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.     

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.     

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.     

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   

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.     

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。     

Weibull distribution function based on an empirical mathematical model for inactivation of Escherichia coli by pulsed electric fields

The pulsed electric field inactivation kinetics of Escherichia coli suspended in orange juices with three different concentrations of carrot juice (0, 20, and 60%) was studied. Electric field strengths ranged from 25 to 40 kV/cm, and treatment times ranged from 40 to 340 micros. Experimental data were fitted to Bigelow, Hülsheger, and Weibull distribution functions, and the Weibull function provided the best fit (with the lowest mean square error). The dependency of each model's kinetic constant on electric field strength and carrot juice concentration was studied. A secondary model was developed to describe the relationship of Weibull parameters a and n to electric field strength and carrot juice concentration. An empirical mathematical model based on the Weibull distribution function, relating the natural logarithm of the survival fraction to treatment time, electric field strength, and carrot juice concentration, was developed. Parameters were estimated by a nonlinear regression. The results of this study indicate that the error rate for the model's predictions was 6.5% and that the model was suitable for describing E. coli inactivation.     

Predicting the thermal inactivation of bacteria in a solid matrix: simulation studies on the relative effects of microbial thermal resistance parameters and process conditions

A combined mathematical model for predicting heat penetration and microbial inactivation in a solid body heated by conduction was tested experimentally by inoculating agar cylinders with Salmonella typhimurium or Enterococcus faecium and heating in a water bath. Regions of growth where bacteria had survived after heating were measured by image analysis and compared with model predictions. Visualisation of the regions of growth was improved by incorporating chromogenic metabolic indicators into the agar. Preliminary tests established that the model performed satisfactorily with both test organisms and with cylinders of different diameter. The model was then used in simulation studies in which the parameters D, z, inoculum size, cylinder diameter and heating temperature were systematically varied. These simulations showed that the biological variables D, z and inoculum size had a relatively small effect on the time needed to eliminate bacteria at the cylinder axis in comparison with the physical variables heating temperature and cylinder diameter, which had a much greater relative effect.     

A mathematical model to describe flavour release from gelatine gels

A theory of flavour release from gelatine-sucrose gels has been developed based on combined interfacial mass and heat transport. The driving force for flavour release is shown to depend on the bulk melting temperature of the gel, which depends on the gelatine and sucrose concentrations. For gels possessing melting points below the mouth temperature, the driving force for flavour release is the rate at which heat can diffuse into the gels matrix and initiate melting. For harder gels with melting points above mouth temperature the diffusion of sucrose from the surface of the gel into the adjacent saliva phase is the rate limiting step for flavour release, because this lowers the melting temperature of the surface layer. The theoretical model gives good agreement with in vitro release experiments using gelatine gels containing sucrose and dye.     

Increased inactivation of ozone-treated Clostridium perfringens vegetative cells and spores on fabricated beef surfaces using mild heat

Ozone treatment of beef surfaces enhanced the effectiveness of cooking temperatures ranging from 45 to 75 degrees C against enterotoxin-producing strains of Clostridium perfringens. Vegetative cells on beef surfaces at an initial concentration of 5.59 +/- 0.17 log CFU/g were reduced significantly (P < 0.05) to 4.09 +/- 0.72 log CFU/g and 3.50 +/- 0.90 log CFU/g after combined treatments with aqueous ozone (5 ppm) and subsequent heating at 45 and 55 degrees C, respectively. Spores on the beef surface were likewise significantly reduced from an initial concentration of 2.94 +/- 0.37 log spores per g to 2.07 +/- 0.38 log spores per g and 1.70 +/- 0.37 log spores per g after the combined treatment with aqueous ozone (5 ppm) and subsequent heating at 55 and 75 degrees C, respectively. Fluorescent nucleic acid stains were used with confocal fluorescence microscopy to show that spores remaining attached to the meat were protected from treatment-specific injury. This study provides evidence for the decreased resistance of both vegetative cells and spores of C. perfringens with ozone treatment that is followed by heat treatment at temperatures that would not otherwise be as effective, thus lowering the requirements for cooking beef while maintaining a margin of safety.     

On modeling and simulating transitions between microbial growth and inactivation or vice versa

Resumed growth of the survivors of a heat or chemical treatment after cooling or a disinfectant dissipation is not an uncommon phenomenon. Similarly, the inverse, the onset of mortality in a growing microbial population as a result of exposure to increasing temperature or concentration of an antimicrobial agent, is also a familiar scenario. Provided that in either regime, the organism has no time to adapt biologically, the continuous transition from growth to inactivation or vice versa can be simulated with conventional growth and inactivation models, whose rate constant is allowed to change sign. Where both the growth and inactivation follow first-order kinetics, the sign change has no effect on the model equation's solutions. The same applies when the growth and inactivation patterns are described by a rate model, like the differential logistic equation or its various variants. However, determination of such models' coefficients from experimental isothermal growth and inactivation data can be difficult for technical reasons, unless the model can be integrated analytically. If not, or when the model itself is unknown a priori, then the rate equation would have to be derived from the fit of empirical models like the Weibull, modified versions of the logistic function and the like. But this may create a new kind of problem as a result of that the log and certain power operations cannot be used for negative numbers. For certain models at least, the problem can be solved through modification of the procedure by which the rate equation is solved numerically. This is demonstrated in simulated transitions between growth and inactivation and between inactivation and growth based on the log linear and Weibullian-power law models and three logistic patterns based on a shifted logistic function, the Baranyi-Roberts model and a shifted arctan model.     

Combined high-pressure and thermal treatments for processing of tomato puree: evaluation of microbial inactivation and quality parameters

The effects of combined high-pressure thermal treatments on consistency, viscosity, colour, lycopene content, enzyme activity and micro-organisms were determined, and compared to conventional pasteurisation and sterilisation processes of tomato puree. High-pressure processing at ambient temperature (HPP) improved the colour and viscosity compared to heat pasteurisation, while the water binding capacity and lycopene content were unaffected by HPP. Products treated at 700 MPa, 20 °C resulted in inactivation of the natural flora to a level below the detection limit. After pressure treatment and during chilled storage a increase in viscosity was observed. HPP caused partial inactivation of polygalacturonase (70%), but activation of pectin methylesterase. After high-pressure sterilisation treatments combined with elevated starting temperatures (≥80 °C, HPS, one or two pulses) an ambient stable product was obtained. HPS (one pulse, 700 MPa, 30 s, 90 °C) reduced B. stearothermophilus spore contamination level in inoculated meatballs in tomato puree with at least 4.5 log units. HPS resulted in more than 99% inactivation of polygalacturonase and pectin methylesterase. HPS resulted in a lower viscosity compared to conventional sterilised samples, whereas the water binding capacity was improved. Colour appreciation was improved and lycopene content was retained compared to a 40% loss after conventional sterilisation.     

A cardinal model to describe the effect of water activity on the growth of moulds

A simple model was proposed to describe the effect of water activity (Aw) on the radial growth rate of moulds. This model is deduced from the cardinal model family proposed by Rosso in 1995, which is only defined from cardinal values of environmental factors (minimum, optimum and maximum values), the growth rate observed at the optimal value of the environmental factors, and n, a shape parameter. For Aw, a simple form of cardinal model is proposed. This form is obtained for n = 2 and Aw(max) = 1.0 (pure water). The final model is so defined from only three parameters: Aw(min), Aw(opt), and optimal radial growth rate (RGR(opt)). This model was successfully fitted on a data set of Aspergillus flavus, Aspergillus nomius, Aspergillus oryzae, Aspergillus parasiticus, Aspergillus candidus, Aspergillus sydowii, Eurotium amstelodami, Eurotium chevalieri, and Xeromyces bisporus. The same quality of fit was obtained for different solutes used to control the Aw (NaCl, glucose/fructose mixture, glycerol), and at different pH values. From this model and using cardinal values extracted from the literature, theoretical evolutions of the RGR of enicillium roqueforti, and Paecilomyces variotii, were proposed and superimposed on data published in the literature. The results showed a good concordance between the predicted and the observed values for these species. The use of this model in Predictive Microbiology is discussed.     

A predictive model to determine the effects of pH, milkfat, and temperature on thermal inactivation of Listeria monocytogenes.

Listeria monocytogenes is a foodborne pathogen of significance because of its comparatively high heat resistance, zero tolerance in ready-to-eat foods, and growth at refrigeration temperatures. A 3 x 3 x 3 factorial study was done to determine the effects of milkfat (0%, 2.5%, 5.0%), pH (5.0, 6.0, 7.0), and processing temperature (55 degrees C, 60 degrees C, 65 degrees C) on the thermal resistance of L. monocytogenes in a formulated and homogenized milk system. Data were fit to a modified Gompertz equation where parameter estimates characterized three regions of a survival curve: the shoulder, maximum slope, and tail. Statistical analysis was done for each of the 27 individual treatment sets to visualize individual effects on parameter estimates and to evaluate how well the Gompertz equation represented the data. A regression model for the Gompertz equation was generated to predict the logarithmic surviving fraction of L. monocytogenes based on all 27 treatments and their single and interactive effects. The shoulder region of the survival curve was affected by pH; however, the maximum slope was affected by temperature, milkfat, and the interaction of temperature x milkfat. Validation of the model suggests that the predictions are best suited for processing above 62 degrees C. Trends over time for a 4-log reduction in cells (4D values) were evaluated using results from the 27 individual treatment sets, the regression model for the Gompertz equation, and a linear equation. At lower temperatures, 4D values by the three methods varied by twofold. At higher temperatures, all methods gave similar 4D values, suggesting that death became more linear. Based on this study all three factors affect heat resistance for specific regions of a survival curve, and a predictive model was developed that can be used as a preliminary estimate for L. monocytogenes inactivation.