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.     

Promoting Bacillus cereus spore germination for subsequent inactivation by mild heat treatment

Sublethal heat treatment may activate dormant spores and thereby potentiate the conversion of spores to vegetative cells. As the germinated spore is known to possess lower heat resistance than its dormant counterpart, it has been postulated that double heat treatment, i.e., spore heat activation followed by germination and then by heat inactivation, can be used to control spores in foods. Production of refrigerated processed foods of extended durability often includes more than one heat treatment of the food components. This work simulates conventional heat treatment procedures and evaluates double heat treatment as a method to improve spore control in model food matrixes of meat broth and cream sauce. Bacillus cereus NVH 1230-88 spores were supplemented in food model matrixes and heat activated at 70°C and then heat inactivated at 80 or 90°C. The samples were held at 29 to 30°C for 1 h between primary and secondary heat treatments, to allow spore germination. Nutrients naturally present in the food matrixes, e.g., amino acids and inosine, could act as germinants that induce germination. The levels of germinants could be too low to produce effective germination within 1 h. Following primary heat treatment, some samples were therefore supplemented with a combination of L-alanine and inosine, a germinant mixture known to be effective for B. cereus spores. In both matrixes, a combination of double heat treatment (heat activation, germination, and inactivation) and addition of germinants gave a reduction in spore counts equivalent to or greater than that obtained with a single heat treatment for 12 min at 90°C. Addition of germinants was essential to induce effective germination in cream sauce during 1 h at 29 to 30°C, and germinants were therefore a crucial supplement to obtain an effect of double heat treatment in this matrix. These data will be valuable when setting up temperature-time-germinant combinations for an optimized spore reduction in mild-heat-treated foods.     

Predicting microbial heat inactivation under nonisothermal treatments

The aim of this study was to develop an equation that accurately predicts microbial heat inactivation under nonisothermal treatments at constantly rising heating rates (from 0.5 to 5 degrees C/min) in media with different pH values (4.0 or 7.4). The survival curves of all bacteria (Enterococcus faecium, Escherichia coli, Listeria monocytogenes, Salmonella Senftenberg 775W, Salmonella Typhimurium, and Staphylococcus aureus) tested under isothermal treatments were nearly linear. For the most heat-resistant microorganism (E. faecium), the estimated DT-values at pH 7.4 were at least 100 times those of the second most thermotolerant microorganism (Salmonella Senftenberg 775W). The heat resistance of E. faecium was up to 30 times lower at pH 4.0 than at pH 7.4. However, E. faecium was still the most heat-resistant microorganism under nonisothermal treatments at both pH values. Inactivation under nonisothermal conditions was not accurately estimated from heat resistance parameters of isothermal treatments when microbial adaptation or sensibilization occurred during the heating up lag phases. The under-prediction of the number of survivors might be greater than 15 log CFU within the nonisothermal treatment conditions investigated. Therefore, the nonisothermal survival curves of the most heat-resistant microorganisms were fitted with the following equation: log S(t) = -(t/delta)P. This equation accurately described the survival curves of all the bacteria tested. We observed a linear relationship between the log of the scale parameter (delta) and the log of the heating rate. A p value characteristic of each microorganism and pH tested was calculated. Two equations capable of predicting the inactivation rate of all bacteria tested under nonisothermal treatments at pH 7.4, 5.5, or 4.0 were developed. The model was evaluated in skim milk and apple juice. The results of this study could be used to help minimize public health risks and to extend the shelf life of those foods requiring long heating up lag phases during processing.     

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).     

A mathematical model to describe the change in moisture distribution in maize starch during hydrothermal treatment

Instantaneous Controlled Pressure Drop, ' Détente Instantanée Contrôlée ' (DIC) was performed on standard maize starch at residual moisture content (∼12%). Changes in moisture distribution were observed during the treatment and modelled through a phenomenological model based on gravimetric data. The model proposes an exponential variation in the moisture content with processing time at various pressures. The predicted data were found to be in good agreement with experimental data. The values of water activity coefficient ( γ ) obtained from the model decrease, when processing pressure increases; 5.86, 3.71 and 3.36 (dry basis)⁻¹ for 1, 2 and 3 bar, respectively. The mass transfer coefficient decreases, when the pressure increases. Its value ranged from 5.89 × 10⁻⁵ m s⁻¹ for 1 bar down to 0.92 × 10⁻⁵ m s⁻¹ for 2 bar and 0.77 × 10⁻⁵ m s⁻¹ for 3 bar. This coefficient is not only controlled by a simple resistance to the mass transfer, but also by gelatinisation phenomenon that progresses when temperature increases.     

A novel approach to predicting microbial inactivation kinetics during high pressure processing

The inactivation kinetics of Escherichia coli (ATCC 25922) during high pressure processing (HPP) was examined from 200 to 400 MPa in 50 MPa increments at 15 degrees C. Although the time course of HPP-induced E. coli inactivation in 0.1% peptone water successfully fitted the Weibull function, this procedure involved curve fitting, and not prediction. The objective of this study was to develop a novel HPP-induced microbial inactivation model to simulate the inactivation kinetics under various pressure conditions. The maximum inactivation rate during HPP was calculated from the inactivation curves at different pressure conditions on a semi-log plot. The relationship between the square root of the absolute value of the inactivation rate (k(max)) and treatment pressure was linear (R(2)=0.99). The linear relationship between k(max) and treatment pressure also successfully described independent data from other studies in the literature. Overall, the newly developed differential equation model, into which was substituted the square root function of the inactivation rate, was capable of simulating the inactivation kinetics during HPP at constant pressure. Additionally, the model could successfully describe the inactivation kinetics during HPP using other researchers' data. The accuracy of prediction of the new model was comparable to that derived from Weibull or modified Gompertz fitting to the observed data. Furthermore, the new model could successfully simulate the inactivation kinetics during dynamic pressure conditions, which included come-up time, changes in holding pressure during treatment, and pressure-release time. Moreover, the effect of pulsed pressure treatment was also simulated successfully using this model. Therefore, the modeling procedure presented in this study will contribute to the advancement of predictive modeling for HPP-induced microbial inactivation.     

Effects of mild heat treatment on microbial growth and product quality of packaged fresh-cut table grapes

ABSTRACT:  The changes in packaged fresh-cut grape quality and microbial growth as affected by mild heat treatments and the retention of grape cap stems during 5 °C storage were evaluated. Each individual grape was either manually pulled off (stemless) from the stems, or cut (cut stem) to allow for a 1- to 2-mm cap stem remaining on the berry. The samples were sanitized in 100 mg/L chlorine solution for 1 min, followed by a mild heat treatment in a water bath (45 °C, 8 min) or an oven (55 °C, 5 min). After cooling, the berries were packaged in rigid trays sealed with a gas permeable film and stored at 5 °C. Product quality and decay rate were evaluated periodically during storage. The results indicate that in the package headspace for hot water treatment of stemless grapes, partial pressures of O₂ declined significantly ( P < 0.05) less and C₂H₄ increased significantly ( P < 0.001) less than for the control and hot air treatment. Stem removal and heat treatment had significant ( P < 0.05) effects on the decay rate of grapes during storage. Hot water treatment maintained a significantly lower decay rate than the control and hot air treatment throughout the entire storage. Color and texture were not significantly ( P > 0.05) affected by either heat treatment or stem removal. Grapes that retained the cap stems and received hot water treatment had the lowest decay rate and lowest microbial growth with the absence of any negative impact on grape color, texture, and flavor.     

Predictive model to describe water migration in cellular solid foods during storage

BACKGROUND: Water migration in cellular solid foods during storage causes loss of crispness. To improve crispness retention, physical understanding of this process is needed. Mathematical models are suitable tools to gain this physical knowledge. RESULTS: Water migration in cellular solid foods involves migration through both the air cells and the solid matrix. For systems in which the water migration distance is large compared with the cell wall thickness of the solid matrix, the overall water flux through the system is dominated by the flux through the air. For these systems, water migration can be approximated well by a Fickian diffusion model. The effective diffusion coefficient can be expressed in terms of the material properties of the solid matrix (i.e. the density, sorption isotherm and diffusion coefficient of water in the solid matrix) and the morphological properties of the cellular structure (i.e. water vapour permeability and volume fraction of the solid matrix). The water vapour permeability is estimated from finite element method modelling using a simplified model for the cellular structure. CONCLUSION: It is shown that experimentally observed dynamical water profiles of bread rolls that differ in crust permeability are predicted well by the Fickian diffusion model. Copyright © 2011 Society of Chemical Industry     

Review: Enzyme inactivation during heat processing of food-stuffs

Enzyme inactivation during heat processing is reviewed with regard to fundamental aspects (structure, thermodynamics and kinetics), mathematical models and the relationship between enzyme activity and food quality. Enzyme stability is related to enzyme structure and to factors in the microenvironment. Kinetics of inactivation are categorized with respect to reaction order and two models are briefly discussed which describe the variation of inactivation rates with temperature. The determination of accurate kinetic parameters is emphasized where the objective is to develop mathematical models of enzyme inactivation in real foods. The value of modelling inactivation is assessed. Enzymes having effects on sensory quality are reviewed with particular emphasis on those enzymes which influence flavour, through lipid degradation, and those which affect texture by catalysing the breakdown of starch, pectin or protein.     

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.     

Using a change-point model to describe temporal bitter relationships among hop-derived compounds

The bitterness of four hop-derived compounds was measured over a range of concentrations using a time–intensity protocol to determine temporal bitterness relationships. Bitter attributes were compared among compounds by applying a three parameter, change-point model to all concentration-dependent attributes whereby α represented the bitter parameter’s magnitude at very low compound concentrations up to a change-point concentration, θ, and β represented the log-linear concentration dependency of the bitter parameter above the change-point concentration, θ. Panelist reliability was determined by evaluating how well their data fit the model parameters as determined via a t-statistic. Analysis of variance of the concentration-dependent parameters, maximum intensity, duration, area-under-curve, and, decreasing area, identified differences among compounds. In the case of panelist × compound interactions, within-panelist analysis of change-point parameters yielded panel-wise relationships not initially detected.     

Combination treatment of alkaline electrolyzed water and citric acid with mild heat to ensure microbial safety, shelf-life and sensory quality of shredded carrots

The objective of this study was to determine the synergistic effect of alkaline electrolyzed water and citric acid with mild heat against background and pathogenic microorganisms on carrots. Shredded carrots were inoculated with approximately 6-7 log CFU/g of Escherichia coli O157:H7 (932, and 933) and Listeria monocytogenes (ATCC 19116, and 19111) and then dip treated with alkaline electrolyzed water (AlEW), acidic electrolyzed water (AcEW), 100 ppm sodium hypochlorite (NaOCl), deionized water (DaIW), or 1% citric acid (CA) alone or with combinations of AlEW and 1% CA (AlEW + CA). The populations of spoilage bacteria on the carrots were investigated after various exposure times (1, 3, and 5 min) and treatment at different dipping temperatures (1, 20, 40, and 50 °C) and then optimal condition (3 min at 50 °C) was applied against foodborne pathogens on the carrots. When compared to the untreated control, treatment AcEW most effectively reduced the numbers of total bacteria, yeast and fungi, followed by AlEW and 100 ppm NaOCl. Exposure to all treatments for 3 min significantly reduced the numbers of total bacteria, yeast and fungi on the carrots. As the dipping temperature increased from 1 °C to 50 °C, the reductions of total bacteria, yeast and fungi increased significantly from 0.22 to 2.67 log CFU/g during the wash treatment (p ≤ 0.05). The combined 1% citric acid and AlEW treatment at 50 °C showed a reduction of the total bacterial count and the yeast and fungi of around 3.7 log CFU/g, as well as effective reduction of L. monocytogenes (3.97 log CFU/g), and E. Coli O157:H7 (4 log CFU/g). Combinations of alkaline electrolyzed water and citric acid better maintained the sensory and microbial quality of the fresh-cut carrots and enhanced the overall shelf-life of the produce.     

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.     

Effectiveness of pulsed light treatments assisted by mild heat on Saccharomyces cerevisiae inactivation in verjuice and evaluation of its quality during storage

The effects of pulsed light (PL) processing parameters such as depth of juice layer (1, 3, 5 mm), distance from the lamp (5, 10 cm) and number of pulses (0–50 pulses) on the inactivation of Saccharomyces cerevisiae in verjuice, a clarified beverage obtained from freshly-squeezed unripe grapes, were investigated. A reduction of 0.96 ± 0.27 log CFU/mL was achieved by applying a dose of 34 J/cm² (1-mm layer depth, 5-cm distance, 50 pulses). PL was combined with mild heating (MH) at 43, 45 and 47 °C to increase its inactivation efficacy. Pasteurization was achieved by applying 17 J/cm² at 45 °C (PLMH45–3) and 6.12 J/cm² at 47 °C (PLMH47–3) to a 3-mm juice layer with S. cerevisiae reductions of 5.10 ± 0.24 and 5.06 ± 0.08 log CFU/mL, respectively. Quality properties of PLMH47–3-pasteurized verjuice were monitored during 6 weeks of storage at refrigerated (5 °C) and room temperature (25 °C), The results were compared to those of untreated and thermally pasteurized (72 °C/18 s) samples. Untreated juice spoiled within 2 weeks at 25 °C. No growth was detected in other conditions for 6 weeks. Among quality characteristics, only optical properties changed slightly during storage. It was concluded that mild MH-assisted pulsed light treatments have potential for verjuice pasteurization compared to conventional thermal pasteurization due to the better preservation of its fresh-like characteristics.     

Scale-up unit of a unique moderately high pressure unit to enhance microbial inactivation

The efficacy of a scale-up of a moderately high pressure unit built in this work was investigated with regards to inactivation of Geobacillus stearothermophilus spores suspended in pumpkin soup, and effect of the process on l-ascorbic acid. In this design saturated steam was used as a heating medium. The treatment unit is a double pipe heat exchanger in which the food is pumped in its inner tube, while steam is passed in the annular region to heat the sample. This technology comprises a unique approach of generating a mild pressure (80-100 MPa) utilizing thermal expansion of the liquid being treated. The results show that this unique application decreased the D-values of Geobacillus stearothermophilus ATCC 7953 spores suspended in soup samples in comparison to thermal treatment alone. The improvement was more significant at lower treatment temperatures. The D-values obtained were in a good agreement with that of the small unit built earlier in which oil was used as a heating medium. The effect of treatment on l-ascorbic acid was similar to that of thermal treatment. The treated samples were subjected to shelf life study by storing them at two different temperatures. No evidence of spore recovery was noted during the post-treatment storage period.     

Bacterial spore inhibition and inactivation in foods by pressure, chemical preservatives, and mild heat

Sucrose laurates, sucrose palmitate, sucrose stearates, and monolaurin (Lauricidin) were evaluated for inhibitory effects against spores of Bacillus sp., Clostridium sporogenes PA3679, and Alicyclobacillus sp. in a model agar system. The combined treatment of sucrose laurate, high hydrostatic pressure, and mild heat was evaluated on spores of Bacillus and Alicyclobacillus in foods. The minimum inhibitory concentrations of the sucrose esters were higher than that of Lauricidin for all spores tested in the model agar system, but Lauricidin was not the most readily suspended in the test media. The sucrose laurates and sucrose palmitate were more effective and more readily suspended than the sucrose stearates. A combined treatment of sucrose laurate (<1.0%), 392 megaPascals (MPa) at 45 degrees C for 10 to 15 min provided 3- to 5.5-log10 CFU/ml reductions from initial populations of 10(6) CFU/ml for Bacillus subtilis 168 in milk, Bacillus cereus 14579 in beef, Bacillus coagulans 7050 in tomato juice (pH 4.5), Alicyclobacillus sp. N1089 in tomato juice (pH 4.5), and Alicyclobacillus sp. N1098 in apple juice. The most notable change in the appearance of the products was temporary foaming during mixing of the sucrose laurate in the foods. The effect of sucrose laurate appeared to be inhibitory rather than lethal to the spores. The inhibitory effects observed on Bacillus and Alicyclobacillus spores by the combined treatment of pressure, mild heat, and sucrose laurate appear promising for food applications where alternatives to high heat processing are desired.     

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     

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.