Kinetic model for the inactivation of Lactobacillus plantarum by pulsed electric fields

The kinetics of Lactobacillus plantarum inactivation by pulsed electric fields (PEF) was studied in two different growth stages (exponential and stationary), but in the same reference medium (0.6% peptone water). Electric field intensity and treatment time varied from 20 to 28 kV/cm and 30 to 240 micros, respectively. The experimental data showed that cells in the exponential growth stage were more sensitive to PEF treatment than those in the stationary stage. The inactivation data were adjusted to the Bigelow and Hülsheger models and the Weibull frequency distribution function, and constants were calculated for both growth stages in each model. The models were tested and their accuracy was assessed by using the Accuracy Factor. According to this parameter, the Weibull frequency distribution function gave better fittings for the inactivation by PEF than Bigelow or Hülsheger models. On the other hand, the Bigelow model gave a good accuracy factor and is simpler.     

Modeling high-intensity pulsed electric field inactivation of a lipase from Pseudomonas fluorescens

The inactivation kinetics of a lipase from Pseudomonas fluorescens (EC 3.1.1.3.) were studied in a simulated skim milk ultrafiltrate treated with high-intensity pulsed electric fields. Samples were subjected to electric field intensities ranging from 16.4 to 27.4 kV/cm for up to 314.5 μS, thus achieving a maximum inactivation of 62.1%. The suitability of describing experimental data using mechanistic first-order kinetics and an empirical model based on the Weibull distribution function is discussed. In addition, different mathematical expressions relating the residual activity values to field strength and treatment time are supplied. A first-order fractional conversion model predicted residual activity with good accuracy (A_f = 1.018). A mechanistic insight of the model kinetics was that experimental values were the consequence of different structural organizations of the enzyme, with uneven resistance to the pulsed electric field treatments. The Weibull model was also useful in predicting the energy density necessary to achieve lipase inactivation.     

Modeling within the Bayesian framework, the inactivation of pectinesterase in gazpacho by pulsed electric fields

The inactivation of pectinesterase (PE) activity in gazpacho (a Spanish ready-to-use cold vegetable soup) under pulsed electric fields (PEFs) was studied. Samples were exposed to 4 μs monopolar or bipolar square-wave pulses at 5–35 kV cm⁻¹ electric field intensity for up to 1500 μs and 200 Hz (temperature below 40 °C). Inactivation of PE was greater when treatment time and electric field intensity increased, and bipolar pulses were more effective inactivating PE than monopolar ones. Estimation of parameters and quantities involved in the tested models were performed within the Bayesian framework. The kinetic evolution of the enzyme was explained using a 3-parameter biexponential model based on a mechanism involving two irreversible consecutive steps. Rate constant k₁ was not dependent on neither electric field intensity nor pulse polarity. Rate constant k₂ and ratio between the activities of intermediate forms and the native ones of the enzyme Λ were affected by those conditions.     

Predictive model of Vibrio parahaemolyticus growth and survival on salmon meat as a function of temperature

The growth and survival curves of a strain of pandemic Vibrio parahaemolyticus TGqx01 (serotype O3:K6) on salmon meat at different storage temperatures (range from 0 °C to 35 °C) were determined. In order to model the growth or inactivation kinetics of this pathogen during storage, the modified Gompertz and Weibull equations were chosen to regress growth and survival curves, respectively, and both equations produced good fit to the observed data (the average R² value equals to 0.990 for modified Gompertz and 0.920 for Weibull equation). The effect of storage temperature on the specific growth rate (μ) was modeled by square root type equation, and the relationship between μ and lag time (λ) was described by a rule of μ × λ = constant. The shape factor (n) and scale factor (b) values of the Weibull equations versus the temperature (°C) were plotted and the temperature effects on these parameters were described by two linear empirical equations. The predicted growth and survival curves from the model were compared to real enumeration results, using the correlation coefficient (R²), bias factor (B_f) and accuracy factor (A_f), to assess the performance of the established model. The results showed that the overall predictions for V. parahaemolyticus TGqx01 growth or inactivation on salmon at tested temperatures agreed well with observed plate counts, and the average R², B_f and A_f values were 0.958, 1.019 and 1.035, respectively.     

Inactivation kinetics of peroxidase and polyphenol oxidase in peach juice treated with gaseous ozone

The effectiveness of gaseous ozone for inactivating peroxidase (POD) and polyphenoloxidase (PPO) in peach juice was investigated. The suitability of first‐order and Weibull models to describe inactivation kinetics was also analysed. Peach juice was exposed to ozone (0.11 and 0.20 mg O₃ min^?1 mL^?1) in a bubble column up to 12 min at 20 ± 1 °C. Enzyme activities were reduced due to treatments. The magnitude of the inactivation increased with ozone level and exposure time. Reductions in activity after 12 min of treatment ranged between 99.5% and 99.8% for POD and between 93.9% and 97.3% for PPO, depending on ozone concentration. Inactivation curves were successfully fitted with the first‐order and Weibull models; although, based on the root‐mean‐square error, the corrected Akaike and the Bayesian Schwarz criterion, the Weibull model showed stronger capability in all cases.     

Effect of temperature and substrate on Pef inactivation of Lactobacillus plantarum in an orange juice–milk beverage

The inactivation kinetics of Lactobacillus plantarum in an orange juice–milk beverage treated by Pulsed Electric Fields (PEF) were studied. Experimental data were fitted to Bigelow and Hülsheger kinetic models and Weibull frequency distribution function. Results indicate that both Hülsheger model and Weibull function fit well the experimental data being Accuracy factor values (Af) closer to 1 and Mean Square Error (MSE) closer to 0. The parameter of the Weibull model can be considered as a kinetic indicator as it expresses the microorganism's resistance to treatment by electric pulses. An increase in temperature favoured the inactivation of L. plantarum by PEF as reflected by a decreased in value. Under the same conditions to those studied by other authors we reached less inactivation of L. plantarum in the beverage used in this study than in substrates with a simpler composition.     

Fractional Differential Equations Based Modeling of Microbial Survival and Growth Curves: Model Development and Experimental Validation

ABSTRACT: A fractional differential equations (FDEs)‐based theory involving 1‐ and 2‐term equations was developed to predict the nonlinear survival and growth curves of foodborne pathogens. It is interesting to note that the solution of 1‐term FDE leads to the Weibull model. Nonlinear regression (Gauss–Newton method) was performed to calculate the parameters of the 1‐term and 2‐term FDEs. The experimental inactivation data of Salmonella cocktail in ground turkey breast, ground turkey thigh, and pork shoulder; and cocktail of Salmonella, E. coli, and Listeria monocytogenes in ground beef exposed at isothermal cooking conditions of 50 to 66 °C were used for validation. To evaluate the performance of 2‐term FDE in predicting the growth curves—growth of Salmonella typhimurium, Salmonella Enteritidis, and background flora in ground pork and boneless pork chops; and E. coli O157:H7 in ground beef in the temperature range of 22.2 to 4.4 °C were chosen. A program was written in Matlab to predict the model parameters and survival and growth curves. Two‐term FDE was more successful in describing the complex shapes of microbial survival and growth curves as compared to the linear and Weibull models. Predicted curves of 2‐term FDE had higher magnitudes of R² (0.89 to 0.99) and lower magnitudes of root mean square error (0.0182 to 0.5461) for all experimental cases in comparison to the linear and Weibull models. This model was capable of predicting the tails in survival curves, which was not possible using Weibull and linear models. The developed model can be used for other foodborne pathogens in a variety of food products to study the destruction and growth behavior.     

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.     

A model of non‐isothermal degradation of nutrients,pigments and enzymes

Published isothermal degradation curves for chlorophyll A and thiamine in the range 100–150 °C and the inactivation curves of polyphenol oxidase (PPO) in the range 50–80 °C could be described by the model C(t)/C₀ = exp[?b(T)tⁿ] where C(t) and C₀ are the momentary and initial concentrations, respectively, b(T) a temperature dependent ‘rate parameter’ and n, a constant. This suggested that the temporal degradation/inactivation events of all three had a Weibull distribution with a practically constant shape factor. The temperature dependence of the ‘rate parameter’ could be described by the log logistic model, b(T) = log_e[1 + exp[k(T ? T_c)], where T_c is a marker of the temperature level where the degradation/inactivation occurs at a significant rate and k the steepness of the b(T) increase once this temperature range has been exceeded. These two models were combined to produce a non‐isothermal degradation/inactivation model, similar to one recently developed for microbial inactivation. It is based on the assumption that the local slope of the non‐isothermal decay curve, ie the momentary decay rate, is the slope of the isothermal curve at the momentary temperature at a time that corresponds to the momentary concentration of the still intact or active molecules. This model, in the form of a differential equation, was solved numerically to produce degradation/inactivation curves under temperature profiles that included heating and cooling and oscillating temperatures. Such simulations can be used to assess the impact of planned commercial heat processes on the stability of compounds of nutritional and quality concerns and the efficacy of methods to inactivate enzymes. Simulated decay curves on which a random noise was superimposed were used to demonstrate that the degradation/inactivation parameters, k and T_c, can be calculated directly from non‐isothermal decay curves, provided that the validity of the Weibullian and log logistic models and the constancy of the shape factor n could be assumed. Copyright © 2004 Society of Chemical Industry     

Thermal Inactivation Kinetics of Peroxidase in Coriander Leaves

Design of efficient blanching treatments requires knowledge of critical factors such as enzyme inactivation kinetic parameters and relative proportions of heat-labile and heat-resistant fractions, which is unique in each vegetable. Thermal inactivation curves for peroxidase in coriander leaves were determined in the temperature range of 70 to 100 °C and in steam. The isothermal data were statistically treated using both linear and nonlinear regression. Applicability of various enzyme inactivation models available in the literature was critically evaluated. The two-fraction first-order model was found to be the best model to describe the peroxidase inactivation kinetics in coriander leaves (R ² > 0.97). Kinetic parameters were determined for heat-labile and heat-resistant isoenzyme fractions. The temperature dependence of the rate parameters in the present study did not follow the Arrhenius relationship.     

Modelling of the inactivation kinetics of the trypsin inhibitors in soy flour

The inactivation kinetics of trypsin inhibitors (TIs) in soy flour was measured over a large range of temperatures (80–134°C) and moisture contents (0.08–0.52 g (g ds)⁻¹). The inactivation of TIs showed a two‐phase inactivation behaviour. The influence of moisture content on the inactivation rate of TIs was large at moisture contents <0.30 g (g ds)⁻¹. Six different inactivation kinetics models were used to describe the decrease of the trypsin inhibitor activity at constant moisture content. The models were compared statistically using a corrected Akaike information criterion. The most parsimonious models at moisture contents ≤0.30 g (g ds)⁻¹ were the model with two first‐order reactions each for a different TI group, and the model with an irreversible inactivation of a native TI to a partially active intermediate TI, followed by a denaturation step. The nth order reaction model was favoured at moisture contents ≥0.40 g (g ds)⁻¹. The kinetics parameters of the model with two firstorder reactions were modelled as a function of moisture content. The overall inactivation model described well the experimental inactivation data of TIs. © 1999 Society of Chemical Industry     

Combined effect of temperature and pulsed electric fields on pectin methyl esterase inactivation in red grapefruit juice (<Emphasis Type="Italic">Citrus paradisi</Emphasis>)

Pulsed electric fields (PEF) were applied to freshly prepared grapefruit juice using a laboratory scale continuous PEF system to study the feasibility of inactivating pectin methyl esterase (PME). Square wave PEF using different combinations of pre-treatment temperature, electric field strength and treatment time were evaluated in this study. Inactivation curves for the enzyme were plotted for each parameter and inactivation kinetics were calculated. Results showed that the highest level of inactivation (96.8%) was obtained using a combination of preheating to 50 °C, and a PEF treatment time of 100 μs at 40 kV/cm. Inactivation of grapefruit PME activity could be described using an exponential decay model. Calculated D-values following a 50 °C preheat were 77.5, 76.0 and 70.4 μs at 20, 30 and 40 kV/cm, respectively. The activation energy for the inactivation of PME by PEF was 36.2 kJ/mol.     

KINETICS OF INACTIVATION OF ESCHERICHIA COLI IN CARROT JUICE BY PULSED ELECTRIC FIELD

The inactivation kinetics of Escherichia coli inoculated into carrot juice by pulsed electric field (PEF) was investigated, and the experimental data were fitted to Hülsheger and Peleg models. The electric field strength ranged from 5 to 20 kV/cm, and the number of pulses was from 207 to 1449. The level of E. coli inactivation increased with the increment of the electric field strength and the number of pulses. As the number of pulses increased, the kinetic constants b_E and E_c^a (Hülsheger model) varied from 0.2429 to 0.5778 cm/kV and from 7.1301 to 5.7842 kV/cm, respectively. The k and E_c^b obtained using the Peleg model varied from 2.3277 to 1.4725 kV/cm and from 12.2523 to 7.4755 kV/cm, respectively. The fitting performance of the two models was evaluated by using a series of indices including accuracy factor, bias factor, sum of the squares of the differences of the natural logarithm of the observed and predicted data, correlation coefficient and the root mean square error between the observed and the predicted data. A comparison among these corresponding parameters indicates that the Peleg model better describes the inactivation kinetics of E. coli by PEF than the Hülsheger model.     

Cross-protective effects of temperature, pH, and osmotic and starvation stresses in Escherichia coli O157:H7 subjected to pulsed electric fields in milk

The effect of exposure of Escherichia coli O157:H7 to prior stress on the effectiveness of pulsed electric field (PEF) treatment of milk was studied. Cells were exposed to a variety of temperatures (7–45 °C), pH (4.0–7.0), osmotic conditions (0–10% NaCl), starvation (100 h at 25 °C), and cold shock (5 °C for 250 h). Stress responses were explained by the Gompertz and Weibull models with similar goodness-of-fit. Using these models, conditions that induced adequate stress were identified and used to pre-condition E. coli O157:H7 cells. The inactivation of the bacterial cells in milk by PEF was characterized by downward concavity with differences in mean time of resistance between cells exposed to temperature, acid or osmotic stress. Application of the Weibullian–Log-Logistic model indicated that, at higher field strengths, inactivation occurred at lower onset temperatures, and this was related to an increase in heat dissipation.     

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.     

Modeling the Transfer of Salmonella Enteritidis during Slicing of Ready‐to‐Eat Turkey Products Treated with Thyme Essential Oil

The increased demand for low‐sodium ready‐to‐eat (RTE) meat products highlights the need for new strategies to ensure food safety. The application of essential oils (EOs) as natural antimicrobials in the meat industry has been suggested to prevent or control cross‐contamination during meat processing operations. This work aims to quantify and model the transfer of Salmonella Enteritidis during the slicing procedure of RTE turkey products treated with thyme essential oil (TEO) at a concentration of 0.1% (v/w). Two products were subjected to the slicing procedure with slicer blades inoculated with S. Enteritidis at 10⁸ cfu/mL. The Weibull and modified Weibull predictive models were fitted to the transfer data. Twenty slices were sampled and showed positive with bacteria, indicating cross‐contamination. The number of cells transferred per slice decreased logarithmically during the assays. The transfer models, based on the Weibull model, were suitable to describe the bacterial transfer trend on slices in most cases. TEO treatment reduced the transfer of Salmonella on a preservative free RTE turkey product. The predictive models obtained in this study can help food‐quality staff and managers on the design and assessment of processes to guard RTE turkey products against Salmonella. This work supports the addition of EOs to reduce microbial risk in RTE meat products.     

Inactivation kinetics of some microorganisms in apple,melon, orange and strawberry juices by high intensity light pulses

The suitability of some models was analyzed to characterize the Pulsed Light (PL) inactivation kinetics for Escherichia coli ATCC 35218, Listeria innocua ATCC 33090, Salmonella Enteritidis MA44 and Saccharomyces cerevisiae KE162 in commercial juices and fresh squeezed juices. A negative relationship was found between the absorbance of juices and PL effectiveness. PL treatment (2.4–71.6 J/cm²) was ineffective in natural strawberry and orange juices. In general, inactivation curves exhibited a marked upward concavity, reaching after 60 s-PL treatment to 0.3–6.9 log-reduction cycles. Nonlinear semilogarithmic survival curves were fitted by conceptually different models: the Weibull model, the biphasic model and a modified version of the Coroller model. Biphasic and Weibull models compared to the modified Coroller model allowed a better fit and more accurate estimation of parameters. A multivariate approach to data analysis by principal components (PCA) showed relevant spatial relationships among estimated model parameters, revealing PL treatment efficacy in the different juices.     

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.     

Optimising the inactivation of grape juice spoilage organisms by pulse electric fields

The effect of some pulsed electric field (PEF) processing parameters (electric field strength, pulse frequency and treatment time), on a mixture of microorganisms (Kloeckera apiculata, Saccharomyces cerevisiae, Lactobacillus plantarum, Lactobacillus hilgardii and Gluconobacter oxydans) typically present in grape juice and wine were evaluated. An experimental design based on response surface methodology (RSM) was used and results were also compared with those of a factorially designed experiment. The relationship between the levels of inactivation of microorganisms and the energy applied to the grape juice was analysed. Yeast and bacteria were inactivated by the PEF treatments, with reductions that ranged from 2.24 to 3.94 log units. All PEF parameters affected microbial inactivation. Optimal inactivation of the mixture of spoilage microorganisms was predicted by the RSM models at 35.0 kV cm^− 1 with 303 Hz pulse width for 1 ms. Inactivation was greater for yeasts than for bacteria, as was predicted by the RSM. The maximum efficacy of the PEF treatment for inactivation of microorganisms in grape juice was observed around 1500 MJ L^− 1 for all the microorganisms investigated. The RSM could be used in the fruit juice industry to optimise the inactivation of spoilage microorganisms by PEF.     

INACTIVATION KINETICS OF SALMONELLA DUBLIN BY PULSED ELECTRIC FIELD

Microbial inactivation kinetic models are needed to predict treatment dosage in food pasteurization processes. In this study, we determined inactivation kinetic models of Salmonella dublin in skim milk with a co-field flow high voltage pulsed electric field (PEF) treatment system. Electric field strength of 15–40 kV/cm, treatment time of 12–127 μs, medium temperatures of 10–50C were tested. A new inactivation kinetic model that combines the effect of treatment time to electric field strength or medium temperature was developed.