Prediction of time to growth of Listeria monocytogenes using Monte Carlo simulation or regression analysis,influenced by sublethal heat and recovery conditions

Stochastic models, including the variability in extent and probability of microbial growth, are useful for estimating the risk of foodborne illness (i.e. Nauta, 2000). Risk assessment typically has to embrace all sources of variability. In this paper, a stochastic approach to evaluate growth of heat damaged Listeria monocytogenes cells influenced by different stresses (pH and presence of eugenol) was performed, using an individual-based approach of growth through OD measurements. Both the lag phase duration and the “work to be done” (h₀ parameter) were derived from the growth curves obtained. From results obtained histograms of the lag phase were generated and distributions were fitted. Histograms showed a shift to longer lag phases and an increase in variability with high stress levels. Using the distributions fitted, predictions of time to unacceptable growth (10² cfu/g) of L. monocytogenes were established by Monte Carlo simulation and they were compared with results from statistical methods. It was evidenced that both methods (Monte Carlo and regression analysis) gave a good indication of the probability of a certain level of growth other than the average. Tornado plots were obtained to establish a sensitivity analysis of the influence of the conditions tested (heat, pH, eugenol) applied to the microorganism and their combinations.     

Predictive modeling of microbial single cells: A review

In practice, food products tend to be contaminated with food-borne pathogens at a low inoculum level. However, the huge potential risk cannot be ignored because microbes may initiate high-speed growth suitable conditions during the food chain, such as transportation or storage. Thus, it is important to perform predictive modeling of microbial single cells. Several key aspects of microbial single-cell modeling are covered in this review. First, based on previous studies, the techniques of microbial single-cell data acquisition and growth data collection are presented in detail. In addition, the sources of microbial single-cell variability are also summarized. Due to model microbial growth, traditional deterministic mathematical models have been developed. However, most models fail to make accurate predictions at low cell numbers or at the single-cell level due to high cell-to-cell heterogeneity. Stochastic models have been a subject of great interest; and these models take into consideration the variability in microbial single-cell behavior.     

Exploring the lag phase and growth initiation of a yeast culture by means of an individual-based model

The performance of fermentation processes is greatly influenced by the size and quality of inocula. The characterization of the replicative age is decided by the number of birth scars each yeast exhibits on its cellular membrane. Yeast ageing and inoculum size are factors that affect industrial fermentation, particularly those processes in which the yeast cells are reused such as the production of beer. This process reuses yeast cropped at the end of one fermentation in the following one, in a process called “serial repitching”. The aim of this study was to explore the effects of inoculum size and ageing on the first stages of the dynamics of yeast population growth. However, only Individual-based Models (IbMs) allow the study of small, well-characterized, microbial inocula. We used INDISIM-YEAST, based on the generic IbM simulator INDISIM, to carry out these studies. Several simulations were performed to analyze the effect of the inoculum size and genealogical age of the cells that made it up on the lag phase, first division time and specific growth rate. The shortest lag phase and time to the first division were obtained with largest inocula and with the youngest inoculated parent cells.     

Uncertainty and sensitivity analysis: Mathematical model of coupled heat and mass transfer for a contact baking process

Similar to other processes, the modelling of heat and mass transfer during food processing involves uncertainty in the values of input parameters (heat and mass transfer coefficients, evaporation rate parameters, thermo-physical properties, initial and boundary conditions) which leads to uncertainty in the model predictions. The aim of the current paper is to address this uncertainty challenge in the modelling of food production processes using a combination of uncertainty and sensitivity analysis, where the uncertainty analysis and global sensitivity analysis were applied to a heat and mass transfer model of a contact baking process. The Monte Carlo procedure was applied for propagating uncertainty in the input parameters to uncertainty in the model predictions. Monte Carlo simulations and the least squares method were used in the sensitivity analysis: for each model output, a linear regression model was constructed and the standardized regression coefficients (SRCs) and R² were computed. The effect of input parameters on model predictions was calculated, and the relative impact of the parameters on each of the outputs was ranked. Results of the uncertainty and sensitivity analysis can be used to prioritize future experimental efforts, as discussed for the contact baking process.     

Comparison between a sire model and an animal model for genetic evaluation of fertility traits in Danish Holstein population

Comparisons between a sire model, a sire-dam model, and an animal model were carried out to evaluate the ability of the models to predict breeding values of fertility traits, based on data including 471,742 records from the first lactation of Danish Holstein cows, covering insemination years from 1995 to 2004. The traits in the analysis were days from calving to first insemination, calving interval, days open, days from first to last insemination, number of inseminations per conception, and nonreturn rate within 56 d after first service. The correlations between sire estimated breeding value (EBV) from the animal model and the sire-dam model were close to 1 for all the traits, and those between the animal model and the sire model ranged from 0.95 to 0.97. Model ability to predict sire breeding value was assessed using 4 criteria: 1) the correlation between sire EBV from 2 data subsets (DATA_A and DATA_B); 2) the correlation between sire EBV from training data (DATA_A or DATA_B) and yield deviation from test data (DATA_B or DATA_A) in a cross-validation procedure; 3) the correlation between the EBV of proven bulls, obtained from the whole data set (DATA_T) and from a reduced set of data (DATA_C1) that contained only the first-crop daughters of sires; and 4) the reliability of sire EBV, calculated from the prediction error variance of EBV. All criteria used showed that the animal model was superior to the sire model for all the traits. The sire-dam model performed as well as the animal model and had a slightly smaller computational demand. Averaged over the 6 traits, the correlations between sire EBV from DATA_A and DATA_B were 0.61 (sire model) versus 0.64 (animal model), the correlations between EBV from DATA_T and DATA_C1 for proven bulls were 0.59 versus 0.67, the correlations between EBV and yield deviation in the cross-validation were 0.21 versus 0.24, and the reliabilities of sire EBV were 0.42 versus 0.46. Model ability to predict cow breeding value was measured by the reliability of cow EBV, which increased from 0.21 using the sire model to 0.27 using the animal model. All the results suggest that the animal model, rather than the sire model, should be used for genetic evaluation of fertility traits.     

Rapid identification and quantitation of the viable cells of Lactobacillus casei in fermented dairy products using an aptamer-based strategy powered by a novel cell-SELEX protocol

An aptamer-based strategy was developed for qualitative and quantitative analysis of viable Lactobacillus casei in dairy products. Three highly specific aptamers for L. casei were obtained using systematic evolution of ligands by exponential enrichment protocol using the whole bacterium cell as the target (cell-SELEX) facilitated by polyethyleneglycol and chitosan modified graphene oxide and complementary ring-mediated rolling circle amplification. Two aptamers, one for separating and enriching the L. casei cells and the other for generating fluorescence signals, were employed to develop an aptamer-based strategy, which was demonstrated for the selective detection of L. casei in commercial dairy drinks, with a dynamic range of 10⁵ to 10⁹ cfu/mL. Viable and nonviable L. casei cells could be discriminated based on the significant difference in fluorescence intensity. This established strategy is of high selectivity and sensitivity, and can be used for rapid analysis of viable L. casei in quality control and food surveillance areas.     

微波法提取西南委陵菜黄酮及其抗氧化活性的细胞模型法评价

利用微波法以乙醇作为提取剂提取了西南委陵菜黄酮,考察了乙醇浓度、料液比、提取温度、微波功率和提取时间对西南委陵菜黄酮提取得率的影响。结果表明,微波法提取西南委陵菜黄酮的最佳条件是乙醇浓度50%、料液比1∶30、提取温度60℃、微波功率400W、提取时间5min。黄酮的最佳得率为5.68%。西南委陵菜黄酮在结肠癌细胞HT-29和小鼠巨噬细胞RAW264.7两种细胞中表现出明显的抗氧化活性,其抗氧化性随浓度增加递增。      

Validation of an approximate REML algorithm for parameter estimation in a multitrait, multiple across-country evaluation model: a simulation study

A multitrait, multiple across-country evaluation (MT-MACE) model permitting a variable number of correlated traits per country allows international genetic evaluation models to more closely match national models. Before the MT-MACE evaluation can be applied, genetic (co)variance components within and across country must be estimated. An approximate REML algorithm for parameter estimation was developed and was validated via simulation. This method is based on the expectation maximization REML (EM-REML) algorithm. Because obtaining the inverse of co-efficient matrix is not usually feasible for large amounts of data, an algorithm using the multiple-trait effective daughter contribution (EDC) is proposed to provide approximate diagonal elements of the inverse matrix. The accuracy of the approximate EM-REML was tested with simulated data and compared with an average information REML (AI-REML) from available software. Two simulation studies were performed. First, data of 2 countries were simulated using a single-trait model. Estimates of across-country genetic correlations with the developed algorithm were unbiased and very precise. The precision, however, depended on the percentage of bulls with data in both countries. The results obtained with the approximate EM-REML software were very close to those obtained with the AI-REML software regarding estimated genetic correlations and bulls’ estimated breeding values. The second simulation assumed a multiple trait model and the same number of traits, pedigree structure, EDC, and pattern of missing records as for actual observations for milk yield obtained from French and German national Holstein evaluations. As with the single-trait scenarios, the approximate EM-REML gave nearly unbiased and very precise estimates of within- and across-country genetic correlations. The results obtained in both simulation studies confirmed the suitability of the MT-MACE model and approximate EM-REML software in a wide range of situations. Even when the genetic trend was incorrectly estimated by the national evaluations, a joint analysis including a time effect in the MT-MACE model adequately corrected for this bias.     

Stochastic control and optimization in retail distribution: an empirical study of a Korean fashion company

Considerable research has recently been conducted on improving the business performance of the fashion industry through supply-chain streamlining. In addition, the accuracy enhancement of sales forecasting by using statistical methods and machine learning algorithms to minimize inventory and improve profitability has been investigated. However, few studies have focused on solving the initial distribution problem to reduce logistical costs and loss of sales opportunities. This study solves the mathematical problems related to initial distributions of fashion products using stochastic control and optimization by conducting an empirical study using real data from a leading Korean fashion company. The initial distribution of a small quantity of items among numerous shops and the distribution of special sizes produced in small quantities were examined. Monte–Carlo simulations and Lebesgue’s convergence theorem were considered useful for determining initial distributions of stock produced in small quantities. Furthermore, optimal initial distributions can be achieved when experience-based expert judgment is combined with mathematical modeling using stochastic control and optimization.     

Moisture diffusivity in pears: experimental determination and derivation of a mathematical prediction model

In the present work the dependence of moisture diffusivity on pear composition (in particular, water and sugar concentrations) was examined from the drying rate data measured experimentally. A model for predicting diffusivity that accounts for the effects of three variables (temperature, moisture content and sugar concentration) was then developed, and compared with the model presented by Zogzas and Maroulis (Drying Technology 1996;14:1543), which accounts only for the influence of temperature and moisture concentration. It was observed that the value for the activation energy predicted by the model that includes the influence of the sugar concentration is higher, showing that the amount of sugar present influences the diffusion of moisture through the pear. From the results obtained it was possible to conclude that at constant temperature the diffusivity is increased for higher water contents and lower sugar concentrations. Furthermore, it was possible to observe that higher temperatures have a much more pronounced influence on the diffusivity, compared with lower temperatures.     

The acoustic characteristics of dual-layered porous nonwovens: a theoretical and experimental analysis

The normal incidence sound absorption coefficient of single-layered porous materials predicted using some prediction models is well known. The published acoustic behaviors prediction models, such as Biot model, Zwikker and Kosten model, Delany and Bazley model, and Champoux and Allard model, can give acceptable prediction results by only taking specific flow resistivity and material thickness as independent variables to estimate the normal incidence sound absorption coefficient. However, the existing literature fails to provide proper knowledge regarding the acoustic characteristics of dual-layered porous nonwoven absorbers. So, the aim of this paper was to propose a theoretical acoustic model for dual-layered porous nonwoven absorber and to verify the proposed model experimentally. In theory aspect, the study focused on the extension algorithm of the Zwikker and Kosten model for dual-layered nonwoven absorber. The theoretical analysis of the impact of thickness and porosity of outer and inner layer on sound absorption coefficient was detailed using numerical simulation method. In experiment aspect, we particularly designed 20 dual-layered nonwoven absorbers with four types of meltblown polypropylene nonwoven materials and five types of hydroentangled E-glass fiber nonwoven materials firstly. Secondly, the calculated sound absorption coefficients using the proposed model were compared with the measured ones of the 20 dual-layered nonwoven absorbers at 250, 500, 1000, and 2000?Hz. Experimental results indicate that the measured and the calculated data have very similar trend with the change of thickness, porosity, and the sound frequency, apart from the obvious difference between them at low frequency.     

Preparation and validation of a growth model for Bacillus cereus: the effects of temperature, pH, sodium chloride and carbon dioxide

The growth responses of a vegetative inoculum of Bacillus cereus as influenced by varying conditions of temperature, pH value and sodium chloride concentration (% w/v) and carbon dioxide concentration (% v/v) were determined in laboratory medium. Growth curves in concentrations of NaCl in the range 0.5–10.5% (w/v), pH values in the range 4.5–7.0, CO₂ concentrations in the range 10–80% (v/v) and storage temperatures from 10 °C to 30 °C were fitted using the regime of Baranyi et al. (1993). A response surface model was prepared and predictions of doubling time, growth rate, lag time and time to 1000-fold increase could be obtained for any set of conditions within the matrix studied. This model is included in Food MicroModel Version 1. Predicted doubling times from the model were compared to observed doubling times in the literature and the model was found to give realistic estimates of doubling time for a range of foods including milk, meat and poultry and carbohydrate-based products.     

Genetic evaluation of mastitis in dairy cattle using linear models, threshold models, and survival analysis: a simulation study

The objective was to study, by simulation, whether survival analysis results in a more precise genetic evaluation for mastitis in dairy cattle than cross-sectional linear models and threshold models by using observation periods for mastitis of 2 lengths (the first 150 d of lactation, and the full lactation, respectively). True breeding values for mastitis liability on the underlying scale were simulated for daughters of 400 sires (average daughter group size, 60 or 150), and the possible event of a mastitis case within lactation for each cow was created. For the linear models and the threshold models, mastitis was defined as a binary trait within either the first 150 d of lactation or the full lactation. For the survival analysis, mastitis was defined as the number of days from calving to either the first case of mastitis (uncensored record) or to the day of censoring (i.e., day of culling, lactation d 150 or day of next calving; censored record). Cows could be culled early in lactation (within 10 d after calving) for calving-related reasons or later on because of infertility. The correlation between sire true breeding values for mastitis liability and sire predicted breeding values was greater when using the full lactation data (0.76) than when using data from the first 150 d (0.70) with an average of 150 daughters per sire. The corresponding results were 0.60 and 0.53, respectively, with an average of 60 daughters per sire. Under these simulated conditions, the method used had no effect on accuracy. The higher accuracy of sire breeding values can be translated into a greater genetic gain, unless counteracted by a longer generation interval.     

Adaptive preference target: Contribution of Kano’s model of satisfaction for an optimized preference analysis using a sequential consumer test

Kano’s model of satisfaction leads to a typology of product attributes to distinguish between those contributing solely to consumer satisfaction, those contributing only to consumer dissatisfaction and those which contribute to both satisfaction and dissatisfaction. In line with this model, we propose a new preference mapping (PrefMap) methodology called adaptive preference target (APT). To explore a given product category APT, using a sequential consumer test, prioritizes products to be tasted by each consumer by taking into account his/her personal preference and rejection. This new approach for external preference mapping enables the classification of the key sensory attributes influencing hedonic appreciation into “attractive”, “must-be” or “performance” attributes and thus hierarchizes the tasks to reach the ideal product for new product development.

APT and standard PrefMap were compared for a sweet dry biscuits survey with the same consumers. Results highlight the relevance of Kano’s model of satisfaction applied to preference mapping. Thanks to this adapted product selection, we conclude that, in our example, we can better explain consumer appreciation. Finally, APT can be considered to be a methodology which reduces the number of products to be tasted while remaining precise in the definition of the ideal product.     

Fluorescent detection of nisin by genetically modified Lactococcus lactis strains in milk and a colonic model: Application of whole-cell nisin biosensors

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Supercritical-CO2 drying of foodstuffs in packed beds: Experimental validation of a mathematical model and sensitive analysis

In this contribution, a mathematical model is built to predict the changes in water concentration in both a solid food matrix and a fluid carrier during supercritical carbon dioxide (SC–CO₂) drying. The mass balance equations of the model involve five dimensionless parameters: Peclet number modified Sherwood number, Fourier number, mass ratio and equilibrium constant. The differential equations were discretized using the finite explicit difference method. The resulting model was implemented and solved in Matlab/Simulink using an explicit Runge–Kutta solver. A very good agreement (ARD = 7.2%) between experimental data, obtained by an independent group, and the present model was observed. The axial dispersion diffusion coefficient seems not to play a significant role during the drying process. A sensitivity analysis revealed that the predictions are relatively more sensitive to the equilibrium constant and the mass ratio than to Peclet and modified Sherwood numbers. Furthermore, in the case of Peclet and modified Sherwood numbers, the sensitivity and the uncertainty of the output are function of the final moisture content. The present model could be used as an optimization tool for kinetic studies to investigate the effects of different operation conditions on the performance and design of the supercritical drying technology.     

Use of global sensitivity analysis in quantitative microbial risk assessment: application to the evaluation of a biological time temperature integrator as a quality and safety indicator for cold smoked salmon

The aim of this study was to apply a global sensitivity analysis (SA) method in model simplification and to evaluate (eO)^®, a biological Time Temperature Integrator (TTI) as a quality and safety indicator for cold smoked salmon (CSS). Models were thus developed to predict the evolutions of Listeria monocytogenes and the indigenous food flora in CSS and to predict TTIs endpoint. A global SA was then applied on the three models to identify the less important factors and simplify the models accordingly. Results showed that the subset of the most important factors of the three models was mainly composed of the durations and temperatures of two chill chain links, out of the control of the manufacturers: the domestic refrigerator and the retail/cabinet links. Then, the simplified versions of the three models were run with 10⁴ time temperature profiles representing the variability associated to the microbial behavior, to the TTIs evolution and to the French chill chain characteristics. The results were used to assess the distributions of the microbial contaminations obtained at the TTI endpoint and at the end of the simulated profiles and proved that, in the case of poor storage conditions, the TTI use could reduce the number of unacceptable foods by 50%.