Application of predictive modelling techniques in industry: From food design up to risk assessment

Recent advances and challenges in the analysis of natural toxins

Natural toxins (NTs) are poisonous secondary metabolites produced by living organisms developed to ward off predators. Especially low molecular weight NTs (MW<∼1 kDa), such as mycotoxins, phycotoxins, and plant toxins, are considered an important and growing food safety concern. Therefore, accurate risk assessment of food and feed for the presence of NTs is crucial. Currently, the analysis of NTs is predominantly performed with targeted high pressure liquid chromatography tandem mass spectrometry (HPLC-MS/MS) methods. Although these methods are highly sensitive and accurate, they are relatively expensive and time-consuming, while unknown or unexpected NTs will be missed. To overcome this, novel on-site screening methods and non-targeted HPLC high resolution mass spectrometry (HRMS) methods have been developed. On-site screening methods can give non-specialists the possibility for broad "scanning" of potential geographical regions of interest, while also providing sensitive and specific analysis at the point-of-need. Non-targeted chromatography-HRMS methods can detect unexpected as well as unknown NTs and their metabolites in a lab-based approach. The aim of this chapter is to provide an insight in the recent advances, challenges, and perspectives in the field of NTs analysis both from the on-site and the laboratory perspective.

Modeling the influence of propionic acid concentration and pH on the kinetics of Salmonella Typhimurium

Salmonella Typhimurium is a foodborne pathogen often found in the poultry production chain. Antibiotics have been used to reduce S. Typhimurium contamination in poultry aviaries and improve chicken growth. However, antibiotics were banned in several countries. Alternatively, organic acids, such as propionic acid (PA), can control pathogens. This study determined the PA minimum inhibitory concentration (MIC), minimum bactericidal concentration (MBC), and mathematically modeled S. Typhimurium growth/inactivation kinetics under the influence of PA at different pH values (4.5, 5.5, and 6.5) which are within the pH range of the chicken gastrointestinal tract. The PA MIC against S. Typhimurium was pH-dependent, resulting in 5.0, 3.5 and 9.0 mM undissociated PA at pH 4.5, 5.5, and 6.5, respectively. The Baranyi and Roberts and the Weibull model fit growth and inactivation data well, respectively. Secondary models were proposed. The validated model predicted 3-log reduction of S. Typhimurium in 3 h at 68.2 mM of undissociated PA and pH 4.5. The models presented a good capacity to describe the kinetics of S. Typhimurium subjected to PA, representing a useful tool to predict PA antibacterial action depending on the pH.

Modeling strain variability in Campylobacter jejuni thermal inactivation by quantifying the number of strains required

There is a limited understanding of the survival responses of Campylobacter jejuni during thermal processing, which must be investigated for appropriate risk assessment and processing. Therefore, we aimed to elucidate the survival response of C. jejuni and develop a predictive model considering strain variability and uncertainty, which are important for quantitative microbial risk assessment (QMRA) or risk-based processing control measures. We employed the most probable curve (MPC) method to consider the uncertainty in cell concentrations. Further, the multivariate normal (MVN) distribution served as a model for strain variability in bacterial survival behavior. The prediction curves from the MVN successfully captured the parameter variability of the most probable curves of each strain. More than ten reference strains effectively described the strain variability in parameters using the MVN distribution. The findings indicated that, with sufficient strain data, the MVN could estimate the strain variability, including unknown strains. The multi-level model for strain variability can potentially become a specialized tool for QMRA and risk-based processing controls. The combined approach of MPC and MVN provides valuable insights into strain variability, emphasizing the importance of accounting for variability and uncertainty in predictive models for QMRA and risk-based processing control measures.

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.

Development of Dynamic Model for Real-Time Monitoring of Ripening Changes of Kimchi during Distribution

This study describes the development of a method for predicting the ripening of Kimchi according to temperature to provide information on how the ripening of Kimchi changes during distribution. Various Kimchi quality factors were assessed according to temperature and time. The acidity (lactic acid %) was selected as a good freshness index, as it is dependent on temperature and correlates strongly with the sensory quality evaluation. Moreover, it is easy to measure and reproducible in the field. The maximum value of acidity in the stationary phase was observed to increase with the storage temperature. A predictive model was developed using the Baranyi and Roberts and Polynomial models to mathematically predict the acidity. A method using the mean kinetic temperature (MKT) was proposed. The accuracy of the model using the MKT was high. It was confirmed that there is no great variation in the maximum acidity, as MKT does not change much if the temperature changes in the stationary phase where the maximum acidity is constant. This study provides important information about the development of models to predict changes in food quality index under fluctuating temperature environments. The developed kinetic model uniquely treated the quality index at the stationary phase as a function of MKT. The predictions using the food temperature histories could help suppliers and consumers make a reasonable decision on the sales, storage, and consumption of foods. The developed model could be applied to other products such as beef for which the quality index at the stationary phase also changes with temperature histories.

Design of Predictive Tools to Estimate Freshness Index in Farmed Sea Bream (Sparus aurata) Stored in Ice

This research studied sea bream freshness evolution through storage time in ice by determining different quality parameters and sensory profiles. Predictive models for freshness index, storage time, and microbial counts were designed from these data. Physico–chemical parameters were assessed to evaluate the quality of fish; microbial growth was controlled to ensure food safety, and sensory analyses were carried out to characterize quality deterioration. Predictive models were developed and improved with the aim of being used as tools for quality management in the seafood industry. Validation was conducted in order to establish the accuracy of models. There was a good relationship between the physico–chemical and microbiological parameters. Sensory analysis and microbial counts allowed for the establishment of a shelf-life of 10 days, which corresponded to a poor quality (according to the European Community’s system of grading fish for marketing purposes), with a freshness index lower than 50%. Sensory profiles showed that gill and flesh texture were the most vulnerable attributes during storage in ice related to spoilage. The predictive models for the freshness index (%) and ice storage time (h) exhibited an accuracy close to 90% following practical validation.

Differentiation of Vegetative Cells into Spores: a Kinetic Model Applied to Bacillus subtilis

Spore-forming bacteria are natural contaminants of food raw materials, and sporulation can occur in many environments from farm to fork. In order to characterize and to predict spore formation over time, we developed a model that describes both the kinetics of growth and the differentiation of vegetative cells into spores. The model is based on a classical growth model and enables description of the kinetics of sporulation with the addition of three parameters specific to sporulation. Two parameters are related to the probability of each vegetative cell to commit to sporulation and to form a spore, and the last one is related to the time needed to form a spore once the cell is committed to sporulation. The goodness of fit of this growth-sporulation model was assessed using growth-sporulation kinetics at various temperatures in laboratory medium or in whey for Bacillus subtilis, Bacillus cereus, and Bacillus licheniformis The model accurately describes the kinetics in these different conditions, with a mean error lower than 0.78 log₁₀ CFU/ml for the growth and 1.08 log₁₀ CFU/ml for the sporulation. The biological meaning of the parameters was validated with a derivative strain of Bacillus subtilis 168 which produces green fluorescent protein at the initiation of sporulation. This model provides physiological information on the spore formation and on the temporal abilities of vegetative cells to differentiate into spores and reveals the heterogeneity of spore formation during and after growth.IMPORTANCE The growth-sporulation model describes the progressive transition from vegetative cells to spores with sporulation parameters describing the sporulation potential of each vegetative cell. Consequently, the model constitutes an interesting tool to assess the sporulation potential of a bacterial population over time with accurate parameters such as the time needed to obtain one resistant spore and the probability of sporulation. Further, this model can be used to assess these data under various environmental conditions in order to better identify the conditions favorable for sporulation regarding the time to obtain the first spore and/or the concentrations of spores which could be reached during a food process.

Characterization of damage on Listeria innocua surviving to pulsed light: Effect on growth, DNA and proteome

The effect of pulsed light treatment on the lag phase and the maximum specific growth rate of Listeria innocua was determined in culture media at 7 °C. Fluences of 0.175, 0.350 and 0.525 J/cm² were tested. The lag phase of the survivors increased as fluence did, showing significant differences for all the doses; an 8.7-fold increase was observed at 0.525 J/cm². Pulsed light decreased the maximum specific growth rate by 38% at the same fluence. Both parameters were also determined by time-lapse microscopy at 25 °C in survivors to 0.525 J/cm², with an increase of 13-fold of the lag phase and a 45% decrease of the maximum specific growth rate. The higher the fluence, the higher the variability of both parameters was. To characterize pulsed light damage on L. innocua, the formation of dimers on DNA was assessed, and a proteomic study was undertaken. In cells treated with 0.525 J/cm², cyclobutane pyrimidine dimers and pyrimidine (6-4) pyrimidone photoproducts were detected at 5:1 ratio. Pulsed light induced the expression of three proteins, among them the general stress protein Ctc. Furthermore, treated cells showed an up-regulation of proteins related to metabolism of nucleotides and fatty acids, as well as with translation processes, whereas flagellin and some glucose metabolism proteins were down-regulated. Differences in the proteome of the survivors could contribute to explain the mechanisms of adaptation of L. innocua after pulsed light treatment.

Stochastic Individual-Based Modeling of Bacterial Growth and Division Using Flow Cytometry

A realistic description of the variability in bacterial growth and division is critical to produce reliable predictions of safety risks along the food chain. Individual-based modeling of bacteria provides the theoretical framework to deal with this variability, but it requires information about the individual behavior of bacteria inside populations. In this work, we overcome this problem by estimating the individual behavior of bacteria from population statistics obtained with flow cytometry. For this objective, a stochastic individual-based modeling framework is defined based on standard assumptions during division and exponential growth. The unknown single-cell parameters required for running the individual-based modeling simulations, such as cell size growth rate, are estimated from the flow cytometry data. Instead of using directly the individual-based model, we make use of a modified Fokker-Plank equation. This only equation simulates the population statistics in function of the unknown single-cell parameters. We test the validity of the approach by modeling the growth and division of Pediococcus acidilactici within the exponential phase. Estimations reveal the statistics of cell growth and division using only data from flow cytometry at a given time. From the relationship between the mother and daughter volumes, we also predict that P. acidilactici divide into two successive parallel planes.

Modelling the effect of combined antimicrobials: A base model for multiple-hurdles

Combining antimicrobials to reduce microbial growth and to combat the potential impact of antimicrobial resistance is an important subject both in foods and in pharmaceutics. Modelling of combined treatments designed to reduce or eliminate microbial contamination in foods (microbiological predictive modelling) has become commonplace. Two main reference models are used to analyse mixtures: the Bliss Independence and the Loewe reference models (LRM). By using optical density to analyse the growth of Aeromonas hydrophila, Cronobacter sakazakii and Escherichia coli in combined NaCl/NaCl (a mock combination experiment) and combined NaCl/KCl experiments, previous models for combined antimicrobials in foods, based on the Bliss approach, were shown to be inconsistent and that models based on the LRM more applicable. The LRM was shown, however, to be valid only in the specific cases where the concentration exponents of all components in a mixture were identical. This is assured for a mock combination experiment but not for a true mixture. This, essentially, invalidates the LRM as a general reference model. A new model, based on the LRM but allowing for mixed exponents, was used to analyse the combined inhibition data, and concluded that the NaCl/KCl system gave the additive effect expected from literature studies. This study suggests the need to revise current models used to analyse combined effects.

Introducing a novel interaction model structure for the combined effect of temperature and pH on the microbial growth rate

Efficient modelling of the microbial growth rate can be performed by combining the effects of individual conditions in a multiplicative way, known as the gamma concept. However, several studies have illustrated that interactions between different effects should be taken into account at stressing environmental conditions to achieve a more accurate description of the growth rate. In this research, a novel approach for modeling the interactions between the effects of environmental conditions on the microbial growth rate is introduced. As a case study, the effect of temperature and pH on the growth rate of Escherichia coli K12 is modeled, based on a set of computer controlled bioreactor experiments performed under static environmental conditions. The models compared in this case study are the gamma model, the model of Augustin and Carlier (2000), the model of Le Marc et al. (2002) and the novel multiplicative interaction model, developed in this paper. This novel model enables the separate identification of interactions between the effects of two (or more) environmental conditions. The comparison of these models focuses on the accuracy, interpretability and compatibility with efficient modeling approaches. Moreover, for the separate effects of temperature and pH, new cardinal parameter model structures are proposed. The novel interaction model contributes to a generic modeling approach, resulting in predictive models that are (i) accurate, (ii) easily identifiable with a limited work load, (iii) modular, and (iv) biologically interpretable.

Microbial growth parameters obtained from the analysis of time to detection data using a novel rearrangement of the Baranyi-Roberts model

AIMS

To explore the predictions of a novel rearrangement of the Baranyi-Roberts model (BRM) with time to detection data obtained from optical density data of microbial growth.

METHODS AND RESULTS

Growth of Escherichia coli and Salmonella Typhimurium under mild conditions of temperature (25-37°C), salt (0·086, 0·51 and 1·03 mol l(-1)) and pH (6·85-4·5) was examined using optical density. Time to detection (TTD) data were fitted to a model based on a rearrangement of the BRM. Observations showed compatibility with standard viable count studies and produced highly accurate specific growth rates and lag phase durations. At high salt and low pH, however, there was a substantial dependency on the initial inoculum for the observation of visible growth. At 30 and 37°C, with 1·03 mol l(-1) salt, and at pH <5·75, no visible growth was recorded for E. coli at initial inoculum levels below 10(7) CFU ml(-1).

CONCLUSIONS

The rearranged BRM can be used directly with TTD data obtained from optical density measurements.

SIGNIFICANCE AND IMPACT OF THE STUDY

A distinct advantage of the rearranged model is that it allows for a very simple interpretation of easily obtainable data using standard nonlinear regression. The rearranged model gives to TTD data the same modelling capability that the BRM gives to plate count data.

Use of simulation tools to illustrate the effect of data management practices for low and negative plate counts on the estimated parameters of microbial reduction models

In the last 20 years, the use of microbial reduction models has expanded significantly, including inactivation (linear and nonlinear), survival, and transfer models. However, a major constraint for model development is the impossibility to directly quantify the number of viable microorganisms below the limit of detection (LOD) for a given study. Different approaches have been used to manage this challenge, including ignoring negative plate counts, using statistical estimations, or applying data transformations. Our objective was to illustrate and quantify the effect of negative plate count data management approaches on parameter estimation for microbial reduction models. Because it is impossible to obtain accurate plate counts below the LOD, we performed simulated experiments to generate synthetic data for both log-linear and Weibull-type microbial reductions. We then applied five different, previously reported data management practices and fit log-linear and Weibull models to the resulting data. The results indicated a significant effect (α = 0.05) of the data management practices on the estimated model parameters and performance indicators. For example, when the negative plate counts were replaced by the LOD for log-linear data sets, the slope of the subsequent log-linear model was, on average, 22% smaller than for the original data, the resulting model underpredicted lethality by up to 2.0 log, and the Weibull model was erroneously selected as the most likely correct model for those data. The results demonstrate that it is important to explicitly report LODs and related data management protocols, which can significantly affect model results, interpretation, and utility. Ultimately, we recommend using only the positive plate counts to estimate model parameters for microbial reduction curves and avoiding any data value substitutions or transformations when managing negative plate counts to yield the most accurate model parameters.

Filamentous Fungi and Mycotoxins in Cheese: A Review

Important fungi growing on cheese include Penicillium, Aspergillus, Cladosporium, Geotrichum, Mucor, and Trichoderma. For some cheeses, such as Camembert, Roquefort, molds are intentionally added. However, some contaminating or technological fungal species have the potential to produce undesirable metabolites such as mycotoxins. The most hazardous mycotoxins found in cheese, ochratoxin A and aflatoxin M1, are produced by unwanted fungal species either via direct cheese contamination or indirect milk contamination (animal feed contamination), respectively. To date, no human food poisoning cases have been associated with contaminated cheese consumption. However, although some studies state that cheese is an unfavorable matrix for mycotoxin production; these metabolites are actually detected in cheeses at various concentrations. In this context, questions can be raised concerning mycotoxin production in cheese, the biotic and abiotic factors influencing their production, mycotoxin relative toxicity as well as the methods used for detection and quantification. This review emphasizes future challenges that need to be addressed by the scientific community, fungal culture manufacturers, and artisanal and industrial cheese producers.

Development of a time-to-detect growth model for heat-treated Bacillus cereus spores

The microbiological safety and quality of Refrigerated Processed Foods of Extended Durability (REPFEDs) relies on a combination of mild heat treatment and refrigeration, sometimes in combination with other inhibitory agents that are ineffective when used alone. In this context, a predictive model describing the time-to-detect growth (measured by turbidimetry) of psychrotrophic Bacillus cereus spores submitted to various combinations of pH, water activity (aw), heat treatment and storage temperature was developed. As the inoculum was high, the time-to-detect growth was the sum of two times: for a large part of the spore lag time (time before germination and outgrowth) and to a lesser extent of the time to have subsequent vegetative cells growing up to a detectable level. A dataset of 434 combinations (of pH, aw, heat treatment, storage temperature and B. cereus strain), originally collected at Ghent University to build a growth/no-growth model for two Bacillus cereus strains, was re-interpreted as time-to-detect growth values. In the growth area (223 combinations) the time-to-detect growth was set as the longest time where none, or only one, of the 8 replicated wells showed growth. In the no-growth area (211 combinations) the time-to-detect growth was set as longer than the time where the experiment was stopped (60days or more) and analysed as a censored response. The factors of variation were heat-treatment intensity (85°C, 87°C and 90°C in a time range of 1 to 38min), storage temperature (8-30°C), pH (5.2-6.4) and aw (0.973-0.995). Two different strains were analysed. The model had a Gamma multiplicative structure; it was solved by Bayesian inference with informative prior distributions. To be implemented in a decision tool, for instance to calculate the process and formulation conditions required to achieve a given detection time, each Gamma term had some constraints: they had to be monotonous, continuous and algebraically simple mathematical functions (i.e. having analytical solution). Overall, the cumulative effect of various stressful conditions (pasteurisation process, low temperature, and low pH) enables to extend the time-to-detect growth up to 60days or more, whereas the heat-treatment on its own did not have a similar effect. For example, with the most heat resistant strain (strain 1, FF140), for a product at aw0.99, stored at 10°C, heat-treated at 90°C for 10min, a time-to-detect growth of 2days was expected when the pH equalled 6.5. Under the same conditions, if the pH was reduced to 5.8, the time-to-detect growth was predicted to be 11days (and 33days at pH5.5). After a pasteurisation at 90°C for 10min, for a product kept at 10°C, combinations of pH and aw such as pH6.0-aw0.97, pH5.7-aw0.98 or pH5.5-aw0.99 were predicted to extend the time-to-detect growth up to 30days. The developed model is a useful tool for REPFED producers to guarantee the safety of their products towards psychrotrophic B. cereus.

Modelling of growth, growth/no-growth interface and nonthermal inactivation areas of Listeria in foods

Growth, growth boundary and inactivation models have been extensively developed in predictive microbiology and are commonly applied in food research nowadays. Few studies though report the development of models which encompass all three areas together. A tiered modelling approach, based on the Gamma hypothesis, is proposed here to predict the behaviour of Listeria. Datasets of Listeria spp. behaviour in laboratory media, meat, dairy, seafood products and vegetables were collected from literature, unpublished sources and from the databases ComBase and Sym'Previus. The explanatory factors were temperature, pH, water activity, lactic and sorbic acids. For the growth part, 697 growth kinetic datasets were fitted. The estimated growth rates and 2021 additional growth primary datasets were used to fit the secondary growth models. In a second step, the fitted model was used to predict the growth/no-growth boundary. For the inactivation modelling phase, 535 inactivation curves were used. Gamma models with and without interactions between the explanatory factors were used for the growth and boundary models. The correct prediction percentage (predicted growth when growth is observed+predicted inactivation when inactivation is observed) varied from 62% to 81% for the models without interactions, and from 85% to 87% for the models with interactions. The median error for the predicted population size was less than 0.34 log(10)(CFU/mL) for all models. The kinetics of inactivation were fitted with modified Weibull primary models and the estimated bacterial resistance was then modelled as a function of the explanatory factors. The error for the predicted microbial population size was less than 0.71 log(10)(CFU/mL) with a median value of less than 0.21 for all foods. The model enables the quantification of the increase or decrease in the bacterial population for a given formulation or storage condition. It might also be used to optimise a food formulation or storage condition in the case of a targeted increase or decrease of the bacterial population.

Effects of salt, sodium pyrophosphate, and sodium lactate on the probability of growth of Escherichia coli O157:H7 in ground beef

Ground beef products are susceptible to contamination with Escherichia coli O157:H7. The objective of this study was to examine the effect of salt, sodium pyrophosphate (SPP), and sodium lactate on the probability of growth of E. coli O157:H7 in ground beef under a temperature abuse condition. Ground beef containing 0 to 2.25% salt, 0 to 0.5% SPP, and 0 to 3% lactate was inoculated with a four-strain mixture of E. coli O157:H7, vacuum packaged, and stored at 10°C for 15 days. A total of 25 combinations of the three additives, each with 20 samples, were tested. A logistic regression was used to model the probability of growth of E. coli O157:H7 (with a 1.0-log CFU/g increase during storage) as a function of salt, SPP, and lactate. The resultant probability model indicated that lactate at higher concentrations decreased the probability of growth of E. coli O157:H7 in ground beef, and the effect was more pronounced at higher salt concentrations. At salt concentrations below 1.3%, the increase of SPP concentration marginally increased the growth probabilities of E. coli O157:H7. The model illustrated the effect of salt, SPP, and lactate on the growth probabilities and growth or no-growth behavior of E. coli O157:H7 in ground beef and can be used to improve the microbial food safety of ground beef products.

Development and validation of an extensive growth and growth boundary model for Listeria monocytogenes in lightly preserved and ready-to-eat shrimp

An existing cardinal parameter growth and growth boundary model for Listeria monocytogenes (O. Mejlholm and P. Dalgaard, J. Food Prot. 70:70-84 and 2485-2497, 2007) was expanded with terms for the effects of acetic, benzoic, citric, and sorbic acids to include a total of 12 environmental parameters and their interactive effects. The new model predicted growth rates (micro(max) values) of L. monocytogenes accurately with bias and accuracy factors of 1.0 and 1.5, respectively, for 16 batches of brined shrimp with benzoic, citric, and sorbic acids. Corresponding values of 0.9 and 1.2, respectively, were obtained for five batches of brined shrimp with acetic and lactic acids. Growth and no-growth responses of L. monocytogenes were also appropriately predicted with 88% correct prediction for 26 experiments with brined shrimp. The new model performed better than existing L. monocytogenes models with a comparable degree of complexity. The high number of environmental parameters, including six organic acids (acetic acid, benzoic acid, citric acid, diacetate, lactic acid, and sorbic acid), allows the new model to predict the effect of substituting one set of preserving parameters for another. The new model also allowed the distance between the growth boundary and specific product characteristics to be quantified by a psi value. This can be of practical importance in the development or reformulation of seafood with preserving parameters that prevent growth of L. monocytogenes and take variability in product characteristics into account.