Structural model requirements to describe microbial inactivation during a mild heat treatment

The classical concept of D and z values, established for sterilisation processes, is unable to deal with the typical non-loglinear behaviour of survivor curves occurring during the mild heat treatment of sous vide or cook-chill food products. Structural model requirements are formulated, eliminating immediately some candidate model types. Promising modelling approaches are thoroughly analysed and, if applicable, adapted to the specific needs: two models developed by Casolari (1988), the inactivation model of Sapru et al. (1992), the model of Whiting (1993), the Baranyi and Roberts growth model (1994), the model of Chiruta et al. (1997), the model of Daughtry et al. (1997) and the model of Xiong et al. (1999). A range of experimental data of Bacillus cereus, Yersinia enterocolitica, Escherichia coli O157:H7, Listeria monocytogenes and Lactobacillus sake are used to illustrate the different models' performances. Moreover, a novel modelling approach is developed, fulfilling all formulated structural model requirements, and based on a careful analysis of literature knowledge of the shoulder and tailing phenomenon. Although a thorough insight in the occurrence of shoulders and tails is still lacking from a biochemical point of view, this newly developed model incorporates the possibility of a straightforward interpretation within this framework.     

Use of Weibull frequency distribution model to describe the inactivation of Alicyclobacillus acidoterrestris by high pressure at different temperatures

The survival curves of Alicyclobacillus acidoterrestris by high hydrostatic pressure were obtained at two pressures (350 and 450 MPa) and three temperature levels (35, 45 and 50 °C) in BAM broth. Tailing (upward concavity) was observed in all survival curves. Weibull model was fitted to these data and goodness of fit of this model was investigated. Regression coefficients (R²), root mean square (RMSE) values and residual plot strongly suggested that Weibull model produced good fit to the data. A better fit was observed for the data at lower pressure (350 MPa). Shape factors of the Weibull model (n values) for 350 MPa at 35, 45 and 50 °C were significantly different from each other (P < 0.05). Two linear emprical equations were obtained for scale factors (b values) at the temperature values studied for 350 and 450 MPa. Such pressure–temperature inactivation models form the engineering basis for design, evaluation and optimization of high hydrostatic pressure processes as a new preservation technique.     

Application of the Weibull model to describe inactivation of Listeria monocytogenes and Escherichia coli by citric and lactic acid at different temperatures

Inactivation of Listeria monocytogenes and Escherichia coli by citric (10‐150 g L^?1) and lactic (1‐60 mL L^?1) acids at different temperatures (4, 20, 40 °C) has been investigated. Bactericidal effect of both acids was dependent on time and temperature of exposure and acid concentration. Survival curves of L. monocytogenes treated by lactic acid were concave downward and those treated by citric acid were linear. On the other hand, survival curves of E. coli treated by both organic acids were concave upward. Shape of survival curves depended on the type of acid but not on the treatment temperature. A mathematical model based on the Weibull distribution accurately described the kinetics of inactivation of both microorganisms by both acids. This model allowed quantification and comparison of the acid resistance of L. monocytogenes and E. coli. Lactic acid was more effective than citric acid and E. coli was more sensitive to both acids than L. monocytogenes. Copyright © 2006 Society of Chemical Industry     

A modified Weibull model for bacterial inactivation

In this paper, a modified Weibull model is proposed to fit microbial survival curves. This model can incorporate shoulder and/or tailing phenomena if they are encountered. We aim to obtain an accurate fit of the “primary” modelling of the bacterial inactivation and to provide a useful and meaningful model for biologists and food industry. A δ parameter close to the classical concept of the D value, established for sterilisation processes, is used in the model. The specific parameterisation of the Weibull model is evaluated for the parameter of interest δ. The goodness-of-fit of the model is compared to the one produced by the model proposed by Geeraerd et al., [Geeraerd, A.H., Herremans, C.H., Van Impe, J.F., 2000. Structural model requirements to describe microbial inactivation during a mild heat treatment. Int. J. Food Microbiol. 59, 185-209.] on experimental data. As our model provides good fits for the different types of survival curves analysed, further research can focus on the development of suitable secondary model types. In this respect, it is interesting to note that the δ parameter is close to the D concept.     

Application of Weibull distribution model to describe the vacuum pulse osmotic dehydration of sardine sheets

Application of Weibull frequency distribution model was investigated for predicting the moisture and salt contents of sardine sheets during vacuum pulse osmotic dehydration using brine at different concentrations (0.15-0.27 g NaCl/g), temperatures (30-38 °C), and applying a vacuum pulse at 11.0 kPa for 10 min. The high regression coefficients (R²>0.99) and low mean relative error (<10%) indicated the acceptability of Weibull model for predicting both moisture and salt contents. The scale parameters for moisture and salt contents as a function of temperature all followed an Arrhenius relationship. Models for scale and shape parameters for moisture and salt contents as a function of brine concentration and temperature were found.     

Empirical model building based on Weibull distribution to describe the joint effect of pH and temperature on the thermal resistance of Bacillus cereus in vegetable substrate

A total of 296 lactic acid bacteria (LAB) isolated from spoiled, vacuum-packaged 'gravad' rainbow trout stored at 3 and 8 degrees C were characterised and identified using a molecular approach. The isolates were initially grouped according to their HindIII restriction endonuclease profiles and further identified to species level using an rRNA gene restriction pattern (ribotype) identification database. Lactobacillus sakei, L. curvatus and Carnobacterium piscicola were the three main species detected. Only one isolate was identified as C. divergens. Most of the carnobacteria were found in the samples stored at 3 degrees C. The relative proportion of L. sakei was higher in the samples stored at 8 degrees C.     

On calculating sterility in thermal preservation methods: application of the Weibull frequency distribution model

A simple and parsimonious model which originated from the Weibull frequency distribution was proposed to describe nonlinear survival curves of spores. This model was suitable for downward concavity curves (Bacillus cereus and Bacillus pumilus), as well as for upward concavity curves (Clostridium botulinum). It was shown that traditional F values calculated from this new model were no longer additive, to such an extent that a heat treatment should be better characterized by the obtained decimal reduction of spores. A modified Bigelow method was then proposed to assess this decade reduction or to optimize the heat treatment for a target reduction ratio.     

Use of the Weibull model for lactococcal bacteriophage inactivation by high hydrostatic pressure

Four lactococcal bacteriophages (phiLl6-2, phiLl35-6, phiLd66-36 and phiLd67-42) in M17 broth were pressurized at 300 and 350 MPa at room temperature and their survival curves were determined at various time intervals. Tailing (monotonic upward concavity) was observed in all survival curves. The resulting non-linear semi-logarithmic survival curves were described by the Weibull model and goodness of fit of this model was investigated. Regression coefficients (R2), root mean square error (RMSE), residual and correlation plots strongly suggested that Weibull model produced a better fit to the data than the traditional linear model. Hazard plots suggested that the Weibull model was fully appropriate for the data being analyzed. These results have confirmed that the Weibull model, which is mostly utilized to describe the inactivation of bacterial cells or spores by heat and pressure, could be successfully used in describing the lactococcal bacteriophage inactivation by high hydrostatic pressure.     

Comparison of the thermal inactivation of Bacillus subtilis spores in foods using the modified Weibull and Bigelow equations

The association of a modified Weibull model and Bigelow model was applied to the thermal inactivation of Bacillus subtilis spores heated in phosphate buffer, milk, kayu (a Japanese style rice porridge) and soy sauce as well. The inactivation kinetics presented a light downward concave profile, the acidic pH increased the efficiency of the heat treatment but on the opposite, lesser the water activity, weaker was the efficiency. The heat treatment kinetics observed in milk, soy sauce and kayu were greatly different from each other, while no large difference between sterilized whole milk, UHT whole milk, sterilized skim milk and UHT skim milk, were observed. The model established in buffer system allowed heat treatment in milk products to be simulated although it could not be employed to describe the inactivation of B. subtilis spores in soy sauce and kayu. For these two latter products, the food itself had to be introduced in the model as a parameter. Finally, this approach combining primary model (to simulate inactivation kinetics) and secondary model (to introduce temperature, pH, a_w and food matrix effect) seemed available for food application, nevertheless validations of results such as challenge-tests, must be performed before it is put to routine use.     

A 3D-CFD-heat-transfer-based model for the microbial inactivation of pasteurized food products

This study coupled a 3D-CFD and heat transfer finite elements model with the microbial inactivation approach proposed by Geeraerd, Herremans, and Van Impe (2000). The CFD-heat transfer model was developed using thermophysical properties for both heating fluid (water) and the processed sample (ground beef). The kinetic microbial parameters were estimated using experimental data from the inactivation of Escherichia coli K12 in a packaged sample. The proposed inactivation model was tested under more severe dynamic conditions than usual (heating rates from 1 to 13 °C/min). The inactivation kinetic parameters were found independent of the heating rate applied. In addition, the results revealed that the Geeraerd et al. (2000) model without a shoulder is sufficient to fit the experimental data. Such a model could be beneficial in simulating microbial inactivation for food products, thus ensuring food safety by limiting, as far as possible, overtreatment.     

On the origin of the deviation from the first-order kinetics in inactivation of microbial cells by pulsed electric fields

A computer model was developed for the estimation of the kinetics of microbial inactivation by pulsed electric field (PEF). The model is based on the electroporation theory of individual membrane damage, where spherical cell geometry and distribution of cell sizes are assumed. The variation of microbial cell sizes was assumed to follow a statistical probability distribution of the Gaussian type. Surviving kinetics was approximated by Weibull equation. The dependencies of two Weibull parameters (shape n and time tau, respectively) versus electric field intensity E and width of cell diameters distribution were studied.     

Use of linear, Weibull, and log-logistic functions to model pressure inactivation of seven foodborne pathogens in milk

Survival curves of six foodborne pathogens suspended in ultra high-temperature (UHT) whole milk and exposed to high hydrostatic pressure at 21.5 degrees C were obtained. Vibrio parahaemolyticus was treated at 300 MPa and other pathogens, Listeria monocytogenes, Escherichia coli O157:H7, Salmonella enterica serovar Enteritidis, Salmonella enterica serovar Typhimurium, and Staphylococcus aureus were treated at 600 MPa. All the survival curves showed a rapid initial drop in bacterial counts followed by tailing caused by a diminishing inactivation rate. A linear model and two nonlinear models were fitted to these data and the performances of these models were compared using mean square error (MSE) values. The log-logistic and Weibull models consistently produced better fits to the inactivation data than the linear model. The mean MSE value of the linear model was 6.1, while the mean MSE values were 0.7 for the Weibull model and 0.3 for the log-logistic model. There was no correlation between pressure resistance and the taxonomic group the bacteria belong to. The order, most to least pressure-sensitive, of the single strains tested was: V. parahaemolyticus (gram negative)相似文献   

A reactor engineering approach to describe bacterial inactivation during continuous UV-C light processing

A reactor engineering approach was used to mathematically describe microbial inactivation during continuous UV-C light processing of liquid foods. The method was followed to analyze the survival curves of Lactobacillus rhamnosus inoculated into sucrose model solutions prepared at different concentrations (8, 10 and 12 g sucrose per 100 g of solution) and pH values (pH 3, 4.5 and 6), and further processed at two different residence times (4.85 and 29.9 min). The inactivation process was considered as an irreversible elemental reaction of unknown order occurring in a continuous stirred tank reactor. The proposed model was expressed in terms of the logarithmic reduction in microbial population and its straight-line form allowed the easy estimation of the inactivation rate constant and reaction order. Results indicated that inactivation of L. rhamnosus followed a variable order kinetic, moving from a first-order rate during unsteady-state operation to a near zero-order inactivation when steady-state operation was reached. Steady-state was reached faster (0.48 ± 0.11 min⁻¹ vs. 0.37 ± 0.7 min⁻¹, p < 0.05) and with a higher steady-state log reduction (5.9 ± 0.2 vs. 5.4 ± 0.6 log CFU/mL, p < 0.05) in experiments conducted with the lowest residence time, UV-C dose and power density (4.85 min, 12.8 J/cm² and 6.6 J/cm³).     

Temperature governs the inactivation rate of vegetative bacteria under growth-preventing conditions

Novel studies, in combination with a meta-analysis of available data, were undertaken to explore the kinetics of non-thermal inactivation of Escherichia coli with particular attention to inactivation in fermented meats and including analogous broth-based model systems. The analyses were based on rates of inactivation and specifically investigated the influence of temperature, pH and water activity at levels that alone, or in combination, prevented growth. When independently-derived inactivation data, obtained using different test conditions and diverse E. coli strains, were presented as Arrhenius plots, temperature was found to have a strong effect on the rate of inactivation, explaining 60% of the variance in the data. The slope of the Arrhenius plot changed, however, at temperatures above approximately 47 degrees C, corresponding to the maximum for growth of E. coli. A strong and consistent effect of pH or water activity on inactivation rate was not observed upon meta-analysis of collated data, but the relative effect of both factors was quantified in an analogous broth-based system. We also observed that inactivation rates of three strains of Listeria monocytogenes in the range 5 to 40 degrees C did not differ systematically from those of four strains of E. coli when growth was prevented by low pH and water activity. The observations of a consistent slope of Arrhenius plots for non-thermal inactivation rate of bacteria under diverse environmental conditions and for different strains and species, but which differ from slopes associated with thermal inactivation, raise the intriguing possibility of a mechanism of inactivation at sub-lethal temperatures, distinct from thermal inactivation, that is common to many vegetative bacteria.     

Thermal inactivation of Bacillus cereus and Clostridium perfringens vegetative cells and spores in pork luncheon roll

The aim of this study was to design a thermal treatment(s) for pork luncheon roll, which would destroy Bacillus cereus and Clostridium perfringens vegetative cells and spores. B. cereus and C. perfringens vegetative and spore cocktails were used to inoculate luncheon meat. Samples were subjected to different temperatures and removal times. The decimal-reduction times (D-values) were calculated by linear regression analysis (D = -1/slope of a plot of log surviving cells versus time). The log(10) of the resulting D-values were plotted against their corresponding temperatures to calculate (-1/slope of the curve) the thermal resistance (z-values) of each cocktail. The D-values for vegetative cells ranged from 1 min (60 degrees C) to 33.2 min (50 degrees C) for B. cereus and from 0.9 min (65 degrees C) to 16.3 min (55 degrees C) for C. perfringens. The D-values for B. cereus spores ranged from 2.0 min (95 degrees C) to 32.1 min (85 degrees C) and from 2.2 min (100 degrees C) to 34.2 min (90 degrees C) for C. perfringens. The z-values were calculated to be 6.6 and 8.5 degrees C for B. cereus vegetative and spores, respectively, and 7.8 and 8.4 degrees C for C. perfringens vegetative cells and spores, respectively. The D-values of B. cereus and C. perfringens suggest that a mild cook of 70 degrees C for 12s and 1.3 min would achieve a 6 log reduction of B. cereus and C. perfringens vegetative cells, respectively. The equivalent reduction of B. cereus and C. perfringens spores would require the pork luncheon meat to be heated for 36 s at 105 and 110 degrees C, respectively. The results of this study provide the thermal inactivation data necessary to design a cooking protocol for pork luncheon roll that would inactivate B. cereus and C. perfringens vegetative cells and spores. The data may also be used in future risk assessment studies.     

微波加热对三种微生物致死的Weibull模型

探讨不同微波功率加热至不同温度下对沙门氏菌、大肠杆菌和金黄色葡萄球菌等三种对象菌的致死作用,运用Weibull模型描述其致死历程,由Weibull模型计算微波加热使微生物数量减少5-log所需要的时间,并验证其模型的精确度。结果表明,Weibull模型描述沙门氏菌、大肠杆菌和金黄色葡萄球菌的致死历程均有较高的拟合度,通过Weibull模型推算出来的沙门氏菌、大肠杆菌和金黄色葡萄球菌减少5-log的时间与实验结果相近。     

Preservation of cultures of vegetative cells for use in antibiotic residue assays

Freeze preservation of suspensions of Micrococcus luteus CECT 4070 (ATCC 9341a) and Staphlococcus epidermidis CECT 231 (ATCC 12228) used for antibiotic residue determination was evaluated. Stability of cell suspensions was monitored during a 6 month period. The best homogeneity in the number of cells from different microtubes was obtained when glycerol was used as cryoprotectant for M. luteus and when methylcellulose was used for S. epidermidis. No significant differences (P < 0·05) were found between preservation at -20° and -80°C.