Development and validation of a mathematical model to describe the growth of Pseudomonas spp. in raw poultry stored under aerobic conditions

Poultry meat spoils quickly unless it is processed, stored, and distributed under refrigerated conditions. Research has shown that the microbial spoilage rate is predominantly controlled by temperature and the spoilage flora of refrigerated, aerobically-stored poultry meat is generally dominated by Pseudomonas spp.

The objective of our study was to develop and validate a mathematical model that predicts the growth of Pseudomonas in raw poultry stored under aerobic conditions over a variety of temperatures.

Thirty-seven Pseudomonas growth rates were extracted from 6 previously published studies. Objectives, methods and data presentation formats varied widely among the studies, but all the studies used either naturally contaminated meat or poultry or Pseudomonas isolated from meat or poultry grown in laboratory media. These extracted growth rates were used to develop a model relating growth rate of Pseudomonas to storage or incubation temperature. A square-root equation [Ratkowsky, D.A., Olley, J., McMeekin, T.A., and Ball, A., 1982. Relationship between temperature and growth rate of bacterial cultures. J. Appl. Bacteriol. 149, 1–5.] was used to model the data. Model predictions were then compared to 20 Pseudomonas and 20 total aerobes growth rate measurements collected in our laboratory. The growth rates were derived from more than 600 bacterial concentration measurements on raw poultry at 10 temperatures ranging from 0 to 25 °C. Visual inspection of the data and the indices of bias and accuracy factors proposed by Baranyi et al. [Baranyi, J., Pin, C., and Ross, T., 1999. Validating and comparing predictive models. Int. J. Food Micro. 48, 159–166.] were used to analyze the performance of the model.

The experimental data for Pseudomonas showed a 4.8% discrepancy with the predictions and a bias of + 3.6%. Percent discrepancies show close agreement between model predictions and observations, and the positive bias factor demonstrates that the proposed model over-predicts growth rate, thus, can be considered fail-safe. Both Pseudomonas spp. as well as total aerobes may be considered good indicators of poultry spoilage.

A properly constructed and validated model for Pseudomonas growth under aerobic conditions can provide a fast and cost-effective alternative to traditional microbiological techniques to estimate the effects of storage temperature on product shelf-life. The model developed here may be used to determine the effect of both initial Pseudomonas concentration and storage temperature on shelf-life of poultry meat under aerobic storage conditions over temperatures from 0 to 25 °C.     

Shelf life modelling of frozen shrimp at variable temperature conditions

The objective of this study was to investigate the effect of variable storage conditions on shelf life and quality characteristics of frozen shrimp. Colour change measured both instrumentally and visually was modelled by apparent zero order equations and showed high dependence on temperature. TVB-N and TMA values increased with storage time and were modelled with apparent first order equations. Taste and overall acceptability scores of frozen shrimp had high correlation with TVB-N and TMA values. The temperature dependence of quality deterioration was adequately modelled by the Arrhenius equation and activation energy ranged from 118 to 156 kJ/mol for the different indices measured. The developed models were validated in fluctuating time-temperature conditions in order to establish their applicability in the real cold chain.     

Dynamic model for predicting growth of Salmonella spp. in ground sterile pork

A predictive model for Salmonella spp. growth in ground pork was developed and validated using kinetic growth data. Salmonella spp. kinetic growth data in ground pork were collected at several isothermal conditions (between 10 and 45 °C) and Baranyi model was fitted to describe the growth at each temperature, separately. The maximum growth rates (μ_max) estimated from the Baranyi model were modeled as a function of temperature using a modified Ratkowsky equation. To estimate bacterial growth under dynamic temperature conditions, the differential form of the Baranyi model, in combination with the modified Ratkowsky equation for rate constants, was solved numerically using fourth order Runge-Kutta method. The dynamic model was validated using five different dynamic temperature profiles (linear cooling, exponential cooling, linear heating, exponential heating, and sinusoidal). Performance measures, root mean squared error, accuracy factor, and bias factor were used to evaluate the model performance, and were observed to be satisfactory. The dynamic model can estimate the growth of Salmonella spp. in pork within a 0.5 log accuracy under both linear and exponential cooling profiles, although the model may overestimate or underestimate at some data points, which were generally < 1 log. Under sinusoidal temperature profiles, the estimates from the dynamic model were also within 0.5 log of the observed values. However, underestimation could occur if the bacteria were exposed to temperatures below the minimum growth temperature of Salmonella spp., since low temperature conditions could alter the cell physiology. To obtain an accurate estimate of Salmonella spp. growth using the models reported in this work, it is suggested that the models be used at temperatures above 7 °C, the minimum growth temperature for Salmonella spp. in pork.     

Kinetic modelling of vitamin C loss in frozen green vegetables under variable storage conditions

A systematic kinetic study of l-ascorbic acid loss of four green vegetables was conducted in the temperature range of freezing storage. The temperature-dependence of vitamin C loss in the −3 to −20 °C range was adequately modelled by the Arrhenius equation and activation energy ranged from 98 to 112 kJ/mol for the four frozen green vegetables. The developed models were validated in fluctuating time–temperature conditions, in order to establish their applicability in the real marketing path of the commercial products. Based on the models, the nutritional level can be estimated, at any point of the freezing chain, when the full time–temperature history is available. Comparison among different green vegetables showed that the type of plant tissue significantly affects the rate of vitamin C loss. Frozen spinach was found to be the most susceptible to vitamin C degradation, peas and green beans demonstrated a moderate retention, whereas okra exhibited a substantially lower loss rate.     

A comparison of three modelling approaches for quantitative risk assessment using the case study of Salmonella spp. in poultry meat

A comprehensive review of both the scientific literature and industry practices was undertaken to identify and quantify all sources of contamination throughout the entire poultry meat production chain by Salmonella spp. This information was used to develop a quantitative risk assessment (QRA) model for Salmonella in the production chain from the breeder farm to the chilled carcass. This was subsequently used as the basis on which to compare the merits of three approaches to QRA modelling in such systems. The original model used a Bayesian Network (BN). The second method was a Markov chain Monte Carlo (MCMC) approach, a numerical Bayesian technique which retained a similar network structure but allowed further development, such as the separation of variability and uncertainty. The third method was a more detailed simulation model. The BN responds immediately to changes, such as entering evidence, because it does not use simulation and can propagate information from any point in the network to all others by Bayesian inference. However, it requires all the variables to be discrete, which introduces errors if continuous variables have to be discretized. These errors can accumulate. The MCMC approach does not require discrete variables while retaining some of the properties of the BN model, such as the ability to draw inferences from evidence. Finally, the simulation offers greater flexibility, such as consideration of the individual carcass, but may be more complex to implement as a result and sacrifices the ability to propagate evidence.     

Prevalence of Campylobacter spp. in poultry and poultry meat in Germany

Of 509 samples from poultry flocks, 209 isolates (41.1%) were Campylobacter positive. The number of positive cases in broiler carcasses was 45.9%. Of 52 pheasants investigated, 25.9% were Campylobacter positive. Campylobacter jejuni was isolated from 86 (42.0%) poultry flock samples, 47 (43%) broiler samples and 15 (28%) wild pheasant samples. C. coli was found at a rate of 1.2% in poultry flocks, 13% in broilers and 21% in pheasants.     

Mathematical modelling of oxygen transport-limited follicle growth

Mathematical modelling was used to investigate oxygen transport in the developing ovarian follicle. In contrast to previous findings, the results show that oxygen can reach the oocyte in large preantral follicles. This is largely due to the inclusion of fluid voidage in the model and improved estimates of oxygen diffusion coefficients through the granulosa. The results also demonstrate that preantral follicles will eventually reach a size beyond which further growth will result in the follicle becoming increasingly anoxic. The predicted size range at which this occurs is consistent with the size range at which antrum formation is observed in many mammals. This suggests that the antrum formation stage of follicular growth may be pivotal to the further development and ultimate fate of the follicle, and that antrum formation itself may represent a mechanism by which the follicle can overcome oxygen limitations. This was supported through extension of the model to the antral follicle, which showed that antrum formation can provide a way in which the follicle can continue to grow and yet avoid becoming hypoxic. The results of the model were consistent with observed follicle development.     

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.     

Stochastic modelling of the growth of a microbial population under changing temperature regimes

The application of models of microbial growth to the design of food safety systems requires consideration of the effect of arbitrary changes in external variables on growth of bacteria. In particular, the effect of changes in external variables, such as temperature, on the probability that the microbial population size will not exceed acceptable levels at a given time needs to be predicted. This paper presents a method of calculating the time-dependent probability distribution of the microbial population size under arbitrary changes of temperature through time. To illustrate this method, the effect of a sudden temporary increase in temperature on the evolution of the probability distribution of Lactobacillus plantarum population size is presented. The effect of this change in temperature on the time taken for the population to reach a critical size, with a given probability, is also calculated and the application of this calculation to the design of HACCP protocols is discussed.     

Occurrence of Campylobacter spp. in poultry and poultry products for sale on the Polish retail market

In 2007 and 2008, a monitoring study was carried out in Poland to examine the occurrence of thermotolerant Campylobacter spp. in raw and cooked chicken products available on the retail market. A total of 912 samples were tested: 443 samples of raw chicken meat, 146 samples of giblets, and 323 ready-to-eat poultry products (150 samples of spit-roasted chicken, 56 samples of smoked chicken, and 117 samples of paté and cold meats). A high level of contamination of raw chicken meat (51.7% of samples) and chicken giblets (47.3% of samples) was detected. However, thermotolerant Campylobacter spp. were found in only 1.2% of the ready-to-eat poultry products.     

Development of a predictive program for microbial growth under various temperature conditions

A predictive program for microbial growth under various temperature conditions was developed with a mathematical model. The model was a new logistic model recently developed by us. The program predicts Escherichia coli growth in broth, Staphylococcus aureus growth and its enterotoxin production in milk, and Vibrio parahaemolyticus growth in broth at various temperature patterns. The program, which was built with Microsoft Excel (Visual Basic Application), is user-friendly; users can easily input the temperature history of a test food and obtain the prediction instantly on the computer screen. The predicted growth and toxin production can be important indices to determine whether a food is microbiologically safe or not. This program should be a useful tool to confirm the microbial safety of commercial foods.     

Mathematical modelling of the growth rate and lag time for Listeria monocytogenes

Growth data for Listeria monocytogenes were collected from the literature and a global model built with existing secondary models describing independently the effects of environmental factors on the growth rate and lag time was based on these data. The growth rates calculated with this model were consistent with the published ones but the fit was poor near the limits of growth of the micro-organism. The model was also less accurate to describe the lag time. It seems then that reliable predictions of the growth rate of L. monocytogenes could be obtained in a wide range of growth conditions, but models should take into account interactions between environmental factors. Furthermore, it is necessary to better model the lag phase duration and particularly to model the effect of the history of the inoculum on the subsequent lag time.     

Growth potential of Salmonella spp. and Listeria monocytogenes in nine types of ready-to-eat vegetables stored at variable temperature conditions during shelf-life

Growth potential (δ) is defined as the difference between the population of a microorganism at the end of shelf-life of specific food and its initial population. The determination of δ of Salmonella and Listeria monocytogenes in RTE vegetables can be very useful to determine likely threats to food safety. However, little is known on the behavior of these microorganisms in several RTE vegetables. Therefore, the aim of this study was to determine the δ of both pathogens in nine different types of RTE vegetables (escarole, collard green, spinach, watercress, arugula, grated carrot, green salad, and mix for yakisoba) stored at refrigeration (7°C) and abuse temperature (15°C). The population of aerobic microorganisms and lactic acid bacteria, including those showing antimicrobial activity has been also determined. Results indicated that L. monocytogenes was able to grow (δ≥0.5 log(10)) in more storage conditions and vegetables than Salmonella. Both microorganisms were inhibited in carrots, although a more pronounced effect has been observed against L. monocytogenes. The highest δ values were obtained when the RTE vegetables were stored 15°C/6days in collard greens (δ=3.3) and arugula (δ=3.2) (L. monocytogenes) and arugula (δ=4.1) and escarole (δ=2.8) (Salmonella). In most vegetables and storage conditions studied, the counts of total aerobic microorganisms raised significantly independent of the temperature of storage (p<0.05). Counts of lactic acid bacteria were higher in vegetables partially or fully stored at abuse temperature with recovery of isolates showing antimicrobial activity. In conclusion, the results of this study show that Salmonella and L. monocytogenes may grow and reach high populations in RTE vegetables depending on storage conditions and the definition of effective intervention strategies are needed to control their growth in these products.     

The introduction of Arcobacter spp. in poultry slaughterhouses

Despite the presence high levels of Arcobacter spp. on chicken carcasses, the source of arcobacter contamination in slaughterhouses still remains unclear. It has been hypothesised in the literature that Arcobacter species that contaminate carcasses originate in in-plant slaughterhouses and/or supply water. The present study aimed to determine the source of Arcobacter contamination in two poultry slaughterhouses in The Netherlands. Carcasses and intestinal tracts from 3 hen flocks and 2 broiler flocks were collected. Water draining off carcasses during processing in 2 slaughterhouses and supply water in one slaughterhouse were also taken. For one flock, cloacal swabs and faecal samples were taken on the farm before slaughtering. ERIC-PCR was applied to study the genetic diversity and relationship among the isolates. No Arcobacter spp. were found in the supply water but on almost all of the sampled carcasses and in carcass-draining-off water arcobacters were identified. Arcobacter spp. were detected in the gut systems of chickens, ranging from 20% to 85% in hens and 3.3% and 51% in broilers. Similar ERIC-PCR genotypes were detected in gut contents as well as on carcasses from the same flock. The present study demonstrated that Arcobacter spp. can be detected in chicken intestines at slaughter and could be brought in this way into slaughterhouses where the bacteria contaminate carcasses during processing.     

Mathematical modelling of microbial growth in ground beef from Argentina. Effect of lactic acid addition, temperature and packaging film

The effects of: (i) storage temperature (0, 4 and 10°C), (ii) gaseous permeability of the packaging film (polyethylene and EVA SARAN EVA for vacuum packaging), and (iii) natural beef pH (5.6, 5.8 and 6.1) on the growth of different bacteria isolated from beef muscle were examined. The bacteria were Klebsiella, Pseudomonas sp. and Escherichia coli. Microbial growth was modelled using Gompertz and linear equations. The effects of temperature on microbial growth rate (μ) and on lag phase duration were modelled using an Arrhenius type equation. In polyethylene, E. coli was the microorganism, that showed the highest μ values and also the greatest effect of pH on μ, especially in samples stored at 4 and 10°C. In the case of Klebsiella sp., neither pH nor temperature had marked effects on μ and on LPD. In ESE film, μ of all the microorganisms were less affected by pH and temperature than in polyethylene. In ESE film E. coli showed the highest effect of pH on μ, at 4 and 10°C. LPD increased significantly with respect to the values in polyethylene, with Klebsiella sp., showing the highest values of LPD, followed by E. coli. Experiments in ground beef with added lactic acid producing a decrease of the original muscle pH from 6.1 to 5.6 showed that the kinetic parameters of the microbial flora did not differ significantly from those of beef samples in which the original pH was 5.6.     

Quantifying the robustness of a broth-based model for predicting Listeria monocytogenes growth in meat and poultry products

Given the importance of Listeria monocytogenes as a risk factor in meat and poultry products, there is a need to evaluate the relative robustness of predictive growth models applied to meat products. The U.S. Department of Agriculture-Agricultural Research Service Pathogen Modeling Program is a tool widely used by the food industry to estimate pathogen growth, survival, and inactivation in food. However, the robustness of the Pathogen Modeling Program broth-based L. monocytogenes growth model in meat and poultry application has not, to our knowledge, been specifically evaluated. In the present study, this model was evaluated against independent data in terms of predicted microbial counts and covered a range of conditions inside and outside the original model domain. The robustness index was calculated as the ratio of the standard error of prediction (root mean square error of the model against an independent data set not used to create the model) to the standard error of calibration (root mean square error of the model against the data set used to create the model). Inside the calibration domain of the Pathogen Modeling Program, the best robustness index for application to meat products was 0.37; the worst was 3.96. Outside the domain, the best robustness index was 0.40, and the worst was 1.22. Product type influenced the robustness index values (P < 0.01). In general, the results indicated that broth-based predictive models should be validated against independent data in the domain of interest; otherwise, significant predictive errors can occur.     

A procedure for mathematical modelling the production of a metabolic marker of Clostridium sporogenes grown under variable nutritional and environmental conditions

This paper describes, in considerable detail, how a mechanistic mathematical model can be constructed to express the activity of an organism of importance to food microbiology. In this demonstration model, a metabolic marker of Clostridium sporogenes (acetic acid production) was the response variable and the environmental variables were medium composition, incubation time and incubation temperature. To construct a mechanistic model, mechanical precautions were observed to minimize experimental and machine errors, and the physiology of the organism is discussed. If those precautions were not observed and the physiology not understood, the result would have been an exercise in curve fitting. The statistical and mathematical procedures used are readily available from commercial sources, and the final equation is simple enough to be programmed into a hand-held calculator. Suggestions were made for the exploitation of this approach to other problems in food microbiology.     

基于假单胞菌生长模型预测冷却牛肉的货架期

假单胞菌（Pseudomonas spp.）的生长繁殖是影响冷却牛肉货架期的重要因素。为确定假单胞菌为冷却牛肉的特定腐败菌并建立其货架期预测模型,将屠宰后的冷却牛肉4 ℃贮藏,测定了假单胞菌数量与菌落总数、挥发性氨基氮（TVBN）值、颜色明度值（L*）及感官评定分值等品质指标,并确定了冷却牛肉的假单胞菌腐败限控量。将冷却牛肉分别置于0 ℃、5 ℃、10 ℃、15 ℃、20 ℃和25 ℃条件下进行假单胞菌计数,建立Gompertz方程的初级生长模型和二级模型,并进行了模型的验证,建立了货架期预测模型。研究表明,Gompertz预测模型能有效预测4～25 ℃条件下假单胞菌在冷却牛肉中的生长情况,在0 ℃、5 ℃和10 ℃温度条件下,对牛肉货架期进行验证,与实际货架期相比偏差＜1 d,表明货架期预测模型适用。     

Predictive modelling of growth and enzyme production and activity by a cocktail of Pseudomonas spp., Shewanella putrefaciens and Acinetobacter sp

The possibility was examined of developing a predictive model that combined microbial growth (increase in cellular number) with extracellular lipolytic and proteolytic enzyme activity of a cocktail of four strains of Pseudomonas spp. and one strain each of Acinetobacter sp. and Shewanella putrefaciens. Environmental conditions within the following matrix of conditions were examined: temperature 2-20 degrees C, pH value 4.0-7.5 and water activity (a(w)) 0.95-0.995 and a model was constructed, which predicted growth based on increase in cell number. Data on lipase production and protease activity were generated and will be available as a database, but no function could be identified, which was a good fit to these data, since most enzymatic production and activity occurred, as expected, during transition from exponential to stationary phase. Even at lower cell numbers, in more unfavourable conditions, hydrolysing effects were detectable, which made it difficult to construct a model combining both microbiological and enzymatic data.