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On calculating sterility in thermal preservation methods : Application of the Weibull frequency distribution model
Abstract
A simple and parsimonious model which originated from the Weibull frequency distribution was proposed to describe nonlinear survival curves of spores. This model was suitable for downward concavity curves (Bacillus cereus and Bacillus pumilus), as well as for upward concavity curves (Clostridium botulinum). It was shown that traditional F values calculated from this new model were no longer additive, to such an extent that a heat treatment should be better characterized by the obtained decimal reduction of spores. A modified Bigelow method was then proposed to assess this decade reduction or to optimize the heat treatment for a target reduction ratio.
... The viable cell counts were converted to log 10 values and plotted against time (min) to obtain survival curves. Survival curves were fitted to log-linear (Bigelow & Esty, 1920) and Weibull (Mafart et al., 2002) models using GlnaFit Excel add-in software (Version 1.8, Geeraerd et al., 2005). The equation for the log-linear model was as follows: ...
... The scale parameter (α) is the time for the first decimal reduction in the population (Mafart et al., 2002). When the ground chicken was heated at 60 C or lower temperatures, the α value was reduced significantly ( p < 0.05) in the presence of herbal extract (Table 2). ...
... Therefore, the inactivation curves can show downward (β > 1) or upward (β < 1) concavity. The curve is linear when β = 1 (Mafart et al., 2002). In the control samples, that is, without herbal extract, β value increased by increasing temperature from 55 to 57.5 C but then decreased with increasing temperature. ...
Thermal death kinetics of Salmonella Enteritidis in ground chicken in the presence of ribwort, sorrel and yarrow extracts mixture (1%) was investigated by fitting the inactivation curves to the log–linear and Weibull models. The thermal inactivation curves were fitted well to both models (r² ≥ 0.94). The times required for 4–log reduction in the S. Enteritidis population were shortened by 47–64% in ground chicken supplemented with the herbal extract mixture (p < 0.05). The 4–log reduction times calculated using the Weibull model were 0.13–13.6% longer than those extrapolated with the log–linear model. The z values in the ground chicken samples with and without herbal extract were 5.08°C (r² = 0.97) and 5.57°C (r²= 0.94), respectively. The results suggest that the mixture of these extracts increased the thermal sensitivity of S. Enteritidis significantly at tested temperatures. In addition, using the Weibull model to calculate thermal death kinetics may reduce the underestimation of the thermal reduction times.
Practical applications
This research aimed to investigate the effects of an herbal extract mixture consisting of ribwort, sorrel, and yarrow on the thermal resistance of Salmonella Enteritidis in ground chicken. While these plants are recognized for their antimicrobial and antioxidant properties, there are not many studies conducted to explore their effects on foodborne pathogens in the food matrix. As far as we know, this is the first study that examines the impact of these plants on the thermal resistance of S. Enteritidis in ground chicken. We determined the thermal death kinetics of S. Enteritidis in ground chicken with and without the herbal extract mixture using curve fitting to log‐linear and Weibull models. The findings of this study could help the food industry to develop cooking conditions for Salmonella‐free chicken products.
... Regardless of the source of lethal agents (chemical-biocides, fungicides, physical-plasma, UV radiation, heat 10 ), in predictive microbiology it is usually assumed that the deactivation process follows first-order kinetics [16][17][18] . This approach results in exponential decreasing of the number of the microorganisms in the affected sample with time. ...
... In particular, the Weibull distribution and its variations (see, e.g. 17,19 ), resp. the Gompertz (sigmoid) model in its alternative forms (e.g. ...
Presented paper deals with a novel application of the (nonlinear) logistic equation to model an elimination of microscopic filaments types of fungi-molds from affected materials via different external inactivation techniques. It is shown that if the inactivation rate of the external source is greater than the maximum natural growth rate of mycelium, the mold colony becomes destroyed after a finite time. Otherwise, the mycelium may survive the external attack only at a sufficiently large initial concentration of the inoculum. Theoretically determined growth curves are compared with the experimental data for Aspergillus brasiliensis mold inactivated by using both cold atmospheric plasma (CAP) and UV-germicidal lamp. Model presented in the article may be applied also to other classes of microorganisms (e.g. bacteria).
... The survival data for three different microorganisms were fitted to the log-linear and Weibull models (John & Ramaswamy, 2020;Mafart et al., 2002). ...
... In this case, f R is analogous to the classic D-value when one log 10 reduction is considered (Mafart et al., 2002). ...
Short‐chain fructooligosaccharides (sc‐FOS) are a soluble dietary fiber with a low calorific value and a sweet taste. The beverage industry is leveraging sc‐FOS in a variety of innovative functional drinks. However, sc‐FOS drinks are vulnerable to microbial spoilage due to the presence of free sugars and high water activity. This study explored the potential of pulsed light (PL) technology to pasteurize water enriched with sc‐FOS at 3% and 6% levels of usage. PL treatments were carried out at 1.7, 1.9, and 2.1 kV for 120, 180, and 240 s, corresponding to fluence ranging between 0.28 and 1.03 J/cm². The microbial inactivation (of Saccharomyces cerevisiae, Escherichia coli, and Listeria monocytogenes), pH, titratable acidity (TA), total soluble solids (TSS), color profile, and sc‐FOS integrity were investigated. A 5‐log10 inactivation in the microbial populations was obtained at 1.9 kV/ 240 s (equivalent to 0.85 J/cm² fluence). Of the log‐linear and Weibull models evaluated, Weibull model was found to best‐fit the inactivation kinetics. Insignificant effects of PL were observed on pH, TA, TSS, and color. More than 98% sc‐FOS content was retained in all samples after PL flashing. Therefore, PL technology can be explored as an industrial antimicrobial intervention for functional beverages, including water enriched with sc‐FOS.
Practical applications
Short‐chain fructooligosaccharides (sc‐FOS) are a soluble dietary fiber with a low calorific value and a sweet taste. This study explored the potential of pulsed light (PL) technology to pasteurize water enriched with sc‐FOS at 3% and 6% levels of usage. The study establishes that pulsed light (PL) treatment can be an effective nonthermal pasteurization condition for functional water enriched with short‐chain fructooligosaccharides (sc‐FOS). A PL fluence of 0.85 J/cm² can be employed for the pasteurization of a 3% sc‐FOS drink (considered a source of dietary fiber) and a drink with 6% sc‐FOS (considered a fiber‐enriched drink). PL fluence up to 1.03 J/cm² has no concerning effect on the total sugars or sc‐FOS content of the water enriched with FOS after PL treatment, thus making it suitable for an industrial application.
... A nonlinear Weibull model can be used to fit data with either a downward or upward concavity, depending on the shape parameter of the fitted curve as shown in Equation 2 (Mafart et al., 2001;Abee et al., 2016;R Core Team, 2019). ...
... In general, the highest level of risk reduction is achieved by the first 2 or 3 logs of inactivation, and these translate to a 99% or 99.9% reduction in bacterial counts. Each Table 3. Inactivation parameters calculated by the Weibull model (Mafart et al. 2001) and goodness of fit (R 2 ) for E. coli O157:H7 and Campylobacter jejuni (Trial 2) 7.1 ± 0.11 1.9 ± 0.12 2.8 ± 0.36 0.99 Campylobacter jejuni (Trial 3) 6.6 ± 0.15 1.0 ± 0.12 1.8 ± 0.29 0.99 Log10N(0), initial population. ...
Drying is one of the oldest methods of food preservation, involving the addition of salt and removal of water to generate a shelf-stable and nutrient-dense product. Pathogens have demonstrated the ability to adapt during a slow drying process, making them more resistant to dehydration and heat treatment. In Ethiopia, an inconsistent electrical grid makes refrigeration unreliable, making dried meat products desirable to consumers. The main dried beef product, qwanta, is very labor intensive to produce. It is therefore not well suited for commercial production and drying at ambient temperatures limits inactivation of pathogenic bacteria. This study quantitatively evaluated the inactivation kinetics of foodborne pathogens during the drying of a restructured beef jerky product produced by a heat treatment that could be applied in anEthiopian butcher shop. A secondary objective was to evaluate effects of including 15% (w/w) pureed dates or raisins into the formulation. Challenge studies were performed on 5 serotypes of Salmonella enterica, 3 strains of Escherichia coli O157:H7, and 3 strains of Campylobacter jejuni. Meat formulations were inoculated with stationary phase cultures, formed into strips, and dehydrated for 6 h in a home-style dehydrator. Samples were weighed pre- and post-drying, plated for enumeration of challenge strains each hour, and water activity (aw) was measured at each sampling interval. Nonlinear predictive models were fit to the inactivation data, revealing an inverse sigmoidal curve for S. enterica and concave downward curves for E. coli and Campylobacter. Salmonella and E. coli were reduced 4.56 ± 0.35 and 6.27 ± 0.69 log (CFU/g),respectively, after 6 h of drying, while Campylobacter was reduced below the limit of detection (>4.32 log [CFU/g] reduction) after 3 h of drying. Including dates (15% w/w) into formulation improved the reduction of S. enterica by 0.63 log (CFU/g) compared to the control (P=0.02), whereas the addition of raisins showed a non-significant improvement (0.50 log CFU/g; P=0.07). Modified processes to improve the safety and extend the shelf life of animal-sourced foods in Ethiopia can reduce the incidence of foodborne disease and provide consumers with a more convenient and accessible source of protein as well as reduce food waste. These predictive models and validation studies may be useful for Ethiopian and US jerky producers, giving them the ability to more accurately assess the microbial risk of their products
... The effects of pH and voltage gradient on Byssochlamys fulva inactivation was investigated through calculating the D value and Z value . As the observed inactivation kinetics behavior was not log-linear, the Weibull model described by Mafart et al. (2002) was chosen for modeling B. fulva death in tomato juice. In order to estimate the main inactivation parameters of the Weibull model δ (time of first decimal reduction) and p (shape parameter), GInaFiT software (Geeraerd et al., 2005) was used. ...
... When p > 1 and p < 1, the concave of survival curve is downward (shoulders) and upward (tailings), respectively. When p = 1, the Weibull model is a simple first-order kinetics (Mafart et al., 2002). ...
Ohmic heating is an emerging direct thermal technology, which uses electricity to heat food products volumetrically. Ohmic heating provides thermal and non-thermal effects like electropermeabilization to inactivate microorganisms. In this study, ohmic heating was used to inactivate Byssochlamys fulva in tomato juice. The main and interaction effects of initial pH (3.5 and 4.5) and voltage gradient (15 and 20 V/cm) were investigated on mold inactivation during ohmic heating at 88, 93, and 98 °C for 20, 10 and 5 min, respectively. The pH, acidity, total soluble solids, and Dvalue were compared. The results showed that pH and voltage gradient had significant effects on Dvalue and Zvalue (p < 0.05). In order to model the survival behavior of Byssochlamys fulva, due to the nonlinearity of the curves, Weibull model gave more accurate estimation compared to classical first-order model.
... The shape parameter (p) has a positive correlation with the scale parameter (δ), such that a greater value of δ corresponds to a more convex shape in the pattern of bacteria survival (p > 1) (Ma et al. 2012;Mafart et al. 2002). In all unsterilized mixtures, the calculated value of p was lower than 1 (p < 1), indicating that the survival dynamics of E. coli NAR in unsterilized mixtures followed a concave shape (Fig. 2b & 1a). ...
... For better comparison of treatments, the Weibull survival model(Mafart et al. 2002) (Eq. 1) was tted to the survival data using GInaFiT version 1.6 (Geeraerd et al. ...
This study evaluated the survival characteristics of Escherichia coli (E. coli), a fecal indicator bacterium, in soil treated with organo-zeolitic substrates with different zeolite particle sizes in micro and nanoscale. For this purpose, we added 5, and 15 grams (g) zeolite or nano-zeolite to 5 g cow manure, and then added these substrates to the different amounts of a loam soil to obtain a 100 g mixture. To examine the net effects of substrates, our experiments were conducted in unsterile and sterile conditions. After the mixture's preparation, all mixtures were inoculated by 10 6 cells of a nalidixic-acid resistant E. coli (E. coli NAR) per g mixtures. Results showed that the application of organo-zeolitic substrates and sterilization significantly influenced E. coli NAR inactivation in soil. in unsterile mixtures, the presence of micro-size zeolite results in a higher td value, and in sterile mixtures, E. coli NAR survived more in mixtures containing nano-zeolite. These results clearly showed that competition and the presence of nutrient resources are the most important factors that control the inactivation of fecal bacteria in soil. These findings could have important implications for soil management and agricultural practices, as well as for the development of new soil remediation strategies.
... Kinetic data (survivor curves) were fitted to equations based on linear, linear with tail, and Weibull (Mafart et al., 2002) models using the USDA Integrated Pathogen Modeling Program (IPMP) 2013 software (Huang, 2014). The equation for the linear model is below. ...
... concave upwards curve, i.e., tailing (ρ < 1), convex or concave downwards curve, i.e., shoulder (ρ > 1) or linear/straight line (ρ = 1) survival curves (Mafart et al., 2002). Using the Weibull model, the time required for x-log reduction, i.e., 3 logs (3-D or t 3D ) can be calculated by using the shape and scale parameters with the equation described by Huang et al. (2013). ...
... The populations (log CFU/g) of L. monocytogenes and S. enterica on both enoki and wood ear mushrooms (10 g initial weight) during dehydration at 70, 80, and 90°C were fitted to the Weibull model (Mafart et al., 2002). Populations during dehydration at 70 and 80°C were also fitted to the log-linear with tail model, while populations during dehydration at 90°C were also fitted to the log-linear with shoulder model (Geeraerd et al., 2000). ...
... The Weibull model is displayed in Eq. 1 (Mafart et al., 2002). This model assumes that the resistance to stress of a microbial population follows the Weibull distribution. ...
Foodborne illness outbreaks in the U.S. associated with consumption of both fresh and dried specialty mushrooms have recently occurred. Dried wood ear mushrooms were implicated in a salmonellosis outbreak in 2020, while fresh enoki mushrooms were associated with two listeriosis outbreaks in 2020 and 2023. These specialty mushrooms are commercially available in both their fresh and dried states. Due to the short shelf life of mushrooms, dehydration is a common method used in both industry and by consumers to extend the shelf life and preserve quality. Therefore, the aim of this study was to evaluate the use of dehydration on the inactivation kinetics of both Listeria monocytogenes and Salmonella enterica on enoki and wood ear mushrooms. Fresh mushrooms were inoculated with four strain cocktails of either L. monocytogenes or S. enterica and dried at ambient conditions for 10 min. Following drying of the inoculum, mushrooms were placed into food dehydrators preheated to 70, 80, or 90°C and treated for up to 24 h. At treatment intervals, mushrooms were removed from the dehydrators for pathogen enumeration. Inactivation kinetics for both pathogens were modeled using the Weibull, log-linear with tail, and log-linear with shoulder models. Pathogen reductions of >4 log CFU/g were achieved on both enoki and wood ear mushrooms during dehydration at 90°C after only 2–4 h. At 70 and 80°C, log reductions of >4 log CFU/g were observed on wood ear mushrooms after 4–8 h. On enoki mushrooms, a tailing effect was observed with residual populations (>2 log CFU/g) of L. monocytogenes and S. enterica remaining even after 24 h of treatment at both 70 and 80°C. This study emphasizes the need for an individualized dehydration strategy for each mushroom type to ensure the effectiveness of dehydration as a process to reduce pathogen populations. Results of this study will aid in informing proper time and temperature combinations for dehydration of specialty mushrooms to ensure product safety.
... This hypothesis has been applied in three equivalent primary models with different parameterizations. The one by Peleg and Cole [26] uses the inactivation rate (b(T)), as shown in Eq. (3), whereas the one by Mafart et al. [27] uses the "delta-value" (δ(T)) which equals the treatment time required to cause the first log-reduction in the microbial population (Eq. 4). ...
... 4). The nonlinearity of the survivor curve is described by the shape factor of the Weibull distribution (n in the parameterization by Peleg [26], p in the parameterization by Mafart [27]). Values of this parameter greater than one introduce a downward curvature of the survivor curve, whereas values lower than one result in curves with an upward curvature. ...
Temperature treatments are one of the most commonly used methods for microbial inactivation in food industries. Microbial inactivation models can support optimization of thermal treatments, due to their ability to predict the response of microbial populations under fixed temperature conditions (isothermal conditions) or variable (dynamic conditions). These models can also consider intrinsic and extrinsic factors involved in the process. This chapter aims to describe a protocol for developing models for thermal inactivation using conceptual data from the literature and empirical experiments. The online and open-source interface bioinactivation (available at https://foodlab-upct.shinyapps.io/bioinactivation4/) was used for the computations. The protocol includes conceptual and empirical phases and defines aspects from elaborating a reasonable hypothesis and selecting commonly used equations to the model fitting and validation.Key wordsPredictive microbiologyParameter estimationModel fittingSimulationMathematical modelingModel validation
... The weibull survival mode (Mafarat et al., 2002) can be calculated using the following equation ...
... The weibull survival mode (Mafarat et al., 2002) can be calculated using the following equation …. (2) Where, N = number of survivors (cfu/g), No = initial inoculum size (cfu/g), dPL = dosage (W/cm 2 ), δ = the time for first decimal reduction of sub-population , p = shape parameter (p>1, convex curve is observed; p<1, concave curve is observed; when p=1, a linear curve is observed. ...
The effect of pulsed light on the survival of E.coli MTCC 433 in tender coconut water was investigated. The sterilized liquid samples were inoculated with E.coli @ 1010 cfu/ml and treated with pulsed light intensities of 0.18, 2 and 5.6 W/cm2 for an exposure time between 0 and 15 sec. The results obtained were fitted with three different models such as log linear plus tail, Weibull and biphasic model. Biphasic model showed the best the performance with 7 smaller RSME values of 9 evaluated kinetics followed by Weibull model. Among the three models, biphasic model fitted well with the inactivation of E.coli MTCC 433 by using pulsed light treatment.
... Peleg's model has been used to successfully fit the inactivation rates of several microorganisms [50,54,56] . The value of E c has been seen to decrease with the number of pulses, although an increase of E c has been found at the largest numbers of pulses [54] . ...
... The above setup enabled the authors to consider models which treat temperature and electric field effects separately [82] . These were of the form of the first-order model (Eqn 37), with the reaction rate constant (k) being a function of temperature and electric field strength: k = Aα (T ) β (E) (56) where α (T) follows the Arrhenius relation: ...
Herein, we discuss the modeling of the pulsed electric field (PEF) process, with attention focused on the originally intended application of pasteurization of liquid foods. We review literature on three classes of models. First are the models for electroporation (of molecular scale), derived from physics and physical chemistry considerations, and their extension to probabilistic approaches which treat pore formation as a random process. We discuss the more recent approaches involving molecular dynamics. Then, we consider treatment-chamber and system scale models, which are based on continuum physics approaches, and rely on computational Multiphysics codes for their solution. We then discuss the base assumptions for several modeling studies. Next, we consider models for inactivation kinetics for bacteria exposed to PEF, including the first order, Hulsheger, Peleg and Weibull models. We close with discussions of other models and experimental approaches for model verification and obtaining kinetic parameters from continuous flow PEF systems.
... Weibull model (Mafart et al., 2002) is a commonly used model to describe such non-linear relations. The Weibull model utilized in this investigation is provided in Equation (2). ...
This study investigated the impact of pulsed light (PL) applied at a fluence of 4–12 J cm⁻² (complying with U.S. Food and Drug Administration standards) on fresh‐cut watermelon, focusing on its efficacy in inactivating various food‐borne pathogenic gram‐positive (Escherichia coli and Staphylococcus aureus) and gram‐negative (Listeria monocytogenes and Salmonella) bacteria. The inactivation data were used to fit the log‐linear and Weibull kinetic models. Additionally, the impact of PL on physicochemical properties, lycopene content, total phenolic content, antioxidant activity, and pectin methylesterase (PME) residual activity (RA) was studied. The results demonstrated that the inactivation rate increases with the increase in fluence. Salmonella was most sensitive to PL, resulting in a reduction of 2.55 ± 0.08 log CFU g⁻¹ and a higher kmax, whereas S. aureus was most resistant, with a reduction of 1.87 ± 0.24 log CFU g⁻¹ and a lower kmax. The Weibull model was the best to predict the inactivation kinetics based on standard statistics and information theory criteria. For all assayed food‐borne pathogens, the inactivation curve showed non‐linearity with upward concavity except for L. monocytogenes, which followed a concave downward curve (β >1). Results showed that PL was effective in the retention of color, firmness, pH levels, total soluble solids, and titratable acidity, and also had a positive effect on enhancing the levels of essential components such as lycopene, total phenolic compounds, and antioxidant activity. Additionally, the PME RA significantly decreased with an increase in fluence due to structural modification. Therefore, PL can be explored to enhance fresh‐cut watermelon's safety and quality attributes.
Practical Applications
The implementation of this research holds significant potential for practical benefits in the fresh‐cut fruit industry. The findings could revolutionize processing practices, ensuring enhanced microbial safety, enzyme inactivation, and an extended shelf‐life of fresh‐cut watermelon. The study strongly contributes to preserving the desirable texture, color, and overall quality of the product, enhancing the retention of lycopene and other valuable antioxidants by standardizing the pulsed light treatment parameters while adhering to U.S. Food and Drug Administration standards for food application. Moreover, this research will scientifically contribute to addressing the critical challenges of foodborne outbreaks in the fresh‐cut fruit sector while providing consumers with a healthy, convenient food choice.
... This type of response leads to a maximum inactivation level, which cannot be exceeded even if the duration of the treatment is extended (Argyraki et al. 2017;Kim et al. 2017;Gabriel et al. 2018). The present data fitted well to the Weibull frequency distribution, and the outcome of this model assumes that a part of the population might be resistant to the applied UV treatment (Mafart et al. 2002). In the literature, different potential causes of a tailing effect have been mentioned, among which the presence of resistant sub-populations, cell aggregation, nonhomogeneity of UV treatment, or even substratum properties (Schenk et al. 2011). ...
Ultraviolet-C light-emitting diodes (UV-C LEDs) are an emerging technology for decontamination applications in different sectors. In this study, the inactivation of bacterial biofilms was investigated by applying an UV-C LED emitting at 280 nm and by measuring both the influence of the initial cell density (load) and presence of an extracellular matrix (biofilm). Two bacterial strains exposing diverging matrix structures and biochemical compositions were used: Pseudomonas aeruginosa and Leuconostoc citreum. UV-C LED irradiation was applied at three UV doses (171 to 684 mJ/cm²) on both surface-spread cells and on 24-h biofilms and under controlled cell loads, and bacterial survival was determined. All surface-spread bacteria, between 10⁵ and 10⁹ CFU/cm², and biofilms at 10⁸ CFU/cm² showed that bacterial response to irradiation was dose-dependent. The treatment efficacy decreased significantly for L. citreum surface-spread cells when the initial cell load was high, while no load effect was observed for P. aeruginosa. Inactivation was also reduced when bacteria were grown under a biofilm form, especially for P. aeruginosa: a protective effect could be attributed to abundant extracellular DNA and proteins in the matrix of P. aeruginosa biofilms, as revealed by Confocal Laser Scanning Microscopy observations. This study showed that initial cell load and exopolymeric substances are major factors influencing UV-C LED antibiofilm treatment efficacy.
Key points
• Bacterial cell load (CFU/cm²) could impact UV-C LED irradiation efficiency
• Characteristics of the biofilm matrix have a paramount importance on inactivation
• The dose to be applied can be predicted based on biofilm properties
Graphical Abstract
... The Weibull model is a flexible mathematical model which has been used to describe the non-linear inactivation of various microorganisms in different experimental conditions (Guan et al., 2021;Mafart et al., 2002;Park et al., 2021). The Weibull model is expressed by the following equation: ...
The objective of this study was to model the inactivation of Escherichia coli O157:H7 under varying relative humidity and gaseous ClO2 concentrations. E. coli was spot-inoculated onto baby-cut carrots and exposed to ClO2 gas at concentrations of 100 ppm, 200 ppm, and 300 ppm, within relative humidity ranges of 50 to 90%. The results demonstrate that the germicidal efficacy of gaseous ClO2 significantly increases with both ClO2 concentration and relative humidity increase (p < 0.05). Two different non-linear inactivation models, the Weibull model and the modified Chick model, were employed to describe the inactivation kinetics of E. coli. The modified Chick model, based on chemical reaction kinetics, proved more suitable (RMSE < 0.356) than the Weibull model (RMSE < 0.469). A multiple regression analysis was subsequently conducted, utilizing the modified Chick model to describe the inactivation of E. coli under varying relative humidity and ClO2 concentrations. At 50% relative humidity and 100 ppm ClO2 concentration, the inactivation rate constant of the modified Chick model was 1.04 × 10⁻³ min⁻¹. The inactivation rate constant increased to 3.63 × 10⁻³ min⁻¹ and 0.0668 min⁻¹ as ClO2 gas concentration increased from 100 to 300 ppm and relative humidity increased from 50 to 90%, respectively. The model developed in this study describes the inactivation of E. coli as a function of relative humidity and ClO2 concentration (R² of 0.985) and can be utilized by the food processing industry to design gaseous ClO2 processes for achieving desired levels of E. coli inactivation.
... And, as ever-growing evidence suggests, loglinear microbial inactivation kinetics might be the exception rather than the rule [1,2]. It has also been largely recognized that a static microbial survival curve, i.e., the plot of the survival ratio vs. time recorded at a constant temperature, pressure, chemical agent concentration, etc., can be viewed as a cumulative form of the individual microbes' times to deactivation distribution [e.g., [3][4][5]. The microbes (germs) themselves can be bacterial (vegetative cells or spores), yeast, fungus, protist, or a virus. ...
Regardless of the targeted microbe type, a thermal or nonthermal food preservation or disinfection method’s efficacy is primarily assessed based on its kinetics. Yet, there is growing realization that inactivation kinetics and the individual microbes’ spectrum of vulnerabilities or resistances to a lethal agent are two sides of the same coin. This creates the possibility to convert traditional survival data plotted on linear or semilogarithmic coordinates to temporal distributions of the individual microbes’ deactivation, or vice versa. Such conversions are demonstrated with simulated microbial survival patterns generated with different kinds of survival models: the two-parameter Weibull distribution of which the single-parameter loglinear model is a special case, the normal, lognormal, and Fermi distribution functions, which imply that complete microbial inactivation is theoretically impossible, the three-parameter Gompertz survival model which allows for definite residual survival, and the three-parameter version of the beta distribution function, allowing for a definite thermal death time beyond which no survivors will ever be found. Also provided are simulated examples of the survival patterns of mixed microbial populations, and they all demonstrate that the common shapes of microbial survival curves do not contain enough information to infer whether the targeted microbial population is genetically or physiologically uniform or a mixture of subpopulations. The presented analysis lends support to the notion that any proposed microbial survival kinetic model’s validity should be tested by its ability to predict survival patterns not used in its formulation and not by statistical fit criteria.
... The effective PL fluence at which 90 percentile reduction of microbial population is achieved is termed as the reliable life (f R ) and can be calculated from the parameters α and β using Equation (2). In this case, the f R is analogous to the classic D-value when a one log 10 reduction is considered (Mafart et al., 2002). ...
Ready‐to‐drink (RTD) mango beverage enriched with short‐chain fructooligosaccharides (scFOS) was developed to reduce added sugar and incorporate a soluble prebiotic fiber. The impact of pulsed light (PL) technology on microbial inactivation, enzyme activity, and quality attributes in scFOS‐enriched mango RTD beverages was investigated. Effective PL fluence of 0.12–1.2 J/cm² was employed on mango beverage in order to maximize the retention of nutritional properties along with inactivation of microbial and enzymatic activity. There is complete inactivation of microbial load and enzymatic activity with 72.45, 84.17, 88, 78.79, and 77.63% retention of ascorbic acid, antioxidants, total phenolics, total flavonoids, and total carotenoids in 6% scFOS mango beverage at an effective fluence of 1.2 J/cm². There is no wide change in TSS, pH, and TA in all the PL treatments. The scFOS increased viscosity, and it also protected bioactives, namely, carotenoids, ascorbic acid, and phenolics, from photoxidation caused by PL. Results showed that scFOS allowed a substantial reduction in added sugar and increased soluble fiber content in the beverage. Sensory score of 3 and 6% scFOS‐enriched beverages were closely comparable with control. The study showcases the potential of scFOS to enhance the nutritional profile of beverages. It also highlights the effectiveness of PL processing in pasteurization fruit beverages, meeting stakeholders' demands for microbial safety, enzymatic stability, and nutrient retention.
Practical applications
The practical applications of this research hold significant promise for the food and beverage industry. The innovative formulations of ready‐to‐drink (RTD) mango beverages not only reduce added sugar by up to 52% but also increase fiber content from 0.6 to 6%, meeting consumer demands for healthier options. The integration of pulsed light technology effectively targets microbial and enzyme inactivation, complying with Food and Drug Administration standards and offering a viable processing method. The incorporation of short‐chain fructooligosaccharides enhances the protection of bioactive compounds during pulsed light treatment, ensuring higher retention of antioxidants, vitamins, and other valuable components. This advancement contributes to improved nutritional profiles while maintaining sensory appeal. These findings have the potential to revolutionize RTD beverage production, addressing health‐conscious consumer preferences, and enhancing product quality.
... The isothermal inactivation processes have been described using the cumulative form of the Weibull distribution [6]. The behaviour of the microorganism under non-isothermal heat treatments was described with the model proposed for the description of dynamic inactivation processes, based also in the Weibull distribution [7]. ...
... Total bacteria concentration, and viable L. monocytogenes remaining in biofilms after exposure to sanitizer were quantified by aerobic plate counts and the MPN method, respectively, as previously described. Survival of L. monocytogenes in multi-family assemblages was fitted to the Weibull model equation [119,120]: ...
Listeria monocytogenes may survive and persist in food processing environments due to formation of complex multi-species biofilms of environmental microbiota that co-exists in these environments. This study aimed to determine the effect of selected environmental microbiota on biofilm formation and tolerance of L. monocytogenes to benzalkonium chloride in formed biofilms. The studied microbiota included bacterial families previously shown to co-occur with L. monocytogenes in tree fruit packing facilities, including Pseudomonadaceae, Xanthomonadaceae, Microbacteriaceae, and Flavobacteriaceae. Biofilm formation ability and the effect of formed biofilms on the tolerance of L. monocytogenes to benzalkonium chloride was measured in single- and multi-family assemblages. Biofilms were grown statically on polystyrene pegs submerged in a R2A broth. Biofilm formation was quantified using a crystal violet assay, spread-plating, confocal laser scanning microscopy, and its composition was assessed using amplicon sequencing. The concentration of L. monocytogenes in biofilms was determined using the most probable number method. Biofilms were exposed to the sanitizer benzalkonium chloride, and the death kinetics of L. monocytogenes were quantified using a most probable number method. A total of 8, 8, 6, and 3 strains of Pseudomonadaceae, Xanthomonadaceae, Microbacteriaceae, and Flavobacteriaceae, respectively, were isolated from the environmental microbiota of tree fruit packing facilities and were used in this study. Biofilms formed by Pseudomonadaceae, Xanthomonadaceae, and all multi-family assemblages had significantly higher concentration of bacteria, as well as L. monocytogenes, compared to biofilms formed by L. monocytogenes alone. Furthermore, multi-family assemblage biofilms increased the tolerance of L. monocytogenes to benzalkonium chloride compared to L. monocytogenes mono-species biofilms and planktonic multi-family assemblages.
These findings suggest that L. monocytogenes control strategies should focus not only on assessing the efficacy of sanitizers against L. monocytogenes, but also against biofilm-forming microorganisms that reside in the food processing built environment, such as Pseudomonadaceae or Xanthomonadaceae.
... Experimental data on virus V-qPCR activity (log viable viral particles mL −1 ) were plotted over exposure time to obtain the virus survival curves. GinaFit software [43] was used to estimate the kinetic parameters (delta-value, expressed as the time at certain temperature for the firstlog viral decline) of the Weibull models [44]. Goodness of fit of the model to the experimental data was expressed as the adjusted R 2 . ...
Background
The particle structure of Emiliania huxleyi virus (EhV), an algal infecting member of nucleocytoplasmic large DNA viruses (NCLDVs), contains an outer lipid membrane envelope similar to that found in animal viruses such as African swine fever virus (ASFV). Despite both being enveloped NCLDVs, EhV and ASFV are known for their stability outside their host environment.
Method
Here we report for the first time, the application of a viability qPCR (V-qPCR) method to describe the unprecedented and similar virion thermal stability of both EhV and ASFV. This result contradicts the cell culture-based assay method that suggests that virus “infectivity” is lost in a matter of seconds (for EhV) and minutes (for ASFV) at temperature greater than 50 °C. Confocal microscopy and analytical flow cytometry methods was used to validate the V-qPCR data for EhV.
Results
We observed that both EhV and ASFV particles has unprecedented thermal tolerances. These two NCLDVs are exceptions to the rule that having an enveloped virion anatomy is a predicted weakness, as is often observed in enveloped RNA viruses (i.e., the viruses causing Porcine Reproductive and Respiratory Syndrome (PRRS), COVID-19, Ebola, or seasonal influenza). Using the V-qPCR method, we confirm that no PRRSV particles were detectable after 20 min of exposure to temperatures up to 100 °C. We also show that the EhV particles that remain after 50 °C 20 min exposure was in fact still infectious only after the three blind passages in bioassay experiments.
Conclusions
This study raises the possibility that ASFV is not always eliminated or contained after applying time and temperature inactivation treatments in current decontamination or biosecurity protocols. This observation has practical implications for industries involved in animal health and food security. Finally, we propose that EhV could be used as a surrogate for ASFV under certain circumstances.
... Techniques explored include a close-to-normal power approximation, logarithmic transformation, and the Box-Cox transformation. The Weibull distribution finds applications in diverse fields, such as insurance (Kreer et al. [1], Hamza and Sabri [2]), food science (Mafart et al. [3], Uribete et al. [4]), ecology (Mikolaj [5]), and medical science (Carroll [6]). In addition, numerous studies have presented examples of wind speed data that follow a Weibull distribution. ...
The Weibull distribution is a continuous probability distribution that finds wide application in various fields for analyzing real-world data. Specifically, wind speed data often adhere to the Weibull distribution. In our study, our aim is to compare the mean wind speed datasets from different areas in Thailand. To achieve this, we proposed simultaneous confidence intervals for all pairwise differences between the means of Weibull distributions. The generalized confidence interval (GCI), method of variance estimates recovery (MOVER), and a Bayesian approach, utilizing both gamma and uniform prior distributions, are proposed to construct simultaneous confidence intervals. Through simulations, we find that the Bayesian highest posterior density (HPD) interval using a gamma prior distribution demonstrates satisfactory performance, while the GCI proves to be a viable alternative. Finally, we applied these proposed approaches to real wind speed data in northeastern and southern Thailand to illustrate their effectiveness and practicality.
... The models were originally published as Bigelow and Esty (1920), Cerf (1977), Geeraerd et al. (2000), Mafart et al. (2002), Albert and Mafart (2005), Geeraerd et al. (2005) and Coroller et al. (2006). Next to the obtained parameter values, the following statistical measures are automatically reported: standard errors of the parameter values, the sum of squared errors, the (root) mean sum of squared errors, the R2 and the adjusted R2. ...
The popularity of biological origin food protection substances is driven by demands from consumers for natural and clean label product, increasing various food‐related safety and health concerns and sustainability issues. Lactic acid bacteria (LAB) are most promising because they are a large group of beneficial microorganisms commonly used in food protection due to their ability to inhibit the growth of pathogenic bacteria and enhance food safety. Extensive scientific research has been conducted to understand the mechanisms by which LAB exert their protective effects in various food systems. Even though LAB activity against various food pathogens and spoilers is distinguished, use of cell‐free supernatant (CFS) is still under investigation. This report is dedicated to present how qualitative measures can elaborate in new bacteria‐origin food additive investigation. As part of the EU‐FORA programme, the fellow was involved in the risk assessment tasks and projects which include gaining basic knowledge in predicative microbiology fundamentals, including different types of modelling strategies; delivering essential understanding about experimental design, knowledge in three specific software tools (MATLAB, GInaFiT and DMFit) and gained overall understanding what are the main differences while modelling growth or inactivation models. Secondary activities were included as a way to expand competences beyond qualitative measures to overall all activities done regarding risk assessment and build a strong network of food safety experts and professionals to continue engaging in risk assessment beyond fellowship programme.
... The models were originally published by Bigelow and Esty (1920), Cerf (1977), Geeraerd et al. (2000Geeraerd et al. ( , 2005, Mafart et al. (2002), Albert and Mafart (2005), and Coroller et al. (2006). Along with the obtained parameter values, some statistical measures are automatically given: standard errors of the parameter values, the sum of squared errors, the (root) mean sum of squared errors, the R2 and the adjusted R2. ...
The EU‐FORA programme ‘Quantitative tools in microbial and chemical risk assessment’ was dedicated to training on predictive microbiology fundamentals, implementation of different modelling strategies, design of experiments and software tools such as MATLAB, GInaFiT and DMFit. The fellow performed MATLAB training on maximum specific growth rate (μmax) determination according to the Ratkowsky model. GInaFiT training on different models for bacterial inactivation and DMFit training on growth parameters of Vibrio parahaemolyticus were also carried out. Optical density measurements of V. parahaemolyticus bacterial cultures were performed. The obtained kinetics of optical density measurements were used to estimate μmax. Hereafter, Minimum inhibitory concentrations and non‐inhibitory concentrations of aminoglycoside antibiotics were estimated based on the quantification of the fractional areas of the optical density vs time. It can be concluded that the results of the quantitative characterisation of V. parahaemolyticus are reliable and can be used for exposure assessments. Also, the turbidimetric assay can be applied for successful estimation of minimum inhibitory concentrations and non‐inhibitory concentrations.
... Additionally, the Weibull model was employed based on the assumption that different fractions of ascospores within the microbial population possess varying resistance to treatment conditions. The Weibull model in the GInaFiT is a model proposed by Mafart et al. [25]. The model follows a cumulative exponential distribution and is expressed as Log 10 (N) = Log 10 (N 0 ) − (t/δ) p where δ represents the scale parameter denoting the time for the first decimal reduction, and the p-value is the shape parameter that describes the concavity or convexity of the curve. ...
The contamination and spoilage of heat-treated fruit juices by heat-resistant mold ascospores present significant challenges to the food industry. Understanding effective strategies to mitigate this contamination is vital for ensuring the shelf-life and microbial safety of heat-treated fruit juices. This study investigated the thermal resistance of ascospores from different heat-resistant mold species, including Aspergillus laciniosus, A. chevalieri, A. denticulatus, A. siamensis, Hamigera pallida, and Talaromyces macrosporus, isolated from pineapple and sugarcane field soils. Ascospores inactivation kinetics in pineapple juice under heat treatment (75–97 °C) were analyzed using log-linear and Weibull models. Among these species, A. laciniosus displayed the highest heat resistance (δ-value: 104.59 min at 85 °C), while A. siamensis exhibited the lowest (δ-value: 3.39 min at 80 °C). Furthermore, A. laciniosus, the most heat-resistant species, showed notable tolerance to sanitizers. The most effective inactivation was achieved using 1.0% (w/v) sodium hypochlorite for 15 min. Chlorine dioxide, however, was generally ineffective and even activated dormant ascospores in some cases. The combination of hot water (65 °C for 5 min) with sanitizer increased ascospore reduction in most species but did not achieve the 3-log reduction required by the European Standard N13697. This study revealed a correlation between ascospore resistance to heat and chlorine dioxide, offering significant findings for practical inactivation strategies.
... The curves of E. coli disinfection (Log 10 CFU mL −1 vs. time) were fitted to two kinetic equations: Log-linear [22] and Weibull model [23]. The equations of these models are as follows: ...
A novel cost-effective and multifunctional nanocomposite was developed based on sustainable macroalgae biomass. The brown seaweed Sargassum latifolium was utilized for alginate extraction and the calcareous red seaweed Tricleocarpa fragilis was utilized as CaCO3 source for nanohydroxyapatite synthesis. The developed Zn²⁺-crosslinked alginate/nanohydroxyapatite (ZA/nHA) beads were characterized by FT-IR, XRD, and TEM. The antimicrobial potential of ZA/nHA to disinfect synthetic Escherichia coli-contaminated water was evaluated at different bacterial load and composite concentrations. The developed ZA/nHA effectively inactivated bacteria at initial concentration ≤ 10⁵ CFU mL⁻¹ and 0.5–1% (w/v) of ZA/nHA within 300–360 min. The kinetics of bacterial disinfection exhibited better fitting to Weibull model than Log-liner model, which confirmed the disinfection process. Furthermore, treatment of the cyanobacterium (Chroococcus sp.) and the microalga (Chlorella sp.) with ZA/nHA showed promising antialgal properties as indicated by reductions in chlorophyll a. The treatment indicated 100% and 90% removal of Chroococcus sp. and Chlorella sp. within 2 and 4 days, respectively. The developed ZA/nHA also exhibited a promising application as a biosorbent for crystal violet (CV). The adsorption process was very fast (0.171 mg CV g⁻¹ adsorbent was removed within 7 min at pH 6.0). The adsorption kinetics exhibited better fitting to the pseudo-second order and Elovich models than the pseudo-first order equation. Besides, Sips model better represented the isotherm data of CV adsorption. The thermodynamic analysis indicated exothermic adsorption, which became more favorable at low temperature and high CV concentration. The developed nanocomposite is eco-friendly and suitable for multiple environmental applications.
Graphical Abstract
... Inactivation models with better fit were nonlinear and adjusted to a Weibull and Weibull tail model proposed by Marfart et al. [41] and by Albert and Mafart [42], respectively (Table 4 and Figure 6). The presence of tails in the data indicates that a bacterial population showed greater resistance regardless of the increase in dose. ...
Vegetative cells of Listeria monocytogenes and Escherichia coli and spores of Bacillus subtilis and Aspergillus niger were inoculated in soy milk at an initial concentration of ≈5 log CFU/mL. Inoculated and control (non-inoculated) soy milk samples were submitted to three types of treatments using a tubular annular thin film short-wave ultraviolet (UV-C) reactor with 1 mm of layer thickness. Treatments applied depended on the flow rate and the number of entries to the reactor, with UV-C doses ranging from 20 to 160 J/mL. The number of entries into the reactor tube (NET) was established as the most determining parameter for the efficiency of the UV-C treatments. Conidiospores of A. niger were reported as the most resistant, followed by B. subtilis spores, while vegetative cells were the most sensible to UV-C, with Listeria monocytogenes being more sensible than Escherichia coli. Treatments of just 80 J/mL were needed to achieve a 5 log CFU/mL reduction of L. monocytogenes while 160 J/mL was necessary to achieve a similar reduction for A. niger spores.
... The model that describes destruction profiles without tails uses equation 1 (Mafart et al., 2002), and the model that fits destruction profiles characterized by a tail uses equation 2 (Albert and Mafart, 2005) are: ...
In the present study, the efficiency of the combined effect of microwave irradiation treatments together with salt concentration was assessed against Escherichia coli and Staphylococcus aureus. Microbial survival has been modeled through a one-step Weibull equation considering the non-isothermal profiles during the heating treatments. Three sodium chloride concentrations 0.5%, 3.5%, and 8.5% ( w/v) treated under three microwave power levels (450, 600, and 800 W) were studied. Predictive models were validated using the determination coefficient ( R ² ), root mean squared error and the acceptable prediction zone with external data obtained from ultra high temperature milk. The results obtained suggested that increasing microwave power levels and decreasing salt concentrations led to a higher microbial inactivation, being the δ values (time for achieving a first decimal reduction) for E coli of 19.57 s at 800 W and 0.5% NaCl. In contrast, experimental data of S aureus showed a higher variability since it presented more resistance to the microwave treatments. The results obtained and generated models can be used as decision-making tools to set specific guidelines on microwave treatments for assuring food safety.
... For each strain, the log of CFU/mL vs. contact time was plotted. From the obtained curves, the Chick model (1) [22], Weibull model (2) [28], and Geeraerd model (3) [13] were evaluated. ...
The disinfection of wastewater is a treatment that allows for its reuse. However, not all pathogenic microorganisms or their resistant structures, e.g., endospores, cysts, or oocysts, are eliminated in conventional treatments. This work compared the removal efficacy of sodium hypochlorite (NaClO) and peracetic acid (PAA) on three strains of bacteria isolated from the tertiary effluent of a wastewater treatment plant. The results of the inactivation kinetics showed that complete inactivation of S. pasteuri was achieved with both NaClO (>12 log, t = 5–10 min, 15–30 mg/L) and PAA (~9 log, t = 20–30 min, 15 mg/L). Likewise, with higher concentration of both disinfectants, the inactivation time decreased. K. pneumoniae showed greater resistance to PAA (3 log, t = 30 min) than to NaClO (8 log, t = 15 min). B. subtilis endospores showed resistance to NaClO (3 log, t = 60–100 min, 15 mg/L); however, PAA was more effective (~4 log, t = 45–100 min), with 15 mg/L regarding these latter four kinetics. The inactivation curves of these strains showed concave and linear tendencies with tail effects, fitting the Weibull and Geeraerd models. Both the inactivation kinetics and the models established for vegetative cells and endospores in this study are conclusive to understand the differences between these biological forms and, consequently, their ability to survive disinfection.
... α is distinguished from the conventional D value, which is derived from the first-order kinetic model and represents the time for a decimal reduction, regardless of the treatment time. α value represents the first decimal reduction of the initial count, this means a reduction of surviving cells from N 0 to N 0 /10 (Mafart et al., 2001;van Boekel, 2002). Otherwise, to estimate the time required (t d ) to reduce 5 Log 10 CFU/mL, Equation (5) was used: ...
High hydrostatic pressure (HHP) is a non-thermal process widely used in the food industry to reduce microbial populations. However, rarely its effect has been assessed in products with high oil content. This study evaluated the efficacy of HHP (200, 250, and 300 MPa) at different temperatures (25, 35, and 45 °C) by cycles (1, 2, or 3) of 10 min in the inactivation of Aspergillus niger spores in a lipid emulsion. After treatments at 300 MPa for 1 cycle at 35 or 45 °C, no surviving spores were recovered. All treatments were modeled by the linear and Weibull models. The presence of shoulders and tails in the treatments at 300 MPa at 35 or 45 °C resulted in sigmoidal curves which cannot be described by the linear model, hence the Weibull + Tail, Shoulder + Log-lin + Tail, and double Weibull models were evaluated to elucidate the inactivation kinetics. The tailing formation could be related to the presence of resistance subpopulations. The double Weibull model showed better goodness of fit (RMSE <0.2) to describe the inactivation kinetics of the treatments with the higher spore reductions. HHP at 200–300 MPa and 25 °C did not reduce the Aspergillus niger spores. The combined HHP and mild temperatures (35–45 °C) favored fungal spore inactivation. Spore inactivation in lipid emulsions by HHP did not follow a linear inactivation. HHP at mild temperatures is an alternative to the thermal process in lipid emulsions.
... (12) and (13)), and shoulder plus tailing effects (Eqn. (14)) were also fitted to the data (Bigelow & Esty, 1920) (Mafart, Couvert, Gaillard, & Leguerinel, 2002) (Geeraerd, Herremans, & van Impe, 2000) (Geeraerd et al., 2000) (Geeraerd et al., 2000) (Geeraerd et al., 2000) log 10 (N) = log 10 (N 0 ) − k max t Ln(10) ...
... The count results obtained for each inactivation curve were fitted with the model presented in equation (1) [6]. ...
Some B. thuringiensis (Bt) strains are used as pesticide agent. This species belongs to B. cereus (Bc) group which contains many species with a high phenotypic diversity, and could be pathogenic like B. cereus. The aim of this study was to characterize the phenotype of 90 strains belonging to Bc group, half of which were Bt. Knowing that Bt strains belong to different phylogenetic Bc groups, do Bt strains have the same phenotype than other Bc group strains? Five phenotypic parameters were estimated for 90 strains in the Bc group, of which 43 were Bt strains: minimal, maximal and optimal growth temperature, cytotoxicity on Caco-2 cells, heat resistance of spores. The dataset was processed by principal component analysis, showing that 53% of the variance of the profiles corresponded to factors linked to growth, heat resistance and cytotoxicity. The phenotype followed the phylogenetic groups based on panC. Bt strains showed similar behavior to other strains in the Bc group, in our experimental conditions. Commercial bio-insecticide strains were mesophilic with low heat resistance.
The performance of two conventional monochromatic ultraviolet-C (UV-C) low pressure mercury (LPM) sources (single and multiple lamps) was measured and compared with three emerging UV sources: a monochromatic KrCl* excimer lamp and UV-LEDs, and a polychromatic pulsed light (UV-C PL) lamp. Fluence-based kinetic parameters and electrical energy per order (EE0) of the UV sources was determined for the inactivation of E. coli bacteria, the reduction of deoxynivalenol (DON) mycotoxin, and F. graminearum spore growth to assess feasibility for various processing targets. The impact on E. coli photoreactivation and dark repair was also assessed. Each of the five UV sources excelled in certain applications while not being feasible for others. The UV-C PL lamp was the most effective for E. coli inactivation, requiring the lowest fluence of 1.4 mJ/cm2 for 5-log10 reduction. The KrCl* excimer lamp was the most effective for preventing subsequent photoreactivation. The UV-LEDs and LPM lamp were equally effective for reducing fungal spore growth requiring 77.0 and 90.1 mJ/cm2 to achieve 90% reduction, respectively. The KrCl* excimer and UV-C PL lamps were the most effective at reducing DON contamination requiring 1250 and 500 mJ/cm2 to achieve 90% reduction, respectively. The evaluation of EE0 showed that the conventional LPM source with multiple lamps had approximately 2–3-fold better electrical efficiency for the reduction of all three tested targets due to its high wall plug efficiency compared to the next best UV-C PL lamp. This indicates that energy efficiency of emerging UV sources needs to be improved in further development.
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Keywords
Pulsed lightUV-LEDsDeoxynivalenolFusariumPhotoreactivationE. coliElectrical efficiency
1. Introduction
Ultraviolet-C (UV-C) light (200–280 nm) has shown to be lethal to most bacteria, viruses, protozoa, fungi and algae (Hijnen et al., 2006). Its use as a disinfection technology for water, air and surfaces has been extensively explored and applied in commercial settings (Koutchma, 2019; Tchonkouang et al., 2023). It has gained traction due to its non-invasive, nonthermal, nonionizing, chemical-free and relatively inexpensive nature compared to other methods such as thermal processing and high-pressure processing. The most common source of artificial UV-C light is the low-pressure mercury (LPM) lamp which emits a monochromatic signal at 253.7 nm. LPM lamps remain the industry standard for UV disinfection due to their high wall plug efficiency up to 30–40% (WPE) and relatively low cost (Koutchma, 2023). However, their implementation in food facilities and processing systems has been slow due to their fragile and bulky nature and the fact that they contain glass and toxic mercury. For this reason, emerging UV light sources such as UV light emitting diodes (UV-LEDs), krypton chloride (KrCl*) excimer lamps and pulsed light (PL) lamps have gained attention from both the research and manufacturing communities.
Desiccation tolerance of pathogenic bacteria is one strategy for survival in harsh environments, which has been studied extensively. However, the subsequent survival behavior of desiccation-stressed bacterial pathogens has not been clarified in detail. Herein, we demonstrated that the effect of desiccation stress on the thermotolerance of Escherichia coli O157:H7 in ground beef was limited, and its thermotolerance did not increase. E. coli O157:H7 was inoculated into a ground beef hamburger after exposure to desiccation stress. We combined a bacterial inactivation model with a heat transfer model to predict the survival kinetics of desiccation-stressed E. coli O157:H7 in a hamburger. The survival models were developed using the Weibull model for two-dimensional pouched thin beef patties (ca. 1 mm), ignoring the temperature gradient in the sample, and a three-dimensional thick beef patty (ca. 10 mm), considering the temperature gradient in the sample. The two-dimensional (2-D) and three-dimensional (3-D) models were subjected to stochastic variations of the estimated Weibull parameters obtained from 1,000 replicated bootstrapping based on isothermal experimental observations as uncertainties. Furthermore, the 3-D model incorporated temperature gradients in the sample calculated using the finite element method. The accuracies of both models were validated via experimental observations under non-isothermal conditions using 100 predictive simulations. The root mean squared errors in the log survival ratio of the 2-D and 3-D models for 100 simulations were 0.25–0.53 and 0.32–2.08, respectively, regardless of the desiccation stress duration (24 or 72 h). The developed approach will be useful for setting appropriate process control measures and quantitatively assessing food safety levels.
IMPORTANCE
Acquisition of desiccation stress tolerance in bacterial pathogens might increase thermotolerance as well and increase the risk of foodborne illnesses. If a desiccation-stressed pathogen enters a kneaded food product via cross-contamination from a food-contact surface and/or utensils, proper estimation of the internal temperature changes in the kneaded food during thermal processing is indispensable for predicting the survival kinetics of desiccation-stressed bacterial cells. Various survival kinetics prediction models that consider the uncertainty or variability of pathogenic bacteria during thermal processing have been developed. Furthermore, heat transfer processes in solid food can be estimated using finite element method software. The present study demonstrated that combining a heat transfer model with a bacterial inactivation model can predict the survival kinetics of desiccation-stressed bacteria in a ground meat sample, corresponding to the temperature gradient in a solid sample during thermal processing. Combining both modeling procedures would enable the estimation of appropriate bacterial survival kinetics in solid food.
The aim of this work was to evaluate the resistance of two pathogenic bacteria (Listeria monocytogenes and Salmonella enterica subsp. enterica serotype Senftenberg), and three airborne food-spoiling filamentous fungi (Hyphopichia burtonii, Penicillium nordicum, and Aspergillus brasiliensis ATCC 16404) to gaseous ozone on stainless steel. Tests were carried out by exposing inoculated tiles to gaseous ozone in a laboratorial chamber at concentrations up to 50 mg/L and at times up to 180 min (bacteria) or 300 min (filamentous fungi). For bacteria, the resistance to gaseous ozone of L. monocytogenes proved markedly higher than that of S. enterica. Their D-values increased by seven times (from 27.3 to 200.7 min for the strain of L. monocytogenes studied; from 7.3 to 48.0 min for the Salmonella species studied) when the ozone concentration were reduced from 12 to 4 mg/L. For filamentous fungi, a substantial effect was observed only at 50 mg/L on single-layered inocula: at these conditions, A. brasiliensis ATCC 16404 proved the most resistant strain to gaseous ozone, its D-value (134.4 min) being higher than those registered for the tested strains of H. burtonii (9.9 min) and P. nordicum (17.1 min). The results demonstrated that the use of gaseous ozone as a sanitizing agent for environments and working surfaces seems to be a potential alternative to chemical sanitizers against the two pathogens studied, whereas it seemed effective against the three filamentous fungi studied only in limited circumstances.
An edible coating based on sesame bioactive compounds combined with Lactobacillus plantarum was studied to evaluate the shelf life of strawberries during storage. Drip loss, fresh firmness, color, total soluble solids, ascorbic acid, lycopene, total phenol, flavonoids, antioxidant activity, and microbial analysis for both coated and non-coated samples were determined during 15 days of storage at 4 °C. The results showed that there was a reduction in drip loss by 47.61% for coated samples compared to the control at the end of storage. On day 3, the phenolic compounds in coated strawberries increased by 72.56% compared to uncoated ones. After 15 days at 4 °C, an enhancement of the antioxidant activity was observed (DPPH 28.92%, ABTS 46.67%, FRAP 213.129%, TAC 474.061%). In addition, a significant effect on reducing microbial populations was found (p < 0.05). All of this suggests that using an edible coating containing probiotics can slow down the ripening process, increase shelf life, and maintain the quality of strawberries stored for 15 days at 4 °C without spoilage or off-flavor.
Conventional survey methods to find rare and endangered aquatic species can be time consuming, expensive, destructive to habitat, and limited by the physical conditions of a site. Sampling for environmental DNA (eDNA) shed by organisms into their environments can overcome these limitations, maximizing conservation resources. However, the optimal spatial sampling interval for eDNA detection is poorly known. We developed and assessed eDNA methods for application to Simpsonaias ambigua (Salamander Mussel), a unionid mussel that is considered at risk throughout most of its range. We developed a quantitative PCR assay and optimized methods to detect S. ambigua eDNA in water samples, and we experimentally determined eDNA shedding and decay rates. We used these rates to populate a previously published eDNA transport model to estimate the maximum downstream distance from the source (i.e., the location of live mussels) at which eDNA could be detected as a function of environmentally relevant source eDNA concentrations and water velocities. The model predicted that maximum detection distance varied greatly depending on source eDNA concentration and water velocity. At low eDNA concentration and water velocity (1.0 copy/mL and ,0.1 m/s, respectively), eDNA will be detected only at the source, requiring spatially intensive eDNA sampling. At higher eDNA concentration and water velocity (5.0 copies/mL and 0.8 m/s, respectively), eDNA can be detected at least 10 km downstream, requiring less intensive sampling. Based on our results, we provide recommendations for the development of optimal eDNA sampling design for detecting rare or endangered species.
E. coli (Escherichia coli) is a bacterium found in human and animal intestines. These bacteria, which can enter the bloodstream through as anyway as the environment or food, can cause many diseases such as diarrhea, respiratory problems, and blood/urinary tract infections especially in human. Therefore, these bacteria have to be removed from drinking water sources by some inactivation methods. Conventional methods as chlorination, ozonation and UV inactivation methods are effective but the development of techniques that do not require the transportation and storage of chemicals and do not produce negative by-products and cost-effective is the basis of environmental engineering studies. In this study, the inactivation effectiveness of hybrid electrode connected electrochemical process as a new approach on E. coli was investigated. The connection system was experienced with Al/SS/SS as Anode/Cathode/Anode electrode. Simultaneously electrocoagulation (EC) and electrooxidation (EO) mechanism works together in this electrode connection system. The inactivation coefficients were determined by the GInaFiT (Geeraerd and Van Impe Inactivation Model Fitting Tool) modeling tool, which is a Microsoft Excel add-on and the model was statistically well fitted with Double-Weibull. 4D degradation of E. coli was achieved as 21 minutes at a current density of 0.3 A and an optical density (O.D.) of 0.21. It has been determined that hybrid electrode connected electro-disinfection process is an effective approach for the E.coli inactivation.
Two specialty mushrooms have recently become novel vectors for foodborne outbreaks in the U.S.: fresh enoki and dried wood ear mushrooms were linked to a listeriosis and salmonellosis outbreak, respectively. The aim of this study was to evaluate the survival kinetics of Listeria monocytogenes and Salmonella enterica on dehydrated enoki and wood ear mushrooms during long-term storage. Following heat dehydration, mushrooms were inoculated with either L. monocytogenes or S. enterica, allowed to dry for 1 h, and then stored for up to 180 d at 25 °C and 33% relative humidity. Both pathogens were enumerated from the mushrooms at intervals during the storage period. Survival kinetics of both pathogens were modeled using both the Weibull and log-linear with tail models. After inoculation and 1 h drying, both pathogen populations decreased 2.26-2.49 log CFU/g on wood ear mushrooms; no decrease was observed on enoki. Both pathogens survived during storage on both mushroom types. On wood ear mushrooms, a 2-log decrease of both pathogens occurred during storage. On enoki mushrooms, 4-log decreases of both pathogens were modeled to occur after 127.50-156.60 d. The results of this study suggest that L. monocytogenes and S. enterica can persist on dehydrated specialty mushrooms during long-term storage.
This work explored the digestion of lily polysaccharides at different stages in the human body through simulation experiments, and studied its rheological properties and biological activities. The structural characteristics of the digested lily polysaccharide were confirmed by infrared spectroscopy and the molecular weight after digestion was determined. Through rheological experiments, the viscosity of digested lily polysaccharide decreased in the flow performance test with the increase of shear rate, showing the characteristics of shear thinning. Meanwhile, after Cross model fitting, its correlation was better, which was consistent with the order of area size of thixotropic rings in thixotropy experiments; its dynamics measurement of viscoelasticity showed that the solutions of LPG 7, LPGI 9 and LPI 7 were in a relatively stable solid state and had good gel properties and system stability. And the interrelationships between the molecules were active, which was in line with the optimal pH and reaction conditions for digestion of lily polysaccharides in the human body. The antioxidant activity of lily polysaccharide after digestion was tested, and it was found that lily polysaccharide after digestion had good scavenging activity on DPPH, ABTS free radicals and FRAP. These results provide changes in the structure and activity of lily polysaccharides after digestion, provide a theoretical basis for further understanding of the mechanism of digestion in vivo, and provide valuable and scientific support for future use as functional foods and drugs.Graphical abstract
The use of primary mathematical models with curve fitting software is dramatically changing quantitative food microbiology. The two most widely used primary growth models are the Baranyi and Gompertz models. A three-phase linear model was developed to determine how well growth curves could be described using a simpler model. The model divides bacterial growth curves into three phases: the lag and stationary phases where the specific growth rate is zero (gm=0), and the exponential phase where the logarithm of the bacterial population increases linearly with time (gm=constant). The model has four parameters: No (Log8 of initial population density), NMAX (Log8 of final population density), tLAG (time when lag phase ends), and tMAX (time when exponential phase ends). A comparison of the linear model was made against the Baranyi and Gompertz models, using established growth data for Escherichia coli 0157:H7. The growth curves predicted by the three models showed good agreement. The linear model was more `robust' than the others, especially when experimental data were minimal. The physiological assumptions underlying the linear model are discussed, with particular emphasis on assuring that the model is consistent with bacterial behavior both as individual cells and as populations. It is proposed that the transitional behavior of bacteria at the end of the lag phase can be explained on the basis of biological variability.
The heat resistance of Listeria monocytogenes was determined in 0.1 M KH2PO4 buffer at three temperatures (50, 55, and 60°C), three pH levels (5, 6, and 7), and three NaCl concentrations (0, 2, and 4%). Survival curves were fit using nonlinear regression with a modified Gompertz equation. The Gompertz equation is capable of fitting survival curves which are linear, those which display an initial lag region followed by a linear region, and those which are sigmoidal. Parameter estimates were used to describe the lag region, death rate, and the tailing region of a survival curve. These estimates were also used to predict single and interactive effects of temperature, pH, and percentage of NaCl on the log surviving fraction (LSF) of bacteria. Interactions among these variables significantly (P < .05) affected the LSF. Generally, increased pH or NaCl concentration lead to an increased (P < .05) LSF, whereas increased time or temperature lead to a decreased (P < .05) LSF. All multiple factor interactions significantly (P < .05) affected the LSF. These interactions differed depending on the heating medium and the region of the survival curve. The correlation of observed LSF and predicted LSF (R2 = .89) indicated that the Gompertz equation was in close agreement with the observations. This study demonstrated that the Gompertz equation and nonlinear regression can be used as an effective means to predict survival curve shape and response to heat of L. monocytogenes in many different environmental conditions.
Thermal destruction ofListeria monocytogenes was determined in a liver sausage slurry (1:1, liver sausage batter and water) using a submerged ampule technique.D-values forL. monocytogenes Scott A grown at 37°C were 8·9 min at 57·2°C, 2·4 min at 60·0°C, and 1·1 min at 62·8°C (Z=6·2°C) based on analysis of the linear portion of the survivor curves.D-values of 6·6, 1·6, and 0·4 min (Z=4·65°C) were obtained when the data were analyzed using non-linear techniques.L. monocytogenes strain V7 (D60=1.0min) was more thermosensitive than Scott A (D60=1·6min) or HO-VJ-S (D60=1·6min). When Scott A was grown at 19°C, there was a decrease in thermal resistance (D60=0·8min). These data indicate thatL. monocytogenes has a thermal resistance in liver sausage comparable to that observed in other food systems.
The heat inactivation of microbial spores and the mortality of vegetative cells exposed to heat or a hostile environment have been traditionally assumed to be governed by first-order reaction kinetics. The concept of thermal death time and the standard methods of calculating the safety of commercial heat preservation processes are also based on this assumption. On closer scrutiny, however, at least some of the semilogarithmic survival curves, which have been considered linear are in fact slightly curved. This curvature can have a significant effect on the thermal death time, which is determined by extrapolation. The latter can be considerably smaller or larger depending on whether the semilogarithmic survival curve has downward or an upward concavity and how the experimenter chooses to calculate decimal reduction time. There are also numerous reports of organisms whose semilogarithmic survival curves are clearly and characteristically nonlinear, and it is unlikely that these observations are all due to a mixed population or experimental artifacts, as the traditional explanation implies. An alternative explanation is that the survival curve is the cumulative form of a temporal distribution of lethal events. According to this concept each individual organism, or spore, dies, or is inactivated, at a specific time. Because there is a spectrum of heat resistance in the population--some organism or spores are destroyed sooner, or later, than others--the shape of the survival curve is determined by its distributions properties. Thus, semilogarithmic survival curves whether linear or with an upward or a downward concavity are only reflections of heat resistance distributions having a different, mode variance, and skewness, and not of mortality kinetics of different orders. The concept is demonstrated with published data on the lethal effect of heat on pathogens and spores alone and in combination with other factors such as pH or high pressure. Their different survival patterns are all described in terms of different Weibull distribution of resistances as a first approximation, although alternative distribution functions can also be used. Changes in growing or environmental condition shift the resistances distribution's mode and can also affect its spread and skewness. The presented concept does not take into account the specific mechanisms that are the cause of mortality or inactivation--it only describes their manifestation in a given microbial population. However, it is consistent with the notion that the actual destruction of a critical system or target is a probabilistic process that is due, at least in part, to the natural variability that exists in microbial populations.
A recently published study of the inactivation of Clostridium botulinum spores at various temperatures in the range of 101 to 121 degrees C and neutral pH revealed that their semilogarithmic survival curves all had considerable upward concavity. This finding indicated that heat inactivation of the spores under these conditions did not follow a first-order kinetics and that meaningful D values could not be calculated. The individual survival curves could be described by the cumulative form of the Weibull distribution, i.e., by log S = -b(T)t(n(T)), where S is the survival ratio and b(T) and n(T) are temperature-dependent coefficients. The fact that at all temperatures in the above range n(T) was smaller than 1 suggested that as time increases sensitive members of the population parish and survivors with increasing resistance remain. If damage accumulation is not a main factor, and the inactivation is path independent, then survival curves under monotonously increasing temperature can be constructed using a relatively simple model, which can be used to calculate the spores' survival in a limiting case. This is demonstrated with computer-simulated heating curves and the experimental constants of the C. botulinum spores, setting the number of decades reduction to 8, 10, and 12 (the current criterion for commercial sterility).
Hypotheses concerning kinetics of heat activation and of thermal death of bacterial spores were formulated, and were employed to derive equations describing nonlogarithmic thermal death curves. The equations permitted evaluation of the validity of experimental data and provided a means for testing the hypotheses presented.
A mathematical technique for integrating growth and thermal inactivation models of microorganisms into a smooth combined model that can be applied to circumstances under which the temperature gradually rises from growth to inactivation regions is described. For the death part of the model, a correction term is introduced to allow for additional resistance of the cells gained during slow heating. The model was validated with Brochothrix thermosphacta heated in broth at rising temperatures.
The dynamics of spore populations during thermal processes were analyzed to determine reasons for substantial discrepancies commonly found between predictions by conventional models and experimental data. From this research a new model was developed that incorporated several microbiological transformations of spores - activation, inactivation, and injury-related activation of alternative germination mechanisms - in accordance with the theory of population dynamics. Isothermal experiments were conducted to obtain parameters of the model and to test its ability to predict dynamics of survivor spore populations. The data used were for B. subtilis in water and C. botulinum in olive oil. The model was found to describe consistently and precisely the dynamics of bacterial spores treated at constant lethal temperature.
There is growing evidence that the mortality of microbial cells, and the inactivation of bacterial spores, exposed to a hostile environment need not follow a first order kinetics. Consequently microbial semi-logarithmic survival curves are frequently non-linear, and their shape can change with temperature or under different chemical agent concentrations, for example. Experimental semi-logarithmic survival curves under unchanging conditions, can be described by an equation whose coefficients are determined by the particular temperature, agent concentration, etc. If the dependency of these coefficients on temperature, agent concentration, etc., can be expressed algebraically, then in principle one can construct the survival curve for the changing or transient conditions that exist in industrial thermal and non-thermal treatments. This is done by incorporating the lethal agent's mode of change, e.g. the heating or pressure curve into the survival curve equation parameters. The result is a mathematical model that would enable the calculation of the time needed to achieve any degree of microbial survival ratio numerically, without the need to assume any mortality kinetics. Such a model can be used to assess, or compare, the efficacy of different preservation processes where the intensity of the lethal agent changes with time. The concept is demonstrated with a special simple case using simulated thermal treatments. The outcome of the simulations is presented as planar log survival vs time relationships and as curves in a three-dimensional log survival–temperature–time or log survival–concentration–time space.
We studied the inactivation of Listeria monocytogenes during the thermal processing of liver sausage. Liver sausage emulsion was prepared and inoculated with L. monocytogenes Scott A to yield an initial population of c. 109 g-1. The inoculated emulsion was stuffed into large diameter, moisture-proof fibrous casings and cooked in a smokehouse. Individual sausages were removed as the product reached various predetermined internal temperatures, and duplicate core samples were analyzed for viable L. monocytogenes by surface plating onto tryptose agar. The viable count remained unchanged in product heated to 140°F. In product heated to 145°F, the number of viable L. monocytogenes decreased and at 155°F, no viable L. monocytogenes were detected. Thus, liver sausage and other large diameter non-fermented sausage product heated to 155°F should be free of viable L. monocytogenes.
Isothermal heat-resistance studies were carried out on two toxin-producing Bacillus cereus strains (AVZ421 and AVTZ415) isolated from foods. Experimental data were analysed using the traditional Bigelow first-order kinetic model and the Weibull distribution model. Semilogarithmic survival curves showed an initial curvature that was more pronounced in the case of the psychrotrophic strain AVTZ415. Regression curves were obtained by means of the traditional Bigelow first-order model and the D values were calculated. Correlation coefficients ranged from 0.983 to 0.989 for the AVZ421 strain and from 0.953 to 0.980 for the AVTZ415 strain. When the Weibull function was applied to experimental data, a good description of the survivor microorganisms was obtained for the two strains considered. Using coefficients describing the survival function, an average of the organism's heat resistance or sensitivity, ‘tc’, at each temperature was estimated. Accuracy factors were obtained for experimental and calculated survivors as predicted by means of the Weibull or the Bigelow model. Results indicated that the accuracy factor was lower when the Weibull model was used (1.10 and 1.10) than when using the Bigelow model (1.20 and 1.30) at 95 and 85°C, respectively.
Summary Thermal inactivation of microorganisms has traditionally been described as log-linear in nature, that is the reduction in log numbers of survivors decreases in a linear manner with time. This is despite a plethora of data that shows consistent deviations from such kinetics for a wide range of organisms and conditions and that cannot be accounted for by experimental artifacts. Existing thermal death models fail to take such deviations into account and also fail to quantify the effects of heating menstruum on heat sensitivity. The thermal inactivation ofListeria monocytogenes ATCC 19115 has been investigated using a factorially-designed experiment comparing 45 conditions of salt concentration, pH value and temperature. Heating was carried out using a Submerged Coil heating apparatus that minimized experimental artifacts. Low pH values increased, whilst high salt concentrations decreased heat sensitivity. Results showed a significant and consistent deviation from log-linear kinetics, particularly at low temperatures. A number of distributions were tested for suitability to describe the variability of heat sensitivity within the population of heated cells (vitalistic approach). The use of the logistic function and log dose (log time) allowed the development of an accurate unifying predictive model across the whole range of heating conditions. It is proposed that this approach should be tested as a generalized modeling technique for death kinetics of vegetative bacteria.
ABSTRACTA mathematical model of Bacillus stearothermophilus spore populations during lethal heating treats activation of dormant spores and inactivation mechanisms affecting dormant/activated spores. Rate constants of activation/inactivation processes were determined from isothermal survivor curves of experiments in 105, 110, 115, and 120°C and corresponding simulations with the model. Variations of rate constants with temperature were incorporated by Arrhenius equations responding to general temperature regimes. Tests demonstrated high correspondence between experimental survivor curves and those generated by simulations with the model for isothermal and dynamic, lethal heating. Tests also indicated Arrhenius rate constants at low lethal temperatures (105-120°C) and the model may apply to ultra high temperature. The new model was more effective than the traditional model in representing and predicting spore population dynamics during lethal heating.
Comparisons of characteristics of recent models and the conventional model of bacterial spore populations during thermal sterilization showed the conventional model was inadequate for general representation because it lacks activation of dormant spores. New models accounting for activation differed in other assumptions but obviated heat shock of indicator spores required when using the conventional model in validations of thermal sterilization. Comparisons of rate constants and simulated and experimental responses of models of B. stearother-mophilus spores in constant and dynamic temperatures showed one new model was more general, more accurate and preferred. Arrhenius equations accurately described temperature dependencies of all rate constants of that model.
The long-term survival of pathogenic microorganisms was evaluated and modeled in simulated fermented and dried, uncooked sausages, such as salami and pepperoni.Listeria monocytogenes andSalmonella were inoculated in BHI broths with added lactic acid or lactate (0–1.5%), NaCl (0–19%) and NaNO2 (0–200 ppm) and then incubated at 4–42C for up to 9 months. Enumerations of surviving cells showed several forms of declining curves, including classic first-order declines, shoulder or lag phases, and two-phase declines with shoulder. Two primary models were tested for their ability to depict the data. The effect of the environmental conditions on the parameters of the models were described with multiple regression equations (secondary models).
Body-esteem is an important dimension in the general concept of body-image. The Body Esteem Scale (BES) was developed and tested in the USA. We tested young men and women in Israel all of whom were university students after their army service. Our results show that Israeli men score lower (feel more negative) on the virility reflecting subscale while Israeli women score higher (feel more positive) in the weight concern subscale--compared to their American counterparts. We discuss the possible explanations of this difference, focusing mainly on the impact of army discharge and the move to the academic field.
In this work, the death of Clostridium botulinum 213B was measured at temperatures between 101 degrees C and 121 degrees C. It was found that at all temperatures tested, survivor curves deviated from log-linearity which prevented their description using traditional first order kinetics. The survivor curves were better described using a vitalistic approach and the log-logistic transformation proposed by Cole et al. (1993). A single equation was derived to describe all survivor curves over the temperature range tested and a comparison of predicted and measured data showed good correlation. The implications of the use of the vitalistic approach to the validity of the 'minimum botulinum cook' is discussed.
The first order kinetic model, the Buchanan model and Cerf's model, can model a linear survival curve, a survival curve with a shoulder and a survival curve with a tailing, respectively. However, they are not suitable for fitting a sigmoidal survival curve. The three models were integrated into a new model that was capable of fitting the four most commonly observed survival curves: linear curves, curves with a shoulder, curves with a tailing (biphasic curves) and sigmoidal curves. The new model was compared with the Whiting-Buchanan model using the survival curves of Staphylococcus aureus. The goodness-of-fit of the proposed model is practically as good as that of the Whiting-Buchanan model. Compared with the Whiting-Buchanan model, the proposed model has a more mechanistic background. Since for non-linear survival curves, such as biphasic and sigmoidal curves, the t(m-D) value (the time required for an m-log-cycle reduction of microorganisms under a given condition) cannot be estimated accurately by the existing or traditional method, a new method is also proposed to predict accurately the t(m-D) value for non-linear survival curves.
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.
Mathematical models for microbial kill by radiation. Food Preservation by Irradiation
- A Brynjolfsson
Brynjolfsson, A., 1978. Mathematical models for microbial kill by radiation. Food Preservation by Irradiation. Proceedings, Inter-national Atomic Energy Agency IAEA-SM-221/56, Vienna, vol. 1, pp. 227 – 239.
Heat penetration in processing canned foods. Bull.-Res. Lab. Natl. Canner Assoc
- W Bigelow
- G Bohart
- A Richardson
- C Ball
Bigelow, W., Bohart, G., Richardson, A., Ball, C., 1920. Heat penetration in processing canned foods. Bull.-Res. Lab. Natl. Canner Assoc. Washington, D. C., 16-L.
Bacterial thermal death kinetics based on probabil-ity distributions: the heat destruction of two important food pathogens
- D C Kilsby
- K W Davies
- P J Mcclure
- C Adair
- W A Anderson
Kilsby, D.C., Davies, K.W., McClure, P.J., Adair, C., Anderson, W.A., 2000. Bacterial thermal death kinetics based on probabil-ity distributions: the heat destruction of two important food pathogens. Proceedings, 3rd International Conference on Pre-dictive Modelling in Foods, September 12 – 15, 2000, Leuven, pp. 98 – 100.
Combined effect of temperature and pH on microbial death in continuous pasteuri-sation of liquids Engineering and Food at ICEF7
- J Chiruta
- K R Davey
- C J Thomas
Chiruta, J., Davey, K.R., Thomas, C.J., 1997. Combined effect of temperature and pH on microbial death in continuous pasteuri-sation of liquids. In: Jowitt, R. (Ed.), Engineering and Food at ICEF7. Sheffield Academic Press, Sheffield, pp. A109 – A112.
Heat penetration in processing canned foods
- Bigelow
Combined effect of temperature and pH on microbial death in continuous pasteurisation of liquids
- Chiruta
Bacterial thermal death kinetics based on probability distributions: the heat destruction of two important food pathogens
- Kilsby
Kinetic effects of lethal temperature on population dynamics of bacterial spores
- Rodrigez