Bayesian modeling of Clostridium perfringens growth in beef-in-sauce products

Ready-to-eat Meat Plant Characteristics Associated with Food Safety Deficiencies During Regulatory Compliance Audits, Ontario, Canada

Food safety deficiencies in ready-to-eat (RTE) meat processing plants can increase foodborne disease risks. The purpose of this study was to identify common deficiencies and factors related to improved food safety performance in RTE meat plants in Ontario. Routine food safety audit records for licensed provincial free-standing meat processing plants (FSMPs) and abattoirs that process RTE meats were obtained and analyzed in Ontario, Canada, from 2015 to 2019. A Bayesian regression analysis was conducted to examine the association between selected plant characteristics and two outcomes: overall audit rating (pass vs. conditional pass or fail) and individual audit item fail rate. The audit rating was examined in a logistic model, while the audit item fail rate was evaluated in a negative binomial model. The majority (87.7%, n = 800/912) of audits resulted in a pass rating (compared to conditional pass or fail). The mean number of employees per plant, among 200/204 plants with employee data available, was 11.6 (SD = 20.6, range = 1-200). For the logistic regression model, FSMPs were predicted to have a much higher probability of passing audits than abattoirs (32.0% on average, with a 95% credible interval [CI] of 13.8-52.8%). The number of plant employees, water source (municipal vs. private), and types of RTE meat products produced had little to no consistent association with this outcome. The negative binomial model predicted a -0.009 points lower fail rate, on average, for audit items among FSMPs than abattoirs (95% CI: -0.001, -0.018). Meat plants producing jerky had a higher audit item fail rate compared to those that did not produce such products. The other investigated variables had little to no association with this outcome. The results found in this study can support and guide future inspection, audit and outreach efforts to reduce foodborne illness risks associated with RTE meats.

A Bayesian Approach to Describe and Simulate the pH Evolution of Fresh Meat Products Depending on the Preservation Conditions

Measuring the pH of meat products during storage represents an efficient way to monitor microbial spoilage, since pH is often linked to the growth of several spoilage-associated microorganisms under different conditions. The present work aimed to develop a modelling approach to describe and simulate the pH evolution of fresh meat products, depending on the preservation conditions. The measurement of pH on fresh poultry sausages, made with several lactate formulations and packed under three modified atmospheres (MAP), from several industrial production batches, was used as case-study. A hierarchical Bayesian approach was developed to better adjust kinetic models while handling a low number of measurement points. The pH changes were described as a two-phase evolution, with a first decreasing phase followed by a stabilisation phase. This stabilisation likely took place around the 13th day of storage, under all the considered lactate and MAP conditions. The effects of lactate and MAP on pH previously observed were confirmed herein: (i) lactate addition notably slowed down acidification, regardless of the packaging, whereas (ii) the 50%CO₂-50%N₂ MAP accelerated the acidification phase. The Bayesian modelling workflow—and the script—could be used for further model adaptation for the pH of other food products and/or other preservation strategies.

Bayesian Generalized Linear Model for Simulating Bacterial Inactivation/Growth Considering Variability and Uncertainty

Conventional regression analysis using the least-squares method has been applied to describe bacterial behavior logarithmically. However, only the normal distribution is used as the error distribution in the least-squares method, and the variability and uncertainty related to bacterial behavior are not considered. In this paper, we propose Bayesian statistical modeling based on a generalized linear model (GLM) that considers variability and uncertainty while fitting the model to colony count data. We investigated the inactivation kinetic data of Bacillus simplex with an initial cell count of 10⁵ and the growth kinetic data of Listeria monocytogenes with an initial cell count of 10⁴. The residual of the GLM was described using a Poisson distribution for the initial cell number and inactivation process and using a negative binomial distribution for the cell number variation during growth. The model parameters could be obtained considering the uncertainty by Bayesian inference. The Bayesian GLM successfully described the results of over 50 replications of bacterial inactivation with average of initial cell numbers of 10¹, 10², and 10³ and growth with average of initial cell numbers of 10^–1, 10⁰, and 10¹. The accuracy of the developed model revealed that more than 90% of the observed cell numbers except for growth with initial cell numbers of 10¹ were within the 95% prediction interval. In addition, parameter uncertainty could be expressed as an arbitrary probability distribution. The analysis procedures can be consistently applied to the simulation process through fitting. The Bayesian inference method based on the GLM clearly explains the variability and uncertainty in bacterial population behavior, which can serve as useful information for risk assessment related to food borne pathogens.

Application of growth rate from kinetic model to calculate stochastic growth of a bacteria population at low contamination level

Traditional predictive microbiology is not suited for cell growth predictions for low-level contamination, where individual cell heterogeneity becomes apparent. Accordingly, we simulated a stochastic birth process of bacteria population using kinetic parameters. We predicted the variation in behavior of Salmonella enterica serovar Typhimurium cells at low inoculum density. The modeled cells were grown in tryptic soy broth at 25 °C. Kinetic growth parameters were first determined empirically for an initial cell number of 10⁴ cells. Monte Carlo simulation based on the growth kinetics and Poisson distribution for different initial cell numbers predicted the results of 50 replicate growth experiments with the initial cell number of 1, 10, and 64 cells. Indeed, measured behavior of 85% cells fell within the 95% prediction area of the simulation. The calculations link the kinetic and stochastic birth process with Poisson distribution. The developed model can be used to calculate the probability distribution of population size for exposure assessment and for the evaluation of a probability that a pathogen would exceed critical contamination level during food storage.

A survey of a blown pack spoilage produced by Clostridium perfringens in vacuum-packaged wurstel

Three hundred Clostridium strains were isolated from spoiled wurstels and were identified by traditional and molecular methods as Clostridium perfringens. The phenotypic characteristics of the strains were studied. All the strains produced acetic and butyric acids and enterotoxin. C. perfringens grew in the spoiled wurstels because it was present in raw meat (Lot 150) at a level of 3.2 log CFU/g due to an unchecked cooling phase that took 28 h to decrease the temperature of the wurstels from 60 to 9-10 °C, which is the lower limit for C. perfringens growth. During the 28 h of cooling, the concentration of C. perfringens increased to 6.5 CFU/g. It was concluded that its presence and the long cooling time were the main factors responsible for the spoilage. Wurstels intentionally made with contaminated meat (3 log CFU/g) but cooled after cooking for 17 h to 9 °C did not support C. perfringens growth; consequently, these wurstels remained unspoiled. The packages of the spoiled wurstels were blown, and the products were soft (soggy), textureless and had the odour of acetic acid, ethanol and sulfur.

A Systematic Review of Beef Meat Quantitative Microbial Risk Assessment Models

Each year in Europe, meat is associated with 2.3 million foodborne illnesses, with a high contribution from beef meat. Many of these illnesses are attributed to pathogenic bacterial contamination and inadequate operations leading to growth and/or insufficient inactivation occurring along the whole farm-to-fork chain. To ensure consumer health, decision-making processes in food safety rely on Quantitative Microbiological Risk Assessment (QMRA) with many applications in recent decades. The present study aims to conduct a critical analysis of beef QMRAs and to identify future challenges. A systematic approach, the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines, was used to collate beef QMRA models, identify steps of the farm-to-fork chain considered, and analyze inputs and outputs included as well as modelling methods. A total of 2343 articles were collected and 67 were selected. These studies focused mainly on western countries and considered Escherichia coli (EHEC) and Salmonella spp. pathogens. Future challenges were identified and included the need of whole-chain assessments, centralization of data collection processes, and improvement of model interoperability through harmonization. The present analysis can serve as a source of data and information to inform QMRA framework for beef meat and will help the scientific community and food safety authorities to identify specific monitoring and research needs.

Describing Uncertainty in Salmonella Thermal Inactivation Using Bayesian Statistical Modeling

Uncertainty analysis is the process of identifying limitations in scientific knowledge and evaluating their implications for scientific conclusions. In the context of microbial risk assessment, the uncertainty in the predicted microbial behavior can be an important component of the overall uncertainty. Conventional deterministic modeling approaches which provide point estimates of the pathogen's levels cannot quantify the uncertainty around the predictions. The objective of this study was to use Bayesian statistical modeling for describing uncertainty in predicted microbial thermal inactivation of Salmonella enterica Typhimurium DT104. A set of thermal inactivation data in broth with water activity adjusted to 0.75 at 9 different temperature conditions obtained from the ComBase database (www.combase.cc) was used. A log-linear microbial inactivation was used as a primary model while for secondary modeling, a linear relation between the logarithm of inactivation rate and temperature was assumed. For comparison, data were fitted with a two-step and a global Bayesian regression. Posterior distributions of model's parameters were used to predict Salmonella thermal inactivation. The combination of the joint posterior distributions of model's parameters allowed the prediction of cell density over time, total reduction time and inactivation rate as probability distributions at different time and temperature conditions. For example, for the time required to eliminate a Salmonella population of about 107 CFU/ml at 65°C, the model predicted a time distribution with a median of 0.40 min and 5th and 95th percentiles of 0.24 and 0.60 min, respectively. The validation of the model showed that it can describe successfully uncertainty in predicted thermal inactivation with most observed data being within the 95% prediction intervals of the model. The global regression approach resulted in less uncertain predictions compared to the two-step regression. The developed model could be used to quantify uncertainty in thermal inactivation in risk-based processing design as well as in risk assessment studies.

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.

Potential application of quantitative microbiological risk assessment techniques to an aseptic-UHT process in the food industry

Aseptic ultra-high-temperature (UHT)-type processed food products (e.g., milk or soup) are ready to eat products which are consumed extensively globally due to a combination of their comparative high quality and long shelf life, with no cold chain or other preservation requirements. Due to the inherent microbial vulnerability of aseptic-UHT product formulations, the safety and stability-related performance objectives (POs) required at the end of the manufacturing process are the most demanding found in the food industry. The key determinants to achieving sterility, and which also differentiates aseptic-UHT from in-pack sterilised products, are the challenges associated with the processes of aseptic filling and sealing. This is a complex process that has traditionally been run using deterministic or empirical process settings. Quantifying the risk of microbial contamination and recontamination along the aseptic-UHT process, using the scientifically based process quantitative microbial risk assessment (QMRA), offers the possibility to improve on the currently tolerable sterility failure rate (i.e., 1 defect per 10,000 units). In addition, benefits of applying QMRA are (i) to implement process settings in a transparent and scientific manner; (ii) to develop a uniform common structure whatever the production line, leading to a harmonisation of these process settings, and; (iii) to bring elements of a cost-benefit analysis of the management measures. The objective of this article is to explore how QMRA techniques and risk management metrics may be applied to aseptic-UHT-type processed food products. In particular, the aseptic-UHT process should benefit from a number of novel mathematical and statistical concepts that have been developed in the field of QMRA. Probabilistic techniques such as Monte Carlo simulation, Bayesian inference and sensitivity analysis, should help in assessing the compliance with safety and stability-related POs set at the end of the manufacturing process. The understanding of aseptic-UHT process contamination will be extended beyond the current "as-low-as-reasonably-achievable" targets to a risk-based framework, through which current sterility performance and future process designs can be optimised.

Growth of Clostridium perfringens during cooling of refried beans

Outbreaks of Clostridium perfringens have been associated with dishes containing refried beans from food service establishments. However, growth of C. perfringens in refried beans has not been investigated, and predictive models have not been validated in this food matrix. We investigated the growth of C. perfringens during the cooling of refried beans. Refried beans (pinto and black, with and without salt added) were inoculated with 3 log CFU/g C. perfringens spores and incubated isothermally at 12, 23, 30, 35, 40, 45, and 50°C. The levels of C. perfringens were monitored 3, 5, 8, and 10 h after inoculation, and then fitted to the Baranyi primary model and the Rosso secondary model prior to solving the Baranyi differential equation. The final model was validated by dynamic cooling experiments carried out in stockpots, thus mimicking the worst possible food service conditions. All refried beans samples supported the growth of C. perfringens, and all models fit the data with pseudo-R(2) values of 0.95 or greater and mean square errors of 0.3 or lower. The estimated maximum specific growth rates were generally higher in pinto beans, with or without salt added (2.64 and 1.95 h(-1), respectively), when compared with black beans, with or without salt added (1.78 and 1.61 h(-1), respectively). After 10 h of incubation, maximum populations of C. perfringens were significantly higher in samples with no salt added (7.9 log CFU/g for both pinto and black beans) than in samples with salt added (7.3 and 7.2 log CFU/g for pinto and black beans, respectively). The dynamic model predicted the growth of C. perfringens during cooling, with an average root mean squared error of 0.44. The use of large stockpots to cool refried beans led to an observed 1.2-log increase (1.5-log increase predicted by model) in levels of C. perfringens during cooling. The use of shallower pans for cooling is recommended, because they cool faster, therefore limiting the growth of C. perfringens.

Bayesian inference for quantifying Listeria monocytogenes prevalence and concentration in minced pork meat from presence/absence microbiological testing

The purpose of this work was to estimate the prevalence and concentration of Listeria monocytogenes in minced pork meat by the application of a Bayesian modeling approach. Samples (n = 100) collected from local markets were tested for L. monocytogenes using in parallel the PALCAM, ALOA and RAPID'L.mono selective media. Presence of the pathogen was confirmed through biochemical and molecular tests. Independent experiments (n = 10) for validation purposes were performed. No L. monocytogenes was enumerated by direct-plating (<10 CFU/g), though the pathogen was detected in 22% of the samples. Sensitivity and specificity varied depending on the culture method. L. monocytogenes concentration was estimated at 14-17 CFU/kg. Validation showed good agreement between observed and predicted prevalence (error = -2.17%). The use of at least two culture media in parallel enhanced the efficiency of L. monocytogenes detection. Bayesian modeling may reduce the time needed to draw conclusions regarding L. monocytogenes presence and the uncertainty of the results obtained.

Modeling of Clostridium perfringens vegetative cell inactivation in beef-in-sauce products: a meta-analysis using mixed linear models

The aim of the present study was to predict Clostridium perfringens vegetative cell inactivation during the final reheating step of two beef-in-sauce products prepared and distributed in a French hospital for exposure in risk assessment. In order to account for variability according to experts and international organization recommendations, published data were used to estimate the thermal inactivation parameters of a probabilistic model. Mixed effects models were proposed to describe variability on D(ref) the decimal reduction time at temperature T(ref). Many models differing by their description of variability on D(ref) were tested. Based on goodness-of-fit and parsimony of the model, the one including three random effects was chosen. That model describes random effects of vegetative cell culture conditions, strains and other uncontrolled experimental factors. In order to check the ability of the model to predict inactivation under dynamic thermal conditions, model validation was carried out on published non isothermal data. This model was then used to predict C. perfringens vegetative cell inactivation using temperature profiles inside beef-in-sauce products registered in a French hospital and to explore control measures easier to apply than French regulations.