Predictive Microbiology Models Research Articles

Evolution and limitations of primary mathematical models in predictive microbiology

PurposeTraditional microbiological methods to monitor the growth or survival of microbes are very labour‐intensive and rather expensive and the knowledge acquired is not cumulative. Predictive microbiology as an alternative approach has been developed utilizing mathematical models to predict the microbial inactivation, survival or growth during food processing. The purpose of this paper is to review the evolutions and limitations of primary mathematical models in predictive microbiology.Design/methodology/approachPrimary models deal with the variation of microbial populations against time under particular environmental and cultural conditions. According to the behaviour of micro organisms during food processing and storage, primary models can be divided into inactivation/survival models and growth models. Literature is reviewed to assess the performance of these mathematical models.FindingsIn order to predict microbial survival or growth curves, some empirical mathematical models have been used. Most of them have no or little microbiological or physiological basis, which make the interpretation of some model parameters difficult and their performances do not match observed microbiological outcomes. To produce a more accurate mathematical model, more mechanisms are necessary to interpret model parameters with a biological basis.Originality/valueThe paper reviews the evolution and limitations of primary mathematical models, which may help future model development.

Growth, survival and inactivation of Pseudomonas aeruginosa and Staphylococcus aureus strains of various origin in the presence of ethanol

The influence of ethanol on the behaviour of Pseudomonas aeruginosa and Staphylococcus aureus strains was evaluated throughout this study. Strains of different origin were used: collection, clinical and industrial strains were selected. Concentrations of ethanol from 0 to 20% (v/v) were evaluated by automated optical density measurements and by enumeration. When growth conditions were observed, predictive microbiology models were used to assess quantitatively for the ethanol effect. Primary modelling of kinetics was performed to determine growth rate values; secondary modelling was performed on these growth rates as influenced by ethanol, and minimum inhibitory concentrations of ethanol were determined for each strain. Staphylococcus aureus strains were more resistant to ethanol than P. aeruginosa strains, in growth conditions as well as in inactivation conditions. Furthermore, clinical S. aureus strains were more resistant than the collection strain. The method was promising for management of microbiological safety in cosmetics.

A risk assessment approach applied to the growth of Erwinia carotovora in vegetable juice for variable temperature conditions

Risk assessment for food spoilage relies on probabilistic models of microbial growth to predict the likelihood that microbial populations will exceed predefined spoilage levels. To assist in the design and management of industrial food quality systems, predictive microbiological models have to incorporate major risk factors such as the variability in the microbial strain, environment and initial contamination levels. In addition, the application of results measured under laboratory conditions to the less controlled environment of an industrial process usually also involves uncertainty. Extra information regarding this uncertainty must be factored into industrial microbial risk assessment. In this paper, based on our previous analysis of the growth of Erwinia carotovora we show how different factors contribute to the risk of microbial spoilage of vegetable juice and we demonstrate an effective way of including these factors into risk assessment models. The association of risk components with different unavoidable and manageable factors is also valuable for the development of optimal strategies for reducing microbial risk.

Estimation of microbial growth using population measurements subject to a detection limit

In this paper we develop a maximum likelihood estimation procedure for determining the mean and variance in microbial population size from microbial population measurements subject to a detection limit. Existing estimation methods generally set non-detectable measurements equal to the detection limit and are highly biased. Because changes in the mean and variance in the microbial population size are typical in industrial processes we also outline statistical tests for detecting such changes when measurements are subject to a detection limit, which is critical for process control. In an industrial process there may also potentially be variability in the microbial growth rate due to variation in the microbial strain, environment, and food characteristics. Accordingly, we also present a maximum likelihood procedure for estimating microbial growth model parameters and their variance components from microbial population measurements subject to a detection limit. Such information can be used to generate the mean and variance through time of the microbial population size, which is vital for the application of predictive microbiological models to risk assessment and food product shelf-life estimation.

Stochastically Modeling Listeria Monocytogenes Growth in Farm Tank Milk

This article presents a Listeria monocytogenes growth model in milk at the farm bulk tank stage. The main objective was to judge the feasibility and value to risk assessors of introducing a complex model, including a complete thermal model, within a microbial quantitative risk assessment scheme. Predictive microbiology models are used under varying temperature conditions to predict bacterial growth. Input distributions are estimated based on data in the literature, when it is available. If not, reasonable assumptions are made for the considered context. Previously published results based on a Bayesian analysis of growth parameters are used. A Monte Carlo simulation that forecasts bacterial growth is the focus of this study. Three scenarios that take account of the variability and uncertainty of growth parameters are compared. The effect of a sophisticated thermal model taking account of continuous variations in milk temperature was tested by comparison with a simplified model where milk temperature was considered as constant. Limited multiplication of bacteria within the farm bulk tank was modeled. The two principal factors influencing bacterial growth were found to be tank thermostat regulation and bacterial population growth parameters. The dilution phenomenon due to the introduction of new milk was the main factor affecting the final bacterial concentration. The results show that a model that assumes constant environmental conditions at an average temperature should be acceptable for this process. This work may constitute a first step toward exposure assessment for L. monocytogenes in milk. In addition, this partly conceptual work provides guidelines for other risk assessments where continuous variation of a parameter needs to be taken into account.

Influence of stress on individual lag time distributions of Listeria monocytogenes.

The effects of nine common food industry stresses on the times to the turbidity (T(d)) distribution of Listeria monocytogenes were determined. It was established that the main source of the variability of T(d) for stressed cells was the variability of individual lag times. The distributions of T(d) revealed that there was a noticeable difference in response to the stresses encountered by the L. monocytogenes cells. The applied stresses led to significant changes of the shape, the mean, and the variance of the distributions. The variance of T(d) of wells inoculated with single cells issued from a culture in the exponential growth phase was multiplied by at least 6 and up to 355 for wells inoculated with stressed cells. These results suggest stress-induced variability may be important in determining the reliability of predictive microbiological models.

INFLUENCE OF STRESS AND GROWTH CONDITIONS ON INDIVIDUAL LAG TIME DISTRIBUTIONS OF LISTERIA MONOCYTOGENES

ISHS III International Symposium on Applications of Modelling as an Innovative Technology in the Agri-Food Chain; MODEL-IT INFLUENCE OF STRESS AND GROWTH CONDITIONS ON INDIVIDUAL LAG TIME DISTRIBUTIONS OF LISTERIA MONOCYTOGENES

Application of Elements of Microbiological Risk Assessment in the Food Industry Via a Tiered Approach

Food safety control is a matter for concern for all parts of the food supply chain, including governments that develop food safety policy, food industries that must control potential hazards, and consumers who need to keep to the intended use of the food. In the future, food safety policy may be set using the framework of risk analysis, part of which is the development of (inter)national microbiological risk assessment (MRA) studies. MRA studies increase our understanding of the impact of risk management interventions and of the relationships among subsequent parts of food supply chains with regard to the safety of the food when it reaches the consumer. Application of aspects of MRA in the development of new food concepts has potential benefits for the food industry. A tiered approach to applying MRA can best realize these benefits. The tiered MRA approach involves calculation of microbial fate for a product and process design on the basis of experimental data (e.g., monitoring data on prevalence) and predictive microbiological models. Calculations on new product formulations and novel processing technologies provide improved understanding of microbial fate beyond currently known boundaries, which enables identification of new opportunities in process design. The outcome of the tiered approach focuses on developing benchmarks of potential consumer exposure to hazards associated with new products by comparison with exposure associated with products that are already on the market and have a safe history of use. The tiered prototype is a tool to be used by experienced microbiologists as a basis for advice to product developers and can help to make safety assurance for new food concepts transparent to food inspection services.

Concepts and Tools for Predictive Modeling of Microbial Dynamics

Description of microbial cell (population) behavior as influenced by dynamically changing environmental conditions intrinsically needs dynamic mathematical models. In the past, major effort has been put into the modeling of microbial growth and inactivation within a constant environment (static models). In the early 1990s, differential equation models (dynamic models) were introduced in the field of predictive microbiology. Here, we present a general dynamic model-building concept describing microbial evolution under dynamic conditions. Starting from an elementary model building block, the model structure can be gradually complexified to incorporate increasing numbers of influencing factors. Based on two case studies, the fundamentals of both macroscopic (population) and microscopic (individual) modeling approaches are revisited. These illustrations deal with the modeling of (i) microbial lag under variable temperature conditions and (ii) interspecies microbial interactions mediated by lactic acid production (product inhibition). Current and future research trends should address the need for (i) more specific measurements at the cell and/or population level, (ii) measurements under dynamic conditions, and (iii) more comprehensive (mechanistically inspired) model structures. In the context of quantitative microbial risk assessment, complexity of the mathematical model must be kept under control. An important challenge for the future is determination of a satisfactory trade-off between predictive power and manageability of predictive microbiology models.

Supply chains to Singapore

Access to export markets for Australian perishable produce can be affected by several factors, technical and non-technical. A template for resolving some of these issues was developed initially for pork into Singapore and is now being used for other chilled products. The template includes understanding the market requirements for a product and ensuring that supply chains deliver those attributes. The major impact on current product attributes such as food safety and shelf life was found to be temperature control. Strategies to improve cold chain management include application of predictive microbiology models.

Appréciation quantitative de la croissance bactérienne potentielle à partir de profils temps/température: Exemples d'application pour la croissance de Salmonella Typhimurium dans un steak haché

The preservation of food safety requires risk analyses and the implementation of preventive measures, as well as the availability of quantitative criteria to help the decision process. Up until now, the main difficulty was to quantify the microbial growth in foodstuffs. This article presents criteria used to calculate the bacterial growth potential, based on predictive microbiology models. In combination with a microbial expert’s report, these criteria predict growth based on time-temperature profiles of a given food. Two practical examples, including a description of the method of calculation, are also given.

Modeling microbial growth within food safety risk assessments.

Risk estimates for food-borne infection will usually depend heavily on numbers of microorganisms present on the food at the time of consumption. As these data are seldom available directly, attention has turned to predictive microbiology as a means of inferring exposure at consumption. Codex guidelines recommend that microbiological risk assessment should explicitly consider the dynamics of microbiological growth, survival, and death in foods. This article describes predictive models and resources for modeling microbial growth in foods, and their utility and limitations in food safety risk assessment. We also aim to identify tools, data, and knowledge sources, and to provide an understanding of the microbial ecology of foods so that users can recognize model limits, avoid modeling unrealistic scenarios, and thus be able to appreciate the levels of confidence they can have in the outputs of predictive microbiology models. The microbial ecology of foods is complex. Developing reliable risk assessments involving microbial growth in foods will require the skills of both microbial ecologists and mathematical modelers. Simplifying assumptions will need to be made, but because of the potential for apparently small errors in growth rate to translate into very large errors in the estimate of risk, the validity of those assumptions should be carefully assessed. Quantitative estimates of absolute microbial risk within narrow confidence intervals do not yet appear to be possible. Nevertheless, the expression of microbial ecology knowledge in "predictive microbiology" models does allow decision support using the tools of risk assessment.

Estimation of uncertainty and variability in bacterial growth using Bayesian inference. Application to Listeria monocytogenes

The usefulness of risk assessment is limited by its ability or inability to model and evaluate risk uncertainty and variability separately. A key factor of variability and uncertainty in microbial risk assessment could be growth variability between strains and growth model parameter uncertainty. In this paper, we propose a Bayesian procedure for growth parameter estimation which makes it possible to separate these two components by means of hyperparameters. This model incorporates in a single step the logistic equation with delay as a primary growth model and the cardinal temperature equation as a secondary growth model. The estimation of Listeria monocytogenes growth parameters in milk using literature data is proposed as a detailed application. While this model should be applied on genuine data, it is highlighted that the proposed approach may be convenient for estimating the variability and uncertainty of growth parameters separately, using a complete predictive microbiology model.

Assessment of Mathematical Models for Predicting Staphylococcus aureus Growth in Cooked Meat Products

The growth of Staphylococcus aureus in commercially available vacuum-packaged cooked ham, turkey breast meat, and chicken breast meat stored at 2.3, 6.5, 10, 13.5, and 17.7°C was studied. Growth rates observed in these food products were compared with those predicted on the basis of various growth models found in the literature and with those generated by the Pathogen Modeling Program and the Food MicroModel software using graphical and mathematical analysis for performance evaluation. In general, the models studied overestimated the growth of S. aureus. The Dengremont and Membré model most closely matched the observed behavior of S. aureus in ham and chicken breast meat, with bias factors of 1.56 and 1.09, respectively. The Eifert et al. model accurately described the growth of S. aureus in turkey breast meat, with a bias factor of 1.51. The remaining models provided safe predictions of the growth rate of S. aureus, but with poor accuracy. Predictive microbiology models have an immediate practical application in improving microbial food safety and quality and are very useful decision support tools, but they should not be used as the sole determinant of product safety.

Practical application of predictive microbiology software programs to HACCP plans.

We studied how predictive microbiology models could practically be applied to HACCP plans with two predictive software programs that are currently available. The software programs were the Food Micromodel elaborated by the Ministry of Agriculture, Fisheries, and Food, U.K. and the Pathogen Modeling Program of Eastern Regional Research Center, U.S. Department of Agriculture. They successfully provided useful information on (i) the determination of Critical Control Points (CCPs), (ii) the estimation of critical limits at CCPs, (iii) the decision of abused products, (iv) the assessment of equivalence of HACCP plans, and further (v) the development of new products. With the information simulated by the software programs, HACCP teams could make scientific and objective decisions for developing their individual plans. It was also confirmed that microbiological process standards for food processing are indispensable for the application of the predictive programs to HACCP plans.

Predictive modelling of the growth and survival of Listeria in fishery products

Predictive microbiology provides a powerful tool to aid the exposure assessment phase of ‘quantitative microbial risk assessment’. Using predictive models changes in microbial populations on foods between the point of production/harvest and the point of eating can be estimated from changes in product parameters (temperature, storage atmosphere, pH, salt/water activity, etc.). Thus, it is possible to infer exposure to Listeria monocytogenes at the time of consumption from the initial microbiological condition of the food and its history from production to consumption. Predictive microbiology models have immediate practical application to improve microbial food safety and quality, and are leading to development of a quantitative understanding of the microbial ecology of foods. While models are very useful decision-support tools it must be remembered that models are, at best, only a simplified representation of reality. As such, application of model predictions should be tempered by previous experience, and used with cognisance of other microbial ecology principles that may not be included in the model. Nonetheless, it is concluded that predictive models, successfully validated in agreement with defined performance criteria, will be an essential element of exposure assessment within formal quantitative risk assessment. Sources of data and models relevant to assessment of the human health risk of L. monocytogenes in seafoods are identified. Limitations of the current generation of predictive microbiology models are also discussed. These limitations, and their consequences, must be recognised and overtly considered so that the risk assessment process remains transparent. Furthermore, there is a need to characterise and incorporate into models the extent of variability in microbial responses. The integration of models for microbial growth, growth limits or inactivation into models that can predict both increases and decreases in microbial populations over time will also improve the utility of predictive models for exposure assessment. All of these issues are the subject of ongoing research.

Adding new factors to predictive models: the effect on the risk of extrapolation

Two aspects of the addition of new environmental factors to predictive microbiology models are discussed. The concept of risk of extrapolation is introduced to characterize the probability that a prediction is outside the model interpolation region. For an empirical model, the interpolation region is defined by the data which are used to estimate the parameters of the model. It is shown that the risk of extrapolation can become unexpectedly high during extending a model to describe the effect of newer factors, if the extension is supported by insufficient data. A convenient method of extending predictive models is also presented to accommodate observations on the effect of additional environmental factors. New factors can be added to a basic common model, in such a way that the basic model will be a special case of the extended models. Conditions under which this approach is useful are discussed. Published data are used to illustrate both points.

Safety evaluation of sous vide-processed products with respect to nonproteolytic Clostridium botulinum by use of challenge studies and predictive microbiological models.

Sixteen different types of sous vide-processed products were evaluated for safety with respect to nonproteolytic group II Clostridium botulinum by using challenge tests with low (2. 0-log-CFU/kg) and high (5.3-log-CFU/kg) inocula and two currently available predictive microbiological models, Food MicroModel (FMM) and Pathogen Modeling Program (PMP). After thermal processing, the products were stored at 4 and 8 degrees C and examined for the presence of botulinal spores and neurotoxin on the sell-by date and 7 days after the sell-by date. Most of the thermal processes were found to be inadequate for eliminating spores, even in low-inoculum samples. Only 2 of the 16 products were found to be negative for botulinal spores and neurotoxin at both sampling times. Two products at the high inoculum level showed toxigenesis during storage at 8 degrees C, one of them at the sell-by date. The predictions generated by both the FMM thermal death model and the FMM and PMP growth models were found to be inconsistent with the observed results in a majority of the challenges. The inaccurate predictions were caused by the limited number and range of the controlling factors in the models. Based on this study, it was concluded that the safety of sous vide products needs to be carefully evaluated product by product. Time-temperature combinations used in thermal treatments should be reevaluated to increase the efficiency of processing, and the use of additional antibotulinal hurdles, such as biopreservatives, should be assessed.

Variability in Growth Characteristics of Different E. coli O157:H7 Isolates, and its Implications for Predictive Microbiology

In growth experiments 75 clinical isolates of Escherichia coli O157:H7 were studied for the variability in seven growth characteristics: minimum, optimum and maximum growth temperature, minimum and optimum pH, minimum water activity and optimum specific growth rate. With these characteristics, growth can be predicted for any given set of conditions (temperature, acidity and water activity), when the “gamma model” is used as predictive microbiology model. The optimum specific growth rate of the 75 strains, as conceptually defined by the model, had a mean value of 4.71 (ln[emsp4 ](count)/h), with a standard deviation of 0.39. It could not be shown that the mean optimum specific growth rate differs significantly per strain, so the variability found will predominantly be the result of other sources of variation. In contrast, the experimental results suggest that the differences in minimum temperature of growth may be partially strain specific. As variability in growth is crucial for quantitative risk assessment, the results were implemented in the gamma model. Predictions at three sets of growth conditions were compared with predictions of the Pathogen Modeling Program (PMP) (USDA) and some published experimental results. This comparison showed that growth rates higher than those published and outside the 95% confidence interval predicted by the PMP are feasible. Although it needs further development and additional tests, our approach offers a promising strategy to predict the variability in growth.

Application of artificial neural networks as a non-linear modular modeling technique to describe bacterial growth in chilled food products

In many chilled, prepared food products, the effects of temperature, pH and %NaCl on microbial activity interact and this should be taken into account. A grey box model for prediction of microbial growth is developed. The time dependence is modeled by a Gompertz model-based, non-linear differential equation. The influence of temperature, pH and %NaCl reflected in the model parameters is described by using low-complexity, black box artificial neural networks (ANN's). The use of this non-linear modeling technique makes it possible to describe more accurately interacting effects of environmental factors when compared with classical predictive microbiology models. When experimental results on the influence of other environmental factors become available, the ANN models can be extended simply by adding more neurons and/or layers.