles), the irregular growth curves were explained by postulating the co-existence of two subpopulations: a more resistant, growing population and a temperature sensitive, inactivating population. In this study, the dynamics of the two subpopulations are studied rigorously at 11 constant temperature levels in the region between 45°C and 46°C, with at least five repetitions per temperature. At all temperatures, the total population follows a sequence of growth, inactivation and re-growth. The sequence of different stages in the growth curves can be explained by the two subpopulations. The first growth phase and the inactivation phase reflect the presence of the sensitive subpopulation. Hereafter, the population's dynamics are dominated by the growth of the resistant subpopulation. Generally, cell counts are characterized by a large variability. The dynamics of the two subpopulations are carefully analyzed using a heterogeneous subpopulation type model to study the relation between the kinetic parameters of the two subpopulations and temperature, and to evaluate if the fraction d of resistant cells varies with temperature. Results indicate that the growth rate of the sensitive subpopulation decreases with increasing temperature within the range of 45-46°C. Furthermore, results point in the direction that the duration of this initial growth phase is approximately constant, i.e., around 2h. Possibly, the stress resistance of the cells decreases after a certain period because the metabolism is fully adapted to exponential growth. Also, the growth rate of the resistant subpopulation decreases with increasing temperature. Due to the extreme variability in the cell density data, derivation of accurate relations was not possible. From the heterogeneous model implementations, given the experimental set-up, both a constant d value and a temperature dependent d value seem plausible.