Quality and shelf-life prediction for retail fresh hake (Merluccius merluccius)

Optimal experimental design (OED) for the growth rate of microbial populations. Are they really more "optimal" than uniform designs?

Secondary growth models from predictive microbiology can describe how the growth rate of microbial populations varies with environmental conditions. Because these models are built based on time and resource consuming experiments, model-based Optimal Experimental Design (OED) can be of interest to reduce the experimental load. In this study, we identify optimal experimental designs for two common models (full Ratkowsky and Cardinal Parameters Model (CPM)) for a different number of experiments (10-30). Calculations are also done fixing one or more model parameters, observing that this decision strongly affects the layout of the OED. Using in silico experiments, we conclude that OEDs are more informative than conventional (equidistant) designs with the same number of experiments. However, OEDs cluster the experiments near the growth limits (Xmin and Xmax) resulting in impractical designs with aggregated experimental runs ~10 times longer than conventional designs. To mitigate this, we propose a novel optimality criterion (i.e., the objective function) that accounts for the aggregated time. The novel criterion provides a reduction in parameter uncertainty with respect to the conventional design, without an increase in the experimental load. These results underline that an OED is only based on information theory (Fisher information), so the results can be impractical when actual experimental limitations are considered. The study also emphasizes that most OED schemes identify where to measure, but do not give an indication on how many experiments should be made. In this sense, numerical simulations can estimate the parameter uncertainty that would be obtained for a particular experimental design (OED or not). These results and methodologies (available in Open Code) can guide the design of future experiments for the development of secondary growth models.

Quality and Shelf-Life Evaluation of Fresh Beef Stored in Smart Packaging

Beef is a perishable food product susceptible to deterioration due to microbial growth. Therefore, this study aimed to ascertain how active and intelligent packaging performs by tracking the change in the quality of fresh beef stored at low temperatures. The intelligent packaging method employed indicators with solutions of Bromo Phenol Blue (BPB) and Phenol Red (PR) to monitor the change in beef quality. Additionally, active packaging used garlic extract with various concentrations at 0%, 15%, and 20% to maintain the quality of beef packaged at 10 °C temperatures. The findings illustrated that a packaging indicator label can be implemented to monitor the change in the quality of fresh beef stored at 10 °C temperatures. This was signified by a change in the indicator color from dark yellow to orange and red, fading to purple. Meanwhile, observations on active packaging demonstrated that 15% and 20% of garlic extract were the most effective approaches for preserving beef quality. The correlation level of indicator label color analysis and the effectiveness of active packaging with all beef spoilage metrics demonstrated a positive correlation in preserving quality and identifying the degree of beef damage. Therefore, these active and intelligent packaging indicators can be applied to monitor and retain the quality of packaged beef.

Microbial diversity of meat products under spoilage and its controlling approaches

Meat spoilage (MS) is a complex microbial ecological process involving multiple specific microbial interactions. MS is detrimental to people's health and leads to the waste of meat products which caused huge losses during production, storage, transportation, and marketing. A thorough understanding of microorganisms related to MS and their controlling approaches is a necessary prerequisite for delaying the occurrence of MS and developing new methods and strategies for meat product preservation. This mini-review summarizes the diversity of spoilage microorganisms in livestock, poultry, and fish meat, and the approaches to inhibit MS. This would facilitate the targeted development of technologies against MS, to extend meat's shelf life, and effectively diminish food waste and economic losses.

Assessment and Prediction of Fish Freshness Using Mathematical Modelling: A Review

Fish freshness can be considered as the combination of different nutritional and organoleptic attributes that rapidly deteriorate after fish capture, i.e., during processing (cutting, gutting, packaging), storage, transport, distribution, and retail. The rate at which this degradation occurs is affected by several stress variables such as temperature, water activity, or pH, among others. The food industry is aware that fish freshness is a key feature influencing consumers’ willingness to pay for the product. Therefore, tools that allow rapid and reliable assessment and prediction of the attributes related to freshness are gaining relevance. The main objective of this work is to provide a comprehensive review of the mathematical models used to describe and predict the changes in the key quality indicators in fresh fish and shellfish during storage. The work also briefly describes such indicators, discusses the most relevant stress factors affecting the quality of fresh fish, and presents a bibliometric analysis of the results obtained from a systematic literature search on the subject.

Multilevel modelling as a tool to include variability and uncertainty in quantitative microbiology and risk assessment. Thermal inactivation of Listeria monocytogenes as proof of concept

Variability is inherent in biology and also substantial for microbial populations. In the context of food safety risk assessment, it refers to differences in the response of different bacterial strains (between-strain variability) and different cells (within-strain variability) to the same condition (e.g. inactivation treatment). However, its quantification based on empirical observations and its incorporation in predictive models is a challenge for both experimental design and (statistical) analysis. In this article we propose the use of multilevel models to quantify (different levels of) variability and uncertainty and include them in the predictions. As proof of concept, we analyse the microbial inactivation of Listeria monocytogenes to thermal treatments including different levels of variability (between-strain and within-strain) and uncertainty. The relationship between the microbial count and time was expressed using a (non-linear) Weibullian model. Moreover, we defined stochastic hypotheses to describe the different types of variation at the level of the kinetic parameters, as well as in the observations (microbial counts). The model parameters (kinetic parameters and variances) are estimated using Bayesian statistics. The multilevel approach was compared against an analogous, single-level model. The multilevel methodology shrinks extreme parameter estimates towards the mean according to uncertainty, thus mitigating overfitting. In addition, this approach enables to easily incorporate different levels of variation (between-strain and/or within-strain variability and/or uncertainty) in the predictions. On the other hand, multilevel (Bayesian) models are more complex to define, implement, analyse and communicate than single-level models. Nevertheless, their ability to incorporate different sources of variability in predictions make them very suitable for Quantitative Microbial Risk Assessment.

Effect of immersion ohmic heating on thawing rate and properties of frozen tuna fish

In the present study, the application of immersion ohmic heating was examined to improve thawing of frozen tuna fish cubes. The experimental tuna cubes (3 × 3 × 3 cm³) were thawed under ohmic heating subjected to three different voltages (40, 50, and 60 V) with three different concentrations (0.3, 0.4, and 0.5% w/v) of brine solution. The parameters associated with the quality of tuna, such as thawing time, thawing rate, thawing loss, cooking and total losses, centrifugal loss, lipid oxidation, texture, and color, were investigated during ohmic heating thawing, and compared with the conventional still air thawing, water thawing at 27 and 40 ℃. The results showed that immersion ohmic thawing significantly decreased the thawing time of frozen tuna fish cubes. Thawing time in ohmic treatment (50 V- 0.3% brine) was 5.95 times shorter than conventional conditions. The lowest thawing and cooking losses were observed at ohmic treatments. In addition, the ohmic treatments (group 1) were evaluated versus conventional methods (group 2) and the results showed that thawing and total losses in group 1 were significantly lower than group 2.

Punica granatum and Citrus spp. Extract Mix Affects Spoilage Microorganisms Growth Rate in Vacuum-Packaged Cooked Sausages Made from Pork Meat, Emmer Wheat (Triticum dicoccum Schübler), Almond (Prunus dulcis Mill.) and Hazelnut (Corylus avellana L.)

Sausage made from pork meat, emmer wheat (Triticum dicoccum Schübler), almond (Prunus dulcis Mill.), and hazelnut (Corylus avellana L.) was integrated with a mix of Punica granatum and Citrus spp. extracts to evaluate the possible effects on the growth and oxidation of spoilage microorganisms. Two concentrations of the mix were added, respectively, during sausage-making, and the final products were compared with a control group, without the extract mix, during storage. The use of the mix, especially at 10 g/1000 g of the whole ingredients, delayed the pH drop and thiobarbituric acid-reactive substances (TBARs) value during storage. Total viable count, lactic acid bacteria and psychrotrophic microbial counts were also affected, as the extract mix lowered the maximum growth rate of the microbial population considered. The sensory analyses revealed an improvement in the shelf-life of 6 and 16 days, respectively, when 5‰ and 10‰ of the mix were used.

Guidelines for the design of (optimal) isothermal inactivation experiments

Kinetic models are nowadays a basic tool to ensure food safety. Most models used in predictive microbiology have model parameters, whose precision is crucial to provide meaningful predictions. Kinetic parameters are usually estimated based on experimental data, where the experimental design can have a great impact on the precision of the estimates. In this sense, Optimal Experiment Design (OED) applies tools from optimization and information theory to identify the most informative experiment under a set of constrains (e.g. mathematical model, number of samples, etc). In this work, we develop a methodology for the design of optimal isothermal inactivation experiments. We consider the two dimensions of the design space (time and temperature), as well as a temperature-dependent maximum duration of the experiment. Functions for its application have been included in the bioOED R package. We identify design patterns that remain optimum regardless of the number of sampling points for three inactivation models (Bigelow, Mafart and Peleg) and three model microorganisms (Escherichia coli, Salmonella Senftenberg and Bacillus coagulans). Samples at extreme temperatures and close to the maximum duration of the experiment are the most informative. Moreover, the Mafart and Peleg models require some samples at intermediate time points due to the non-linearity of the survivor curve. The impact of the reference temperature on the precision of the parameter estimates is also analysed. Based on numerical simulations we recommend fixing it to the mean of the maximum and minimum temperatures used for the experiments. The article ends with a discussion presenting guidelines for the design of isothermal inactivation experiments. They combine these optimum results based on information theory with several practical limitations related to isothermal inactivation experiments. The application of these guidelines would reduce the experimental burden required to characterize thermal inactivation.

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

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

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.

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.

Seafood spoilage microbiota and associated volatile organic compounds at different storage temperatures and packaging conditions

Seafood comprising of both vertebrate and invertebrate aquatic organisms are nutritious, rich in omega-3 fatty acids, essential vitamins, proteins, minerals and form part of healthy diet. However, despite the health and nutritional benefits, seafood is highly perishable. Spoilage of seafood could be as a result of microbial activity, autolysis or chemical oxidation. Microbial activity constitutes more spoilage than others. Spoilage bacteria are commonly Gram negative and produce off odours and flavours in seafood as a result of their metabolic activities. Storage temperature, handling and packaging conditions affect microbial growth and thus the shelf-life of seafood. Due to the complexity of the microbial communities in seafood, culture dependent methods of detection may not be useful, hence the need for culture independent methods are necessary to understand the diversity of microbiota and spoilage process. Similarly, the volatile organic compounds released by spoilage bacteria are not fully understood in some seafood. This review therefore highlights current knowledge and understanding of seafood spoilage microbiota, volatile organic compounds, effects of storage temperature and packaging conditions on quality of seafood.

Toward predictive food process models: A protocol for parameter estimation

Mathematical models, in particular, physics-based models, are essential tools to food product and process design, optimization and control. The success of mathematical models relies on their predictive capabilities. However, describing physical, chemical and biological changes in food processing requires the values of some, typically unknown, parameters. Therefore, parameter estimation from experimental data is critical to achieving desired model predictive properties. This work takes a new look into the parameter estimation (or identification) problem in food process modeling. First, we examine common pitfalls such as lack of identifiability and multimodality. Second, we present the theoretical background of a parameter identification protocol intended to deal with those challenges. And, to finish, we illustrate the performance of the proposed protocol with an example related to the thermal processing of packaged foods.