Analysis of mathematical models of Pseudomonas spp. growth in pallet-package pork stored at different temperatures

Prediction of Pseudomonas spp. Population in Food Products and Culture Media Using Machine Learning-Based Regression Methods

Machine learning approaches are alternative modelling techniques to traditional modelling equations used in predictive food microbiology and utilise algorithms to analyse large datasets that contain information about microbial growth or survival in various food matrices. These approaches leverage the power of algorithms to extract insights from the data and make predictions regarding the behaviour of microorganisms in different food environments. The objective of this study was to apply various machine learning-based regression methods, including support vector regression (SVR), Gaussian process regression (GPR), decision tree regression (DTR), and random forest regression (RFR), to estimate bacterial populations. In order to achieve this, a total of 5618 data points for Pseudomonas spp. present in food products (beef, pork, and poultry) and culture media were gathered from the ComBase database. The machine learning algorithms were applied to predict the growth or survival behaviour of Pseudomonas spp. in food products and culture media by considering predictor variables such as temperature, salt concentration, water activity, and acidity. The suitability of the algorithms was assessed using statistical measures such as coefficient of determination (R²), root mean square error (RMSE), bias factor (Bf), and accuracy (A_f). Each of the regression algorithms showed appropriate estimation capabilities with R² ranging from 0.886 to 0.913, RMSE from 0.724 to 0.899, B_f from 1.012 to 1.020, and A_f from 1.086 to 1.101 for each food product and culture medium. Since the predictive capability of RFR was the best among the algorithms, externally collected data from the literature were used for RFR. The external validation process showed statistical indices of B_f ranging from 0.951 to 1.040 and A_f ranging from 1.091 to 1.130, indicating that RFR can be used for predicting the survival and growth of microorganisms in food products. Therefore, machine learning approaches can be considered as an alternative to conventional modelling methods in predictive microbiology. However, it is important to highlight that the prediction power of the machine learning regression method directly depends on the dataset size, and it requires a large dataset to be employed for modelling. Therefore, the modelling work of this study can only be used for the prediction of Pseudomonas spp. in specific food products (beef, pork, and poultry) and culture medium with certain conditions where a large dataset is available.

Establishment and Application of a Predictive Growth Kinetic Model of Salmonella with the Appearance of Two Other Dominant Background Bacteria in Fresh Pork

To better guide microbial risk management and control, growth kinetic models of Salmonella with the coexistence of two other dominant background bacteria in pork were constructed. Sterilized pork cutlets were inoculated with a cocktail of Salmonella Derby (S. Derby), Pseudomonas aeruginosa (P. aeruginosa), and Escherichia coli (E. coli), and incubated at various temperatures (4-37 °C). The predictive growth models were developed based on the observed growth data. By comparing R² of primary models, Baranyi models were preferred to fit the growth curves of S. Derby and P. aeruginosa, while the Huang model was preferred for E. coli (all R² ≥ 0.997). The secondary Ratkowsky square root model can well describe the relationship between temperature and μ_max (all R² ≥ 0.97) or Lag (all R² ≥ 0.98). Growth models were validated by the actual test values, with B_f and A_f close to 1, and MSE around 0.001. The time for S. Derby to reach a pathogenic dose (10⁵ CFU/g) at each temperature in pork was predicted accordingly and found to be earlier than the time when the pork began to be judged nearly fresh according to the sensory indicators. Therefore, the predictive microbiology model can be applied to more accurately predict the shelf life of pork to secure its quality and safety.

Growth Prediction of the Total Bacterial Count in Freshly Squeezed Strawberry Juice during Cold Storage Using Electronic Nose and Electronic Tongue

The growth models of total bacterial count in freshly squeezed strawberry juice were established by gas and taste sensors in this paper. By selecting the optimal sensors and fusing the response values, the Modified Gompertz, Logistic, Huang and Baranyi models were used to predict and simulate the growth of bacteria. The results showed that the R² values for fitting the growth model of total bacterial count of the sensor S7 (an electronic nose sensor), of sweetness and of the principal components scores were 0.890-0.944, 0.861-0.885 and 0.954-0.964, respectively. The correlation coefficients, or R-values, between models fitted by the response values and total bacterial count ranged from 0.815 to 0.999. A single system of electronic nose (E-nose) or electronic tongue (E-tongue) sensors could be used to predict the total bacterial count in freshly squeezed strawberry juice during cold storage, while the higher rate was gained by the combination of these two systems. The fusion of E-nose and E-tongue had the best fitting-precision in predicting the total bacterial count in freshly squeezed strawberry juice during cold storage. This study proved that it was feasible to predict the growth of bacteria in freshly squeezed strawberry juice using E-nose and E-tongue sensors.

Mathematical Modeling of the Effects of Temperature and Modified Atmosphere Packaging on the Growth Kinetics of Pseudomonas Lundensis and Shewanella Putrefaciens in Chilled Chicken

The effects of modified atmosphere packaging (MAP) on the growth and spoilage characteristics of Pseudomonas lundensis LD1 and Shewanella putrefaciens SP1 in chilled chicken at 0–10 °C were studied. MAP inhibited microbial growth, TVB-N synthesis, and lipid oxidation. The inhibitory effect of MAP became more significant as the temperature decreased. The kinetic models to describe the growth of P. lundensis LD1 and S. putrefaciens SP1 at 0–10 °C were also established to fit the primary model Gompertz and the secondary model Ratkowsky. The models had a high degree of fit to describe the growth of dominant spoilage bacteria in chilled chicken. The observed numbers of P. lundensis LD1 and S. putrefaciens SP1 at 2 °C were compared with the predicted numbers, and the accuracy factor and bias factor ranged from 0.93 to 1.14. These results indicated that the two models could help predict the growth of P. lundensis and S. putrefaciens in chilled chicken at 0–10 °C. The analyzed models provide fast and cost-effective alternatives to replace traditional culturing methods to assess the influence of temperature and MAP on the shelf life of meat.

Analysis and mathematical modeling of the survival kinetics of Staphylococcus aureus in raw pork under dynamic and static temperature conditions

The incidence of frequent foodborne disease outbreaks due to Staphylococcus aureus contamination necessitates the urgent searching for effective methods to monitor S. aureus. This research aims to construct model with a dynamic survival curve and some static growth curves to predict the behavior of S. aureus in raw pork. Lack of research about S. aureus kinetics in pork under fluctuating temperature conditions across freezing and thawing necessitates this study. One-step analysis was used to determine the model parameters, which was more efficient than conventional model analysis with two steps. The results of kinetic analysis showed that Tmin (minimum growth temperature) was 6.85°C, which is close to the estimated values in previous reports. Subsequently, validation results indicated the integrated model can accurately predict the behavior of S. aureus regardless of isothermal or nonisothermal conditions with the root-mean-square errors (RMSE < 0.44 log CFU/g, 73.9% of the errors of prediction falls within ±0.5 log CFU/g), accuracy factors Af and bias factors Bf were both close to 1. This work may offer an effective method for the assessment of microbial security related to S. aureus in pork.

Predictive Growth Modeling of Listeria monocytogenes in Rice Balls and Its Risk Assessment

This study aimed to investigate the growth of Listeria monocytogenes in rice balls and to conduct its microbial risk assessment based on the Korean dietary pattern. Each tuna or ham rice ball was mixed with mayonnaise, soy sauce, or gochujang, a Korean traditional fermented red peeper paste, which was artificially contaminated with L. monocytogenes and then stored at 7°C–25°C to assess bacterial growth. Growth data were analyzed using three primary models (the Huang, Baranyi, and Gompertz models), and the growth pattern was found to fit well to the Baranyi model based on the following five statistical criteria: root mean square error (0.38–0.56), Akaike’s information criterion (−51.55–−26.99), coefficient of determination (0.72–0.97), bias factor (0.97–1.01), and accuracy factor (1.06–1.18). The effects of temperature on bacterial growth rate and lag time were evaluated using the square root model. The minimum growth temperature for L. monocytogenes in tuna or ham rice balls was the lowest when they were mixed with mayonnaise (−9.44°C or −15.37°C, respectively). Risk assessment using FDA-iRISK showed that tuna or ham rice balls mixed with gochujang exhibited the highest microbial risk among all the rice balls tested, regardless of the storage temperature. Tuna or ham rice balls mixed with gochujang had the highest disability-adjusted life years per year (0.015) followed by ham rice balls mixed with soy sauce (0.011–0.015) or mayonnaise (0.006–0.015) and then tuna rice balls mixed with soy sauce (0.006–0.008) or mayonnaise (<0.001). In conclusion, our results, determined using predictive growth models, allow the assessment of potential risk ranking associated with the consumption of rice balls contaminated with L. monocytogenes based on the number of illnesses experienced per serving and the disease burden.

Application of gas sensors for modelling the dynamic growth of Pseudomonas in pork stored at different temperatures

Pseudomonas have a faster growth rate over other bacteria in chilled meat under aerobic conditions. A non-destructive method for modelling the dynamic growth of Pseudomonas in pork stored at different temperatures using gas sensors was presented in our work. Based on selected gas sensor data, the first-order kinetic equations (Gompertz and Logistic Functions) combined with the secondary model (Square-root Function) effectively simulated Pseudomonas growth in pork at different temperatures with R² and RMSE values of 0.71-0.97 and 0.27-0.84, respectively. Additionally, these models showed high accuracy with correlation coefficients greater than 0.90, in addition to several individual accuracy values. Furthermore, HS-SPME/GC-MS results demonstrated the presence of identified key volatiles in samples inoculated with Pseudomonas, including three amine compounds (mercaptamine, 1-octanamine and 1-heptadecanamine), phenol and indole. Our work showed that gas sensors are a rapid, easy and non-destructive method with acceptable feasibility in modelling the dynamic growth of spoilage microorganisms in meat.

Use of modified Richards model to predict isothermal and non-isothermal microbial growth

Mathematical models are often used to predict microbial growth in food products. An important class of these models involves the adaptation of classical sigmoid functions, such as the Gompertz and logistic functions. This study aimed to validate the use of the modified Richards model in various situations, which have not previously been tested. The model was obtained through solving a system of two differential equations and could be applied to both isothermal and non-isothermal environments. To test and validate this model, we used published datasets containing data for the growth of Pseudomonas spp. in fish products. The results obtained after fitting the model showed that it could be effectively used to describe and predict the Pseudomonas growth curves under various temperature regimens. However, the influence of the shape parameter on the growth curve is an issue that needs further evaluation.

Application of a Predictive Growth Model of Pseudomonas spp. for Estimating Shelf Life of Fresh Agaricus bisporus

For prediction of the shelf life of the mushroom Agaricus bisporus, the growth curve of the main spoilage microorganisms was studied under isothermal conditions at 2 to 22°C with a modified Gompertz model. The effect of temperature on the growth parameters for the main spoilage microorganisms was quantified and modeled using the square root model. Pseudomonas spp. were the main microorganisms causing A. bisporus decay, and the modified Gompertz model was useful for modelling the growth curve of Pseudomonas spp. All the bias factors values of the model were close to 1. By combining the modified Gompertz model with the square root model, a prediction model to estimate the shelf life of A. bisporus as a function of storage temperature was developed. The model was validated for A. bisporus stored at 6, 12, and 18°C, and adequate agreement was found between the experimental and predicted data.