Quantifying the effects of heating temperature, and combined effects of heating medium pH and recovery medium pH on the heat resistance of Salmonella typhimurium

The influence of heating treatment temperature, pH of heating and recovery medium on the survival kinetics of Salmonella typhimurium ATCC 13311 is studied and quantified. From each non-log linear survival curve, Weibull model parameters were estimated. An average shape parameter value of 1.67 was found, which is characteristic of downward concavity curves and is in agreement with values estimated from other S. typhimurium strains. Bigelow type models quantifying the heating temperature, heating and recovery medium pH influences are fitted on scale parameter delta data (time of first decimal reduction), which reflects the bacterial heat resistance. The estimate of z(T) (4.64 degrees C) is in the range of values given in the literature for this species. The influence of pH of the heating medium on the scale parameter (z(pH): 8.25) is lower than that of the recovery pH medium influence (z(')(pH): 3.65).     

On the use of the Weibull model to describe thermal inactivation of microbial vegetative cells

This paper evaluates the applicability of the Weibull model to describe thermal inactivation of microbial vegetative cells as an alternative for the classical Bigelow model of first-order kinetics; spores are excluded in this article because of the complications arising due to the activation of dormant spores. The Weibull model takes biological variation, with respect to thermal inactivation, into account and is basically a statistical model of distribution of inactivation times. The model used has two parameters, the scale parameter alpha (time) and the dimensionless shape parameter beta. The model conveniently accounts for the frequently observed nonlinearity of semilogarithmic survivor curves, and the classical first-order approach is a special case of the Weibull model. The shape parameter accounts for upward concavity of a survival curve (beta < 1), a linear survival curve (beta = 1), and downward concavity (beta > 1). Although the Weibull model is of an empirical nature, a link can be made with physiological effects. Beta < 1 indicates that the remaining cells have the ability to adapt to the applied stress, whereas beta > 1 indicates that the remaining cells become increasingly damaged. Fifty-five case studies taken from the literature were analyzed to study the temperature dependence of the two parameters. The logarithm of the scale parameter alpha depended linearly on temperature, analogous to the classical D value. However, the temperature dependence of the shape parameter beta was not so clear. In only seven cases, the shape parameter seemed to depend on temperature, in a linear way. In all other cases, no statistically significant (linear) relation with temperature could be found. In 39 cases, the shape parameter beta was larger than 1, and in 14 cases, smaller than 1. Only in two cases was the shape parameter beta = 1 over the temperature range studied, indicating that the classical first-order kinetics approach is the exception rather than the rule. The conclusion is that the Weibull model can be used to model nonlinear survival curves, and may be helpful to pinpoint relevant physiological effects caused by heating. Most importantly, process calculations show that large discrepancies can be found between the classical first-order approach and the Weibull model. This case study suggests that the Weibull model performs much better than the classical inactivation model and can be of much value in modelling thermal inactivation more realistically, and therefore, in improving food safety and quality.     

Modelling thermal inactivation of Listeria monocytogenes in sucrose solutions of various water activities

The heat resistance of Listeria monocytogenes was determined in sucrose solutions with water activity (a(w)) ranging from 0.99 to 0.90. At all temperatures investigated shape of the survival curves depended on the a(w) of the treatment medium. The survival curves for a(w)=0.99 appeared to be linear, for a(w)=0.96 were slightly upwardly concaved and for a(w)=0.93 and 0.90 were markedly concave upward. A mathematical model based on the Weibull distribution provided a good fit for all the survival curves obtained in this investigation. The effect of the temperature and a(w) on the Weibull model parameters was also studied. The shape parameter (p) depended on the a(w) of the treatment medium but in each medium of different a(w) the temperature did not have a significant effect on this parameter. The p parameter followed a linear relationship with a(w). The scale parameter (delta) decreased with the temperature following an exponential relationship and increased by decreasing the a(w) in the range from 0.99 to 0.93. However the delta parameter of survival curves obtained at a(w)=0.90 were lower than those obtained at a(w)=0.93. A mathematical model based on the Weibull parameters was built to describe the joint effect of temperature and a(w) on thermal inactivation of L. monocytogenes. This model provides a more complete information on the influence of the a(w) on the L. monocytogenes than the data initially generated. The model developed indicated that the effect of the a(w) on the thermal resistance of L. monocytogenes varied depending upon the temperature of treatment.     

Validation of an overall model describing the effect of three environmental factors on the apparent D-value of Bacillus cereus spores

Several factorial models extending the famous Bigelow model to describe the influence of the heating and recovery pH and a_w conditions on bacterial heat resistance have been developed. These models can be associated in an overall multifactorial model describing the influences of heating and recovery conditions on D values. For Bacillus cereus strain ADQP 407 the model parameters characterising the environmental factor influences (pH, Temperature, a_w) were evaluated. Determination of bacterial heat resistance in cream chocolate have been realised to validate these parameter values and to evaluate the level of the influence of food texture or different compounds not taken account of in the model.     

Modelling inactivation of Listeria monocytogenes by pulsed electric fields in media of different pH

A study of the effect of square-wave pulsed electric fields (PEF) on the inactivation of Listeria monocytogenes in McIlvaine buffer of different pH (3.5-7.0) was conducted. L. monocytoges was more PEF sensitive at higher electric field strengths (E) and in media of low pH. A treatment at 28 kV/cm for 400 mus that inactivated 1.5, 2.3 and 3.0 Log10 cycles at pH 7.0, 6.5 and 5.0 respectively destroyed almost 6.0 Log10 cycles at pH 3.5. The general shape of survival curves of L. monocytogenes PEF treated at different pH was convex/concave upwards. A mathematical model based on the Weibull distribution accurately described these survival curves. At each pH, the shape parameter (n value) did not depend on E. The relationship between n value of the Weibull model and the pH of the treatment medium was described by the Gompertz equation. A multiple linear regression model using three predictor variables (E, E2, pH2) related the Log10 of the scale paramenter (b value) of the Weibull model with E and pH of the treatment medium. A tertiary model developed using McIlvaine buffer as treatment medium predicted satisfactorily the inactivation of L. monocytogenes in apple juice.     

Heritability,reliability of genetic evaluations and response to selection in proportional hazard models

The purposes of this study were 1) to investigate the heritability, reliability, and selection response for survival traits following a Weibull frailty proportional hazard model; and 2) to examine the relationship between genetic parameters from a Weibull model, a discrete proportional hazard model, and a binary data analysis using a linear model. Both analytical methods and Monte Carlo simulations were used to achieve these aims. Data were simulated using the Weibull frailty model with two different shapes of the Weibull distribution. Breeding values of 100 unrelated sires with 50 to 100 progeny (with different levels of censoring) were generated from a normal distribution and two different sire variances. For analysis of longevity data on the discrete scale, simulated data were transformed to a discrete scale using arbitrary ends of discrete intervals of 400, 800, or 1200 d. For binary data analysis, an individual's longevity was either 0 (when longevity was less than the end of interval) or 1 (when longevity was equal or greater than the end of interval). Three different statistical models were investigated in this study: a Weibull model, a discrete-time model (a proportional hazard model assuming that the survival data are measured on a discrete scale with few classes), and a linear model based upon binary data. An alternative derivation using basic expressions of reliabilities in sire models suggests a simple equation for the heritability on the original scale (effective heritability) that is not dependent on the Weibull parameters. The predictions of reliabilities using the proposed formulae in this study are in very good agreement with reliabilities observed from simulations. In general, the estimates of reliability from either the discrete model or the binary data analysis were close to estimates from the Weibull model for a given number of uncensored records in this simplified case of a balanced design. Although selection response from the binary data analysis depends on the end of interval point, there is a relatively good agreement between selection responses in the Weibull model and the binary data analysis. In general, when the underlying survival data is from a Weibull distribution, it appears that the method of analyzing data does not greatly affect the results in terms of sire ranking or response to selection, at least for the simplified context considered in this study.     

超高压对泡萝卜的杀菌效果及其动力学研究

研究300～600 MPa超高压条件下处理四川泡萝卜5～25 min,对其细菌总数的影响、对霉菌、酵母菌及大肠菌群的杀灭效果的影响。并采用3 种模型对不同压力条件下杀菌动力学过程进行分析比较。结果表明：随处理压力和时间的增加,超高压对泡萝卜的杀菌效果增强;霉菌和酵母菌对压力较为敏感,500 MPa处理5 min可被全部杀死;Weibull模型能很好地拟合泡萝卜超高压杀菌的动力学过程（决定系数R2＞0.99）,且相较Log-logistic模型更简洁、灵活实用。尺度参数b随处理压力的增加而增大,形状参数n则随压力的增加而减小。     

Thermal inactivation of Escherichia coli O157:H7 when grown statically or continuously in a chemostat

The objective of this study was to determine if survivor curves for heat-inactivated Escherichia coli O157:H7 were affected by the physiological state of the cells relative to growth conditions and pH of the heating menstruum. A comparison was made between the log-linear model and non-log-linear Weibull approach. Cells were grown statically in aerobic culture tubes or in an aerobic chemostat in tryptic soy broth (pH 7.2). The heating menstruum was unbuffered peptone or phosphate buffer (pH 7.0). Thermal inactivation was carried out at 58, 59, 60, and 61°C, and recovery was on a nonselective medium. Longer inactivation times for statically grown cells indicated potential stress adaptation. This was more prevalent at 58°C. Shape response was also significantly different, with statically grown cells exhibiting decreasing thermal resistance over time and chemostat cells showing the opposite effect. Buffering the heating menstruum to ca. pH 7 resulted in inactivation curves that showed less variability or scatter of data points. Time to specific log reduction values (t(d)) for the Weibull model were conservative relative to the log-linear model depending upon the stage of reduction. The Weibull model offered the most accurate fit of the data in all cases, especially considering the log-linear model is equivalent to the Weibull model with a fixed shape factor of 1. The determination of z-value for the log-linear model showed a strong correlation between log D-value and process temperature. Correlations for the Weibull model parameters (log δ and log p) versus process temperature were not statistically significant.     

Pressure inactivation kinetics of Yersinia enterocolitica ATCC 35669

The survival curves of Yersinia enterocolitica ATCC 35669 inactivated by high hydrostatic pressure were obtained at four pressure levels (300, 350, 400, and 450 MPa) in sodium phosphate buffer (0.1 M, pH 7.0) and four pressure levels (350, 400, 450, 500 MPa) in UHT whole milk. Tailing was observed in all the survival curves. A linear model and three nonlinear models were fitted to these data and the performances of these models were compared. The linear regression model for survival curves at four pressure levels had regression coefficients (R2) values of 0.785-0.962 and mean square error (MSE) of 0.265-0.893. A residual plot strongly suggested that a linear regression function was not appropriate as there was strong curvature in the plotted data. The nonlinear regression model using the log-logistic had R2 values of 0.946-0.982 and MSE values of 0.110-0.320. The Weibull model had R2 values of 0.944-0.975 and MSE values of 0.153-0.349. These results indicated that both were better models to describe the pressure inactivation kinetics of Y. enterocolitica in milk and buffer. Among the three nonlinear models studied, the modified Gompertz model produced the poorest fit to data. The number of parameters of the log-logistic model was reduced from four to two so that the model was greatly simplified. The reduced log-logistic model still produced a fit comparable to the full model. Since pressure had no significant effect on the shape factors of the Weibull model at the pressure levels of 300-400 MPa for buffer and 400-500 MPa for milk, models were developed to predict survival curves of Y. enterocolitica at pressures different from the experimental pressures.     

Pressure inactivation kinetics of phage lambda cI 857

Inactivation curves of phage lambda cI 857 inactivated by high hydrostatic pressure were obtained at three pressure levels (300, 350, and 400 MPa) in buffered media and ultrahigh-temperature 2% reduced fat milk. Pressurization of phage lambda in buffered media at 300 MPa for 300 min, 350 MPa for 36 min, and 400 MPa for 8 min reduced the titer of phage lambda by 7.5, 6.7, and 7.7 log, respectively. Pressurization of phage lambda in milk at 300 MPa for 400 min, 350 MPa for 80 min, and 400 MPa for 20 min reduced the titer of phage lambda by 5.4, 6.4, and 7.1 log, respectively. Tailing was observed in all inactivation curves, indicating that the linear model was not adequate for describing these curves. Among the three nonlinear models studied, the Weibull and log-logistic models consistently produced best fits to all inactivation curves, and the modified Gompertz model the poorest. Because there were no significant differences in the values of shape factor (n) for suspension medium buffer, we reduced the number of parameters in the Weibull model from two to one by setting n at the mean value. The simplified Weibull model produced a fit comparable to the full model. Additionally, the simplified Weibull model allowed predictions to be made at pressures different from the experimental pressures. Menstruum was found to significantly affect the pressure resistance of phage lambda. Comparison of pressure inactivation of hepatitis A virus and phage lambda indicated that phage lambda is more sensitive to pressure than hepatitis A virus in Dulbecco's modified Eagle medium with 10% fetal bovine sera.     

Uni- and bimodal Weibull distribution for analyzing the tensile strength of Diss fibers

The present work considered several statistical distribution functions with the aim to critically analyze the strength data of natural Diss fibers. Besides the Weibull two-parameter distributions, three-parameter and bimodal Weibull were used. Kolmogorov–Smirnov, Anderson–Darling and chi-square goodness-of-fit test were used to judge how accurate the theoretical Weibull probability density function (PDF) fits with tensile strength data.

Tensile test results indicated that the fibers have good tensile strength and Young’s modulus. However, their fracture strength exhibits high scatters due to the presence of defects within the fiber and/or on the fiber surface. Microscopic observation revealed that the rupture of the fibers is governed by two types of defects, the rough surface of the fiber formed by several spines and the internal defects such as the defects of connection between fibrils.

The statistical analysis of variability in strength showed that the results of the shape and scale parameters calculated using bimodal Weibull distribution give larger values compared to those using the single Weibull distribution. Also, the strength data points fit well to the bimodal Weibull PDF curve. All three goodness-of-fit tests indicated also that the bimodal Weibull model gives a more accurate prediction of data strength compared to the unimodal Weibull model.     

Predictive abilities of different statistical models for analysis of survival data in dairy cattle

The objective of this study was to compare alternative trait definitions and statistical models for genetic evaluation of survival in dairy cattle. Data from the first 5 lactations of 808,750 first-crop daughters of 3,064 Norwegian Red sires were analyzed. Seven sire models were used for genetic analyses: linear and threshold cross-sectional models for binary survival scores from first lactation; a linear multi-trait model for survival scores from the first 3 lactations; linear and threshold repeatability models for survival scores from the first 5 lactations; a Weibull frailty model for herd life in first lactation; and a Weibull frailty model for herd life in the first 5 lactations. The models were compared to assess predictive ability of sire estimated breeding values with respect to average survival 365 d after first calving for second-crop daughters (not included in calculation of predicted transmitting abilities) of 375 elite sires. Generally, the linear multi-trait model analyzing survival in the first 3 lactations as correlated traits gave more-accurate predicted sire breeding values compared with both linear and Weibull frailty models using data from first lactation only, even when the latter models were extended to include data up to the sixth lactation. The Weibull frailty models did not improve predictive ability of sire estimated breeding values over what was obtained using a simple cross-sectional linear model for binary survival in first lactation.     

基于反演法计算不同温度下小麦面团的水分扩散系数

水分扩散系数是食品加工过程中重要的物理参数。估算水分扩散系数的主要方法是基于第二菲克定律,但在应用这些定律的方式上存在显著差异。本研究采用Peleg、Weibull、双指数这三种常用的食品水分吸附动力学模型拟合了冻干面团在20、30及40℃时的吸湿曲线。在此基础上,通过COMSOL软件分别建立了瞬时平衡、对流、平行指数边界三种条件下的面团吸湿模型,并通过反演法计算出对应模型下的水分扩散系数。结果表明,Weibull模型和双指数模型决定系数均在0.999以上,较为适合冻干面团吸湿曲线的拟合;平行指数边界模型能较好的模拟出不同温度条件下冻干面团的吸附水分变化规律。同时证明了水分扩散系数随温度升高而变大,且不能被当作一个常数。     

Predicting heat inactivation of Staphylococcus aureus under nonisothermal treatments at different pH

The aim was to assess whether heat resistance data obtained from isothermal treatments allow the estimation of survivors of Staphylococcus aureus under nonisothermal conditions and to find a model that accurately predicts its heat inactivation at constantly rising heating rates (0.5-9 degrees C/min) in media of different pH (4.0-7.4). S. aureus showed a higher heat resistance under isothermal treatments at pH 4.0 than at pH 5.5-7.4. However, under nonisothermal treatments S. aureus increased its heat resistance at pH 5.5-7.4 and became more thermotolerant than at pH 4.0. Estimations of survival curves under nonisothermal treatments obtained from heat resistance parameters of isothermal treatments did not adequately fit experimental values. Whereas the number of survivors was much higher than estimated at pH 5.5-7.4, that obtained at the slower heating rates at pH 4.0 was lower. An equation based on the Weibullian-like distribution (log10 S(t) = (t/delta)p) accurately described survival curves obtained under nonisothermal conditions. A nonlinear relationship was observed among the scale parameter (delta) and the heating rate which allowed the development of two equations capable of predicting the inactivation rate of S. aureus under nonisothermal treatments. This study might contribute to prevent public health risks in foods requiring long heating lag phases during their processing.     

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   

Predicting heat inactivation of Listeria monocytogenes under nonisothermal treatments

The aim of this study was to find a model that accurately predicts the heat inactivation of Listeria monocytogenes (ATCC 15313) at constantly rising heating rates (0.5 to 9 degrees C/min) in media of different pH values (4.0 to 7.4). Survival curves of L. monocytogenes obtained under isothermal treatments at any temperature were nearly linear. Estimations of survival curves under nonisothermal treatments obtained from heat resistance parameters of isothermal treatments adequately fit experimental values obtained at pH 4.0. On the contrary, survivors were much higher than estimations at pH 5.5 and 7.4. The slower the heating rate and the longer the treatment time, the greater the differences between the experimental and estimated values. An equation based on the Weibullian-like distribution, log S(t) = (t/delta)p, accurately described survival curves of L. monocytogenes obtained under nonisothermal conditions within the range of heating rates investigated. A nonlinear relationship was observed between the scale parameter (delta) and the heating rate, which allowed the development of an equation capable of predicting the inactivation rate of L. monocytogenes under nonisothermal treatments at pH 5.5 and 7.4. The model predictions were a good fit to the measured data independent of the magnitude of the thermotolerance increase. This work might contribute to the increase in safety of those food products that require long heating lag phases during the pasteurization process.     

多酚氧化酶的射频加热灭活效果及动力学分析

为了阐述多酚氧化酶(PPO)射频加热对灭活规律,本文研究了板间距和溶酶磷酸盐缓冲液电导率对加热速度及酶灭活效果的影响,进行了酶灭活动力学模型研究。结果表明:极板间距和电导率影响射频加热速度,极板间距越大升温越慢,电导率为0.1 S/m时,升温速度最快。在极板间距120 mm,电导率0.1 S/m时,射频加热105 s,PPO的灭活率为91.88%。对酶灭活的动力学曲线分别用一级动力学模型、Weibull模型和Log-Logistic模型进行拟合。通过对模型的拟合评价参数即精确因子Af、偏差因子Bf、根平均方差RMSE和决定系数R2进行比较,PPO的灭活动力学曲线不符合一级反应动力学模型,Weibull和Log-Logistic模型都能较好的拟合PPO失活曲线。通过衡量三种模型的预测值和实测值的一致性,Log-Logistic模型能最好地拟合射频加热条件下多酚氧化酶的失活曲线。     

Statistical evaluation of mathematical models for microbial growth

The aim of this study was to evaluate the suitability of several mathematical functions for describing microbial growth curves. The nonlinear functions used were: three-phase linear, logistic, Gompertz, Von Bertalanffy, Richards, Morgan, Weibull, France and Baranyi. Two data sets were used, one comprising 21 growth curves of different bacterial and fungal species in which growth was expressed as optical density units, and one comprising 34 curves of colony forming units counted on plates of Yersinia enterocolitica grown under different conditions of pH, temperature and CO(2) (time-constant conditions for each culture). For both sets, curves were selected to provide a wide variety of shapes with different growth rates and lag times. Statistical criteria used to evaluate model performance were analysis of residuals (residual distribution, bias factor and serial correlation) and goodness-of-fit (residual mean square, accuracy factor, extra residual variance F-test, and Akaike's information criterion). The models showing the best overall performance were the Baranyi, three-phase linear, Richards and Weibull models. The goodness-of-fit attained with other models can be considered acceptable, but not as good as that reached with the best four models. Overall, the Baranyi model showed the best behaviour for the growth curves studied according to a variety of criteria. The Richards model was the best-fitting optical density data, whereas the three-phase linear showed some limitations when fitting these curves, despite its consistent performance when fitting plate counts. Our results indicate that the common use of the Gompertz model to describe microbial growth should be reconsidered critically, as the Baranyi, three-phase linear, Richards and Weibull models showed a significantly superior ability to fit experimental data than the extensively used Gompertz.     

A PREDICTIVE MODEL FOR HIGH-PRESSURE CARBON DIOXIDE INACTIVATION OF MICROORGANISMS

The Weibull model, which is commonly used for thermal inactivation of microorganisms in literature, was used to describe microbial inactivation by high-pressure carbon dioxide (HPCD). The number of parameters of the model was reduced from two to one in order to avoid interrelationship of these parameters with a slight loss of goodness-of-fit. A second-order polynomial function fulfilling a number of constraints was proposed for the secondary modeling of the time-constant parameter of the reduced Weibull model. This function consists of both pressure and temperature and therefore can be used for HPCD treatments.

PRACTICAL APPLICATIONS

The application of any new technology in food preservation requires a reliable model that accurately describes and predicts the inactivation data of microorganisms. In principle, the methodology presented here could be used to describe and predict the survival data for high-pressure carbon dioxide inactivation of microorganisms at least for some pressure and temperature ranges if the isobaric/isothermal survival curves of these microorganisms are linear, concave upward or downward.